Harmonics and Transient Overvoltages Due to Capacitor Switching
Overvoltages During Line Dropping of Compensated Lines
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[email protected] Overvoltages During Line Dropping of Compensated Lines M Owen Beca Pty Ltd Australia SUMMARY This paper addresses the Temporary Overvoltages (TOV) that occur when a long unloaded compensated line is dropped. This topic has been raised in previous Cigré publications [1] although to date a complete analysis has not been presented. The current work was initiated following the study of a long 220kV AC cable circuit of length in the order of 100km. Traditionally HVAC cables have only been applied over relatively short distances. Application of AC cable circuits in the range of 100km is relatively new application of the technology. During the EMTP study work, line side step increases in voltage, and low frequency resonance were noticed upon disconnection of the compensated unloaded circuit. An out-of-phase voltage condition was observed across the circuit breaker contacts due to the difference in system frequency applied at the source side and the resonant frequency determined by the line capacitance components and shunt reactor inductance. The shunt reactor was linear due to its gapped core and lacked mutual coupling between phases due to its five limbed core construction. Previous work [2] examined the phenomenon in respect of overhead lines and concluded, based upon a limited amount of analysis, that the overvoltage is restricted only to the case of non-transposed circuits. This paper has now extended that work using the Clarke component method which is appropriate for transient study. It is shown that the effect can occur on perfectly transposed lines, and that the non- simultaneous interruption of the current is a contributing factor to the effect. The analysis considers a simple lumped model of the basic circuit. Similarity in the results observed between the simple model and EMTP simulations of distributed line models give confidence in accuracy of the latter. The paper concludes that careful attention be paid to the out-of-phase power frequency recovery voltage of the circuit breaker where such resonant overvoltages may potentially arise. It considers the IEC standard for High Voltage AC Circuit Breakers [3] which states that ‘for out-of-phase breaking tests, the power frequency recovery voltage shall be 2.0/√3 times the rated voltage for solidly earthed neutral systems and 2.5/√3 times the rated voltage for other systems’. The standard also requires that the power frequency recovery voltage be withstood during test for a period of at least 0.3s. In solidly earthed systems which are prevalent at EHV system voltages, it is shown that the IEC test limits may be exceeded. KEYWORDS Temporary Overvoltage, Compensation, Out-of-Phase breaking, Recovery Voltage, EMTP 21, rue d’Artois, F-75008 PARIS C4-105 CIGRE 2012 http : //www.cigre.org
description
Overvoltages During Line Dropping of Compensated Lines
Transcript of Overvoltages During Line Dropping of Compensated Lines
Overvoltages During Line Dropping of Compensated Lines
M Owen Beca Pty Ltd
Australia SUMMARY This paper addresses the Temporary Overvoltages (TOV) that occur when a long unloaded compensated line is dropped. This topic has been raised in previous Cigré publications [1] although to date a complete analysis has not been presented. The current work was initiated following the study of a long 220kV AC cable circuit of length in the order of 100km. Traditionally HVAC cables have only been applied over relatively short distances. Application of AC cable circuits in the range of 100km is relatively new application of the technology. During the EMTP study work, line side step increases in voltage, and low frequency resonance were noticed upon disconnection of the compensated unloaded circuit. An out-of-phase voltage condition was observed across the circuit breaker contacts due to the difference in system frequency applied at the source side and the resonant frequency determined by the line capacitance components and shunt reactor inductance. The shunt reactor was linear due to its gapped core and lacked mutual coupling between phases due to its five limbed core construction. Previous work [2] examined the phenomenon in respect of overhead lines and concluded, based upon a limited amount of analysis, that the overvoltage is restricted only to the case of non-transposed circuits. This paper has now extended that work using the Clarke component method which is appropriate for transient study. It is shown that the effect can occur on perfectly transposed lines, and that the non-simultaneous interruption of the current is a contributing factor to the effect. The analysis considers a simple lumped model of the basic circuit. Similarity in the results observed between the simple model and EMTP simulations of distributed line models give confidence in accuracy of the latter. The paper concludes that careful attention be paid to the out-of-phase power frequency recovery voltage of the circuit breaker where such resonant overvoltages may potentially arise. It considers the IEC standard for High Voltage AC Circuit Breakers [3] which states that ‘for out-of-phase breaking tests, the power frequency recovery voltage shall be 2.0/√3 times the rated voltage for solidly earthed neutral systems and 2.5/√3 times the rated voltage for other systems’. The standard also requires that the power frequency recovery voltage be withstood during test for a period of at least 0.3s. In solidly earthed systems which are prevalent at EHV system voltages, it is shown that the IEC test limits may be exceeded. KEYWORDS Temporary Overvoltage, Compensation, Out-of-Phase breaking, Recovery Voltage, EMTP
21, rue d’Artois, F-75008 PARIS C4-105 CIGRE 2012 http : //www.cigre.org
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CONFIGURATION
There are instances where large loads are supplied via a long distance circuits. The conventional supply may be via an HVAC line, either overhead or underground cable. In order to facilitate the connection application, it is common for Network Service Providers to prescribe limits at the connection point on operating variables such power factor, voltage etc.. Reactive compensation is conventionally provided to meet those requirements. The limits imposed for Mvar import / export can result in requirements for high percentages of reactive compensation, which in turn can lead to missing current zeros when the line is energized. Figure 2 below demonstrates typical transients that can occur when a compensated line is energized. Standard interrupting tests are not performed on circuit breakers with such high levels of DC offsets. Because the circuit breaker may be called upon by protection to interrupt directly following line energization, some utilities [4] either adopt countermeasures or apply circuit breakers that have been subject to DC interruption tests [5]. One solution is to install two or more smaller reactors that are switched to match the circuit load. Compensation may be applied as a set of two of three 30% switched reactors.
(a) 90% compensated (b) 60% compensated Figure 2. Line entry currents – unloaded line
This paper reports on resonance effects noticed during ATP-EMTP simulation studies for de-energization of a compensated unloaded line. A reactor with a five limb core was chosen to align with an existing installation, and to avoid the resonance effect, reported by others [6], due to mutual coupling between the reactor phases. MODELLING The elementary circuit is shown below in Figure 1. This model is used to facilitate understanding, and provides a lumped circuit which may be constructed in ATP-EMTP to exhibit the basic phenomenon. A distributed parameter model similar to an existing circuit was also built to demonstrate that the same effects also occur on a realistic model.
Other authors [2] have analyzed this basic circuit using Clarke components and reported that upon circuit de-energization, high voltages occur due to resonance effects on untransposed lines. That analysis is extended in this paper to show that high resonant voltages can also occur on perfectly transposed lines for non-simultaneous interruption between phases. An overview of the Clarke method is included in the Appendix. Full derivation of the Clarke equivalent network is reported in a separate text [7]. In Figures 1a and 1b, the overhead line or underground cable circuit are modeled as a set of lumped capacitors, with the circuit breaker pole opening shown by the switch sequence 1, 2 and 3. Figure 1d shows the Clarke equivalent network for the circuit, again with the corresponding circuit breaker pole opening shown by the switches 1, 2 and 3.
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o Cs = 1.1 nF·km-1, Cg = 7.7 nF·km-1. o Lr = 6.2 H (30% compensation @ 500km), reactor X/R ratio = 200.
Compensated cable lumped capacitance model.
o Cs = 6 µF·km-1, Cc = 1.43, µF·km-1, Cg = 12 µF·km-1. o Lr = 2500 mH (30% compensation @ 100km), reactor X/R ratio = 200.
Compensated distributed parameter cable model based upon manufacturer’s data:
o Total length 100 km, compensation at mid-way point. o Fully cross bonded - minor section lengths 1.667 km. o Sheaths solidly bonded together and to earth at major sections with earth resistance 50Ω. o Copper conductor radius 13.45 mm. o Aluminum sheath inner radius 44.83 mm. o Aluminum sheath outer radius 45.50 mm. o Serving radius 47.00 mm. o Trefoil formation, distance between conductor centers 51.00 mm. o Cs = 6 µF·km-1, Cc = 1.43 µF·km-1, Cg = 12 µF·km-1.
- permittivity adjusted to suit [8]. o Lr = 2500 mH (30% compensation @ 100km), reactor X/R ratio = 200.
Lines unloaded.
Solidly earthed neutral system. The circuit breaker pole span upon opening is a parameter reported [9] to contribute to overvoltage upon de-energization. For the current work, a maximum value of 4ms was assumed, although for modern well maintained equipment a value less than 2ms is expected. In all simulations, the current chopping level was set to 1A. RESULTS The results plotted in Figures 2 to 21 demonstrate various combinations of parameters for:
500 km overhead line lumped capacitance model 100 km lumped capacitance cable model 100 km distributed parameter cable model
In each case the results for compensation levels of 60% and 30% are recorded. Results are obtained for switch opening pole spans at 0ms and 4ms. On the power frequency recovery voltage plots, lines are drawn to match the power frequency recovery voltage test limits of the IEC standard for High Voltage AC Circuit Breakers [3]. The limits are drawn for a 245 kV system and are ±400 kV for solidly earthed neutral systems, and ±500 kV for other systems. During testing, the circuit breaker is expected to withstand the power frequency recovery voltage for 0.3s. It is immediately apparent from the results, that on occasions following interruption, the line side voltages at the circuit breaker exhibit an oscillation that display a beat characteristic with peak voltages that exceed the nominal value. This reflects onto the power frequency recovery voltage across the circuit breaker, and test limits are exceeded within the 0.3s period. The effect is more noticeable when the pole span is 4ms.
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Inspection of the Clarke network in Figure 1 shows that the resonant frequency of the α and β circuits are the same (cable and overhead line 27.2 Hz, at 30% compensation ), however the resonant frequency of the γ circuit is different (cable – 28.1 Hz, overhead line – 14.6 Hz, at 30% compensation). When the γ circuit is introduced into the network by operation of switch 1, currents and voltages exhibit a resultant beat due to the difference in the α, β and γ frequencies. If however, all switch currents were to chop current concurrently (Figure 21), the γ circuit never receives any excitation, and the beat in frequency is not expected. Two current interrupting patterns are observed, one in which two of the slopes at interruption are of the same sign, with one different (e.g. Figure 5a), and each interruption is separated by 3.33ms; and the other in which the slopes at interruption are all the same sign (e.g. Figures 2a), and each interruption is separated by 6.66ms. The latter case is associated with a pole span of 4ms. A slight interference on the second and third phases of the interrupting current is also observed. Suppression of the peak of the second phase current to interrupt may be seen in Figure 2a, and careful measurement shows that current zero of the last phase to interrupt is slightly extended over the normal power frequency value. This effect is anticipated due to evolving nature of the circuit. For similar current interruption patterns, similar power frequency recovery voltages are observed. The Figures also show the Clarke component currents flowing into the reactor, and voltages across the cable entry point respectively. The reason for the high voltage becomes clear when it is observed that the γ component slowly shifts its phase relative to the α and β components. At some point, it is in anti-phase to the others. Application of the inverse Clarke transform via equation A.6 demonstrates that differences in the signs of the instantaneous Clarke component voltages can result in high voltages in the phase components. The results with a 4ms pole span generally exhibit more severe power frequency recovery voltages than those with a 0ms pole span. This is expected, since inspection of Figure 1a shows that the the γ circuit will experience a longer period of excitation due to a greater duration between the operation of switches 1, 2 and 3. Comparison of the results at 30% and 60% compensation show a tendency for higher recovery voltages at lower levels of compensation. This may be attributed to the magnitude of current flowing prior to the interruption. The higher the initial current the higher are the voltages developed in the equivalent Clarke network (Figure 1d) following switch operation, and consequently the recovery voltage is more severe. The effect of increased resistance to earth at the first major section bonding point is shown in Figure 17. The sheath voltage measured for the default study parameter of 50Ω for resistance to earth is compared to the voltage obtained with a 1Ω value. As might be expected, the sheath voltage is higher by an order of magnitude with the higher earth resistance. The other results for that case, recorded in Figures 14 to 16 remain substantially the same.
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500km 220kV lumped capacitance overhead line model, pole span 4ms
(a)Breaker currents
- scale ticks 50A (b) Breaker power frequency recovery voltage
- scale ticks 200kV (c) Phase voltages at cable entry
- scale ticks 62.5kV Figure 2. 500km 220kV overhead line (unloaded) - 60% compensated lumped capacitor model. Pole span = 4 ms
(a)Breaker currents - scale ticks 100A
(b) Breaker power frequency recovery voltage - scale ticks 200kV
(c) Phase voltages at cable entry - scale ticks 87.5kV
Figure 3. 500km 220kV overhead line (unloaded) - 30% compensated lumped capacitor model. Pole span = 4 ms
(a) Reactor currents - scale ticks 125A – γ component, – α component, ∆ – β component
(b) Sequence voltages at cable entry - scale ticks 125kV – γ component, – α component, ∆ – β component
Figure 4. 500km 220kV overhead line (unloaded) - 30% compensated lumped capacitor model. Pole span = 4 ms
500km 220kV lumped capacitance overhead line model, pole span 0ms
(a)Breaker currents
- scale ticks 50A (b) Breaker power frequency recovery voltage
- scale ticks 125kV (c) Phase voltages at cable entry
- scale ticks 62.5kV Figure 5. 500km 220kV overhead line (unloaded) - 60% compensated lumped capacitor model. Pole span = 0 ms
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(a)Breaker currents - scale ticks 100A
(b) Breaker power frequency recovery voltage - scale ticks 200kV
(c) Phase voltages at cable entry - scale ticks 100kV
Figure 6. 500km 220kV overhead line (unloaded) - 30% compensated lumped capacitor model. Pole span = 0 ms
(a) Reactor currents - scale ticks 100A – γ component, – α component, ∆ – β component
(b) Sequence voltages at cable entry - scale ticks 125kV – γ component, – α component, ∆ – β component
Figure 7. 500km 220kV overhead line (unloaded) - 30% compensated lumped capacitor model. Pole span = 0 ms
100km 220kV lumped capacitance cable model, pole span 4ms
(a)Breaker currents - scale ticks 100A
(b) Breaker power frequency recovery voltage - scale ticks 125kV
(c) Phase voltages at cable entry - scale ticks 62.5kV
Figure 8. 100km cable (unloaded) – 60% compensated, lumped capacitance cable model. Pole span = 4ms
(a)Breaker currents - scale ticks 200A
(b) Breaker power frequency recovery voltage - scale ticks 125kV
(c) Phase voltages at cable entry - scale ticks 100kV
Figure 9. 100km cable (unloaded) – 30% compensated, lumped capacitance cable model. Pole span = 4ms
(a) Reactor currents - scale ticks 400A – γ component, – α component, ∆ – β component
(b) Sequence voltages at cable entry - scale ticks 125kV – γ component, – α component, ∆ – β component
Figure 10. 100km cable (unloaded) – 30% compensated, lumped capacitance cable model. Pole span = 4ms
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100km 220kV lumped capacitance cable model, pole span 0ms
(a)Breaker currents - scale ticks 100A
(b) Breaker power frequency recovery voltage - scale ticks 125kV
(c) Phase voltages at cable entry - scale ticks 50kV
Figure 11. 100km cable (unloaded) – 60% compensated, lumped capacitance cable model. Pole span = 0ms
(a)Breaker currents - scale ticks 200A
(b) Breaker power frequency recovery voltage - scale ticks 125kV
(c) Phase voltages at cable entry - scale ticks 50kV
Figure 12. 100km cable (unloaded) – 30% compensated, lumped capacitance cable model. Pole span = 0ms
(a) Reactor currents - scale ticks 175A – γ component, – α component, ∆ – β component
(b) Sequence voltages at cable entry - scale ticks 125kV – γ component, – α component, ∆ – β component
Figure 13. 100km cable (unloaded) – 30% compensated, lumped capacitance cable model. Pole span = 0ms
100km 220kV distributed parameter cable, pole span 4ms
(a)Breaker currents - scale ticks 125A
(b) Breaker power frequency recovery voltage - scale ticks 125kV
(c) Phase voltages at cable entry - scale ticks 62.5kV
Figure 14. 100km cable (unloaded) – 60% compensated, fully cross bonded distributed parameter model. Pole span = 4ms
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(a)Breaker currents - scale ticks 175A
(b) Breaker power frequency recovery voltage - scale ticks 125kV
(c) Phase voltages at cable entry - scale ticks 100kV
Figure 15. 100km cable (unloaded) – 30% compensated, fully cross bonded distributed parameter model. Pole span = 4ms
(a) Reactor currents - scale ticks 150A – γ component, – α component, ∆ – β component
(b) Sequence voltages at cable entry - scale ticks 125kV – γ component, – α component, ∆ – β component
Figure 16. 100km cable (unloaded) – 30% compensated, fully cross bonded distributed parameter model. Pole span = 4ms
Sheath voltages at first joint - scale ticks 2000V Sheath voltages at first joint - scale ticks 150V Resistance to earth at major section joints - 50 ohm Resistance to earth at major section joints - 1 ohm
Figure 17. 100km cable (unloaded) – 30% compensated, fully cross bonded distributed parameter model.
100km 220kV distributed parameter cable, pole span 0ms
(a)Breaker currents - scale ticks 125A
(b) Breaker power frequency recovery voltage - scale ticks 125kV
(c) Phase voltages at cable entry - scale ticks 62.5kV
Figure 18. 100km cable (unloaded) – 60% compensated, fully cross bonded distributed parameter model. Pole span = 0ms
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(a)Breaker currents - scale ticks 175A
(b) Breaker power frequency recovery voltage - scale ticks 125kV
(c) Phase voltages at cable entry - scale ticks 62.5kV
Figure 19. 100km cable (unloaded) – 30% compensated, fully cross bonded distributed parameter model. Pole span = 0ms
(a) Reactor currents - scale ticks 200A – γ component, – α component, ∆ – β component
(b) Sequence voltages at cable entry - scale ticks 125kV – γ component, – α component, ∆ – β component
Figure 20. 100km cable (unloaded) – 30% compensated, fully cross bonded distributed parameter model. Pole span = 0ms
(a)Breaker currents - scale ticks 200A
(b) Breaker power frequency recovery voltage - scale ticks 100kV
(c) Phase voltages at cable entry - scale ticks 50kV
Figure 21. 100km cable (unloaded) – 30% compensated, fully cross bonded distributed parameter model. Simultaneous current chop.
CONCLUSIONS This paper has examined the effects of de-energizing an unloaded compensated line. This corresponds to an “out-of-phase breaking case” [3], due to the sustained resonant voltage at the line side of the circuit breaker following interruption. A simple lumped model of the circuit representing the power frequency recovery voltage has been analyzed to determine the transient currents and voltages. The similarity between the results observed between the simple model and the distributed line model give confidence in the accuracy of the latter. It has been established that high power frequency recovery voltages can occur when relatively low levels (30%) of compensation are employed, however the effects are still occasionally observable even at commonplace (60%) compensation levels. The pole span during circuit breaker opening is shown to have a detrimental effect if it is of sufficient duration to affect the sequence of current interruption between the phases. This is observed to occur above about 4ms. With modern well maintained equipment however, a pole span greater than 2ms is not expected.
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400
*103
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35-200
-150
-100
-50
0
50
100
150
200
*103
11
Circuit breaker test limits for power frequency recovery voltage are specified in the IEC standard for High Voltage AC Circuit Breakers [3]. It states that ‘for out-of-phase breaking tests, the power frequency recovery voltage shall be 2.0/√3 times the rated voltage for solidly earthed neutral systems and 2.5/√3 times the rated voltage for other systems’. The standard also requires that the power frequency recovery voltage be withstood during test for a period of at least 0.3s. This paper has demonstrated that the act of de-energizing an unloaded compensated line may cause those limits to be exceeded. The standard however does include a caveat to say that operation leading to a power-frequency recovery voltage higher than that corresponding to the rated voltage of the circuit-breaker, in particular, at the end of long lines, should be subject to an agreement between manufacturer and user. ACKNOWLEDGMENT The author acknowledges the support of Beca Pty Ltd in the presentation of this paper. BIBLIOGRAPHY [1] Cigré Working Group 33.10, “Temporary Overvoltages: Causes, Effects and Evaluation,”
Paper 33-210, Cigré Conference (1990), Paris. [2] T. F. Garity, J. C. Haahr, L.Knudsen, M. C. Raezer, “Experience with the AEP 765-kV
System. Part-V, Overvoltage and Staged Fault Tests: Analysis”, IEEE Trans. PAS, vol. 92, No. 3, pp. 1074-1084, (1973).
[3] IEC 62271-100: “High voltage switchgear and controlgear”. [4] F. Anan, et. al., “Countermeasures for Substation Equipment Against Various Special
Phenomena in Japan’s Longest (54 km) 66 kV AC Cable Transmission System”, IEEE PES General meeting, vol. 1, pp. 490-495, (2004).
[5] K. Kobayashi, et. al., “Current zero missing phenomena caused by DC current which flows from shunt reactor at the ground fault and its interruption”, Trans. Inst. Electr. Eng. Jpn., vol.127, No.1, pp. 277-283, (2007).
[6] J. Vernieri, J, B. Barbieri, P. Arnea, “Influence of the representation of the distribution transformer core configuration on voltages developed during unbalanced operations”, IPST, (2001).
[7] M. Owen, “Transient Analysis Using Component Transforms”, PEAM, (2011). [8] “Power System Transients - Parameter Determination”, CRC Press (2010). [9] M. Kizilcay, “Switching Overvoltages in a 400-kV Cable System”, PSCC, 2008.
12
APPENDIX CLARKE ANALYSIS The problem under consideration is transient in nature. In this paper Clarke analysis is adopted as the method of analysis due to its validity under instantaneous conditions, and also to avoid the inconvenience of the complex operator associated with the Symmetrical Component method. Both the Symmetrical Component and Clarke transformations are each particular solutions to the eigenvalue problem. The following relationship holds true:
=
(A.1) Where impedance is represented as:
=
2 0 00 00 0
(A.2)
for:
=
(A.3)
The same form is also applicable to capacitance (C), inductance (L) and resistance (R) matrices respectively, and:
= (A.4)
where ( I ) is the unit matrix. The phase (p) components (a, b & c) and Clarke ( ) components (γ, α & β) are represented as:
,
(A.5)
Similarly for , where and are the instantaneous currents and voltages respectively.
The transformations used are:
=
1√2
1 0
1√2
12
√32
1√2
12
√32
(A.6)
or: = (A.7)
=
1√2
1√2
1√2
1 12
12
0 √32
√32
(A.8)
or: = (A.9)
It may be observed from the above equations that the γ component is √3 times the zero sequence value from the Symmetrical Component method. It may also be observed that the Clarke component impedances and Symmetrical Component impedances are equal.
