FREQUENCY CONTROL OF THE VOLTAGE OF A SYNCHRONOUS GENERATOR

A. D. Mitaenko

(Presented by the Scientific and Technical Seminar of the Research Institute of Nuclear Physics at TPI)

In direct-current electric trains, on sea and river vessels, in aircraft, and also in mobile electric power stations, electromechanical converter units are widely used to supply alternating-current consumers. Such converter units usually contain a three-phase synchronous generator and a separately excited direct-current driving motor. The frequency of the output voltage of the synchronous generator is usually taken as 50 or 400 hertz.

The operating conditions of such converters may be rather severe. This applies especially to electric trains, where the converter unit operates under conditions of constant shaking and vibration, a wide temperature range from \(-40^\circ\text{C}\) to \(+60^\circ\text{C}\), and sharp fluctuations in the voltage of the contact network and in the load. The driving motor of the synchronous generator on electric trains is usually high-voltage and receives power directly from the contact network. The load of the synchronous generator may consist of asynchronous motors of air compressors and fans, control and lighting circuits, battery-charging circuits, and supply circuits for elements of the automatic-control system. At the same time, the load may be unbalanced and of various kinds.

During operation of a synchronous generator, the frequency of its output voltage may vary considerably, mainly with fluctuations in the supply voltage of the driving motor and changes in the generator load from no-load to nominal. A change in the frequency of the output voltage has a harmful effect on the operation of consumers. In particular, the operating regime of asynchronous motors changes sharply, accompanied by changes in rotational speed, motor torque, and power factor. Fluctuations in voltage frequency also affect the operation of magnetic elements of automation. Operating practice shows that a decrease in voltage frequency leads to a noticeable increase in reactive-power consumption [1]; thus, when the frequency is reduced by only 1%, the reactive power of an asynchronous motor and a transformer increases by 2%.

From the foregoing follows the need to stabilize the frequency of the output voltage of electromechanical converter units. At the same time, difficulties arise in designing a frequency sensor, which is a necessary element of an automatic-control system. There are several methods of measuring frequency [2].

1. Methods using passive tuned systems [3]. The elements of such systems are inductances, capacitances, and their combinations. The best-known sensor designs use reso-

L-C circuits. The schematic diagram and characteristic of such a sensor are shown in Fig. 1.

The output quantity of such sensors is current; therefore magnetic amplifiers are usually used as the power amplifier. The use of thyristor amplifiers is difficult. The absolute value of the current \(I\) is determined by the active and reactive resistance of the circuit. For reasons of sensitivity and operability, the operating point is kept away from resonance, which causes an increase in the reactive resistance of the circuit and limits the output power. The accuracy of such circuits does not exceed 2%, and during operation adjustment of the circuit is required. Somewhat better characteristics are obtained with bridge phase-sensitive circuits, but they are more complex. In addition, the circuits considered operate poorly in the presence of higher harmonics in the voltage.

Fig. 1

1. The method of charging—discharging a capacitor is based on monitoring the deviation of the voltage across the capacitor with a change in frequency from the voltage at the nominal frequency. This method is simple, but does not provide high accuracy. For stable operation of the sensor, its temperature stabilization is necessary.

2. The method of comparing the measured frequency with a reference frequency. This method gives high measurement accuracy, but requires bulky equipment unsuitable for operation in nonstationary installations. In this case, automation of the measurement and control process is also difficult.

3. Discrete methods of frequency measurement [2, 4]. Two methods of frequency measurement may be distinguished. The first is based on counting the number of periods of the measured signal over a certain fixed, reference interval of time. However, when measuring a low frequency, the interval of reference time becomes inadmissibly large from the standpoint of sensor response speed and the provision of high accuracy.

The second method is based on counting the number of periods of the reference frequency during one or several periods of the measured frequency.

Discrete methods provide high measurement accuracy, on the order of \(\pm 0.1\), but the apparatus is thereby excessively complicated, which affects the reliability of the control system. This circumstance limits the field of application of discrete methods of frequency measurement. These methods are suitable for monitoring and, to a lesser degree, for purposes of frequency regulation of the voltage of electrical machines.

1. For measuring and regulating frequency, electronic methods for measuring small time intervals can be successfully applied. The use of this method makes it possible to employ power thyristor amplifiers for frequency regulation; their practical inertia-free operation is one of the most important conditions for obtaining high-quality transient processes.

For regulating and stabilizing the frequency of the output voltage of electrical machines, it is not necessary to know the value of the frequency; one can measure and regulate the duration of the period of the sinusoidal voltage, or measure only part of this period.

A method is described below for controlling the voltage frequency of a synchronous generator, based on measuring part of the period of the output voltage. This method is used in the automatic control system for the voltage frequency of a synchronous generator. The essence of the method is explained with the aid of Fig. 2.

The voltage period \(T\) is divided into two intervals: a constant interval, independent of the period \(T\), of duration \(t_0\), and an interval \(t_1=f(T)\) that varies with the change in the period \(T\) (frequency). In the first interval \(t_0\), by means of an integrating device, a linearly varying voltage \(U_2\) is formed. When the voltage \(U_2\) reaches a certain constant level, the integrating device is switched off and, simultaneously, a second integrator is switched on, in which the linear part of the voltage \(U_6\) is formed; its amplitude is proportional to the time interval \(t_1\), i.e., it depends on the frequency (period) of the alternating voltage. At the end of the period \(T\), the second integrator is switched off. In contrast to the first integrator, the decay of the voltage \(U_6\) does not occur instantaneously, but with a certain time constant. The instant at which the falling portion of the voltage \(U_6\) is compared with the reference level \(U_э\) is recorded and used to control the power amplifier. When the period \(T\) increases, the recorded instant shifts to the right; when it decreases, it shifts to the left.

Since the voltage frequency of a synchronous generator is uniquely determined by the rotational speed of the driving motor,

\[ \omega=\frac{2\pi f}{p}, \]

where \(p\) is the number of pole pairs of the generator stator winding, frequency regulation can be accomplished only by regulating the speed of the d.c. driving motor. In the case under consideration, regulation of the speed of the driving motor is carried out through the excitation-winding circuit. This method is simpler, since regulation is performed in a low-power circuit, and it is especially convenient for regulating high-voltage motors. The excitation winding can be supplied either from a controlled three-phase rectifier or from a thyristor d.c. amplifier supplied by rectified voltage and operating in switching mode. In the first case, the voltage on the excitation winding \(U_{\mathrm{в}}\) varies depending on the control angle of the bridge valves and is determined by the expression:

\[ U_{\mathrm{в}}=U_{\mathrm{в}0}\cdot\frac{1+\cos\alpha}{2}, \]

where \(U_{\mathrm{в}0}\) is the maximum rectified voltage at control angle \(\alpha=0\).

When the excitation winding is supplied from a thyristor switch, the voltage on the excitation winding is determined by the relative duration of the on-state of the regulating thyristor

\[ U_{\mathrm{в}}=U_{\mathrm{н}}\cdot\frac{t_{\mathrm{в}}}{T}, \]

where \(U_{\mathrm{н}}\) is the constant voltage at the input of the thyristor switch;
\(t_{\mathrm{в}}\) is the on-state time of the regulating thyristor;
\(T\) is the voltage period of the synchronous generator.

The instant at which the bridge valves are switched on (or the control angle \(\alpha\)) when the excitation winding is supplied from the controlled rectifier, as well as the instant at which the regulating thyristor is switched on when the excitation winding is supplied from the thyristor switch, vary depending on the generator voltage frequency and are determined by the instant at which the falling part of the voltage \(U_6\) is compared with the reference voltage \(U_э\) (Fig. 2). The regulating thyristor is switched off at the end of each voltage period of the generator.

Stabilization of the generator voltage frequency is carried out as follows. When the frequency decreases (increases), the ...

the period \(T\) of the generator voltage increases (decreases), and the instant of comparison of the voltages \(U_{6}\) and \(U_{\mathrm{e}}\) is shifted to the right (left), which is equivalent to an increase (decrease) in the control angle \(\alpha\) or to a decrease (increase) in the on-state time of the regulating thyristor. In this case the voltage on the field winding decreases (increases), while the speed of the drive motor and the frequency of the synchronous generator increase (decrease).

Figure 3,a shows a block diagram of the frequency measuring element, and Fig. 3,b its basic electrical circuit. The operation of the measuring element is explained by the timing diagrams shown in Fig. 2.

The voltage \(U_{\mathrm{sg}}\) of the synchronous generator is converted, through step-down transformer 1 and diode 2, into unipolar rectangular pulses \(U_{1}\), whose duration is equal to half the period \(T\). This conversion is performed by the shaper \(F\) (transistors 3 and 4). The differentiated trailing edge of the voltage pulses \(U_{1}\) flips the static trigger \(Tr\) into one of its stable states. The left arm of the trigger (transistor 11) controls the operation of the first integrator \(I_{1}\) (capacitor 7),

Fig. 2.

while the right arm of the trigger (transistor 12) controls the operation of integrator \(I_{2}\) (capacitor 18). When there is no negative potential \(U_{4}\) at the collector of transistor 11, transistor 8 is cut off and capacitor 7 is charged during the time \(t_{0}\) through resistor 5 from the stabilized source \(-E\). For given parameters of integrator \(I_{1}\), the duration \(t_{0}\) is constant, does not depend on the period \(T\) of the voltage \(U_{\mathrm{sg}}\), and is determined only by the value of the reference voltage \(U_{\mathrm{e}1}\), set by potentiometer 6. At the instant of comparison of the voltages \(U_{2}\) and \(U_{\mathrm{e}1}\) at comparator \(K_{1}\) (tran-

Fig. 3.

transistor 10 and pulse transformer 9), a pulse \(U_3\) is formed on the output winding of the pulse transformer, flipping the trigger into its second stable state. Transistor 11 closes, and the negative potential \(U_4\) at its collector opens the discharge transistor 8. Capacitor 7 discharges practically instantaneously. At the same time transistor 16 of integrator \(I_2\) closes, and capacitor 18 begins to charge from the source \(E\) through resistor 13 and diode 15. The amplitude \(U_b\) of the volta-

the voltage on capacitor 18 depends on the period \(T\) and is determined by the time interval \(t_1\). At the end of the period \(T\), trigger \(Tr\) is reset to its initial state; at the same time the charging of capacitor 7 begins, transistor 16 opens, and capacitor 18 discharges with a certain time constant through diode 17 and resistor 19. The instant at which the voltages \(U_{\mathrm{b}}\) and the reference voltage \(U_{\mathrm{e}}\), set by potentiometer 14, are compared is fixed by comparator \(K_2\) (transistor 21 and pulse transformer 20), the pulses \(U_7\) from whose output winding are applied to open the regulating thyristor in the field-winding circuit of the drive motor of the synchronous generator. Thereafter the processes in the frequency-measuring element are repeated.

To determine the static characteristics of the frequency-measuring element, let us consider the processes that occur during operation of the second integrator. In deriving the basic equations, the following assumptions are adopted:

1) the semiconductor diodes are ideal;
2) discharge transistor 16 is considered as an ideal switch;
3) the resistance of the winding of the pulse transformer is neglected.

The equivalent circuit is shown in Fig. 4.

Fig. 4.

Here the following are denoted (see Fig. 3, b):

\(r_1, r_2\) — resistors 13 and 19, respectively,

\(d_1, d_2\) — diodes 15 and 17, respectively,

\(C\) — capacitor 18.

Transistor 16 is represented by a switch.

During the time interval \(t_1\) the switch is open and the capacitor is charged with the time constant

\[ \tau_1=\frac{r_1\cdot r_2}{r_1+r_2}\,C . \]

Taking into account the initial condition for the quasi-steady process \(U_c(0)=U_{\mathrm{e}}\), after time \(t_1\) the voltage on the capacitor will be determined by the expression

\[ U_c(t_1)=\beta E\cdot\left[1-\exp\left(-\frac{t_1}{\tau_1}\right)\right] +U_{\mathrm{e}}\cdot\exp\left(-\frac{t_1}{\tau_1}\right), \]

where

\[ \beta=\frac{r_2}{r_1+r_2}. \]

During the time \(t_0\) the switch is closed, and the capacitor discharges through resistor \(r_2\) with the time constant \(\tau_2=r_2\cdot C\). The discharge of the capacitor ceases when the voltage on the capacitor reaches the value \(U_{\mathrm{e}}\), since it is then blocked by diode \(D_2\). The discharge time \(t_2\) is determined from the condition

\[ U_c\cdot \exp\left(-\frac{t_2}{\tau_2}\right)=U_{\mathrm{e}} . \tag{2} \]

Taking (1) into account and representing the exponential function by a Taylor series, from expression (2) we determine \(t_2\):

\[ t_2=\frac{\tau_2}{\tau_2+t_1} \left(\frac{\beta E}{U_{\mathrm{e}}}-1\right)t_1 . \tag{3} \]

In increments, equality (3) will have the form:

\[ \Delta t_2=\frac{k t_2\cdot t_1}{(\tau_1+t_1)^2}\cdot\left(\frac{\beta E}{U_{\mathrm{э}}}-1\right)\cdot\Delta t_1 . \tag{4} \]

The coefficient appearing on the right-hand side of (4) characterizes the gain of the measuring element and its sensitivity. An increase in the gain and in the accuracy of regulation, while preserving the regulation zone, is achieved by: 1) reducing the duration of the time interval \(t_1\) and the magnitude of the reference voltage \(U_{\mathrm{э}}\);

2) increasing the charging current of the capacitor \(i_{\mathrm{э}}=\dfrac{E}{r_1}\) and the discharge resistance \(r_2\).

In the experimental installation the following voltage values were adopted: \(U_{\mathrm{э}}=1.5\) V, \(E=40\) V. The accuracy of frequency maintenance in this case was of the order of 1%.

The proposed method of frequency control is simple to implement and can be used in automatic-control systems for electrical machines.

REFERENCES

1. L. V. Litvak. Rational Compensation of Reactive Loads. Gosenergoizdat, 1963.

2. A. S. Kasatkin. Automatic Processing of Signals from Frequency Sensors. “Energiya,” 1966.

3. V. L. Bunakov and R. G. Gasparov. Semiconductor Voltage and Frequency Regulators. “Energiya,” 1966.

4. G. Z. Botorod and V. A. Kiblitskii. Digital Regulators and Speed Meters. “Energiya,” 1966.