ON THE INFLUENCE OF RESIDUAL FLUX DENSITIES IN CURRENT TRANSFORMER CORES ON THE EFFECTIVENESS OF BALANCING THE ARMS OF DIFFERENTIAL PROTECTION

V. S. KOLESNIKOV

(Presented by the scientific seminar of the Department of Electric Power Stations and Networks)

It is known that, in the cores of current transformers of differential protection, under certain conditions residual flux densities may appear and persist for a long time. In this case the cores of the current transformers forming the arms of the differential protection may have residual flux densities differing not only in magnitude but also in sign. The presence of residual magnetization, especially when its signs are different, leads to a considerable increase in the transient unbalance current of differential protection during external short circuits, the consequence of which is false operation of the protection.

According to data from a number of researchers [1], [2], [3], standard high-voltage current transformers may acquire, under operating conditions, residual flux density of up to 7.0–10.0 kilogauss, depending on the grade of steel of the cores.

It has already been pointed out earlier [5] that the effectiveness of balancing the arms of differential protection with rapidly saturating elements is practically independent of the magnitudes and sign relationship of the residual flux densities in the cores of the current transformers. The present article considers certain regularities of transient processes in the secondary circuits of differential protection that make it possible, to a considerable degree, to explain the preservation of the effect of arm balancing despite the presence of residual magnetization in the current transformers.

First of all, let us estimate the influence of residual fluxes on the magnitude and character of the time variation of the magnetizing currents of current transformers, assuming that these transformers are connected differentially according to the circulating-current scheme. Figure 1 gives curves of variation of the magnetic flux densities in the core of one of the current transformers (TT-1) during the transient process for residual flux densities differing in magnitude and sign. Figure 2 shows curves of variation of the magnetizing currents of current transformers TT-1 (curves 1 and 1′) and TT-2 (curve 2). The dependences \(B(t)\) and \(i_0(t)\) were obtained as a result of graphical calculations carried out by the method of Yu. M. Korshunov [4], taking remagnetization along partial magnetization curves into account. The calculation was performed for the case when, at the moment the primary current (the current of an external short circuit) was switched on, it contained the largest possible aperiodic component (that is, it is assumed that the switching-on …

occurs at the moment when the voltage passes through zero, with a practically purely inductive resistance of the primary circuit). The main parameters of the current transformers are given in Table 1.

Table 1

The calculated value of the primary current is 10 amperes, with the time constant of the primary circuit equal to 0.07 sec. The specific parameters of transformers TT-1 and TT-2 (i.e., their actual parameters referred to 1 cm of length, 1 cm² of core cross section, and one turn of the winding) [3] differ from one another by approximately a factor of six. The same difference between the specific parameters of standard high-voltage current transformers GPSHFD-10 3000/5 and TVD-110 750/5 or TFND-110 1500/5 and TVD-220 600/5. Thus, in terms of its parameters, the calculation scheme under consideration approaches to a significant degree the real schemes of differential protection of power transformers.

Fig. 1.

Analyzing the curves \(B(t)\) and \(i_0(t)\) (Figs. 1, 2), it is not difficult to establish that, when the sign of the residual induction coincides with the direction of increase of the dc component of the flux, the aperiodic component of the magnetizing current and the corresponding flux reach their maximum the sooner, the greater the absolute value of the residual induction.

If, however, the direction of increase of the dc component of the flux is opposite in sign to the residual induction, then the larger the value of this induction, the later the aperiodic component of the magnetizing current and the corresponding flux reach their maximum values. Let us compare the curves of variation of the magnetizing currents of TT-1 (Fig. 2) for the following two cases:

a) at the maximum value of the residual induction (6 kgf) in the core of the current transformer and with the sign of this induction coinciding with the direction of increase of the dc component of the flux (curve 1);

b) with the same direction of increase of the dc component of the flux and the same residual induction in magnitude, but opposite in sign (curve \(1'\)).

Fig. 2.

In the first case, already in the first period after the occurrence of the external short circuit, the magnetizing current of the current transformer reaches a considerable value (6 A, or 42.5% of the amplitude of the primary current); the maximum magnetizing current is observed in the second period and reaches 21 A (149% of the amplitude of the primary current). In the second case, during the first two periods after the occurrence of the external short circuit, the magnetizing current amounts to no more than 5–10% of the amplitude of the primary current; the maximum occurs in the third period and is equal to 17 A (120% of the amplitude of the primary current). Following this maximum, the character of variation of the magnetizing currents under consideration becomes completely identical (i.e., curves 1 and \(1'\) merge).

Let us now consider the character of variation of the unbalance current with the differential connection of CT-1 and CT-2, likewise for two cases:

a) before the external short circuit, both transformers had maximum (6 kgf) residual inductions identical in sign;

b) before the external short circuit, both transformers had residual inductions maximum in magnitude but opposite in sign.

In the first case (Fig. 2, curve 3), the unbalance current has a maximum in the first period (10 A) and, as the process develops further, does not exceed 2.4 A (17.0% of the amplitude of the external short-circuit current). In the second case (Fig. 2, curve \(3'\)), a very considerable unbalance current is observed over the course of three periods after the occurrence of the external short circuit, and its maximum reaches 20 A, i.e., 140% of the amplitude of the external short-circuit current.

Toward the end of the third period, the nature of the change in the unbalance current becomes exactly the same as in the first case. It should be especially noted that during the first three periods the unbalance current is dominated by the aperiodic component.

The calculated and experimental data of I. M. Sirota [3] and other authors also prove the sharply pronounced aperiodic character of the unbalance current in the presence of residual flux densities in the cores of differentially connected current transformers. It is known that, when fast-saturating elements are present in the differential-protection circuit and the aperiodic component predominates in the unbalance current, nonselective operation of the protection is precluded. From the foregoing it follows that the presence, in the cores of current transformers before an external short circuit, of residual fluxes should not affect the effectiveness of balancing the arms of differential protection.

This proposition has been verified experimentally. In Fig. 3, curves are presented for the dependence of the magnitudes of the transient unbalance currents on the ratio of the resistances of the arms of the differential protection for two cases. In the first case (curves 2 and \(2'\)), TT-1 and TT-2 are connected according to the current-circulation scheme with the following circuit parameters: primary current

10 A, the time constant of the primary circuit was 0.07 sec; an ET-521/10 relay without fast-saturating elements was connected into the differential circuit.

When curves 1 and 2 were recorded, before each switching-on of the primary current (the external short-circuit current), residual flux densities of opposite signs were created in the current-transformer cores. When curves \(1'\) and \(2'\) were recorded, the occurrence of residual flux densities of different signs was excluded. Consideration of these curves shows that residual magnetism of different sign greatly reduces the effectiveness of balancing the arms of differential protection if the latter is not equipped with fast-saturating transformers. For example, for the pair TT-1 and TT-2 the minimum value of the unbalance current increases from 2.3 A to 5.6 A (or from 23 to 56% of the rms value of the primary current). Correspondingly, for the other pair of current transformers it increases from 2.9 A to 15.3 A (or from 5.8 to 31% of the rms value of the primary current). At the same time, it should be noted that even when residual flux densities of different signs are present in the current-transformer cores, the effect of balancing the arms is retained to a considerable degree, while the value of the optimum arm ratio changes little.

TT-1, \(w_2 = 150\)
TT-2, \(w_2 = 60\) with RNT-562

\(I_1 = 10\) A  \(T_k = 0.07\) sec

Fig. 4.

Figure 4 presents analogous curves of the dependence \(I_{\mathrm{unb}} = f(\eta)\) for the pair TT-1 and TT-2. In this case, however, an RNT-562 relay was connected into the differential circuit. When curve 1 was recorded, the occurrence in the current-transformer cores of residual fluxes of different signs was excluded. Curve 2 was recorded for the case in which, before each switching-on of the primary current, residual fluxes of different signs were artificially created in the cores of TT-1 and TT-2. Comparing these curves, it is not difficult to establish that in this case the effectiveness of balancing the arms and the value of the optimum ratio of their resistances \((\eta_{\mathrm{opt}})\) practically do not depend on the values and sign

of residual inductions in the cores of current transformers. In the second case (curve 2), the minimum unbalance current in the secondary winding of the RNT-562 increased by 12% (from 98 ma to 110 ma), and the optimum ratio of the arm resistances changed from 0.73 to 0.62.

Along with this it is necessary to note that, when the cores of the current transformers are magnetized in “opposite directions,” the critical multiple of arm unbalancing decreases (i.e., the multiple corresponding to the onset of nonselective operation). In the case where, before an external short circuit, the appearance in the cores of the current transformers of residual inductions of different sign was excluded, the critical multiple of arm unbalancing was equal to 6.5 (point a of curve 1). In the presence in the cores of the current transformers of residual fluxes of different sign, the critical multiple of arm unbalancing decreased to 3.8, i.e., by a factor of 1.7 (point b of curve 2). In both cases the primary current was equal to 10 a, the transformation ratios of the current transformers were \(n_1 = 1.0\), \(n_2 = 1.2\), the primary operating current of the RNT-562 was \(= 3 a\), the secondary operating current \(I_p = 0.218 a\); the time constant of the primary circuit was \(T_k = 0.07\) sec.

Thus, analysis of the curves of the dependence \(I_{\text{nb}} = f(\eta)\) for both variants of differential-protection circuits quite clearly shows that, with the arms balanced, the negative influence of residual magnetism of the current-transformer cores is manifested to the least degree (for circuits using fast-saturating elements, one may say that it is not manifested at all).

Fig. 5.

The oscillograms presented in Fig. 5 are very characteristic. The oscillogram of Fig. 5,a corresponds to the case where, before the primary current was switched on, there was no residual induction in the core of CT-1, while in the core of CT-2 there was residual induction of the order of 5–7 kgs, and the direction of rise of the dc component of the flux coincided with the sign of this induction. When the oscillograms of Fig. 5,b were taken, the cores of CT-1 and CT-2, before the external short circuit, had residual inductions of opposite signs with a magnitude of 6–7 kgs, and the sign of the induction in the core of CT-1 coincided with the direction of rise of the dc component of the flux. The ratio of the arm resistances in all three cases was equal to the optimum; the circuit parameters were the same as when taking the curves of Fig. 4. The oscillograms considered very clearly illustrate the fact that the effect of balancing the arms of differential protection with fast-saturating transformers is preserved when residual inductions are present in the cores of the current transformers.

of residual fluxes of different sign. In view of the clearly aperiodic character of the current in the differential winding \((i_{w\mathrm{d}})\) during the first two or three periods after the occurrence of a short circuit (Figs. 5, 6), the current in the secondary winding of the PCT \((i_p)\) remains very small.

A generalization of all the foregoing permits the following conclusions to be drawn.

1. The presence in the cores of current transformers, before the occurrence of an external short circuit, of residual inductions unequal in magnitude (especially inductions of different sign) leads to a sharp disturbance of the balance of the arms, if they had previously been balanced by a corresponding selection of the ratio of the arm resistances [5], [6].

2. In the second to fourth period after the occurrence of a short circuit, the balance of the arms is restored again. This circumstance is especially important for differential-protection circuits using rapidly saturating transformers, since for such protections it is especially important that the balance of the arms be maintained approximately from the third to the sixth period after the occurrence of an external short circuit [6].

3. The transient unbalance current when the balance of the arms is disturbed, caused by the presence of residual fluxes of different sign, contains a very significant aperiodic component. Consequently, the disturbance of the balance of the arms arising as a result of residual magnetism of the cores of current transformers should not affect the effectiveness of balancing the arms of differential protection if the circuit of this protection contains intermediate rapidly saturating transformers.

REFERENCES

1. N. N. Potashev. Residual induction in current transformers. Vestnik elektropromyshlennosti, No. 3, 1937.

2. I. D. Kutyanin. The influence of residual magnetism of current transformers on the operation of differential protections. Izvestiya Tomskogo politekhnicheskogo instituta, vol. 82, 1956.

3. I. M. Sirota. Transient operating regimes of current transformers. Academy of Sciences of the Ukrainian SSR, Kiev, 1961.

4. Yu. M. Korshunov. A graphical method for calculating transient processes in current transformers. Elektrichestvo, No. 10, 1953.

5. V. S. Kolesnikov. The condition for balance of the arms of transformer differential protection under an external short circuit. Izv. vuzov SSSR—Energetika, No. 7, 1960.

6. V. S. Kolesnikov. On the operating regime of current transformers in differential-protection circuits. Izv. vuzov SSSR—Energetika, No. 2, 1963.