Proceedings of the Tomsk Order of the Red Banner of Labor Polytechnic Institute named after S. M. Kirov

Vol. 98　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1960

On Certain Properties of Longitudinal Differential Protection of Generators Implemented Using a Scheme with Balanced Secondary EMFs

T. V. Baginskii

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

In recent years a number of measures have been carried out aimed at increasing the selectivity and reliability of longitudinal differential protection of generators. The most important place among these measures is occupied by the use of fast-saturating transformers (FST) and by increasing relay settings in order to obtain primary operating currents up to \(I_{\mathrm{op}} = (1.3\text{--}1.5) I_{\mathrm{ng}}\). The latter eliminates the possibility of false operation of the protection in the event of faults in its circuits. However, this measure is not capable of ensuring selective operation of the protection under external short circuits, since the unbalance currents in this case may reach tens of amperes [1]. In practice, a case has already been recorded of nonselective protection operation at \(I_{\mathrm{op}} = 1.2 I_{\mathrm{ng}}\) during an external short circuit [2].

The use of FST ensures reliable detuning from unbalance currents even when \(I_{\mathrm{op}} < I_{\mathrm{ng}}\). However, the scheme currently used has the property of responding to faults in the connecting wires. Thus, none of these measures can simultaneously increase the reliability and selectivity of the protection.

Long operating experience, as well as studies carried out at the Department of Electric Power Stations, Networks, and Systems of the Tomsk Polytechnic Institute, show that a differential-protection scheme with balanced secondary EMFs, when properly adjusted, can meet all the requirements imposed on the main protection of generators.

The scheme of differential protection of generators with balanced secondary EMFs was examined in detail by G. V. Zeveke in [3], who investigated the principal properties of this scheme with respect to its sensitivity, the latter proving to be practically higher than the sensitivity of the scheme with circulating currents. On this basis G. V. Zeveke came to the conclusion that the scheme under consideration could be used as differential-ground protection for generator neutrals grounded through active resistances. For this purpose, the number of turns of the secondary windings of the EMF-balance circuit...

of the current transformers \(w_2\) is selected in such a way that the resistance of the relay circuit \(z_2\) and the mutual-induction resistance \(z_M\) are in the ratio \(z_2 = 4z_M\). In this case the relay setting must be chosen from the condition of obtaining the required primary operating current for earth faults.

This method of adjusting the protection has very significant shortcomings, caused by the attempt not only to combine the functions of differential and earth protection in one circuit, but also to have, in this circuit, operating elements common to both protections. Therefore, with settings that ensure the necessary sensitivity of the protection against earth faults, the protection may operate nonselectively during external short circuits. In addition, the high sensitivity of the relay entails a large value of its resistance and, consequently, overvoltages during short circuits in the protection zone.

Since at the present time generator neutrals are not grounded, it is impossible to implement differential-earth protection without complicating the design of the current transformers. Therefore, the adjustment of the circuit must meet only the requirements of protection against internal phase-to-phase faults. As is known, these requirements must be most stringent when protecting hydrogenerators with a coil winding. In this case the protection must operate selectively at \(I_{1\mathrm{op}} = 0.5 I_{HG}\), with a sensitivity coefficient \(k_4 = 2\); moreover, dangerous overvoltages in the circuit, as well as operation of the protection in the event of faults in its circuits, are inadmissible.

Fig. 1.

The requirements with respect to the sensitivity and selectivity of the protection can be satisfied by introducing active additional resistances into the relay circuit [4]. Their quantitative influence on the protection characteristics is shown in Fig. 1. The dependences presented in Fig. 1 were obtained experimentally under the following conditions. The current transformers had a mean magnetic-path length \(l_{\mathrm{av}} = 45.6\ \text{cm}\), a core cross-section \(q = 37\ \text{cm}^2\), and the number of turns of the primary

and secondary windings \(w_1=200,\; w_2=w_3=100\); the maximum discrepancy of the volt-ampere characteristics of the transformers was \(10.9\%\). The resistance of the current-circulation circuit \(r_3\) was selected so that, at \(I_1=I_{HG}\), the induction in the cores would be \(B=500\) G. Before each connection of the circuit for an external short circuit, the current-transformer cores were magnetized by direct current in opposite directions to saturation, in order to obtain maximum residual fluxes of different signs. The rated current was taken as \(I_{HG}=2.5\) A. The maximum transient unbalance current \(I_{2M}\) was measured at \(I_1=6I_{HG}\) by a carefully adjusted relay of type ET-520, whose operation was registered by an intermediate relay connected according to a “self-holding” circuit. The primary circuit was supplied from a synchronous generator at a voltage of about 600 V through a choke with high inductance. The value \(I_{1cp}\) was determined by smoothly increasing the primary current from zero until the relay operated, with the setting \(I_y=k_H I_{2M}\) (where the reliability factor \(k_H=3\)), and \(k_4=I_{2P}:k_H I_{2M}\). The current in the relay for a fault in the protected zone \(I_{2P}\) was measured at \(I_1=2.4 I_{HG}=6\) A, which corresponds to the minimum possible current of a two-pole short circuit at the terminals of hydrogenerators.

From the curves in Fig. 1 it follows that, in order to achieve selective operation of the protection at \(I_{1cp}=(1.3\text{--}1.5)I_{HG}\), it is sufficient to have a relay-circuit resistance \(r_2=(20\text{--}30)\ \Omega\), and at \(I_{1cp}=(0.4\div0.6)I_{HG}\), \(r_2=(40\text{--}60)\ \Omega\). In this case dangerous voltages will not arise in the protection circuits, since \(r_2=(40\text{--}60)\ \Omega\) corresponds to the resistance of the relay circuit of differential protection with circulating currents \(r_p=(10\text{--}15)\ \Omega\) [3]. The latter has been operated for a long time with additional resistances of about \((10\text{--}20)\ \Omega\), and not a single case of the occurrence of dangerous voltages has been recorded.

Additional resistances in the relay circuits are additional elements and therefore to some extent complicate the circuit. A valuable property of differential protection with balanced e.m.f.s is the possibility of achieving the same selectivity at specified \(I_{1cp}\) without the use of additional resistances. For this it is sufficient to reduce the number of turns \(w_2\) of the windings connected for balancing the e.m.f.s, with such a calculation that the resistances of these windings of the current transformers, the relay, and the connecting leads \(r_{np}\), referred to the number of turns of the windings of the current-circulation circuit \(w_3\), would be equal to \(r'_2=(40\text{--}60)\ \Omega\), that is,

\[ r'_2=2r_{\text{turn}}w_2\frac{w_3^2}{w_2^2}+r_{np}\frac{w_3^2}{w_2^2}+r_p\frac{w_3^2}{w_2^2}. \]

Here \(r_{\text{turn}}\) is the resistance of one turn of the secondary winding of the e.m.f.-balancing circuit. Solving this equation gives the required number of turns:

\[ w_2=\frac{r_{\text{turn}}}{r'_2}w_3^2+w_3\sqrt{\frac{r_{\text{turn}}^2}{r_2^{\prime 2}}w_3^2+\frac{r_{np}}{r'_2}+\frac{r_p}{r'_2}}. \tag{1} \]

Since relays of no greater sensitivity than ET-520/10 may be used in the circuit under consideration, \(r_p\ll r_{np}\) and may be disregarded in the calculations. Calculations show that connecting leads with a cross section \(s=2.5\ \text{mm}^2\) should be used and that the thermal

their stability will be ensured with a sufficient margin. The ratio of the numbers of turns of the secondary windings of the current-circulation and emf-balance circuits lies within the range

\[ \frac{w_3}{w_2} = (5—10). \]

It should be noted that the degree of selectivity inherent in protection with balanced emf’s \((k_H = 3)\) is unattainable for protection with balanced currents when the relay-circuit resistance is equivalent \((r_p = 0.25\, r_\phi)\). This is explained by the ideal balancing of the protection circuit with balanced emf’s. In protection with circulating currents, there may exist an imbalance of the arms of the order of 20—30%, which can cause the unbalance current to increase by a factor of 2—3 compared with its values for balanced arms. Thus, according to data in [5], an arm imbalance of 30% causes the transient unbalance current to increase by a factor of 3.3.

It should also be noted that, in the circuit with circulating currents, the use of additional resistances leads to some reduction in the reliability of the circuit, since the resistances themselves are additional elements.

Fig. 2.

Let us consider the reliability of the differential-protection circuit with balanced emf’s at the setting recommended above. As is known, the following types of damage to the circuit are possible (see Fig. 2): 1. A short circuit in the emf-balance circuit (point \(P_1\)). 2. A short circuit in the current-circulation circuit (point \(P_2\)). 3. An open circuit in the current-circulation circuit (point \(P_3\)).

Since the voltage between the conductors at point \(P_1\) is zero, the emf-balance circuits can be divided into two circuits. Taking this into account, the equivalent circuit for the case of a metallic short circuit between the conductors of the emf-balance circuit takes the form shown in Fig. 3.

In the 1939 edition of the guiding instructions on relay protection it is asserted that short circuits in the emf-balance circuit cause false operation of the protection. Using the circuit of Fig. 3, it is not difficult to show that this assertion is valid only for the circuit setting proposed by G. V. Zeveke, or in the case where additional resistances are used. In the first case, the false operation is caused by an excessively low relay setting \((I_{1cp} \ll I_{HT})\). Although in this case the fraction of the current transformed into the relay circuit is substantially limited by the resistance of the latter, the primary current is large enough to cause, in the relay coil, the release of power considerably exceeding \(0.1\) VA. When additional resistances are used, false—

an incorrect operation will occur if the point \(P_1\) is located between it and the relay.

If the circuit is designed according to expression (1), the resistance \(r_2\) is uniformly distributed over the entire balancing circuit of the e.m.f. The point \(P_1\) divides it into two parts, that is, \(z_2 = z_{2A} + z_{2B}\). The current in each of these parts (loops) will be the greater, the smaller the resistance of this part.

Fig. 3.

The loop containing the relay will have the least resistance when the point \(P_1\) is located in the immediate vicinity of the relay, that is, when \(z_{2A} \simeq z_{2B} \simeq 0.5 z_2\). Then the current in the relay in the mode under consideration, after neglecting small terms, is expressed as follows:

\[ I_{2A}=\frac{I'_1 z'_3}{z_2+z'_3}. \tag{2} \]

Here all quantities are referred to the number of turns \(w_2\). Let us determine what the resistance \(z_2\) must be for the relay to operate at \(I_1=I_{\mathrm{HT}}\); for this purpose we set \(I'_1=I'_{\mathrm{HT}}\), \(I_2=I_x\), and \(\dfrac{I_x}{I'_{\mathrm{HT}}}=\alpha\). Then

\[ z_2=z'_3\left(\frac{1}{\alpha}-1\right). \tag{3} \]

It follows from equation (2) that for the relay to operate at \(I_x=0.2 I'_{\mathrm{HT}}\) (this approximately corresponds to \(I_{\mathrm{cp}}=0.4 I_{\mathrm{HT}}\)), \(z_2\) must be very small. For example, with \(z_3=1\ \Omega\), \(\dfrac{w_2}{w_3}=0.2\), and \(\alpha=0.3\), we have:

\[ z_2=1\cdot 0.2^2\left(\frac{1}{0.2}-1\right)=0.16\ \Omega. \]

The actual value of \(z_2\) for \(z'_2=40\ \Omega\) is

\[ z_2=40\,\frac{w_2^2}{w_3^2}=40\cdot 0.2^2=1.6\ \Omega. \]

Consequently, operation of the relay with the given setting is entirely impossible.

The validity of equations (2) and (3) has been verified experimentally.

The equivalent circuit of the protection circuits under a short circuit in the current-circulation circuit is shown in Fig. 4. It is obvious that a short circuit in the middle of the conductors of the current-circulation circuit forms, as it were, an additional differential circuit with a resistance equal to zero and with balanced arms. Therefore the balancing circuit of the d.c. is shunted by this new differential circuit and \(I_1 = 0\). Therefore the greatest current \(I_2\) will occur at the maximum inequality of \(z_{3A}\) and \(z_{3B}\), that is, when point \(P_2\) (Fig. 2) is located at the terminals of one of the current transformers, for example, \(B\). In this case \(z_{3A} + z_{3B} = z_3\), and \(z_{3A} - z_{3B} = r_{pr}\). The solution of the loop equations for these conditions, after neglecting small terms, will have the following form:

Fig. 4.

\[ r'_{pr}=I_2\,\frac{z'_3+z_2}{I'_1}. \tag{4} \]

Applying the same substitutions as for the case of a short circuit at point \(P_1\), we determine the value \(r'_{pr}\) at which the protection may operate falsely:

\[ r'_{pr}=\alpha\left(z_2+z'_3\right). \tag{5} \]

It is obvious that equation (5) is valid only for the condition \(\alpha<1\), since \(r'_{pr}<z'_3\). In addition, \(z_2\) is greater than \(r'_{pr}\) by no less than \(\left(\dfrac{w_3}{w_2}\right)^2\) times, and therefore operation of the protection is possible only when \(\alpha<0.2\). Consequently, in the event of a short circuit in the current-circulation circuit, false operation of the protection is impossible.

Equations (4) and (5) agree well with the experimental data.

The most frequently encountered type of damage in differential-protection schemes is an open circuit in the current-circulation circuit. In [3] it is asserted that in this mode false operation of the protection is inevitable, since practically the entire primary current in this case is magnetizing. In this case the volt-ampere characteristics

supposedly diverge considerably. One cannot agree with this assertion. In fact, B. A. Nechaev [6] showed that the volt-ampere characteristics in the region of high inductions converge, rather than diverge, if the cores are made of steel of the same grade. Moreover, differential protection with balanced secondary no-load EMFs of the current transformers [7] operates without any circulating-current circuit at all, and its selectivity is higher than that of a scheme with circulating currents.

Fig. 5.

To confirm these conclusions, the following experiments were carried out. In the circuit shown in Fig. 5, the same current transformers were used as in the experiment from whose results the curves in Fig. 1 were plotted. The resistance of the secondary-EMF balancing circuit was purely active and was equal to \(r_2 = 1\ \Omega\). For various \(I_1\), the currents \(I_2\) were measured, and from the measurement results curve 1 was plotted (see Fig. 6). There, straight line 3 represents the dependence \(I_p = f(Iw_1)\)

Fig. 6.

at \(I_{\text{sr}} = 0.5\,I_{\text{ng}}\), if each of the values of \(I_1\) occurring in the experiment is taken as \(I_{\text{ng}}\). This experiment shows that even at \(r'_2 \ll 40\ \Omega\) the relay is quite reliably restrained from \(I_2\). For a quantitative assessment of the stability of the circuit with respect to this type of fault, the dependence \(I_2 = f(Iw_1)\) was taken at \(r'_2 = 43\ \Omega\) (see curve 2 in Fig. 6). In this case, for each reading it was assumed that \(Iw_1 = I_{\text{ng}}\). The resistance of the relay circuit was calculated as follows.

\[ r_2 = 43\left(\frac{100}{I w_1}\cdot 5\right), \]
since \(w_3 \cong \dfrac{I w_1}{5}\). The values of the resistances \(r_2\) calculated in this way, which were inserted into the relay circuit in this experiment, are marked in Fig. 6 under the corresponding values \(I w_1\). Curve 2 in Fig. 6 shows that the reliability margin at \(I_{\mathrm{op}} = 0.5 I_{\mathrm{ng}}\) and with the recommended adjustment of the circuit is not less than 2. Consequently, even if the current-circulation circuit is broken, false operation of the protection is impossible.

The stability of the circuit with respect to this type of damage can be checked by means of a graph-analytical calculation using the known parameters of the circuit and the no-load characteristics of the current transformers. In fact, the current \(I_2\) in the circuit of Fig. 5 can be expressed through its parameters as follows:

\[ I_2 = \frac{\dot E_A - \dot E_B}{z_2}, \tag{6} \]

\[ \dot I_2 = \dot I'_1 \frac{z_{MA} - z_{MB}}{z_2 + z_{MA} + z_{MB}} . \tag{7} \]

Equation (7) shows that the limiting influence of \(z_2\) on the current \(I_2\) will become appreciable only in the case where the quantities \(z_2\) and \(z_{MA} + z_{MB}\) are commensurable. With class “D” current transformers, \(z_2\) will differ from \(z_{MA} + z_{MB}\) by no less than one order of magnitude. Therefore the vectors \(\dot I_2\) and \(\dot I'_1\) will practically coincide in phase, while \(\dot E_A\) and \(\dot E_B\) will be displaced by an angle of approximately \(180^\circ\).

Fig. 7.

These considerations make it possible to use the following calculation method. Fig. 7 gives the no-load characteristics \(E_2 = f(I'_1)\) in actual values. It is obvious that if \(z_2 = \infty\) and \(I_2 = 0\), the magnetizing currents would be equal to \(I_{HA} = I_{HB} = I'_1\). Then, at \(I'_1 = I'_{\mathrm{ng}}\), from the no-load curves we would have \(E_A\) and \(E_B\) for this case. If, however, \(I_2 \ne 0\), then \(I_{HA} = I'_1 - I_2\) and \(I_{HB} = I'_1 + I_2\), and

\[ I_2 = \frac{I_{HB} - I_{HA}}{2}. \tag{8} \]

Laying off, from the value \(I'_1 = I'_{\mathrm{ng}}\), the value \(I_2\) on both sides, we obtain the magnitudes of the magnetizing currents \(I_{HA}\) and \(I_{HB}\), to which the e.m.f.’s \(E_A\) and \(E_B\) will correspond. The fact that the e.m.f.’s of current transformers A and B are unequal indicates the presence in the secondary circuit of a resistance of magnitude

\[ r_2 = \frac{E_A - E_B}{I_2}. \]

If the resistance \(r_2\) were negligibly small, then \(E_A \simeq E_B\), and in this case we would have the greatest possible current in the relay circuit.

It follows from this that, in order to determine \(I_{2\max}\), it is sufficient to superpose, on one graph, the no-load curves of the current transformers \(E_2=f(I'_1)\), to restore a perpendicular from the point on the \(I'_1\) axis corresponding to the desired value of the primary current, and to draw a horizontal line between the curves \(E_2=f(I'_1)\) in such a way that the perpendicular divides it into equal segments. Then each of these segments, on the scale of \(I_1\), will be equal to the current \(I_{2\max}\) in rms values. In an analogous way the current \(I_2\) can be calculated with allowance for the influence of \(r_2\) (if the inequality \(r_2 \ll z_{MA}+z_{MB}\) is observed). In this case the problem is complicated by the fact that, from the graph of Fig. 7, one has to select such a value of the current \(I_2\) as would satisfy equation (6).

The calculation method described gives rather limited accuracy for the following reasons:

1. The nonsinusoidal nature of the current \(I_2\) is not taken into account. Meanwhile, as a result of substantial saturation of the cores, the current \(I_2\) contains a high percentage of higher harmonics.

2. The accuracy of graphical constructions cannot be high, since in the region of construction the curves run very gently.

3. It is impossible to take into account the influence of the inductance of the secondary circuit on the higher harmonics of the current \(I_2\).

In order to have some reliability margin in the results of the calculation, the limiting influence of the resistance \(r_2\) on the current \(I_2\) should not be taken into account.

To check the calculation method described, curve 1 in Fig. 6 was constructed by calculation (see the dashed line in Fig. 6) up to values \(I'_{\alpha1}=1500\) A, at which it may still be assumed that \(r_2 \ll z_{MA}+z_{MB}\) (\(r_2=1\ \Omega\), \(z_{MA}+z_{MB}=13.3\ \Omega\)). From a comparison of the experimental and calculated curves in Fig. 6 it follows that the calculation error does not exceed \((10\text{–}15)\%\). Such an error is commensurate with the error that may occur when adjusting the scheme and therefore is acceptable from the standpoint of engineering calculations.

Conclusions

1. Longitudinal differential protection with balanced secondary e.m.f.s can be successfully used for the protection of powerful hydrogenerators. In this case high selectivity is attainable at \(I_{1cp}=(0.4\text{–}0.6)\,I_{HG}\) (\(k_H=3\)).

2. High selectivity is achieved by reducing the numbers of turns of the secondary windings of the current transformers connected for e.m.f. balance, with such a calculation that the referred value of the sum of the resistances of the connecting leads and these windings would be \(r'_2=(40\text{–}60)\ \Omega\), if \(I_{1cp}=(0.4\text{–}0.6)\,I_{HG}\), and \(r'_2=(20\text{–}30)\ \Omega\), if \(I_{1cp}=(1.2\text{–}1.5)\,I_{HG}\).

3. The scheme possesses extremely high reliability. None of the types of damage to the scheme causes false operation of the protection even at \(I_{1cp}=(0.4\text{–}0.6)\,I_{HG}\). In this case the reliability margin is not less than 2 for the most dangerous faults. The fault can easily be detected by applying the signaling circuit conventional for differential protection.

4. High reliability coefficients with respect to selectivity and stability against faults in its circuits indicate

on the inadvisability of special selection of current transformers for a set for differential protection of generators with balancing of secondary EMFs.

REFERENCES

1. Tsarev M. I. Differential protection of generators with auxiliary fast-saturating transformers, Elektricheskie stantsii, 1949, No. 7.

2. Drozdov A. D. On differential protection of generators and transformers, Elektricheskie stantsii, No. 9, 1955.

3. Zeveke G. B. Differential protection of electrical machines, Elektricheskie stantsii, No. 1, 1940.

4. Kutyavin I. D., Bagnisky L. V., Bagniskaya A. S. Increasing the selectivity of differential protection of generators by including an additional-resistance relay in the circuit, Proceedings of the Tomsk Order of the Red Banner of Labor Polytechnic Institute named after S. M. Kirov, vol. 98, 1959.

5. Kutyavin I. D. On methods for balancing the arms of differential protection of generators. Proceedings of the Tomsk Order of the Red Banner of Labor Polytechnic Institute named after S. M. Kirov, vol. 70, 1951.

6. Nechaev B. A. Current transformers with a small steel cross section in generator differential-protection schemes, Elektricheskie stantsii, No. 1, 1956.

7. Bagnisky L. V. On the use of current transformers with a small volume of steel for differential protection of generators, Proceedings of the Tomsk Order of the Red Banner of Labor Polytechnic Institute named after S. M. Kirov, vol. 94, 1959.