Differential Protection of Transformers Based on Voltage Balance

N. V. Lisetskii

At the present time, differential protections of transformers, as a rule, are implemented according to schemes with circulating currents. However, as applied to generators, protection based on voltage balance has a number of advantages over protection according to a circulating-current scheme [1]. It is therefore expedient to consider the possibility of applying such protection also to transformers.

The diagram of one of the fundamentally possible variants of implementing protection with balanced voltages for a single-phase transformer, or for one phase of a three-phase transformer having a winding-connection scheme \(Y/\Delta — 12\), is shown in Fig. 1.

Current transformers included in the scheme have two secondary windings each on one common core. One of the secondary windings of each current transformer is connected in a circulating-current scheme. The other windings are connected in opposition, forming a voltage-balance circuit. For complete balancing of the voltages, an additional winding of an autotransformer is included in the above-mentioned circuit. The number of turns of this winding is selected so that the sum of the electromotive forces in the relay circuit under rated operating conditions and during through short circuits would be equal to zero.

Fig. 1.

Under normal transformer operating conditions, the ampere-turns of the primary windings of the current transformers are balanced by the ampere-turns of the secondary windings connected according to the circulating-current scheme.

The magnetic fluxes in the cores of the current transformers are determined by the magnitude of the electromotive force required to cover the voltage drop in the circulating-current circuit, and by the errors of the autotransformer. The magnetic flux of the autotransformer core is determined by the difference of the ampere-turns of the windings included in the circulating circuit. The magnetic fluxes are small in magnitude and, consequently, the electromotive forces induced in the oppositely connected windings of the transformers are also small.

Unbalance currents flow through the relay because of a certain difference in the electromotive forces of the secondary windings, caused by the nonidentity of the characteristics of the transformers.

In the event of a short circuit outside the protection zone, the magnetic induction in the cores of the current transformers increases, the difference in electromotive forces increases, and the unbalance currents increase. To avoid false operation of the protection, the pickup current of the relay must be higher than the possible unbalance current during through short circuits.

In the event of a short circuit in the protection zone, the ampere-turns prove to be unbalanced. In this case, unequal electromotive forces are induced in the oppositely connected windings of the current transformers, and a current flows through the relay, causing the protection to operate.

A similar phenomenon may also occur when the transformer is switched on. However, a considerable part of the asymmetrical inrush magnetizing current, with an appropriate selection of the circuit parameters or by connecting the relay through a rapidly saturating transformer, can be branched off into the magnetizing circuit, and the protection may not operate.

When comparing this type of protection with protection implemented according to a circulating-current scheme, it may turn out that this type of protection is more sensitive and more reliable in operation for the following reasons.

The resistance of the voltage-balance circuit is several times greater than the resistance of the circulating circuit and varies to a lesser extent depending on the magnitude of the current in the primary circuit. This leads to an increase in the shunt into the circulating circuit when the transformer is switched on at no load and thereby facilitates the detuning of the protection from the action of inrush magnetizing currents. The decay of transient processes in the voltage-balance circuit will occur faster than in the circulating-current circuit, since the active resistance of all its elements is connected in series, and the time constant

$$ T = \frac{L}{r} $$

for this circuit will be smaller, which will also increase the selectivity of the protection operation.

In addition, protection with balanced voltages has a number of operational advantages compared with protection implemented according to a circulating-current scheme.

One of the disadvantages of differential protection implemented according to the circulating-current scheme is operation of the protection when the circulating circuit is broken. Protection with balanced voltages has this same disadvantage; nevertheless, this protection still has advantages, since its circulating circuit is very simple, it need not be brought to the relay panel, has no intermediate terminal assemblies, and can therefore be made very reliable.

The second important advantage is the convenience of checking the selectivity of the protection at any saturation of the iron of the current transformers.

With the usual method of checking selectivity by applying a short circuit outside the protection zone and raising the current from zero, rheostats must be inserted into the circulating-current circuit. By changing the resistance of the latter, one can check the magnitude of the unbalance current at different saturations of the iron of the current transformers.

For a final judgment on protection based on voltage balance, it is necessary to consider the questions of its sensitivity and selectivity. Then a comparison should be made with protection implemented according to the circulating-current scheme, as G. V. Zeveke did with respect to generator protection [1], and the necessary experiments should be carried out.

Sensitivity of the Protection

(without taking the unbalance current into account)

In considering questions of sensitivity we shall proceed from the circuit of Fig. 1, for a short circuit at point “\(K_1\).” The adopted directions of the currents are shown in the diagram. In all derivations the notation for the complex form is omitted. The resistances and currents flowing in the circuit are denoted as follows:

\(I_{n1}\) and \(I_2\)—the primary and secondary load current (or short-circuit current) of the power transformer, having transformation ratio \(N\), equal to the ratio of the line voltages; \(I_0\)—the no-load current of the power transformer; \(i_1\) and \(i_2\)—the secondary currents of the protective current transformers, having transformation ratios \(n_1\) and \(n_2\) and no-load branch resistances \(z_{01}\) and \(z_{02}\); \(i_{01}\) and \(i_{02}\)—the magnetizing currents of these current transformers; \(i_{0a}\)—the magnetizing current of the autotransformer, having transformation ratio \(n_a\) and no-load branch resistance \(z_{0a}\); \(i_p\)—the current flowing through the relay; \(z_p\)—the resistance of the voltage-balance circuit; \(z_1\) and \(z_2\)—the total resistances of all series-connected elements of the circulation circuit (current-transformer windings, connecting leads, etc.).

The transformation ratio of the autotransformer windings connected into the circulation circuit, from the conditions of equalization of the secondary currents during normal operation of the power transformer and during through short circuits, is taken as

\[ n_a=\frac{N n_2}{n_1}. \tag{1} \]

The transformation ratio for the autotransformer winding connected into the voltage-balance circuit, from the condition of compensation of the difference of the electromotive forces of the secondary windings of the current transformers under analogous operating conditions, must be

\[ n'_a=1-n_a, \tag{2} \]

where \(n'_a\) represents a certain conventional transformation ratio, the product of which by the electromotive force of the autotransformer gives the electromotive force of the voltage-adding turns, which compensates the difference of the electromotive forces of the current transformers.

Assuming that the voltage drop in the resistances \(z_1\) and \(z_2\) is small, it may be considered that

\[ e_1=e_a=\frac{e_2}{n_a}. \tag{3} \]

If the number of turns of the current-transformer windings connected into the voltage-balance circuit is, respectively, equal to the number of turns of the windings connected into the circulation circuit, then, on the basis of Kirchhoff’s second law for the relay circuit, one may write

\[ e_1-e_a(1-n_a)+e_2=i_p z_p. \tag{4} \]

On the basis of Kirchhoff’s first law, for the equivalent circuits of the current transformers the magnetizing currents of the latter are expressed as:

a) of current transformer “1”

\[ i_{01}=\frac{I_1}{n_1}-i_1-i_p; \tag{5} \]

b) the autotransformer

\[ i_{0a}=i_1-i_2 n_a+i_p(1-n_a); \tag{6} \]

c) current transformer “2”

\[ i_{02}=i_2-i_p. \tag{7} \]

The electromotive forces are related to the magnetizing currents by the following relations:

\[ \begin{aligned} e_1&=i_{01}z_{01},\\ e_2&=i_{02}z_{02},\\ e_a&=i_{0a}z_{0a}. \end{aligned} \tag{9} \tag{10} \]

Eliminating \(e_2\) and \(e_a\) from (3) and (4) and substituting the value of \(e_1\) from (8), we find

\[ i_{01}=i_p\frac{z_p}{2z_{01}n_a}. \tag{11} \]

Eliminating \(e_1\) and \(e_a\) from (3) and (4) and substituting the value of \(e_2\) from (9), we obtain

\[ i_{02}=i_p\frac{z_p}{2z_{02}}. \tag{12} \]

Eliminating \(e_1\) and \(e_2\) from (3) and (4) and substituting the value of \(e_a\) from (10), we find

\[ i_{0a}=i_p\frac{z_p}{2z_{0a}n_a}. \tag{13} \]

Solving equations (7) and (12) simultaneously, we have

\[ i_2=i_p+i_{02}=i_p+i_p\frac{z_p}{2z_{02}} =i_p\left(1+\frac{z_p}{2z_{02}}\right). \tag{14} \]

Substituting the value of \(i_{0a}\) from (13) and \(i_2\) from (14) into (6), we find

\[ \begin{aligned} i_1&=i_{0a}+i_2 n_a-i_p(1-n_a) =i_p\frac{z_p}{2z_{0a}n_a} +i_p\left(1+\frac{z_p}{2z_{02}}\right)n_a\\ &\quad -i_p(1-n_a) =2i_p n_a-i_p+i_p\frac{z_p}{2z_{0a}n_a} +i_p\frac{z_p}{2z_{02}}\,n_a. \end{aligned} \tag{15} \]

Substituting the value of \(i_1\) from (15) and \(i_{01}\) from (11) into (5), we find the relation between the primary current and the current in the relay

\[ i_p\frac{z_p}{2z_{01}n_a} =\frac{I_1}{n_1}-2i_p n_a+i_p-i_p\frac{z_p}{2z_{0a}n_a} -i_p\frac{z_p}{2z_{02}}n_a-i_p, \]

\[ \frac{I_1}{n_1} =2i_p n_a+i_p\frac{z_p}{2z_{01}n_a} +i_p\frac{z_p}{2z_{0a}n_a} +i_p n_a\frac{z_p}{2z_{02}} \]

\[ =i_p n_a\left[ 2+\frac{z_p}{2} \left( \frac{ z_{02}z_{0a}n_a^2+z_{01}n_a^2 z_{02}+z_{01}n_a^2 z_{0a}n_a^2 }{ z_{01}n_a^2\cdot z_{0a}n_a^2\cdot z_{02} } \right) \right]. \tag{16} \]

Taking the first derivative of \(\left(\dfrac{I_1}{n_1}\right)\) with respect to \(i_p\) and equating it to zero, we find the minimum conditions for \(\left(\dfrac{I_1}{n_1}\right)\) under which the protection will operate,

\[ \frac{d\left(\dfrac{I_1}{n_1}\right)}{di_p} =n_a\left[ 2+\frac{z_p}{2} \left( \frac{ z_{02}z_{0a}n_a^2+z_{01}n_a^2 z_{02}+z_{0a}n_a^2 z_{01}n_a^2 }{ z_{01}n_a^2\cdot z_{0a}n_a^2\cdot z_{02} } \right) \right]=0. \]

Hence the absolute value of the resistance of the relay circuit will be

\[ z_p=4\left(\frac{z_{01}n_b^{2}\cdot z_{0a}n_a^{2}z_{02}} {z_{01}n_a^{2}\cdot z_{02}+z_{0a}n_a^{2}\cdot z_{02}+z_{01}n_a^{2}z_{0a}n_a^{2}}\right). \tag{17} \]

Comparing the equality obtained with the expression for the relay resistance for protection with circulating currents (see the author’s paper “Increasing the Sensitivity and Selectivity of Differential Protection of Power Transformers”), it is easy to note that the value of the most advantageous resistance of the relay circuit for protection with balanced voltages is 4 times greater than for protection with circulating currents.

Analogous relationships for generator protections were obtained by G. V. Zeveke [1]. Consequently, all the conclusions he drew for generator protection are also valid for transformer protection; that is, with the same number of turns of the secondary windings and identical cores of the current transformers to which the relays are connected in both schemes, the conditions for equal sensitivity of the protections reduce to the following:

1. The pickup current of the protection with circulating currents must be 2 times greater than the pickup current of the protection with balanced voltages.

2. The resistance of the relay circuit of the protection with circulating currents must be 4 times smaller in comparison with the resistance of the relay circuit of the protection based on voltage balance.

Unbalance currents and the possibility of selective operation of the protection

In deriving the expression for the unbalance current, we shall proceed from the scheme of Fig. 1 for a short circuit at point \(K_2\). For the designations of currents and resistances we shall use the same ones as in all the preceding derivations.

On the basis of Kirchhoff’s first law, for the equivalent circuit of current transformer “1” one may write:

\[ \frac{I_{n1}+I_0}{n_1}=i_1+i_p+i_{01}, \tag{18} \]

for the equivalent circuit of the autotransformer

\[ i_1+i_p(1-n_a)-i_{0a}=i_2n_a, \tag{19} \]

for the equivalent circuit of current transformer “2”

\[ \frac{I_2}{n_2}=\frac{I_{n1}}{Nn_2}=i_2-i_p+i_{02}. \tag{20} \]

Substituting in expression (19) the values of \(i_1\) and \(i_2\) from (18) and (20) and replacing \(n_a\) according to (1), we obtain

\[ \frac{I_{n1}}{n_1}+\frac{I_0}{n_1}-i_p-i_{01}+i_p(1-n_a)-i_{0a} = \frac{I_{n1}}{Nn_2}\cdot\frac{Nn_2}{n_1}+i_p n_a-i_{02}n_a; \]

\[ \frac{I_0}{n_1}-i_{01}-i_{0a}+i_{02}n_a=2i_p n_a. \]

Hence the current in the relay, which is the unbalance current, will be

\[ i_p=i_{nb}=\frac{1}{2}\left[\frac{I_0}{n_1n_a}-\frac{i_{01}}{n_a}-\frac{i_{0a}}{n_a}+i_{02}\right]. \tag{21} \]

From comparison of the equality obtained with the expression for the unbalance current for protection with circulating currents (see the author’s work cited above), it is evident that expression (21) differs from the analogous expression for protection with circulating currents only by the factor \(1/2\). Consequently,

the conditions for selecting and arranging the equipment of the circuit remain the same as for protection with circulating currents. In this case the unbalance currents are obtained as half as large as compared with the unbalance currents of protection implemented according to the circuit with circulating currents.

The conditions for selective operation of the protection also remain the same. Only the relay resistance for protection based on voltage balance should be chosen 4 times greater than for protection with circulating currents.

Simplification of the Basic Circuit and Construction of Protection Circuits for Three-Phase Transformers

In the circuit of Fig. 1, in order to compensate the difference of electromotive forces in the voltage-balance circuit, an additional winding is provided on the autotransformer. If the number of turns of both secondary windings of the current transformers is the same, then the number of turns of this additional winding is selected so as to provide a transformation ratio equal to

\[ n'_a = 1 - n_a . \]

The same transformation ratio can be provided by the part of the autotransformer winding that represents the difference between the numbers of turns included in the arms of the circulation circuit. It is therefore expedient not to wind an additional winding, but to use the indicated part of the winding for compensating the difference of electromotive forces in the voltage-balance circuit, as shown in the circuit of Fig. 2.

and for compensating the difference of electromotive forces in the voltage-balance circuit, as indicated in the circuit of Fig. 2.

The resulting circuit is much simpler than the preceding one; it does not require an additional autotransformer winding and saves a considerable amount of connecting leads. Experimental investigations of the circuit of Fig. 2 showed that all the conclusions drawn for the circuit of Fig. 1 are also valid for ...

of the given circuit; therefore, when assembling three-phase protection circuits for transformers it is more expedient to proceed from the circuit of Fig. 2.

In three-phase transformers with winding connection \(Y/Y—12\), the primary and secondary voltages and currents coincide in phase. Therefore, the protection circuit for such a transformer will be a three-phase implementation of the circuit of Fig. 2, as shown in Fig. 3.

In three-phase transformers with winding connection \(Y/\Delta—11\), the secondary voltages and currents are displaced relative to the primary ones by 30 degrees. In differential-protection circuits this displacement must be compensated. For this purpose, as is known, the reduced values of the currents and electromotive forces of the secondary windings of the current transformers located on the delta side should be compared with the difference of the currents and electromotive forces of the current transformers installed on the star side. The protection circuit based on these provisions is shown in Fig. 4.

The circulation circuit of the protection in this arrangement is formed by the windings of current transformers “\(1ц\),” “\(2ц\),” and by an autotransformer. The voltage-balance circuit is formed by the windings of transformers “\(1p\),” “\(2p\),” and by part of the autotransformer winding.

This circuit was tested in the relay-protection laboratory of the Tomsk Polytechnic Institute. The test results were exactly the same as for the circuit of Fig. 2, and therefore are not given in the present work.

Magnitude of the Voltages in the Secondary Circuits of the Protection

Differential protection with balanced voltages first began to be used for generators. The principal difficulties in designing this protection were the excessively high voltages appearing in the secondary circuits during short circuits in the protected zone. In order to reduce these voltages to values safe for insulation, it is recommended that the windings of the current transformers of the voltage-balance circuit be made with a smaller number of turns, and that rapidly saturating reactors be connected between the conductors of the circulation circuit [1].

Differential protection based on voltage balance is the same in principle for generators and transformers. However, the possibilities for increasing the voltage in the protection circuits of these units are different.

When bushing-type or low-power current transformers are used and the parameters of the circuit are properly selected, the voltage in the circuits of the transformer differential protection cannot rise to dangerous values. This occurs because, at currents only slightly exceeding the rated currents, the cores of the current transformers become saturated, and a further increase in current does not lead to any appreciable increase in the electromotive force, but only distorts the shape of its curve.

As an example of such a phenomenon, the results are given below of tests of a differential protection in one arm of which a low-power current transformer was connected. The test results showed that a sharp rise of voltage in the protection circuits was observed up to values of the short-circuit current approximately equal to twice the rated current; moreover, the magnitude of the resulting voltage did not exceed eighty volts. A further increase in the multiple of the short-circuit current changed the voltage in the protection circuits hardly at all.

For transformer protection implemented by means of powerful current transformers, as also for generator protection, the possibility is not excluded that voltages dangerous to the insulation may appear in the secondary circuits. However, it is inadvisable to apply the methods recommended for generator protection in order to reduce voltages in transformer protection circuits, for the following reasons:

1. Inequality in the numbers of turns of the secondary windings of the current transformers makes it necessary to wind an additional winding on the autotransformer in order to compensate the difference of electromotive forces in the voltage-balance circuit. This considerably complicates the circuit and makes it inconvenient in operation.

2. The insertion, between the wires of the circulating-current circuit, of rapidly saturating reactors leads to the appearance of additional magnetizing currents. This violates the conditions for selecting the circuit parameters and may cause the appearance of considerable unbalance currents. In this case, the role of the reactors is performed by the autotransformers or by rapidly saturating transformers.

For the reasons indicated, no special measures should be provided to reduce the voltages arising in transformer protection circuits. Where powerful current transformers are used, it is more expedient to raise the insulation level of the secondary circuits.

Experimental verification of the theoretical conclusions

For carrying out the experiments, two current transformers with two secondary windings and an autotransformer were manufactured. The current transformers were designed for a rated number of ampere-turns equal to 500 and had different cross sections of core iron. The parameters of the autotransformer were selected from the condition of a minimum of unbalance currents (see the author’s work cited above). In all the tests, an active resistance was connected instead of a relay; the value of this resistance was selected from the conditions for optimum sensitivity of the protection when the current transformers operated with the maximum resistance of the magnetizing circuits.

The comparison of the magnitudes of the unbalance current for protections with balanced voltages and with circulating currents was carried out as follows: a circuit was assembled that simulated transformer differential protection with balanced voltages, according to Fig. 2. In the event of a short circuit outside the protected zone (point “K₂,” Fig. 2), currents of a definite multiple relative to the rated current were established by raising the current from zero; measurements were then made of the unbalance current flowing in the relay circuit.

Then, using these same current transformers and these same connecting leads, a circuit was assembled that simulated differential protection of a transformer with circulating currents. The resistance of the relay circuit was reduced fourfold, and measurements analogous to the preceding ones were carried out.

From the data obtained, curves were plotted for the dependence of the unbalance current on the multiple of the through short-circuit current; these are shown in Fig. 5. Curve “a” in Fig. 5 shows the dependence of the unbalance current on the multiple of the through short-circuit current for protection with balanced voltages,

Fig. 5.

and curve “b” shows the analogous dependence for protection with circulating currents.

From a comparison of the curves presented it is evident that, with the selected circuit parameters, the unbalance currents of the protection with balanced voltages are approximately half as large as the unbalance currents in the circuit with circulating currents, and this ratio is maintained in all operating regimes of the power transformer. Consequently, the theoretical conclusions of this part of the work were confirmed by experiment.

The next question in the experimental verification was the possibility of selective operation of protection with balanced voltages when using the main current transformers and an autotransformer as a rapidly saturating current transformer. For this purpose the circuit of Fig. 2 was assembled, and an additional resistance equal to 4 ohms was introduced into its circulating circuit. The transformer was then switched on at no load at full operating voltage, and, at reduced voltage, an artificial fault was created outside the protected zone; the magnitude of the resulting short-circuit current corresponded to three times the rated current. The currents flowing in the primary circuit of the power transformer and in the relay circuit were recorded by oscillograph.

The oscillograms obtained are shown in Figs. 6 and 7.

The upper curves of the oscillogram show the currents in the primary circuit of the power transformer, and the lower ones show the currents in the relay circuit. The oscillogram of Fig. 6 shows the currents when the power transformer is switched on at no load, while the oscillogram of Fig. 7 shows the currents during a short circuit outside the protection zone.

From examination of the oscillograms presented it is evident that the current transformers included in the circuit filter out the aperiodic component of the primary current to a sufficient degree, and that the current in the relay circuit during pe-

transient processes in the primary circuit does not exceed the values of the setting current. It follows from this that, with the appropriate adjustment of the circuit, selective operation of the protection can be achieved under all operating conditions of the power transformer, and that the theoretical conclusions concerning the possibility of such adjustment are correct.

Next, the question was considered of the possibility of an increase of voltage in the protection circuits during a short circuit in the protected zone. For this purpose

Fig. 6

Fig. 7

a short circuit was made in the protection zone, arranged according to the circuit of Fig. 2. Voltmeters were connected between the conductors of the circulating-current circuit and in parallel with the relay. Then, by raising the current from zero, the dependences of the voltages arising at the relay terminals and between the conductors of the circulating-current circuit on the multiple of the primary current with respect to the rated current were recorded. The dependences obtained are shown in Fig. 8.

Fig. 8.

Fig. 9

Curve “a” in Fig. 8 shows the voltage at the relay terminals as a function of the multiple of the short-circuit current. Curve “b” shows the analogous dependence for the voltage between the conductors of the circulating-current circuit.

From the curves considered in Fig. 8 it is evident that a sharp increase of voltage in the protection circuits occurs as the current rises to values at which the cores of the current transformers become saturated. With a further increase

with an increase in current the voltage almost does not increase, and the magnitude of the resulting voltage is not dangerous for the insulation.

It was further established that it is possible for the voltage in the protection circuits to rise during the transient process of a short circuit. For this purpose, while the transformer was operating at no load, a sudden short circuit was produced in the protection zone. The magnitude of the steady-state short-circuit current corresponded to three times the rated current. The current at the point of the short circuit and the voltage arising at the relay terminals were recorded by oscillograph. The oscillograms obtained are shown in Fig. 9.

The upper curve in the indicated figure shows the current flowing at the point of the short circuit, and the lower curve—the voltage at the relay terminals.

From the oscillograms presented it is evident that the voltage at the relay terminals at the beginning of the transient process has a value smaller than in the steady-state condition; consequently, the transient process of the short circuit does not cause any additional rise of voltage in the protection circuits and is not dangerous for the insulation of the latter.

Conclusions

On the basis of all the theoretical derivations and experiments, the following conclusions may be drawn:

1. Differential protection based on voltage balance can be implemented for transformers without the use of additional equipment, but with the necessity of winding one more secondary winding on the cores of the current transformers.

2. By applying the indicated type of protection to transformers, it is possible to increase significantly the sensitivity and selectivity of the latter.

3. Differential protection with balanced voltages has a number of operational advantages in comparison with protection implemented according to the scheme with circulating currents.

LITERATURE

1. G. V. Zeveke. Differential protection of electrical machines, journal Electric Stations, No. 1, 1940.