ON METHODS FOR BALANCING THE ARMS OF GENERATOR DIFFERENTIAL PROTECTION

I. D. Kutyavin

The guiding instructions on relay protection, 1945 edition (directive part), in paragraph 163 recommend “striving to equalize the resistances of the arms of differential protection by means of the conductors themselves, and only when this is impossible to use an additional resistance.”

The necessity of equalizing the resistances of the protection arms is evident from Fig. 1, in which curve (1) represents the dependence of the effective value of the unbalance current on the ratio of the arm resistances under the normal operating conditions of the generator (scale of the ordinate axis in \(ma\)), while curve (2) represents the dependence of the greatest amplitude of the unbalance current on the ratio of the arm resistances during the transient process (scale of the ordinate axis in \(a\)). As is seen from this figure, a difference in the arm resistances exceeding 5–10% causes a sharp increase in the unbalance current.

The equalization of the resistances of the protection arms by means of the conductors themselves can be carried out in three ways:

1) by soldering off to the relay from the middle of connecting conductors of identical cross-section;

2) by a corresponding selection of the cross-sections and lengths of the conductor arms; and

3) by balancing the arms at the expense of the outgoing and return conductors.

In the first method of balancing, the conductors of the circulating-current circuit connecting the current transformers are laid without entering the control panel and have the same cross-section over their entire length. The soldering off to the relay is made from the middle of the connecting conductors by means of a tee branch coupling, as shown in Fig. 2. As a result, the conductors of the protection arms turn out to be of identical length and equal cross-section.

Fig. 1

In the second method of balancing, the connecting conductors are brought onto the control panel. Their length and cross-section are selected so that they satisfy the condition: \(s_1 : s_2 = l_1 : l_2\), which corresponds to equality of the arm resistances.

When standard conductor cross-sections are used, only a stepped adjustment of the arm resistances can be obtained; therefore, exact equalization of the resistances must be achieved by a corresponding selection of the cross-section and length of the conductors. Thus, for example, the construction lengths of the conductors

\(l_1 = 75 \text{ m}\) and \(l_2 = 60 \text{ m}\). We take the conductor cross section of the second arm \(s_2\) equal to \(4 \text{ mm}^2\). The conductor cross section of the first arm is

\[ s_1 = s_2 \cdot \frac{l_1}{l_2} = 4 \cdot \frac{75}{60} = 5 \text{ mm}^2. \]

We take the nearest larger standard cross section, \(6 \text{ mm}^2\). Then the length of this conductor must be increased to

\[ l_1 = l_2 \cdot \frac{s_1}{s_2} = 60 \cdot \frac{6}{4} = 90 \text{ m}. \]

The excess cable of the first arm (\(15 \text{ m}\)) can be laid in the cable mezzanine or under the floor decking behind the control panel.

The third method of balancing consists in connecting each pair of current transformers of the same phase by outgoing and return conductors without entering the control panel, as shown in Fig. 3. The relay is connected into the diagonal of the bridge formed by the current transformers and the connecting conductors.

Fig. 2

Fig. 3

All three methods considered make it possible to achieve complete equality of the resistances of the protection arms, and therefore the recommendation of the guiding instructions to use an additional resistance in some cases is not justified.

Let us compare the indicated balancing methods according to the following criteria:

1) copper consumption;
2) reliability of the circuit in the event of a break in a conductor of the circulating-current circuit;
3) convenience in operation;
4) magnitude of the unbalance current.

In terms of copper consumption, the first method is the most economical, the second is less economical, and the third is still less economical. The third method may require 1.5–2 times more copper than the first.

In terms of reliability of the scheme with respect to a break in a conductor of the circulating-current circuit, the first and third methods are the best, since they have the smallest number of connecting contacts in each phase of the circulating-current circuit.

In terms of convenience in operation (for example, during adjustment tests), the second method is the best, while the other two are equivalent.

In terms of the magnitude of the unbalance current, the first method should be the best, since it has the shortest length of connecting conductors in the circulating-current circuit, while the other two methods are approximately equivalent.

Conclusion

Each of the three methods indicated above for balancing the arms of differential protection completely solves the problem under consideration; therefore, in application to this circuit there is no need for additional resistances. Moreover, the first balancing method can provide a substantial saving of control-and-measuring cable and reduce the unbalance current in comparison with the circuits currently in use. This first method is the best and, undoubtedly, can be recommended for preferential application.