THE INFLUENCE OF RESIDUAL MAGNETISM OF CURRENT TRANSFORMERS ON THE OPERATION OF DIFFERENTIAL PROTECTION

I. D. Kutyavin

(Presented by Prof. V. K. Shcherbakov, Doctor of Technical Sciences)

Any transient process in the primary winding of current transformers, accompanied by the appearance of an aperiodic component in the magnetizing current, creates residual magnetism in their cores [1, 2].

As studies by N. P. Pogashev [1, 2] and other authors have shown, the residual induction in solid cores of current transformers may reach 6–7 kG and is quite stable under normal operating conditions. However, it must be borne in mind that transformers of one and the same phase of the protections under consideration may have different resistances in the secondary circuits, which is of particular importance in the case of short circuits in the primary circuit; they may also be under different conditions with respect to mechanical vibrations and ambient temperature. Thus, for example, current transformers of generator differential protection located in the switchgear are not subjected to mechanical vibrations and in winter may be under conditions of negative temperature. Current transformers located at the neutral terminals have a high positive ambient temperature and are under conditions of constant vibration of the supporting structures. This condition continues from one short circuit to another for several weeks or even months. This may lead to the fact that, before the next short circuit outside the zone, the cores of current transformers of one and the same phase of the generator differential protection may have residual magnetism different in magnitude. The cores of current transformers of one and the same phase of bus differential protection (and of three-winding transformers) may have different residual magnetism not only in magnitude, but also in sign. This is explained by the fact that external short circuits may occur on different outgoing lines. In such a case, the current transformers of the outgoing line will participate in carrying the short-circuit current only when that particular line is damaged, while the transformers of the supply lines will do so in all cases.

The presence of different residual magnetism in transformers of one and the same phase causes the appearance of large unbalance currents during through short circuits and often leads to incorrect operation of the protection.

In order to reduce the unbalance currents of generator differential protection, the current transformers intended for its implementation are selected by the manufacturer as a set in such a way that the transformers of one and the same phase are supplied with identical no-load characteristics. However, it is necessary to bear in mind that the form of the indicated characteristics under operating conditions will also depend ...

...and by the appearance in transformer cores of residual magnetism, which can distort these characteristics very strongly.

To illustrate what has been said, Fig. 1 shows the process of magnetization of the core of a current transformer during a short circuit in the primary circuit, when the core steel had, before the short circuit, a residual induction \(+B_0 = oa\). For greater clarity of the example, a particular case has been taken in which the induction \(B_0\) present in the steel before the occurrence of the short circuit is equal to the residual induction established in this transient process. In this case the change in induction \(B\) as a function of the magnetizing current \(i_0\) will proceed along the partial hysteresis loop \(ab\) in the direction of the arrows, and as a function of time \(t\)—along the curve shown at the left. In this case the average saturation of the steel remains constant, the magnetizing resistance of the transformer \(Z_0 = f(t)\) also does not change (see Fig. 1, left), and the amplitude of the current \(i_0\) does not change either.

Fig. 1.                                                                                                Fig. 2.

Figure 2 presents the nature of the change in the induction in the current-transformer core \(B\) and in the magnetizing resistance \(Z_0\) during a short circuit in the primary circuit, when the core steel before the transient process was completely demagnetized. The initial magnetization of the steel in this case occurs along the curve \(oa\), as the current \(i_0\) changes during the first half-period from 0 to \(2i_{k0}\), and the subsequent changes in induction \(B = \varphi_1(i_0)\) will proceed along the partial hysteresis loops \(ab\), \(bc\), \(cd\), \(de\), etc., in the direction of the arrows. Correspondingly, the induction in the steel \(B = \varphi_2(t)\) will change along the curve \(o, a, b, c, \ldots\), shown at the left. In this case the saturation of the core steel increases with time, the amplitude of the magnetizing current \(i_{k0}\) also increases, and the resistance \(Z_0 = f_2(t)\) decreases, asymptotically approaching \(Z'_0\).

Finally, Fig. 3 shows the change in the same quantities for the case when, before the occurrence of the transient process, the steel of the transformer core had a negative residual induction \(-B_0 = oa\). With the onset of the transient process, the induction in the core steel \(B = \varphi_2(t)\) during the first several half-periods passes from the negative region into the positive region and rapidly increases, changing in the direction \(a, b, c, d, \ldots\). The magnetizing resistance \(Z_0 = f_2(t)\) at the beginning of the process

has a large value, since the magnetization of the steel occurs in a region close to the maximum magnetic permeability, and then, as the steel becomes saturated, this resistance decreases sharply, approaching \(Z_o'''\). In connection with the decrease of \(Z_o\), the amplitude of the magnetizing current increases from one half-period to the next.

The curves in Figs. 1, 2, and 3 are constructed approximately and characterize only the physical aspect of the process of variation of the quantities \(i_o\), \(B\), and \(Z_o\) of a current transformer during a short circuit in the primary circuit and for various values of residual magnetism. In drawing up these figures, a number of assumptions were adopted, of which we shall indicate the following:

1) it was assumed that the aperiodic component of the magnetizing current at any instant of time is equal to the amplitude of the periodic component;

2) point \(b\) in Fig. 1, points \(a\), \(c\), \(e\) in Fig. 2, and points \(g\), \(k\), and \(m\) in Fig. 3 lie on the initial magnetization curve. In reality these points lie on the curves of subsequent magnetization, beginning at point \(d\) in Fig. 1, at points \(b\), \(d\), and \(f\) in Fig. 2, and at points \(h\), \(l\), \(n\) in Fig. 3, which lie above the initial magnetization curve.

Fig. 3.

The minimum magnetizing impedances \(Z_o'\), \(Z_o''\), and \(Z_o'''\), toward which the impedance \(Z_o\) in Figs. 1–3 tends, are in the following relation:

\[ Z_o' < Z_o'' < Z_o'''. \]

The equality sign here will occur for very high saturations of the steel and a large time constant of the transformer secondary circuit.

The initial values of the impedance \(Z_o\) in Figs. 2 and 3 will be different, and moreover \(Z_{on}'' < Z_{on}'''\), since in Fig. 3 the remagnetization of the steel proceeds from the negative region to the positive one, and the change of induction in the transformer core in the first half-periods occurs in the region close to the maximum magnetic permeability. This also explains the more rapid decrease of \(Z_o\) in Fig. 2 than in Fig. 3. The initial value of \(Z_o\) in Fig. 1 is equal to its minimum value \(Z_o'\).

Let us try further to find at least an approximate relation between the initial and minimum values of \(Z_o\) in Figs. 2 and 3. For this purpose it is necessary to take into account that the aperiodic component of the magnetizing current produces bias magnetization of the core steel and thereby has a very strong influence on the magnitude of the impedance \(Z_o\). This influence is evident from Fig. 4, which gives the dependence of \(Z_o \simeq \omega L_o\) on the maximum induction in the core \(B\), for various values of the relative aperiodic component of the magnetizing current \(\beta\), found experimentally.

The data for constructing the curves of Fig. 4 were obtained with simultaneous magnetization of the core steel by sinusoidal and direct currents. The impedance \(\omega L_o\) was determined from the ratio of the winding e.m.f. to the magnetizing periodic current. The maximum induction \(B\), plotted on the abscissa axis, was found from the total ampere-turns, consisting

from the ampere-turns of the sinusoidal and direct currents. The ratio of the ampere-turns of the direct current to the amplitude ampere-turns of the alternating current is denoted by \(\beta\).

For Figs. 1–3, the relative aperiodic current is \(\beta = 1\). As investigations by many authors have shown, in the transformation of short-circuit currents containing a large aperiodic component, the value of \(\beta > 1\). Let us now consider the question of interest to us.

The minimum value of \(Z_0\) in Figs. 1–3 occurs at \(\beta = 1\) and when the magnetizing current reaches its greatest value. The value of the resistance \(Z_0\) in this condition (or of the resistances \(Z'_0\), \(Z''_0\), \(Z'''_0\)) is characterized by the curve \(\beta = 1\) (Fig. 4) (resistance \(Z_0 = \omega L_0\)). During the first several half-periods, the ampere-turns of the aperiodic component in Figs. 2 and 3 are expended on remagnetizing the steel; therefore the initial value of \(Z_0\) in these figures, characterized by the slope of the partial hysteresis loops, is determined by the curve \(\beta \cong 0\), Fig. 4. A comparison of the curves for \(\beta = 0\) and \(\beta = 1\) in Fig. 4 shows that the initial value of \(Z_0\) may be several times greater than the minimum (in Fig. 4, four times). In reality the values of the resistances \(Z'_0\), \(Z''_0\), and \(Z'''_0\) will be considerably smaller than those indicated, since the maximum transient magnetizing current often has \(\beta > 1\).

Fig. 4.

As indicated above, the current transformers of generator differential protection, during short circuits outside the protection zone, acquire residual magnetism of one sign; however, the magnitude of the residual induction before the next through short circuit may be different, since one of the transformers may retain its residual induction at the maximum level (6–7 kGs), while another (of the same phase) by that time may prove to be completely demagnetized. Therefore, the magnetizing impedances of transformers of one and the same phase may differ by several times. In the differential protection of power transformers and busbars, the residual magnetism of current transformers of one and the same phase may be of different sign; therefore the difference in the magnetizing impedances of the transformers of these protections will be still greater.

As can be seen from Figs. 2 and 3, the difference between the initial and minimum values of the magnetizing impedances disappears after several half-periods; therefore large surges of unbalance current caused by the influence of residual magnetism of the transformers can be expected only in the first half-periods. This is confirmed by Fig. 5, which gives oscillograms of the primary short-circuit current (curves 1 and 3) and of the corresponding unbalance current (curves 2 and 4) for the busbar differential protection shown in Fig. 6. The circuit was assembled from three current transformers 1, 2, and 3 in accordance with one supply line and two outgoing lines. The current transformers had a solid core with a cross section of \(10\ \text{cm}^2\), assembled from steel of type TP current transformers. The windings had 100 turns each. The primary current was recorded by loop \(i_1\), and the unbalance current by loop \(i_{\text{unb}}\).

The magnitude of the primary current in the steady-state process was \(15\ a\). The total impedances of the protection arms were approximately the same, and the relay resistance was equal to the loop resistance and amounted to \(0.3\ \Omega\).

To clarify the processes recorded in Fig. 5, let us assume that interphase short circuits occur outside the protection zone, in succession

Fig. 5.

on the outgoing lines \(a\) and \(b\) (Fig. 6). These short circuits can be simulated by successively switching the selector to points \(a\) and \(b\). Let us suppose that, when the selector is switched to point \(a\) (see curves 1 and 2), current transformers 1 and 2, during the transient process, are magnetized to a certain negative residual induction in accordance with the negative aperiodic component of the primary current. Then

Fig. 6.

(the short circuit occurs on line \(b\)) the selector is placed at point \(b\), and transformers 1 and 3 are magnetized to a certain positive residual induction, since the aperiodic component of the primary current is positive. But then the short circuit may occur again on line \(a\), for example, with a negative aperiodic component of the primary current (the selector is switched to point \(a\)). Before this short circuit, transformer 1 had a positive residual induction and therefore, with the occurrence of the short circuit, must be remagnetized as shown in Fig. 3,

whereas transformer 2 had negative induction and will be magnetized in accordance with Fig. 1. In connection with this, the unbalance current upon short-circuit at point \(a_2\), during the first two periods (while transformer 1 is being remagnetized), reaches \(14a\), with a primary-current amplitude of \(21a\) and a transformation ratio equal to 1.

It is interesting to note that both at the first switching of the switch to point \(a\) and at the second (see curve 1), the primary current is approximately the same in magnitude and in the character of its variation, whereas the corresponding unbalance current (see curve 2) in the second switching was twice as large as in the first. The same phenomenon can also be observed in studying curves 3 and 4 of Fig. 5. Of interest is oscillogram \(4\)—\(b_2\), in which the unbalance current during the first period, while transformer 3 is being remagnetized, is inverted and reaches a large value, while in the second period it returns to the normal phase.

When analyzing the curves of Fig. 5 it is necessary to bear in mind that the oscillograms shown were cut from a photographic-paper tape on which several dozen transient processes had been recorded. Therefore the oscillograms of the unbalance current \(a_1\), \(b\), \(a_2\) on curve 2 and the oscillograms \(b_1\), \(a\), \(b_2\) on curve 4 depend on the preceding magnetic state of the transformers.

Fig. 7.

Fig. 7 is very interesting; it presents an oscillogram of the primary transient current (curve 1) and oscillograms of the transient unbalance current (curves 2–4), obtained according to the circuit of Fig. 6.

Curve 2 represents an oscillogram of the transient unbalance current taken according to the circuit of Fig. 6 with alternate switching of the switch to points \(a\) and \(b\). In this oscillogram the influence of the residual magnetism of the transformers is most sharply reflected; in connection with this, during the first several periods the unbalance current has a large value. Curve 3 represents the greatest transient unbalance current for the same circuit (Fig. 6), but the switch was switched only to point \(a\) (or to point \(b\)); therefore the current transformers traversed by the primary transient current have the same residual magnetism before each transient process. In view of this, the greatest unbalance current proved to be considerably smaller than the preceding one. Finally, curve 4 shows the greatest unbalance current of a protection made with current transformers having an air gap \(3\) mm long. The remaining data of the transformers and of the protection circuit were the same as in Fig. 6. When oscillogram 4 was taken, the switch in the circuit of Fig. 6 was switched alternately to points \(a\) and \(b\).

The foregoing makes it possible to draw the following conclusions:

1) the initial magnetizing resistances of current transformers whose cores have different residual magnetism may differ from one another by several times, if the magnetizing current contains an aperiodic component;

2) differential-protection circuits made with normal current transformers are subject to the influence of residual magnetism and may have very large transient unbalance currents;

3) differential-protection schemes implemented with current transformers having an air gap will have a significantly smaller unbalance current than the schemes indicated in item 2.

REFERENCES

1. Potashev N. P. Operation of current transformers under transient processes. Electric Stations, 10, 1935.

2. Potashev N. P. Residual induction in current transformers. Bulletin of the Electrical Industry, 3, 1937.