Electrical Machines Ii Compiled By Mumtaz Buriro

Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Transformers 1

Introduction Michael Faraday propounded the principle of electro-magnetic induction in 1831.

It states that a voltage appears across the terminals of an electric coil when the flux linked with the same changes. The magnitude of the induced voltage is proportional to the rate of change of the flux linkages. This finding forms the basis for many magneto electric machines. The earliest use of this phenomenon was in the development of induction coils. These coils were used to generate high voltage pulses to ignite the explosive charges in the mines. As the d.c. power system was in use at that time, very little of transformer principle was made use of. In the d.c. supply system the generating station and the load center have to be necessarily close to each other due to the requirement of economic transmission of power. Also the d.c. generators cannot be scaled up due to the limitations of the commutator. This made the world look for other efficient methods for bulk power generation and transmission. During the second half of the 19th century the alternators, transformers and induction motors were invented. These machines work on alternating power supply. The role of the transformers became obvious. The transformer which consisted of two electric circuits linked by a common magnetic circuit helped the voltage and current levels to be changed keeping the power invariant. The efficiency of such conversion was extremely high. Thus one could choose a moderate voltage for the generation of a.c. power, a high voltage for the transmission of this power over long distances and finally use a small and safe operating voltage at the user end. All these are made possible by transformers. The a.c. power systems thus got well established.

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Transformers can link two or more electric circuits. In its simple form two electric circuits can be linked by a magnetic circuit, one of the electric coils is used for the creation of a time varying magnetic filed. The second coil which is made to link this field has an induced voltage in the same. The magnitude of the induced emf is decided by the number of turns used in each coil. Thus the voltage level can be increased or decreased by changing the number of turns. This excitation winding is called a primary and the output winding is called a secondary. As a magnetic medium forms the link between the primary and the secondary windings there is no conductive connection between the two electric circuits. The transformer thus provides an electric isolation between the two circuits. The frequency on the two sides will be the same. As there is no change in the nature of the power, the resulting machine is called a ‘transformer’ and not a ‘converter’. The electric power at one voltage/current level is only ‘transformed’ into electric power, at the same frequency, to another voltage/current level.

Even though most of the large-power transformers can be found in the power systems, the use of the transformers is not limited to the power systems. The use of the principle of transformers is universal. Transformers can be found operating in the frequency range starting from a few hertz going up to several mega hertz. Power ratings vary from a few milliwatts to several hundreds of megawatts. The use of the transformers is so wide spread that it is virtually impossible to think of a large power system without transformers. Demand on electric power generation doubles every decade in a developing country. For every MVA of generation the installed capacity of transformers grows by about 7MVA. These figures show the indispensable nature of power transformers.

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Basic Principles As mentioned earlier the transformer is a static device working on the principle of

Faraday’s law of induction. Faraday’s law states that a voltage appears across the terminals of an electric coil when the flux linkages associated with the same changes. This emf is proportional to the rate of change of flux linkages. Putting mathematically, e=

dψ dt

(1)

Where, e is the induced emf in volt and ψ is the flux linkages in Weber turn. Fig. 1 shows a

Figure 1: Flux linkages of a coil

coil of N turns. All these N turns link flux lines of φ Weber resulting in the Nφ flux linkages. In such a case, ψ = Nφ

(2)

dφ dt

(3)

and e=N

volt

The change in the flux linkage can be brought about in a variety of ways • coil may be static and unmoving but the flux linking the same may change with time. 3

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• flux lines may be constant and not changing in time but the coil may move in space linking different value of flux with time. • both 1 and 2 above may take place. The flux lines may change in time with coil moving in space. These three cases are now elaborated in sequence below, with the help of a coil with a simple geometry.

L B

X

-

+

Figure 2: Static coil

Fig. 2 shows a region of length L m, of uniform flux density B Tesla, the flux lines being normal to the plane of the paper. A loop of one turn links part of this flux. The flux φ linked by the turn is L ∗ B ∗ X Weber. Here X is the length of overlap in meters as shown in the figure. If now B does not change with time and the loop is unmoving then no emf is induced in the coil as the flux linkages do not change. Such a condition does not yield any useful machine. On the other hand if the value of B varies with time a voltage is induced in the coil linking the same coil even if the coil does not move. The magnitude of B 4

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is assumed to be varying sinusoidally, and can be expressed as, B = Bm sin ωt

(4)

where Bm is the peak amplitude of the flux density. ω is the angular rate of change with time. Then, the instantaneous value of the flux linkage is given by, ψ = Nφ = NLXBm sin ωt

(5)

The instantaneous value of the induced emf is given by, e=

dψ π = Nφm .ω cos ωt = Nφm .ω. sin(ωt + ) dt 2

(6)

Here φm = Bm .L.X. The peak value of the induced emf is em = Nφm .ω

(7)

and the rms value is given by E=

Nφm .ω √ 2

volt.

Further, this induced emf has a phase difference of π/2 radian with respect to the flux linked by the turn. This emf is termed as ‘transformer’ emf and this principle is used in a transformer. Polarity of the emf is obtained by the application of Lenz’s law. Lenz’s law states that the reaction to the change in the flux linkages would be such as to oppose the cause. The emf if permitted to drive a current would produce a counter mmf to oppose this changing flux linkage. In the present case, presented in Fig. 2 the flux linkages are assumed to be increasing. The polarity of the emf is as indicated. The loop also experiences a compressive force.

Fig. 2(b) shows the same example as above but with a small difference. The flux density is held constant at B Tesla. The flux linked by the coil at the current position is 5

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φ = B.L.X Weber. The conductor is moved with a velocity v = dx/dt normal to the flux, cutting the flux lines and changing the flux linkages. The induced emf as per the application of Faraday’s law of induction is e = N.B.L.dx/dt = B.L.v volt.(Here N=1)

Please note,the actual flux linked by the coil is immaterial. Only the change in the flux linkages is needed to be known for the calculation of the voltage. The induced emf is in step with the change in ψ and there is no phase shift. If the flux density B is distributed sinusoidally over the region in the horizontal direction, the emf induced also becomes sinusoidal. This type of induced emf is termed as speed emf or rotational emf, as it arises out of the motion of the conductor. The polarity of the induced emf is obtained by the application of the Lenz’s law as before. Here the changes in flux linkages is produced by motion of the conductor. The current in the conductor, when the coil ends are closed, makes the conductor experience a force urging the same to the left. This is how the polarity of the emf shown in fig.2b is arrived at. Also the mmf of the loop aids the field mmf to oppose change in flux linkages. This principle is used in d.c machines and alternators.

The third case under the application of the Faraday’s law arises when the flux changes and also the conductor moves. This is shown in Fig. 2(c).

The uniform flux density in space is assumed to be varying in magnitude in time as B = Bm sin ωt. The conductor is moved with a uniform velocity of

dx dt

= v m/sec. The

change in the flux linkages and hence induced emf is given by e = N.

d(Bm . sin ωt.L.X) dx = N.L.X.Bm .ω. cos ωt. + N.Bm . sin ωt.L. V olt. dt dt

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(8)

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

The first term is due to the changing flux and hence is a transformer emf. The second term is due to moving conductor or is a speed emf. When the terminals are closed such as to permit a current the conductor experiences a force and also the mmf of the coil opposes the change in flux linkages. This principle is used in a.c. machines where the field is time varying and conductors are moving under the same.

The first case where there is a time varying field and a stationary coil resulting in a transformer emf is the subject matter in the present section. The case two will be revisited under the study of the d.c machines and synchronous machines. Case three will be extensively used under the study of a.c machines such as induction machines and also in a.c. commutator machines.

Next in the study of the transformers comes the question of creating a time varying filed. This is easily achieved by passing a time varying current through a coil. The winding which establishes the field is called the primary. The other winding, which is kept in that field and has a voltage induced in it, is called a secondary. It should not be forgotten that the primary also sees the same time varying field set up by it linking its turns and has an induced emf in the same. These aspects will be examined in the later sections. At first the common constructional features of a transformer used in electric power supply system operating at 50 Hz are examined.

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Constructional features Transformers used in practice are of extremely large variety depending upon the

end use. In addition to the transformers used in power systems, in power transmission and distribution, a large number of special transformers are in use in applications like electronic supplies, rectification, furnaces, traction etc. Here the focus is on power transformers only. The principle of operation of these transformers also is the same but the user requirements differ. Power transformers of smaller sizes could be air cooled while the larger ones are oil cooled. These machines are highly material intensive equipments and are designed to match the applications for best operating conditions. Hence they are ‘tailor made’ to a job. This brings in a very large variety in their constructional features. Here more common constructional aspects alone are discussed. These can be broadly divided into 1. Core construction 2. Winding arrangements 3. Cooling aspects

3.1

Core construction Transformer core for the power frequency application is made of highly permeable

material. The high value of permeability helps to give a low reluctance for the path of the flux and the flux lines mostly confine themselves to the iron. Relative permeability µr well over 1000 are achieved by the present day materials. Silicon steel in the form of thin laminations is used for the core material. Over the years progressively better magnetic properties are obtained by going in for Hot rolled non-oriented to Hot rolled grain oriented steel. 8

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Later better laminations in the form of cold Rolled Grain Oriented (CRGO), -High B (HiB) grades became available. The thickness of the laminations progressively got reduced from over 0.5mm to the present 0.25mm per lamination. These laminations are coated with a thin layer of insulating varnish, oxide or phosphate. The magnetic material is required to have a high permeability µ and a high saturation flux density, a very low remanence Br and a small area under the B-H loop-to permit high flux density of operation with low magnetizing current and low hysteresis loss. The resistivity of the iron sheet itself is required to be high to reduce the eddy current losses. The eddy current itself is highly reduced by making the laminations very thin. If the lamination is made too thin then the production cost of steel laminations increases. The steel should not have residual mechanical stresses which reduce their magnetic properties and hence must be annealed after cutting and stacking. In the case of very small transformers (from a few volt-amperes to a few kilo voltamperes) hot rolled silicon steel laminations in the form of E & I, C & I or O as shown in Fig. 3 are used and the core cross section would be a square or a rectangle. The percentage of silicon in the steel is about 3.5. Above this value the steel becomes very brittle and also very hard to cut. The saturation flux density of the present day steel lamination is about 2 Tesla. Broadly classifying, the core construction can be separated into core type and shell type. In a core type construction the winding surrounds the core. A few examples of single phase and three phase core type constructions are shown in Fig. 4. In a shell type on the other hand the iron surrounds the winding. In the case of very small transformers the conductors are very thin and round. These can be easily wound on a former with rectangular or square cross section. Thus no special care is needed for the construction of the core. The cross section of the core also would be square or rectangular. As the rating of the transformer increases the conductor size 9

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

(a )

(b)

(c) Figure 3: E and I,C and I and O Type Laminations

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

1.phase 3.phase

LV HV

HV LV core Single phase

LV HV

Three phase

(a)Core type

(b) Shell type

Figure 4: Core and Shell Type Construction also increases. Flat conductors are preferred to round ones. To wind such conductor on a rectangular former is not only difficult but introduces stresses in the conductor, at the bends. From the short circuit force with stand capability point of view also this is not desirable. Also, for a given area enclosed the length of the conductor becomes more. Hence it results in more load losses. In order to avoid all these problems the coils are made cylindrical and are wound on formers on heavy duty lathes. Thus the core construction is required to be such as to fill the circular space inside the coil with steel laminations. Stepped core construction thus becomes mandatory for the core of large transformers. Fig. 5 shows a few typical stepped core constructions. When the core size increases it becomes extremely difficult to cool the same (Even though the core losses are relatively very small). Cooling ducts have to be provided in the core. The steel laminations are grain oriented exploiting the simple geometry of the transformer to reduce the excitation losses. The iron losses in the lamination, when the flux

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

0.16

0.1

0.16

0.14

0.14 0.42

0.53

0.1 0.07 0.12 0.09

0.3

0.07 0.12 0.09

0.71D

d

d

d duct

Figure 5: Stepped Core Construction

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duct

Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

is oriented in the direction of grain orientation, is about 30% of that in the normal direction. Another important aspect to be carefully checked and monitored is the air gaps in Path of flux HV

LV

Windings Core

(a)

(b)

Figure 6: Typical stacked Core and wound core Construction series in the path of the main flux. As the reluctance of air path is about 1000 times more than that of the steel, an air path of 1mm will require a mmf needed by a 1 meter path in iron.

Hence butt joints between laminations must be avoided. Lap joints are used to provide alternate paths for flux lines thus reducing the reluctance of the flux paths. Some typical constructional details are shown in Fig. 6. In some power transformers the core is built up by threading a long strip of steel through the coil in the form of a toroid. This construction is normally followed in instrument transformers to reduce the magnetizing current and hence the errors.

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Large cores made up of laminations must be rendered adequately stiff by the provision of stiffening plates usually called as flitch plates. Punched through holes and bolts are progressively being avoided to reduce heating and melting of the through bolts. The whole stack is wrapped up by strong epoxy tapes to give mechanical strength to the core which can stand in upright position. Channels and angles are used for the frame and they hold the bottom yoke rigidly.

3.2

Windings Windings form another important part of transformers. In a two winding trans-

former two windings would be present. The one which is connected to a voltage source and creates the flux is called as a primary winding. The second winding where the voltage is induced by induction is called a secondary. If the secondary voltage is less than that of the primary the transformer is called a step down transformer. If the secondary voltage is more then it is a step up transformer. A step down transformer can be made a step up transformer by making the low voltage winding its primary. Hence it may be more appropriate to designate the windings as High Voltage (HV) and Low Voltage (LV) windings. The winding with more number of turns will be a HV winding. The current on the HV side will be lower as V-I product is a constant and given as the VA rating of the machines. Also the HV winding needs to be insulated more to withstand the higher voltage across it. HV also needs more clearance to the core, yoke or the body. These aspects influence the type of the winding used for the HV or LV windings. Transformer coils can be broadly classified in to concentric coils and sandwiched coils Fig. 7. The former are very common with core type transformers while the latter one 14

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HV

LV

Core LV HV

(a)Concentric coil

LV

HV

Core

(b) Sandwich coil

Figure 7: Concentric and Sandwich Coils

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are common with shell type transformers. In the figure the letters L and H indicate the low voltage and high voltage windings. In concentric arrangement, in view of the lower insulation and clearance requirements, the LV winding is placed close to the core which is at ground potential. The HV winding is placed around the LV winding. Also taps are provided on HV winding when voltage change is required. This is also facilitated by having the HV winding as the outer winding. Three most common types of coils viz. helical, cross over and disc coils are shown in Fig. 8. Helical coils Disc coils

cross over coils

Figure 8: Disc, Crossover and Helical Coil Construction

Helical Windings One very common cylindrical coil arrangement is the helical winding. This is made up of large cross section rectangular conductor wound on its flat side. The coil progresses as a helix. This is commonly used for LV windings. The insulation 16

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requirement also is not too high. Between layers no insulation (other than conductor insulation) is needed as the voltage between layers is low. The complexity of this type of winding rapidly increases as the current to be handled becomes more. The conductor cross section becomes too large and difficult to handle. The eddy current losses in the conductor rapidly increases. Hence two or more conductors have to be wound and connected in parallel. The parallel circuits bring in problems of current sharing between the circuits. Transpositions of the parallel paths have to be adopted to reduce unequal current distribution. The modern practice is to use continuously transposed and bunched conductors. Cross over coils The second popular winding type is the cross over coil. These are made of circular conductors not exceeding 5 to 6 sq mm in cross section. These are used for HV windings of relatively small transformers. These turns are wound in several layers. The length and thickness of each block is made in line with cooling requirements. A number of such blocks can be connected in series, leaving cooling ducts in between the blocks, as required by total voltage requirement. Disc coils Disc coils consist of flat conductors wound in a spiral form at the same place spiralling outwards. Alternate discs are made to spiral from outside towards the center. Sectional discs or continuous discs may be used. These have excellent thermal properties and the behavior of the winding is highly predictable. Winding of a continuous disc winding needs specialized skills. Sandwich coils Sandwich windings are more common with shell type core construction. They permit easy control over the short circuit impedance of the transformer. By bringing HV and LV coils close on the same magnetic axis the leakage is reduced and the mutual flux is increased. By increasing the number of sandwiched coils the 17

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reactance can be substantially reduced.

3.3

Insulation The insulation used in the case of electrical conductors in a transformer is varnish

or enamel in dry type of transformers. In larger transformers to improve the heat transfer characteristics the conductors are insulated using un-impregnated paper or cloth and the whole core-winding assembly is immersed in a tank containing transformer oil. The transformer oil thus has dual role. It is an insulator and also a coolant. The porous insulation around the conductor helps the oil to reach the conductor surface and extract the heat. The conductor insulation may be called the minor insulation as the voltage required to be withstood is not high. The major insulation is between the windings. Annular bakelite cylinders serve this purpose. Oil ducts are also used as part of insulation between windings. The oil used in the transformer tank should be free from moisture or other contamination to be of any use as an insulator.

3.4

Cooling of transformers Scaling advantages make the design of larger and larger unit sizes of transformers

economically attractive. This can be explained as below. Consider a transformer of certain rating designed with certain flux density and current density. If now the linear dimensions are made larger by a factor of K keeping the current and flux densities the same the core and conductor areas increase by a factor of K 2 . The losses in the machine, which are proportional to the volume of the materials used, increase by a factor of K 3 .The rating of the machine increases by a factor of K 4 .

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

The surface area however increases by a factor of K 2 only. Thus the ratio of loss per surface area goes on increasing by a factor of K. The substantial increase in the output is the major attraction in going in for larger units. However cooling of the transformer becomes more and more difficult. As the rating increases better cooling techniques are needed.

Simple air cooling of the transformers is adopted in dry type transformers. The limit for this is reached by the time the rating is a few kVA. Hence air cooling is used in low voltage machines. This method of cooling is termed as AN(Air Natural). Air Blast(AB) method improves on the above by directing the blast of air at the core and windings. This permits some improvement in the unit sizes.

Substantial improvement is obtained when the transformer is immersed in an oil tank. The oil reaches the conductor surface and extracts the heat and transports the same to the surface of the tank by convection. This is termed as ON (Oil Natural) type of cooling. This method permits the increase in the surface available for the cooling further by the use of ducts, radiators etc.

OB(Oil Blast) method is an improvement over the ON-type and it directs a blast of air on the cooling surface. In the above two cases the flow of oil is by natural convective forces. The rate of circulation of oil can be increased with the help of a pump, with the cooling at the surface remaining natural cooling to air. This is termed as OFN (Oil Forced Natural). If now a forced blast of air is also employed, the cooling method become OFB( Oil Forced Blast). A forced circulation of oil through a radiator is done with a blast of air 19

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Main tank Radiator

Tubes

(a) Conservator Bushing

& Breather

water outlet

Radiator

oil pump

water inlet

(b) Conservator& Breather

Bushing

Radiator

Oil pump

Fan motor

for O.F.B

(c) 20 Figure 9: Some Typical Cooling Arrangements

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over the radiator surface. Substantial amount of heat can be removed by employing a water cooling. Here the hot oil going into the radiator is cooled by a water circuit. Due to the high specific heat of water, heat can be evacuated effectively. Next in hierarchy comes OFW which is similar to OFB except that instead of blast of air a forced circulation of cool water in the radiator is used in this. Some cooling arrangements are shown in Fig. 9.

In many large sized transformers the cooling method is matched with the amount of heat that is required to be removed. As the load on the transformer changes the heat generated within also changes. Suitable cooling method can be pressed into service at that time. This gives rise to the concept of mixed cooling technique. ON/OB Works as ON but with increased load additional air blast is adopted. This gives the ratings to be in the ratio of 1:1.5 ON/OB/OFB Similarly gives the ratings in the ratio of 1:1.5:2 The temperature rise permitted in the British standard specification for power transformers are tabulated below. Type winding Class A ◦

C

oil

core

Class B ◦

C

◦

C

AN,AB

55

75

-

As

ON,OB,OW

60

-

50

for

OFN,OFB

65

-

50

adjacent

OFW

70

-

50

winding

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3.4.1

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Properties of the transformer coil Even though the basic functions of the oil used in transformers are a) heat conduc-

tion and b) electrical insulation, there are many other properties which make a particular oil eminently suitable. Organic oils of vegetative or animal origin are good insulators but tend to decompose giving rise to acidic by-products which attack the paper or cloth insulation around the conductors.

Mineral oils are suitable from the point of electrical properties but tend to form sludge. The properties that are required to be looked into before selecting an oil for transformer application are as follows: Insulting property This is a very important property. However most of the oils naturally fulfil this. Therefore deterioration in insulating property due to moisture or contamination may be more relevant. Viscosity It is important as it determines the rate of flow of the fluid. Highly viscous fluids need much bigger clearances for adequate heat removal. Purity The oil must not contain impurities which are corrosive. Sulphur or its compounds as impurities cause formation of sludge and also attack metal parts. Sludge formation Thickening of oil into a semisolid form is called a sludge. Sludge formation properties have to be considered while choosing the oil as the oil slowly forms semi-solid hydrocarbons. These impede flows and due to the acidic nature, corrode metal parts. Heat in the presence of oxygen is seen to accelerate sludge formation. If the hot oil is prevented from coming into contact with atmospheric air sludge formation 22

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can be greatly reduced. Acidity Oxidized oil normally produces CO2 and acids. The cellulose which is in the paper insulation contains good amount of moisture. These form corrosive vapors. A good breather can reduce the problems due to the formation of acids. Flash point And Fire point Flash point of an oil is the temperature at which the oil ignites spontaneously. This must be as high as possible (not less than 160◦ C from the point of safety). Fire point is the temperature at which the oil flashes and continuously burns. This must be very high for the chosen oil (not less than 200◦ C). Inhibited oils and synthetic oils are therefore used in the transformers. Inhibited oils contain additives which slow down the deterioration of properties under heat and moisture and hence the degradation of oil. Synthetic transformer oil like chlorinated diphenyl has excellent properties like chemical stability, non-oxidizing, good dielectric strength, moisture repellant, reduced risk due fire and explosion.

It is therefore necessary to check the quality of the oil periodically and take corrective steps to avoid major break downs in the transformer.

There are several other structural and insulating parts in a large transformer. These are considered to be outside the scope here.

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Ideal Transformer Earlier it is seen that a voltage is induced in a coil when the flux linkage associated

with the same changed. If one can generate a time varying magnetic field any coil placed in the field of influence linking the same experiences an induced emf. A time varying field can be created by passing an alternating current through an electric coil. This is called mutual induction. The medium can even be air. Such an arrangement is called air cored transformer. Indeed such arrangements are used in very high frequency transformers. Even though the principle of transformer action is not changed, the medium has considerable influence on the working of such devices. These effects can be summarized as the followings. 1. The magnetizing current required to establish the field is very large, as the reluctance of the medium is very high. 2. There is linear relationship between the mmf created and the flux produced. 3. The medium is non-lossy and hence no power is wasted in the medium. 4. Substantial amount of leakage flux exists. 5. It is very hard to direct the flux lines as we desire, as the whole medium is homogeneous. If the secondary is not loaded the energy stored in the magnetic field finds its way back to the source as the flux collapses. If the secondary winding is connected to a load then part of the power from the source is delivered to the load through the magnetic field as a link. The medium does not absorb and lose any energy. Power is required to create the field and not to maintain the same. As the winding losses can be made very small by proper choice of material, the ideal efficiency of a transformer approaches 100%. The large magnetizing 24

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Primary Leakage flux

x

Secondary Mutual flux

(a)

Leakage flux

X Primary Mutual flux

Secondary Iron core

(b)

Figure 10: Mutual Induction a) air core b) iron core

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

current requirement is a major deterrent. However if now a piece of magnetic material is introduced to form the magnetic circuit Fig. 10(b) the situation changes dramatically. These can be enumerated as below. 1. Due to the large value for the permeance ( µr of the order of 1000 as compared to air) the magnetizing current requirement decreases dramatically. This can also be visualized as a dramatic increase in the flux produced for a given value of magnetizing current. 2. The magnetic medium is linear for low values of induction and exhibits saturation type of non-linearity at higher flux densities. 3. The iron also has hysteresis type of non-linearity due to which certain amount of power is lost in the iron (in the form of hysteresis loss), as the B-H characteristic is traversed. 4. Most of the flux lines are confined to iron path and hence the mutual flux is increased very much and leakage flux is greatly reduced. 5. The flux can be easily ‘directed’ as it takes the path through steel which gives great freedom for the designer in physical arrangement of the excitation and output windings. 6. As the medium is made of a conducting material eddy currents are induced in the same and produce losses. These are called ‘eddy current losses’. To minimize the eddy current losses the steel core is required to be in the form of a stack of insulated laminations. From the above it is seen that the introduction of magnetic core to carry the flux introduced two more losses. Fortunately the losses due to hysteresis and eddy current for the available grades of steel is very small at power frequencies. Also the copper losses in the 26

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

winding due to magnetization current is reduced to an almost insignificant fraction of the full load losses. Hence steel core is used in power transformers.

In order to have better understanding of the behavior of the transformer, initially certain idealizations are made and the resulting ‘ideal’ transformer is studied. These idealizations are as follows: 1. Magnetic circuit is linear and has infinite permeability. The consequence is that a vanishingly small current is enough to establish the given flux. Hysteresis loss is negligible. As all the flux generated confines itself to the iron, there is no leakage flux. 2. Windings do not have resistance. This means that there are no copper losses, nor there is any ohmic drop in the electric circuit. In fact the practical transformers are very close to this model and hence no major departure is made in making these assumptions. Fig. 11 shows a two winding ideal transformer. The primary winding has T1 turns and is connected to a voltage source of V1 volts. The secondary has T2 turns. Secondary can be connected to a load impedance for loading the transformer. The primary and secondary are shown on the same limb and separately for clarity.

As a current I0 amps is passed through the primary winding of T1 turns it sets up an mmf of I0 T1 ampere which is in turn sets up a flux φ through the core. Since the reluctance of the iron path given by R = l/µAis zero as µ −→ ∞, a vanishingly small value of current I0 is enough to setup a flux which is finite. As I0 establishes the field inside the transformer

27

Indian Institute of Technology Madras

Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

io

~

µ

φ

8

v1=V1mcosωt 0

+

+

T1

e1

i1

-

i2

+ +

+ T2

e2

v1=V1sinωt e1

e2

-

+

-

(a)Unloaded machine

(b) Circuit form µ

φ

8

v1=V1cosωt i1 +

+ N

T1

e1

-

i2 + ZL

T2

e2 -

(c)Loaded machine

Figure 11: Two winding Ideal Transformer unloaded and loaded

28

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

it is called the magnetizing current of the transformer. F lux φ =

mmf I0 T1 I0 T1 Aµ = l = . Reluctance l µA

(9)

This current is the result of a sinusoidal voltage V applied to the primary. As the current through the loop is zero (or vanishingly small), at every instant of time, the sum of the voltages must be zero inside the same. Writing this in terms of instantaneous values we have, v1 − e1 = 0

(10)

where v1 is the instantaneous value of the applied voltage and e1 is the induced emf due to Faradays principle. The negative sign is due to the application of the Lenz’s law and shows that it is in the form of a voltage drop. Kirchoff’s law application to the loop will result in the same thing.

This equation results in v1 = e1 or the induced emf must be same in magnitude to the applied voltage at every instant of time. Let v1 = V1peak cos ωt where V1peak is the peak value and ω = 2πf t. f is the frequency of the supply. As v1 = e1 ; e1 = dψ1 /dt but e1 = E1peak cos ωt ∴ E1 = V1 . It can be easily seen that the variation of flux linkages can be obtained as ψ1 = ψ1peak sin ωt. Here ψ1peak is the peak value of the flux linkages of the primary. Thus the RMS primary induced emf is dψ1 d(ψ1peak sin ωt) = dt dt = ψ1peak .ω. cos ωt or the rms value

e1 =

E1 =

ψ1peak .ω 2πf T1 φm √ √ = = 4.44f φmT1 2 2 29

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(11) (12) volts

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Here ψ1peak is the peak value of the flux linkages of the primary. The same mutual flux links the secondary winding. However the magnitude of the flux linkages will be ψ2peak = T2 .φm . The induced emf in the secondary can be similarly obtained as , dψ2 d(ψ2peak sin ωt) = dt dt = ψ2peak .ω. cos ωt or the rms value

e2 =

2πf T2 φm √ = 4.44f φmT2 2

E2 =

(13) (14)

volt

which yields the voltage ratio as T1 E1 = E2 T2

(15)

I1 I2

+ + V1

E1

E2

V2

-

-

Figure 12: Dot Convention

The voltages E1 and E2 are obtained by the same mutual flux and hence they are in phase. If the winding sense is opposite i.e., if the primary is wound in clockwise sense and the secondary counter clockwise sense then if the top terminal of the first winding is at maximum potential the bottom terminal of the second winding would be at the peak potential. Similar problem arises even when the sense of winding is kept the same, but the 30

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

two windings are on opposite limbs (due to the change in the direction of flux). Hence in the circuit representation of transformers a dot convention is adopted to indicate the terminals of the windings that go high (or low) together. (Fig. 12). This can be established experimentally by means of a polarity test on the transformers. At a particular instant of time if the current enters the terminal marked with a dot it magnetizes the core. Similarly a current leaving the terminal with a dot demagnetizes the core.

So far, an unloaded ideal transformer is considered. If now a load impedance ZL is connected across the terminals of the secondary winding a load current flows as marked in Fig. 11(c). This load current produces a demagnetizing mmf and the flux tends to collapse. However this is detected by the primary immediately as both E2 and E1 tend to collapse. The current drawn from supply increases up to a point the flux in the core is restored back to its original value. The demagnetizing mmf produced by the secondary is neutralized by additional magnetizing mmf produces by the primary leaving the mmf and flux in the core as in the case of no-load. Thus the transformer operates under constant induced emf mode. Thus, i1 T1 − i2 T2 = i0 T1 i2 T2 = i1 T1

but i0 → 0

(16)

and the rms value I2 T2 = I1 T1 .

(17)

If the reference directions for the two currents are chosen as in the Fig. 12, then the above equation can be written in phasor form as, T2 or I¯1 = .I¯2 T1 T1 I2 = = E1 I1 = E2 I2 T2 I1

I¯1 T1 = I¯2 T2 Also

E1 E2

31

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(18) (19)

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Thus voltage and current transformation ratio are inverse of one another. If an impedance of ZL is connected across the secondary, E¯2 I¯2 = ¯ ZL

E¯2 or Z¯L = ¯ I2

(20)

The input impedance under such conditions is E¯1 T1 E¯2 T1 Z¯i = ¯ = ( )2 . ¯ = ( )2 .Z¯L T2 I2 T2 I1

(21)

An impedance of ZL when viewed ‘through’ a transformer of turns ratio ( TT12 ) is seen as ( TT21 )2 .ZL . Transformer thus acts as an impedance converter. The transformer can be interposed in between a source and a load to ‘match’ the impedance.

V1

E1 I2 E2

V2

I1 θ2

θ1 φ

φ

Figure 13: Phasor diagram of Operation of an Ideal Transformer

Finally, the phasor diagram for the operation of the ideal transformer is shown in Fig. 13 in which θ1 and θ2 are power factor angles on the primary and secondary sides. As 32

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

the transformer itself does not absorb any active or reactive power it is easy to see that θ1 = θ2 .

Thus, from the study of the ideal transformer it is seen that the transformer provides electrical isolation between two coupled electric circuits while maintaining power invariance at its two ends. However, grounding of loads and one terminal of the transformer on the secondary/primary side are followed with the provision of leakage current detection devices to safe guard the persons working with the devices. Even though the isolation aspect is a desirable one its utility cannot be over emphasized. It can be used to step up or step down the voltage/current at constant volt-ampere. Also, the transformer can be used for impedance matching. In the case of an ideal transformer the efficiency is 100% as there are no losses inside the device.

33

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5

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Practical Transformer An ideal transformer is useful in understanding the working of a transformer. But it

cannot be used for the computation of the performance of a practical transformer due to the non-ideal nature of the practical transformer. In a working transformer the performance aspects like magnetizing current, losses, voltage regulation, efficiency etc are important. Hence the effects of the non-idealization like finite permeability, saturation, hysteresis and winding resistances have to be added to an ideal transformer to make it a practical transformer. Conversely, if these effects are removed from a working transformer what is left behind is an ideal transformer.

Finite permeability of the magnetic circuit necessitates a finite value of the current to be drawn from the mains to produce the mmf required to establish the necessary flux. The current and mmf required is proportional to the flux density B that is required to be established in the core. B = µH;

B=

φ A

(22)

where A is the area of cross section of the iron core m2 . H is the magnetizing force which is given by, H = i.

T1 l

(23)

where l is the length of the magnetic path, m. or φ = B.A =

Aµ(iT1 ) l

=

permeance ∗ mmf (here that of

primary)

(24)

The magnetizing force and the current vary linearly with the applied voltage as long as the magnetic circuit is not saturated. Once saturation sets in, the current has to vary in 34

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

a nonlinear manner to establish the flux of sinusoidal shape. This non-linear current can be resolved into fundamental and harmonic currents. This is discussed to some extent under harmonics. At present the effect of this non-linear behavior is neglected as a secondary effect. Hence the current drawn from the mains is assumed to be purely sinusoidal and directly proportional to the flux density of operation. This current can be represented by a current drawn by an inductive reactance in the circuit as the net energy associated with the same over a cycle is zero. The energy absorbed when the current increases is returned to the electric circuit when the current collapses to zero. This current is called the magnetizing current of the transformer. The magnetizing current Im is given by Im = E1 /Xm where Xm is called the magnetizing reactance. The magnetic circuit being lossy absorbs and dissipates the power depending upon the flux density of operation. These losses arise out of hysteresis, eddy current inside the magnetic core. These are given by the following expressions: Ph ∝ B 1.6 f

(25)

Pe ∝ B 2 f 2 t2

(26)

Ph -Hysteresis loss, Watts B- Flux density of operation Tesla. f - Frequency of operation, Hz t - Thickness of the laminations of the core, m.

For a constant voltage, constant frequency operation B is constant and so are these losses. An active power consumption by the no-load current can be represented in the input circuit as a resistance Rc connected in parallel to the magnetizing reactance Xm . Thus the no-load current I0 may be made up of Ic (loss component) and Im (magnetizing component

35

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Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

as ) I¯0 = I¯c − j I¯m

(27)

Ic2 Rc – gives the total core losses (i.e. hysteresis + eddy current loss) 2 Im Xm - Reactive volt amperes consumed for establishing the mutual flux.

Finite µ of the magnetic core makes a few lines of flux take to a path through the air. Thus these flux lines do not link the secondary winding. It is called as leakage flux. As the path of the leakage flux is mainly through the air the flux produced varies linearly with the primary current I1 . Even a large value of the current produces a small value of flux. This flux produces a voltage drop opposing its cause, which is the current I1 . Thus this effect of the finite permeability of the magnetic core can be represented as a series inductive element jxl1 . This is termed as the reactance due to the primary leakage flux. As this leakage flux varies linearly with I1 , the flux linkages per ampere and the primary leakage inductance are constant (This is normally represented by ll1 Henry). The primary leakage reactance therefore becomes xl1 = 2πf ll1

ohm

(28)

A similar effect takes place on the secondary side when the transformer is loaded. The secondary leakage reactance jxl2 arising out of the secondary leakage inductance ll2 is given by

xl2 = 2πf ll2

(29)

Finally, the primary and secondary windings are wound with copper (sometimes aluminium in small transformers) conductors; thus the windings have a finite resistance (though 36

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

I1 V1

r1

jxl1

φ

I’2

Io

+

~

Rc

+

jXm

E1

T1

-

r2

jxl2

I2 +

ZL

V2

T2

E2 -

(a)Physical arrangement

I1

r1

jXl1

I’2

r2 jXl2 I2

Io

Ic V1

Rc

Im

E1

jXm

E2

(b)Equivalent circuit

Figure 14: A Practical Transformer

37

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ZL V2

Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

small). This is represented as a series circuit element, as the power lost and the drop produced in the primary and secondary are proportional to the respective currents. These are represented by r1 and r2 respectively on primary and secondary side. A practical transformer sans these imperfections (taken out and represented explicitly in the electric circuits) is an ′

ideal transformer of turns ratio T1 : T2 (voltage ratio E1 : E2 ). This is seen in Fig. 14. I2 in the circuit represents the primary current component that is required to flow from the mains in the primary T1 turns to neutralize the demagnetizing secondary current I2 due to the load in the secondary turns. The total primary current ′ vectorially is I¯1 = I¯2 + I¯0 ′

Here I2 T1 = I2 T2

(30) ′

or I2 = I2

T2 T1

T2 Thus I¯1 = I¯2 + I¯0 T1

(31) (32)

By solving this circuit for any load impedance ZL one can find out the performance of the loaded transformer.

The circuit shown in Fig. 14(b). However, it is not very convenient for use due to the presence of the ideal transformer of turns ratio T1 : T2 . If the turns ratio could be made unity by some transformation the circuit becomes very simple to use. This is done here by replacing the secondary by a ‘hypothetical’ secondary having T1 turns which is ‘equivalent ’ to the physical secondary. The equivalence implies that the ampere turns, active and reactive power associated with both the circuits must be the same. Then there is no change as far as their effect on the primary is considered. Thus ′

V2 = aV2 , where a -turns ratio

′

I2 =

I2 , a

′

r2 = a2 r2 ,

T1 T2

38

Indian Institute of Technology Madras

′

xl2 = a2 xl2

′

ZL = a2 ZL .

Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

This equivalent circuit is as shown in Fig. ??(a). As the ideal transformer in this case has a turns ratio of unity the potentials on either side are the same and hence they may be conductively connected dispensing away with the ideal transformer. This particular equivalent circuit is as seen from the primary side. It is also possible to refer all the primary parameters to secondary by making the hypothetical equivalent primary winding on the input side having the number of turns to be T2 . Such an equivalent circuit having all the parameters referred to the secondary side is shown in fig. 15.

The equivalent circuit can be derived, with equal ease, analytically using the Kirchoff’s equations applied to the primary and secondary. Referring to fig. 14(a), we have (by neglecting the shunt branch) V1 = E1 + I1 (r1 + jxl1 )

(33)

E2 = V2 + I2 (r2 + jxl2 )

(34)

T1 I0 = T1 I1 + T2 I2 = − a =

or I1 = −

I2 + I0 a

(35)

I2 + Ic + Im a

T1 . T2

Multiply both sides of Eqn.34 by ‘a’ [This makes the turns ratio unity and retains the power invariance]. aE2 = aV2 + aI2 (r2 + jxl2 ) Substituting in Eqn.33 we have

39

Indian Institute of Technology Madras

but aE2 = E1

(36)

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

V1 = aV2 + aI2 (r2 + jxl2 ) + I1 (r1 + jxl1 ) ′

= V2 + I1 (a2 r2 + ja2 xl2 ) + I1 (r1 + jxl1 ) ′

′

′

= V2 + I1 (r1 + r2 + jxl1 + xl2 )

(37)

A similar procedure can be used to refer all parameters to secondary side. (Shown in fig. 15.)

r’1

jx’l1

r2

I’1

jxl2

I2

I’o I’c

R’c

V’1

I’m

jX’m

ZL

V2

Figure 15: Equivalent Circuit Referred to the Secondary Side

40

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6

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Phasor diagrams

r1

I1

r’2

jxl1

jx’l2

Io Ic

Im

Rc

V1

jXm

V’2

Z’L

R

jX

(a)

I1 Ic V1 Rc

r1

I’2

jxl1

r’2

jx’l2

I1

I’2

R=r1+r’2

Io Im

Z’L jxm

V’2 x=xl1+x’l2

V’2

V1

I1=I’2

(b)

(c)

Figure 16: Exact,approximate and simplified equivalent circuits

The resulting equivalent circuit as shown in Fig. 16 is known as the exact equivalent circuit. This circuit can be used for the analysis of the behavior of the transformers. As the no-load current is less than 1% of the load current a simplified circuit known as ‘approximate’ equivalent circuit (see Fig. 16(b)) is usually used, which may be further 41

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

simplified to the one shown in Fig. 16(c).

On similar lines to the ideal transformer the phasor diagram of operation can be drawn for a practical transformer also. The positions of the current and induced emf phasor are not known uniquely if we start from the phasor V1 . Hence it is assumed that the phasor φ is known. The E1 and E2 phasor are then uniquely known. Now, the magnetizing and loss components of the currents can be easily represented. Once I0 is known, the drop that takes place in the primary resistance and series reactance can be obtained which when added to E1 gives uniquely the position of V1 which satisfies all other parameters. This is represented in Fig. 17(a) as phasor diagram on no-load.

Next we proceed to draw the phasor diagram corresponding to a loaded transformer. The position of the E2 vector is known from the flux phasor. Magnitude of I2 and the load power factor angle θ2 are assumed to be known. But the angle θ2 is defined with respect to the terminal voltage V2 and not E2 . By trial and error the position of I2 and V2 are determined. V2 should also satisfy the Kirchoff’s equation for the secondary. Rest of the construction of the phasor diagram then becomes routine. The equivalent primary current ′

I2 is added vectorially to I0 to yield I1 . I1 (r1 + jxl1 )is added to E1 to yield V1 . This is shown in fig. 17(b) as phasor diagram for a loaded transformer.

42

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

V1 IoX l1 Ior1

E1

E2

Io φ

Il

Im

φ

(a)No-load

V1 I1X l1

E1

I1r1 E2

I2x2 I r 2 2

I2 V2

I’2

Il Io

φ (b)On-load

Figure 17: Phasor Diagram of a Practical Transformer

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φ

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7

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Testing of Transformers The structure of the circuit equivalent of a practical transformer is developed earlier.

The performance parameters of interest can be obtained by solving that circuit for any load conditions. The equivalent circuit parameters are available to the designer of the transformers from the various expressions that he uses for designing the transformers. But for a user these are not available most of the times. Also when a transformer is rewound with different primary and secondary windings the equivalent circuit also changes. In order to get the equivalent circuit parameters test methods are heavily depended upon. From the analysis of the equivalent circuit one can determine the electrical parameters. But if the temperature rise of the transformer is required, then test method is the most dependable one. There are several tests that can be done on the transformer; however a few common ones are discussed here.

7.1

Winding resistance test This is nothing but the resistance measurement of the windings by applying a small

d.c voltage to the winding and measuring the current through the same. The ratio gives the winding resistance, more commonly feasible with high voltage windings. For low voltage windings a resistance-bridge method can be used. From the d.c resistance one can get the a.c. resistance by applying skin effect corrections.

44

Indian Institute of Technology Madras

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

V3 S

A2

Vs

~

a2

a2

V1

+

A2 +

V2

V -

A1

a1 A1

(a)A.C.test

a1 (b)D.C.test

Figure 18: Polarity Test

7.2

Polarity Test This is needed for identifying the primary and secondary phasor polarities. It is

a must for poly phase connections. Both a.c. and d.c methods can be used for detecting the polarities of the induced emfs. The dot method discussed earlier is used to indicate the polarities. The transformer is connected to a low voltage a.c. source with the connections made as shown in the fig. 18(a). A supply voltage Vs is applied to the primary and the readings of the voltmeters V1 , V2 and V3 are noted. V1 : V2 gives the turns ratio. If V3 reads V1 −V2 then assumed dot locations are correct (for the connection shown). The beginning and end of the primary and secondary may then be marked by A1 − A2 and a1 − a2 respectively. If the voltage rises from A1 to A2 in the primary, at any instant it does so from a1 to a2 in the secondary. If more secondary terminals are present due to taps taken from the windings they can be labeled as a3 , a4 , a5 , a6 . It is the voltage rising from smaller number towards larger ones in each winding. The same thing holds good if more secondaries are present. 45

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Fig. 18(b) shows the d.c. method of testing the polarity. When the switch S is closed if the secondary voltage shows a positive reading, with a moving coil meter, the assumed polarity is correct. If the meter kicks back the assumed polarity is wrong.

7.3

Open Circuit Test

W A V1

Io

V2

V

Im V1

jXm

Ic Rc

(a)Physical Arrangement (b)Equivalent Circuit Figure 19: No Load Test

As the name suggests, the secondary is kept open circuited and nominal value of the input voltage is applied to the primary winding and the input current and power are measured. In Fig. 19(a) V, A, W are the voltmeter, ammeter and wattmeter respectively. Let these meters read V1 , I0 and W0 respectively.Fig. 19(b) shows the equivalent circuit of the transformer under this test. The no load current at rated voltage is less than 1 percent of nominal current and hence the loss and drop that take place in primary impedance r1 + jxl1 due to the no load current I0 is negligible. The active component Ic of the no load current I0 46

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

represents the core losses and reactive current Im is the current needed for the magnetization. Thus the watt meter reading W0 = V1 Ic = Pcore W0 V q1 = I02 − Ic2

(38)

∴ Ic = ∴ Im

Rc =

V1 Ic

(39) or

andXm =

(40) V1 Im

(41)

V1

Io Figure 20: Open Circuit Characteristics

The parameters measured already are in terms of the primary. Sometimes the primary voltage required may be in kilo-Volts and it may not be feasible to apply nominal voltage to primary from the point of safety to personnel and equipment. If the secondary voltage is low, one can perform the test with LV side energized keeping the HV side open circuited. In this case the parameters that are obtained are in terms of LV . These have to be referred to HV side if we need the equivalent circuit referred to HV side.

47

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Sometimes the nominal value of high voltage itself may not be known, or in doubt, especially in a rewound transformer. In such cases an open circuit characteristics is first obtained, which is a graph showing the applied voltage as a function of the no load current. This is a non linear curve as shown in Fig. 20. This graph is obtained by noting the current drawn by transformer at different applied voltage, keeping the secondary open circuited. The usual operating point selected for operation lies at some standard voltage around the knee point of the characteristic. After this value is chosen as the nominal value the parameters are calculated as mentioned above.

7.4

Short Circuit Test The purpose of this test is to determine the series branch parameters of the equiv-

alent circuit of Fig. 21(b). As the name suggests, in this test primary applied voltage, the current and power input are measured keeping the secondary terminals short circuited. Let these values be Vsc , Isc and Wsc respectively. The supply voltage required to circulate rated current through the transformer is usually very small and is of the order of a few percent of the nominal voltage. The excitation current which is only 1 percent or less even at rated voltage becomes negligibly small during this test and hence is neglected. The shunt branch ′

is thus assumed to be absent. Also I1 = I2 as I0 ≃ 0. Therefore Wsc is the sum of the copper losses in primary and secondary put together. The reactive power consumed is that absorbed by the leakage reactance of the two windings. ′

2 Wsc = Isc (r1 + r2 )

Vsc I qsc ′ 2 − (r + r ′ )2 (xl1 + xl2 ) = Zsc 1 2 Zsc =

48

Indian Institute of Technology Madras

(42) (43) (44)

Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

W

A Vsc

V

(a)Physical Arrangement

Isc

r1

jxl1

r’2

Vsc

(b)Equivalent Circuit Figure 21: Short Circuit Test

49

Indian Institute of Technology Madras

jx’l2

Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

If the approximate equivalent circuit is required then there is no need to separate r1 ′

′

and r2 or xl1 and xl2 . However if the exact equivalent circuit is needed then either r1 or ′

r2 is determined from the resistance measurement and the other separated from the total. ′

As for the separation of xl1 and xl2 is concerned, they are assumed to be equal. This is a fairly valid assumption for many types of transformer windings as the leakage flux paths are through air and are similar.

7.5

Load Test Load Test helps to determine the total loss that takes place, when the transformer

is loaded. Unlike the tests described previously, in the present case nominal voltage is applied across the primary and rated current is drown from the secondary. Load test is used mainly 1. to determine the rated load of the machine and the temperature rise 2. to determine the voltage regulation and efficiency of the transformer. Rated load is determined by loading the transformer on a continuous basis and observing the steady state temperature rise. The losses that are generated inside the transformer on load appear as heat. This heats the transformer and the temperature of the transformer increases. The insulation of the transformer is the one to get affected by this rise in the temperature. Both paper and oil which are used for insulation in the transformer start getting degenerated and get decomposed. If the flash point of the oil is reached the transformer goes up in flames. Hence to have a reasonable life expectancy the loading of the transformer must be limited to that value which gives the maximum temperature rise tolerated by the insulation. This aspect of temperature rise cannot be guessed from the electrical equivalent circuit. Further, the losses like dielectric losses and stray load losses are not modeled in the 50

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equivalent circuit and the actual loss under load condition will be in error to that extent. Many external means of removal of heat from the transformer in the form of different cooling methods give rise to different values for temperature rise of insulation. Hence these permit different levels of loading for the same transformer. Hence the only sure way of ascertaining the rating is by conducting a load test.

It is rather easy to load a transformer of small ratings. As the rating increases it becomes difficult to find a load that can absorb the requisite power and a source to feed the necessary current. As the transformers come in varied transformation ratios, in many cases it becomes extremely difficult to get suitable load impedance.

Further, the temperature rise of the transformer is due to the losses that take place ‘inside’ the transformer. The efficiency of the transformer is above 99% even in modest sizes which means 1 percent of power handled by the transformer actually goes to heat up the machine. The remaining 99% of the power has to be dissipated in a load impedance external to the machine. This is very wasteful in terms of energy also. ( If the load is of unity power factor) Thus the actual loading of the transformer is seldom resorted to. Equivalent loss methods of loading and ‘Phantom’ loading are commonly used in the case of transformers. The load is applied and held constant till the temperature rise of transformer reaches a steady value. If the final steady temperature rise is lower than the maximum permissible value, then load can be increased else it is decreased. That load current which gives the maximum permissible temperature rise is declared as the nominal or rated load current and the volt amperes are computed using the same.

51

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In the equivalent loss method a short circuit test is done on the transformer. The short circuit current is so chosen that the resulting loss taking place inside the transformer is equivalent to the sum of the iron losses, full load copper losses and assumed stray load losses. By this method even though one can pump in equivalent loss inside the transformer, the actual distribution of this loss vastly differs from that taking place in reality. Therefore this test comes close to a load test but does not replace one.

W

1

A Io

Io

2Io V1 V I’2

I2

W A Vs

I2

I’2

2

V

Figure 22: Back to Back Test - Phantom Loading

In Phantom loading method two identical transformers are needed. The windings are connected back to back as shown in Fig. 22. Suitable voltage is injected into the loop formed by the two secondaries such that full load current passes through them. An equiv52

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alent current then passes through the primary also. The voltage source V1 supplies the magnetizing current and core losses for the two transformers. The second source supplies the load component of the current and losses due to the same. There is no power wasted in a load ( as a matter of fact there is no real load at all) and hence the name Phantom or virtual loading. The power absorbed by the second transformer which acts as a load is pushed back in to the mains. The two sources put together meet the core and copper losses of the two transformers. The transformers work with full flux drawing full load currents and hence are closest to the actual loading condition with a physical load.

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Per Unit Calculations As stated earlier, transformers of various sizes, ratings, voltage ratios can be seen

being used in a power system. The parameters of the equivalent circuits of these machines also vary over a large range. Also the comparison of these machines are made simple if all the parameters are normalized. If simple scaling of the parameters is done then one has to carry forward the scaling factors in the calculations. Expressing in percent basis is one example of scaling. However if the scaling is done on a logical basis one can have a simple representation of the parameters without the bother of the scaling factors. Also different units of measurement are in use in the different countries (FPS, CGS, MKS, etc;). These units also underwent several revisions over the years. If the transformer parameter can be freed from the units then the system becomes very simple. The ‘per unit’ system is developed keeping these aspects in mind. The parameters of the transformer are referred to some base values and thus get scaled. In the case of power system a common base value is adopted in view of different ratings of the equipments used. In the case of individual equipments, its own nominal parameters are used as base values. Some base parameters can be chosen as independent base values while some others become derived base parameters. Once the base values are identified the per unit values are calculated for any parameter by dividing the same by its base value. The units must be the same for both the parameters and their bases. Thus the per unit value is a unit-less dimensionless number. Let us choose nominal voltage and nominal current on the primary side of a transformer as the base values Vbase and Ibase . Other base values like volt ampere Sbase , short circuit impedance Zbase can be

54

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calculated from those values. Pbase , Qbase , Sbase = Vbase ∗ Ibase Vbase Ibase Ibase = Vbase

(45)

Rbase , Xbase , Zbase =

(46)

Gbase , Bbase , Ybase

(47)

Normally Sbase and Vbase are known from name plate details. Other base values can be derived from them. V (volt) , Vbase (volt) I(amps) I(Amps) = Sbase = Ibase (amps) V

Vp.u = Ip.u

(48)

base

Zp.u

Z(ohm) Ibase Sbase = = Z(ohm) ∗ = Z(ohm). 2 Zbase (ohm) Vbase Vbase

(49)

Many times, when more transformers are involved in a circuit one is required to choose a common base value for all of them. Parameters of all the machines are expressed on this common base. This is a common problem encountered in the case of parallel operation of two or more transformers. The conversion of the base values naturally lead to change in the per unit values of their parameters. An impedance Zp.u.old on the old base of Sbaseold and Vbaseold shall get modified on new base Sbasenew ,Vbasenew as Zp.u.new = (Zp.u.old.

2 Vbase Sbase

old old

)

Sbase 2 Vbase

new

(50)

new

The term inside the bracket is nothing but the ohmic value of the impedance and this gets converted into the new per unit value by the new Sbase and Vbase .

If all the equivalent circuit parameters are referred to the secondary side and per unit values of the new equivalent circuit parameters are computed with secondary voltage and 55

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

current as the base values, there is no change in the per unit values. This can be easily seen by, ′

′

Zp.u.

S = Zohm . base ′2 Vbase ′

′

but Zohm =

1 .Zohm a2

(51)

Where a - is the turns ratio of primary to secondary Z - impedance as seen by primary, ′

Z - impedance as seen by secondary. ′

Sbase = Sbase - as the transformer rating is unaltered. ′

Vbase = Vbase . a1 ′

From the above relationships it can be seen that Zp.u. = Zp.u..

This becomes obvious if we realize that the mmf of the core for establishing a given flux is the same whether it is supplied through primary or the secondary. Also the active power and reactive power absorbed inside the transformer are not dependant on the winding connected to supply. This is further illustrated by taking the equivalent circuit of a transformer derived earlier and expressing the same in per unit form.

Thus the per unit values help in dispensing away the scaling constants. The veracity of the parameters can be readily checked. Comparison of the parameters of the machines with those of similar ones throw in useful information about the machines. Comparing the efficiencies of two transformers at any load one can say that the transformer with a higher p.u.resistance has higher copper losses without actually computing the same.

Application of per unit values for the calculation of voltage regulation, efficiency and load sharing of parallel connected transformers will be discussed later at appropriate places. 56

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9

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Voltage Regulation Modern power systems operate at some standard voltages. The equipments work-

ing on these systems are therefore given input voltages at these standard values, within certain agreed tolerance limits. In many applications this voltage itself may not be good enough for obtaining the best operating condition for the loads. A transformer is interposed in between the load and the supply terminals in such cases. There are additional drops inside the transformer due to the load currents. While input voltage is the responsibility of the supply provider, the voltage at the load is the one which the user has to worry about. If undue voltage drop is permitted to occur inside the transformer the load voltage becomes too low and affects its performance. It is therefore necessary to quantify the drop that takes place inside a transformer when certain load current, at any power factor, is drawn from its output leads. This drop is termed as the voltage regulation and is expressed as a ratio of the terminal voltage (the absolute value per se is not too important).

The voltage regulation can be defined in two ways - Regulation Down and Regulation up. These two definitions differ only in the reference voltage as can be seen below. Regulation down: This is defined as ” the change in terminal voltage when a load current at any power factor is applied, expressed as a fraction of the no-load terminal voltage”. Expressed in symbolic form we have, Regulation =

|Vnl | − |Vl | |Vnl |

(52)

Vnl and Vl are no-load and load terminal voltages. This is the definition normally used in the case of the transformers, the no-load voltage being the one given by the power 57

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supply provider on which the user has no say. Hence no-load voltage is taken as the reference. Regulation up: Here again the regulation is expressed as the ratio of the change in the terminal voltage when a load at a given power factor is thrown off, and the on load voltage. This definition if expressed in symbolic form results in Regulation =

|Vnl | − |Vl | |Vl |

(53)

Vnl is the no-load terminal voltage. Vl is load voltage. Normally full load regulation is of interest as the part load regulation is going to be lower.

This definition is more commonly used in the case of alternators and power systems as the user-end voltage is guaranteed by the power supply provider. He has to generate proper no-load voltage at the generating station to provide the user the voltage he has asked for. In the expressions for the regulation, only the numerical differences of the voltages are taken and not vector differences.

In the case of transformers both definitions result in more or less the same value for the regulation as the transformer impedance is very low and the power factor of operation is quite high. The power factor of the load is defined with respect to the terminal voltage on load. Hence a convenient starting point is the load voltage. Also the full load output voltage is taken from the name plate. Hence regulation up has some advantage when it comes to its application. Fig. 23 shows the phasor diagram of operation of the transformer under loaded ′

condition. The no-load current I0 is neglected in view of the large magnitude of I2 . Then 58

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Re

jXe I’2

V1

V’2

(a) Equivalent Circuit V1

A

O

θ B I2’Xe

V’2

φ

I2’Re

I2’

(b)Phasor Diagram Figure 23: Regulation of Transformer

59

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D

C E

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′

I1 = I2 . ′

′

V1 = I2 (Re + jXe ) + V2 p OD = V1 = [OA + AB + BC]2 + [CD]2 q ′ ′ ′ ′ ′ = [V2 + I2 Re cos φ + I2 Xe sin φ]2 + [I2 Xe cos φ − I2 Re sin φ]2

(54)

(55)

φ - power factor angle, e θ- internal impedance angle=tan−1 X Re

Also, ′

′

′

′

V1 = V2 + I2 .(Re + jXe )

(56)

= V2 + I2 (cos φ − j sin φ)(Re + jXe ) ′ q |V1 | − |V2 | ∴ RegulationR = = (1 + v1 )2 + v22 − 1 ′ |V2 | (1 + v1 )2 + v22 ≃ (1 + v1 )2 + v22 .

(57)

2(1 + v1 ) v22 v22 +[ ]2 = (1 + v1 + )2 (58) 2(1 + v1 ) 2(1 + v1 ) 2(1 + v1 )

Taking the square root q (1 + v1 )2 + v22 = 1 + v1 +

(59) v22 2(1 + v1 )

(60)

where v1 = er cos φ + ex sin φ and v2 = ex cos φ − er sin φ ′

er =

I2 Re ′ =per V2

unit resistance drop

′

ex =

I2 Xe ′ =per V2

unit reactance drop

as v1 and v2 are small. v2 v22 − 1 ≃ v1 + 2 2(1 + e1 ) 2 (ex sin φ − er cos φ)2 ∴ regulation R = er cos φ ± ex sin φ + 2 ∴ R ≃ 1 + v1 +

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(61) (62)

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v22 (1 − v1 ) v22 v22 v22 ≃ . ≃ .(1 − v1 ) ≃ 2(1 + v1 ) 2 (1 − v12 ) 2 2

(63)

Powers higher than 2 for v1 and v2 are negligible as v1 and v2 are already small. As v2 is small its second power may be neglected as a further approximation and the expression for the regulation of the transform boils down to regulation R = er cos φ ± ex sin φ

The negative sign is applicable when the power factor is leading. It can be seen from the above expression, the full load regulation becomes zero when the power factor is leading and er cos φ = ex sin φ or tan φ = er /ex or the power factor angle φ = tan−1 (er /ex ) = tan−1 (Re /Xe ) leading.

Similarly, the value of the regulation is maximum at a power factor angle φ = tan−1 (ex /er ) = tan−1 (Xe /Re ) lagging. An alternative expression for the regulation of a transformer can be derived by the method shown in Fig. 24. Here the phasor are resolved along the current axis and normal to it. We have, OD 2 = (OA + AB)2 + (BC + CD)2 ′

′

′

(64) ′

= (V2 cos φ + I2 Re )2 + (V2 sin φ + I2 Xe )2 (65) ′

OD − V2 OD ∴ RegulationR = = ′ −1 ′ V2 V2 s

′

′

2

′

′

2

(V2 cos φ + I2 Re ) (V sin φ + I2 Xe ) + 2 −1 ′ ′ V2 V2 q 2 = (cos φ + Rp.u )2 + (sin φ + Xp.u) −1 61

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V1

I2’Xe

V2

O

D

θ

φ

I2’Re

I2’

C

A B Figure 24: An Alternate Method for the Calculation of Regulation

Thus this expression may not be as convenient as the earlier one due to the square root involved.

Fig. 25 shows the variation of full load regulation of a typical transformer as the power factor is varied from zero power factor leading, through unity power factor, to zero power factor lagging. It is seen from Fig. 25 that the full load regulation at unity power factor is nothing but the percentage resistance of the transformer. It is therefore very small and negligible. Only with low power factor loads the drop in the series impedance of the transformer contributes substantially to the regulation. In small transformers the designer tends to keep the Xe very low (less than 5%) so that the regulation performance of the transformer is satisfactory.

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5 4 3 %Regulation 2 power factor 1

leading

0

1.0

0.5

0.5

0

lagging

-1 -2 -3 -4 -5

Figure 25: Variation of Full Load Regulation with Power Factor

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A low value of the short circuit impedance /reactance results in a large short circuit current in case of a short circuit. This in turn results in large mechanical forces on the winding. So, in large transformers the short circuit impedance is made high to give better short circuit protection to the transformer which results in poorer regulation performance. In the case of transformers provided with taps on windings, so that the turns ratio can be changed, the voltage regulation is not a serious issue. In other cases care has to be exercised in the selection of the short circuit impedance as it affects the voltage regulation.

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D.C Machines 1

Introduction The steam age signalled the beginning of an industrial revolution. The advantages

of machines and gadgets in helping mass production and in improving the services spurred the industrial research. Thus a search for new sources of energy and novel gadgets received great attention. By the end of the 18th century the research on electric charges received a great boost with the invention of storage batteries. This enabled the research work on moving charges or currents. It was soon discovered ( in 1820 ) that, these electric currents are also associated with magnetic field like a load stone. This led to the invention of an electromagnet. Hardly a year later the force exerted on a current carrying conductor placed in the magnetic field was invented. This can be termed as the birth of a motor. A better understanding of the inter relationship between electric and magnetic circuits was obtained with the enumeration of laws of induction by Faraday in 1831. Parallel research was contemporarily being done to invent a source of energy to recharge the batteries in the form of a d.c. source of constant amplitude (or d.c. generator). For about three decades the research on d.c. motors and d.c. generators proceeded on independent paths. During the second half of the 19th century these two paths merged. The invention of a commutator paved the way for the birth of d.c. generators and motors. These inventions generated great interest in the generation and use of electrical energy. Other useful machines like alternators, transformers and induction motors came into existence almost contemporarily. The evolution of these machines was very quick. They rapidly attained the physical configurations that are being used even today. The d.c. power system was poised for a predominant place as a preferred

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system for use, with the availability of batteries for storage, d.c. generators for conversion of mechanical energy into electrical form and d.c. motors for getting mechanical outputs from electrical energy.

The limitations of the d.c. system however became more and more apparent as the power demand increased. In the case of d.c. systems the generating stations and the load centers have to be near to each other for efficient transmission of energy. The invention of induction machines in the 1880s tilted the scale in favor of a.c. systems mainly due to the advantage offered by transformers, which could step up or step down the a.c.voltage levels at constant power at extremely high efficiency. Thus a.c. system took over as the preferred system for the generation transmission and utilization of electrical energy. The d.c. system, however could not be obliterated due to the able support of batteries. Further, d.c. motors have excellent control characteristics. Even today the d.c. motor remains an industry standard as far as the control aspects are concerned. In the lower power levels and also in regenerative systems the d.c. machines still have a major say.

In spite of the apparent diversity in the characteristics, the underlying principles of both a.c. and d.c. machines are the same. They use the electromagnetic principles which can be further simplified at the low frequency levels at which these machines are used. These basic principles are discussed at first.

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1.1

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Basic principles Electric machines can be broadly classified into electrostatic machines and electro-

magnetic machines. The electrostatic principles do not yield practical machines for commercial electric power generation. The present day machines are based on the electro-magnetic principles. Though one sees a variety of electrical machines in the market, the basic underlying principles of all these are the same. To understand, design and use these machines the following laws must be studied. 1. Electric circuit laws -

Kirchof f ′ s Laws

2. Magnetic circuit law -

Ampere′ s Law

3. Law of electromagnetic induction - F araday ′s Law 4. Law of electromagnetic interaction -BiotSavart′ s Law Most of the present day machines have one or two electric circuits linking a common magnetic circuit. In subsequent discussions the knowledge of electric and magnetic circuit laws is assumed. The attention is focused on the Faraday’s law and Biot Savart’s law in the present study of the electrical machines.

1.1.1

Law of electro magnetic induction Faraday proposed this law of Induction in 1831. It states that if the magnetic

flux lines linking a closed electric coil changes, then an emf is induced in the coil. This emf is proportional to the rate of change of these flux linkages. This can be expressed mathematically, e∝ 3

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dψ dt

(1)

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where ψ is the flux linkages given by the product of flux lines in weber that are linked and N the number of turns of the coil. This can be expressed as, e∝N

dΦ dt

(2)

Here N is the number of turns of the coil, and Φ is the flux lines in weber linking all these turns. The direction of the induced emf can be determined by the application of Lenz’s law. Lenz’s law states that the direction of the induced emf is such as to produce an effect to oppose this change in flux linkages. It is analogous to the inertia in the mechanical systems. The changes in the flux linkages associated with a turn can be brought about by (i) changing the magnitude of the flux linking a static coil (ii) moving the turn outside the region of a steady field (iii) moving the turn and changing the flux simultaneously These may be termed as Case(i), Case(ii), and Case(iii) respectively. This is now explained with the help of a simple geometry. Fig. 1 shows a rectangular loop of one turn (or N=1). Conductor 1 is placed over a region with a uniform flux density of B Tesla. The flux lines, the conductor and the motion are in mutually perpendicular directions. The flux linkages of the loop is BLN weber turns. If the flux is unchanging and conductor stationary, no emf will be seen at the terminals of the loop. If now the flux alone changes with time such that B = Bm . cos ωt, as in Case(i), an emf given by e=

d (Bm .L.N cos ωt) = −(Bm .L.Nω). sin ωt. dt = −jBm .L.Nω. cos ωt volt 4

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L B X

-

+

Figure 1: Faraday’s law of Induction appears across the terminals. This is termed as a ”transformer” emf. If flux remains constant at Bm but the conductor moves with a velocity v, as in Case(ii), then the induced emf is e=

d(Bm .L.N) dX dψ = = Bm .L.N dt dt dt

volts

(4)

but dX =v dt

∴ e = Bm .L.N.v

volts

(5)

The emf induced in the loop is directly proportional to the uniform flux density under which it is moving with a velocity v. This type of voltage is called speed emf (or rotational emf). The Case(iii) refers to the situation where B is changing with time and so also is X. Then the change in flux linkage and hence the value of e is given by e=

dψ d(Bm .L.X.N. cos ωt) dX = = Bm . cos ωt.L.N. − Bm .L.X.N.ω. sin ωt. dt dt dt

In this case both transformer emf and speed emf are present.

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The Case(i) has no mechanical energy associated with it. This is the principle used in transformers. One coil carrying time varying current produces the time varying field and a second coil kept in the vicinity of the same has an emf induced in it. The induced emf of this variety is often termed as the transformer emf.

The Case(ii) is the one which is employed in d.c. machines and alternators. A static magnetic field is produced by a permanent magnet or by a coil carrying a d.c. current. A coil is moved under this field to produce the change in the flux linkages and induce an emf in the same. In order to produce the emf on a continuous manner a cylindrical geometry is chosen for the machines. The direction of the field, the direction of the conductor of the coil and the direction of movement are mutually perpendicular as mentioned above in the example taken.

In the example shown above, only one conductor is taken and the flux ’cut’ by the same in the normal direction is used for the computation of the emf. The second conductor of the turn may be assumed to be far away or unmoving. This greatly simplifies the computation of the induced voltage as the determination of flux linkages and finding its rate of change are dispensed with. For a conductor moving at a constant velocity v the induced emf becomes just proportional to the uniform flux density of the magnetic field where the conductor is situated. If the conductor, field and motion are not normal to each other then the mutually normal components are to be taken for the computation of the voltage. The induced emf of this type is usually referred to as a rotational emf (due to the geometry).

Application of Faradays law according to Case(iii) above for electro mechani6

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cal energy conversion results in the generation of both transformer and rotational emf to be present in the coil moving under a changing field. This principle is utilized in the induction machines and a.c. commutator machines.

The direction of the induced emf is

emf and current

Force

Motion

F

B (a)

(b)

Figure 2: Law of induction-Generator action decided next. This can be obtained by the application of the Lenz’s law and the law of interaction. This is illustrated in Fig. 3.

In Case(i), the induced emf will be in such a direction as to cause a opposing mmf if the circuit is closed. Thus, it opposes the cause of the emf which is change in ψ and hence φ. Also the coil experiences a compressive force when the flux tries to increase and a tensile force when the flux decays. If the coil is rigid, these forces are absorbed by the supporting structure.

In Case(ii), the direction of the induced emf is as shown. Here again one could derive the same from the application of the Lenz’s law. The changes in the flux linkages is 7

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emf

current F

Motion,Force

B (a)

(b)

Figure 3: Law of interaction- Motor action brought about by the sweep or movement of the conductor. The induced emf, if permitted to drive a current which produces an opposing force, is as shown in the figure. If one looks closely at the field around the conductor under these conditions it is as shown in Fig. 2(a)and (b). The flux lines are more on one side of the conductor than the other. These lines seem to urge the conductor to the left with a force F . As F opposes v and the applied force, mechanical energy gets absorbed in this case and the machine works as a generator. This force is due to electro magnetic interaction and is proportional to the current and the flux swept. Fig. 3(a)and (b) similarly explain the d.c.motor operation. The current carrying conductor reacts with the field to develop a force which urges the conductor to the right. The induced emf and the current are seen to act in opposite direction resulting in the absorption of electric energy which gets converted into the mechanical form.

In Case (iii) also the direction of the induced emf can be determined in a similar manner. However, it is going to be more complex due to the presence of transformer

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emf and rotational emf which have phase difference between them. Putting mathematically, in the present study of d.c.machines, F = B.L.I

Newton

When the generated voltage drives a current, it produces a reaction force on the mechanical system which absorbs the mechanical energy. This absorbed mechanical energy is the one which results in the electric current and the appearance of electrical energy in the electrical circuit. The converse happens in the case of the motor. If we force a current against an induced emf then the electrical power is absorbed by the same and it appears as the mechanical torque on the shaft. Thus, it is seen that the motoring and generating actions are easily changeable with the help of the terminal conditions.

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Principles of d.c. machines D.C. machines are the electro mechanical energy converters which work from a d.c.

source and generate mechanical power or convert mechanical power into a d.c. power. These machines can be broadly classified into two types, on the basis of their magnetic structure. They are, 1. Homopolar machines 2. Heteropolar machines. These are discussed in sequence below.

2.1

Homopolar machines

Homopolar generators Even though the magnetic poles occur in pairs, in a homopolar generator the conductors are arranged in such a manner that they always move under one polarity. Either north pole or south pole could be used for this purpose. Since the conductor encounters the magnetic flux of the same polarity every where it is called a homopolar generator. A cylindrically symmetric geometry is chosen. The conductor can be situated on the surface of the rotor with one slip-ring at each end of the conductor. A simple structure where there is only one cylindrical conductor with ring brushes situated at the ends is shown in Fig. 4. The excitation coil produces a field which enters the inner member from outside all along the periphery. The conductor thus sees only one pole polarity or the flux directed in one sense. A steady voltage now appears across the brushes at any given speed of rotation. The polarity of the induced voltage can be reversed by reversing either the excitation or the direction of 10

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N

+

Brush

B

A

Flux S

S

Field coil

A

B

+

N

Figure 4: Homopolar Generator

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rotation but not both. The voltage induced would be very low but the currents of very large amplitudes can be supplied by such machines. Such sources are used in some applications like pulse-current and MHD generators, liquid metal pumps or plasma rockets. The steady field can also be produced using a permanent magnet of ring shape which is radially magnetized. If higher voltages are required one is forced to connect many conductors in series. This series connection has to be done externally. Many conductors must be situated on the rotating structure each connected to a pair of slip rings. However, this modification introduces parasitic air-gaps and makes the mechanical structure very complex. The magnitude of the induced emf in a conductor 10 cm long kept on a rotor of 10 cm radius rotating at 3000 rpm, with the field flux density being 1 Tesla every where in the air gap, is given by

e = BLv = 1 ∗ 0.1 ∗ 2π ∗ 0.1 ∗

3000 = 3.14 volt 60

The voltage drops at the brushes become very significant at this level bringing down the efficiency of power conversion. Even though homopolar machines are d.c. generators in a strict sense that they ’generate’ steady voltages, they are not quite useful for day to day use. A more practical converters can be found in the d.c. machine family called ”hetero-polar” machines.

2.2

Hetero-polar d.c. generators

In the case of a hetero-polar generator the induced emf in a conductor goes through a cyclic change in voltage as it passes under north and south pole polarity alternately. The induced emf in the conductor therefore is not a constant but alternates in magnitude. For 12

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b

N a c B

d + A S

Load

Figure 5: Elementary hetro-polar machine

Field coil

Pole v v

N 10 9

11

8

12

S1 1

B

7

-

F1 S2

v

Armature core

A+

v

Commutator

F2

v

2

6

F4

F3 S4

S3

Yoke

5

3 4

S

Figure 6: Two pole machine -With Gramme ring type armature 13

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a constant velocity of sweep the induced emf is directly proportional to the flux density under which it is moving. If the flux density variation is sinusoidal in space, then a sine wave voltage is generated. This principle is used in the a.c generators. In the case of d.c. generators our aim is to get a steady d.c. voltage at the terminals of the winding and not the shape of the emf in the conductors. This is achieved by employing an external element, which is called a commutator, with the winding.

Fig. 5 shows an elementary hetero-polar, 2-pole machine and one-coil armature. The ends of the coil are connected to a split ring which acts like a commutator. As the polarity of the induced voltages changes the connection to the brush also gets switched so that the voltage seen at the brushes has a unidirectional polarity. This idea is further developed in the modern day machines with the use of commutators. The brushes are placed on the commutator. Connection to the winding is made through the commutator only. The idea of a commutator is an ingenious one. Even though the instantaneous value of the induced emf in each conductor varies as a function of the flux density under which it is moving, the value of this emf is a constant at any given position of the conductor as the field is stationary. Similarly the sum of a set of coils also remains a constant. This thought is the one which gave birth to the commutator. The coils connected between the two brushes must be ”similarly located” with respect to the poles irrespective of the actual position of the rotor. This can be termed as the condition of symmetry. If a winding satisfies this condition then it is suitable for use as an armature winding of a d.c. machine. The ring winding due to Gramme is one such. It is easy to follow the action of the d.c. machine using a ring winding, hence it is taken up here for explanation.

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Fig. 6 shows a 2-pole, 12 coil, ring wound armature of a machine. The 12 coils are placed at uniform spacing around the rotor. The junction of each coil with its neighbor is connected to a commutator segment. Each commutator segment is insulated from its neighbor by a mica separator. Two brushes A and B are placed on the commutator which looks like a cylinder. If one traces the connection from brush A to brush B one finds that there are two paths. In each path a set of voltages get added up. The sum of the emfs is constant(nearly). The constancy of this magnitude is altered by a small value corresponding to the coil short circuited by the brush. As we wish to have a maximum value for the output voltage, the choice of position for the brushes would be at the neutral axis of the field. If the armature is turned by a distance of one slot pitch the sum of emfs is seen to be constant even though a different set of coils participate in the addition. The coil which gets short circuited has nearly zero voltage induced in the same and hence the sum does not change substantially. This variation in the output voltage is called the ’ripple’. More the number of coils participating in the sum lesser would be the ’percentage’ ripple.

Another important observation from the working principle of a heterogeneous generator is that the actual shape of the flux density curve does not matter as long as the integral of the flux entering the rotor is held constant; which means that for a given flux per pole the voltage will be constant even if the shape of this flux density curve changes (speed and other conditions remaining unaltered). This is one reason why an average flux density over the entire pole pitch is taken and flux density curve is assumed to be rectangular.

A rectangular flux density wave form has some advantages in the derivation of the voltage between the brushes. Due to this form of the flux density curve, the induced

15

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emf in each turn of the armature becomes constant and equal to each other. With this back ground the emf induced between the brushes can be derived. The value of the induced in one conductor is given by Ec

=

Bav .L.v

Volt

(7)

where Bav - Average flux density over a pole pitch, Tesla. L- Length of the ’active’ conductor, m. v- Velocity of sweep of conductor, m/sec. If there are Z conductors on the armature and they form b pairs of parallel circuits between the brushes by virtue of their connections, then number of conductors in a series path is Z/2b. The induced emf between the brushes is E = Ec .

Z 2b

E = Bav .L.v.

(8) Z 2b

Volts

(9)

But v = (2p).Y.n where p is the pairs of poles Y is the pole pitch, in meters, and n is the number of revolutions made by the armature per second.

Also Bav can be written in terms of pole pitch Y , core length L, and flux per pole φ as Bav =

φ (L.Y )

Tesla

(10)

Substituting in equation Eqn. 9, E=

φ Z .L.(2p.Y.n). (L.Y ) 2b

=

φpZn b

volts

(11)

The number of pairs of parallel paths is a function of the type of the winding chosen. This 16

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will be discussed later under the section on the armature windings.

2.2.1

Torque production

When the armature is loaded, the armature conductors carry currents. These current carrying conductors interact with the field and experience force acting on the same. This force is in such a direction as to oppose their cause which in the present case is the relative movement between the conductors and the field. Thus the force directly opposes the motion. Hence it absorbs mechanical energy. This absorbed mechanical power manifests itself as the converted electrical power. The electrical power generated by an armature delivering a current of Ia to the load at an induced emf of E is EIa Watts. Equating the mechanical and electrical power we have 2πnT = EIa

(12)

where T is the torque in Nm. Substituting for E from Eqn. 11, we get 2πnT =

p.φ.Z.n .Ia b

(13)

which gives torque T as T =

1 Ia .p.φ.( )Z Nm 2π b

(14)

This shows that the torque generated is not a function of the speed. Also, it is proportional to ’total flux’ and ’Total ampere conductors’ on the armature, knowing that Ia /2b is Ic the conductor current on the armature. The expression for the torque generated can also be derived from the first principles by the application of the law of interaction. The law of interaction states that the force experienced by a conductor of length L kept in a

17

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uniform field of flux density B carrying a current Ic is proportional to B,L and Ic . Force on a single conductor Fc is given by, Fc = B.L.Ic

Newton

(15)

The total work done by an armature with Z conductors in one revolution is given by, Wa = Bav .L.Ic .Z.(2p.Y ) Joules

=

φ .L.Ic .Z.2p.Y L.Y

Joules

(16)

The work done per second or the power converted by the armature is, Pconv = φ.2p.Z.Ic .n watts Ia 2b Ia = φ.p.Z.n. b AsIc =

(17) (18) (19)

which is nothing but EIa .

The above principles can easily be extended to the case of motoring mode of operation also. This will be discussed next in the section on motoring operation of d.c. machines.

2.2.2

Motoring operation of a d.c. machine In the motoring operation the d.c. machine is made to work from a d.c. source and

absorb electrical power. This power is converted into the mechanical form. This is briefly discussed here. If the armature of the d.c. machine which is at rest is connected to a d.c. source then, a current flows into the armature conductors. If the field is already excited then 18

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these current carrying conductors experience a force as per the law of interaction discussed above and the armature experiences a torque. If the restraining torque could be neglected the armature starts rotating in the direction of the force. The conductors now move under the field and cut the magnetic flux and hence an induced emf appears in them. The polarity of the induced emf is such as to oppose the cause of the current which in the present case is the applied voltage. Thus a ’back emf’ appears and tries to reduce the current. As the induced emf and the current act in opposing sense the machine acts like a sink to the electrical power which the source supplies. This absorbed electrical power gets converted into mechanical form. Thus the same electrical machine works as a generator of electrical power or the absorber of electrical power depending upon the operating condition. The absorbed power gets converted into electrical or mechanical power. This is briefly explained earlier with the help of Figure 3(a) and 3(b). These aspects would be discussed in detail at a later stage.

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Constructional aspects of d.c. machines

As mentioned earlier the d.c. machines were invented during the second half of the 19th century. The initial pace of development work was phenomenal. The best configurations stood all the competition and the test of time and were adopted. Less effective options were discarded. The present day d.c. generator contains most, if not all, of the features of the machine developed over a century earlier. To appreciate the working and the characteristics of these machines, it is necessary to know about the different parts of the machine - both electrical and non-electrical. The description would also aid the understanding of the reason for selecting one form of construction or the other.

An exploded view of a small d.c.

Figure 7: Exploded view of D.C.Machine machine is shown in Fig. 7. Click here to see the assembling of the parts. The major parts can be identified as, 1. Body 2. Poles 20

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3. Armature 4. Commutator and brush gear 5. Commutating poles 6. Compensating winding 7. Other mechanical parts The constructional aspects relating to these parts are now discussed briefly in sequence. Body The body constitutes the outer shell within which all the other parts are housed. This will be closed at both the ends by two end covers which also support the bearings required to facilitate the rotation of the rotor and the shaft. Even though for the generation of an emf in a conductor a relative movement between the field and the conductor would be enough, due to practical considerations of commutation, a rotating conductor configuration is selected for d.c. machines. Hence the shell or frame supports the poles and yoke of the magnetic system. In many cases the shell forms part of the magnetic circuit itself. Cast steel is used as a material for the frame and yoke as the flux does not vary in these parts. In large machines these are fabricated by suitably welding the different parts. Those are called as fabricated frames. Fabrication as against casting avoids expensive patterns. In small special machines these could be made of stack of laminations suitably fastened together to form a solid structure. Main poles Solid poles of fabricated steel with seperate/integral pole shoes are fastened to the frame by means of bolts. Pole shoes are generally laminated. Sometimes pole body and pole shoe are formed from the same laminations. Stiffeners are used on both

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sides of the laminations. Riveted through bolts hold the assembly together. The pole shoes are shaped so as to have a slightly increased air gap at the tips. Inter-poles These are small additional poles located in between the main poles. These can be solid, or laminated just as the main poles. These are also fastened to the yoke by bolts. Sometimes the yoke may be slotted to receive these poles. The inter poles could be of tapered section or of uniform cross section. These are also called as commutating poles or compoles. The width of the tip of the compole can be about a rotor slot pitch. Armature The armature is where the moving conductors are located. The armature is constructed by stacking laminated sheets of silicon steel. Thickness of these lamination is kept low to reduce eddy current losses. As the laminations carry alternating flux the choice of suitable material, insulation coating on the laminations, stacking it etc are to be done more carefully. The core is divided into packets to facilitate ventilation. The winding cannot be placed on the surface of the rotor due to the mechanical forces coming on the same. Open parallel sided equally spaced slots are normally punched in the rotor laminations. These slots house the armature winding. Large sized machines employ a spider on which the laminations are stacked in segments. End plates are suitably shaped so as to serve as ’Winding supporters’. Armature construction process must ensure provision of sufficient axial and radial ducts to facilitate easy removal of heat from the armature winding. Field windings In the case of wound field machines (as against permanent magnet excited machines) the field winding takes the form of a concentric coil wound around the main poles. These carry the excitation current and produce the main field in the machine. Thus the poles are created electromagnetically. Two types of windings are generally employed. In shunt winding large number of turns of small section copper conductor is 22

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used. The resistance of such winding would be an order of magnitude larger than the armature winding resistance. In the case of series winding a few turns of heavy cross section conductor is used. The resistance of such windings is low and is comparable to armature resistance. Some machines may have both the windings on the poles. The total ampere turns required to establish the necessary flux under the poles is calculated from the magnetic circuit calculations. The total mmf required is divided equally between north and south poles as the poles are produced in pairs. The mmf required to be shared between shunt and series windings are apportioned as per the design requirements. As these work on the same magnetic system they are in the form of concentric coils. Mmf ’per pole’ is normally used in these calculations. Armature winding As mentioned earlier, if the armature coils are wound on the surface of the armature, such construction becomes mechanically weak. The conductors may fly away when the armature starts rotating. Hence the armature windings are in general pre-formed, taped and lowered into the open slots on the armature. In the case of small machines, they can be hand wound. The coils are prevented from flying out due to the centrifugal forces by means of bands of steel wire on the surface of the rotor in small groves cut into it. In the case of large machines slot wedges are additionally used to restrain the coils from flying away. The end portion of the windings are taped at the free end and bound to the winding carrier ring of the armature at the commutator end. The armature must be dynamically balanced to reduce the centrifugal forces at the operating speeds. Compensating winding One may find a bar winding housed in the slots on the pole shoes. This is mostly found in d.c. machines of very large rating. Such winding is called compensating winding. In smaller machines, they may be absent. The function

23

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and the need of such windings will be discussed later on.

4 3 1

2

2

1.Clamping cone 2.Insulating cups 3.Commutator bar 4.Riser 5.Insulating gasket

5

Figure 8: Cylindrical type commutator-a longitudinal section

Commutator Commutator is the key element which made the d.c. machine of the present day possible. It consists of copper segments tightly fastened together with mica/micanite insulating separators on an insulated base. The whole commutator forms a rigid and solid assembly of insulated copper strips and can rotate at high speeds. Each commutator segment is provided with a ’riser’ where the ends of the armature coils get connected. The surface of the commutator is machined and surface is made concentric with the shaft and the current collecting brushes rest on the same. Under-cutting the mica insulators that are between these commutator segments has to be done periodically to avoid fouling of the surface of the commutator by mica when the commutator gets worn out. Some details of the construction of the commutator are seen in Fig. 8. Brush and brush holders Brushes rest on the surface of the commutator. Normally electro-graphite is used as brush material. The actual composition of the brush depends on the peripheral speed of the commutator and the working voltage. The hardness of the graphite brush is selected to be lower than that of the commutator. When the 24

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brush wears out the graphite works as a solid lubricant reducing frictional coefficient. More number of relatively smaller width brushes are preferred in place of large broad brushes. The brush holders provide slots for the brushes to be placed. The connection

Pigtail

Pressure spring Brush

Brush holder box

(a) Radial

Trailing Reaction

Motion of commutator

(b)

Figure 9: Brush holder with a Brush and Positioning of the brush on the commutator from the brush is taken out by means of flexible pigtail. The brushes are kept pressed on the commutator with the help of springs. This is to ensure proper contact between 25

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the brushes and the commutator even under high speeds of operation. Jumping of brushes must be avoided to ensure arc free current collection and to keep the brush contact drop low. Fig. 9 shows a brush holder arrangement. Radial positioning of the brushes helps in providing similar current collection conditions for both direction of rotation. For unidirectional drives trailing brush arrangement or reaction arrangement may be used in Fig. 9-(b) Reaction arrangement is preferred as it results in zero side thrust on brush box and the brush can slide down or up freely. Also staggering of the brushes along the length of the commutator is adopted to avoid formation of ’tracks’ on the commutator. This is especially true if the machine is operating in a dusty environment like the one found in cement plants. Other mechanical parts End covers, fan and shaft bearings form other important mechanical parts. End covers are completely solid or have opening for ventilation. They support the bearings which are on the shaft. Proper machining is to be ensured for easy assembly. Fans can be external or internal. In most machines the fan is on the non-commutator end sucking the air from the commutator end and throwing the same out. Adequate quantity of hot air removal has to be ensured. Bearings Small machines employ ball bearings at both ends. For larger machines roller bearings are used especially at the driving end. The bearings are mounted press-fit on the shaft. They are housed inside the end shield in such a manner that it is not necessary to remove the bearings from the shaft for dismantling. The bearings must be kept in closed housing with suitable lubricant keeping dust and other foreign materials away. Thrust bearings, roller bearings, pedestal bearings etc are used under special cases. Care must be taken to see that there are no bearing currents or axial forces on the shaft both of which destroy the bearings.

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Armature Windings Main field

X

N

Commutator & Brush

Compole field

X

x

x

X

x

x

x

X

Shaft S

x

x x x

x x x

v

x

S

Compensating winding

X

x

x

x

x X

x

Armature winding

X

Yoke

N

X

Figure 10: Cross sectional view Fig. 10 gives the cross sectional view of a modern d.c. machine showing all the salient parts. Armature windings, along with the commutators, form the heart of the d.c. machine. This is where the emf is induced and hence its effective deployment enhances the output of the machine. Fig. 11(a) shows one coil of an armature of Gramme ring arrangement and Fig. 11(b) shows one coil as per drum winding arrangement. Earlier, a simple form of this winding in the form of Gramme ring winding was presented for easy understanding. The Gramme ring winding is now obsolete as a better armature winding has 27

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X

X

Ν

Ν

X

X

φ

φ Α

Α

φ/2

Α’

φ/2

φ/2

φ/2

Α’ (a) Ring winding

(b) Drum winding

Figure 11: Ring winding and drum winding

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been invented in the form of a drum winding. The ring winding has only one conductor in a turn working as an active conductor. The second conductor is used simply to complete the electrical connections. Thus the effectiveness of the electric circuit is only 50 percent. Looking at it differently, half of the magnetic flux per pole links with each coil. Also, the return conductor has to be wound inside the bore of the rotor, and hence the rotor diameter is larger and mounting of the rotor on the shaft is made difficult. In a drum winding both forward and return conductors are housed in slots cut on the armature (or drum). Both the conductors have emf induced in them. Looking at it differently the total flux of a pole is linked with a turn inducing much larger voltage induced in the same. The rotor is mechanically robust with more area being available for carrying the flux. There is no necessity for a rotor bore. The rotor diameters are smaller. Mechanical problems that existed in ring winding are no longer there with drum windings. The coils could be made of single conductors (single turn coils) or more number of conductors in series (multi turn coils). These coils are in turn connected to form a closed winding. The two sides of the coil lie under two poles one north and the other south, so that the induced emf in them are always additive by virtue of the end connection. Even though the total winding is a closed one the sum of the emfs would be zero at all times. Thus there is no circulating current when the armature is not loaded. The two sides of the coil, if left on the surface, will fly away due to centrifugal forces. Hence slots are made on the surface and the conductors are placed in these slots and fastened by steel wires to keep them in position. Each armature slot is partitioned into two layers, a top layer and a bottom layer. The winding is called as a double layer winding. This is a direct consequence of the symmetry consideration. The distance, measured along the periphery of the armature from any point under a pole to a similar point under the neighboring pole is termed as a pole pitch. The forward conductor is housed in the top layer of a slot and the return conductor is housed in the bottom layer 29

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Upper coil side B

A

S

N

C D

Lower coil side A’

N

S

(a) End view

Upper coil side

Lower coil side

B

Inactive Active S

A

N

Armature

A’

S

Inactive C

D

(b) Developed view

Figure 12: Arrangement of a single coil of a drum winding

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of a slot which is displaced by about one pole pitch. The junction of two coils is terminated on a commutator segment. Thus there are as many commutator segments as the number of coils. In a double layer winding in S slots there are 2S layers. Two layers are occupied by a coil and hence totally there are S coils. The S junctions of these S coils are terminated on S commutator segments. The brushes are placed in such a manner that a maximum voltage appears across them. While the number of parallel circuits in the case of ring winding is equal to the number of poles, in the case of drum winding a wide variety of windings are possible. The number of brushes and parallel paths thus vary considerably. The physical arrangement of a single coil is shown in Fig. 12 to illustrate its location and connection to the commutators. Fig. 13 shows the axial side view while Fig. 13-(b) shows the cut and spread view of the machine. The number of turns in a coil can be one (single turn coils) or more (multi turn coils ). As seen earlier the sum of the instantaneous emfs appears across the brushes. This sum gets altered by the voltage of a coil that is being switched from one circuit to the other or which is being commutated. As this coil in general lies in the magnetic neutral axis it has a small value of voltage induced in it. This change in the sum expressed as the fraction of the total induced voltage is called as the ripple. In order to reduce the ripple, one can increase the number of coils coming in series between the brushes. As the number of coils is the same as the number of slots in an armature with two coil sides per slot one is forced to increase the number of slots. However increasing the slot number makes the tooth width too narrow and makes them mechanically weak. To solve this problem the slots are partitioned vertically to increase the number of coil sides. This is shown in Fig. 14. In the figure, the conductors a, b and c belong to a coil. Such 2/3 coils occupy the 2/3 top coil sides of the slot. In the present case the number of coils in the armature is 2S/3S. 31

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(a)End view 11

2’

10

3’ 1’

12

1

3

2

4

5

7

6

N

8

S

9

11

10

N

12

S

12

1’ 2’

11

12

1

-

2

3

4

+

5

6

7

-

8

(b)Developed view Figure 13: Lap Winding 32

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10

+

11

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Press board Copper Mica Tape

Press board

(a) Single coil-side perlayer

(b) More coil sides perlayer Figure 14: Partitioning of slots

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

As mentioned earlier, in a drum winding, the coils span a pole pitch where ever possible. Such coils are called ’full pitched’ coils. The emf induced in the two active conductors of such coils have identical emfs with opposite signs at all instants of time. If the span is more than or less than the full pitch then the coil is said to be ’chorded’. In chorded coils the induced emfs of the two conductor may be of the same sign and hence oppose each other( for brief intervals of time). Slight short chording of the coil reduces overhang length and saves copper and also improves commutation. Hence when the pole pitch becomes fractional number, the smaller whole number may be selected discarding the fractional part.

Similar to the pitch of a coil one can define the winding pitch and commutator pitch. In a d.c. winding the end of one coil is connected to the beginning of another coil (not necessarily the next), this being symmetrically followed to include all the coils on the armature. Winding pitch provides a means of indicating this. Similarly the commutator pitch provides the information regarding the commutators to which the beginning and the end of a coil are connected. Commutator pitch is the number of ’micas’ between the ends of a coil. For all these information to be simple and useful the numbering scheme of the coils and commutator segments becomes important. One simple method is to number only the top coil side of the coils in sequence. The return conductor need not be numbered. As a double layer is being used the bottom coil side is placed in a slot displaced by one coil span ′

′

from the top coil side. Some times the coils are numbered as 1 − 1 , 2 − 2 etc. indicating ′

′

the second sides by 1 , 2 etc. The numbering of commutators segments are done similarly. The commutator segment connected to top coil side of coil 1 is numbered 1. This method of numbering is simple and easy to follow. It should be noted that changing of the pitch

34

Indian Institute of Technology Madras

Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

of a coil slightly changes the induced emf in the same. The pitch of the winding however substantially alters the nature of the winding.

The armature windings are classified into two families based on this. They are called lap winding and wave winding. They can be simply stated in terms of the commutator pitch used for the winding.

4.1

Lap winding The commutator pitch for the lap windings is given by yc = ±m,

m = 1, 2, 3...

(20)

where yc is the commutator pitch, m is the order of the winding. For m = 1 we get a simple lap winding, m = 2 gives duplex lap winding etc. yc = m gives a multiplex lap winding of order m. The sign refers to the direction of progression of the winding. Positive sign is used for ‘progressive’ winding and the negative sign for the ‘retrogressive’ winding. Fig. 15 shows one coil as per progressive and retrogressive lap winding arrangements.

Fig. 16 shows a developed view of a simple lap winding for a 4-pole

armature in 12 slots. The connections of the coils to the commutator segments are also shown. The position of the armature is below the poles and the conductors move from left to right as indicated. The position and polarity of the brushes are also indicated. Single turn coils with yc = 1 are shown here. The number of parallel paths formed by the winding equals the number of poles. The number of conductors that are connected in series between the brushes therefore becomes equal to Z/2b. Thus the lap winding is well suited for high current generators. In a symmetrical winding the parallel paths share the total line current 35

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Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Retrogressive yc = -1

Progressive yc =+1

s1

s2

1

F1 F2

2

F2

3

1

s2

F3

2

s3

3

4

(a) Lap winding

Coil span

s1 1

F1 _1 c+ p

2

(b) Wave winding

Figure 15: Typical end connections of a coil and commutator

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Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

1

2

S

S

N

13

14

1

A1

2 +

4

3

N

5

B1

6 -

7

A2

S

8

9 +

Figure 16: Developed view of a retrogressive Lap winding

37

Indian Institute of Technology Madras

10

11

B2

12

Motion -

Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

equally.

The increase in the number of parallel paths in the armature winding brings about a problem of circulating current. The induced emfs in the different paths tend to differ slightly due to the non-uniformities in the magnetic circuit. This will be more with the increase in the number of poles in the machine. If this is left uncorrected, circulating currents appear in these closed parallel paths. This circulating current wastes power, produces heat and over loads the brushes under loaded conditions. One method commonly adopted in d.c. machines to reduce this problem is to provide equalizer connections. As the name suggests these connections identify similar potential points of the different parallel paths and connect them together to equalize the potentials. Any difference in the potential generates a local circulating current and the voltages get equalized. Also, the circulating current does not flow through the brushes loading them. The number of such equalizer connections, the cross section for the conductor used for the equalizer etc are decided by the designer. An example of equalizer connection is discussed now with the help of a 6-pole armature having 150 commutator segments. The coil numbers 1, 51 and 101 are identically placed under the poles of same polarity as they are one pole-pair apart. There are 50 groups like that. In order to limit the number of links to 5(say), the following connections are chosen. Then 1,11,21,31, and 41 are the coils under the first pair of poles. These are connected to their counter parts displaced by 50 and 100 to yield 5 equalizer connections. There are 10 coils connected in series between any two successive links. The wave windings shall be examined next.

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

1 S

N

S

N

20 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 A2 + A1 + - B2 - B1

Motion

(a)Winding layout _ 5 Full pitch: 21/4=5.25 ~

Span : 1 to 6 Yc=

_1 11 _1 + C+ = 21 = 2 2 10

}

Commutator pitch 1-11 for retrogressive winding 1-11-21-10-20-9-19-8-18-7-17v A2

A1

v

6-16-5-15-4-14-3-13-2-12-1 B2 B1

(b)Parallel paths

Figure 17: Developed view of a Retrogressive Wave winding 39

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4.2

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Wave windings In wave windings the coils carrying emf in the same direction at a time are all

grouped together and connected in series. Hence in a simple wave winding there are only two paths between the brushes, the number of conductors in each path being 50 percent of the total conductors. To implement a wave winding one should select the commutator pitch as yc =

C±1 p

(21)

where C is the total segments on the commutator. yc should be an integer number; C and p should satisfy this relation correctly. Here also the positive sign refers to the progressive winding and the negative sign yields a retrogressive winding. yc = (C ± m)/p yields a multiplex wave winding of order m. A simple wave winding for 4 poles in 21 slots is illustrated in Fig. 17. As could be seen from the figure, the connection to the next (or previous) adjacent coil is reached after p coils are connected in series. The winding closes on itself after all the coils are connected in series. The position for the brushes is indicated in the diagram.

It is seen from the formula for the commutator pitch, the choice of commutator segments for wave winding is restricted. The number of commutator segments can only be one more or one less than some multiple of pole pairs. As the number of parallel circuits is 2 for a simple wave winding irrespective of the pole numbers it is preferred in multi polar machine of lower power levels.

As mentioned earlier the simple wave winding forms two parallel paths, duplex wave winding has 2*2=4 etc. The coils under all the north poles are grouped together in

40

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

one circuit and the other circuit collects all the coils that are under all the south poles. Two brush sets are therefore adequate. Occasionally people employ brush sets equal to the number of poles. This arrangement does not increase the number of parallel circuits but reduces the current to be collected by each brush set. This can be illustrated by an example. A 4-pole wave connected winding with 21 commutator segments is taken. yc = (21 − 1)/2 = 10 . A retrogressive wave winding results. The total string of connection can be laid out as shown below. If coil number 1 is assumed to be in the neutral axis then other neutral axis coils are a pole pitch apart i.e. coils 6, 11, 16.

If the brushes are kept at commutator segment 1 and 6, nearly half the number of coils come under each circuit. The polarity of the brushes are positive and negative alternately. Or, one could have two brushes at 11 and 16 or any two adjacent poles. By having four brushes at 1, 6, 11 and 16 and connecting 1,11 and 6,16 still only two parallel circuits are obtained. The brush currents however are halved. This method permits the use of commutator of shorter length as lesser current is to be collected by each brush and thus saving on the cost of the commutator. Fig. 17(b) illustrates this brush arrangement with respect to a 21 slot 4 pole machine. Similarly proceeding, in a 6-pole winding 2,4 or 6 brush sets may be used.

Multiplex windings of order m have m times the circuits compared to a simplex winding and so also more restriction on the choice of the slots, coil sides, commutator and brushes. Hence windings beyond duplex are very uncommon even though theoretically possible. The duplex windings are used under very special circumstances when the number of parallel paths had to be doubled.

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4.3

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Dummy coils and dummy commutator segments Due to the restrictions posed by lap and wave windings on the choice of number

of slots and commutator segments a practical difficulty arises. Each machine with a certain pole number, voltage and power ratings may require a particular number of slots and commutator segments for a proper design. Thus each machine may be tailor made for a given specification. This will require stocking and handling many sizes of armature and commutator.

Sometimes due to the non-availability of a suitable slot number or commutator, one is forced to design the winding in an armature readily available in stock. Such designs, obviously, violate the symmetry conditions as armature slots and commutator segment may not match. If one is satisfied with approximate solutions then the designer can omit the surplus coil or surplus commutator segment and complete the design. This is called the use of a ’dummy’. All the coils are placed in the armature slots. The surplus coil is electrically isolated and taped. It serves to provide mechanical balance against centrifugal forces. Similarly, in the case of surplus commutator segment two adjacent commutator segments are connected together and treated as a single segment. These are called dummy coils and dummy commutator segments. As mentioned earlier this approach must be avoided as far as possible by going in for proper slot numbers and commutator. Slightly un-symmetric winding may be tolerable in machines of smaller rating with very few poles.

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5

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Armature reaction Earlier, an expression was derived for the induced emf at the terminals of the

armature winding under the influence of motion of the conductors under the field established by field poles. But if the generator is to be of some use it should deliver electrical output to a load. In such a case the armature conductors also carry currents and produce a field of their own. The interaction between the fields must therefore must be properly understood in order to understand the behavior of the loaded machine. As the magnetic structure is complex and as we are interested in the flux cut by the conductors, we primarily focus our attention on the surface of the armature. A sign convention is required for mmf as the armature and field mmf are on two different members of the machine. The convention used here is that the mmf acting across the air gap and the flux density in the air gap are shown as positive when they act in a direction from the field system to the armature. A flux line is taken and the value of the current enclosed is determined. As the magnetic circuit is non-linear, the field mmf and armature mmf are separately computed and added at each point on the surface of the armature. The actual flux produced is proportional to the total mmf and the permeance. The flux produced by field and that produced by armature could be added to get the total flux only in the case of a linear magnetic circuit. The mmf distribution due to the poles and armature are discussed now in sequence.

5.0.1

MMF distribution due to the field coils acting alone Fig. 18 shows the distribution of mmf due to field coils over two pole pitches. It

is a step curve with the width being equal to the pole arc. The permeance variation at the surface is given by Fig. 18 assuming the air gap under the pole to be uniform and neglecting

43

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

N

S

mmf

Permeance

Practical Flux density Ideal flux density

Figure 18: Mmf and flux variation in an unloaded machine

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

the slotting of the armature. The no-load flux density curve can be obtained by multiplying mmf and permeance. Allowing for the fringing of the flux, the actual flux density curve would be as shown under Fig. 18.

5.0.2

MMF distribution due to armature conductors alone carrying currents

N

S

N-Pole

A S-Pole

Generator

Flux mmf

Figure 19: Mmf and flux distribution under the action of armature alone carrying current The armature has a distributed winding, as against the field coils which are concentrated and concentric. The mmf of each coil is shifted in space by the number of slots. For a full pitched coil, each coil produces a rectangular mmf distribution. The sum of the mmf due to all coils would result in a stepped triangular wave form. If we neglect slotting and have uniformly spaced coils on the surface, then the mmf distribution due to the armature working alone would be a triangular distribution in space since all the conductors carry equal currents. MMF distribution is the integral of the ampere conductor distribution. 45

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

This is depicted in Fig. 19. This armature mmf per pole is given by 1 Ic .Z Fa = . 2 2p where Ic is the conductor current and Z is total number of conductors on the armature. This peak value of the mmf occurs at the inter polar area, shifted from the main pole axis by half the pole pitch when the brushes are kept in the magnetic neutral axis of the main poles.

Total mmf and flux of a loaded machine Brush axis

5.0.3

N

S

A D

Generator

c

B

C

a

Field flux

B A

o

o’

b Armature flux Total flux

Figure 20: Flux distribution in a loaded generator without brush shift The mmf of field coils and armature coils are added up and the resultant mmf distribution is obtained as shown in Fig. 20.

46

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

This shows the decrease in the mmf at one tip of a pole and a substantial rise at the other tip. If the machine has a pole arc to pole pitch ratio of 0.7 then 70% of the armature reaction mmf gets added at this tip leading to considerable amount of saturation under full load conditions. The flux distribution also is shown in Fig. 20. This is obtained by multiplying mmf and permeance waves point by point in space. Actual flux distribution differs from this slightly due to fringing. As seen from the figure, the flux in the inter polar region is substantially lower due to the high reluctance of the medium. The air gaps under the pole tips are also increased in practice to reduce excessive saturation of this part. The advantage of the salient pole field construction is thus obvious. It greatly mitigates the effect of the armature reaction. Also, the coils under going commutation have very little emf induced in them and hence better commutation is achieved. Even though the armature reaction produced a cross magnetizing effect, the net flux per pole gets slightly reduced, on load, due to the saturation under one tip of the pole. This is more so in modern d.c. machines where the normal excitation of the field makes the machine work under some level of saturation.

5.0.4

Effect of brush shift In some small d.c. machines the brushes are shifted from the position of the mag-

netic neutral axis in order to improve the commutation. This is especially true of machines with unidirectional operation and uni-modal (either as a generator or as a motor) operation. Such a shift in the direction of rotation is termed ‘lead’ (or forward lead). Shift of brushes in the opposite to the direction of rotation is called ‘backward lead’. This lead is expressed in terms of the number of commutator segments or in terms of the electrical angle. A pole pitch corresponds to an electrical angle of 180 degrees. Fig. 21 shows the effect of a forward

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Indian Institute of Technology Madras

Brush axis

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Geometric Neutral axis

Electrical Machines I

S

N

Rotation a c

Field flux

b Armature flux

Total flux

(a)Armature reaction with brush shift

N Rotation b’ a’

a

θ b

S (b)Calculation of demagnetizing mmf per pole

Figure 21: Effect of brush shift on armature reaction 48

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

brush lead on the armature reaction. The magnetization action due to the armature is no longer entirely cross magnetizing. Some component of the same goes to demagnetize the main field and the net useful flux gets reduced. This may be seen as the price we pay for improving the commutation. Knowing the pole arc to pole pitch ratio one can determine the total mmf at the leading and trailing edges of a pole without shift in the brushes. Fmin = Ff − α.Fa

(22)

Fmax = Ff + α.Fa where Ff is the field mmf, Fa is armature reaction mmf per pole, and α is the pole arc to pole pitch ratio. 1 Z.Ic . 2 2p

Fa =

(23)

The net flux per pole decreases due to saturation at the trailing edge and hence additional ampere turns are needed on the pole to compensate this effect. This may be to the tune of 20 percent in the modern d.c. machines.

The brush shift gives rise to a shift in the axis of the mmf of the armature reaction. This can be resolved into two components, one in the quadrature axis and second along the pole axis as shown in Fig. 21.(b) The demagnetizing and cross magnetizing component of the armature ampere turn per pole can be written as 2θ .Fa π 2θ Fq = (1 − ).Fa π Fd =

(24) (25)

where θ is the angle of lead . In terms of the number of commutator segments they are Fd =

Cl Ic Z . C 4p 4p 49

Indian Institute of Technology Madras

or

Cl .Ic .Z C

(26)

Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

where, Cl is the brush lead expressed in number of commutator segments.

5.0.5

Armature reaction in motors As discussed earlier, for a given polarity of the field and sense of rotation, the

motoring and generating modes differ only in the direction of the armature current. Alternatively, for a given sense of armature current, the direction of rotation would be opposite for the two modes. The leading and trailing edges of the poles change positions if direction of rotation is made opposite. Similarly when the brush leads are considered, a forward lead given to a generator gives rise to weakening of the generator field but strengthens the motor field and vice-versa. Hence it is highly desirable, even in the case of non-reversing drives, to keep the brush position at the geometrical neutral axis if the machine goes through both motoring and generating modes.

The second effect of the armature reaction in the case of motors as well as generators is that the induced emf in the coils under the pole tips get increased when a pole tip has higher flux density. This increases the stress on the ‘mica’ (micanite) insulation used for the commutator, thus resulting in increased chance of breakdown of these insulating sheets. To avoid this effect the flux density distribution under the poles must be prevented from getting distorted and peaky.

The third effect of the armature reaction mmf distorting the flux density is that the armature teeth experience a heavy degree of saturation in this region. This increases the iron losses occurring in the armature in that region. The saturation of the teeth may be too great as to have some flux lines to link the thick end plates used for strengthening 50

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the armature. The increase in iron loss could be as high as 50 percent more at full load compared to its no-load value. The above two effects can be reduced by providing a ’compensating’ mmf at Commutating pole

s S

N

N

N

S Compensating winding

Main pole

N s

Figure 22: Compensating winding the same spatial rate as the armature mmf. This is provided by having a compensating winding housed on the pole shoe which carries currents that are directly proportional to the armature current. The ampere conductors per unit length is maintained identical to that of

51

Indian Institute of Technology Madras

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

+ + + + + + + + + +

+ + + + + +

+

+

+

+

S

N

Rotation

mmf of compensating winding

Resultant mmf compole mmf

Armature mmf

Main field mmf

Figure 23: Armature reaction with Compensating winding

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Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

the armature. The sign of the ampere conductors is made opposite to the armature. This is illustrated in Fig. 22 and Fig. 23 . Since the compensating winding is connected in series with the armature, the relationship between armature mmf and the mmf due to compensating winding remains proper for all modes of working of the machine. The mmf required to be setup by the compensating winding can be found out to be Fc =

Ic .Z polearc . 4p polepitch

(27)

Under these circumstances the flux density curve remains unaltered under the poles between no-load and full load.

The axis of the mmf due to armature and the compensating winding being the same and the signs of mmf being opposite to each other the flux density in the region of geometric neutral axis gets reduced thus improving the conditions for commutation. One can design the compensating winding to completely neutralize the armature reaction mmf. Such a design results in overcompensation under the poles. Improvement in commutation condition may be achieved simply by providing a commutating pole which sets up a local field of proper polarity. It is better not to depend on the compensating winding for improving commutation.

Compensating windings are commonly used in large generators and motors operating on weak field working at high loads.

From the analysis of the phenomenon of armature reaction that takes place in a d.c. machine it can be inferred that the equivalent circuit of the machine need not be modified to include the armature reaction. The machine can simply be modelled as a voltage 53

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

source of internal resistance equal to the armature circuit resistance and a series voltage drop equal to the brush contact drop, under steady state. With this circuit model one can arrive at the external characteristics of the d.c. machine under different modes of operation.

5.1

Commutation As seen earlier, in an armature conductor of a heteropolar machine a.c. voltages

are induced as the conductor moves under north and south pole polarities alternately. The frequency of this induced emf is given by the product of the pole-pairs and the speed in revolutions per second. The induced emf in a full pitch coil changes sign as the coil crosses magnetic neutral axis. In order to get maximum d.c. voltage in the external circuit the coil should be shifted to the negative group. This process of switching is called commutation. During a short interval when the two adjacent commutator segments get bridged by the brush the coils connected in series between these two segments get short circuited. Thus in the case of ring winding and simple lap winding 2p coils get short circuited. In a simple wave winding in a 2p pole machine 2 coils get short circuited. The current in these coils become zero and get reversed as the brush moves over to the next commutator segment. Thus brush and commutator play an important role in commutation. Commutation is the key process which converts the induced a.c. voltages in the conductors into d.c. It is important to learn about the working of the same in order to ensure a smooth and trouble free operation of the machine.

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Indian Institute of Technology Madras

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

1 Ia Ia

2

3

4

2Ia 4

1

2

3

(a)

tb 3 2 Ia

4

4

i

Length

Entering Edge

dth Wi

I1

2

3

Ia

1

I2

1

x

(b)

Thickness

2Ia

2Ia

tb

2 Ia Ia 1

3

4 Leaving Edge

2Ia 4 (c)

(a)Location of Brush

3

2

tb

(b)Process of commutation

Figure 24: Location of the brush and Commutation process

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Indian Institute of Technology Madras

1 2Ia

Motion

Electrical Machines I

5.1.1

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Brushes Brush forms an important component in the process of commutation. The coil

resistance is normally very small compared to the brush contact resistance. Further this brush contact resistance is not a constant. With the brushes commonly used, an increase in the current density of the brushes by 100 percent increases the brush drop by about 10 to 15 percent. Brush contact drop is influenced by the major factors like speed of operation, pressure on the brushes, and to a smaller extent the direction of current flow.

Major change in contact resistance is brought about by the composition of the brush. Soft graphite brushes working at a current density of about 10A/cm2 produce a drop of 1.6V (at the positive and negative brushes put together) while copper-carbon brush working at 15A/cm2 produces a drop of about 0.3V. The coefficient of friction for these brushes are 0.12 and 0.16 respectively. The attention is focussed next on the process of commutation.

5.1.2

Linear Commutation If the current density under the brush is assumed to be constant through out the

commutation interval, a simple model for commutation is obtained. For simplicity, the brush thickness is made equal to thickness of one commutator segment. In Fig. 24(b), the brush is initially solely resting on segment number 1. The total current of 2Ia is collected by the brush as shown. As the commutator moves relative to the brush position, the brush position starts to overlap with that of segment 2. As the current density is assumed to be constant, the current from each side of the winding is proportional to the area shared on the

56

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

two segments. Segment 1 current uniformly comes down with segment 2 current increasing uniformly keeping the total current in the brush constant. The currents I1 and I2 in brush segments 1 and 2 are given by I1 = 2Ia (1 −

x ) and tb

I2 = 2Ia

x tb

(28)

giving I1 + I2 to be 2 Ia . Here ‘x’ is the width of the brush overlapping on segment 2. The process of commutation would be over when the current through segment number 1 becomes zero. The current in the coil undergoing commutation is i = I1 − Ia = Ia − I2 =

(I1 − I2 ) 2x = Ia (1 − ) 2 tb

(29)

The time required to complete this commutation is Tc =

tb vc

(30)

where vc is the velocity of the commutator. This type of linear commutation is very close to the ideal method of commutation. The time variation of current in the coil undergoing commutation is shown in Fig. 25.(a). Fig. 25.(b) also shows the timing diagram for the currents I1 and I2 and the current densities in entering edge αe , leaving edge αl and also the mean current density αm in the brush. Machines having very low coil inductances, operating at low load currents, and low speeds, come close to this method of linear commutation.

In general commutation will not be linear due to the presence of emf of self induction and induced rotational emf in the coil. These result in retarded and accelerated commutation and are discussed in sequence.

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Ia

2Ia I1

I2

i 0

Tc

αm = α’ = α"

Time

Time of communication

Tc Time of commutation

0

-Ia

(a)

(b) Figure 25: Linear commutation

5.1.3

Retarded commutation Retarded commutation is mainly due to emf of self induction in the coil. Here

the current transfer from 1 to 2 gets retarded as the name suggests. This is best explained with the help of time diagrams as shown in Fig. 26.(a). The variation of i is the change in ′

the current of the coil undergoing commutation, while i is that during linear commutation. Fig. 26(b) shows the variation of I1 and current density in the brush at the leaving edge and Fig. 26.(c) shows the same phenomenon with respect to I2 at entering edge. The value of current in the coil is given by i undergoing commutation. αm is the mean current density in the brush given by total current divided by brush area of cross section. αl and αe are the current density under leaving and entering edges of the brush. As before, I1 = Ia + i

and

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Indian Institute of Technology Madras

I2 = Ia − i

(31)

Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

2Ia

α’=AB/AC

P B

+Ia

+Ia

i 0

t

I1=Ia+i αm

C

Tc i’

Q A

0

-Ia

(a) commutation

(b) Leaving edge density 2Ia E

I2=Ia-i F α"=DF/DE

0

t

D

Tc

t

(c)Entry edge density Figure 26: Diagrams for Retarded commutation

59

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t

Tc

Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

The variation of densities at leaving and entering edges are given as αl =

AB .αm AC

(32)

αe =

DF .αm DE

(33)

At the very end of commutation, the current density ′

αe

di di = αm . / dt dt di 2Ia = αm . / dt Tc

(34)

If at this point di/dt = 0 the possibility of sudden breaking of the current and hence the creation of an arc is removed .

Similarly at the entering edge at the end of accelerated commutation, shown in Fig. 27.(b). αe = αm .

di 2Ia / dt Tc

(35)

Thus retarded communication results in di/dt = 0 at the beginning of commutation (at entering edge) and accelerated communication results in the same at the end of commutation (at leaving edge). Hence it is very advantageous to have retarded commutation at the entry time and accelerated commutation in the second half. This is depicted in Fig. 27.(b1 ). It is termed as sinusoidal commutation.

Retarded commutation at entry edge is ensured by the emf of self induction which is always present. To obtain an accelerated commutation, the coil undergoing commutation must have in it an induced emf of such a polarity as that under the pole towards which it is moving. Therefore the accelerated commutation can be obtained by i) a forward 60

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α’ =AB/AC α" =DB/DC

α" Ia

D

αm

C

Ia

α’

B

0 0

i

i’

i

Tc

Tc

i’

B

A

-Ia

-Ia

(a1 )

(a2 ) α"

α’

Ia

C

Ia

S

A

B

αm

R

α’ =PR/PQ α" =SR/SQ

Q

i

Leaving edge Entering edge

Tc

0

Tc

0

time

time

i’

i -Ia

P

-Ia

(b1 )

(b2 ) Figure 27: Accelerated and Sinusoidal commutation

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lead given to the brushes or by ii) having the field of suitable polarity at the position of the brush with the help of a small pole called a commutating pole. In a non-inter pole machine the brush shift must be changed from forward lead to backward lead depending upon generating or motoring operation. As the disadvantages of this brush shifts are to be avoided, it is preferable to leave the brushes at geometric neutral axis and provide commutating poles of suitable polarity (for a generator the polarity of the pole is the one towards which the conductors are moving). The condition of commutation will be worse if commutating poles are provided and not excited or they are excited but wrongly.

The action of the commutating pole is local to the coil undergoing commutation. It does not disturb the main field distribution. The commutating pole winding overpowers the armature mmf locally and establishes the flux of suitable polarity. The commutating pole windings are connected in series with the armature of a d.c. machine to get a load dependent compensation of armature reaction mmf.

The commutating pole are also known as compole or inter pole. The air gap under compole is made large and the width of compole small. The mmf required to be produced by compole is obtained by adding to the armature reaction mmf per pole Fa the mmf to establish a flux density of required polarity in the air gap under the compole Fcp .This would ensure straight line commutation. If sinusoidal commutation is required then the second component Fcp is increased by 30 to 50 percent of the value required for straight line commutation.

The compole mmf in the presence of a compensating winding on the poles 62

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will be reduced by Fa * pole arc/pole pitch. This could have been predicted as the axis of the compensating winding and armature winding is one and the same. Further, the mmf of compensating winding opposes that of the armature reaction.

5.2

Methods of excitation It is seen already that the equivalent circuit model of a d.c. machine becomes very

simple in view of the fact that the armature reaction is cross magnetizing. Also, the axis of compensating mmf and mmf of commutating poles act in quadrature to the main field. Thus flux under the pole shoe gets distorted but not diminished (in case the field is not saturated). The relative connections of armature, compole and compensating winding are unaltered whether the machine is working as a generator or as a motor; whether the load is on the machine or not. Hence all these are connected permanently inside the machine. The terminals reflect only the additional ohmic drops due to the compole and compensating windings. Thus commutating pole winding, and compensating winding add to the resistance of the armature circuit and can be considered a part of the same. The armature circuit can be simply modelled by a voltage source of internal resistance equal to the armature resistance + compole resistance + compensating winding resistance. The brushes behave like non-linear resistance; and their effect may be shown separately as an additional constant voltage drop equal to the brush drop.

5.2.1

Excitation circuit The excitation for establishing the required field can be of two types a) Permanent

magnet excitation(PM) b) Electro magnetic excitation. Permanent magnet excitation is

63

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Yoke

ly

lt lg

lg lt

lp

lp

Pole

Field coil

la

Armature

da

Figure 28: Magnetization of a DC machine

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employed only in extremely small machines where providing a field coil becomes infeasible. Also, permanent magnet excited fields cannot be varied for control purposes. Permanent magnets for large machines are either not available or expensive. However, an advantage of permanent magnet is that there are no losses associated with the establishment of the field.

Electromagnetic excitation is universally used. Even though certain amount of energy is lost in establishing the field it has the advantages like lesser cost, ease of control.

The required ampere turns for establishing the desired flux per pole may be computed by doing the magnetic circuit calculations. MMF required for the poles, air gap, armature teeth, armature core and stator yoke are computed and added. Fig. 28 shows two poles of a 4-pole machine with the flux paths marked on it. Considering one complete flux loop, the permeance of the different segments can be computed as, P = A.µ/l Where P- permeance A- Area of cross section of the part mu- permeability of the medium l- Length of the part

A flux loop traverses a stator yoke, armature yoke, and two numbers each of poles, air gap, armature teeth in its path. For an assumed flux density Bg in the pole region the flux crossing each of the above regions is calculated. The mmf requirement for

65

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establishing this flux in that region is computed by the expressions Flux = mmf . permeance = B.A From these expressions the mmf required for each and every part in the path of the flux is computed and added. This value of mmf is required to establish two poles. It is convenient to think of mmf per pole which is nothing but the ampere turns required to be produced by a coil wound around one pole. In the case of small machines all this mmf is produced by a coil wound around one pole. The second pole is obtained by induction. This procedure saves cost as only one coil need be wound for getting a pair of poles. This produces an unsymmetrical flux distribution in the machine and hence is not used in larger machines. In large machines, half of total mmf is assigned to each pole as the mmf per pole. The total mmf required can be produced by a coil having large number of turns but taking a small current. Such winding has a high value of resistance and hence a large ohmic drop. It can be connected across a voltage source and hence called a shunt winding. Such method of excitation is termed as shunt excitation. On the other hand, one could have a few turns of large cross section wire carrying heavy current to produce the required ampere turns. These windings have extremely small resistance and can be connected in series with a large current path such as an armature. Such a winding is called a series winding and the method of excitation, series excitation. A d.c. machine can have either of these or both these types of excitation. These are shown in Fig. 29. When both shunt winding and series winding are present, it is called compound excitation. The mmf of the two windings could be arranged to aid each other or oppose each other. Accordingly they are called cumulative compounding and differential compounding. If the shunt winding is excited by a separate voltage source 66

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Shunt field

Shunt field A2

F2

A2

F2

F1 A1 A1

F1

(a)Separate excitation

(b) Self excitation Long shunt

S2

Diverter

S2

Series field S1

Short shunt A2

F2

A1

F1

(c)Series excitation

(d)Compound excitation

Figure 29: D.C generator connections

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S1 A2

A1

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then it is called separate excitation. If the excitation power comes from the same machine, then it is called self excitation. Series generators can also be separately excited or self excited. The characteristics of these generators are discussed now in sequence.

5.2.2

Separately excited shunt generators Ia=0

A2 Prime mover

Induced e.m.f

E

n=const

A1

+

F2

Decreasing Magnetisation Increasing magnetisation

If

Vdc e.m.f. due to Residual Magnetism

F1

Exciting Current

-

(a)

(b)

Figure 30: Magnetization characteristics Fig. 30 shows a shunt generator with its field connected to a voltage source Vf through a regulating resistor in potential divider form. The current drawn by the field winding can be regulated from zero to the maximum value. If the change in the excitation required is small, simple series connection of a field regulating resistance can be used. In all these cases the presence of a prime mover rotating the armature is assumed. A 68

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separate excitation is normally used for testing of d.c. generators to determine their open circuit or magnetization characteristic. The excitation current is increased monotonically to a maximum value and then decreased in the same manner, while noting the terminal voltage of the armature. The load current is kept zero. The speed of the generator is held at a constant value. The graph showing the nature of variation of the induced emf as a function of the excitation current is called as open circuit characteristic (occ), or no-load magnetization curve or no-load saturation characteristic. Fig. 30(b). shows an example. The magnetization characteristic exhibits saturation at large values of excitation current. Due to the hysteresis exhibited by the iron in the magnetic structure, the induced emf does not become zero when the excitation current is reduced to zero. This is because of the remnant field in the iron. This residual voltage is about 2 to 5 percent in modern machines. Separate excitation is advantageous as the exciting current is independent of the terminal voltage and load current and satisfactory operation is possible over the entire voltage range of the machine starting from zero.

5.2.3

Self excitation In a self excited machine, there is no external source for providing excitation current.

The shunt field is connected across the armature. For series machines there is no change in connection. The series field continues to be in series with the armature.

Self excitation is now discussed with the help of Fig. 31.(a) The process of self excitation in a shunt generator takes place in the following manner. When the armature is rotated a feeble induced emf of 2 to 5 percent appears across the brushes depending upon the speed of rotation and the residual magnetism that is present. This voltage 69

Indian Institute of Technology Madras

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oh ms

Electrical Machines I

1500 rev/min

oh m s

25 0

210

A2

F2

n

Prime mover

17 0

ohm s

500 rev/min

60 30

1.0 Exciting current,Amperes

(b) characteristics

200

210

80

150

25 0o hm s

120

40

60 oh ms

120

180 12 5o hm s

160

Open circuit e.m.f,volts

Critical Resistance

Induced emf on open circuit

(a)Physical connection

0 14

1000 rev/min s m oh

90

0

A1

F1

280

120

37 5

Open circuit e.m.f,volts

150

oh ms

180

90 60 30

400

200

0

Total field circuit resistance, ohms

(c)Critical resistance

(d) Critical speed

Figure 31: Self excitation

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speed in rev/min

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D

Open circuit characteristic

C

Q’

Voltage

R’ QL

Q

P’

R

RL

P O’

0

PL P1

Q1 A’

P"

Q"

Armature drop characteristic

A

Excitation current If Armature current Ia

Figure 32: External characteristics of a self excited of a shunt generator

gets applied across the shunt field winding and produces a small mmf. If this mmf is such as to aid the residual field then it gets strengthened and produces larger voltage across the brushes. It is like a positive feed back. The induced emf gradually increases till the voltage induced in the armature is just enough to meet the ohmic drop inside the field circuit. Under such situation there is no further increase in the field mmf and the build up of emf also stops. If the voltage build up is ‘substantial’, then the machine is said to have ‘self excited’. Fig. 31(b) shows the magnetization curve of a shunt generator. The field resistance line is also shown by a straight line OC. The point of intersection of the open circuit charac-

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teristic (OCC) with the field resistance line, in this case C, represents the voltage build up on self excitation. If the field resistance is increased, at one point the resistance line becomes a tangent to the OCC. This value of the resistance is called the critical resistance. At this value of the field circuit resistance the self excitation suddenly collapses. See Fig. 31(c). Instead of increasing the field resistance if the speed of the machine is reduced then the same resistance line becomes a critical resistance at a new speed and the self excitation collapses at that speed. In this case, as the speed is taken as the variable, the speed is called the critical speed. In the linear portion of the OCC the ordinates are proportional to the speed of operation, hence the critical resistance increases as a function of speed Fig. 31.(b) and (d).

The conditions for self excitation can be listed as below. 1. Residual field must be present. 2. The polarity of excitation must aid the residual magnetism. 3. The field circuit resistance must be below the critical value. 4. The speed of operation of the machine must be above the critical speed. 5. The load resistance must be very large. Remedial measures to be taken if the machine fails to self excite are briefly discussed below. 1. The residual field will be absent in a brand new, unexcited, machine. The field may be connected to a battery in such cases for a few seconds to create a residual field.

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2. The polarity of connections have to be set right. The polarity may become wrong either by reversed connections or reversed direction of rotation. If the generator had been working with armature rotating in clockwise direction before stopping and if one tries to self excite the same with counter clockwise direction then the induced emf opposes residual field, changing the polarity of connections of the field with respect to armature is normally sufficient for this problem. 3. Field circuit resistance implies all the resistances coming in series with the field winding like regulating resistance, contact resistance, drop at the brushes, and the armature resistance. Brush contact resistance is normally high at small currents. The dirt on the commutator due to dust or worn out mica insulator can increase the total circuit resistance enormously. The speed itself might be too low so that the normal field resistance itself is very much more than the critical value. So ensuring good speed, clean commutator and good connections should normally be sufficient to overcome this problem. 4. Speed must be increased sufficiently to a high value to be above the critical speed. 5. The load switch must be opened or the load resistance is made very high.

5.2.4

Self excitation of series generators The conditions for self excitation of a series generator remain similar to that of

a shunt machine. In this case the field circuit resistance is the same as the load circuit resistance and hence it must be made very low to help self excitation. To control the field mmf a small resistance called diverter is normally connected across the series field. To help in the creation of maximum mmf during self excitation any field diverter if present must be 73

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Terminal voltage

Electrical Machines I

Open circuit characteristic

PS=PQ-PR Q Armature characteristic

S A

R

P 0

B External characteristic

Load Current

Figure 33: External characteristics of a Series Generator

open circuited.In a series generator load current being the field current of the machine the self excitation characteristic or one and the same. This is shown in Fig. 33

5.2.5

Self excitation of compound generators Most of the compound machines are basically shunt machines with the series wind-

ing doing the act of strengthening/weakening the field on load, depending up on the connections. In cumulatively compounded machines the mmf of the two fields aid each other and in a differentially compounded machine they oppose each other. Due to the presence of the shunt winding, the self excitation can proceed as in a shunt machine. A small difference exists however depending up on the way the shunt winding is connected to the armature. It can be a short shunt connection or a long shunt connection. In long shunt connection the shunt field current passes through the series winding also. But it does not affect the process of self excitation as the mmf contribution from the series field is negligible. 74

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Both series field winding and shunt field winding are wound around the main poles. If there is any need, for some control purposes, to have more excitation windings of one type or the other they will also find their place on the main poles. The designed field windings must cater to the full range of operation of the machine at nominal armature current. As the armature current is cross magnetizing the demagnetization mmf due to pole tip saturation alone need be compensated by producing additional mmf by the field.

The d.c. machines give rise to a variety of external characteristics with considerable ease. The external characteristics are of great importance in meeting the requirements of different types of loads and in parallel operation. The external characteristics, also known as load characteristics, of these machines are discussed next.

5.3

Load characteristics of d.c. generators Load characteristics are also known as the external characteristics. External char-

acteristics expresses the manner in which the output voltage of the generator varies as a function of the load current, when the speed and excitation current are held constant. If they are not held constant then there is further change in the terminal voltage. The terminal voltage V can be expressed in terms of the induced voltage E and armature circuit drop as V = E − Ia Ra − Vb

(36)

Vb - brush contact drop, V Ia - armature current, A Ra - armature resistance + inter pole winding resistance+ series winding resistance + com75

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Open circuit e.m.f C Induced e.m.f B

Volts

Terminal voltage V

Ohmic Drop IaRa 0

A Load current,Ia

Figure 34: External characteristics of a separately excited shunt generator pensating winding resistance.

As seen from the equation E being function of speed and flux per pole it will also change when these are not held constant. Experimentally the external characteristics can be determined by conducting a load test. If the external characteristic is obtained by subtracting the armature drop from the no-load terminal voltage, it is found to depart from the one obtained from the load test. This departure is due to the armature reaction which causes a saturation at one tip of each pole. Modern machines are operated under certain degree of saturation of the magnetic path. Hence the reduction in the flux per pole with load is obvious. The armature drop is an electrical drop and can be found out even when the machine is stationary and the field poles are unexcited. Thus there is some slight droop in the external characteristics, which is good for parallel operation of the generators.

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One could easily guess that the self excited machines have slightly higher droop in the external characteristic as the induced emf E drops also due to the reduction in the applied voltage to the field. If output voltage has to be held constant then the excitation current or the speed can be increased. The former is preferred due to the ease with which it can be implemented. As seen earlier, a brush lead gives rise to a load current dependent mmf along the pole axis. The value of this mmf magnetizes/demagnetizes the field depending on whether the lead is backward or forward.

5.4

External characteristics of a shunt generator For a given no-load voltage a self excited machine will have more voltage drop at

the terminals than a separately excited machine, as the load is increased. This is due to the dependence of the excitation current also on the terminal voltage. After certain load current the terminal voltage decreases rapidly along with the terminal current, even when load impedance is reduced. The terminal voltage reaches an unstable condition. Also, in a self excited generator the no-load terminal voltage itself is very sensitive to the point of intersection of the magnetizing characteristics and field resistance line. The determination of the external characteristics of a shunt generator forms an interesting study. If one determines the load magnetization curves at different load currents then the external characteristics can be easily determined. Load magnetization curve is a plot showing the variation of the terminal voltage as a function of the excitation current keeping the speed and armature current constant. If such curves are determined for different load currents then by determining the intersection points of these curves with field resistance line one can get the external characteristics of a shunt generator. Load saturation curve can be generated from no-load saturation curve /OCC by subtracting the armature drop at each excitation point. Thus 77

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it is seen that these family of curves are nothing but OCC shifted downwards by armature drop. Determining their intercepts with the field resistance line gives us the requisite result. Instead of shifting the OCC downwards, the x axis and the field resistance line is shifted ‘upwards’ corresponding to the drops at the different currents, and their intercepts with OCC are found. These ordinates are then plotted on the original plot. This is shown clearly in Fig. 32. The same procedure can be repeated with different field circuit resistance to yield external characteristics with different values of field resistance. The points of operation up to the maximum current represent a stable region of operation. The second region is unstable. The decrease in the load resistance decreases the terminal voltage in this region.

5.4.1

External characteristics of series generators In the case of series generators also, the procedure for the determination of the

external characteristic is the same. From the occ obtained by running the machine as a separately excited one, the armature drops are deducted to yield external /load characteristics. The armature drop characteristics can be obtained by a short circuit test as before. Fig. 33 shows the load characteristics of a series generator. The first half of the curve is unstable for constant resistance load. The second half is the region where series generator connected to a constant resistance load could work stably. The load characteristics in the first half however is useful for operating the series generator as a booster. In a booster the current through the machine is decided by the external circuit and the voltage injected into that circuit is decided by the series generator. This is shown in Fig. 35

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-

S1

+ E2

A2

A1

A2

F2

S2

Booster Generator

E1

F1

E=E1 +- E2

A1 Main generator Figure 35: Series generator used as Booster

5.4.2

Load characteristics of compound generators In the case of compound generators the external characteristics resemble those of

shunt generators at low loads. The load current flowing through the series winding aids or opposes the shunt field ampere turns depending upon whether cumulative or differential compounding is used. This increases /decreases the flux per pole and the induced emf E. Thus a load current dependant variation in the characteristic occurs. If this increased emf cancels out the armature drop the terminal voltage remains practically same between no load and full load. This is called as level compounding. Any cumulative compounding below this value is called under compounding and those above are termed over- compounding. These are shown in Fig. 36. The characteristics corresponding to all levels of differential compounding lie below that of a pure shunt machine as the series field mmf opposes that of the shunt field.

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IL S2 If S1

F2

A2 Load

#

Vf

Prime mover

A1 F1 (a)-Connection Over compounded

Terminal voltage

Level compounded Under compounded Shunt machine

Differential compounding

Load current

(b)-Characteristics Figure 36: External characteristic of Compound Generator 80

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External characteristics for other voltages of operation can be similarly derived by changing the speed or the field excitation or both.

5.5

Parallel operation of generators D.C. generators are required to operate in parallel supplying a common load when

the load is larger than the capacity of any one machine. In situations where the load is small but becomes high occasionally, it may be a good idea to press a second machine into operation only as the demand increases. This approach reduces the spare capacity requirement and its cost. In cases where one machine is taken out for repair or maintenance, the other machine can operate with reduced load. In all these cases two or more machines are connected to operate in parallel.

5.5.1

Shunt Generators Parallel operation of two shunt generators is similar to the operation of two storage

batteries in parallel. In the case of generators we can alter the external characteristics easily while it is not possible with batteries. Before connecting the two machines the voltages of the two machines are made equal and opposing inside the loop formed by the two machines. This avoids a circulating current between the machines. The circulating current produces power loss even when the load is not connected. In the case of the loaded machine the difference in the induced emf makes the load sharing unequal. Fig. 37 shows two generators connected in parallel. The no load emfs are made equal to E1 = E2 = E on no load; the current delivered by each machine is zero. As the load is gradually applied a total load current of I ampere is drawn by the load. The load voltage 81

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s1

Prime mover

s2

v

A2

A2 Load

G2

G1

A1

A1

F2

F2

Vf1

Vf2

F1

F1

Figure 37: Connection of two shunt generators in Parallel

E1

V2

k

V0

j

Total char a

Terminal Voltage

E2 V

A

cteristic

B

C V2 V1

I1 I2 I=I1+I2

O

Load current

D

Figure 38: Characteristics of two shunt generators in Parallel

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under these conditions is V volt. Each machines will share this total current by delivering currents of I1 and I2 ampere such that I1 + I2 = I.

Also terminal voltage of the two machines must also be V volt. This is dictated by the internal drop in each machine given by equations V = E1 − I1 Ra1 = E2 − I2 Ra2

(37)

where Ra1 and Ra2 are the armature circuit resistances. If load resistance RL is known these equations can be solved analytically to determine I1 and I2 and hence the manner in which to total output power is shared. If RL is not known then an iterative procedure has to be adopted. A graphical method can be used with advantage when only the total load current is known and not the value of RL or V . This is based on the fact that the two machines have a common terminal voltage when connected in parallel. In Fig. 38 the external characteristics of the two machines are first drawn as I and II . For any common voltage the intercepts OA and OB are measured and added and plotted as point at C. Here OC = OA + OB . Thus a third characteristics where terminal voltage is function of the load current is obtained. This can be called as the resultant or total external characteristics of the two machines put together. With this, it is easy to determine the current shared by each machine at any total load current I.

The above procedure can be used even when the two voltages of the machines at no load are different. At no load the total current I is zero ie I1 + I2 = 0 or I1 = −I2 . Machine I gives out electrical power and machine II receives the same. Looking at the voltage equations, the no load terminal equation Vo becomes Vo = E1 − I1nl Ra1 = E2 + I2nl Ra2 83

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As can be seen larger the values of Ra1 and Ra2 larger is the tolerance for the error between the voltages E1 and E2 . The converse is also true. When Ra1 and Ra2 are nearly zero implying an almost flat external characteristic, the parallel operation is extremely difficult.

5.5.2

Series generators Series generators are rarely used in industry for supplying loads. Some applications

like electric braking may employ them and operate two or more series generates in parallel. Fig. 39 shows two series generators connected in parallel supplying load current of I1 and I2 . If now due to some disturbance E1 becomes E1 + ∆E1 then the excitation of the machine I increases, increasing the load current delivered. As the total current is I the current supplied by machine II reduces, so also its excitation and induced emf. Thus machine I takes greater and greater fraction of the load current with machine II shedding its load. Ultimately the current of machine II becomes negative and it also loads the first machine. Virtually there is a short circuit of the two sources, the whole process is thus highly unstable. One remedy is for a problem as this is to make the two fields immune to the circulating current between the machines. This is done by connecting an equalizer between the fields as shown in Fig. 39-a . With the equalizer present, a momentary disturbance does not put the two machines out of action. A better solution for such problems is to cross connect the two fields as shown in Fig. 39-b. A tendency to supply a larger current by a machine strengthens the field of the next machine and increases its induced emf . This brings in stable conditions for operation rapidly.

84

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

I1

I1+I2

+

A2

+

A2

I2

I1 A1

A1

-

S2

I1+I2

-

V

S2

Equaliser

F2

F1

S1

S1

I1+I2

(a)Equalizer connection

I1 +

A2

A2

+

G2

G1 A1

I1+I2

I2

Load

-

A1

-

I1 S2

S1

S2

I2

-

I2

-

S1

I1+I2

(b)Cross connection of fields Figure 39: Series Generator working in parallel

85

Indian Institute of Technology Madras

V

Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

F2

F1

+

A2

-

A1

F2

F1

+

A2

A1

-

Load

V

Load

V

Equalizer S2

S2

S1

S1

(a)Equalizer connection F2

F1

+

A2

-

A1 F1

S2

S1

F2

+

A2

A1

-

S2

S1

(b)Cross connection of series fields

Figure 40: Compound generators operating in parallel 86

Indian Institute of Technology Madras

Electrical Machines I

5.5.3

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Compound Generators The parallel operation of compound machines is similar to shunt generators. Dif-

ferential compounding would produce a drooping external characteristics and satisfactory parallel operation is made easy. But most of the generators are used in the cumulatively compounded mode. In such cases the external characteristics will be nearly flat making the parallel operation more difficult. By employing equalizer connection for the series windings this problem can be mitigated. Fig. 40 shows the connection diagram for parallel operation of two compound generators.

5.6

D.C. motors D.C. motors have a place of pride as far as electrical drives are considered. The

simplicity, and linearity of the control method makes them highly preferred machines in precision drives. In spite of the great advancements in a.c. drives these machines are still sought after by the industries. Apart from high precision application they are preferred in stand alone systems working on batteries and high speed drives off constant voltage mains. After the field is excited if we pass a current through the armature the rotor experiences a torque and starts rotating. The direction of the torque can be readily obtained from the law of interaction. These moving conductors cut the field and induce emf, usually called the ’back emf’ according to Lenz’s law and act as a sink of electrical power from the electrical source. This absorbed power appears as mechanical power. The converted mechanical power should overcome the frictional and iron losses before useful work could be done by the same. The connections to the supply of a d.c. shunt motor are given in Fig. 41.

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

+

+

F2 A2

F2

A2

A1

F1

A1

F1

-

(a)Separate excitation

(b) Shunt excitation

s1

+

F2

s2 A2

DC Supply F1

A1

(c)Practical arrangement

Figure 41: Shunt motor connections

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Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Commonly used connection is where in both the field and the armature are energized simultaneously Fig. 41(b). As the field has higher inductance and time constant torque takes some time to reach the full value corresponding to a given armature current. In Fig. 41.(c), the switch S1 is closed a few seconds prior to switch S2 . By then the field current would have reached the steady value. So the torque per ampere is high in this case. The only difference in the second connection Fig. 41.(a) is that the shunt field winding is connected to a separate source. This connection is used when the armature and field voltage are different as is common in high voltage d.c. machines. The field voltage is kept low in such cases for the sake of control purposes. Here again the field circuit must be energized prior to the armature. Suitable interlock should be provided to prevent the armature switch being closed prior to / without closing of field circuit as the armature currents reach very large values still not producing any torque or rotation. The relevant equations for the motoring operation can be written as below V − E − Ia Ra − Vb = 0 or E = V − Ia Ra − Vb p.φ.Z.n pZ = Ke φ.n where Ke = b b 1 pZ 1 p.φ.ZIa . = Kt φIa where Kt = . = 2π b 2π b dw and TM − TL = J dt E=

TM

where TL - Load torque TM - Motor torque J - polar moment of inertia. w - angular velocity = 2π.n

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Indian Institute of Technology Madras

(39) (40) (41) (42)

Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

The first one is an electrical equation, the second and the third are electro mechanical in nature and the last equation is the mechanical equation of motion. Ke and Kt are normally termed as back emf constant and torque constant respectively. Under steady speed of operation the fourth equation is not required. Using these equations one can determine the torque speed characteristics of the machine for a given applied voltage. These characteristics are similar to the external characteristics for a generator. Here the torque on the machine is assumed to be varying and the corresponding speed of operation is determined. This is termed as the torque speed characteristic of the motor.

5.7

Torque speed characteristics of a shunt motor A constant applied voltage V is assumed across the armature. As the armature

current Ia , varies the armature drop varies proportionally and one can plot the variation of the induced emf E. The mmf of the field is assumed to be constant. The flux inside the machine however slightly falls due to the effect of saturation and due to armature reaction. The variation of these parameters are shown in Fig. 42. Knowing the value of E and flux one can determine the value of the speed. Also knowing the armature current and the flux, the value of the torque is found out. This procedure is repeated for different values of the assumed armature currents and the values are plotted as in Fig. 42-(a). From these graphs, a graph indicating speed as a function of torque or the torque-speed characteristics is plotted Fig. 42-(b)(i).

As seen from the figure the fall in the flux due to load increases the speed due to the fact that the induced emf depends on the product of speed and flux. Thus the speed

90

Indian Institute of Technology Madras

Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Flux, Speed and Torque

A

No load speed

Line voltage B Speed C

Back emf

E F Flux

Torque

G Armature current

0

(a)Load characteristics (ii)

Speed

(i)

0

Torque (b)Torque speed curve

Figure 42: DC Shunt motor characteristics

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

of the machine remains more or less constant with load. With highly saturated machines the on-load speed may even slightly increase at over load conditions. This effects gets more pronounced if the machine is designed to have its normal field ampere turns much less than the armature ampere turns. This type of external characteristics introduces instability during operation Fig. 42(b)(ii) and hence must be avoided. This may be simply achieved by providing a series stability winding which aids the shunt field mmf.

5.8

Load characteristics of a series motor Following the procedure described earlier under shunt motor, the torque speed

characteristics of a series motor can also be determined. The armature current also happens to be the excitation current of the series field and hence the flux variation resembles the magnetization curve of the machine. At large value of the armature currents the useful flux would be less than the no-load magnetization curve for the machine. Similarly for small values of the load currents the torque varies as a square of the armature currents as the flux is proportional to armature current in this region. As the magnetic circuit becomes more and more saturated the torque becomes proportional to Ia as flux variation becomes small. Fig. 43(a) shows the variation of E1 , flux , torque and speed following the above procedure from which the torque-speed characteristics of the series motor for a given applied voltage V can be plotted as shown in Fig. 43.(b) The initial portion of this torque-speed curve is seen to be a rectangular hyperbola and the final portion is nearly a straight line. The speed under light load conditions is many times more than the rated speed of the motor. Such high speeds are unsafe, as the centrifugal forces acting on the armature and commutator can destroy them giving rise to a catastrophic break down. Hence series motors are not recommended for use where there is a possibility of the load becoming zero. In order to 92

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Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Terminal voltage Back emf

Torque, Flux and Speed

No load Magnetisation curve

Useful Flux Useful Torque

Developed Torque

Speed

Load current

Speed

(a)Load characteristics

0

Torque (b)-Torque speed curve

Figure 43: Load characteristics of a Series Motor

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

safeguard the motor and personnel, in the modern machines, a ‘weak’ shunt field is provided on series motors to ensure a definite, though small, value of flux even when the armature current is nearly zero. This way the no-load speed is limited to a safe maximum speed. It is needless to say, this field should be connected so as to aid the series field.

5.9

Load characteristics of a compound motor Two situations arise in the case of compound motors. The mmf of the shunt field

and series field may oppose each other or they may aid each other. The first configuration is called differential compounding and is rarely used. They lead to unstable operation of the machine unless the armature mmf is small and there is no magnetic saturation. This mode may sometimes result due to the motoring operation of a level-compounded generator, say by the failure of the prime mover. Also, differential compounding may result in large negative mmf under overload/starting condition and the machine may start in the reverse direction. In motors intended for constant speed operation the level of compounding is very low as not to cause any problem.

Cumulatively compounded motors are very widely used for industrial drives. High degree of compounding will make the machine approach a series machine like characteristics but with a safe no-load speed. The major benefit of the compounding is that the field is strengthened on load. Thus the torque per ampere of the armature current is made high. This feature makes a cumulatively compounded machine well suited for intermittent peak loads. Due to the large speed variation between light load and peak load conditions, a fly wheel can be used with such motors with advantage. Due to the reasons provided under shunt and series motors for the provision of an additional series/shunt winding, it can be 94

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seen that all modern machines are compound machines. The difference between them is only in the level of compounding.

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6

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Parallel operation of d.c. motors As in the case of generators motors may also be required to operate in parallel

driving a common load. The benefits as well as the problems in both the cases are similar. As the two machines are coupled to a common load the speed of the load is the common parameter in the torque speed plane. The torque shared by each machine depends on the intersection of the torque speed curves. If the torque speed lines are drooping the point of intersection remains reasonably unaltered for small changes in the characteristics due to temperature and excitation effects. However if these curves are flat then great changes occur in torque shared by each machine. The machine with flatter curve shares a larger portion of the torque demand. Thus parallel operation of two shunt motors is considerably more difficult compared to the operation of the same machines as generators. The operation of level compounded generators is much more difficult compared to the same machines working as cumulative compounded motor. On a similar count parallel operation of cumulative compounded motors is easier than shunt motors. Series motors are, with their highly falling speed with the load torque, are ideal as far as the parallel operation is considered. Considerable differences in their characteristics still do not affect adversely their parallel operation. One application where several series motors operate in parallel is in electric locomotives. Due to the uneven wear and tear of the wheels of the locomotive the speeds of the rotation of these motors can be different to have the same common linear velocity of the locomotive. The torque developed by each machine remains close to the other and there is no tendency for derailment.The torque speed curves for parallel operation of series motors are given in Fig. 44

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Indian Institute of Technology Madras

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Speed

Electrical Machines I

A

0

C

B

D Motors I and II

I

II

in parallel

Torque

Figure 44: Parallel operation of Series motors

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7

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Series operation of motors In the case of series operation the motors shafts of the two machines are connected

to the same load and also the two armatures are series connected. This forces a common armature current through both the machines and the torques developed by the machines are proportional to the flux in each machine. Series operation of series motors is adopted during starting to improve the energy efficiency. This method is ideally suited for shunt and compound machines with nearly flat torque speed characteristics. Such machines can go through high amount of dynamics without the fear of becoming unstable. This configuration is used in steel mills. Having two smaller machines connected to the shaft is preferred over there in place of one large machine as the moment of inertia of the motors is much reduced, thus improving the dynamics.

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8

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Application of d.c. motors Some elementary principles of application alone are dealt with here. The focus is

on the mechanical equation of dynamics which is reproduced here once again. TM − TL = J

dw dt

(43)

Here TM and TL are the motor torque and the load torques respectively which are expressed as functions of ω. Under steady state operation dω/dt will be zero. The application of motors mainly looks at three aspects of operation. 1. Starting 2. Speed control 3. Braking The speed of the machine has to be increased from zero and brought to the operating speed. This is called starting of the motor. The operating speed itself should be varied as per the requirements of the load. This is called speed control. Finally, the running machine has to be brought to rest, by decelerating the same. This is called braking. The torque speed characteristics of the machine is modified to achieve these as it is assumed that the variation in the characteristics of the load is either not feasible or desirable. Hence the methods that are available for modifying the torque speed characteristics and the actual variations in the performance that these methods bring about are of great importance. When more than one method is available for achieving the same objective then other criteria like, initial cost, running cost, efficiency and ease operation are also applied for the evaluation of the methods. Due to the absence of equipment like transformer, d.c. machine operation in 99

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general is assumed to be off a constant voltage d.c. supply.

The relevant expressions may be written as, E V − Ia Ra − Vb = Ke φ pZφ/b 1 p.Z . .φIa = Kt .φ.Ia = 2π b dω = J dt

n = TM TM − TL

(44) (45) (46)

As can be seen, speed is a function of E and φ and T is a function of φ and Ia . Using these equations, the methods for starting , speed control and braking can be discussed.

8.1

Starting of d.c. machines For the machine to start, the torque developed by the motor at zero speed must

exceed that demanded by the load. Then TM − TL will be positive so also is dω/dt, and the machine accelerates. The induced emf at starting point is zero as the ω = 0 The armature current with rated applied voltage is given by V /Ra where Ra is armature circuit resistance. Normally the armature resistance of a d.c. machine is such as to cause 1 to 5 percent drop at full load current. Hence the starting current tends to rise to several times the full load current. The same can be told of the torque if full flux is already established. The machine instantly picks up the speed. As the speed increases the induced emf appears across the terminals opposing the applied voltage. The current drawn from the mains thus decreases, so also the torque. This continues till the load torque and the motor torque are equal to each other. Machine tends to run continuously at this speed as the acceleration is zero at this point of operation. The starting is now discussed with respect to specific machines. 100

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8.1.1

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

DC shunt motor If armature and field of d.c. shunt motor are energized together, large current is

drawn at start but the torque builds up gradually as the field flux increases gradually. To improve the torque per ampere of line current drawn it is advisable to energize the field first. The starting current is given by V /Ra and hence to reduce the starting current to a safe value, the voltage V can be reduced or armature circuit resistance Ra can be increased. Variable voltage V can be obtained from a motor generator set. This arrangement is called Ward-Leonard arrangement. A schematic diagram of Ward-Leonard arrangement is shown in Fig. 45. By controlling the field of the Ward-Leonard generator one can get a variable voltage at its terminals which is used for starting the motor. The second method of starting with increased armature circuit resistance can be obtained by adding additional resistances in series with the armature, at start. The current and the torque get reduced. The torque speed curve under these conditions is shown in Fig. 46(a) . It can be readily seen from this graph that the unloaded machine reaches its final speed but a loaded machine may crawl at a speed much below the normal speed. Also, the starting resistance wastes large amount of power. Hence the starting resistance must be reduced to zero at the end of the starting process. This has to be done progressively, making sure that the current does not jump up to large values. Starting of series motor and compound motors are similar to the shunt motor. Better starting torques are obtained for compound motors as the torque per ampere is more. Characteristics for series motors are given in fig. 47.

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

+ A2 Load

A2 M

variable voltage

F2

F1

A2 M

G

A1

-

A1

+

A1 F2

+

+

F1

-

-

F2

constant voltage mains

F1

(a) +

A2 Variable voltage dc

Constant voltage ac mains

Auto transformer

Diode bridge

Load

A1

-

F2

+

Static Ward Leonard system

F1

-

(b)

Figure 45: Ward-Leonard arrangement 102

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Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

v

F2

-

+

Rext

Rext = 0 Rext increasing

A2

Speed

E1

A1

F1

Constant voltage 0 source

Torque

(a)

F2 Rext

+

If >

-

A2 If2 < If rated

Vf

E1

A1

F1

If2 If rated

Speed

v

Constant voltage source

0

Torque

(b) +

F2

F1

A2

V1 V

E1

A1

V2 Speed

Vf

-

V3 V3 < V2 < V1

Variable voltage source 103 0

Torque

(c) Indian Institute of Technology Madras

Figure 46: Shunt Motor characteristics

Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

v

S2 S1

-

+

Rext

Speed

A2 E1

Rext = 0

A1

Rext > 0 Constant voltage 0 sources

Torque

(a) +

-

v

S2

A2

Rd =

E1 Constant voltage 0 sources

A1

Rd reducing Torque

(b)

S2

+

-

V

Variable voltage

A2 M

Speed

S1 Vrated

A1 104

V reducing 0

Torque

(c) Indian Institute of Technology Madras

Figure 47: Series motor control

8

S1

Speed

Rd

Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

F2

A2

ra

Rn+1 A1

n+1 n n-1

R3 R2 R1

rn

F1

rn-1 r2

3 2 1

r1

(a)Physical connection graphical method Rn+1 Rn Rn-1

Starting current with time Imax

Volts

R3 R2

0

Ia

Imin

Imin

R1 Imax

0

(b) Characteristics

Time

(c) Time-current plot

Figure 48: Calculation of starter resistance steps

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Indian Institute of Technology Madras

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8.1.2

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Grading of starting resistance for a shunt motor If the starting resistor is reduced in uniform steps then the current peaks reached

as we cut down the resistances progressively increase. To ascertain that at no step does the current jump to a large value non-uniform reduction of resistances must be assorted to. This use of a non-uniform resistance step is called ‘grading’ of the resistors. The calculations for a starter resistance of a shunt motor are shown below with the help of Fig. 48. In the figure an n element or n+1 step starter is shown. The armature resistance when all the external resistances are cut off is ra . The total armature circuit resistance at step 1 is R1 = (r1 + r2 + ... + rn ) + ra . The field winding is connected across the supply. The starting current reaches a maximum value Im ax when we move on to a step. One resistance element is cut from the circuit when the current falls down to Im in . During the instant when the element is cut the speed and hence the induced emf does not change but the current jumps back to Im ax . Thus during the starting the current changes between two limits Im ax and Im in. Writing the expression for the current before and after the resistance is changed on step Ri and Ri+1 , we have Im in =

V −E Ri

Im ax =

V −E Ri+1

or

Im ax Ri = Im in Ri+1

(47)

Proceeding this way for all the steps Im ax R2 Rn−1 Rn R1 = = ... = = = k(say) = Im in R2 R3 Rn Rn+1 r R1 R2 R1 Rn R1 R1 n k = ∗ ∗ ... ∗ = = k= n R2 R3 Rn+1 Rn+1 ra ra

106

Indian Institute of Technology Madras

(48) (49)

Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Sometimes the ratio k may be required to be fixed. Then the number of steps required can be calculated as log Rra1 R1 n log k = log ,n = ra log k log R1 − log Rn log k

(50)

Also, R=

r n

V = I1 ra

r n

V = RI2 ra

r

n+1

V I2 ra

(51)

From these expressions it is seen that to have the ratio k to be unity, the number of steps should be infinity. Smaller the number of steps larger is the ratio of maximum to minimum current. Also, it is not possible to choose n and k independently. Im ax is set by the maximum possible starting current from the point of view of commutation. Im in is found from the minimum torque against which the starting is required to be performed. Similar method exists in the case of series motors and compound motors. In these cases the ratio of currents and the ratio of fluxes are needed. The equation becomes non-linear and a graphical method is normally adopted for the design of the resistances in those cases.

Resistance method of starting is cheaper and simple and hence is used universally. But it wastes energy in the starting resistor. Hence this method is not advised when frequent starting of the motor is required. Ward-Leonard method gives a energy efficient method of starting. With the help of a auto transformer and rectifier set one can get variable voltage d.c. supply from a constant voltage a.c power source. This is some times called a static Ward-Leonard arrangement. This method is becoming more popular over the rotating machine counter part.

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8.2

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Speed control of d.c. motors In the case of speed control, armature voltage control and flux control methods

are available. The voltage control can be from a variable voltage source like Ward-Leonard arrangement or by the use of series armature resistance. Unlike the starting conditions the series resistance has to be in the circuit throughout in the case of speed control. That means considerable energy is lost in these resistors. Further these resistors must be adequately cooled for continuous operation. The variable voltage source on the other hand gives the motor the voltage just needed by it and the losses in the control gear is a minimum. This method is commonly used when the speed ratio required is large, as also the power rating.

Field control or flux control is also used for speed control purposes. Normally field weakening is used. This causes operation at higher speeds than the nominal speed. Strengthening the field has little scope for speed control as the machines are already in a state of saturation and large field mmf is needed for small increase in the flux. Even though flux weakening gives higher speeds of operation it reduces the torque produced by the machine for a given armature current and hence the power delivered does not increase at any armature current. The machine is said to be in constant power mode under field weakening mode of control. Above the nominal speed of operation, constant flux mode with increased applied voltage can be used; but this is never done as the stress on the commutator insulation increases.

Thus operation below nominal speed is done by voltage control. Above the nominal speed field weakening is adopted. For weakening the field, series resistances are used for shunt as well as compound motors. In the case of series motors however field weakening 108

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is done by the use of ’diverters’ . Diverters are resistances that are connected in parallel to the series winding to reduce the field current without affecting the armature current.

8.3

Braking the d.c. motors When a motor is switched off it ‘coasts’ to rest under the action of frictional forces.

Braking is employed when rapid stopping is required. In many cases mechanical braking is adopted. The electric braking may be done for various reasons such as those mentioned below: 1. To augment the brake power of the mechanical brakes. 2. To save the life of the mechanical brakes. 3. To regenerate the electrical power and improve the energy efficiency. 4. In the case of emergencies to step the machine instantly. 5. To improve the through put in many production process by reducing the stopping time. In many cases electric braking makes more brake power available to the braking process where mechanical brakes are applied. This reduces the wear and tear of the mechanical brakes and reduces the frequency of the replacement of these parts. By recovering the mechanical energy stored in the rotating parts and pumping it into the supply lines the overall energy efficiency is improved. This is called regeneration. Where the safety of the personnel or the equipment is at stake the machine may be required to stop instantly. Extremely large brake power is needed under those conditions. Electric braking can help in these situations also. In processes where frequent starting and stopping is involved the 109

Indian Institute of Technology Madras

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process time requirement can be reduced if braking time is reduced. The reduction of the process time improves the throughput.

Basically the electric braking involved is fairly simple. The electric motor can be made to work as a generator by suitable terminal conditions and absorb mechanical energy. This converted mechanical power is dissipated/used on the electrical network suitably. Braking can be broadly classified into: 1. Dynamic 2. Regenerative 3. Reverse voltage braking or plugging These are now explained briefly with reference to shunt ,series and compound motors.

8.3.1

Dynamic braking

• Shunt machine In dynamic braking the motor is disconnected from the supply and connected to a dynamic braking resistance RDB . In and Fig. 49 this is done by changing the switch from position 1 to 2 . The supply to the field should not be removed. Due to the rotation of the armature during motoring mode and due to the inertia, the armature continues to rotate. An emf is induced due to the presence of the field and the rotation. This voltage drives a current through the braking resistance. The direction of this current is opposite to the one which was flowing before change in the connection. Therefore, torque developed also gets reversed. The machine acts like a brake. The 110

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torque speed characteristics separate by excited shunt of the machine under dynamic braking mode is as shown in Fig. 49(b) for a particular value of RDB . The positive torque corresponds to the motoring operation. Fig. 50 shows the dynamic braking of a shunt excited motor and the corresponding torque-speed curve. Here the machine behaves as a self excited generator. Below a certain speed the self-excitation collapses and the braking action becomes Zero. • Series machine In the case of a series machine the excitation current becomes zero as soon as the armature is disconnected from the mains and hence the induced emf also vanishes. In order to achieve dynamic braking the series field must be isolated and connected to a low voltage high current source to provide the field. Rather, the motor is made to work like a separately excited machine. When several machines are available at any spot, as in railway locomotives, dynamic braking is feasible. Series connection of all the series fields with parallel connection of all the armatures connected across a single dynamic braking resistor is used in that case. • Compound generators In the case of compound machine, the situation is like in a shunt machine. A separately excited shunt field and the armature connected across the braking resistance are used. A cumulatively connected motor becomes differentially compounded generator and the braking torque generated comes down. It is therefore necessary to reverse the series field if large braking torques are desired.

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2

F2 +

A2

Vf

F1

+

1

RDB

E

-

A1

2 1

(a)Connections

Speed

RDB increasing

Torque (b)Characteristics

Figure 49: Dynamic Braking of a shunt motor 112

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0

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

2

F2 +

A2

Vf

F1

+

1

RDB

E

-

A1

2 1

(a)Connections

Speed

RDB increasing

Torque

0

(b)Characteristics

Figure 50: Dynamic braking of shunt excited shunt machine 113

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8.3.2

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Regenerative braking In regenerative braking as the name suggests the energy recovered from the rotating

masses is fed back into the d.c. power source. Thus this type of braking improves the energy efficiency of the machine. The armature current can be made to reverse for a constant voltage operation by increase in speed/excitation only. Increase in speed does not result in braking and the increase in excitation is feasible only over a small range, which may be of the order of 10 to 15%. Hence the best method for obtaining the regenerative braking is to operate, the machine on a variable voltage supply. As the voltage is continuously pulled below the value of the induced emf the speed steadily comes down. The field current is held constant by means of separate excitation. The variable d.c. supply voltage can be obtained by Ward-Leonard arrangement, shown schematically in Fig. 51. Braking torque can be obtained right up to zero speed. In modern times static Ward-Leonard scheme is used for getting the variable d.c. voltage. This has many advantages over its rotating machine counter part. Static set is compact, has higher efficiency, requires lesser space, and silent in operation; however it suffers from drawbacks like large ripple at low voltage levels, unidirectional power flow and low over load capacity. Bidirectional power flow capacity is a must if regenerative braking is required. Series motors cannot be regeneratively braked as the characteristics do not extend to the second quadrant.

8.3.3

Plugging The third method for braking is by plugging.Fig. 52 shows the method of connection

for the plugging of a shunt motor. Initially the machine is connected to the supply with the switch S in position number 1. If now the switch is moved to position 2, then a reverse voltage is applied across the armature. The induced armature voltage E and supply voltage 114

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

+

-

If

Variable votage V source

A2

F2

Vf

E

F1

A1

(a)Physical connection

Speed A V1

B C

V2 V1 > V2

Torque

0

(b)Characteristics

Figure 51: Regenerative braking of a shunt machine

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RB

2

-

+

F2

1

+

A2

V

Vf F1

E 2

-

A1 1 (a)Physical connection A

Speed

B

C

0

Torque

(b)Characteristics

Figure 52: Plugging or reverse voltage braking of a shunt motor 116

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V aid each other and a large reverse current flows through the armature. This produces a large negative torque or braking torque. Hence plugging is also termed as reverse voltage braking. The machine instantly comes to rest. If the motor is not switched off at this instant the direction of rotation reverses and the motor starts rotating the reverse direction. This type of braking therefore has two modes viz. 1) plug to reverse and 2) plug to stop. If we need the plugging only for bringing the speed to zero, then we have to open the switch S at zero speed. If nothing is done it is plug to reverse mode. Plugging is a convenient mode for quick reversal of direction of rotation in reversible drives. Just as in starting, during plugging also it is necessary to limit the current and thus the torque, to reduce the stress on the mechanical system and the commutator. This is done by adding additional resistance in series with the armature during plugging. • Series motors In the case of series motors plugging cannot be employed as the field current too gets reversed when reverse voltage is applied across the machine. This keeps the direction of the torque produced unchanged. This fact is used with advantage, in operating a d.c. series motor on d.c. or a.c. supply. Series motors thus qualify to be called as ‘Universal motors’. • Compound motors Plugging of compound motors proceeds on similar lines as the shunt motors. However some precautions have to be observed due to the presence of series field winding. A cumulatively compounded motor becomes differentially compounded on plugging. The mmf due to the series field can ’over power’ the shunt field forcing the flux to low values or even reverse the net field. This decreases the braking torque, and increases the duration of the large braking current. To avoid this it may be advisable to deactivate 117

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the series field at the time of braking by short circuiting the same. In such cases the braking proceeds just as in a shunt motor. If plugging is done to operate the motor in the negative direction of rotation as well, then the series field has to be reversed and connected for getting the proper mmf. Unlike dynamic braking and regenerative braking where the motor is made to work as a generator during braking period, plugging makes the motor work on reverse motoring mode.

8.4

Application of d.c motors and generators

It is seen from the earlier sections that the d.c.machine is capable of having variety of torque-speed characteristics depending on the circuit conditions. The need for generating these characteristics will be clear only when they are seen along with the characteristics of the loads that they operate with. Even though a detailed treatment of motor load systems is outside the scope here, it may be useful to look into the typical torque-speed characteristics of some of the common loads. Loads are broadly divided into, (a) Passive loads (b) Active loads They may be unidirectional in operation or work in either direction (Reversible loads).

Passive loads absorb the mechanical energy developed by the motors while active loads are capable of working as both sinks and sources for mechanical energy. The direction of rotation may be taken to be clockwise/counter clockwise rotation. Normally the 118

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

direction in which the load operates most of the time, is taken as the positive direction of rotation. Any torque which accelerates the motor load system in the positive direction of rotation is termed as a positive toque. With this rotation torques of motors, generators or loads can be represented graphically on a four quadrantal diagram. The torque being taken as an independent variable, is represented along the x-axis. Y-axis represents the speed. Quadrants. I and III in Fig. 53(a) represent ‘forward motoring’ and ‘reverse motoring’ operation respectively. Quadrants II and IV similarly represent generating/braking quadrants as they absorb mechanical power and cause braking action. Fig. 53(b) shows a few typical load characteristics on a four quadrantal diagram. The characteristics a, b,and c correspond to frictional torque, cutting torque and fan torque respectively. While the frictional torque is not a function of speed, the cutting toque is proportional to the speed and the fan torque varies as the square of the speed. These can only absorb mechanical power and hence are represented in quadrantal II for positive direction of rotation. Similar loads produce characteristics in quadrant IV for negative direction of rotation. Fig. 54 shows a typical behaviour of an active load. Here an elevator is taken as an example. Here the counter weight is assumed to be heavier than the cage and similarly the loaded cage in assumed to be heavier than the counter weight. As seen from the Fig. 54 the torque is constant and depends on the difference in the weight of the case and the counter weight, and the radius of the drum. The characteristics of the load exists in all the four quadrants and is capable of delivering as well as absorbing mechanical power. Hence it is called as an active load. The governing equation when the motor and a load are connected together is TM (w) − TL (w) = J

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dw dt

(52)

Electrical Machines I

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Speed

II

I

Torque

III

IV

(a)

b

a Speed

c Torque

c

a

b

(b)

Figure 53: Typical load characteristics on a four quadrantal diagram

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W T

speed Hoisting an empty cage

W

T

Hoisting a loaded cage

Torque o

T W

W T

Lowering a loaded cage

Lowering an empty cage

Figure 54: Four quadrantal diagram

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where TM (w) and TM (w) are motor and load torques respectively. J is the polar moment of inertia of the motor and load put together at the motor shaft.

dw dt

is made positive when the

speed has to be increased in the positive direction and negative when reducing the speed. Under steady operation TM (w) − TL (W ) = 0. Both motor and load torques are expressed as functions of the speed. The speed at which motor and load torques are equal and opposite is the steady state operating speed. By varying the characteristics of the motor (or the load), this speed can be changed to suit our requirements. Normally the torque speed characteristics of a load cannot be changed easily. Thus most speed control methods adopt, varying the motor characteristics to achieve speed control. Some typical loads and the motors commonly used to drive the same are tabulated in Table. d.c. shunt motor

lathes,fans,pumps disc and band saw drive requiring moderate torques.

d.c. series motor

Electric traction, high speed tools

d.c. compound motor

Rolling mills and other loads requiring large momentary toques.

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9

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Testing of d.c. machines A d.c. machine has to be tested for proper fabrication and trouble free operation.

From the tests one can determine the external characteristics needed for application of these machines. Also, one can find the efficiency, rating and temperature rise of the machine. Some of the tests are discussed in sequence now.

9.1

Measurement of armature resistance Measurement of winding resistances of field windings and armature winding are

performed by v-i method. Field is not excited during this test. Even though any value of applied voltage can be used, the highest permissible voltage/current is chosen during the test to minimize the errors. The armature circuit consists of two resistances in series. They are armature winding resistance and resistance due to the brushes and the brush drop. The brush contact drop behaves like a non-linear resistance. To separate this from the armature circuit resistance and brush resistance a number of v-i readings are taken. An equation of V = Vb + IRa form is fitted through these test points shown graphically in Fig. 55. For large values of I the equivalent armature resistance is taken to be V /I ohm. If the value of brush drop Vb can be neglected then the armature resistance Ra = V /I ohm.

9.2

Open Circuit Characteristic (OCC) The OCC is of great value as it shows the mmf and hence the field current required

to generate a given voltage at any speed, on no load. It is a graph showing the variation 123

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

v

+

A

A2

DC Supply

V

A1

-

(a)Physical connection I.V. Characteristic Ra =

dv di

dv di

V

Vb

0

I

(b)Characteristics

Figure 55: Measurement of Armature resistance and Brush drop

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of the induced emf as a function of excitation current, when the speed is held constant, with the load current being zero. It is also called the no-load saturation curve or no load magnetization characteristic. This is experimentally determined by running the machine as a separately excited generator on no-load at a constant speed and noting the terminal voltage as a function of the excitation current. This curve can be used to find the OCC at other speeds and also the self excited voltage when the machine works as a shunt generator.

9.3

Short circuit characteristics:(SCC) In the case of short circuit test the armature is kept short circuited through an

ammeter. The machine is demagnetized and an extremely small field current is passed through the field. The variation of the short circuit current as a function of excitation current is plotted as the SCC. The speed is to be held constant during this test also. The short circuit test gives an idea of the armature drop at any load current.

9.4

Load test To assess the rating of a machine a load test has to be conducted. When the

machine is loaded, certain fraction of the input is lost inside the machine and appears as heat, increasing the temperature of the machine. If the temperature rise is excessive then it affects the insulations, ultimately leading to the breakdown of the insulation and the machine. The load test gives the information about the efficiency of a given machine at any load condition. Also, it gives the temperature rise of the machine. If the temperature rise is below the permissible value for the insulation then the machine can be safely operated at that load, else the load has to be reduced. The maximum continuous load that can be

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delivered by the machine without exceeding the temperature rise for the insulation used, is termed as the continuous rating of the machine. Thus the load test alone can give us the proper information of the rating and also can help in the direct measurement of the efficiency.

9.5

Measurement of rotor inertia The moment of inertia value is very important for the selection of a proper motor

for drives involving many starts and stops or requiring very good speed control characteristics. The inertia can be determined by a retardation test.

The test works on the principle that when a motor is switched off from the mains it decelerates and comes to rest. The angular retardation at any speed is proportional to the retarding torque and is inversely proportional to the inertia. The torque lost at any speed is calculated by running the motor at that speed steadily on no load and noting the power input.From this power the losses that takes place in the armature and field are deducted to get the power converted into mechanical form. All this power is spent in over coming the mechanical losses at that speed. This can be repeated at any defined speed to get the lost power (PL ) and torque lost (Tlost ) due to mechanical losses. In a retardation test the motor speed is taken to some high value and the power to the motor is switched off. The torque required by the losses is supplied by the energy stored in the motor inertia. The lost torque at any speed can be written as PL = Tlost .ω Tlost = PL /w = J Here the

dw dt

(53) dw dt

is the slope of the retardation curve and the (Tlost ) is the torque required to be 126

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met at the given speed. From these values the moment of inertia can be computed as J=

9.6

Tlost dw dt

=

PL kgm2 w. dw dt

(54)

Efficiency of a d.c. machine A machine when loaded yields an output. The input to the machine is measured

at that operating point. The the efficiency in per unit is given as the ratio of output power to input power. output power input power Input power − power lost inside the machine = input power output power = output power + power lost inside the machine

η =

(55)

The first definition is used in the direct estimation of the efficiency . The other two definitions are known as determination of efficiency using the loss segregation. For the segregation of losses one must know the losses that take place inside a d.c. machine. The losses that take place inside a d.c. machine can be listed as below. 1. Armature copper loss. 2. Brush and brush contact loss. 3. Shunt field loss 4. Series field loss 5. Commutating pole loss

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6. Compensating winding loss 7. Mechanical losses 8. Iron losses 9. Stray load losses Out of these items 1,2,7,8 and 9 will be present in all the d.c. machines. Out of the remaining one or more may be present depending on which winding is present. These losses change with temperature of operation. Mechanical losses vary with variation in speed. Iron losses change with the degree of saturation and distortion of the shape of the field flux distribution under the poles.

When a d.c. machine is loaded using a suitable load the output delivered by the machine increases. The input requirement also increases along with the output. The difference between the input and output powers is the power lost inside the machine as loss. The efficiency of power conversion is given by the ratio of output power to input power. Putting in mathematical form for a motor, η=

V I − losses VI

(56)

for constant speed operation, the speed dependant losses remain constant. The load dependant losses form the variable losses. While the loss that takes place in the brush drop in the brushes is proportional to the load current, the loss that takes place in the resistance of the armature is proportional to the square of the load current. Even though the loss that takes place in a field winding is proportional to the square of the current through that winding, it is classified under constant losses as the excitation current is held constant during loading.

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Thus the total losses in a d.c. motor can be expressed in the form

η= When A =

a V

,B =

b V

PL = a + bI + cI 2

(57)

V I − PL A = 1 − ( + B + CI) VI I

(58)

and C = cV .

The term inside the brackets is sometimes referred to as the deficiency. For a typical d.c.motor these are plotted in Fig. 56(a) as a function of the load current. The curves a,b,c in the figure represent the efficiency curve taking one component of the loss at a time. The curve d is the efficiency curve with all three components taken together. The resultant curve exhibits a maximum. This can be easily seen from the graph that this maximum occurs when constant losses equal the variable losses. AI = CI or A = CI 2 . Fig. 56(b) depicts a typical output vs η curve of a d.c.machine.

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Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

b c

Efficiency

a d

current

Efficiency

(a)Efficiency Vs Load current

Output (b)Output Vs Efficiency

Figure 56: Efficiency of a D.C.machine

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