ON THE ISSUE OF PROTECTING GENERATORS FROM OVERCURRENTS

I. D. Kutyavin and N. V. Lisetskii

At present, to protect generators from overcurrents, maximum-current protection with undervoltage starting is used. The following functions are assigned to this protection:

1. Protection of the station busbars (if the busbars have special protection, then the protection under consideration serves as a backup to it).
2. Backup of the main protection of generators against interphase faults.
3. Backup of the protection of feeders departing from the station busbars.

The primary pickup current of the protection under consideration is usually set within the limits of \((1.3—1.5)\) of the rated generator current, and the pickup voltage within the limits of \((0.7—0.75)\) of rated voltage. With such settings the protection is capable of performing only the first two of the indicated functions with sufficient reliability, while it will perform the third function at stations with reactored feeders only in the case when the residual voltage on the busbars is equal to or less than the protection pickup voltage.

The indicated relation between the residual voltage on the busbars and the protection pickup voltage is satisfied only for short circuits on reactored feeders of medium and high power. In the case of short circuits beyond the reactors of low-power feeders, the residual voltage on the busbars may considerably exceed the pickup voltage of the protection under consideration, and if the feeder protection fails to operate, the fault can be cleared only manually by the operating personnel. Such prolonged flow of fault currents may cause extensive destruction in the feeder cubicle.

In view of the foregoing, it would be of interest to find the conditions for reliable operation of the indicated protection as a backup to the feeder protection. For this purpose it is necessary to investigate the dependence of the residual voltage on the busbars and of the fault current flowing in the generator windings on the degree of reactoring of the feeders and on the generator load preceding the short circuit. Here, by the degree of reactoring of the feeders is meant the ratio of the reactance of the feeder reactor \(X_p\) to the reactance of the system \(X_c\):

\[ K = \frac{X_p}{X_c}. \tag{1} \]

Let us first consider the dependence of the residual voltage on the busbars at the initial instant of a three-phase short circuit beyond the feeder reactor on various degrees of reactoring \(K\). For this case the residual voltage, as a percentage of rated voltage, can be expressed through the reactances in the following manner:

\[ U^{(3)}_f = \frac{X_p}{X_c + X_p}\,100 = \frac{\dfrac{X_p}{X_c}}{1 + \dfrac{X_p}{X_c}}\,100 = \frac{100K}{1 + K}. \tag{2} \]

The curve \(U_{0}^{(3)}=f(k)\) at \(t=0\), constructed according to expression (2), is shown in Fig. 1 (curve 1).

However, to clarify the complete picture of the change in residual voltage in the operating condition under consideration, it is also desirable to know the dependence of the residual voltage in the steady-state short-circuit process, \(U_{0y}^{(3)}=f(k)\). The latter can be calculated by first determining, from the calculated reactance \(X=X_c(1+K)\), the relative value of the steady-state three-pole short-circuit current \(I_{zy}^{(3)}\); then

\[ U_{0y}^{(3)}=I_{zy}^{(3)}x_p100=Kx_cI_{zy}^{(3)}100. \tag{3} \]

Fig. 1

Curve (2) in Fig. 1 gives the dependence \(U_{0y}^{(3)}=f(K)\) for \(x_c=0.125\), i.e., for its minimum possible value, which should give the greatest value of \(U_{0y}^{(3)}\).

Let us now compare the obtained residual-voltage values with the pickup and dropout voltages of the voltage-blocking relays. The pickup voltage is determined by the well-known formula

\[ U_{pm}=\frac{K_n U_{rab.\,min}}{k_v n_n}. \tag{4} \]

The minimum operating voltage of the installation \(U_{rab.\,min}\) is recommended to be taken as equal to 95% of the rated voltage \((U_{nom})\), and the reliability factor \(K_n=0.95\); then

\[ U_{pm}=\frac{0.9U_{nom}}{k_v n_n}. \tag{5} \]

When using EN relays, whose dropout coefficient is \(K_v=1.2\), we obtain

\[ U_{pm}=0.75\frac{U_{nom}}{n_n}, \]

which amounts to 75% of the primary voltage. The dropout voltage \(U_{rb}\) under these conditions will be equal to 90% of the rated voltage.

The voltages \(U_{pm}\) and \(U_{rb}\) are plotted in Fig. 1. As can be seen from this figure, the voltage blocking will operate at the initial instant of a three-

phase short circuit only when \(K<3\); when \(3<K<3.5\), the blocking will operate as the short-circuit current decays, and when \(K>3.5\) it will not operate at all.

On the basis of the indicated curves one may draw the further conclusion that, in the case of faults beyond reactors with large degrees of reactance, the voltage part of the protection may block the current part if their settings are not coordinated.

Fig. 2

To coordinate the settings it is necessary to determine the magnitude of the fault currents flowing in the generator windings in the event of a short circuit beyond the feeder reactor for various degrees of reactance \(K\). For this purpose we shall determine the short-circuit current supplied by the generator, taking account of individual damping.

Let us assume that the equivalent circuit of the short-circuit circuit is characterized by Fig. 2a, where \(x_2\) is the generator reactance, \(x_c\) is the system reactance, and \(x_p\) is the reactor reactance.

The reactance of the generator branch according to the equivalent circuit (Fig. 2b) will be:

\[ x_{2p}=x_2+\frac{x_p}{c}=x_2+\frac{x_p}{\dfrac{x_c}{x_c+x_2}}=x_2(1+K). \tag{6} \]

Then the current of a three-phase short circuit flowing in the generator circuit at \(t=0\), in relative units, is expressed as:

\[ I^{(3)}_{t=0}=\frac{1}{x_{2p}}=\frac{1}{x_2(1+K)}. \tag{7} \]

At the same time the generator will retain some load, the magnitude of which will depend on the residual voltage on the bus section of the given generator and on the load shunted by the short circuit.

Let us assume that before the short circuit the generator was operating at no load; then during the short circuit the current in the generator windings will be determined entirely by expression (7).

Let us further suppose that before the short circuit the generator had a load

\[ \dot I_{н2}=I'_{н2}+jI''_{н2} \tag{8} \]

and that the short circuit beyond the feeder reactor shunts part of this generator load, so that its residual load may be accounted for by the coefficient \(\alpha\) (\(\alpha<1\)).

Let us assume that the voltage drop on the busbars causes a proportional decrease in the reactive component of the load current \(I''_{н2}\) and an inversely proportional increase in the active component—\(I'_{н2}\). Then the effective value of the periodic component of the generator current, in relative units, for the initial instant of a short circuit beyond the feeder reactor, in complex form, will be:

\[ \dot I_2=\frac{\alpha}{U^{(3)}_{0}}\,I'_{н2} +j\left[ \alpha U^{(3)}_{0} I''_{н2} +\frac{1}{x_2(1+K)} \right]. \tag{9} \]

and the rms value of this current

\[ I_z=\sqrt{\left(\frac{a}{U_0^{(3)}} I'_{ng}\right)^2+ \left[aU_0^{(3)}I''_{ng}+\frac{1}{x_c(1+K)}\right]^2}. \tag{10} \]

The magnitude of the steady-state current in the generator windings can be determined as follows: from the calculated reactance of the generator branch (see expression 6), for the specified degree of reactoring \(K\), we find the steady-state current and substitute it into (9) and (10) in place of the initial value of the periodic component of the short-circuit current, while replacing \(U_0^{(3)}\) by \(U_{0y}^{(3)}\). Then the generator current in the steady-state short-circuit condition will be

\[ \dot I_{zy}^{(3)}= \frac{a}{U_{0y}^{(3)}} I'_{ng} +j\left(aU_{0y}^{(3)}I''_{ng}+I_{zy}^{(3)}\right). \tag{11} \]

The rms value of this current is

\[ I_{zy}^{(3)}= \sqrt{ \left(\frac{a}{U_{0y}^{(3)}} I'_{ng}\right)^2+ \left(aU_{0y}^{(3)}I''_{ng}+I_{zy}^{(3)}\right)^2 }. \tag{12} \]

Fig. 1 shows curves of the change in current in the generator windings as a function of \(K\) at \(t=0\) and \(t=\infty\) for the cases in which, before the short circuit, the generator was operating at no load and at rated load. The shunting factor \(a\) is taken as 0.7. Curve (3) gives the dependence \(I_z=f(K)\) at \(t=0\) and \(I_{ng}=0.8+j0.6\); curve (4), at \(t=0\) and \(I_{ng}=0\). Curve (5) is plotted for \(I_{zy}=f(K)\) at \(I_{ng}=0.8+j0.6\) and \(t=\infty\), and curve (6) for \(I_{ng}=0\) and \(t=\infty\).

As is seen from Fig. 1, with a reactoring ratio \(K<3.5\), the primary pickup current of the overcurrent relays may be increased to 1.7 times the rated generator current. A current setting lower than 1.7 times the rated generator current is inadvisable, since, with lower settings and faults beyond a reactor having a reactoring ratio greater than 3.5, the voltage interlock will still not permit the protection to operate. For faults beyond smaller reactances, however, the fault current will always be greater than 1.7 times the rated generator current.

Analogous calculations can also be made for a two-pole short circuit. In this case the residual voltage between the faulted phases \(U_0^{(2)}\) at \(t=0\), expressed as a percentage of rated voltage, is also calculated from expression (2). Its magnitude is determined by curve (1) in Fig. 3.

The residual voltage across the section between the faulted phases \(a_yU^{(2)}\) at \(t=\infty\) can be calculated as follows: from the calculated reactance \(x_{\text{calc}}=2x_c(1+K)\) and from the attenuation curves, the relative steady-state positive-sequence current \(I_{zy1}\) is determined; then the residual voltage, as a percentage of rated voltage, is calculated from the following expression:

\[ U_{0y}^{(2)}= \frac{\sqrt{3}\,I_{zy1}\,2x_p\,100}{\sqrt{3}} = 2Kx_cI_{zy1}100. \tag{13} \]

The curve of residual voltage between the faulted phases at \(t=\infty\), plotted from expression (13) for \(x_c=0.125\), is shown in Fig. 3 (curve 2). On the same figure are plotted the pickup and reset voltages of the voltage interlock, respectively equal to 75 and 90% of rated voltage.

It is evident from the indicated figure that the voltage interlock will operate reliably at \(K<3\).

To calculate the currents in a two-phase short circuit, assume that, before the occurrence of the short circuit, the generator had a load determined by expression (8), and that the dependence of this load on the degree of shunting \(\alpha\) and on the residual voltage at the buses \(U_0\) will be the same as in a three-phase short circuit. In this case the current in the undamaged phase will be equal to the load current, while in the damaged phases it will be determined by the following expressions:

a) for the leading phase

\[ I_{op} = \left( \frac{I'_{ng}\alpha}{U_0} + I_k \cos 60^\circ \right) + j \left( \alpha U_0 I''_{ng} + I_k \sin 60^\circ \right), \tag{14} \]

b) for the lagging phase

\[ I_{ot} = \left( \frac{I'_{ng}\alpha}{U_0} - I_k \cos 60^\circ \right) - j \left( \alpha U_0 I''_{ng} + I_k \sin 60^\circ \right), \tag{15} \]

where \(U_0\) is the residual voltage of the positive sequence,
\(I_k\) is the current of the two-phase short circuit.

Fig. 3

Fig. 4

Expressions (14) and (15) are written on the basis of the vector diagram of currents constructed for a two-phase short circuit between phases \(B\) and \(C\). The above-mentioned vector diagram is shown in Fig. 4; from its consideration it is evident that the leading-phase current will always be the larger in absolute value, and its smallest value will occur when the generator has no load before the short circuit.

For this case the curves of the dependence of the leading-phase current on the degree of reactance \(K\), shown in Fig. 3, have been plotted. Curve (3) gives the dependence \(I_{op}=f(k)\) at \(t=0\) and \(I_{ng}=0\), while curve (4) gives the dependence \(I_{op}=f(k)\) at \(t=\infty\) and \(I_{ng}=0\).

As is seen from Fig. 3, at a reactance ratio \(K \le 3\), the primary pickup current of maximum-current relays can be increased, without impairing the sensitivity of the protection in a two-phase short circuit, up to 1.8 times the rated current of the generator. However, proceeding from the sensitivity of the protection in a three-phase short circuit, the current setting of the maximum-current relays should be increased only up to 1.7 times the rated current of the generator.

On the basis of the curves in Figs. 1 and 3 one may also draw the conclusion that, at small degrees of reactance \((K < 3)\), voltmeter blocking with a primary setting \(U_{tr} = 0.75\,U_{nom}\) will operate quite reliably for all types of short circuit. This condition is difficult to satisfy for low-power feeders if reactors with nominal reactances of 2 to 6% are used on them. The question should be raised of manufacturing reactors for currents of 100–400 amperes with small reactances of 0.5–1%, which would make these reactors cheaper and, on the other hand, would make it possible to make maximum-current protection with voltmeter blocking more reliable. Another way out of this situation is to combine low-power feeders under one circuit breaker, i.e., to create group feeders.

Of very great interest is another solution to the problem of protecting generators from overcurrents—the use of low-relay schemes with increased sensitivity and selectivity. In Fig. 5 two variants of such schemes are given. The scheme of Fig. 5a was proposed by Candidate of Technical Sciences I. A. Syromyatnikov¹. In this scheme relay 1 is intended

Fig. 5

for protecting the generator against overload by operating current and acts on a signal with a time delay of 8–10 sec. Relay 2 has voltmeter blocking and protects the generator against three-phase short circuits with a time delay of 6–10 sec. Finally, relay 3 is included in the circuit through a negative-sequence current filter and operates with the same time delay as relay 2.

The scheme of Fig. 5b differs from the preceding one in that relays 2 and 3 are included through a combined positive- and negative-sequence current filter.

The sensitivity of the protection carried out by means of relay 2 was examined in detail above; therefore we shall not dwell on it here.

The sensitivity of the negative-sequence maximum-current protection is characterized by Fig. 6, which gives the dependences of the negative-sequence currents for a two-pole short circuit at \(t = 0\) (curve 1) and at \(t = \infty\) (curve 2). As is evident from this figure, negative-sequence maximum-current protection with a primary pickup current of 0.5 of the generator nominal current will operate at degrees of reactance \(K < 7\). Consequently, the low-relay protection scheme under consideration extends the limit of sensitivity for two-pole—

short circuit from \(K = 3\) to \(K = 7\), while for a three-phase short circuit the limit \(K < 3.5\) is retained.

If the feeders are enlarged by grouping them in such a way that the response multiplicity does not exceed 3.5, or these response limits are achieved by using reactors with reactances of \(0.5 \div 1\%\) on low-power feeders, then at \(U_{rp} = 0.75 U_{\text{nom.}}\) the low-relay scheme will ensure operation of the protection in all cases.

Fig. 6

If one adheres to the indicated point of view, then when selecting feeder reactors it is necessary to observe the condition that \(K < 3.5\). But then doubt may arise as to the effectiveness of using feeder reactors from the standpoint of limiting the interrupting capacity. How effective the use of reactors is at \(K = 3.5\) is evident from Fig. 7, where the dependence of the limiting system capacity \(S_c\) on the breaker interrupting capacity \(S_o\) and the system reactance \(x_c\) is plotted, \(S_c = f(S_o, x_c)\). In constructing the characteristics of Fig. 7, the system reactance in relative units was plotted along the abscissa, and the permissible system capacity in MVA along the ordinate. In these coordinate axes a family of straight lines was constructed for

Fig. 7

of various breaking capacities \(S_o\). The equation on the basis of which the indicated straight lines were constructed was obtained as follows.

The rms value of the periodic component of the current of a three-pole short circuit at \(t = 0\), in relative units, can be expressed as

\[ I_z^{(3)}=\frac{1}{x_c+x_p}=\frac{1}{x_c(1+K)}, \]

then the breaking capacity of the installation \((S_{oy})\), in relative units, at \(t = 0\) and a three-pole short circuit will have the following expression:

\[ S_{oy}=\frac{S_c}{x_c(1+K)}. \]

The breaking capacity of the circuit breaker of the reactor feeder may be written as:

\[ S_o=\frac{k_z S_c}{x_c(1+K)}, \]

where \(k_z\) is the safety factor, recommended by the “Guidelines for calculating short-circuit currents” to be taken within the range \(1.5 \div 2\).

Hence the permissible system power is:

\[ S_c=S_o x_c \frac{1+K}{k_z}. \tag{16} \]

The characteristics shown in Fig. 7 were constructed on the basis of equation (16). In the construction it was assumed that \(K = 3.5\) and \(k_z = 1.5\).

It is seen from Fig. 7 that, when using a VMG—133 type circuit breaker in 10.5 kV networks and with \(K = 3.5\) and \(x_c = 1\), the system power can be brought up to 1000 MVA. The use of MT—10 type circuit breakers increases the permissible system power (at \(x_c = 1\)) to 1500 MVA.

In conclusion, the following conclusions may be drawn.

1. To increase the sensitivity of generator protection against overcurrents, low-relay schemes with negative-sequence current filters should be used. This would extend the limits of protection sensitivity for a two-pole short circuit to \(K = 7\) and for a three-pole short circuit to \(K = 3.5\).

2. When designing the protection, a careful analysis of its sensitivity should be carried out and, if necessary, a reduction of “\(K\)” to the maximum permissible value should be achieved by using grouped feeders, installing reactors with large rated currents on low-power feeders, and by other means.

1. See Elektricheskie stantsii No. 3 for 1948, p. 42. ↩