Current Transformers Biased by Secondary Current for Differential Protection

A. S. Baginskaya

(Presented by Professor, Doctor of Technical Sciences I. D. Kutyavin)

Current transformers biased by secondary current have until recently been used only for measuring purposes. In [1] it is noted that they cannot be used in relay-protection circuits because, under overcurrents, the error of such transformers increases considerably. However, investigations carried out by the firm AEG showed that the presence of additional magnetization does not worsen the errors under overcurrents in the primary circuit of the transformer (does not reduce the Überstromkennziffer). Thus, for example, AEG transformers with additional magnetization at a 20-fold current have a current error of about 5%, and at a 30-fold current—about 10% [2].

At the same time, magnetizing the cores of current transformers to an induction of about 6000 gauss excludes the presence of residual fluxes in them. The latter is especially important in those cases where current transformers in protection circuits operate together, as, for example, in differential-protection circuits. In such circuits current transformers may acquire residual fluxes that differ in magnitude and very often in direction, which leads to a considerable increase in the unbalance current during through short circuits. It is known that the majority of cases of false operation of differential protections occur for the reason indicated above [3].

The contradiction of opinions regarding the errors of transformers with series biasing under overcurrents, as well as their positive property of self-demagnetization in operating conditions (with a definite choice of parameters), made it necessary to investigate the possibility of using the indicated transformers in relay-protection circuits and, in particular, in differential-protection circuits.

The transformers proposed for differential-protection circuits are, in their construction, analogous to compensated current transformers with demagnetization. In contrast to the latter, the parameters of these current transformers are determined from the condition of magnetizing them by the normal operating current to an induction of 6000–7000 gauss, at which residual fluxes may practically be disregarded.

The analysis of the operation of a transformer with series biasing was performed on its model, shown in Fig. 1. Laboratory current transformers that were tested were made according to the same principle. In contrast to the actual transformer construction, its model has bias windings, containing \(w_{n/m}\) turns, on both halves of the core, while the numbers of turns of the primary and secondary windings are determined by the relation:

\[ w_2 = k_n w_1, \]

where \(k_n\) is the nominal transformation ratio of the current transformers.

The secondary winding is connected in series with the bias windings, which are connected to one another in series opposition.

The vector diagram of the magnetizing forces, fluxes, and e.m.f.’s, constructed for a transformer model with bias under the assumptions of linearity of the magnetic circuit, a small value of the inductive resistance of the secondary winding, a purely active load, and the absence of losses in the steel, is given in Fig. 2. The resultant magnetizing forces of the core halves \(\theta'_0\) and \(\theta''_0\) create in them fluxes \(\Phi'\) and \(\Phi''\). The fluxes \(\Phi'\) and \(\Phi''\) induce e.m.f.’s \(E'_2\) and \(E''_2\) in the secondary winding, and \(E'_{n/m}\) and \(E''_{n/m}\) in the bias windings. The resultant e.m.f. in the secondary circuit is \(E\), and it determines the magnitude of the secondary current, which, with an active load, coincides with it in phase. Neglecting the nonlinearity of the magnetic circuit, the e.m.f. of the bias windings is shifted with respect to \(E\), and therefore with respect to \(I_2\), by an angle \(\pi/2\), and represents the e.m.f. of self-induction of the bias windings. Such an e.m.f. may be represented as the opposite vector of the voltage drop from the current \(I_2\) in the inductive resistance \(j x_{n/m}\). In the transformer equivalent circuit, the resistance \(j x_{n/m}\) must be connected in series with the resistance of the transformer secondary winding and the active resistance of the bias windings.

Fig. 1.

Fig. 2.

The nonlinear dependence \(B=f(H)\), which manifests itself most strongly during overcurrents in the primary circuit, leads to a decrease in the angle between \(E_{n/m}\) and \(E\). In this general case, the e.m.f. \(E_{n/m}\) may be represented as the opposite vector of the voltage drop from the current \(I_2\) in some equivalent inductive-active resistance, which in the transformer equivalent circuit must be connected in series in the secondary circuit. The active resistance \(r_e\) has a positive value at small inductions and a negative value when the current transformer operates beyond the knee of the magnetization curve. The inductive resistance \(j x_e\) is always positive. The magnitude of these resistances is not constant. It depends on the degree of saturation of the transformer core, i.e., on the magnitude of the primary current.

Figure 3 gives the dependences of the equivalent active and inductive resistances of a laboratory current transformer with a core cross-section \(q=20\ \text{cm}^2\), with the number of turns of the primary and secondary windings \(w_1=w_2=100\) turns, and with the number of turns of the bias windings \(w_{n/m}=10\) turns, on the magnitude of the primary current. They were obtained

on the basis of experimentally obtained vector diagrams of the e.m.f. with an active resistance of \(0.1\ \Omega\) connected into the secondary winding of the transformer. As follows from the graphs presented, the negative equivalent active resistance (in the operating mode and during overcurrents) is small in magnitude and therefore cannot in any substantial way affect the transformation of the primary current. The positive inductive resistance \(jx_e\) considerably exceeds \(r_e\) in magnitude and is comparable with the resistance of the transformer secondary circuit during its normal operation in the differential-protection scheme. It loads the current transformer and to some extent worsens its output. However,

Fig. 3.            Fig. 4.

as experiments have shown, the influence of \(x_e\) on the accuracy of transformer operation is very insignificant, especially when supplementary resistances of the relay are connected in series.

The possibility of applying current transformers with biasing in differential-protection schemes can be established only by a careful investigation of the behavior of such transformers under transient conditions. In doing so, it is important to determine how the transient magnetizing current depends on the number of turns of the biasing windings and how effectively the transformers are demagnetized by the operating current.

To solve the questions posed, dependences were obtained of the maximum rms value of the magnetizing current on the magnitude of the primary current for different values of the number of turns of the biasing windings (Fig. 4). During the experiment the transient process in the primary circuit was accompanied by the flow of a current with the maximum possible aperiodic component. Curve 1 shows the variation of the maximum rms value of the magnetizing current with the primary current when the number of turns of the biasing windings is \(w_{n/m}=0\) turns and with preliminary magnetization of the transformer core to a residual induction of \(5\text{–}6\ \mathrm{kGs}\). Curves 2, 3, and 4 respectively depict the dependences of the maximum rms value of the magnetizing current on the primary current for \(w_{n/m}=0\) turns and a preliminarily demagnetized core, \(w_{n/m}=10\) turns, and \(w_{n/m}=20\) turns.

As can be seen from the graphs presented, the maximum magnetizing current practically does not change when the number of turns of the biasing windings is increased from 0 to 20. Residual magnetism leads to a considerable increase in the magnetizing current.

The results of the experiment indicate a positive influence of additional biasing of the cores of current transformers. Indeed, by eliminating residual magnetism, it at the same time does not lead to an increase in the transient magnetizing current; i.e., a current transformer with biasing behaves in the transient mode in the same way as a demagnetized transformer with a larger volume of steel.

Since the probability that residual fluxes are present in the cores of current transformers is very high, it is quite obvious that premagnetization leads to a considerable reduction in the maximum magnetizing current.

The weak dependence of such a current on the number of turns of the premagnetizing windings is explained as follows. During a transient process in the primary circuit, the transformer core is magnetized to a considerable induction by the aperiodic component of the magnetizing current. Additional premagnetization of parts of the core in opposite directions leads to the fact that, at any given moment, one half of the core is magnetized and its dynamic magnetic permeability decreases—and the more turns the premagnetizing winding has, the more it decreases—while the other half is demagnetized and its dynamic magnetic permeability increases. As a result, the equivalent magnetic permeability changes little with changes in the premagnetizing turns, and the transient magnetizing current is practically independent of the magnitude of the latter.

Fig. 5.

Fig. 6.

The magnitude of the steady-state magnetizing current increases as \(w_{p/m}\) increases, owing to the growth of saturation in both halves of the core.

It is interesting to note that, in the transient mode, the rms value of the alternating component of the magnetizing current is smaller than in the steady-state process (see the oscillogram of the primary current, secondary current, and magnetizing current, taken for a laboratory current transformer with \(w_{p/m}=20\) turns and shown in Fig. 5). This is caused by the fact that, in the indicated mode, successive demagnetization of the core halves occurs down to the region of maximum magnetic permeability. The latter leads to an increase in the equivalent magnetic permeability and, consequently, to a decrease in the alternating component of the magnetizing current. In this case the secondary current increases approximately to the magnitude of the referred primary current, and the transformer error decreases sharply. In view of the noted property of current transformers with series premagnetization, the possibility of a delay in the operation of a differential-protection relay during faults in the protected zone is eliminated.

How effective the use of transformers with premagnetization by the secondary current is in differential-protection circuits can be seen from Fig. 6, which presents the dependences of the maximum value of the amplitude of the transient unbalance current on the load current for various values of the short-circuit current. The graphs shown were obtained

for the differential protection of buses with one incoming and two outgoing circuits, implemented with laboratory current transformers having a core cross-section of \(10\ \text{cm}^2\). In carrying out the experiment, a pair of transformers participating in the conduction of the short-circuit current was magnetized to the maximum residual inductions of opposite sign, after which, with the aid of an oscillograph, the maximum unbalance current was recorded when a current with the greatest possible aperiodic component flowed through the primary circuit.

As can be seen from Fig. 6, elimination of the residual fluxes by the normal operating current is capable of reducing the transient unbalance current of the protection by approximately a factor of 10. Reducing the operating current to one-half of the normal value leads to a very small increase in the unbalance current. It has been established experimentally that the demagnetization time of transformer cores by the operating current does not exceed \(1\ \text{s}\).

Thus, premagnetization of transformers by the secondary current can, to a significant degree, increase the sensitivity of differential protection or, at a given sensitivity, its selectivity. Such transformers may find application in differential-protection schemes for generators, whose operation at less than half load is unlikely, and also in protection schemes for other elements whose minimum possible operating currents amount to \(40\%\) of the normal load current.

References

1. Butkevich Yu. V. et al. Electrical Part of Stations and Substations (ed. A. A. Glazunov), Gosenergoizdat, 1951.

2. Gorodetskii S. S. Measurements at High Voltage, Energoizdat, 1934.

3. Atabekov G. I. Relay Protection of High-Voltage Networks, Gosenergoizdat, 1949.