Lecture 4

LECTURE 4 Alternating-Current Indicating Instruments [1] Contents : 1 2 3 4 5 6 7 8

Rectifier-type instruments.................................................................................... Thermoinstruments............................................................................................... Electrostatic voltmeter.......................................................................................... Electrodynamometers in power instruments........................................................ Watthour meter..................................................................................................... Power-factor meter............................................................................................... Frequency meters.................................................................................................. Instrument transformers.......................................................................................

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4.1

Rectifier-Type Instruments [1] This method is very attractive, because it has a higher sensitivity than either the

electrodynamometer or the moving-iron instrument. Rectifier-type instrument generally use a PMMC movement in combination with some rectifier arrangement. Rectifiers for instruments work sometimes consist of four diodes in a bridge configuration, providing full-wave rectification. Figure 4-1 shows an ac voltmeter circuit consisting of a multiplier, a bridge rectifier, and a PMMC movement.

FIGURE 4-1 Full-wave rectifier ac voltmeter [1] The bridge rectifier produces a pulsating unidirectional current through the meter movement over the complete cycle of the input voltage. Because of the inertia of the moving coil, the meter will indicate a steady deflection proportional to the average value of the current. Since alternating currents and voltages are usually expressed in rms values, the meter scale is calibrated i terms of the rms value of a sinusoidal waveform.. A nonsinusoidal waveform has an average value that may differ considerably from the average value of a pure sine wave (for which the meter is calibrated) and the indicated reading may be very errorneous. The form factor relates the average value and the rms value of time varying voltages and currents : form factor =

effective value of the ac wave average value of the ac wave

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For a sinusoidal waveform :

form factor =

E rms E average

 2 E  2 m   = = 1.1 ................................................................(4-1) 2 Em

( π)

The ideal rectifier element should have zero forward and infinite reverse resistance. In practise, however, the rectifier is a nonlinier device, indicated by the characteristic curves of Figure 4-2.

FIGURE 4-2 Characteristic curves of a solid-state rectifier [1] The resistance of the rectifying element changes wit varying temperature, one of the major drawbacks of rectifier-type ac instruments. The meter accuracy is usually satisfactory under normal operating conditions at room temperature and is generally on the order of + 5 % of full-scale reading for sinusoidal waveforms. At very much higher or lower temperatures, the resistance of the rectifier changes the total resistance of the measuring circuit sufficiently cause the meter to be gravely in error. Frequency also affects the operation of the rectifier elements. The rectifier exhibits capasitive properties and tends to bypass the higher frequencies. Meter readings may be in error by as much as 0.5 % decrease for every 1-kHz rise in frequency. General rectifier-type ac voltmeters often use the arrangement shown Figure 4-3. The commercial multimeter often uses the same scale markings for both its dc and ac voltage ranges. Since the dc component of a sine wave for half-wave rectification equals 0.45 times the rms value, a poblem arises immediately. In order to obtain the same deflection on coresponding dc and ac voltage ranges, the multiplier for the ac range must be lowered proportionately. The circuit of Figure 4-4 illustrates a solution to the problem. Figure 4-5 shows a multirange ac voltmeter circuit of the Simpson Model 260 multimeter.

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FIGURE 4-3 Typical ac voltmeter section of a commercial multimeter [1]

FIGURE 4-4 Computation of the multiplier resistor and the ac voltmeter sensitivity [1]

FIGURE 4-5 Multirange ac voltmeter circuit of the Simpson Model 260 multimeter (courtesy of the Simpson Electric Cimpany) [1]

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4.2

Thermoinstruments [1]

The historical foreruner of the thermoinstruments is the hot-wire mechanism, shown schematically in Figure 4-6.

FIGURE 4-6 Schematic representation of the hot-wire ammeter [1] The current under measurement passes through a fine wire tightly stretched between two terminals. A second wire is attached to the fine wire at one end and, at the other, to a spring, which exerts a download pull on the fine wire. This second wire passes over a roller to which the pointer connected. The current under measurement causes the fine wire to heat and thus expand approximately in proportion to the heating current squared. The change in wire length drives the pointer, which indicates the magnitude of the current. Instability due to wire stretch, sluggishness in response, and lack of ambient temperature compensation have made this mechanism commercially unsatisfactory. Figure 4-7 shows a combination of a thermocouple and a PMMC movement that can be used to measure both ac and dc. This combination is called a thermocouple instrument, since its operation is based on the action of the thermocouple element. In Figure 4-7, CE and DE represent the two disiimilar metals, joined at point E, and are drawn as a light and a heavy line, to indicate dissimilarity. The potential difference between C and D depends on the temperature of the so-called cold junction, E. A rise in temperature causes an increase in the voltage and this is used to advantage in the termocouple. Heating element AB, hich is in mechanical contact wit he junction of the two metals at point E, forms part of the circuit in

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which the current is to be measured. AEB is called the hot junction. Heat energy generated by the current in the heating element raises the temperature of the cold junction and causes an increase in the voltage generated across terminals C and D. The potential difference causes a dc current is directly proportional to the current squared (I2R), and the temperature rise (and hence the generated voltage) is proportional to the square of the rms current. The deflection of the indicating instrument will therefore follow a square-law relationship.

FIGURE 4-7 Schematic representation of a basic thermocouple instrument using thermocouple CDE and a PMMC movement. [1]

FIGURE 4-8 Compensated thermocouple to measure the thermovoltage prouced by current i alone. Couple terminals C and D are in thermal contact with heater terminals A and B, but are electrically insulated from them. [1] The compensated thermoelement, shown schematically in Figure 4-8, produces a thermoelectric voltage in the thermocouple CED, which is directly proportional to the current through circuit AB. Since the developed couple voltage is a function of the temperature difference between its hot and cold ends, this temperature difference must be caused only by the current being measured. Therefore, for accurate measurements, points C and D must be at the mean temperature of points A and B. This accomplished by attaching couple ends C and D to the center of separate copper strips, whose ends are in thermal contact with A and B, but electrically insulated from them.

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Self-contained thermoelectric instruments of the compensated type are available in the 0.5-20-A range. Higher current ranges are available, but in this case the heating element is external to the indicator. Thermoelements used for current ranges over 60 A are gnerally provided with air cooling fins. Current measurements in the lower ranges, from approximately 0.1-0.75 A, use a bridge-type thermoelement, shown schematically in Figure 4-9. This arrangement does not use a separate heater: the current to be measured passes directly through the hermoelements and raises their temperature in portion to I2R. The cold junctions (marekd c) are the pins which are embedded in the insulating frame, and the hot junctions (marked h) are at splices midway between the pins. The couples are arranged as shown in Figure 4-9, and the resultant thermal voltage generates a dc potential difference across the indicating instruments. Since the bridge arms have equal resistances, the ac voltage across the meter is 0 V. The use of several thermocouples in series provides a greater output voltage and deflection than is possible with a single element, resulting in an instrument with increased sensitivity.

FIGURE 4-9 Bridge-type thermocouple instrument [1] Thermocouple voltmeters are available in ranges of up to 500 V and sensitivities of approximately 100 to 500 Ω

V

.

A major advantage of a thermocouple instrument is that its accuracy can be as high as 1 %, up to frequencies of approximately 50 MHZ. For this reason, it is classified as an RF instrument. Above 50 MHZ, the skin effect thends to force the current to the outer surface of

the conductor, increasing the effective resistance of the heating wire and reducing instrument accuracy. 48

4.3

Electrostatic Voltmeter [1]

The electrostatic voltmeter, or electrometer, is the only instrument that measures voltage directly rather than by the effect of the current it produces. This instrument has one distinguishing characteristic : It consumes no power (except during the brief transient peiod of initial connection to the circuit) and it therefore represents an infinite mpedance to the circuit under measurement. Its action depends on the reaction between two electrically charged bodies (Coulomb's law). The electrostatic mechanism resembles a variable capacitor, where the force existing between the two parallel plates is a function of the potential difference applied to them. Figure 4-10 illustrates the principle of this instrument.

FIGURE 4-10 Schematic representation of an electrostatic voltmeter [1] From Figure 4-10, the instantaneous energy stored in the electric field is W=

1 q2 1 2 = Ce ....................................................................................................(4-1) 2 C 2

The instantanous torque may be found by keeping e constant and permitting the movable plates to undergo a small angular displacement, ∂θ . The developed torque then is

Tθ =

∂W ∂  1 2  1 2 ∂C = ........................................................................(4-2)  Ce  = e ∂θ ∂θ  2  2 ∂θ

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Equation (4-2) indicates that the instantaneous torque is proportional to the square of the instantaneous voltage and also depends on the manner in which C charges with θ . The average torque over an entire period T of the alternating voltage is T

Tav =

T

1 1 1 ∂C 2 ................................................................(4-3) Tθ ∂t = ∫ e 2 ∂t = KE rms ∫ T 0 T 0 2 ∂θ

The electrometer can be used on either dc or ac and over fairly large range of frequencies. The instrument may be calibrated with dc and the calibration is valid for ac since the deflection is independent of the waveform of the applied voltage. The use of the instrument is limited to certain special applications, particularly in ac circuits of relatively high voltage, where the current taken by other instuments would result in errorneous indications. A protective resistor is generally used in series with the instrument to limit the current in case of a short circuit between the plates. 4.4

Electrodynamometers in Power Measurements [1]

The electrodynamometer movement is used extensively in measuring power. It may be used to indicate both dc and ac power for any waveform of voltage and current and it is not restricted to sinusoidal waveforms. When used as a single phase power meter, the coils are connected in a different arrangement (see Figure 4-11).

FIGURE 4-11 Diagram of an electrodynamometer wattmeter, connected to measure the power of a single-phase load. [1]

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The difficulty in placing the connection of the potential coil is overcome in the compensated wattmeter, shown schematically in Figure 4-12.

FIGURE 4-12 Diagram of compensated wattmeter in which the effect of the current in the potential coil is canceled by the current in the compensating winding [1]

4.5

Watthour Meter [1]

The watthour meter is not often found in a laboratory situation but it is widely used for the commercial measurement of electrcal energy. In fact, it is evident wherever a power company supplies the industrial or domestic consumer with electrical energy. Figure 4-13 shows the elements of a single-phase watthour meter in schematic form.

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FIGURE 4-13 Elemets of a single-phase watthour meter [1] 4.6

Power-factor Meters [1]

The power-factor, by definition, is the cosine of the phase angle between voltage and current, and the power-factor measurements usually involve the determination of this phase angle. This is demonstrated in the operation of the crossed-coil power-factor meter. The instrument is basically an electrodynamometer movement, where the moving element consists of two coils, mounted on the same shaft but at right angles to each other. The moving coils rotate in the magnetic field provided by the field coil hat carries the line current. The connection of this meter in a single-phase circuit are shown in the circuit diagram of Figure 414. The polarized-vane power-factor meter s shown in the construction sketch of Figure 415. This instrument is used primarily in three-phase power systems, because its operating principle depends on the application of three-phase voltage.

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FIGURE 4-14 Connections for a single-phase crossed-coil power-factor meter [1]

FIGURE 4-15 Polarized-vane power-factor meter (courtesy General Electric Company Limited) [1]

4.7

Frequency Meters [1]

Frequency can be determined in a variety of ways, but at the moment we are concerned with indicating instruments; in this category, frequency meters use the effect of frequency 53

upon such factors as mutual inductance, resonance of a tuned circuit, and mechanical resonance. An examplem of the use of tuned circuits is found in the electrodynamometer-type frequency meter, shown schematically in Figure 4-16. In this frequency meter, the field coils form part of two separate resonant circuits. In the case of powerline frequencies, the circuits qould be uned to frequencies of 50 Hz and 70 Hz, respectively, with 60 Hz in the middle of the scale. The torque on the movable element is proportional to the current through the moving coil. This current consists of the sum of the two field-coil currents. For an applied frequency within the limits of the instrument range, the circuit of field coil 1 operates above the resonant frequency with current i1 lagging the applied voltage. The circuit of field coil 2 operates below its resonance frequency and is therefore capasitive with current i2 leading the applied voltage. The torques produced by the two currents on the movable coil are therefore in opposition, and the resulting torque is a function of the frequency of the applied voltage. For each given frequency within the range of the instrument, the resulting torque on the movable element causes the pointer to take up a given position and the pointer deflection is calibrated in terms of the given frequency. The restoring torque is provided by a small iron vane mounted on the moving coil. The range of operation of this instrument is usually limited to the powerline frequencies and it finds its major application in this field where it is used for monitoring the frequency of a power system. The saturable-core frequency meter, which can comfortably handle and measure a wide range of frequencies, is shown schematically in Figure 4-17. The secondary winding consists of of two parts : one of the winding is wound on the magnetic core and the other half of the winding on he nonmgnetic core. The secondary windings are connected in series in such a way that the voltage induced in the windings oppose each other. When power is supplied to he primary winding, transformer action induces secondary voltages in the secondary windings. Because of the low saturation value of the magnetic core, this core will saturate at very small secondary voltages. As soon as this core is saturated, the rate of increase of induced voltage in that winding will be equal to the rate of increase of the induced voltage in the winding on the nonmagnetic core. Therefore the rate of increase of induced voltages cancels out, since the emfs in the secondary windings oppose each other. The secondary voltage will then not be a function of the primary applied voltage, but will depend only on the frequency of the voltage. The secondary output voltage is rectified and applied to a dc meter,

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whose deflection is proportional to the frequency. The meter scale is calibrated in terms of frequency.

FIGURE 4-16 Circuit arrangement of the electrodynamometer-type frequency meter [1]

FIGURE 4-17 Schematic representation of the saturable-core frequency meter [1]

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The tuned-reed frequency meter operates on the principle of mechanical resonance. 4.8

Instrument Transformers [1]

FIGURE 4-18 High-voltage potential Corporation) [1]

transformer

(courtesy

Westinghouse

Electric

Instrument transformers are used to measure ac at generating stations, transformer stations, and at transmission lines, in conjuction with ac measuring instruments (voltmeters, ammeters, wattmeters, VARmeters, etc.). Instrument transformer are classified according to their use and are referred to as current transformers (CT) and potential transformers (PT).

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