DIFFERENTIAL BUSBAR PROTECTION USING CURRENT TRANSFORMERS WITH AN AIR GAP

I. D. Kutyavin and A. S. Sharygina

The differential protection of busbars currently in use, as is known, has very low sensitivity and selectivity. The reason for this is the large unbalance current that appears in the relay circuit under through short-circuit currents containing a considerable aperiodic component. In addition, the magnitude of the unbalance current of differential busbar protection is greatly affected by the magnitude and sign of the residual magnetism of the cores of the current transformers participating in the conduction of the through short-circuit current.

In view of the unsatisfactory performance of the differential busbar protection being used, many proposals have recently appeared for improving this protection; among them, special attention is deserved by differential busbar protection with current transformers without steel cores, in which the influence of residual magnetism and iron saturation on the magnitude of the unbalance current is completely eliminated. However, current transformers with cores made of nonmagnetic material have very low power, as a result of which difficulty arises in selecting the type of relay.

However, the same result can be obtained by using current transformers with steel cores having air gaps. With the aid of an air gap it is possible to eliminate the influence of residual magnetism and to make the current transformers operate on the rectilinear portion of the magnetization curve. To illustrate this situation, Fig. 1 gives the principal characteristics for a current transformer with a transformation ratio equal to unity and with a steel-core cross section of \(10\ \text{cm}^2\). The core of this current transformer was assembled from the iron of a TPO-type transformer and provided with an air gap of \(2.5\ \text{mm}\). The primary and secondary windings each had 100 turns. The resistance of the no-load branch at small magnetizing currents was \(3\ \Omega\).

Fig. 1

Curve 1 of this figure expresses the dependence of the secondary current on the primary current (with a load resistance of 0.35 ohm) and makes it possible to judge the magnitude of the current error, which for this transformer is approximately 5%. It is interesting to note that the current error for current transformers with an air gap will be constant at an induction in the core up to 8000–10000 gauss and will depend only on the magnitude of the external resistance.

Curve 2 of Fig. 1 gives the dependence of the secondary e.m.f., or the induction \(B\), on the primary magnetizing current \(I_1\), with the current transformer operating at no load. This curve shows that saturation of the core for this transformer begins to appear at 1000 ampere-turns, or at 22 av/cm, and that the voltage at the terminals of the open secondary winding of current transformers with an air gap does not reach a dangerous value.

With the use of current transformers with an air gap, it is in principle possible to apply two protection schemes, namely: 1) differential protection with voltage balance and 2) protection with current balance. The present article is devoted to consideration of these protection schemes.

Differential busbar protection with voltage balance

The schematic diagram of the protection is shown in Fig. 2. The current transformers in this scheme are connected phase by phase, in series with one another and with the relay. In contrast to the protection of the ASEA firm, the circulating-current circuit is entirely absent, since under normal operating conditions and during through short circuits the voltages at the terminals of the current transformers are not large.

As is known, for selective operation of any differential protection it is necessary that the relay pickup current be greater than the maximum unbalance current flowing in the relay during a through short circuit in the primary circuit. Therefore it is necessary to establish the dependence of the unbalance current on the basic parameters of the protection. For this purpose we shall use the equivalent circuit of the protection, shown in Fig. 3, and assume that the through short-circuit current flows only in the first two circuits in the direction of the arrows. We neglect the residual load current of the other circuits. The designations of all quantities are given in the diagram and do not require additional explanation. In all derivations we shall use resistances and currents referred to the number of turns of the primary winding.

Fig. 2

The sum of the e.m.f.s and voltage drops in the secondary circuit of the protection:

\[ (I_k - I_{nb}) z_{01} + (-I_k - I_{nb}) z_{02} + I_{nb}(z_1 + z_2 + z_3 + z_4 + z_{03} + z_{04} + z_p). \tag{1} \]

The unbalance current on the basis of (1) is:

\[ I_{ub}=\frac{I_k(z_{01}-z_{02})}{(z_{01}+z_1)+(z_{02}+z_2)+(z_{03}+z_3)+(z_{04}+z_4)+z_p}. \tag{2} \]

To simplify the problem, one may neglect the difference in the resistances of the magnetizing circuits \(z_{01}, z_{02}\ldots\) and in the resistances of the secondary windings of the transformers \(z_1, z_2\ldots\), which enter into the denominator of expression (2), assuming that

Fig. 3

\[ z_{01}+z_1=z_{02}+z_2=z_{03}+z_3=z_4+z_{04}=z_x. \tag{3} \]

In addition, let us denote by \(m\) the number of current transformers connected in series in the circuit. Then expression (2) will have the following form:

\[ I_{ub}=\frac{I_k(z_{01}-z_{02})}{mz_x+z_p}. \tag{4} \]

As is evident from (4), the unbalance current depends not only on the parameters of the current transformers, but also on their number connected into the circuit.

A dependence analogous to expression (4) can also be obtained for any number of transformers participating in operation. Let, for example, in the circuit of Fig. 3 a short circuit occur on the extreme right feeder with current \(I_4\), while the left feeders feed the short-circuit point, sending currents \(I_1\), \(I_2\), and \(I_3\) to the buses, so that the primary currents have the following relation:

\[ I_1+I_2+I_3=I_4. \tag{5} \]

The sum of the electromotive forces and voltage drops will have the following expression:

\[ (I_1-I_{ub})z_{01}+(I_2-I_{ub})z_{02}+(I_3-I_{ub})z_{03}+(-I_4-I_{ub})z_{04}= \]

\[ =I_{ub}(z_1+z_2+z_3+z_4+z_p). \tag{6} \]

The unbalance current from expression (6) is

\[ I_{ub}=\frac{I_1z_{01}+I_2z_{02}+I_3z_{03}-I_4z_{04}}{mz_x+z_p}. \tag{7} \]

If one sets \(z_{01}=z_{02}=z_{03}\), then expression (7) becomes (4). The dependence of \(I_{ub}\) on the short-circuit current is shown in Fig. 4, from which it is evident that this dependence has the form of a magnetization curve. This is explained by the fact that the unbalance current is proportional to the sum of the electromotive forces of the circuit, which have the form of the magnetization curve (curve 2

Fig. 1), since, despite the presence of an air gap in the core, at large magnetizing currents saturation of the iron begins to appear.

Figure 4 also shows the dependence of the unbalance current on the number of current transformers in the circuit. As the number of current transformers connected in series is increased, the unbalance current decreases, which is in complete agreement with expressions (4) and (7). The decrease of \(I_{nb}\) in the figure occurs somewhat more rapidly because of the appearance of iron saturation.

Curves of the unbalance current similar to those in Fig. 4 can easily be obtained during adjustment tests of the protection by applying the load current to the busbars or by raising from zero the current connected directly

Fig. 4

Fig. 5

to the busbars of a specially assigned generator. The curves obtained can be extended (bearing in mind that their shape is analogous to the magnetization curve) to an abscissa equal to the greatest rms value of the through short-circuit current, and in this way the maximum periodic unbalance current \(I_{nbm}\) can be determined. But for setting the protection it is necessary to know the maximum unbalance current flowing through the relay under through overcurrents. To determine the magnitude of the unbalance current in this condition, several dozen oscillograms were taken, one of which is given in Fig. 5. Curve (1) of this figure expresses the changes in the primary overcurrent, and curve (2) the unbalance current. As was to be expected, the amplitude of the periodic unbalance current remains constant throughout the entire duration of the transient process and is equal to the amplitude of the steady-state current, since there is no saturation of the transformer iron.

The aperiodic unbalance current in this case will also consist of two components: a part of the aperiodic component generated by the secondary circuit of the current transformers, and a part of the aperiodic component of the primary current.

At the first instant of the transient process, the first component of the aperiodic current has the predominant value, but then this component rapidly decays; therefore the aperiodic unbalance current, before it de—

decay, changes its sign. This is explained by the fact that the time constant \(T_2\) of the secondary circuit of the current transformers with an air gap used in our experiments was less than the time constant of the primary circuit \(T_1\). It should be expected that, under actual operating conditions, in most cases we shall have such a relationship between the time constants.

It follows from the foregoing that the unbalance current will have its greatest value in the first half-period after the beginning of the transient process. If, in doing so, the damping of the total aperiodic current is neglected, which will increase the safety factor, then the rms value of the total unbalance current \(I_{nbr}\) can be determined on the following basis:

\[ I_{nbr}=\sqrt{3}\cdot I_{nbm}, \tag{8} \]

where \(I_{nbm}\) is the maximum periodic unbalance current, determined by the method described above for the maximum through overcurrent.

The pickup current of the instantaneous relay must be greater than the current \(I_{nbr}\) determined from (8):

\[ I_{pt}=k_n I_{nbr}=\sqrt{3}\,k_n I_{nbm}, \tag{9} \]

where \(k_n>1\) is a safety factor, the value of which can be established only on the basis of operating experience.

When experimentally determining the value of \(I_{nbm}\) by the method described above, it is necessary to bear in mind that the magnitude of this current will also depend on the number and combination of current transformers participating in carrying the through overcurrent.

However, the sensitivity of the protection depends not only on the magnitude of the unbalance current, but also on the current in the relay for faults in the protected zone, and consequently also on the accuracy of operation of the current transformers.

To clarify the dependence of the relay current on the fault current, let us use the circuit of Fig. 3. Suppose that the fault has occurred on the protected buses and that the fault current flows to the buses only through the extreme left feeder.

Then, on the basis of Kirchhoff’s second law:

\[ (I_k-I_p)z_{01}=I_p(z_1+z_2+z_3+z_4+z_{02}+z_{03}+z_{04}+z_p). \tag{10} \]

The relay current from (10) is

\[ I_p=\frac{I_k z_{01}}{mz_x+z_p}. \tag{11} \]

In the case where the buses are fed through the three left-hand feeders (Fig. 3), and with a fault in the protection zone, in expression (7) the current \(I_4=0\). Then the relay current will have the following expression:

\[ I_p=\frac{I_1 z_{01}+I_2 z_{02}+I_3 z_{03}}{mz_x+z_p}. \tag{12} \]

It follows from expressions (11) and (12) that the relay current for faults on the protected buses is also inversely proportional to the number of current transformers connected in series in the protection scheme. What has been said is well illustrated by Fig. 6, which plots the dependence of \(I_p\) on the short-circuit current, obtained experimentally.

Expressions (11) and (12) are practically identical, and when \(z_{01}=z_{02}=z_{03}\), expression (12) becomes (11).

Comparison of expressions (4) and (11), (7) and (12) shows that the unbalance current in the relay under through overcurrents and the relay current under faults on

the protected buses have the same law of dependence on the number of transformers connected into the circuit and on the relay resistance. Therefore, the sensitivity of this protection will not depend on the number of feeders connected to the protected buses.

If the sensitivity of the protection is defined as the ratio of the unbalance current from (4) or (7) to the current in the relay when there is a fault on the buses from (11)

Fig. 6

or (12), then this sensitivity, on the basis of (4) and (11), will have the following expression:

\[ a=\frac{I_{nb}}{I_p}=\frac{z_{01}-z_{02}}{z_{01}} . \tag{13} \]

The same, on the basis of (7) and (12):

\[ a=\frac{I_1 z_{01}+I_2 z_{02}+I_3 z_{03}-I_4 z_{04}} {I_1 z_{01}+I_2 z_{02}+I_3 z_{03}} . \tag{14} \]

And here expression (14), when \(z_1=z_{02}=z_{03}\), is transformed into (13). In addition, expressions (13) and (14) confirm the conclusion made above that the sensitivity of this protection will not depend on the relay resistance \(z_p\) and the number of current transformers in phase \(m\).

It can further be proved that this protection will have optimum sensitivity when \(z_p=mz_x\). To prove this, we determine the value of the sum \(\Sigma Iz\), appearing in the numerator of the right-hand side of expression (12), as a function of \(I_{pT}\).

\[ \Sigma Iz=I_{pT}(mz_x+z_p)=mz_x I_{pT}+\frac{s_p}{I_{pT}}, \tag{15} \]

where \(s_p\) is the power consumed by the relay coil at the pickup current.

The first derivative of the function \(\Sigma Iz=f(I_{pT})\):

\[ \frac{d(\Sigma Iz)}{dI_{pT}}=mz_x-\frac{s_p}{I_{pT}^2}=mz_x-z_p=0, \tag{16} \]

whence we obtain that

\[ z_p=mz_x . \tag{17} \]

The pickup current corresponding to the optimum operating conditions of the protection is

\[ I_{pT}=\sqrt{\frac{s_p}{mz_x}} . \tag{18} \]

All tests with this protection scheme were carried out using the current transformers described at the beginning, with \(z_p = 0.35\ \Omega\) (the resistance \(z_p\) includes also the resistance of the connecting leads).

Differential busbar protection with current balance

The schematic diagram of the protection for one of the phases is shown in Fig. 7. In the scheme under consideration, the secondary windings of the current transformers, under normal conditions and during through overcurrents, are traversed by a secondary current that produces a demagnetizing action on the primary; therefore, the induction in the cores of the current transformers in this protection scheme,

Fig. 7

other conditions being equal, will be smaller than in the protection with voltage balance considered above. As a result, this protection will have a smaller unbalance current in comparison with the preceding one.

In determining the magnitude of the unbalance current for this scheme, let us first also consider the simplest case, when only the two left-hand transformers participate in carrying the through overcurrent. The equivalent circuit for this mode is shown in Fig. 8.

Fig. 8

Suppose that in the primary circuit the current \(I_1\) flows only through the extreme left-hand feeder. Then we can write the following relation, using the notation adopted earlier:

\[ (I_1 - I_1') z_{01} = I_1' z_1 + I_1' \frac{z_x z_p}{z_x + (m - 1) z_p}. \tag{19} \]

From equation (19) one can determine the current \(I_1'\):

\[ I_1'=\frac{I_1 z_{01}\left[z_x+(m-1)z_p\right]}{z_x\left(z_x+m z_p\right)} . \tag{20} \]

Let us now determine that part of the current \(I_1'\) which enters the relay:

\[ I_{p1}=I_1'\frac{z_x}{z_x+(m-1)z_p} =\frac{I_1 z_{01}}{z_x+m z_p}. \tag{21} \]

Analogous expressions can also be obtained for the currents in the relay supplied by the current transformers of the other feeders.

Then the unbalance current in the relay in the case under consideration, when only the two left-hand feeders take part in carrying the through overcurrent, will have the following expression:

\[ I_{nb}=I_{p1}-I_{p2} =\frac{I_1 z_{01}-I_1 z_{02}}{z_x+m z_p} =\frac{I_1\left(z_{01}-z_{02}\right)}{z_x+m z_p}. \tag{22} \]

In the case where the buses are supplied through three left-hand feeders, and the through short circuit has occurred on the right-hand feeder, the unbalance current will have the following expression:

\[ I_{nb}=\frac{I_1 z_{01}+I_2 z_{02}+I_3 z_{03}-I_4 z_{04}}{z_x+m z_p}. \tag{23} \]

As is seen from (22) and (23), also for the protection under consideration the unbalance current is inversely dependent on the number of transformers in the scheme and on the relay resistance. This is also confirmed by Fig. 9, which shows the

Fig. 9

dependence of \(I_{nb}\) on the primary through overcurrent and on the number of transformers \(m\), obtained experimentally.

Curves analogous to Fig. 9 can also be easily obtained during adjustment of the protection by raising the current on the buses from zero with a short circuit outside the protection zone.

These curves should have the form of a straight line if the induction in the core does not exceed 8000–10000 gauss. At higher inductions the unbalance current will increase sharply.

The limiting primary current at which the induction in the core of the most heavily loaded current transformer will not exceed the indicated values can be determined from the following expression:

\[ I_{pr}=\frac{222\,q\,w_2\,B_m\,n_T}{K_2\,z_2\,10^8}; \tag{24} \]

where \(q\) is the cross section of the transformer core,
\(w_2\) is the number of turns of the secondary winding,
\(n_T\) is the transformation ratio,
\(B_m\) is the maximum permissible induction,
\(z_2\) is the total resistance of the secondary circuit of the current transformer together with the connecting leads,
\(K_0\) is a coefficient taking into account the error of the current transformer and equal to the secondary current, expressed in relative units of the primary current. This coefficient is easily determined experimentally.

To avoid the appearance of large unbalance currents in the relay circuit, it is necessary that the greatest effective surge current of the fault be less than the limiting current determined from (24).

In order to clarify the nature of the change in unbalance current in this scheme under through overcurrents, we also recorded several dozen oscillograms, the most characteristic of which is shown in Fig. 10. It is evident from this figure that, with a primary current (curve 1) containing the full aperiodic current, the aperiodic component in the unbalance current (curve 2) is almost absent. We did not succeed in obtaining a more offset unbalance current, evidently because the time constant of the secondary circuit of the protection was close to zero owing to the very small total inductance of the current transformers connected in parallel. However, in order to increase the reliability of operation of the protection implemented according to this scheme, the greatest calculated unbalance current may be determined from expression (8), and the relay pickup current from expression (9).

Fig. 10

To determine the magnitude of the current in the relay during a fault in the zone of the protection under consideration, we shall use expressions (22) and (23).

The current in the relay when the busbars are fed only through the left feeder is determined from (22) with \(I_2=0\):

\[ I_p=\frac{I_1 z_{01}}{z_x+m z_p}. \tag{25} \]

The current in the relay when the busbars are fed through the three left feeders can be determined from (23) with \(I_4=0\):

\[ I_p=\frac{I_1 z_{01}+I_2 z_{02}+I_3 z_{03}}{z_x+m z_p}. \tag{26} \]

The sensitivity of the protection when the buses are fed by one feeder will be equal to the ratio of the unbalance current from (22) to the current in the relay from (25):

\[ \alpha=\frac{z_{01}-z_{02}}{z_{01}} . \tag{27} \]

The same, when the buses are fed by the three left-hand feeders, on the basis of (23) and (26):

\[ \alpha=\frac{I_1 z_{01}+I_2 z_{02}+I_3 z_{03}-I_4 z_{04}} {I_1 z_{01}+I_2 z_{02}+I_3 z_{03}} . \tag{28} \]

From the expressions obtained, (27) and (28), it is evident that the sensitivity of differential busbar protection with current balance also does not depend on the number of transformers in the circuit or on the resistance of the relay.

Moreover, expressions (27) and (28) are respectively identical with expressions (13) and (14), obtained for protection with voltage balance; this indicates that the sensitivity of the two circuits under consideration is the same for all values of the relay resistance.

The structure of expressions (13), (14), (27), and (28) also shows that the sensitivity of the protection circuits under consideration will be determined mainly by the accuracy of the dimensions of the air gap of the cores, since the resistances of the magnetizing circuits of the transformers \(z_0\) depend almost exclusively on the air gap. The other factors (quality of the iron, presence of residual magnetization, difference in the resistances of the secondary circuits of the transformers, etc.) will not have a noticeable effect on \(z_0\).

Fig. 11.

Using the above method for determining the conditions of optimal protection sensitivity, it can be established that this optimal sensitivity for the protection under consideration will occur at a relay resistance

\[ z_p=\frac{z_x}{m} \tag{29} \]

and relay pickup current

\[ I_{pT}=\sqrt{\frac{m s_p}{x}} . \tag{30} \]

The expressions obtained, (25) and (26), agree well with the data of Fig. 11, in which the dependence \(I_1=f(I_1,m)\), obtained experimentally, is plotted.

All experiments for this protection were carried out using the current transformers described at the beginning, with \(z_p=0.35\ \Omega\) (the resistance \(z_p\) also includes the resistance of the connecting wires).

In conclusion, the following should be noted:

1. The use of current transformers with an air gap for differential busbar protection is of great interest, since it may lead to an increase in the sensitivity of the protection. The information given on p. 392 in G. I. Atabekov’s book Relay Protection of High-Voltage Networks concerning the sensitivity of this protection requires substantial correction.

2. In order to determine the advantages of current transformers with an air gap in differential busbar protection schemes, trial operation of several protection sets using them should be organized.

3. Current transformers of this type must be manufactured from iron produced with one and the same die, so that their characteristics are as nearly identical as possible.

4. The cost of current transformers with an air gap will differ little from the cost of ordinary ones; therefore, the economic factor will not hinder their application.

5. Although the theoretical sensitivity of the protections considered has proved to be the same, protection with current balance will probably find wider use, since the current transformers of this protection will have less magnetization owing to the demagnetizing action of the secondary current. Therefore, when the same current transformers are used, this protection will have lower unbalance currents.