Power System Transient Recovery Voltages
6.2 THE TRANSIENT RECOVERY VOLTAGE FOR DIFFERENT TYPES OF FAULTS
The TRV, which stresses the circuit breaker after current interruption, depends on the type of fault, the location of the fault and the type of circuit switched. To determine the TRV after current interruption, we can make use of the superposition principle: when an identical current of opposite polarity is superimposed on the short-circuit current, the original short-circuit current is interrupted. The TRV can be determined by injecting a corresponding current across the opening breaker poles in the network in which the voltage sources are short-circuited and the current sources, if any, are removed. Figure 6.4 shows the three-phase-to-ground fault supplied from a delta-wye transformer. This fault has already been introduced in Chapter 2, The Transient Analysis of Three Phase Power Systems, where the neutral of the supply was grounded via an impedance and the three-phase-to-ground fault was treated with fault impedance Zf and Zg. The connection of the sequence networks in Figure 6.4b resembles Figure 2.9 with Zf= Zg= 0.
The steady-state voltage on the fault side of the first opening pole of the breaker is zero, whereas on the supply side, the value of the steady-state voltage is 1.0 per unit. In other words, the first-pole-to-clear factor is 1.0 because the grounded supply and the three phase grounded fault make it a symmetrical system. The supplying transformer is not only a pure short-circuit reactance but also has a capacitance between the windings and a
THE TRANSIENT RECOVERY VOLTAGE FOR DIFFERENT TYPES OF FAULTS117
Figure 6.4 The TRV for a three-phase-to-ground fault: (a) one-line system representation;
(b) connection of the sequence networks; (c) transient network; (d) system voltages
capacitance to ground. This distributed capacitance can be represented as a lumped capacitance as shown in Figure 6.4c. Further, it is assumed that the supplying synchronous generators are electrically far away, and the influence of the sequence impedance of the generators on the sequence networks can be neglected. When the three breaker poles are still arcing, the voltages on both sides of the breaker are equal to zero. Immediately after the first pole clears the current, Vl remains equal to zero but Vs increases to E, which is 1.0 per unit. With no damping in the circuit, Vs would reach a peak value of 2.0 per unit, because the transient voltage oscillation is a (1-cosine) waveform as illustrated in Chapter 1, Basic Concepts and Simple Switching Transients, but with damping (which is always present in a practical situation due to iron and copper losses), the peak voltage would be somewhat less than 2.0 per unit. A typical value is a peak value of 1.8 per unit. The frequency of the transient voltage
oscillation is a function of the inductance and the lumped capacitance of the transformer.
Figure 6.5 shows a similar calculation for an ungrounded three-phase fault. When the first-pole-to-clear has interrupted the current, the three-phase system is not symmetrical anymore. At the supply side of the breaker, the voltage is 1.0 per unit, but at the fault side, the voltage is−0.5 per unit (see Chapter 2, The Transient Analysis of Three-Phase Power Systems).
Vs starts at zero and oscillates around E, with a frequency determined by the transformer inductance and capacitance and would reach without damping a peak value of 2.0 per unit. Vl at the load side of the breaker starts at zero and oscillates around−0.5 per unit at the same frequency.
G (a)
(b)
(c)
(d)
Three-phase ungrounded fault
E
s l
Z1
s l
Z2
s l
Z0
E
E
0.5E Lt
Ct Vs
Vs
Vs and Vl
Vl
Vl +
−
Vl1 =Vl2 = 0 Vl0 = −0.5E Vl = −0.5E
Vs1 =Vs2 = 0.5E Vs0 = 0 Vs = 1.0E
Figure 6.5 The TRV for a three-phase-ungrounded fault: (a) one-line system representa-tion; (b) connection of the sequence networks; (c) transient network; (d) system voltages
REFERENCES 119
The TRV across the breaker terminals is Vs− Vl and reaches, with no damping, a peak value of 3.0 per unit.
If the neutral of the supply transformer in Figure 6.4a is ungrounded, the zero-sequence source circuit is open, so that Vs1, Vs2, and Vs0 in Figure 6.4b are all equal to 0.5 E. The steady-state value of the voltage at the supply side of the circuit breaker is in that case 1.5 per unit. The value of the steady-state voltage at the fault side of the breaker is zero and so the voltage across the breaker terminals is again 1.5 per unit, and the TRV again an oscillatory wave with a peak vale of 3.0 per unit assuming no damping. Thus a three-phase grounded fault in an ungrounded system results in the same TRV as a three-phase ungrounded fault in a grounded system. In both situations, the first-pole-to-clear factor is 1.5.
These circuits, in which the fault current is supplied from a single source, show the basics behind the TRV oscillations and the influence of system grounding. The circuit layout is rather simple, but in practice (especially at the higher system voltages), the configuration is more complex. The source of the fault current is not only a local transformer but a considerable part of the current is supplied from other sources further away over transmission lines. This results, after interruption of the fault current, in a TRV, which is composed of a local oscillation from the lumped transformer inductance and capacitance, and from reflecting and refracting travelling waves from the transmission lines. (See Section 3.7, The Origin of Transient Recovery voltages.) In practice, the waveshape is therefore different for each fault situation and can have, in some cases, a rather unpredictable shape.
The testing standards can obviously not cope with this and therefore TRV waveforms are standardised with two-parameter and four-parameter envelopes.
6.3 REFERENCES
6.1 Park, R. H. and Skeats, W. F., ‘‘Circuit breaker recovery voltages, Magnitudes and Rates of Rise’’, Trans. A.I.E.E., 204–239 (1931).
6.2 Catenacci, G., ‘‘Le frequenze proprie della rete Edison ad A.T.,’’
L’Elettrotrechnica XLIII(3), (1956).
6.3 Pouard, M., ‘‘Nouvelles notions sur les vitesses de r´etablissement de la tension aux bornes de disjoncteurs `a haute tension,’’ Bulletin de la Soci´et´e Fran¸caise des Electriciens, 7th series VIII(95), 748–764 (1958).
6.4 von Hochrainer, A., ‘‘Das Vier-Parameter-Verfahren zur Kennzeichnung der Einschwingspannung in Netzen’’ ETZ 78(Part 19), 689–693 (1957).
6.5 Baltensperger, P., ‘‘D´efinition de la tension transitoire de r´etablissement aux bornes d’un disjoncteur par quatre param`etres, possibilit´es des stations d’essais de court-circuit,’’ Bulletin de l’Association Suisse des Electriciens 3, (1960).
6.6 Ozaki, Y., ‘‘Switching surges on high-voltage systems,’’ Central Research Ins-titute of Electric Power Industry, Tokyo, Japan, 1994.
6.7 Catenacci, G., Paris, L., Couvreux, J. P., and Pouard, M., ‘‘Transient recovery voltages in French and Italian high-voltage networks,’’ IEEE, PAS 1986(11), 1420–1431 (1967).
6.8 Barret, J. P., ‘‘D´eveloppements r´ecents des m´ethodes d’´etude des tensions tran-sistoires de manoeuvre sur les r´eseaux `a haute tension, ’’ Revue g´en´erale de l’´electricit´e, 441–470 (1965).
6.9 Braun, A. et al., ‘‘Characteristic values of the transient recovery voltage for different types of short circuits in an extensive 420 KV system,’’ ETZ-A, 97, 489–493 (1976).
6.10 Novotry, V. et al., ‘‘Transient recovery voltages in medium-voltage networks,’’
Electra 88, 49–88 (1983).
6.11 Parrot, P. G., ‘‘A review of transformer TRV conditions,’’ Electra 102, 87–118 (1985).
6.12 Bonfanti, I. et al., ‘‘Transient recovery voltages in medium-voltage networks,’’
Electra 181, 139–151 (1998).
Transients in Power Systems Lou van der Sluis Copyright 2001 John Wiley & Sons Ltd ISBNs: 0-471-48639-6 (Hardback); 0-470-84618-6 (Electronic)