Use of an Electromagnetic Parametric Frequency Divider as a Reference Current Source for Ground Fault Protection in Compensated Networks
Abstract Generated abstract
The paper examines the use of an electromagnetic parametric frequency divider as a source of 25 Hz test current for ground fault protection in compensated electrical networks. It formulates requirements for such a source, analyzes the divider when its output winding is connected in series with the arc suppression coil, and derives design relations for rated power and for an alternative oscillatory circuit using a series inductor and capacitor. Laboratory tests and operation in a 6 kV compensated network indicate that the divider can maintain the half frequency output during ground faults while having little effect on neutral circuit impedance, with the modified circuit substantially reducing required power and influence on compensation current.
Full Text
Using an Electromagnetic Parametric Frequency Divider as a Source of Test Current for Ground-Fault Protection in Compensated Networks
R. A. Weinstein, L. I. Voronova, A. V. Shmoilov
(Presented by the scientific seminar of the Department of Electric Power Stations)
In ground-fault protection for compensated networks, based on the superposition on the network of a current with a frequency different from the network frequency, the most important element is the source of auxiliary (test) current (STC). The special requirements imposed on this source are determined chiefly by the fact that, in the event of a ground fault, depending on the method by which it is connected to the neutral, it is subjected either to the full phase voltage of the network or the full current of the arc-suppression coil flows through it. At the same time, the internal resistance of the STC to industrial-frequency current must be such that the resistance in the neutral circuit changes only slightly. In a number of cases, such requirements for the STC have led to its being made in the form of a nonlinear resistance connected into the neutral circuit [1]. Such a source generates a test current of elevated frequency only when industrial-frequency current flows through it, i.e., when network points whose potential is not equal to 0 are grounded. A source constructed in this way has a fundamental effect on the magnitude of the neutral current, since the source of energy for obtaining the test current is precisely the current itself flowing in the neutral circuit. In addition, the conversion coefficient of the first-harmonic current into higher-harmonic currents is always less than unity; that is, on the nonlinear STC there also appears a certain first-harmonic voltage when connected in series, and a certain part of the current branches off into it when connected in parallel. This chiefly explains the appreciable influence of nonlinear STCs on the neutral current. The absence of test current in normal operation and during a fault near the neutral points of generators deprives protection with superposition of a test current on the network of an important advantage—the possibility of providing 100% protection of generators against ground faults.
In our opinion, protection with the superposition of test current on the network will be fully competitive if the STC satisfies the following requirements.
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The voltage of the test-current source must remain constant when a fault occurs at any point of the electrically connected network.
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Connection of the STC into the circuit of the arc-suppression coil must not lead to a noticeable change in the resistance in the neutral circuit to industrial-frequency current.
The use of the EFCT in a power installation as a mass-produced device also requires meeting the requirements of high reliability, ease of manufacture, and ease of adjustment.
These requirements are met to a considerable extent by an electromagnetic parametric frequency divider with appropriately selected parameters and with certain changes in the circuit, with its output winding connected in series in the arc-suppression coil circuit. Moreover, as shown in [2] and also in [3], protection at a frequency below the industrial frequency has better properties in comparison with protection at an increased frequency. And when it is used for generators operating in a unit with a transformer, the use of an increased frequency with series connection of the EFCT is fundamentally impossible.
A frequency divider used as an EFCT operates under special conditions, since in the event of a ground fault in the network the full current of the arc-suppression coil flows through it. In this case requirement (1) must not be violated; i.e., oscillations of half frequency must be maintained when a large current of industrial frequency flows through the divider output windings.
The circuit of the frequency divider and the method of connecting it into the arc-suppression coil circuit are shown in Fig. 1.
Fig. 1
The winding of the oscillatory circuit \(W_k\) and the output winding \(W_v\) have transformer coupling with one another, while the excitation winding \(W_{\mathrm{exc}}\) is intended for periodic variation of the magnetic permeability of the material of the divider cores.
In this connection, the equivalent circuit of the divider may be represented as the equivalent circuit of a transformer whose magnetizing-branch inductance varies periodically with a frequency of \(50\ \mathrm{Hz}\) (Fig. 2). In the event of a ground fault, the industrial-frequency current \(I_{50}\) branches between the magnetizing branch \(X'_n\) and the capacitor reactance \(X'_c\). These currents are denoted by \(I'_n\) and \(I'_c\). In this mode the resistance of the magnetizing branch is a function of the working-frequency current and of the pulsating excitation current \(I_n\).
The frequency-division process is maintained as long as the field strength created by the part of the working-frequency current corresponding to
in the magnetizing branch will not reach such a value at which the periodic law of variation of \(X_{\mathrm{n}}\) is substantially disturbed.
Even without the use of special measures, the divider can be used as a test-current source, owing to the fact that the magnetizing branch is strongly shunted by the capacitor reactance \(X'_c\), since at a frequency of 50 Hz
\[ \frac{X'_{\mathrm{n}}}{X'_c}=4. \]
The ratio of the reactances follows from the fact that the resonant frequency of the circuit formed by \(X'_{\mathrm{n}}\) and \(X'_c\) is close to 25 Hz.
Fig. 2
The field strength of the external field in the cores of the frequency divider is
\[ H_{50}=\frac{K_p I_{50} W_{\mathrm{v}}}{l_{\mathrm{av}}}, \tag{1} \]
where \(K_p\) is the coefficient of distribution of currents between \(X'_{\mathrm{n}}\) and \(X'_c\);
\(W_{\mathrm{v}}\) is the number of turns of the output winding;
\(l_{\mathrm{av}}\) is the length of the mean line of force of one core of the frequency divider.
The number of turns of the output winding can be expressed by the following relation:
\[ W_{\mathrm{v}}=\frac{U}{K_1 B_{25}\cdot q}, \tag{2} \]
where \(K_1\) is a proportionality coefficient;
\(B_{25}\) is the induction at a frequency of 25 Hz, assumed sinusoidal;
\(q\) is the cross-sectional area of one core of the frequency divider;
\(U\) is the voltage at a frequency of 25 Hz on the output winding of the divider, determined by the condition of producing the required value of the test current under a metallic fault.
Substituting (2) into (1), we obtain
\[ K_1 H_{50} B_{25} l_{\mathrm{av}} q = K_p I_{50} U. \tag{3} \]
In (3), the product \(H_{50}\cdot B_{25}\cdot l_{\mathrm{av}}\cdot q\) is proportional to the volume of the cores of the frequency divider, i.e., to its rated power [4].
\[ S_p=K_2 H_{50} B_{25} l_{\mathrm{av}}\cdot q. \tag{4} \]
From (3) and (4) we obtain
\[ S_{\mathrm{p}} = I_{50} U \frac{K_{\mathrm{p}}}{K_{\mathrm{z}}}, \tag{5} \]
where \(K_{\mathrm{z}} = K_1 \cdot K_{\mathrm{o}}\).
Formula (5) can be expressed in terms of the required value of the test current and the line voltage of the network:
\[ S_{\mathrm{p}} = \frac{K_{\mathrm{p}}}{K_{\mathrm{z}}} \cdot \frac{I_{\mathrm{t}} U_{\mathrm{l}}}{2\sqrt{3}}, \tag{6} \]
where \(I_{\mathrm{t}}\) is the required value of the test current, and the voltage \(U\), according to the circuit of Fig. 1, has been replaced by the voltage drop across the arc-suppression coil due to the current \(I_{\mathrm{t}}\).
\[ U = \frac{U_{\mathrm{l}} I_{\mathrm{t}}}{2\sqrt{3}\, I_{50}} . \]
The value of the coefficient \(K_{\mathrm{p}}/K_{\mathrm{z}}\) was determined by testing a frequency divider with a rated power of 40 VA according to the circuit of Fig. 1. These tests made it possible to establish that the divider operates reliably if \(K_{\mathrm{p}}/K_{\mathrm{z}} = 0.5\).
It follows from (6) that the power of the divider can be reduced owing to a decrease in \(K_{\mathrm{p}}\).
A reduction of \(K_{\mathrm{p}}\) without violating the resonance condition at a frequency of 25 Hz can be achieved by replacing the capacitor in the frequency divider with a circuit consisting of a linearly connected inductor \((L)\) and capacitor \((C)\), selected so that the reactance of the entire external circuit of the tank winding satisfies the following conditions:
\[ \text{at a frequency of } 50\ \text{Hz}, \quad X = 0; \tag{7} \]
\[ \text{at a frequency of } 25\ \text{Hz}, \quad X = -\frac{2}{\omega C_{\mathrm{p}}}, \tag{8} \]
where
\[ \omega = 2\pi f, \]
\[ f = 50\ \text{Hz}, \]
\(C_{\mathrm{p}}\) is the capacitance satisfying the resonance condition at a frequency of 25 Hz.
Expanding (7) and (8), we obtain
\[ \frac{\omega_0^2}{\omega^2} = 1, \tag{9} \]
\[ L = \frac{4}{3} \cdot \frac{1}{\omega^2 C_{\mathrm{p}}}, \tag{10} \]
where
\[ \omega_0 = \frac{1}{\sqrt{LC}} . \]
Relations (9) and (10) are design relations for determining \(L\) and \(C\). In this case it is clear that the reduction of \(K_{\mathrm{p}}\) will be greater the higher the quality factor of the inductor \(L\).
From the standpoint of the influence of the frequency divider on the current of the arc-suppression coil, the important quantity is the impedance with respect to the terminals of the output winding. From the circuit of Fig. 2 it may be considered approximately equal to
\[ Z'_{\mathrm{p}} = Z_{\mathrm{v}} + Z'_{\mathrm{k}} + Z'_{\mathrm{kvn}}, \]
where \(Z_{\mathrm{v}}\) is the total impedance of the output winding;
\(Z'_{\mathrm{k}}\) is the total impedance of the tank winding, referred to the number of turns of the output winding;
\(Z'_{\mathrm{kvn}}\) is the total resistance of the external circuit of the tank winding, referred to the number of turns of the output winding.
The resistance \(Z_p\) of real frequency dividers made on shell-type or core-type magnetic cores is considerably less than the resistance of the arc-suppression coil, if their power is determined from (6).
Owing to the smallness of \(Z'_p\), switching the frequency divider into the circuit of the arc-suppression coil practically does not change the compensation current.
It is also easy to establish that \(Z_p \equiv I_t^2\), since
\[ W_{\mathrm{v}} \equiv U \equiv I_t, \qquad \text{and} \qquad Z_p \equiv W_{\mathrm{v}}^2 . \tag{11} \]
From (6) and (11) it follows that the power of the frequency divider and its influence on the compensation regime are the smaller, the smaller \(I_t\) is, i.e., the higher the sensitivity of the frequency-selective responding elements.
To verify what was stated above, an experiment was carried out with the circuit of Fig. 1. A divider of \(7\ \mathrm{VA}\) power was used, with a half-frequency voltage on the output winding of \(7\ \mathrm{V}\). The resistance \(X_k\), simulating the arc-suppression coil, was \(20\ \Omega\). When the divider was switched on, the current \(I_{50}\) changed insignificantly. The frequency-division process was disturbed at a current \(I_{50}=2\ \mathrm{A}\). When an \(L—C\) circuit with parameters determined from (16) and (17) was connected instead of the capacitor \(C\), the frequency-division process was preserved at a current \(I_{50}=18 \div 20\ \mathrm{A}\). The half-frequency voltage component in this case practically did not change. That is, now the value of the coefficient \(K_p K_z\) can be reduced to \(0.05 \div 0.06\).
When the capacitor is replaced by an \(L—C\) circuit, the influence of the divider on the current of the arc-suppression coil becomes many times smaller, since in this case the reaction of the divider to the \(50\ \mathrm{Hz}\) current is analogous to the reaction of a transformer whose secondary winding is short-circuited.
For illustration, let us give the corresponding parameters of frequency dividers installed in the compensated \(6\ \mathrm{kV}\) network of the Barnaul TETs-2 in order to provide protection against ground faults in the cable network.
Two dividers, connected into the circuits of two arc-suppression coils, each rated at \(60\ \mathrm{A}\), provide a test current of \(1.2\ \mathrm{A}\).
The calculated power of the dividers was determined without taking account of the \(L—C\) circuit and was equal to \(600\ \mathrm{VA}\). The number of turns of the tank winding is 1000, and that of the output winding is 15. The capacitance providing resonance at a frequency of \(25\ \mathrm{Hz}\) is \(7\ \mu\mathrm{F}\). The resistance of the capacitor at \(50\ \mathrm{Hz}\), referred to the number of turns of the output winding, is \(X_c = 0.1\ \Omega\).
The total short-circuit resistance between the tank and output windings, referred to the number of turns of the output winding, is
\[ Z'_{\mathrm{kz}} = 2.25 \cdot 10^{-1}\ \Omega . \]
The resistance of the arc-suppression coils is many times greater than these resistances (at a frequency of \(50\ \mathrm{Hz}\), \(60\ \Omega\)). When the capacitor is replaced by an \(L—C\) circuit, the resistance of the divider becomes still smaller, since in the circuit of the tank winding at a frequency of \(50\ \mathrm{Hz}\) only the active resistance is perceived, which, when referred to the number of turns of the output winding, is equal to \(2.7 \cdot 10^{-3}\ \Omega\).
Observation of the operation of the dividers was carried out during artificial ground faults in the network mentioned. Changes in the current of the arc-suppression coil due to switching on the dividers, measured with an ammeter of accuracy class 0.2, were naturally not observed.
The half-frequency voltage on the output winding also did not change either in magnitude or in phase.
The dividers have been in trial operation for one year. During this time there were about 10 ground faults in the network. No disturbances in the operation of the dividers were observed.
Conclusions
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In implementing protection against steady ground faults in compensated networks by superimposing on the network a current with a frequency of 25 Hz, it is possible to use a parametric frequency divider as the source of this current, with its output winding connected directly into the arc-suppression-coil circuit.
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The influence of the frequency divider on the resistance of the neutral circuit in determining its rated power by (6) is insignificant.
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A substantial reduction is achieved in the rated power of the divider and in its influence on the resistance of the neutral circuit when the capacitor of the oscillatory circuit is replaced by an \(L—C\) circuit with parameters selected according to (9) and (10).
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The conclusions obtained are well confirmed by experiments carried out in the laboratory and under industrial conditions.
References
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Signaling of ground faults in compensated networks. Collection of articles edited by Engineer V. I. Iozelson. Gosenergoizdat, 1962.
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R. A. Vainshtein. Certain problems in creating ground-fault signaling in compensated networks, implemented by superimposing on the network a current with a frequency different from the network frequency. Collection of reports for the Scientific and Technical Conference on summarizing experience in the design and construction of power-transmission lines and substations. Novosibirsk, 1964.
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R. A. Vainshtein, A. V. Shmoilov. On one-hundred-percent protection of synchronous generators against ground faults on the stator winding. In the present collection.
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K. G. Mityushkin. Magnetic frequency divider. Elektrichestvo, No. 8, 1957.