ON THE POSSIBILITY OF EXTRACTING A SMALL SIGNAL WITH A FREQUENCY OF 25 Hz AGAINST A BACKGROUND OF LARGE INTERFERENCE

R. A. Vainshtein, V. T. Getmanov

(Presented by the scientific seminar of the Department of Electrical Systems and Networks)

The problem of extracting a small signal with a frequency of 25 Hz against a background of large interference arose because, in order to implement protection against ground faults in the stator winding of synchronous generators operating in enlarged units with direct connection of the generators on an injected current, it is necessary to measure the component with frequency 25 Hz in the zero-sequence current at the generator terminals.

In practice, for measuring the current we have only the possibility of connecting the protection elements into the neutral conductor of one of the groups of current transformers installed at the generator terminals. In this case, a three-transformer zero-sequence filter operates under conditions in which a monitoring current with frequency 25 Hz flows through the damaged phase, while the cores are simultaneously magnetized by a current with frequency 50 Hz.

Let us determine the magnitude of the secondary monitoring current to which the protection must respond:

\[ I_{25}=\frac{2U_{25}}{X_L n_T} k_{\text{tap}}, \tag{1} \]

where \(U_{25}\) is the voltage of the monitoring-current source;
\(X_L\) is the inductive reactance of the arc-suppression coil at a frequency of 50 Hz;
\(k_{\text{tap}}\) is a coefficient taking into account the tapping of the monitoring current into the magnetizing branch of the current transformers;
\(n_T\) is the transformation ratio of the current transformers of the filter.

From the standpoint of transmission of current with frequency 25 Hz, the design operating condition is the generator no-load condition, when the cores of the current transformers are not magnetized by industrial-frequency current, and 50–60% of the current with frequency 25 Hz branches into the magnetizing branch. The protection is intended for installation on an enlarged unit of the Saratov Hydroelectric Power Station. For it, \(n_T=6000/5\), \(X_L=1000\ \Omega\), \(U_{25}=220\ \text{V}\).

The magnitude of the secondary monitoring current, determined from (1), is only \(0.2\ \text{mA}\), while the maximum possible unbalance current of the zero-sequence filter, composed of three single-phase current transformers, at the rated generator current is \(0.1\text{ A}\) [1]. Thus, the problem of extracting an insignifi-

component with a frequency of 25 Hz against a background of large interference with a frequency of 50 Hz.

The extraction of a small useful signal by known methods presents a certain difficulty. The use of reactive filters for this purpose requires a large inductance at a high quality factor [2], which, naturally, is impossible for such a low frequency without a considerable increase in the geometrical dimensions of the filters. The use of a ferromagnetic core, in turn, poses the problem of creating linear inductance over the entire range of current variation. At the same time, an increase in the unbalance current of the zero-sequence filter under external phase-to-phase short circuits, as well as double earth faults, does not permit such filters to be used because of the inadmissible overvoltages arising on the filter elements.

Fig. 1. Circuit for experimental investigation of a parametric amplifier.

The use of rejection \(RC\)-filters likewise does not give the required results, since they do not have a frequency region within which their own attenuation would be zero; this, of course, reduces the useful signal. In addition, when frequency-selective circuits with a large input resistance are used, a matching transformer is required, in which the useful signal is also attenuated.

Fig. 2. Dependences of the voltage on the tank circuit of the parametric amplifier on the current in the signal winding: 1 — with a frequency of 25 Hz; 2 — with a frequency of 50 Hz; 3 — frequency detuning coefficient.

A practical solution to the problem of extracting a small signal with a frequency of 25 Hz against a background of large interference proved possible owing to the use of a special inductive parametric amplifier with periodically varying inductance, possessing selective properties with respect to frequency. The parametric amplifier used here has been investigated and described in [3].

Below are presented the principal experimental data of the parametric amplifier, indicating the possibility of using such a design as a protection element that permits the necessary extraction of the useful signal. The experimental investigations were carried out according to the circuit of Fig. 1.

Here it is first of all necessary to note the linear dependence of the voltage on the tank circuit of the parametric amplifier on the signal current \(I\) flowing through the signal winding (Fig. 2), which is favorable for implementing protection. Figure 2 also gives the dependence of the voltage on the tank circuit on the industrial-frequency current. On the basis of these curves, the dependence was constructed of the frequency-detuning coefficient \(k_f\) on the signal current, representing the ratio of the currents with frequencies of 25 and 50 Hz at which the voltages of these frequencies at the amplifier output are equal (Fig. 2). It is seen from Fig. 2 that \(k_f \approx 55\) and remains practically constant over the entire range of signal variation, which is also no less important.

The parametric amplifier is connected by its signal winding into the neutral conductor of a zero-sequence filter. In the amplifier used, the signal winding contains a small number of turns and therefore can be made thermally stable under double ground faults. The resistance of the amplifier at a frequency of 50 Hz, measured with respect to the terminals of the signal winding, is \(\approx 0.2\ \Omega\).

Fig. 3. Dependences of the voltage on the tank circuit of the parametric amplifier: 1 — with stabilization; 2 — without stabilization.

Fig. 4. Voltage on the tank circuit for pump phases corresponding to maximum (1) and minimum amplification (2).

For the example given above (the generators of the Saratov State District Power Station), at the amplifier output the voltage with a frequency of 50 Hz exceeds the voltage with a frequency of 25 Hz by a factor of 10, whereas the ratio of the currents at the amplifier input is 500. Further extraction of the signal can already be accomplished by any technical means.

It is known [3] that for normal operation of a parametric amplifier it is necessary that the depth of inductance modulation remain constant. It should be noted that the inevitable operating fluctuations of the voltage of the pump-current source lead to an impermissible change in the gain factor or to transition of the amplifier into a generator mode. In the present case, constancy of the modulation depth is achieved by using a special circuit for precise stabilization of the amplifier pump voltage (Fig. 1). The voltage between points \(d\) and \(b\) is stabilized insufficiently. With the selected parameters of the stabilization circuit, a change in the input voltage by 10% causes a change in the voltage \(U_{ab}\) by 2%. Therefore the output voltage is taken from tap \(C\), which is chosen so that the voltage \(U_{ac}\) is less than the voltage \(U_{ab}\) by the unstabilized part of the voltage \(U_{cb}\). In this case precise sta-

stabilization can be obtained when the voltage \(U_{cb}\) is the fifth part of the voltage \(U_{db}\) [4]. The effectiveness of stabilization of the pump voltage can be judged from the curves of the dependence of the voltage on the tuned circuit of the parametric amplifier on the pump voltage (Fig. 3).

To eliminate the influence of temperature fluctuations on the gain of the parametric amplifier, measures are provided that increase the temperature stability of the device.

It is known from [3] that, in implementing the phase-sensitive properties of a parametric amplifier, strict phasing of the pump current and the signal is required. Figure 4 shows the dependences of the voltage on the tuned circuit at pump phases corresponding to maximum and minimum gain. Other conditions being equal, the voltage on the tuned circuit is 6 times greater at the pump phase corresponding to maximum gain than the voltage at the pump phase corresponding to minimum gain. The pump circuit of the parametric amplifier is powered from a line voltage; moreover, from the three line voltages it is necessary to select the one for which the phase angle between the pump current and the signal will be close to optimum. The selected optimum phase of the pump current must remain strictly unchanged during operation.

Conclusions

1. Interference with a frequency of 50 Hz exceeds the signal at the terminals of the generators of the integrated unit, when protection is performed using a superimposed current, by a factor of 500.

2. A satisfactory solution to the problem of extracting a small signal with a frequency of 25 Hz against a background of large interference proved possible thanks to the use of a parametric amplifier.

3. To achieve constancy of the gain of the parametric amplifier, stabilization of the pump current is necessary.

LITERATURE

1. A. M. Fedoseev. Relay Protection. Moscow, GEI, 1961.

2. G. I. Atabekov. Fundamentals of Circuit Theory. “Energiya,” 1969.

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

4. Yu. Kh. Lukes. Circuits Using Semiconductor Diodes. “Energiya,” 1972.