Voltage, Power And Current Ratings Of Series Voltage Controllers

Voltage, power and current ratings of series voltage controllers M.H.J. Bollen, Senior Member, IEEE Chalmers University of Technology 41296 Gothenburg, Sweden

Abstract: The active power injection requirements are calculated for a series voltage controller (or DVR) under various system and load conditions, for different fault types, for three-phase load and for single-phase load. It is shown that the power requirement depends on the sag magnitude and phase-angle jump as well as on the power factor of the load. For controllers with an energy reservoir the voltage-tolerance curve of the load-controller combination is obtained. For a combined shunt-series controller the current rating of the shunt controller is found. Finally the voltage rating of the series controller is assessed.

discussed for controllers using energy storage as well as for series controllers obtaining the active power from an additional shunt-connected controller.

Keywords: power quality, voltage sag, custom power.

Throughout this paper an “ideal controller” will be consider in accordance with Fig. 1. For the series controller, the loadside voltage equals the system-side voltage plus the voltage injected by the controller. Using complex phasors instead of time domain voltages, this gives:

I. INTRODUCTION Several methods are available to prevent equipment maloperation due to voltage sags. The two obvious solutions, at first sight, are a reduction of the number of faults and improvement of equipment immunity. However, experience has shown that in many practical cases neither of these methods is suitable. The most common mitigation method remains the installation of additional equipment between the power system and the equipment, either directly with the equipment terminals or at the customer-utility interface. The uninterruptable power supply (UPS) has traditionally been the method of choice for small power, single-phase equipment. For large equipment several methods are in use and under development, one of which is the series voltage controller, also known under the name “dynamic voltage restorer” or DVR [1,2]. The series voltage controller injects a voltage in series with the supply voltage. This voltage is chosen such that the loadside voltage remains constant during faults in the system. To maintain the voltage at the load-side, the series controller has to inject a certain amount of active power. In this paper, expressions are derived for the active power requirements as a function of the sag characteristics (magnitude and phase angle jump). Expressions are derived for balanced sags, for unbalanced sags, for three-phase controllers and for singlephase controllers.

II. ACTIVE POWER REQUIREMENTS A. Controller model

+ ,-@LT+

I Fig. 1, Circuit diagram model of power system, controller and load.

The voltage at the load-side of the controller remains constant, and equal to 1 pu. The voltage does not show any phase-angle jump.

The voltage at the system-side of the controller (i.e. the during-sag voltage) is characterized through a magnitude V and a phase-anglejump K ,I

-

Vsog = V cosy + j V sin y

.

The load current is equal to 1 pu, with a lagging power factor cos@:

I;oad =cos@-jsin@, The active power injection requirements are an important part in the design of a series voltage controller. The consequences of the active power injection requirements for the design are

(3)

(4)

So that the active power taken by the load is: 4wd

= cos$

(5)

From (1) and (2), the voltage injected by the controller is found:

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The current through the controller equals the load current:

f,,

= e-’@.

(7)

The complex power injected by the controller is obtained from ( 6 ) and (7):

s,,,,= (I - Eug )eJ@.

(8)

For single-phase equipment, the (complex) voltages in the individual phases are needed to determine the behavior. These are for a type A sag:

G=V vb=-p - q E L 2j JT & ,

(13)

=-Lr++jPJ;j 2

The active power injected is the real part of the complex power, leading to the following expression, by using (5): (9)

For zero phase-angle jump, the injected power is independent of the load power factor: pco,,

P - VIP,,

=

.

(10)

The effect of the power factor and the phase-angle jump will be discussed below.

B.

Voltage sag model

The voltage during a sag can be obtained from the so-called voltage divider model [3,4]:

-

C. Balanced sags, three-phase controllers

-7

where

TF is the impedance between the fault and the point-

zs

is of-common coupling (pcc) of the fault and the load, the source impedance at the pcc, the pre-event voltage is considered equal to 1 pu, and all load is assumed to be of the constant-impedance type. Equation (1 1) can be written as follows:

I-

I

<

-

.

. This expression can be used to get corresponding values for sag magnitude and phase-angle jump for a given feeder, i.e. for a given value of the “impedance angle” a. Theoretical consideration [3] as well as measurements [7] indicate values between zero and -60” for the impedance angle.

Balanced voltage sags are due to three-phase faults, leading to sags of type A. The three voltages for a balanced sag are given by expression (13). The event is identical in the three phases, so that ( 8 ) and (9) hold for each phase with the characteristic voltage being the sag voltage in all

vSug

three phases. The total injected power is thus three times the power injected in each phase. The total load power is also three times the power taken in one phase, so that (9) holds with Pen, the total injected power and eoad the total (active power) load. This expression is used to calculate the injected power as a function of the load power factor and the impedance angle of the faulted feeder. Some of the results are shown in Fig. 2. Sag magnitude and phase-angle jump have been calculated from (12) with a = -60’ and for 2 between zero and infinite.

I

The voltage-divider model gives the so-called “characteristic voltage” for the voltages in the three phases. The model can be applied directly to study the effect of voltage sags on three-phase equipment. A distinction needs to be made between three types of sags: type A is due to three-phase faults; types C and D are due to non-symmetrical faults [5,6,71. Sag magn. in pu

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Fig. 2, Injected power for impedance angle -60" and four values of the load power factor: I .O (solid line); 0.9 (dashed); 0.8(dash-dot); and 0.7 (dotted).

It follows from Fig. 2 that the injected power decreases for decreasing power factor. The active part of the load was kept constant here, so that the load current will increase for decreasing power factor. Note that, for zero phase-angle jump, the injected power is independent of the load power factor, according to (IO). The reduction in injected power, with decreasing power factor, is explained in Fig. 3. Due to the phase-angle jump, the voltage' at the system side of the controller, becomes more in phase with the load current. The amount of active power taken from the supply thus increases and the active power requirement of the controller is reduced. This holds for a negative phase-angle jump and a lagging power factor. For a leading power factor, a negative phaseangle jump increases the amount of active power that needs to be injected by the controller.

The total apparent power is again equal to 1 pu, to enable a direct comparison with the balanced case. This leads to the factor in the expressions for the load currents. From (16) the following expression is obtained:

-

sco,,= { - $ (C

+ iic + z2E)JJ@.

(1 8)

This expression is identical to (9), with complex sag voltage replaced by the positive-sequence voltage:

ysog =$(E +a5 +a2<). From (14) and (15) it follows that for both a type C and a type D sag, the positive sequence voltage is obtained

Eag

from the characteristic voltage expression:

7

by using the following

-

vsag= ++fr.

(19)

Substituting (19) into (9) gives an expression for the complex power injected by the controller during an unbalanced sag: LI

sag without phaseangle jump

load voltage

L

Rul

The injected power during an unbalanced sag is half the amount injected during a balanced sag with the same characteristic magnitude and phase-angle jump. Fig. 2 and the conclusions drawn from it, thus also hold for unbalanced sags. From the above it also follows that the zero-sequence and negative-sequence voltage do not affect the injected power requirements of the series controller.

phase-anglejump

I

E. Single-phase controllers

Fig. 3, Phasor diagram with (dashed) and without (solid) phase-angle jump.

D. Unbalanced sags, three-phase controllers For an unbalanced sag (type C or type D), expressions (8) and (9) need to be applied to each phase separately, where it is important to consider that the load-side voltage and current are also shifted over 120" compared to each other. The total injected power is found by adding the injected powers in the three phases: +sb

gco",

+&,

where

-

S, =

(I-c

k e j @,

(16)

For single-phase controllers, the voltages in the individual phases need to be considered, according to (1 3) through (1 5). Like before, complex characteristic voltage has been calculated from (12), after which the voltages in the three individual phases are obtained from (13) through (1 5). These voltages are inserted in (9) to get the injected power for each phase. This results in five curves: three for type D sags, two for type C. The third phase for a type C sag is not affected so that the injected power is zero. A three-phase fault (sag type A) will give the same result as one of the phases for a type D sag. Some of the results are shown in Fig. 4 and Fig. 5, where solid lines are due to sags of type D, and dashed lines due to sags of type C. Note that the single-phase controller cannot distinguish between sags of type C or type D. This classification has only been used to represent the origin of the sags as experienced by the single-phase equipment.

and

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for the controller equal to 1 pu, it would be possible to mitigate all voltage sags, as long as the energy storage cap'acity is sufficient. But a smaller voltage rating may be significantly cheaper without leading to many additional equipment trips. A.

Voltage tolerance: magnitude and phase-angle jump

To assess the effect of the voltage rating, the sag voltage in the complex plane needs to be considered. This is shown in Fig. 6. This plot shows the complex plane: real versus imaginary part of the sag voltage in (3). It is assumed

cog

0

0.5

Sag magnitude

1

Fig. 4, Injected power for single-phasecontrollers, for load power factor 1.0 (left) and 0.7 (right), for zero phase-angle jump. Solid lines correspond to a sag of type D, dashed lines to a sag of type C.

Fig.4 gives the results for zero impedance angle. For unity power factor the five curves combine to three curves and the injected power is roughly proportional to the drop in voltage. For 0.7 lagging power factor five different curves appear. The sag magnitude is no longer a good indication for the injected power. For some sags the controller even needs to absorb active power. Also note that the worst case is no longer for a zero-magnitude sag, and that the injected power may exceed the active power taken by the load. A non-zero impedance angle, Fig& gives more or less the same result.

that the equipment without controller is able to operate for a certain range of magnitude and phase-angle. The effect of the series-voltage controller is that this range is enlarged by an amount equal to the maximum voltage that can be injected. Note that the injected voltage is limited in magnitude, but not in phase angle. In Fig. 6, a hypothetical range of complex sag voltages is plotted. The actual range needs to be determined beforehand for the specific supply, or some general range needs to be used. Part of this range is not covered by the controller in combination with the load. For these sags the equipment will still trip, despite the series controller. Note that it is assumed in Fig. 6 that all sags are of equal duration. This is obviously not correct. For a correct analysis a three-dimensional voltage-tolerance plane is needed. This is considered outside of the scope of this paper, but is clearly something which needs to be addressed in the future. voltage tolerance of

,*'

j

equipment

,

areanot protected

:

i

range of

possible sags

voltage tolerance of equipment +controller

~

------..--*

4.2t 0

.

--.--___ 4 ---._ ---._

0.5

Sag magnitude

Fig. 5, Injected power for single-phasecontrollers, for load power factor 1.0 (left) and 0.7 (right), for an impedance angle equal to -30". Solid lines correspond to a sag of type D, dashed lines to a sag of type C.

Fig. 6, protected part of the complex voltage plane, for a given Qoltagerating of the controller.

I l l . VOLTAGE RATINGS, VOLTAGE TOLERANCE

B.

The voltage injected by the series controller is not equal to the drop in voltage magnitude, but to the complex difference between the system-side voltage and the load-side voltage. For a sag with zero phase-angle jump this is still equal to the drop in voltage magnitude. This problem has been discussed in several other publications [1,2,3]. By using a voltage rating 0-7803-5935-6/00/$10.00 (c) 2000 IEEE

Voltage tolerance: magnitude and duration

The more classical voltage-tolerance curve is shown in Fig. 7. Magnitude of the sag is plotted against the duration of the sag. The voltage-tolerance curve divides the sags into those that lead to mal-operation of the equipment and those that do not. The voltage-tolerance curve for many devices has a rectangular shape as indicated by the dashed line in the figure

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obtain the active power from a shunt controller. The result is that the sag duration no longer affects the voltage-tolerance of the load-controller combination. Each sag with a remaining voltage above a certain minimum value will be tolerated. One of the criteria to obtain the minimum voltage is according to Fig. 6. The voltage rating of the series controller should be sufficient to bring the voltage on load-side of the controller within the voltage-tolerance of the load. The second criterion is that the current through the shunt controller should not exceed its rating.

[8]. The voltage-tolerance curve of the combination of controller and load, depends on the way in which the controller obtains the energy needed to -inject the reactive power.

It is assumed that the shunt controller takes a current in phase with the system voltage during the sag:

-

Ishunt

= Ishunt COSY + .ilshunt sin w

9

(24)

so that the active power taken from the supply is maximal: 0.2&hunt

"0

2

4

6

Duration in seconds

8

If the controller is equipped with an energy reservoir, there will be a maximum duration for which the deepest sag can be compensated. The deepest sag is here defined as the lowest during-sag voltage for which the equipment to be protected will not trip. This duration can easily be calculated from the expressions derived before. For simplicity the zero-phaseangle-jump case is considered here. From (10) we find the energy needed to ride through a sag of magnitude V and duration T:

= (1 -

vo )TOpl,Cld -

(21)

(22)

The minimum sag magnitude for a given sag duration T is found from combining (21) and (22), leading to the following expression for the voltage-tolerancecurve: T v = l - ( l - v o )A T This is the curve from the design point to the right in Fig. 7. The voltage-tolerance curve of the load-controller combination obtains its final shape by realizing that any sag tolerated without controller can also be tolerated with controller. The area between the curves is the gain in voltage tolerance due to the controller.

i -3

6

2

OO 1

Fig. 8, current requirements for a shunt-series controller, impedance angle 60". Load power factor equal to 1.0 (solid), 0.9 (dashed), 0.8(dash-dotted), 0.7 (dashed).

IV. CURRENT RATINGS

It was assumed in the derivation of Fig. 7, that the controller has a limited energy reservoir. However, some suggested designs only have a very small energy reservoir but instead 0-7803-5935-6/00/$10.00 (c) 2000 IEEE

(25)

This current is plotted in Fig. 8, as a function of the characteristic magnitude, for an impedance angle equal to -60", and four different values of the load power factor. The effect of the load power factor is relatively small, as the behavior is dominated by the first term in (26). For a given current rating of the shunt controller, the minimum remaining voltage can be calculated. For a proper design, this minimum remaining voltage should be similar to the minimum remaining voltage obtained from the voltage rating of the series controller.

Let (T0,Vo) be the design point as indicated in Fig. 7, so that the total stored energy is: 4nax

.

The shunt current can be calculated by setting the shunt power equal to the power injected by the series controller. For three-phase faults and three-phase controllers we get:

10

Fig. 7, protected part of the magnitude-duration plane, with (solid line) and without (dashed line) series controller.

E=(I-V)TP,,,.

= V1shunt

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V. CONCLUSIONS

Vi. REFERENCES

It is shown that the active power requirements of a series voltage controller depend on magnitude and phase-angle jump of the sag as well as on the power factor of the load. The general trend is that the injected power increases with decreasing sag magnitude. A negative phase-angle jump with a lagging load power factor reduces the injected power.

[I] N.H. Woodley, L. Morgan, A. Sundaram, Experience with an inverterbased dynamic voltage restorer, IEEE Transactions on Power Delivery, Vo1.14,NO.3, July 1999,pp.1181-1186. [2] S,W. Middlekauf, E.R. Collins, System and customer impact: considerations for series custom power devices, IEEE Transactions on Power Delivery, Vo1.13, No. 1, January 1998, pp.278-282. [3] M.H.J. Bollen, Understanding power quality problems: voltage sags and interruptions, New York, IEEE Press, 1999 [4] IEEE Recommended practice for the design of reliable industrial and commercial power systems, IEEE Std.493-1997. Chapter 9: Voltage sag analysis. [5] M.H.J. Bollen, Characterization of voltage sags experienced by threephase adjustable-speed drives, IEEE Transactions on Power Delivery, Vo1.12, No.4, October 1997, pp.1666-1671. [6] L.D. Zhang, M.H.J. Bollen, A method for characterizing unbalanced dips (sags) with symmetrical components, Power Engineering Review, Vol. 18, N0.7, July 1998, pp.50-52. [7] L.D. Zhang, M.H.J. Bollen, Characteristics of voltage dips (sags) in power systems, IEEE Int. Conf. On Harmonics and Quality of Power (ICHQP), October 1998, Athens, Greece.

It is shown that the active power requirement for a threephase controller only depends on the positive-sequence voltage. For unbalanced sags, the injected power is half the injected power during a balanced sag with the same characteristic magnitude and phase-angle jump. For single-phase controllers, the sag magnitude is no longer a good indication of the injected power. For low load power factor, the worst case occurs for a magnitude around 50% of nominal. For some shallow sags the controller has to be able to absorb active power.

VII. BIOGRAPHY It is shown that the voltage tolerance of the load-controller combination depends on the voltage rating and the amount of stored energy of the controller. For combined shunt-series controllers also the current rating of the shunt controller affects the voltage tolerance.

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Math Bollen (M’94, SM’96) is an associate professor in the department of electric power engineering, Chalmers university of Technology, Gothenburg, Sweden. He obtained the M.Sc. and Ph.D. degrees from Eindhoven University of Technology in The Netherlands. Before joining Chalmers in 1996 he was research associate in Eindhoven and lecturer in UMIST, Manchester, UK. His research interest includes power system reliability and various aspects of power quality. Math is co-chair of the IEEE-IAS power system reliability subcommittee.

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