DIFFERENTIAL PROTECTION FOR SYNCHRONOUS JMACHINES
TECHNICAL FIELD
The present invention relates to differential protection of AC electrical machines, particularly electrical generators such as synchronous generators, and in particular to circuits and methods for differential protection.
BACKGROUND
The differential protection method is a commonly used protective method that can detect shunt faults on the armature windings of AC electrical machines, see Fig. 1 in which windings 1A, 1B, lc of an AC electrical machine are illustrated. The windings are interconnected in a neutral point N 7 and have Une terminals 5A, 5B, 5C connected to some power distribution structure such as a busbar. Each winding has a relay or control device 3A, 3B, 3 C. Electrical currents IM, hi, la, enter the windings and electrical currents 'hi, Ici leave the respective windings. The currents are sensed by current transformers 13A, 13B, 13C and 9A, 9B, 9C respectively connected to the relays. In the case where the absolute value of the difference of the two currents in one phase winding is too large the respective relay 3A, 3B, 3C issues an alarm. The sensitivity of circuits using such a differential protection method depends mainly on the accuracy of the current transformers used and the risk for unwanted operation for external shunt faults. Several methods exist to increase the security when the through fault current is high. One commonly used method is to stabilize the differential protection by introducing an additional condition as described below.
Equation (1) defines the differential current IM for pliase winding 1 whereas equation (2) defines the stabilizing current IAS for the same winding:
J* =M+M ( )
According to the conventional method of stabilized differential protection an alarm signal will be issued if the following relation (3) is true
The condition for alarm is thus that the absolute difference of the currents leaving and incoming to a winding should be greater than a threshold value ho and for high currents in the winding also greater than the stabilizing current multiplied by a suitably chosen positive constant k. This traditional differential protection method works well for conventional AC electrical machines comprising windings having relatively small capacitances to earth. The introduction of AC electrical machines having cable windings, such as the Powerformer™ generator, has in operational experience presented application problems to the traditional differential protection method. Thus, in Fig. 2 also capacitances C to earth in the protected zone are illustrated as connected to the central points of the windings 1A, 1B, lc-
For example, a conventional generator having a rated voltage of 13.8 kN and a HN synchronous generator of the Powerformer type having a rated voltage of 138 kN can be considered for comparison. The two machines are assumed to have the same rated apparent power. It is further assumed that the phase-to-earth capacitance of each of the phase windings of the Powerformer generator is three times larger than the phase-to-earth capacitance of the conventional generator. The electrical charge on a phase winding of the Powerformer generator at voltage maximum is then 3-10 = 30 times larger than the charge on a phase winding of the conventional generator. The reason is the higher capacitances of the windings and the higher voltages induced. The time required to discharge the winding capacitances by the rated current of the machine is a measure of the importance of the winding capacitances. This discharge time is 30/0.1 = 300 times longer for the Powerformer generator than for the conventional generator. This means that when as above comparing the currents leaving and incoming to a winding, they will not even for normal operation be substantially equal to each other since a relatively large AC current, the capacitive differential current, will pass the capacitance of the winding.
The capacitances in the windings to be protected by relay circuits connected for differential protection thus cause two problems:
- The operate value of the differential protection circuits must be increased to avoid unwanted operation caused by the capacitive differential current.
- The differential protection circuits must repress transients in the differential current to avoid unwanted operation caused by the capacitive outrush current.
Results from simulations of a 25 J VA and 78 kN synchronous machine such as a Powerformer generator directly connected to a resonant earthed network will now be used to illustrate these problems.
Differential Protection in Normal Operation of Exemplary AC machine
The active output power of the considered synchronous machine is approximately 10 JMW. The diagram of Fig. 3 shows the current in the winding of phase A at the neutral end N or 7 of the winding as a function of time during normal operation. The diagram of Fig. 4 shows the current IAI in phase A at the line terminal 5 A of the winding 1A as a function of time during normal operation. The diagram of Fig. 5 shows the differential current IM iu phase A as a function of time during normal operation. The RMS value of the differential current is equal to 6.9 amperes. The rated current is equal to 185 amperes, which means that the differential current is 3.7% of the rated current. The diagram of Fig. 6 shows the average winding voltage on phase A as a function of time during normal operation. The RMS value of the average winding voltage is equal to 23.3 kilovolts. The differential current assumes its peak value when the average winding voltage crosses zero. The diagram of Fig. 7 shows the stabilizing current IAS in phase winding 1A as a function of time during normal operation of the generator. The diagram of Fig. 8 shows the absolute value Ihdl of the instantaneous differential current as a function of the stabilizing current I s during normal operation. The criterion for the stabilized differential protection method is in the figure indicated by the area above the broken dotted line. For values in this region an alarm would be issued according to this protection method.
As observed in the figure, the absolute differential current Ihdl reaches its maximum value when the stabilizing current IAS is very low. The output from the synchronous machine is assumed to be substantially active (real) power and hence the load current for each phase is in phase with the Une terminal voltage VA2, VBI, VB2 of the respective winding. The average voltage on the winding is essentiatty half the terminal voltage and the differential current is substantiaUy proportional to the derivative of the terminal voltage with respect to time. The fundamental frequency differential current hence leads the fundamental frequency terminal voltage by 90 electrical degrees. This means that the stabiUzation in the protection criterion, i.e. that for an alarm the condition that the absolute differential current must be greater than the stabiUzing current multipUed by a constant must be fulfiUed, is ineffective during normal operation. Furthermore the minimum operate-value ho must be set considerably higher than the steady state differential
current derived from the capacitances of the windings.
Differential Protection in a Faulty Phase of the exemplary machine
It is now assumed that a single phase-to-earth fault occurs on phase A of the busbar. This is an external fault and the differential protection circuit must not operate. The diagram of Fig. 9 shows the differential current in phase A as a function of time for an external phase-to-earth fault on phase A of the busbar.
The peak value of the differential current is equal to 58 amperes. The peak value of the rated current is equal to 262 amperes, which means that the peak value of the capacitive differential current is 22% of the peak value of the rated current. The RMS value of the differential current decreases from 6.9 amperes during steady state to 6.5 amperes after fault inception. The differential current has a phase shift of 180 degrees at fault inception. The diagram of Fig. 10 shows the average winding voltage on phase A.
The RMS value of the average winding voltage decreases from 22.3 kN before fault inception to 21.3 kN after fault inception. The average winding voltage has a phase shift of 180 degrees at the fault inception. The induced phase-to-neutral voltage is almost constant for single phase-to earth faults in non-effectively earthed systems. The neutral point displacement is close to zero before fault inception. The neutral displacement voltage becomes close to normal phase-to-earth voltage after fault inception but with a phase shift of 180 degrees in relation to the induced voltage in phase a. The diagram of Fig. 11 shows the absolute value of the differential current in phase A as a function of the stabiUzing current at an external phase-to-earth fault in phase A. The fault occurs when the phase-to-earth voltage is only 25% of its peak value. It may, therefore, be expected that the peak value could be as high as 232 amperes or 90% of the peak value of the rated current.
Differential Protection in a Healthy Phase of the exemplary machine
It is now assumed that a single phase-to-earth fault occurs on phase B of the busbar. This is an external fault and the differential protection must not operate. The diagram of Fig. 12 shows the differential current in phase A as a function of time for an external phase-to-earth fault on phase B of the busbar.
The peak value of the differential current is equal to 82 amperes. The peak value of the rated
current is equal to 262 amperes, which means that the peak value of the capacitive differential current is 31% of the peak value of the rated current. The RMS value of the steady state differential current increases from 6.9 amperes during the steady state as shown in Fig. 5 to 17.3 amperes as shown in Fig. 12 or to 250% of its value before occurrence of the fault. The differential current has a positive phase shift of approximately 30 degrees in relation to its value before occurrence of the fault
The diagram of Fig. 13 shows the absolute value of the differential current in phase A as a function of the stabiUzing current at an external phase-to-earth fault in phase B.
The fault occurs when the phase-to-earth voltage is 70% of its peak value. It may, therefore, be expected that the peak value could be as high as 117 amperes or 45% of the peak value of the rated current. The diagram of Fig. 14 shows the average winding voltage on phase A as a function of time for an external fault on phase B. The average winding voltage increases from 22.3 kN before fault inception to 58.0 kN after fault inception or to 2.6 times its pre-fault value.
The theoretical value is equal to Ϊ or 2.65. The average winding voltage has a positive phase shift of approximately 30 degrees, which is equal to the theoretical value.
Concluding remarks on the exemplary machine
The steady state differential currents mainly derived from the capacitances of the windings dictate the minimum setting of a conventional differential protection circuit. The minimum value should be in the order of 1.5 -v7 ~ 4 times the differential current measured during normal operation. In this particular case this means about 30 a or 16% of the rated current of the synchronous machine.
There is a risk that a fast differential protection circuit that uses the rectified instantaneous value of the through fault current operates at external earth faults in non-effectively earthed systems. The peak value of the capacitive outrush current may amount to more than 50% of the peak value of the rated current of the machine. Field tests and workshop tests for Powerformer generators indicate that the capacitive outrush current may be much higher than several times the peak value of the rated current. There is thus a need for a method of differential protection working also for AC machines in which the capacitances of the windings are important.
SUMMARY OF THE INVENTION
It is an object of the invention to provide rehable differential protection for an AC electric machine having significant capacitances of the phase windings to earth.
A circuit for differential protection generaUy comprises one current transformer at the neutral end of each phase winding, one current transformer at the line terminal of each phase winding and one voltage transformer at the line terminal of each phase winding that can provide a value of the residual voltage or the zero sequence voltage. In addition the circuit may have a voltage transformer at the neutral point but this is not necessary. Furthermore, fourier filters extract the fundamental frequency phasors from the voltages at the secondary windings of the transformers.
The general protection circuit includes first circuits for non-stabiUzed differential protection for main protection of the winding, second circuits for compensated differential protection for main protection of the winding, third circuits for zero sequence overvoltage protection for back-up protection and fourth circuits, a blocking element, for blocking the second circuits and optionaUy the first circuits.
GeneraUy then, in an AC electric generator such as the Powerformer™ voltages are induced in phase windings connected at one end to each other at a neutral point and at an opposite end to phase terminals. For each phase winding a value indicative of the magnitude of an excess or rest electric current flowing into the winding that is not related to the currents at the neutral point and phase terminal ends and not to the current flowing through the capacitance of the phase winding is calculated and compared to a threshold value. Circuit breakers are activated and an alarm can be issued if the calculated magnitude is found to be higher than the threshold value. These actions can be inhibited or blocked if some other conditions apply such as that the magnitudes of the currents at the neutral point and phase terminal ends are sufficiently high.
A circuit for compensated differential protection is obtained capable of detecting shunt faults occurring in the windings.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention wiU now be described by way of non-limiting embodiments with reference to the accompanying drawings, in which:
- Fig. 1 is a simpUfied circuit diagram iUustrating conventional differential protection,
- Fig. 2 is a circuit diagram iUustrating the capacitance in the protection zone,
- Fig. 3 is a diagram of the current in phase A at the neutral end of the winding,
- Fig.4 is a diagram of the current in phase A at the line terminal of the winding,
- Fig. 5 is a diagram of the differential current in phase A during normal operation,
- Fig. 6 is a diagram of the average winding voltage on phase A during normal operation,
- Fig. 7 is a diagram of the stabiUzing current in phase A during normal operation,
- Fig. 8 is a diagram of the absolute value of the differential current as a function of the stabiUzing current during normal operation,
- Fig. 9 is a diagram of the differential current in phase A at a busbar fault on phase A,
- Fig. 10 is a diagram of the average winding voltage on phase A,
- Fig. 11 is a diagram of the absolute value of the differential current in phase A as a function of the stabiUzing current at an external phase-to-earth fault in phase A,
- Fig. 12 is a diagram of the differential current in phase A at a busbar fault on phase B,
- Fig. 13 is a diagram of the absolute value of the differential current in a healthy phase as a function of the stabiUzing current at an external phase-to-earth fault,
- Fig. 14 is a diagram of the average winding voltage on phase A at external fault on phase B, and
- Fig. 15 is a circuit diagram of the phase windings of a three-phase electric machine having differential protection.
DESCRIPTION OF A PREFERRED EMBODIMENT
A three-phase synchronous machine or possibly another similar AC electric device that has phases A, B, C and in particular phase windings 1A, 1B, IC and is provided with protection circuits is iUustrated in Fig. 15. The Une ends of the phase windings are connected to output terminals 5A, 5B, 5C and their neutral ends are connected to a common node 7 or N, the neutral point or neutral node. A first group of current transformers 9A, 9B, 9C are connected at the neutral ends of the windings and thus their primary windings have a low resistance and are actuaUy portions of the phase windings 1A, 1B, IC- The secondary windings are connected to fourier filters 11A, HB, 11C- A second group of current transformers 13A, 13B, 13C are in the similar way connected at the line terminal ends of the windings and their secondary windings are connected to respective fourier filters 15A, 15B, 15C- Voltage transformers 17A, 17B, 17C have their primary windings connected to the respective phase windings at the generator terminals and have their secondary windings connected to fourier filters 19A, 19B, 19C.
The fourier filters 11A, 11B, 11C; 15A, 15B, 15C; 19A, 19B, 19C may be finite impulse response
(FIR) filters or infinite impulse response (IIR) filters. The fourier filters provide complex phasors, i.e. generaUy quantities describing both the magnitude, direction and phase of the respective currents or voltages, as listed below:
Table 2 Output of the fourier filters.
The complex phasors can be used in various ways for defining protection conditions under which an alarm can be issued, signalling a fault in windings and in many cases also the winding in which the fault has occurred. Before issuing the alarm the circuit breakers 25A, 25B, 25C can be activated which are connected between the line terminals 5A, 5B, 5C and e.g. some busbar as iUustrated in the figure, the circuit breakers acting to disconnect the windings from the network/busbar.
Thus, the following equations (4), (5) and (6) define three starting criteria kda, kdb, føc of a method for non-stabiUzed differential protection according to prior art. The parameter ho is an operate Umit for the non-stabiUzed differential protection method.
In order to carry out this method the foUowing logical blocks can be used, the blocks e.g. being implemented as procedures or functions executed by one or more suitable microprocessors comprised in relays or control devices 3A, 3B, 3c, see Figs. 1 and 2. Thus, in the blocks 31
A, 31
B, 31c the absolute values of the differences hi - I
a2, hi - Ib2, hi - Id are calculated and are compared to the parameter ho in the blocks 33A, 33B, 33 c. If the result of the comparison is that any of the absolute values is larger than the parameter, a signal is sent to the circuit breakers 25
A, 25
B, 25
C in blocks 35A, 35
B, 35
C, possibly with some delay, the delay being chosen so that accurate readings of the respective fourier filters are obtained. Then, in blocks 37
A, 37
B, 37
C alarms can be issued to some monitoring device, alarm indication panel or operator that a fault has occurred in the respective phase winding. The delay can be obtained by arranging a step counter, not shown, for each phase. The step counter for phase A (phase B or phase C) is incremented if the stating criterion for phase A (phase B or phase C) is equal to 1. The step counter for phase A (phase B or phase C) is decremented if the stating criterion for phase A (phase B or phase C) is equal to 0. The non-stabiUzed protection issues an operate-signal for phase A (phase B or phase C) if the step counter for phase A (phase B or phase C) exceeds a pre-set Umit. This Umit should aUow the fourier filters 11A, 11
B, He to settle before the protection issues an operate-signal.
Furthermore, a procedure for compensated differential protection can be arranged in the system of Fig. 15. Such protection comprises four steps: (1) estimation of the neutral point voltage Vnp, (2) calculation of compensating currents, (3) calculation of compensated differential current and (4) evaluation of starting criteria. Equations (7), (8) and (9) define the complex voltages Vaι, Vu, Vci at the neutral end 5 of the windings 1A, 1B, IC-
Vπp if directly available va\ ~ Va2 +Vb2 +Vc2 _,.. (7) else
In order to estimate the current flowing through the capacitances of the windings 1A, 1B, IC, it
can e.g. be assumed that one portion α-Cw of the total phase-to-earth capacitance Cw of a considered winding can be associated with the voltage at the neutral end of the phase winding while the rest (l-α)Cw can be associated with the voltage at the line teπninal of the winding, oc being a number between 0 and 1. This is a possible representation of a winding having a graded insulation. However, more complicated representations can be easily found. Equations (10), (11) and (12) define compensating currents Ica, hb, he, i-e. the complex currents flowing through the capacitances to earth of the windings 1A, 1B, IC using the described assumption.
Ica=jω- -Cw-Val+jω-{l- )-Cw-Va2 =
(10) = ω-Cw-[ - al + (l-α)-Fa2] = yω-Cw-r0 avg,a
Icc=jω-a-Cw-Vcl + jω-{l- )-Cw-Vc2 = (12) = yω-Cw-[α.Fel + (l-α)-F = ω.Cw- a
where the definition of the average voltages Vavgιa, Vavg,b, Vmsfi is obvious.
Equations (13), (14) and (15) define the compensated differential currents Idc,a, Idc.b, I<,c-
dc,a
= a\ ~ ca ~
' at ^H>
dc,c
= *Λ — cc — c2 (15)
Equations (16), (17) and (18) define the three starting criteria føc,α, &<&,&, føc,e of the compensated differential protection. The parameter Idco is the operate limit for the compensated differential protection.
In a block 41 the complex voltages Vaι, Vbi, Vcι at the neutral end of the windings are calculated as the average of the voltages at the line terminal ends of the windings, i.e. the value (Va2 + Vb2 + Vcι)l3 is calculated. This value is provided to blocks 43A, 43B, 43 c in which the averages Vavg,a, VaVg,b, Vavg,c of the voltage in the phase windings are determined as is obtained from Equations (10), (11), (12), i.e. Vavg,a= -Val + (l- )-Va2, Vmg,h= -VM + (l-a)-Vb2, Vmg,c= -Vcl + (1- )-Vd. GeneraUy, the average voltage can be determined in any suitable way, such as by using a more complex and accurate model of the distributed capacitance of the windings. The average voltages are used to determine the compensating currents Ica, hb, he in blocks 47A, 47B, 47c by multiplication by a suitable constant, compare Equations (10), (11), (12). The compensating differential currents hc.a, hc,b, Idc,c are calculated in the blocks 49A, 49B, 49C, which receive the values of the compensating currents from the blocks 47A, 47B, 47C, the values of the neutral end currents from the fourier filters 11A, HB, He, and the values of the line terminal end currents from the fourier filters 15A, 15B, 15C- The absolute values of the compensating differential currents are compared to the parameter Idc.o in the blocks 51A, 51B, 51C- If the result of the comparison is that any of the absolute values is larger than the parameter, a signal is sent to the circuit breakers 25A, 25B, 25C in blocks 53 A, 53B, 53c, possibly with some delay, the delay being chosen so that accurate readings of the respective fourier filters are obtained, the signal turning the circuit breakers off. Then, in blocks 55A, 55B, 55C alarms can be issued to some monitoring device, alarm indication panel or operator that a fault has occurred in the respective phase winding. The delay can as described above be obtained by arranging a step counter, not shown, for each phase. The step counter for phase A (phase B or phase C) is incremented if the starting criterion for phase A (phase B or phase C) is equal to 1. The step counter for phase A (phase B or phase C) is decremented if the starting criterion for phase A (phase B or phase C) is equal to 0. The non-stabiUzed protection issues an operate-signal for phase A (phase B or phase C) if the step counter for phase A (phase B or phase C) exceeds a pre-set limit. This limi should aUow aU the fourier filters involved in the quantities required in the comparison of blocks 51A, 51B, 51c, i.e. the fourier filters 11A, HB, He, 15A, 15B, 15C and 19A, 19B, 19C or optionaUy 23, to settle before any of the protection circuits or blocks issues any operate-signal.
Equation (19) defines the starting criteria k^, for the circuit part including a zero sequence overvoltage protection. The parameter Vzo is the operate Umit for the zero sequence overvoltage
protection.
1 if Λ + * + Λ > V
3 z.0 (19) else
The comparison of Equation (19) is performed in the block 57 that receives the average value of the Une end terminal voltages from the block 41. If the result of the comparison is that the absolute value of average Une end voltage is larger than the parameter Vzo, a signal is sent to the circuit breakers 25A, 25B, 25C in a block 59 and an alarm can be issued in a block 61. In the same way as above a delay of the signal from the blocks 59 and 61 can be arranged by means of a step counter, not shown. The step-counter is incremented if the stating criterion for the zero sequence overvoltage protection is equal to 1. The step-counter is decremented if the stating criterion for the zero sequence overvoltage protection is equal to 0. The zero sequence overvoltage protection issues an operate-signal if the step-counter for the zero sequence overvoltage protection exceeds a pre-set limit. This limit should aUow the fourier filters 19A, 19B, 19C involved in the calculation of the Une end average voltage to settle before any signal is issued.
Equations (20), (21) and (22) define three blocking criteria koa, hb, fac for the compensated differential protection circuit. The parameter Vbo is the operate limit for the blocking element.
The blocking element operates if anyone of the blocking criteria k
ba, fa
b, k
bc is equal to 1. The operation of the blocking element blocks the circuit of compensated differential protection from issuing signals but not the circuit for zero sequence overvoltage protection. Suitable time grading of the back up zero sequence overvoltage protection wiU create necessary coordination with circuits, not shown, for main earth fault protection. The blocking element may or may not block the circuit for non-stabiUzed differential protection. The blocking element is a circuit part
that comprises blocks 63A, 63
B, 63
C i which the quantities max
max are determined. These quantities are in blocks 65A, 65
B, 65C compared to the parameter V
bo, the operate limit. If the quantities higher than the parameter, blocks 67A, 67B, 67
C are executed in which a blocking signal is sent to the corresponding one of the blocks 53A, 53B, 53C to command them not to send any signal to the circuit breakers 25A, 25B, 257C and also to the blocks 55
A, 55
B, 55
C commanding them not to issue alarm signals.