CONTROL CURRENT SOURCE FOR GROUND-FAULT PROTECTION IN NETWORKS WITH A COMPENSATED NEUTRAL

R. A. VAINSTEIN, A. V. SHMOILOV

Presented by the scientific seminar of the departments of electric power stations and electrical networks and systems

The problem of implementing selective ground-fault protection for networks with a compensated neutral remains relevant at the present time [1]. The small magnitude of the reactive component of the zero-sequence current, as well as the uncertainty of the sign of this component on the damaged element owing to regulation of the compensation mode, force one to abandon its use for protection from the outset. The distribution of the active component of the zero-sequence current is favorable for selecting the damaged element. However, the magnitudes of this current in most practical cases are negligibly small, which creates considerable difficulties in developing the responding element. Studies [1, 2] show that protection responding to the active component of the current can in a number of practical cases prove satisfactory, provided that the responding element is appropriate.

Recently, promising developments have appeared [1, 3, 4] that use, for protection, a control current artificially imposed on the network.

In [3], studies and the development of network protection are presented that use a control current, artificially imposed on the network, with a frequency of 25 Hz. The studies carried out there, as well as additional studies, show that the most economical and technically simplest way to impose the control current on the network is by connecting a control-current source (CCS) in series with the arc-suppression coil.

The studies show that in this case the CCS must meet the following requirements:

1. The switching-on of the CCS must not practically change the operating mode of the arc-suppression coil (ASC), i.e., the internal resistance of the CCS for the industrial frequency must be close to zero.

2. The operating mode of the CCS must not practically depend on the current of the arc-suppression coil during a ground fault.

3. The frequency of the control current must be lower than the industrial frequency.

The fulfillment of these requirements can be achieved most simply by shunting the CCS output with a series resonant \(L—C\) circuit tuned to the frequency of the industrial current and connected in series in the ASC circuit. However, calculations show that, in the normal operating mode of the network, for acceptable parameters of the \(L—C\) circuit, a very large leakage of the control current into the \(L—C\) circuit is obtained (more than 60%).

This phenomenon is unacceptable when a phase-sensitive device, responding to a change in the phase of the control current during a fault, is used as the actuating element of the protection, since in the normal operating mode of the network the braking in the actuating element will be insufficient.

This circumstance imposes yet another requirement on the control-current source (ICS), namely that the \(L\)—\(C\) circuit, together with the other elements, must be a necessary component part of the ICS and, together with them, ensure the ICS operating mode.

These requirements are met by specially developed designs of parametric frequency dividers (PFD) for protection. Below is given a description of the operating principle of a PFD on the basis of the equivalent circuit, the test results, and the procedure for engineering calculation.

In Fig. 1a is shown the circuit of a conventional PFD design. A PFD of conventional design consists of two ferromagnetic cores with excitation windings \(W_{\mathrm{v}}\), circuit windings \(W_{\mathrm{k}}\), and output windings \(W_{\mathrm{out}}\) wound on them. The windings \(W_{\mathrm{v}}\) are supplied from a source of sinusoidal voltage of 50 Hz through the semiconductor valve \(V\). They are connected in opposition-series with respect to the circuit windings, which are connected in series and short-circuited by the capacitor \(C\). The inductance of the circuit windings together with the capacitor \(C\) forms an oscillatory circuit tuned to a frequency close to 25 Hz. The output windings are connected in accordance with the circuit windings. By terminals 1-1 the PFD is connected into the ASC circuit. In Fig. 1b is shown the equivalent circuit of the PFD as seen from the output-winding side. This circuit, as seen from the output windings, is an ordinary equivalent circuit of a transformer with a capacitive load \(C\), the inductance of whose magnetizing branch is periodically varying in time \((L_{\mathrm{n}})\). The remaining designations in the circuit are:

Fig. 1.

\(L'_{p\,\mathrm{out}}\) and \(r'_{\mathrm{out}}\)—the leakage inductance and active resistance of the output windings, referred to the number of turns of the circuit winding;

\(L_{p\mathrm{k}}\) and \(r_{\mathrm{k}}\)—the leakage inductance of the circuit winding and the active resistance of the oscillatory circuit;

\(L_{\mathrm{d}}\)—additional inductance.

The additional inductance must be chosen so that, together with the inductance \(L_{p\mathrm{k}}\) and the capacitor \(C\), it forms a series resonant circuit at the frequency of the industrial current. Then the input resistance of the PFD for the current of the arc-suppression coil will be determined by the small geometric sum of the resistances \(x'_{p\,\mathrm{out}}\), \(r'_{\mathrm{out}}\), \(r_{\mathrm{k}}\). At the same time, in this case the branching of the 50-Hz current into the magnetizing branch of the PFD will be minimal. Thus, the inclusion of the additional inductance eliminates the influence of the PFD on the current of the arc-suppression coil and the influence of this current on the electromagnetic processes in the PFD that ensure frequency division.

The inclusion of the additional inductance \(L_{\mathrm{d}}\) fundamentally does not

changes the operating mode of the CCS. Let us show this. With full resonance tuning at a frequency of 50 Hz, for the circuit \((L_{\mathrm{rk}} + L_{\mathrm{d}}) - C\) relative to the points \(O—O\), two equations can be written at frequencies of 50 and 25 Hz:

\[ \left\{ \begin{aligned} \omega (L_{\mathrm{rk}} + L_{\mathrm{d}}) &= \frac{1}{\omega C},\\ \frac{2}{\omega C_{\mathrm{e}}} - \frac{\omega}{2}(L_{\mathrm{rk}} + L_{\mathrm{d}}) &= -\frac{2}{\omega C}, \end{aligned} \right. \tag{1} \]

where

\[ \begin{aligned} \omega &\text{ is the industrial-current frequency;}\\ C_{\mathrm{e}} &\text{ is a certain equivalent capacitance connected to the magnetizing branch and corresponding to a capacitive reactance at a frequency of 25 Hz when } L_{\mathrm{d}} \text{ is switched on.} \end{aligned} \]

From (1)

\[ C_{\mathrm{e}} = \frac{4}{3} C. \tag{2} \]

Switching on \(L_{\mathrm{d}}\) increases the equivalent capacitance of the oscillatory circuit. To obtain the CCS mode preceding the switching-on of \(L_{\mathrm{d}}\), it is necessary to reduce the capacitance of the capacitor \(C\) by a factor of \(4/3\).

Thus, the described CCS circuit fully satisfies the requirements for a CCS for protection of compensated networks against ground faults.

The equivalent circuit of specially developed CCS designs does not differ in principle from that shown in Fig. 1b. The difference between these designs and the usual one consists in the fact that, owing to the rational arrangement of ferromagnetic cores and the placement of windings on them, the consumption of conductor material is substantially reduced (approximately by a factor of 2), while the additional inductance is provided by the increased leakage of the winding of the oscillatory circuit; moreover, the leakage inductance can be regulated.

The operation of the CCS as a CCS for compensated networks differs from the operation of a power CCS. This difference consists in the fact that, in the normal operating mode of the network, the CCS is loaded by the sum of the resistances of the zero sequence and of the arc-suppression coil, which has a capacitive character at a frequency of 25 Hz, whereas during a ground fault it is loaded by the inductive resistance of the ASC. The ratio of these resistances at a frequency of 25 Hz, with full compensation of the capacitive currents of the network, is equal to \(3 : 1\). In addition, it is known that, when the CCS operates into a capacitive load, the voltage at its output increases somewhat depending on the saturation mode of the cores (the less the saturation, the greater the increase). Therefore, when considering the CCS as a CCS, it is necessary first of all to know its external characteristics when operating into an inductive load.

In Figs. 2a and b are given, in relative units, the dependences \(U^{(L)}_{\mathrm{out}*}(S_*)\) and \(U^{(L)}_{\mathrm{out}}(I_{25*})\) during operation into an inductive load, where

\[ \begin{aligned} U^{(L)}_{\mathrm{out}*} &\text{ is the voltage at the CCS output,}\\ S_* &\text{ is the delivered power,}\\ I_{25*} &\text{ is the current in the inductive load.} \end{aligned} \]

The base quantities adopted are: the voltage at the CCS output at no load, \(U_{\mathrm{out\,xx}}\); the total power of the oscillatory circuit at no load, \(S_{\mathrm{k}}\). As the base value of current, the current corresponding to the maximum delivered power \(S_{\max *}\) is adopted.

Figure 2 also gives the dependence \(I_{25*}(S_*)\).

Considering the dependences of Fig. 2, one may conclude:

1. The maximum delivered power of the CCS \(S_{\max *}\) is substantially

Fig. 2

less than the power circulating in the oscillatory circuit.

1. The well-known stiffness of the external characteristics of parametric generators when operating into an active load is not observed. The characteristics when operating into an inductive load possess a considerable droop coefficient.

2. The characteristics can be divided into two parts: part I—from no-load operation to the maximum delivered power—the working part; part II—from the maximum power and further into the region of smaller inductive resistances—the nonworking part.

When the PFC operates on the nonworking part of the external characteristics, it is unstable; this consists in the fact that, upon disappearance and subsequent restoration of the excitation voltage, the frequency-division processes are not restored. In addition, when operating on this part of the characteristics, the output voltage of the PFC is much less than the no-load voltage.

Taking these circumstances into account, operation of the PFC as a CCS for protection may be permitted only on the working part of the characteristics.

According to the experimental studies carried out, the delivered power should be taken as no higher than 0.9 of the maximum delivered power. We shall denote this coefficient by \(k_y\) and call it the coefficient of stability of parametric oscillations upon disappearance and subsequent restoration of the excitation voltage.

Of great interest when using a PFC as a CCS for protection of compensated networks are the dependences of the output voltage and of the 25-cps current flowing through the inductive resistance with which the PFC is loaded on the 50-cps current passed through the input windings of the PFC.

It is precisely under such conditions that the PFC operates during a ground fault in a compensated network.

In Figs. 3a and b are shown, in relative units, the dependences \(U^{(L)}_{\text{out}*}(I_{50*})\) and \(I_{25*}(I_{50*})\). As the base value of the 50-cps current, the current of the arc-suppression coil of the Bratsk HPP was taken, reduced to the parameters of the tested PFC model. The numbers above the curves denote the value of the stability coefficient \(k_y\). The curves shown in Figs. 3a and b make it possible to conclude that the dependences \(U^{(L)}_{\text{out}*}(I_{50*})\) and \(I_{25*}(I_{50*})\), characterizing the stability of 25-cps oscillations under pro-

Fig. 3

leakage through the \(25\)-Hz current source have sufficient stiffness up to \(I_{50*}=2\). This is achieved by including an additional inductance \(L_d\) in the oscillatory-circuit branch. In the absence of \(L_d\) in the circuit of the \(25\)-Hz current source, oscillations practically disappear at \(I_{50*}<0.5\).

The plotted dependences make it possible, from the accepted output power of the \(25\)-Hz current source into an inductive load, to calculate the necessary power circulating in the oscillatory circuit at no load and, from it, to calculate the required parameters of the \(25\)-Hz current source.

Thus, calculation of the \(25\)-Hz current source should begin with determining the delivered power.

1. In the general case the delivered power of the \(25\)-Hz current source must be calculated from two conditions: 1) the required control current during a ground fault in the network, \(I_{L25}\); 2) the required control current in the normal operating mode of the network, \(I_{C25}\).

\[ S_L = U_{\text{out}*}^{(L)} \cdot U_{\text{out,oc}} I_{L25}, \tag{3} \]

\[ S_C = U_{\text{out}*}^{(C)} \cdot U_{\text{out,oc}} I_{C25}, \tag{4} \]

where \(U_{\text{out,oc}}\) is the output voltage in volts at no load;

\(S_L\) is the delivered power in VA during a fault in the network;

\(S_C\) is the delivered power in VA in the normal operating mode of the network;

\(U_{\text{out}*}^{(L)}\) is the output voltage in relative units when the \(25\)-Hz current source operates into an inductive load;

\(U_{\text{out}*}^{C}\) is the output voltage in relative units when the \(25\)-Hz current source operates into a capacitive resistance.

The powers \(S_L\) and \(S_C\) can also be determined from the expressions:

\[ S_L = I_{L25}^2 \cdot X_L, \tag{5} \]

\[ S_C = I_{C25}^2 \cdot X_C, \tag{6} \]

where \(X_L\) is the resistance of the arc-suppression coil at a frequency of \(25\) Hz;

\(X_C\) is the sum of the zero-sequence resistances of the network and the arc-suppression coil at a frequency of \(25\) Hz.

As noted earlier, \(X_C\) is capacitive in character and, with full compensation of the capacitive current of the network, \(X_C = 3X_L\). Taking this into account, we determine the delivered power of the \(25\)-Hz current source during a fault in the network, \(S'_L\), if the delivered power \(S_C\) in the normal operating mode is specified.

network. For this purpose we carry out transformations. From (4),

\(U_{\mathrm{out}\,xx}=S_C/U^{C}_{\mathrm{out}*}\cdot I_{C25}\). By Ohm’s law,

\(I_{L25}=U^{L}_{\mathrm{out}*}\cdot U_{\mathrm{out}\,xx}/X_L\);

\(I_{C25}=U^{C}_{\mathrm{out}*}\cdot U_{\mathrm{out}\,xx}/3X_L\). Substituting the obtained formulas into (2), we obtain

\[ S'_L=3\,\frac{\left(U^{(L)}_{\mathrm{out}*}\right)^2} {\left(U^{(C)}_{\mathrm{out}*}\right)^2}\,S_C . \tag{7} \]

In (7), \(S_C\) is determined from (6), and \(U^{L}_{\mathrm{out}*}=U^{L}_{\mathrm{out}*}(k_y S_{\max *})\) from the dependence in Fig. 2, a. \(U^{C}_{\mathrm{out}*}\) should in the general case be determined from the dependence \(U^{C}_{\mathrm{out}*}(S_*)\). However, taking into account (7), and also, as noted earlier, the increasing character of this dependence with increasing \(S_*\), one may take \(U^{C}_{\mathrm{out}*}=1\), which will provide a margin of stability for the operation of the PDC on an inductive load when the excitation voltage disappears and is subsequently restored.

Thus, the power delivered by the PDC when setting the control currents in the normal operating mode of the network and during a fault must be determined from expressions (5) and (7). The larger value should be adopted as the calculated delivered power \(S_{\mathrm{calc}}\).

1. The power circulating in the oscillatory circuit is equal to

\[ S_k=\frac{S_{\mathrm{calc}}}{k_y S_{\max *}} . \tag{8} \]

1. The capacitance of the PDC capacitor \(C\) is specified, and the equivalent capacitance \(C_e\) is determined from (2).

2. The reactances of \(C_e\) and \(C\) at a frequency of 25 Hz, \(X^{(25)}_{C e}\), \(X^{(50)}_{C}\), and also the reactance of \(C\) at a frequency of 50 Hz, \(X^{(50)}_{C}\), are determined.

3. The current in the oscillatory circuit is

\[ I_{k25}=\sqrt{\frac{S_k}{X^{(25)}_{C e}}}. \tag{9} \]

1. The voltage with a frequency of 25 Hz on the magnetizing branch is

\[ U_{k25}=\frac{S_k}{I_{k25}} . \tag{10} \]

1. The transformation ratio between the circuit and output windings is

\[ k_T=\frac{U_{k25}}{U_{\mathrm{out}\,xx}}, \tag{11} \]

where

\[ U_{\mathrm{out}\,xx}= \frac{U^{L}_{\mathrm{out}}} {U^{(L)}_{\mathrm{out}*}(k_y S_{\max *})}; \tag{12} \]

\(U^{(L)}_{\mathrm{out}*}(k_y S_{\max *})\) is determined from \(U^{L}_{\mathrm{out}*}(S_*)\),

\[ U^{(L)}_{\mathrm{out}}=S_{\mathrm{calc}}/I_{L25\,\mathrm{calc}} . \tag{13} \]

In (13), \(I_{L25\,\mathrm{calc}}=I_{L25}\) when \(S_{\mathrm{calc}}=S_L\). When \(S_{\mathrm{calc}}=S'_L\),

\[ I_{L25\,\mathrm{calc}}=\sqrt{\frac{S'_L}{X_L}} . \tag{14} \]

1. The 50 Hz current flowing in the oscillatory circuit is determined, under the condition that the total leakage inductance and the capacitance \(C\) are tuned to resonance at a frequency of 50 Hz:

\[ I_{k50}=\frac{I_{\mathrm{arc}}}{k_T}, \tag{15} \]

where \(I_{\mathrm{arc}}\) is the current of the arc-suppression coil.

1. The amplitude of the maximum voltage across the capacitor is determined:

\[ U_{mc}=\sqrt{2}\,[I_{k50}X_c^{(50)}+I_{k25}X_c^{(25)}]. \tag{16} \]

1. The mean magnetic path length of the CCS cores is specified, and the active cross section of the ferromagnetic material and the numbers of turns of the tank and output windings are calculated. The calculation is based on three formulas:

\[ L_{\mathrm{sr\,n}}=\mu_{\mathrm{sr}} W_k^2 q/l_{\mathrm{sr}}; \tag{17} \]

\[ q=\frac{2U_{k25}}{\omega W_k B_{25}}; \tag{18} \]

\[ \omega/2\,L_{\mathrm{sr\,n}}=\frac{2}{\omega C_e}, \tag{19} \]

where

\(L_{\mathrm{sr\,n}}\) — mean inductance of the CCS magnetizing branch;
\(\mu_{\mathrm{sr}}\) — mean magnetic permeability of the ferromagnetic material when the CCS operates at no load;
\(q\) — total active cross section of both cores;
\(l_{\mathrm{sr}}\) — mean magnetic path length of the cores;
\(B_{25}\) — rms value of the induction at a frequency of 25 Hz;
\(W_k\) — number of turns of the tank windings;
\(\omega\) — power-frequency angular frequency.

From (19) one obtains

\[ L_{\mathrm{sr\,n}}=4/\omega^2 C_e. \tag{20} \]

Substituting (18) and (20) into (17) and carrying out the transformations, we obtain

\[ W_k=\frac{2l_{\mathrm{sr}}B_{25}}{\omega C_e\mu_{\mathrm{sr}}U_{k25}}. \tag{21} \]

The quantities \(\mu_{\mathrm{sr}}\) and \(B_{25}\) in (21) are determined empirically by calculating them from expressions (17) and (18) for CCS units in service. For CCS units made of E310 steel, Fig. 4 gives the dependence \(B_{25}(\mu_{\mathrm{sr}})\). The slope of the curve depends on the grade of steel and the quality of the core manufacturing technology.

As the quality of core manufacture is improved, the slope of the curve decreases.

Fig. 4.

For calculations of the PDC with steel E310, \(B_{25}\) may be recommended within the limits \(1.1 \div 1.3\) T.

After determining \(W_k\), the total active cross section according to (18) and the number of turns of the output windings are determined:

\[ W_{\text{out}}=\frac{W_k}{k_T}. \tag{22} \]

1. The number of turns of the excitation windings is determined. Because of the complexity of the derivation, we give the final formulas:

\[ B_n= \left[ \frac{ \omega^{3/4}\,qW_k^2 k\mu^{1/k}\sqrt{\pi}\,C_{\mathrm{e}}T \left(\frac{1}{2k}+0.5\right) }{ l_{\mathrm{cp}}\Gamma\left(\frac{1}{2k}\right) } \right]^{\frac{k}{1-k}}; \tag{23} \]

\[ W_v=\frac{2U_m}{q\omega B_n}\cdot \left(\frac{1.1B_f}{B_n}\right)^3, \tag{24} \]

where

\(B_n\) is the amplitude of the induction at the boundary of excitation of the PDC;
\(k\) and \(\mu\) are the coefficients of the power approximation of the magnetization curve of the core, \(\beta=\mu H_k\);
\(\Gamma\) is the gamma function;
\(U_m\) is the amplitude of the excitation voltage;
\(B_f\) is the value of the induction at the lower point of intersection of the magnetization curve with its power approximation.

The coefficients \(\mu\) and \(k\) are determined by the method of selected points on the main magnetization curve.

The use of (23), (24) gives an underestimated number of turns of the excitation windings by 15–30%.

By the described method, several variants of the PDC were calculated for protection against ground faults of the hydrogenerators of the Bratsk HPP. According to one of the variants, a PDC was manufactured. Tests showed good agreement between the calculated and experimental data.

Conclusions

1. On the basis of the equivalent circuit, the operating modes of the PDC were analyzed when it is used as an ICT for the protection of compensated networks against ground faults.

2. A PDC circuit is proposed that makes it possible to use it under ICT conditions.

3. Designs of PDCs with a reduced consumption of conductor material have been developed.

4. A method for engineering calculation of the PDC is proposed.

Literature

1. Signaling of ground faults in compensated networks. Collection of articles edited by Eng. V. I. Iozelson, GEI, 1962.

2. R. A. Vainshtein, A. V. Shmoilov. Application of low-frequency inductive parametry without premagnetization by direct current in protection against ground faults in networks with compensated and isolated neutrals. Izvestiya TPI, vol. 152, 1966.

3. R. A. Vainshtein. Application of low-frequency parametric systems for protection against ground faults in compensated networks. Dissertation, Tomsk, 1965.

4. R. A. Vainshtein. Inventor’s certificates Nos. 177958, 178862.