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Double Earth Faults in Power Stations Georg S. Koeppl , Dieter Braun , Member, IEEE, and Martin Lakner
Abstract—Single-phase-to-ground faults in power stations sometimes cause a second phase-to-ground fault in another phase. If the phase-to-ground faults are located on different sides of the generator circuit breaker (CB), one has a double earth fault of a special and so far not analyzed kind with respect to the CB. It may lead to high stresses for the last CB pole to clear. The general expressions for the current, the rate of rise of recovery voltage, and the power frequency recovery voltage across this CB pole have been deduced as function of the sequence values of the short-circuit impedances and surge impedances, respectively. The corresponding results are discussed for typical cases. A detailed case analysis by means of the Electromagnetic Transients Program shows that at rated load, such a double earth fault, produces CB stresses comparable to out-of-phase conditions. A combination of double earth fault and out-of-phase conditions, however, causes a peak value of the transient recovery voltage, which will significantly exceed the values laid down in the standards.
Fig. 1. Synchronous generator—generator CB—step-up transformer—HV system, double earth fault in phases B and C.
Index Terms—Double earth fault, fault current, generator CB, power station, recovery voltage, two-phase fault.
I. INTRODUCTION
E
SPECIALLY in power stations where the connection between the generator and the associated step-up transformer is made by an isolated phase bus duct (IPB), three-phase faults occur very rarely. The most likely faults are single-phase-to-ground faults (earth faults) and out-of-phase conditions. Single-phase-to-ground faults in a system with a high-impedance grounded neutral sometimes cause a second phase-to-ground fault in another phase due to the high transient and stationary line-to-ground voltages in the healthy phases at the occurrence of the first phase-to-ground fault (the probability of this case even grows when the generator is allowed to operate under earth fault conditions for long periods). A generator with its step-up transformer forms such a system: the generator neutral is normally grounded via a high-ohmic resistor or preferably [1], [2] via a Petersen coil or, in general, via high impedance (including an isolated neutral), and the low-voltage (LV) side of the step-up transformer is normally delta connected. Manuscript received April 07, 2014; revised June 23, 2014; accepted August 07, 2014. Paper no. TPWRD-00392-2014. G. S. Koeppl and D. Braun are with Koeppl Power Experts, Wettingen CH-5430, Switzerland (e-mail:
[email protected]). M. Lakner is with the High Voltage Products Division of ABB Switzerland Ltd., Zurich CH-8050, Switzerland (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRD.2014.2350033
Fig. 2. Two systems coupled by the CB, double earth fault in phases B and C, and current through last pole to clear.
If both phase-to-ground faults are located on the same side of the generator circuit breaker (CB), one has, from a CB point of view, a classical two-phase-to-ground fault. The fault currents, the currents through the CB, and the transient recovery voltage (TRV) (which is distributed across two CB poles in series) are well known. This case is amply covered by the requirements listed in the standards for three-phase fault current interruption. The generator CB is, however, differently stressed if the phase-to-ground faults are located on different sides of the CB. Suppose that the CB pole in the only healthy phase opens last, it has to interrupt a fault current against a TRV composed of a generator side voltage plus a transformer side voltage. In principle, we then have two independent three-phase voltage sources (synchronous generator and HV system) with their source impedances which are directly coupled in one phase and through earth faults in the two other phases. To our knowledge, there is no reference giving a closed solution for this problem. The basic scheme synchronous generator—generator CB—step-up transformer–HV system is shown in Fig. 1. It is the aim of this study to derive for the last pole to clear of this CB • a general formula for the current to be interrupted; • a general formula for the corresponding RRRV; • a general formula for the corresponding power frequency recovery voltage and to discuss the results and verify them by means of the Alternative Transients Program (ATP) [3].
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II. GENERAL FORMULATION OF THE PROBLEM AND SOLUTION A. Current Through Last CB Pole to Clear The two systems involved with a double earth fault on different sides of the CB are shown in Fig. 2. It should be mentioned that if CB poles A and B or A and C are still closed, the currents through these poles are different so that at an interruption in phase B or C the current in phase A is not automatically also interrupted. On the left side of Fig. 2, there is a system W (synchronous generator) and on the right side, a system Z (step-up transformer plus HV system). Both systems are supposed to be symmetrical and are characterized by complex impedances in symmetric components (short-circuit impedances of the components) [4], that is, and , respectively, and the corresponding source voltages and (only in the positive-sequence system). It is assumed that the phase-to-ground faults are in phase B on the W-side and in phase C on the Z-side and that the CB poles of phases B and C are already open. The last phase to open therefore is phase A. For the phase voltages and currents, the following six conditions apply:
This system of 12 equations may be solved by substitution and delivers the sequence values of voltages and currents as function of and the sequence impedances. Back transformation into phase values then yields the general expression for the current through the last pole to clear (all quantities are complex), as shown in (1) at the bottom of the page. For a discussion of this result, some simplifying assumptions are made: • all impedances shall be predominantly inductive and shall have the same impedance angle (same X/R ratio); • the positive-sequence impedances and the negative-sequence impedances shall be equal (this applies to all passive systems and approximately also for synchronous generators ( : direct axis subtransient reactance); • the absolute values of and shall be equal . A realistic assumption for a configuration according to Fig. 1 further is . Equation (1) then becomes
(2) With quence currents
and
, this yields for the se-
and for the sequence voltages
The correlation between sequence voltages and sequence currents is given by another six equations
Fig. 3 shows the course of as a function of the angle . For , that is, when the synchronous generator operates at no load, becomes unity. The maximum at 2.0 corresponds to an angle of 120 between and . and, hence, becomes zero at , which means that is lagging by 60 . The two latter situations constitute an unrealistic operating condition for a synchronous generator but could occur during an out-of-phase synchronization. In power stations, usually ranges between and . attains its highest value for , which represents a typical situation in a large power station. Under this assumption, (2) simplifies to (3) is the three-phase short-circuit It should be noted that current of the synchronous generator. Consequently, for normal operating conditions , the current in phase A remains below the generator shortcircuit current. It is only at out-of-phase conditions that this magnitude is exceeded (by a factor of 1.15 at maximum for an out-of-phase angle of 120 ).
(1)
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Fig. 5. Two systems coupled by CB, double earth fault in phases B and C, RRRV across last pole to clear.
Fig. 3. Course of function
Fig. 4. Vector diagram for .
B. Rate of Rise of Recovery Voltage Across the Last CB Pole to Clear
.
earth faults in phase
and
Worthy of an explanation is also the case of zero current at . This is clarified by the vector diagram of Fig. 4. The phase-to-ground faults let the voltage vector – rotate around the new zero point and the voltage vector – around the new zero point , respectively. Both voltage vectors have the same amplitude and phase angle. Hence, the current between these sources must be zero. A case not related to power stations but also of some practical importance would be and . This corresponds to the case of a coupling CB between two similar HV systems. In this case, (1) becomes
and with the additional assumption
, one obtains
For the calculation of the rate of rise of recovery voltage (RRRV) across the last CB pole to clear, the same procedure as used in [5] has been chosen, that is, the injection of current into the contacts of the CB pole to open. Since only the voltage difference across the CB contacts is of interest, a superposition of the steady-state voltage before interruption is not required. Again, the method of symmetrical components is used. In this case, the two systems W and Z are characterized by their surge impedances in sequence values , and , respectively. Those values are considered to be real magnitudes, neglecting the normally very small imaginary part. It should be noted that these surge impedances are independent of the short-circuit impedances of section A. The calculation is only valid until the first reflected voltage wave arrives at a CB terminal, but nevertheless allows a comparison of the RRRV with the RRRV in case of the classical three-phase fault. For a current injector in phase A, the scheme of Fig. 5 applies. The relations between sequence voltages and sequence currents are simpler than those in section A since the steady-state source voltages must not be taken into account. The conditions for phase B and C are the same as in section A. A current injection in phase A yields
If the phase magnitudes are expressed in sequence values and solved by using
and the corresponding equations for system Z, then by backtransformation, one obtains
(4) again varies between 0 and The value of the function 2.0. For , it becomes zero and the maximum at 2.0 corresponds to an angle of 158.2 , that is, is 0.916 at maximum, a case near phase opposition. Other cases of interest may be similarly derived from (1).
(5) should be interpreted as the RRRV across the CB terminals, as the steepness of the current at current zero (i.e., ), and the expression in brackets as the surge impedances
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(9) is the same function as in (2), and its course is depicted in Fig. 3. The highest power frequency recovery voltage across the last CB pole-to-clear occurs in case of a 120 out-of-phase condition. Fig. 6. Two systems coupled by the CB, double earth fault in phases B and C, and power frequency recovery voltage across the last pole to clear.
adjacent to the CB terminals. The RRRV is proportional to the steepness of the phase current and to the sum of the two independent surge impedances of the two systems. These surge impedances are identical in structure. Again, simplifying assumptions shall be made: • the surge impedances shall be same for positive- and negative-sequence systems. Equation (5) then becomes (6) A further simplification is and (6) then takes the following simple form:
. Equation
III. ANALYSIS OF GENERATOR—STEP-UP TRANSFORMER CONFIGURATION An example of a synchronous generator—generator CB—step-up transformer—HV system configuration was used to analyze different fault scenarios by means of the ATP and to compare the results with the corresponding analytical solutions. The analysis was based on a 60-Hz system with the following typical technical data: • synchronous generator (turbogenerator): 600 MVA, 25 kV, 25%; • step-up transformer (Yd01): 600 MVA, 500/25 kV, 10%; • HV system: 500 kV, 24 000 MVA. The equivalent circuit diagram corresponds to that of Fig. 2. The following relations are valid for the short-circuit impedances:
(7) From this result, high RRRV values that will appear across the terminals of the last CB pole to clear follow. C. Power Frequency Recovery Voltage Across the Last CB Pole to Clear After the interruption of the current in the last CB pole to clear, the systems on the two sides of the generator CB become independent of each other. Both systems are characterized by their short-circuit impedances and the corresponding source voltages, and are subjected to an earth fault. The location of the phase-to-ground faults is unchanged (Fig. 6). According to [6, p. 351], the voltages and on the two sides of the last CB pole to clear are given by the following expressions:
With , one obtains for the power frequency recovery voltage across the last CB pole to clear
(8) Assuming that
, (8) becomes
For a detailed representation, the generator as well as the step-up transformer have been modelled as 10 distributed inductances and capacitances each per phase [7] with • F [8, p. 446]; • 25 nF. That is, a kind of surge impedance representation has been used. Additional capacitances to ground (bus ducts, auxiliary transformers, etc.) have been taken into consideration at the generator and step-up transformer terminals. Damping has been realized by ohmic resistances connected in parallel to the distributed inductances. The generator neutral is grounded via a resistor of 1000 . The models have been checked regarding no load, load flow, and short-circuit conditions and found to yield correct results. The initial condition before the double earth fault and the opening of the generator CB in phases B and C was a load flow of 600 MVA with a power factor of 0.95. For comparison purposes, the behavior during a three-phase short circuit has been analyzed first. A. Three-Phase-to-Ground Fault on the Transformer Side Due to the generator prefault voltage of 1.07 p.u. (from the load-flow condition), the fault current calculated with the ATP program amounts to 59.4 kA. The TRV of the first pole to clear is shown in Fig. 7. The RRRV amounts to 2.0 kV/ s and the peak value of the TRV is 48 kV [i.e., 1.92 V, with V being the rated voltage (25 kV)]. This is a reasonable fit with the values given in [9, Table VI] for generator ratings between 401 and 800 MVA (RRRV: 2.0 kV/ s, peak value: 1.84 V). With an RRRV of 2.0 kV/ s and a of 31.65 A/ s the resulting surge impedance (real
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Fig. 7. Three-phase fault on the transformer side, TRV across first pole to clear.
Fig. 8. Three-phase fault on the generator side, TRV across the first pole to clear.
magnitude) is , it follows from [5] that
. Assuming that .
B. Three-Phase-to-Ground Fault on the Generator Side The calculation with the ATP program yields a fault current of 111.2 kA, that is, about twice the value of the fault current in case of a fault on the transformer side, which is in accordance with the premises. Due to the twice as high fault current and since surge impedances of transformers are generally higher than those of generators, the TRV in this case is significantly more severe (Fig. 8). The RRRV amounts to 5.0 kV/ s and the peak value to 38 kV which corresponds to 1.52 V. These values are also well in line with the values given in [9, Table V], that is, an RRRV of 5.0 kV/ s and a peak value of 1.84 V. The lower peak value of 1.52 V in case of the simulation can be explained by the fact that the short-circuit power of the feeding HV system is not infinite. When calculating the resulting surge impedance at the transformer side from these results, one finds . This value is also applicable to the sequence surge impedances (i.e., ). C. Double Earth Fault on Different Sides of the Generator CB Under Rated Load Conditions The assumed load-flow scenario of 600 MVA with a power factor of 0.95 leads to an angle between the source voltages and of . Considering the vector group Yd01 of the step-up transformer, is leading. If
Fig. 9. Double Earth fault at rated load flow, TRV across last pole to clear.
a double earth fault occurs and the currents in phases B and C are interrupted, the current in phase A of the generator CB amounts to 42.4 kA, which corresponds to 71.4% of the generator shortcircuit current. A similar result is obtained for an angle of 19.3 from divided by (see Fig. 3). The resulting TRV across the CB contacts after the interruption of this current is shown in Fig. 9. The RRRV reaches 3.3 kV/ s and the peak value amounts to 60 kV or 2.40 V. The most appropriate reference in [9] would be the section about out-of-phase current switching [9, Tables 9 and 12]. There, the out-of-phase switching current is specified as 50% of the rated short-circuit current of the CB (in the given case 50% of 111.2 kA) and the RRRV and peak value of the corresponding TRV amount to 4.7 kV/ s and 2.60 V, respectively. These requirements correspond to a 90 out-of-phase condition. The values calculated for a double earth fault under rated load-flow conditions are somewhat lower than but not very distant from these values. When calculating the resulting surge impedance from the RRRV and the steepness of the current through the CB, one obtains , which is practically the sum of the surge impedances calculated for each side. D. Double Earth Fault on Different Sides of Generator CB Under Out-of-Phase Conditions Significantly more severe conditions for the CB would arise from closing under out-of-phase conditions and a double earth fault occurring immediately afterwards. It is a well-established fact that out-of-phase conditions from time to time occur in power stations [7]. These conditions are not always immediately cleared by the protection system. Since out-of-phase conditions lead to high electrical and mechanical stresses being imposed on the synchronous generator and step-up transformer, respectively, the occurrence of a single-phase-to-ground fault and the extension of this fault to a double earth fault cannot be completely ruled out in such a situation. Although this constitutes a triple contingency and seems to be unrealistic, it is not at all an unlikely case and an analysis of the corresponding CB stresses is therefore appropriate. The cases with an out-of-phase angle of 90 , 120 , and 180 have been analyzed by means of the ATP program. The corresponding results are summarized in Table I. As expected from Fig. 3, the highest stresses are imposed on the last CB pole to
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Fig. 10. Double earth fault at different out-of-phase conditions, TRV across last pole to clear (with an extended time axis) • red curve: 90 out-of-phase condition; • green curve: 120 out-of-phase condition; • blue curve: 180 out-of-phase condition.
TABLE I DOUBLE EARTH FAULT AT DIFFERENT OUT-OF-PHASE CONDITIONS
the RRRV is proportional to the sum of the positive-sequence surge impedances of both sides. Further, a generally valid expression for the power frequency recovery voltage across the last CB pole to clear as a function of the angle between the source voltages on both sides has been deduced. Finally, an analysis of a typical synchronous generator—generator CB—step-up transformer—HV system configuration was carried out by means of the ATP program. The corresponding results were found to be in good agreement with the theoretical analysis. When a double earth fault occurs under load-flow conditions currents and TRVs are close to but remain below the limits given in [9] for the out-of-phase current switching. In case of a double earth fault occurring under an out-of-phase condition, the peak value of TRV will, however, significantly exceed the values laid down in [9]. There is a range of out-of-phase angles (i.e., 60 to 180 ) where even the TRV stipulated in [7] for a 180 out-of-phase condition is exceeded. Although this case constitutes a triple contingency, its occurrence is not completely unlikely. However, these stresses are so high that due to their low probability of occurrence, it is not justifiable to specify generator CBs that can cope with these requirements. REFERENCES
clear in case of an out-of-phase angle of 120 . In Fig. 10, the TRV across the last CB pole to clear is depicted for out-of-phase angles of 90 , 120 , and 180 , respectively, with an extended time axis. From Table I, the TRV values across the last CB pole to clear in case of a double earth fault under out-of-phase conditions exceed the values laid down in the section about out-of-phase current switching of [9]. On the other hand, some generator CBs are subjected to tests representing a 180 out-of-phase condition. There is, however, still a range of out-of-phase angles (i.e., 60 to 180 ) where even the TRV stipulated in [7] for a 180 out-of-phase condition is exceeded.
IV. CONCLUSION For the case of a double earth fault on different sides of a generator CB, a general expression for the current through the last CB pole to clear has been deduced as a function of the short-circuit impedances in (complex) sequence components of both sides (i.e., synchronous generator side and the step-up transformer plus the HV system side) and as a function of the independent source voltages on both sides. The results are then discussed for some typical cases. For usual conditions, the current through the last pole to clear does not exceed the short-circuit current supplied by the generator. The corresponding RRRV has been derived as a function of the surge impedances in sequence values of both sides and as a function of the injected current. Under realistic assumptions,
[1] D. Braun and G. S. Koeppl, “Intermittent line-to-ground faults in generator stator windings and consequences on neutral grounding,” IEEE Trans. Power Del., vol. 25, no. 2, pp. 876–881, Apr. 2010. [2] G. Koeppl and D. Braun, “New aspects for neutral grounding of generators considering intermittent faults,” presented at the CIDEL, Buenos Aires, Argentina, Sept. 27–29, 2010. [3] “ATP (Alternative Transients Program) Rule Book. 1987–1992,” Canadian/American EMTP User Group. [4] Short-Circuit Currents in Three-Phase A.C. Systems—Part 0: Calculation of Currents, International Standard IEC 60909-0, 2001, 1st ed. [5] G. Koeppl and P. Geng, “Determination of the transient recovery voltage in symmetrical three phase systems,” Brown Boveri Rev., vol. 53, no. 4/5, pp. 311–325, 1966. [6] H. Happoldt and D. Oeding, Elektrische Kraftwerke und Netze, 5. Auflage. Berlin, Germany: Springer-Verlag, 1978. [7] D. Braun and G. Koeppl, “Transient recovery voltages during the switching under out-of-phase conditions,” presented at the IPST, New Orleans, LA, USA, Sep. 28–Oct. 2, 2003. [8] A. Greenwood, Electrical Transients in Power Systems, 2nd ed. New York, USA: Wiley, 1991. [9] IEEE Standard for AC High-Voltage Generator Circuit Breakers Rated on a Symmetrical Current, IEEE Standard C37.013-1997 (R2008), 1997.
Georg S. Koeppl, photograph and biography not available at the time of publication.
Dieter Braun (M’83), photograph and biography not available at the time of publication.
Martin Lakner, photograph and biography not available at the time of publication.
