International Conference on Large High Voltage Electric Systems

112, boulevard Haussmann - 75008 Paris

1988 Session - 28th August - 3rd September

EVALUATION OF METHODS FOR CONTROLLING THE OVERVOLTAGES PRODUCED BY THE ENERGEATION

OF A SHUNT CAPACITOR BANK

R. P. O’LEARY, R. H. HARNER S&C Electric Company

(United States)

ABSTRACT A computer study was performed to evaluate the switching-surge voltages associated with the energiza- tion of shunt capacitor banks. Various methods of controlling these switching-surge voltages are studied and a comparative analysis is made. The methods studied are the use of fixed inductors, pre-insertion (closing) resistors and inductors, and synchronous closing of the switching device. The investigation emphasizes overvoltages generated at a remote, radially fed transformer terminal, rather than the overvoltages produced at the local substation bus. The influence of various system parameters on the overvoltages are evaluated. A pre-insertion inductor is shown to have advantages over other control methods.

KEY WORDS: Switching - overvoltage - shunt capacitor banks - closing impedance - inductors - resistors - synchro- nous closing.

1 .O INTRODUCTION Fixed inductors or pre-insertion (closing) resistors have been applied by the electric utility industry for many years to control switching transients resulting from the energization of shunt capacitor banks. These methods have also been used to control interference in instru- mentation circuits resulting from the inrush currents associated with the energization of back-to-back capacitor banks. The nature of these inrush currents and the overvoltages associated with capacitor switching operations has been studied in the literature (1, 2, 3, 4). The overvoltages produced at a remote radially fed transformer terminal have recently been shown to be of concern (5, 6). As a result, it is believed that the switching-surge voltage-withstand capabilities of power transformers may be inadequate. The emphasis within industry standards has been to ensure an adequate transformer phase-to-ground switching-surge voltage- withstand capability. Phase-to-phase switching-surge voltage-withstand values are not defined in present

* S & C E l e c t r i c Company, 6601 N . Ridge Blvd, Chicago

standards at voltages of 230 kV and below, and perhaps are not adequate at the higher voltages. There has been an increasing interest within the industry to determine under what conditions severe overvoltages might be generated and what means can be used to control these overvoltages.

I t is the intent of this paper to study various switching-surge overvoltage-control methods. The available literature does suggest that the use of pre- insertion resistors is an effective means of controlling these overvoltages (5, 6). Another method suggested is the synchronous closing of the switching device contacts (7, 8, 9). Pre-insertion resistors have been used on both high-voltage switches and circuit breakers. A number of utilities have used fixed inductors, but the objective in these instances has primarily been to control inrush currents associated with energizing back-to-back capacitor banks. Typically the value of these fixed inductors has been on the order of hundreds of mic- rohenries. It has not been recognized that the inductor may also provide a more effective control of switching- surge overvoltages.

Extensive computer studies have been performed to illustrate the comparative performance of the available control methods. The conditions producing the worst- case overvoltages are examined initially, followed by an expanded study to determine the influence of system configurations and various system parameters. The advantages and disadvantages of the various control methods are reviewed and, finally, the design alterna- tives of pre-insertion impedances are summarized.

2.0 GENERAL SYSTEM STUDY The intent of this study is to compare, on a worst-case basis, the overvoltages experienced when energizing a capacitor bank with and without a controlling means. The worst-case method was chosen to most clearly present and promote a fundamental understanding of the overvoltage phenomena. In that worst-case line lengths will not, in all probability, be encountered in

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the field; the switching voltages that will actually appear will very likely be less than those suggested by this study. A simplified computer model, Figure 1, was developed using only the elements necessary to dem- onstrate the overvoltage phenomena. The capacitor- bank size, length of transmission line, and available fault current, as well as the closing sequence of the switch, were all selected to maximize the switching overvoltages at the remote terminal. Phase-to-ground surge arresters were not modeled. Phase-to-ground surge arresters applied at the terminal of a transformer could limit phase-to-ground overvoltages to 2.2 per unit. Even with the use of phase-to-ground surge arresters, phase-to- phase voltage could be as high as 4.4 per unit (5).

(20 kA Available) Capadtor BUS

Transmission Remote Bus

Source Impedance A Source (138 kV)

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Capacitor Bank

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Figure 1. 138 kV system model used lor computer study 01 overvoltages produced by capacltor-bank energizations.

Upon energizing an isolated capacitor bank (a single capacitor bank without other energized capacitor banks on the bus), moderate inrush-current transients and severe voltage transients can be generated. When energizing a capacitor bank with other energized capacitor banks on the bus (back-to-back switching), current transients can be more severe; yet, the voltage transients are mitigated to some extent by the support given the bus voltage by the energized capacitor banks. Since this study is concerned with the generation of overvoltages, the only cases considered are those involving an isolated capacitor bank being energized.

When pre-insertion impedances are used to control inrush currents, there are two transient periods. The first occurs when the capacitor bank is initially energized through the pre-insertion impedance. The second occurs when the pre-insertion impedance is removed from the circuit. The voltage transients associated with the initial energization of a capacitor bank through a pre-insertion impedance are much greater than the voltage transients associated with the shorting out of the pre-insertion impedance. The first voltage transient is driven by full system voltage, while the second transient voltage is driven only by the voltage drop across the pre-insertion impedance, typically on the order of 10% to 40% of full system voltage. The current transients associated with both the initial energization of the capacitor bank and the removal of the pre-insertion impedance can be significant.

If the capacitor bank neutral is grounded in a grounded supply system, all three phases can act independently. Thus, simultaneous closing of two phases should be highly unlikely. It has been observed, however, that with closely coupled phases on a grounded system, the transients experienced when one phase is energized may induce a second phase to prestrike, thereby creating a simultaneous closing of two phases. If the capacitor bank or the supply system is ungrounded, a simultaneous energization of the first two phases will occur. Under the assumption that the first two phases close simultaneously, the overvoltages associated with the simultaneously closing phases are the same for a grounded and an ungrounded capacitor bank. The computer studies for uncontrolled energiza- tion and for energization through pre-insertion impe- dances are applicable to grounded or ungrounded banks. For an energization with synchronous closing, the optimal time for energizing the second phase differs for grounded and ungrounded banks; therefore, both conditions are studied.

Upon energizing a capacitor bank, the voltage at the capacitor-bank bus will undergo a transient oscillation, having a frequency generally on the order of a few hundred Hertz. The frequency of this transient oscil- lation is determined primarily by the system inductance resonating with the capacitance of the bank. Overvol- tages at the remote transformer location are maximized when the transmission line has a length such that the round-trip travel time for a switching surge is equal to the time to peak of the transient oscillation. In the case of the computer model illustrated, the critical length of transmission line is approximately 142 km.

The phase-to-ground overvoltage at the remote terminal will be maximized when the bank is energized slightly before peak system voltage to allow the peak of transient overvoltage to occur at the peak of the supply-system-frequency voltage. In the model, B phase closes just before peak phase-to-ground voltage on B phase.

The switching sequence which results in maximum phase-to-phase overvoltages at the remote terminal requires two phases to close simultaneously at nearly equal and opposite voltages (slightly before the peak of the phase-to-phase voltage between those phases). Simultaneous closing of two phases with opposite polarity ensures that the transient overvoltages occur at the remote terminal simultaneously with opposite polarities, thereby maximizing the voltage difference. In the model, A and C phases close simultaneously with equal, but opposite, phase-to-ground voltages.

When analyzing the case of an uncontrolled ener- gization, an energization through a pre-insertion resistance, or a synchronized closing, the peak overvol- tages are not significantly affected by the system load. This is primarily because the peak overvoltages in these cases are associated with very steeply rising waveforms. The fast-changing transients cannot interact with loads which are located beyond the leakage impedances of transformers. When dealing with a fixed inductor or a pre-insertion inductor, however, the effect of loads becomes significant. Transients generated when ener- gizing a capacitor bank through an inductor generally have moderately rising ramp voltages instead of fast-

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rising step voltages. There is a significant time-to-peak value of these ramp voltages such that some interaction occurs with the loads connected to the system. When comparing pre-insertion inductors to pre-insertion resistors, it is therefore important to appropriately model system load, particularly at the remote terminal.

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2.1 UNCONTROLLED ENERGIZATION (REFERENCE CASE)

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2.1.1 Phase-to-ground overvoltages The phase-to-ground voltages at the capacitor-bank bus during an uncontrolled energization of the capacitor bank are shown in Figure 2. Energization of A and C phases occurs simultaneously with equal and opposite voltages at approximately 18 milliseconds on the time scale. Energization of B phase occurs approximately 3 milliseconds later, just before the peak of B-phase line- to-ground voltage.

Time (ms)

Figure 2. Voltages at the capacitor-bank bus during an uncon- trolled energization.

At the instant of capacitor-bank energization, the bus voltage abruptly falls to zero, since the capacitor bank instantaneously appears as a very low impedance. This abrupt change of voltage injects a step-voltage wave into the transmission lines connected to the capacitor-bank bus. A negative step-voltage wave is transmitted on A phase, while a positive step-voltage wave is transmitted on C phase. After the initial drop to zero voltage, the phase voltages recover in a transient oscillatory fashion. The frequency of this transient is determined by the source inductance and the capacitance of the bank. Damping of this transient is due primarily to the surge impedance of the transmission lines connected to the capacitor-bank bus. Some additional damping may come from system load connected at the capacitor-bank bus. Because this transient is under-damped, the transient voltage overshoots the source voltage. In this case, C phase overshoots more than A phase because C-phase source voltage is increasing during the initial transient, whereas A-phase source voltage is decreasing during the initial transient.

Figure 3 shows an expansion of C-phase voltage at the capacitor-bank bus during the time just before and after capacitor-bank energization. The voltage on C phase at the remote bus is also plotted. A-phase voltage responds in a similar fashion, having an opposite polarity and a somewhat lower magnitude of overvol- tage. The collapse in bus voltage on the C-phase remote

bus occurs approximately 480 microseconds after the collapse of voltage at the capacitor-bank bus; this time delay is the travel time of the step-voltage wave along the 142 km line to the remote bus. Note that the voltage at the remote bus does not simply collapse to zero, but rather swings to the opposite polarity of the bus voltage prior to the collapse. The steeply rising step wave sees the remote bus and transformer as a very high surge impedance. Initially, therefore, the reflection coeffi- cient at the remote bus is very nearly plus LO. A second reflected wave of lesser magnitude but of the same polarity as the incident wave is thus generated. The step change in voltage at the remote bus is the sum of the incident reflected waves, which is very nearly twice the magnitude of the initial wave. The step overvoltage will decay exponentially with a time constant determined by the X/R of the load at the remote bus and the surge impedance of the line.

The second wave is transmitted back to the capacitor- bank bus. Since the surge impedance of the capacitor bank is very small and therefore looks like a short- circuit to such a steeply rising wave, the reflection coefficient is nearly minus 1.0. Thus, a third wave is generated and transmitted to the remote bus. This third wave is of opposite polarity to the original step wave. When the third wave reaches the remote bus, a fourth wave of approximately equal magnitude is generated. The third and fourth waves are the same polarity as the transient voltage on C phase. The first and second waves have been attenuated due to the load at the remote bus. The net result is that the third and fourth waves add to the transient oscillation, thereby yielding an overvoltage to ground of 3.5 per unit [1.0 per unit = ( fi / 4 6 ) rated system voltage].

2.1.2 Phase-to-phase overvoltage A-phase experiences a transient voltage similar to that of C-phase, except for slightly lower magnitudes and an opposite polarity. A-phase line-to-ground voltage approaches 3.0 per unit, but of opposite polarity to C-phase line-to-ground voltage. C-phase to A-phase voltage therefore approaches 6.5 per unit, as shown in Figure 4.

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4 , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- 8 8 16 17 18 19 20 21 22 23

Time (ms)

Figure 4. C-phase-A-phase voltage at the remote bus during an uncontrolled energizatlon.

2.2 ENERGIZATION THROUGH A PRE-INSERTION RESISTOR

2.2.1 Phase-to-ground overvoltage For this study, a 40-ohm pre-insertion resistor is inserted during the energization of the capacitor bank. In this case, bus voltage at the capacitor bank does not collapse to zero. The extent to which the bus voltage collapses depends upon the ratio of the resistance of the pre-insertion resistor to the resultant surge impe- dance of the transmission lines connected to the capacitor-bank bus. Three transmission lines of approx- imately 380 ohms each are connected in the bus, yielding an effective surge impedance of 125 ohms. The capac- itor-bank bus voltage drops to a value determined by the ratio of 40 ohms to the sum of 125 ohms plus 40 ohms, or approximately 25% of the system voltage at the time of energization. This reduction in the collapse of bus voltage manifests itself as a reduction in the step- voltage wave injected into the system. As shown in Figure 5, the pre-insertion resistor results in the capacitor-bank transient oscillation being nearly critically damped, so that very little overswing of the capac itor-bank voltage occurs.

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Time (ms)

Figure 5. Voltages at the capacitor-bank bus when energizing through a 40 ohm pre-insertion resistor.

During the transient period, there are small discon- tinuities in the bus voltage at the capacitor bank. These discontinuities occur because traveling waves returning from the remote bus will see the 4O-ohm pre-insertion resistor rather than the very low surge impedance of the capacitor bank. The reflection coefficient at this bus is approximately minus 0.8, resulting in less-than- perfect cancellation of the incident wave.

With the pre-insertion resistor, the initial collapse of voltage at the remote bus, Figure 6, transmits a step

wave of approximately 75% of the magnitude of the reference case, Figure 3, for an uncontrolled energi- zation. This results in a voltage doubling at the remote bus of a smaller wave and therefore the extent to which the voltage collapses to an opposite polarity is much smaller. As in the case of an uncontrolled energization, a second wave is generated and transmitted toward the capacitor-bank bus. Upon reaching this bus, the voltage wave is reduced somewhat in magnitude due to the effect of the $0-ohm pre-insertion resistor, and it is also changed in polarity and transmitted as a third wave toward the remote bus. The third wave is again doubled upon reaching the remote bus. It is important to note, however, that with the pre-insertion resistor the initial step wave has been reduced due to the effect of the resistor, and subsequently the third wave has also been reduced. Further, the transient oscillatory voltage has been considerably reduced due to the damping effect of the resistor. The result is that the peak C-phase line- to-ground voltage is reduced to 2.2 per unit, approx- imately 63% of the voltage experienced with an uncon- trolled energization.

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Time (ms)

Figure 6. C-phase line-to-ground voltages when energizing through a 40 ohm pre-insertion resistor.

2.2.2 Phase-to-phase overvoltage The effect of the pre-insertion resistor, as shown in Figure 7, has reduced the phase-to-phase overvoltage by approximately 38%, or from 6.5 per unit to 4.0 per unit.

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Time (ms)

Figure 7. C-phase-A-phase voltage at the remote bus when energizing through a 40 ohm pre-Insertion resistor.

2.3 ENERGIZATION THROUGH A PRE-INSERTION INDUCTOR

2.3.1 Phase-to-ground overvoltage For this analysis, the energization of the capacitor bank

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occurs through a 10-mH pre-insertion inductor. As is the case with the pre-insertion resistor, the extent to which voltage collapses at the capacitor-bank bus is reduced, largely due to the surge impedance of the pre- insertion inductor, Figure 8. In fact, because the inductor has a very high surge impedance relative to the surge impedance of the lines connected .to the bus, there is no abrupt step change in bus voltage. Rather, the voltage initially decays exponentially as determined by an LR circuit comprised of the inductance of the pre-insertion inductor and the surge impedance of the lines connected to the capacitor-bank bus. As in the reference case, the capacitor-bank bus voltage recovers in an oscillatory fashion. Because the initial drop of voltage at the capacitor-bank bus is significantly lower than that of the reference case, the magnitude of the transient oscillation voltage is reduced. Since the pre- insertion inductor has a relatively low resistance, the transient oscillation is not significantly damped as it is with the pre-insertion resistor.

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Time (ms)

Figure 8. Voltages at the capacitor-bank bus when energizing through a 10 mH pre-insertion inductor.

As shown in Figure 9, the capacitor-bank bus voltage does not collapse abruptly, but falls at a moderate rate. Because the bus voltage falls at a moderate rate, a ramp voltage wave is transmitted down the line which, upon reaching the remote bus, does not double. At this lower rate-of-change of voltage, the transformer at the remote bus acts like a high, but not infinite, impedance. Thus, the second voltage wave generated at the remote bus is of a lower magnitude than that for either an uncon- trolled energization or for use of a pre-insertion resistor. Consequently, upon returning to the capacitor-bank

bus, the third voltage wave generated is of a substan- tially lower magnitude. The result is that C-phase line- to-ground voltage at the remote bus is approximately 54% of that for an uncontrolled energization, as compared to 63% for the pre-insertion resistor.

2.3.2 Phase-to-phase overvoltage With the pre-insertion inductor, the phase-to-phase overvoltage, Figure 10, between C and A phases is approximately 3.3 per unit or 51% of that for uncon- trolled energization, as compared to 62% for the pre- insertion resistor.

2 44

-4 16 17 18 19 20 21 22 23

Time (ms)

Figure 10. C-phase-A-phase voltage at the remote bus when energizing through a 10 mH pre-insertion inductor.

2.3.3 Consideration of rates of change of voltage at the transformer terminal There is a significant benefit to the fact that the overvoltages produced by the use of a pre-insertion inductor are characterized by a ramp function rather than a step function as produced by an uncontrolled energization or energization through a pre-insertion resistor. It has been suggested (10) that low-magnitude, steep-rising wave forms, appropriately timed, may cause damaging internal resonances in transformers. Also, for a steeply rising transient voltage wave, the voltage distribution across a transformer winding will be initially determined by stray capacitances rather than the inductance of the winding, creating stress concen- trations in the first several turns of the winding (11). Even without high peak overvoltages, rapid changes in voltage, with their associated stress concentrations, may be harmful to transformers. The lower rate of change of voltage produced by the pre-insertion inductor will allow the voltage to be distributed more evenly across the initial turns of winding of the transformer.

2.4 SYNCHRONOUS CLOSING Synchronous energization of a capacitor bank can be an extremely effective means of controlling overvoltages (7, 8, 9). To accomplish synchronous closing at or near a voltage zero, thereby avoiding high prestrike voltages, it is necessary to apply a switching device which maintains a dielectric strength sufficient to withstand system voltage until its contacts touch.Also, a highly consistent operating mechanism is required. Such ideal closing characteristics may be difficult to attain with present-day high-voltage switches and circuit breakers. Consequently, it has been suggested (9) that, if the switching device has a closing consistency within k 2 milliseconds, overvoltage magnitudes will be limited to acceptable values.

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There is a fundamental difference between grounded and ungrounded systems when applying controlled closing. In a grounded system, closing of each phase should occur at a phase-to-ground voltage zero, assuming an uncharged capacitor bank is being ener- gized. In an ungrounded system, energization of the first phase can occur at random. The second phase should be closed when the phase-to-phase voltage between the second phase and the first phase is zero, which occurs when both phase-to-ground voltages are of the same polarity and have a magnitude of one-half per unit. The third phase is then closed when its phase-to-ground voltage is zero. The optimum time for energizing a capacitor bank, therefore, is different for an ungrounded system than for a grounded system. The overvoltages which result from errors in closing, i.e., not closing at the ideal time, are also fundamentally different for grounded systems and ungrounded systems.

2.4.1 Phase-to-ground overvoltage - grounded banks An ideal closing, as shown in Figure 11, occurs when the phase-to-ground voltages are zero for each phase. Under this condition, there is a slight distortion of the phase voltages at the capacitor-bank bus due to a modest transient current; however, overvoltages are minimal and the rate of change of voltage is also very low. Overvoltages at the remote station are therefore also minimal and consequently have not been illustrated.

Figure 12 is similar to Figure 11, except the closing times of each phase have been delayed by 2 ms, representing a maximum closing tolerance for con-

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Time (ma)

Figure 11. Voltages at the capacitor-bank bus during an ener- gitation of a grounded bank by means of ideal synchronous closing.

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Time (ms)

trolled closing. The voltages shown are similar to those depicted in Figure 2, for an uncontrolled energization; however, there are two major differences. The peak overvoltages shown in Figure 12 are significantly less. Also, there has been no attempt to simulate simultane- ous closing on two phases, which could occur should one phase close early and another phase close late within the 2 ms tolerance.

The peak phase-to-ground voltage at the remote bus, Figure 13, has been reduced from 3.5 per unit to 2.8 per unit, because energization occurred at less than peak phase-to-ground voltage.

2

1

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v

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-4 16 17 18 19 20 21 22 23

Time (ms)

Figure 13. C-phase line-lo-ground voltages during an energiza- tlon of a grounded bank with closing shifted 2 ms from synchronous.

2.4.2 Phase-to-phase overvoltage - grounded banks The peak overvoltage for this case is 3.9 per unit, Figure 14, versus 6.5 per unit for an uncontrolled energization. Most of the reduction in phase-to-phase voltage at the remote terminal has occurred because of the non-simultaneous closing of the two phases.

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Time (ms)

Figure 14. C-phase-A-phase voltage at the remote bus during an energization of a grounded bank with closing shifted 2 ms from synchronous.

Figure 12. Voltages at the capacitor-bank bus during an ener- gitation of 8 grounded bank with closing shifted 2 ms from synchronous.

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2.4.3 Phase-to-ground overvoltage - ungrounded banks In Figure 15, A phase has been closed at a time of approximately 5 ms. C phase closes at approximately 16 ms, or 2 ms after the ideal time for synchronous closing. B phase closes at approximately 20 ms, or 2 ms after its voltage zero. For these assumptions, A phase closes nearly at peak voltage, but unlike the condition of an uncontrolled energization with a grounded bank, the collapse in A-phase voltage occurs only to the point midway between A-phase and C-phase voltages.

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Time (ms)

Figure 15. Voltages at the capacitor-bank bus during an ener- gization 01 an ungrounded bank with closing shifted 2 ms from synchronous.

A-phase line-to-ground voltages have been plotted in Figure 16 because, for the particular switching sequence chosen, A-phase line-to-ground voltages are the highest. Peak overvoltage-to-ground of A phase at the remote bus is 2.7 per unit. Figure 16 closely resembles Figure 3 of the reference case, except for the polarity difference and a slightly smaller transient magnitude.

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-1 x Remote Bus o Capacitor Bus

16 17 18 19 20 21 22 23 lime (ms)

Figure 16. A-phase line-to-ground voltages during an energiza- lion of an ungrounded bank with closing shifted 2 ms from synchronous.

2.4.4 Phase-to-phase overvoltage - ungrounded banks For an ungrounded bank, simultaneous energization of two phases is assured. Because of the simultaneous energization of A and C phases, the step-voltage waves can add at the remote terminal. The net result is a peak phase-to-phase overvoltage of 5.0 per unit, Figure 17, compared to 3.9 per unit for the sequential closing of a grounded bank, as illustrated in Figure 14.

16 17 18 19 20 21 22 23

Time (ms)

Flgure 17. C-phase-A-phase voltage at the remote bus during an energization of an ungrounded bank with closing shifted 2 ms from synchronous.

A closing tolerance of 2 ms, as used in this study, is at the limit of that suggested within the literature (9). It is likely that systems can be developed which on the average will have less than a 2-ms error. Such systems will produce average overvoltages less than those described by this study; however, these systems may not have the capability of consistently controlling overvoltages to as reliable an extent as the use of pre- insertion impedances.

The phase-to-phase overvoltages for all cases studied, as shown in Figures 4, 7, 10, and 17, are consolidated in Figure 18 for a convenient comparison.

16 17 18 19 20 21

Time (ms)

Figure 18. Comparison of phase-to-phase overvoltages deve- loped at a remote radially led transformer using various control means, during the energization of a shunt capacitor bank.

3.0 EXTENSION OF RESULTS TO OTHER SYSTEM CON FIGURATIONS The simplified model shown in Figure 1 was chosen for illustrative purposes to establish in principle the performance of pre-insertion impedances and synchro- nous closing compared to using no controlling means. This circuit was selected to produce worst-case over- voltages. Other system configurations will, of course, produce different results. As an aid in evaluating a given system for the production of overvoltages, a further study was made to illustrate the influence of a variety of system parameters.

Figure 19 shows the relationship between length of line to the remote bus and peak phase-to-phase overvoltage. The criterion for highest overvoltages is met by a transmission line length such that the round- trip travel time on that transmission line will equal the

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time-to-peak of the transient oscillation produced by the recovery of capacitor-bank bus voltage. This ensures that the third wave is generated at the capacitor-bank bus at the peak of the transient oscillation and con- sequently will arrive at the remote bus simultaneously with the peak of the transient oscillation. If the transmission line were half of the length used in this model, then four travel times would have elapsed before the peak. of the transient oscillation occurs at the capacitor-bank bus. Because it is the fifth wave which travels to the remote bus along with the peak of the transient oscillation and not the third wave, the polarity of the step wave is opposite to that of the transient oscillation and therefore subtracts from it. Thus, a 71-km transmission line represents a relative minimum of peak overvoltage versus line length. At a line length of 47 km, the seventh wave is generated at the peak of the transient oscillation and is of a polarity to add to the transient peak. Therefore, at 47 km, a relative maximum of peak overvoltage versus line length occurs. The pattern of relative minima and maxima theoret- ically repeats as the line length is reduced; however, with the extra reflections and the damping which occurs at each reflection, the magnitudes of the maxima are reduced as the line length is reduced. In the limit, as the transmission line length becomes very short, during the time to the peak of the transient oscillation voltage, many reflections can occur and due to the damping at each reflection, the step or ramp part of the transient can be damped to zero. In this situation, use of the inductor will result i n a greater net-peak low-frequency transient voltage than if a pre-insertion resistor is used, due to the fact that the transient oscillation is not significantly damped by the inductor. As an example, refer to Figure 20 in which the transmission line length is reduced to 6.4 km. With pre-insertion impedances the step waves have been attenuated to near zero by the time the transient oscillation reaches a peak. The pre-insertion inductor circuit generates 2.3 per unit overvoltage versus 2.0 per unit for the pre-insertion resistor circuit. Note, however, that the initial step change in voltage for the resistor is substantially greater than that for the inductor. This rapid change of approximately 2.6 per unit voltage, associated with the resistor, may be harmful to the transformer insulation. Note, also, that for an uncontrolled energization, the peak overvoltage is still relatively high at 3.6 per unit, suggesting that even for this relatively mild case, a control means would be desirable.

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1 +a With Pro-inwrtion Inductor l ' " ' l ' ' ~ ~ " ~ ' " ~ ~ ~ ' l ~ ' ' ~ l ' ~ ' ' 0 50 100 150 200 250 300

Line Length (krn)

Figure 19. Effect of line length to remote bus on the phase-to- phase overvoltage at the remote bus for the system of Figure 1.

0

o Energized Through a 10 mH inductor Energized Through o 40 Ohm Red&or -

? '1 1 -

. . . . . . . . . . . . . . . . . . . . . . . 18.0 18.5 19.0 19.5 20.0

Time (rns)

Figure 20. Phase-to-phase voltages at the remote bus with a line length of 6.4 km to remote bus for the system of Figure 1.

w Uncontrolled Energizotion e-+ Wlth Pro-ineartion Reaidor a-a Wlth Pro-ineartion Inductor

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I I I I

Figures 21 and 22 show the relationship of peak phase-to-phase overvoltage to capacitor-bank size, and system available fault current, respectively.

A smaller capacitor bank or higher available fault current at the capacitor-bank bus would result in a higher frequency of the transient oscillation such that the time-to-peak of this transient would be shorter. This shorter time-to-peak would require a shorter transmis- sion line to fit the maximum overvoltage criterion of two travel times equaling the time to reach peak transient overvoltage. Referring to Figure 21, for an uncontrolled energization, there is a relative minimum for a capacitor-bank size of approximately 20 MVAR.

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7 '1 v-v Uncontrolled Energizotion 1 M W ~ h Pro-insertion Resistor

1 e-e With Pro-insertion Inductor 0 20 40 60 80 100 120 140 160 180 200

Capacitor Bank Size (MVAR)

l ' l ' l ' l ' l ' l ' l ' l ' l ~ l '

Figure 21. Effect of capacitor bank size on phase-to-phase overvoltage at the remote bus for the system of Figure 1.

8 I I I I

The reduction in capacitor-bank size has increased the frequency of the transient oscillation to the point where

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it peaks in one-half the time that would elapse with a 75-MVAR capacitor bank. In this case, the third step- voltage wave is generated at a relative minimum of the transient oscillation and is therefore out of phase with that voltage. The same phenomenon can be seen in Figure 22, where a relative minimum of the phase-to- phase overvoltage without pre-insertion impedance will occur at approximately an available fault current of 80 kA.

The effect of additional transmission lines, Figure 23, at the capacitor-bank bus was investigated by utilizing models having no additional lines (only the line to the remote bus), one, two, or six additional lines. Only very moderate changes in the phase-to-phase overvoltage are experienced when adjusting this parameter of the model, particularly when using pre-insertion impedance. The effect of adding lines is to change the parallel-damping characteristic of the resonant LC circuit. When adding a line, the effective damping is increased, but not enough to effect a large change in the peak of the transient oscillation.

-e. 2.0- I . * 1.0-

o.o

8 1 r%

- v-v Uncontrolled Energlzation -++ With Pro-lnsertlon Resistor - M With Pro-lnsertlon Inductor

I - I ' 1 ' 1 ' I ' -

P-v Uncontrolled Energlzotlon

0-0 With Pro-insertion Inductor 0 1 2 3 4 5 6

Number of Lines ot the Copacitor Bus

Figure 23. Effect of the number of transmission lines connected to the capacltor bank bus on the phase-to-phase overvoltage at the remote bus for the system of Figure 1.

Finally, the effect of system load is shown in Figure 24. The overvoltages at the transformer termi- nal, when using a pre-insertion resistor as the control means, are not significantly affected by system load. The load does not significantly add to the damping obtained from the resistor. When using a low-loss device, such as a pre-insertion inductor, or when using no control means, adding load has a substantial effect on the damping of the transient oscillation.

8 . 0 - ~ . I I I . I . , I I

p 5.0

8 3.0 4*o*i

4.0 APPLICATION CONSIDERATIONS FOR

To varying degrees of efficiency, all control methods will limit peak switching-surge voltages, both at the local capacitor-bank station and at a remote, radially fed station. Table I summarizes, on a relative basis, various aspects of the application of these methods. The costs of implementing a control means appear to be of the same order of magnitude, except for fixed inductors. Fixed inductors generally must be designed to carry normal load current, to have a system BIL rating, and to withstand system short-time currents. As a result, the inductors are physically large, relatively expensive, and may require costly mounting structures. Further- more, the fixed inductor losses add to the cost of utilizing the inductor. Because the pre-insertion inductor is only inserted for a few cycles, the normal current, short-time current, and full BIL ratings are not required. As a result, for a given inductance, a pre- insertion inductor may be made much lighter and smaller than a fixed inductor. Because the pre-insertion inductor is so small and lightweight, it can be mounted directly on the switching device, thereby obviating the need for a mounting structure and possibly additional space in the substation. Figures 25 and 26 illustrate the installation of pre-insertion inductors on SF6 high- voltage switches.

Pre-insertion resistors have the advantage of yielding the lowest phase-to-ground voltages at the capacitor- bank station, with moderate phase-to-ground and phase- to-phase voltages at remote, radially fed stations. There are two principal disadvantages associated with pre- insertion resistors. The resistors are not effective in reducing the very high rate of change of voltage associated with the energization of a capacitor bank. Additionally, pre-insertion resistors may have thermal- capability limitations. Typically, pre-insertion resistors absorb large amounts of energy with each energization of a capacitor bank. Depending upon the type of switching device utilized, the energy capability of the resistor can limit the size of the capacitor bank which can be switched, as well as the frequency of switching operations.

Synchronous closing has the potential of being an ideal means of controlling overvoltages and inrush currents associated with energizing capacitor banks. With the constraints of practical switching devices, an ideal synchronized closing of capacitor banks is unat- tainable. Performance of a controlled closing system, operating within an accuracy attainable with present- day technology, will allow a degree of control of overvoltages similar to that obtainable with a pre- insertion resistor, without the thermal disadvantage of the pre-insertion resistor. The main disadvantage of a controlled closing scheme may be its complexity. Since the ideal time to close is different for each of the three phases, the switching device must have three independ- ent closing mechanisms or an accurate mechanical delay between the three poles. The scheme also relies on accurately monitoring voltages, both at the capacitor- bank bus and on the capacitor bank. The requirements for timing electronics and a highly reliable switching device and operating mechanism are formidable. This

VARIOUS OVERVOLTAGE-CONTROL MEANS

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relatively complex systems approach, compared to a relatively simple pre-insertion impedance, suggests that

the reliablility of controlled closing schemes may be less than that for a pre-insertion impedance control means.

Energlzation Overvoltage Local Bus Remote Bus Rate 01 Change ~ Installation

Requirements@ Control Means Phase-Ground Phase-Phase of Voltage

PUO PUO (Rise Time)@

None High (1.6) High (6.5) Very High ( 1 ) -

Estimated Rellablllty@

Relatlve Estlmated

Cor@

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I Fixed Inductor 1 Moderate (1 4) 1 Low (3.3) 1 Low (100) I Difficult I Very High I Good to Excellent I

I Moderate Good to Excellent I Minimal I Low (100) I Moderate (1.4) Low (3.3) Pre-Insertion Inductor

I Moderate Good to Excellent I Minimal I Low (1 1 ) Pre-Insertion Resistor

Closing@ (1 0-1.4) (1.7-5 0 ) (1 -1 000) Moderate Fair to Good Controlled None to High Low to Very High

@ Relarive phase-to-ground or phase-phaae overvoltages and per unir values in parenthese5 based on worst-case computer studies ( 1 PtI = phase-ground peak voltage).

@ @ cxperience.

Estimare of ease of installation of control means.

Esrimare of costs and reliability based on literature and field

0 Relative rare of change of overvoltage and an order of magnitude 0 Range o f in synchronous closing.

are for ideal synchronous to a 2-ms shift of risc times i n microseconds within parentheses.

Pre-insertion .

Pre-insertion

Figure 25. A single 10 mH pre-insertion inductor mounted on each pole of a 115 kV sF6 Circuit-Switcher.

Figure 26. Two 10 mH pre-insertion inductors act in series on a 230 kV sF6 Circuit-Switcher (single-pole illustrated).

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5.0 DESIGN CONSIDERATIONS OF

As indicated in paragraph 2.0, in utilizing pre-insertion impedances, there are two transient periods. Again, the first transient is associated with the initial energization of the capacitor bank through the pre-insertion impe- dance, while the second transient occurs when the switch which bypasses the impedance closes.

Forty-ohm pre-insertion resistors utilized in the computer study have been in service many years on high-voltage switches used to switch shunt capacitor banks. The 40-ohm value for a 138-kV system voltage was chosen to provide optimum control of inrush currents in back-to-back switching. A lower resistance will cause an increase in the inrush current during the first transient period referred to above. An increase in resistance beyond 40 ohms will increase the inrush current during the second transient period. Forty ohms is an optimal value, yielding approximately the same inrush current for both transient periods. Should the emphasis for the use of a pre-insertion resistor be placed solely on the control of overvoltages, disregarding inrush currents, a higher resistance value would be more appropriate.

An inductance of 10 millihenries was chosen for the pre-insertion inductor, such that it would yield approx- imately the same initial inrush current as that for a 40-ohm pre-insertion resistor. Because the impedance of the pre-insertion inductor is significantly lower at supply system frequency, the inrush currents expe- rienced during the second transient period will be significantly lower than the initial inrush currents. There is a possibility that the pre-insertion inductor could be further optimized for both inrush-current control and overvoltage control. Further reductions in inrush currents, as well as overvoltages, could be obtained with a higher inductance pre-insertion inductor; however, higher inductances needed to optimize inrush current and overvoltage control may not be economically feasible.

PRE-INSERTION IMPEDANCES

0

0

6.0 CONCLUSIONS The overvoltages produced at a remote, radially fed transformer terminal, as a result of energizing a shunt capacitor bank, are shown to be of a magnitude that possibly may exceed the phase-to-phase switching-surge voltage-withstand capability of the connected trans- former. Various means of controlling these overvoltages are evaluated and a relative comparison is made. The various control means evaluated are pre-insertion (closing) resistors and inductors, fixed inductors, and a controlled closing of the switching device contacts.

A worst-case computer study is utilized for a com- parative analysis and indicates that, without a control- ling means, the phase-to-phase switching overvoltage may be as high as 6.5 per unit. Under the same worst- case conditions, a pre-insertion resistor will reduce this overvoltage to 4.0 per unit; a fixed inductor or pre- insertion inductor will reduce this overvoltage to 3.3 per unit; and, a synchronized closing of the switching device contacts has a theoretical potential of reducing this voltage to 1.7 per unit. For practical controlled closing systems, however, depending upon the nature of the switching device and the ability to reliably control

the mechanical and electrical closing sequence, the overvoltages may be significant.

Perhaps equally as important as the absolute mag- nitude of the switching overvoltage at the remote transformer terminal is the rise time or rate of change of voltage seen by the transformer. The rise times of the switching surge overvoltages, as produced with no control means, with a pre-insertion resistor, or with a practical controlled closing means, is on the order of microseconds. The rise time for either a fixed inductor or a pre-insertion inductor is on the order of 100 microseconds. A slower rise time or longer time-to-peak voltage will clearly impose a less severe duty on the transformer, since the voltage will be more equally distributed along the winding of the transformer, as compared to that which would occur for a transient having a very short rise time.

This study suggests that either a pre-insertion inductor or a synchronized closing of the switching- device contacts would be preferred as a means of mitigating switching overvoltages. The use of a pre- insertion inductor may be the preferred method, particularly from the standpoint that not only are the peak overvoltages modest, but the rise time of the transients generated are considerably less severe than that which might be generated by using other control means.

6.0 REFERENCES 1. H. M. Pflanz, G. N. Lester - Control of Overvol-

tages on Energizing Capacitor Banks, IEEE Transac- tions on Power Apparatus & Systems, Volume PAS-92, pages 907-915, May/June, 1973.

2. E. W. Boehne, S . S. Low - Shunt Capacitor Energization with Vacuum Interrupters--A Possible Source of Overvoltage, IEEE Transactions on Power Apparatus & Systems, Volume PAS-88, pages 1424- 1443, September, 1969.

3. Sue S. Mikhail, Mark F. McGranaghan - Evalua- tion of Switching Concerns Associated with 345 kV Shunt Capacitor Applications, IEEE Paper 85 SM 401-5, presented at the IEEE Power Engineering Society Meeting, July, 1985.

4. K. L. Spurling, A. E. Poitras, M. F. McGra- naghan, J. H. Shaw - Analysis and Operating Expe- rience for Back-to-Back 115 kV Capacitor Banks, IEEE Paper No. 86 TD 602-7 presented at the IEEE Power Engineering Society Transmission & Distribution Conference & Exposition, September, 1986.

5. Robert A. Jones, Hoke S. Fortson, Jr. - Consid- eration of Phase-to-Phase Surges in the Application of Capacitor Banks, IEEE Transactions Power Delivery, Vol. PWRD-1, No. 3, pages 240-244, July, 1986.

6. L. Lishchyna, R. H. Brierley - Phase-to-Phase Switching Swges Due to Capacitor Energization, Canadian Electrical Association, 1986 Transactions of Engineering & Operations, V25, Part 4, Paper NO. P86-SP- 148.

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7. E. Maury - Synchronous Closing of 525 kV and 765 kV Circuit Breakers: A Means of Reducing Switch- ing Surges on Unloaded Lines, CIGRE #143,1966.

10. R. S. Bayless, J. D. Selman, D. E. Truax, W. E. Reid - Capacitor Switching and Transformer Tran- sients, IEEE Paper 86 SM 419-6, presented at the IEEE Power Engineering Society Meeting, July, 1986.

11. IEEE Guide for Transformer Impulse Tests, IEEE No. 93, June 1968/ANSI (37.37.

8. J. H. Brunke, G. G. Schockelt - Synchronous Energization of Shunt Capacitors at 230 kV, IEEE Paper A78 148-9, presented at the IEEE Power Engineering Society Meeting, January, 1978.

9. R. W. Alexander - Synchronous Closing Control for Shunt Capacitors, IEEE Transactions on Power Apparatus & Systems, Vol. PAS-104, pages 2619-2626, February, 1985.

Excerpt from International on Large High 1988 Session

Voltage Elecfric Sysferns

IMPRIMERII LOUIS JEAN - OSWZ GAP

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