Possibility of Obtaining Additional Information on the Nature of a Fault When Implementing Earth Fault Protection Using a Current with a Frequency of 25 Hz
Abstract Generated abstract
This paper examines ground fault protection for compensated electric networks in which substation feeders consist of several parallel cables, requiring selective identification of the damaged cable and possible fault location. It analyzes a method that superimposes a 25 Hz control current on the network through an arc suppression coil circuit, deriving equivalent circuit relations for current distribution between the faulty and healthy cables as a function of fault distance, cable number, and cable length. The results indicate conditions under which protection operates selectively on the damaged cable and show that the distance to the fault can be estimated from measured 25 Hz currents, provided the protection elements and zero sequence current transformers have sufficient stability, linearity, and consistency.
Full Text
POSSIBILITY OF OBTAINING ADDITIONAL INFORMATION ON THE NATURE OF DAMAGE WHEN IMPLEMENTING GROUND-FAULT PROTECTION USING A CURRENT WITH A FREQUENCY OF 25 Hz
B. G. TRET’YAKOV
(Presented by the scientific and technical seminar of the Department of Electric Power Stations)
In practice, cases are often encountered in which the outgoing feeders of substations consist of several parallel cables. In this connection, it becomes necessary to provide selective indication of ground faults not only for the feeder itself, but also for each of its cables, and also to determine the location of the fault. Certain possibilities in solving this problem are provided by a method based on superimposing a control current with a frequency of 25 Hz on an industrial-frequency network, developed at the Department of Electric Power Stations of Tomsk Polytechnic Institute.
As the source of the control current, an electromagnetic parametric frequency divider of special design is used, connected in series in the circuit of the arc-suppression coil [1]. The choice of a frequency below the industrial frequency is due to the fact that the distribution of low-frequency current during a fault is better than that of higher-frequency current, since it is less shunted by the capacitances of the undamaged elements [2]. In addition, the method used in this case makes it possible to selectively monitor the presence of a fault in the network even when operating supply has been removed from it.
Let us consider the equivalent circuit of a feeder consisting of \(n\) parallel cables, one of which has a ground fault at point \(k\), located at a distance \(l\) from the busbars (Fig. 1). In the figure the following designations are used:
\(L\) — total cable length;
\(U\) — voltage of the control-current source;
\(I\) — ground-fault current with a frequency of 25 Hz;
\(x\) — resistance of the arc-suppression coil;
\(C_1 \div C_n\) — capacitances of the corresponding cables to ground;
\(z_1 = z_2 = z_n\) — cable resistances;
TNP — zero-sequence current transformers.
We carry out the calculation using the equivalent circuit shown in Fig. 2, in which
\[ z = \frac{R_0 L}{n - 1} + R_0(L - l), \qquad z_1 = R_0 l, \]
where \(R_0\) is the resistance of the cable per unit length.
\[ I = \frac{U}{x + \dfrac{z \cdot z_1}{z + z_1}} . \tag{1} \]
Current through the CT of the damaged cable
\[ I_1 = I \cdot \frac{z}{z+z_1}. \tag{2} \]
Total current of the healthy cables
\[ I_2 = I \cdot \frac{z_1}{z+z_1}. \tag{3} \]
Fig. 1. Equivalent zero-sequence circuit of a feeder in a compensated network, consisting of \(n\) parallel cables
Substituting the resistance values into (1), (2), and (3), after a number of transformations we obtain
\[ I=\frac{U}{x+lR_0\left[1-\frac{l}{L}\left(1-\frac{1}{n}\right)\right]}; \tag{4} \]
\[ I_1= \frac{U[Ln-l(n-1)]} {xLn+lR_0Ln\left[1-\frac{l}{L}\left(1-\frac{1}{n}\right)\right]}; \tag{5} \]
\[ I_2= \frac{Ul(n-1)} {xLn+lR_0Ln\left[1-\frac{l}{L}\left(1-\frac{1}{n}\right)\right]}. \tag{6} \]
The quantity
\[ lR_0\left[1-\frac{l}{L}\left(1-\frac{1}{n}\right)\right] \]
may be neglected because of its smallness in comparison with the resistance of the arc-suppression coil. Formulas (4), (5), and (6) take the form:
\[ I=\frac{U}{x}; \tag{7} \]
\[ I_1=\frac{U[Ln-l(n-1)]}{xLn}; \tag{8} \]
\[ I_2=\frac{Ul(n-1)}{xLn}. \tag{9} \]
The current with a frequency of 25 Hz flowing through one of the healthy cables is
\[ I_2'=\frac{I_2}{n-1}. \tag{10} \]
Fig. 2. Equivalent calculation circuit for the zero sequence of a feeder of a compensated network consisting of \(n\) parallel cables
Figure 3 shows the nature of the distribution of currents over the healthy and damaged cables during a fault. The slope of the characteristics \(I_1\), \(I_2\), \(I_2'\) as functions of \(l\) depends on the number of parallel cables and on their length.
Fig. 3. Nature of the current distribution when one of the cables is faulted, as a function of the distance of the fault location from the busbars
From Fig. 3 it is seen that, in the event of a ground fault at a distance from the busbars satisfying the condition \(l<l_1\), the protection will operate only on the damaged cable. The value \(l_1\) can be determined from the equation
\[ I'_2=I_{\mathrm{op}}, \tag{11} \]
where \(I_{\mathrm{op}}\) is the operating current of the protection. Substituting (9) and (10) into equation (11), we obtain
\[ l_1=\frac{I_{\mathrm{op}}\chi Ln}{U}. \tag{12} \]
It follows from (12) that, in order to increase \(l_1\), it is necessary to increase the operating current of the protection. However, as is seen from Fig. 3, \(I_{\mathrm{op}}\) must always remain less than \(I_{1\min}\). Under such restrictions, satisfying the indicated requirement means that the actuating element of the protection must be made with a highly stable operating level.
The analysis carried out also shows that, on feeders consisting of several parallel cables, it is possible to determine the distance to the fault location by measuring currents at a frequency of 25 Hz in the steady-fault mode. The distance to the fault location, for known currents \(I_1\) and \(I_2\), is determined by a formula obtained by dividing expression (8) by (10):
\[ l=\frac{Ln}{\dfrac{I_1}{I_2}+n-1}. \tag{13} \]
Implementation of this method for determining the distance to the fault location imposes certain requirements on the stability and linearity of the amplitude characteristic of the actuating element, and during adjustment requires verification of the identity of the zero-sequence current transformers.
Conclusions
The proposed method makes it possible selectively to determine the damaged cable from a bundle of parallel cables of one of the feeders of a compensated network and, with sufficient accuracy, the distance to the fault location.
REFERENCES
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R. A. Vaynshteyn, A. V. Shmoilov. Sources of control current for protection against ground faults in networks with a compensated neutral. Izv. TPI, vol. 172, 1967.
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R. A. Vaynshteyn. Some questions concerning the signaling of ground faults in compensated networks, implemented by applying to the network a current with a frequency different from the network frequency. Collection of reports. Novosibirsk, 1964.