Relay with Equal Sensitivity to Different Types of Faults
Abstract Generated abstract
This paper addresses the unequal sensitivity of conventional relay protections to different short-circuit types, which can restrict the use of simpler protection schemes. It proposes a relay arrangement using a functional current converter whose harmonic output differs for three-phase and two-phase faults, with a series capacitor selected to equalize the rms relay currents at the operating point. The authors derive the equality condition, describe experimental refinement of the capacitance and relay winding parameters, and identify the larger of two capacitance values as preferable for maintaining sensitivity. For networks with large earth-fault currents, the paper extends the scheme by adding an auxiliary transformer to introduce a zero-sequence component, enabling comparable operation for single-phase ground faults.
Full Text
Relay of Equal Sensitivity to Different Types of Faults
N. V. Lisetskii, V. I. Khuduguev, Yu. A. Kulaga
(Presented by the scientific seminar of the Department of Electric Power Stations)
Analyzing all types of modern relay protections against multiphase short circuits, one can identify one common negative feature: the unequal sensitivity of many protections to different types of short circuits. As is known, this circumstance makes it necessary to check the sensitivity of protections for a two-phase short circuit and, when the sensitivity is insufficient, limits the field of application of simpler protections.
The use of a functional converter [1] makes it possible to obtain a relay of equal sensitivity to currents for different short circuits at the same distance from the protection installation point. Functional converters (F.C.) can be used for simple and complex protections, ensuring equal sensitivity.
For networks with small earth-fault currents, when current transformers are installed in two phases, the circuit for connecting the converter is shown in Fig. 1.
According to [1], the output voltage of the converter has a nonuniform harmonic composition for different types of short circuits, and its rms value is determined from the expressions:
a) for a three-phase short circuit
\[ U^{(3)} = \sqrt{U_3^2 + U_9^2 + \ldots} \tag{1} \]
where \(U_3\), \(U_9\) are the rms values of the voltages of the 3rd and 9th harmonics of the F.C. output for a three-phase short circuit, determined by the formula
\[ U_k = 3 \frac{\lg \sqrt{3}\, I_{\text{ef}} - a_k}{b_k}, \qquad k = 3; 9; \ldots \]
Fig. 1
\(a_k,\ b_k\) are coefficients constant for the given grade of iron;
\(H_{\mathrm{eff}}\) is the effective value of the magnetic-field intensity;
\[ H_{\mathrm{eff}}=\frac{I^{(3)}\cdot w_1}{l_{\mathrm{av}}}; \]
\(I^{(3)}\) is the current of a three-phase short circuit, referred to the secondary side of the current transformers;
\(w_1\) is the number of turns of the primary winding of the FP;
\(l_{\mathrm{av}}\) is the length of the mean line of force;
b) for a two-phase short circuit
\[ U^{(2)}=\sqrt{\sum_{k=1} U_k^2}, \qquad k=1,\ 3,\ 5,\ 7,\ 9, \tag{2} \]
\(U_k\) is the rms value of the voltage of the \(k\)-th harmonic of the FP output in the case of a two-phase short circuit, determined from expression [1]:
\[ U_k=\frac{a_k-\lg\frac{H_{\mathrm{eff}}}{2}}{b_k}; \]
\[ H_{\mathrm{eff}}=\frac{I^{(2)}\cdot w_1}{l_{\mathrm{av}}}; \]
\(I^{(2)}\) is the current of a two-phase short circuit, referred to the secondary side of the current transformers.
The presence of a different harmonic composition of the FP output voltage for three-phase and two-phase short circuits makes it possible to equalize the rms values of the currents through the relay. This is achieved by connecting a capacitor in series with the relay coil (Fig. 1). The capacitance of this capacitor is determined from the condition of equality of the rms values of the relay currents for three-phase and two-phase short circuits.
\[ I_p^{(3)}=I_p^{(2)} \qquad \text{or} \qquad \tag{3} \]
\[ \sqrt{ \frac{U_3^2}{R^2+\left(3\omega L-\frac{1}{3\omega C}\right)^2} + \frac{U_9^2}{R^2+\left(9\omega L-\frac{1}{9\omega C}\right)^2} +\ldots } = \]
\[ = \sqrt{ \frac{U_1^2}{k^2+\left(\omega L-\frac{1}{\omega C}\right)^2} + \frac{U_3^2}{R^2+\left(3\omega L-\frac{1}{3\omega C}\right)^2} + \frac{U_5^2}{R^2+\left(5\omega L-\frac{1}{5\omega C}\right)^2} + \frac{U_7^2}{R^2+\left(7\omega L-\frac{1}{7\omega C}\right)^2} + \frac{U_9^2}{R^2+\left(9\omega L-\frac{1}{9\omega C}\right)^2} }. \]
\(R\) is the total active resistance of the secondary winding of the FP, the relay coil, and the connecting wires;
\(\omega L\) is the inductive reactance of the FP load circuit;
\(C\) is the capacitance connected in series with the relay.
The analytical solution of this equation gives two positive values of the capacitance. These values require experimental refinement, since:
- The inductance of the relay varies as a function of the current.
- The voltage drop in the secondary winding of the FP is not taken into account.
For experimental determination of the capacitances that ensure equal sensitivity, curves are constructed showing the dependence of the relay current on the value of the capacitance connected in series with its winding, when symmetrical three-phase and single-phase currents flow in the primary circuits of the phase converter (three-phase and two-phase short-circuit modes).
Fig. 2
The magnitude of the primary current is constant and equal to the relay operating current. The intersection of the curves (Fig. 2) gives two capacitance values, \(C_{\max}\) and \(C_{\min}\). The larger value, \(C_{\max}\), provides equal relay sensitivity in the best way, since, if it is determined with insufficient accuracy, the equality of the relay currents is disturbed only slightly. In addition, for fault currents greater than the operating current, the indicated equality is better maintained, as can be seen from Fig. 3.
Fig. 3
As the responding element, a relay of type ET was used. Depending on the required setting range, the number of turns of the relay was varied. The parameters of the relay winding were determined with the aid of the external characteristic of the phase converter \(U_2^{(r)} = f(I_2)\) (Fig. 4). This characteristic was plotted at a constant primary current equal to the operating current of the protection. Since, for this relay system, the magnetizing force
operation at the mean setting \((F_{\mathrm{cp}})\) remains constant, the number of relay turns was determined from the expression:
\[ w_{\mathrm{p}}=\frac{F_{\mathrm{cp}}}{I_{\mathrm{p}}} \]
\(I_{\mathrm{p}}\) is the relay operating current.
The value of the operating current \((I'_{\mathrm{p}})\) is specified using the external characteristic, provided that the operating mode of the FP is approximated to the no-load mode [1].
Fig. 4
The cross section of the relay-coil wire is determined from the condition [2].
\[ z_{\mathrm{n}}=\frac{U'_2}{I'_2}, \]
\((U'_2\) corresponds to \(I'_{\mathrm{p}}\) on the external characteristic). Experiments have shown that capacitance has little effect on the calculation of the relay winding; therefore it is not taken into account in the calculations.
For networks with large ground-fault currents, equal sensitivity of the protection can also be achieved for single-phase faults. For this purpose, a component proportional to the zero-sequence current must be introduced into the output voltage of the FP. This is provided by adding an additional single-phase transformer to the FP circuit (Fig. 5).
For phase-to-phase short circuits, the resultant current in the neutral conductor is zero and the primary winding of the additional transformer carries no current. In a single-phase ground fault, the electromotive forces induced in two phases of the secondary winding of the FP cancel each other, since they are equal in magnitude and oppositely directed. Through the neutral conductor and the primary winding of the additional transformer there passes the secondary current of the single-phase fault. Therefore a voltage proportional to the zero-sequence current is applied to the relay.
The number of turns of the secondary winding of the additional transformer \((W'_2)\) is determined from the condition of equality of the currents through the relay for a three-phase and a single-phase short circuit at the instant of relay operation.
Fig. 5
For application of an equal-sensitivity relay in different networks with high earth-fault currents, the secondary winding of the auxiliary transformer is made with taps.
Conclusions
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The use of an equal-sensitivity relay eliminates the need to check the sensitivity of protections for a two-phase short circuit. The field of application of simple protections is expanded.
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The use of a single responding element for different types of short circuits.
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In networks with high earth-fault currents, it is possible to dispense with the installation of special earth-fault protection.
References
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N. V. Lisetskii, V. I. Khuduguev, Yu. A. Kulaga. Determination of the harmonic composition of the functional current converter. Izvestiya TPI, vol. 191.
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V. L. Fabrikant. Theory of Alternating-Current Windings. Gosenergoizdat, 1958.