PROCEEDINGS
OF THE TOMSK ORDER OF THE RED BANNER OF LABOR
POLYTECHNIC INSTITUTE named after S. M. KIROV

Vol. 161　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1967

A THYRISTOR PULSE SYSTEM FOR EXCITATION OF DIRECT-CURRENT GENERATORS

S. A. KITAEVA

(Recommended by the scientific seminar of the Electromechanical Faculty)

Pulse systems for regulating the voltage of direct-current generators have recently begun to attract attention because of their rapid response and high accuracy.

The appearance of industrial series of controlled semiconductor valves—thyristors—and their use for supplying the excitation windings of electric machines opens up new possibilities for the application of pulse technology [1].

A feature of thyristor control is the necessity of using special methods for blocking them. For this purpose, in the control of thyristors, artificial-commutation circuits are used, implemented with the aid of capacitor energy-storage devices. Artificial-commutation circuits may be used when the load is supplied both from a direct-current network and from an alternating-current network [2].

In such pulse systems the excitation winding is supplied with a constant voltage modulated by pulses of increased frequency, determined by the frequency with which the unlocking signal is applied to the control power thyristor.

The pulse method of excitation regulation is especially expedient in view of the considerable inductance of the excitation winding, which gives rise to a large value of the time constant \(T_{\mathrm{в}} = \dfrac{L}{R}\).

Therefore, for any values of the relative duration of thyristor conduction and in the presence of a valve shunting the excitation winding, a continuous-current mode is possible in the latter, owing to the fact that during the pulse the energy stored in the inductance of the excitation winding increases, while during the pause the current is maintained by the energy stored in the electromagnetic field. Such an operating mode has a favorable effect on the energy characteristics of the electric machine, since the effective value of the excitation current differs only slightly from the mean value and, consequently, the heat losses increase only slightly.

The quality of voltage stabilization is determined by the modulation of the output voltage; in this connection, the switching frequency of the thyristor

it is advisable to increase. However, from the standpoint of reducing losses due to eddy currents and reducing the heating of the thyristors, the lower limit of the switching frequency is chosen from the condition of a specified current ripple factor and the relative on-time [3].

Let us consider the processes of current buildup in the field winding of a generator under pulse thyristor regulation. In this case rectangular voltage pulses with amplitude \(U\), repetition period \(T\), and duty factor \(\gamma\) are applied to the generator field winding.

Such a field-current regulation system may be represented in the form of an equivalent circuit, where the control valve is represented by an automatic switch that performs commutation in the main and shunting circuits (Fig. 1).

Fig. 1

The processes of field-current buildup in such a system are considered in the time intervals

\[ nT \leq t \leq T(n+\gamma) \]

and

\[ T(n+\gamma) \leq t \leq T(n+1), \]

where \(n\) is an integer, under the assumption that

1. the inductance and resistance of the field winding are constant;
2. armature reaction is absent;
3. diode \(D\) is ideal;
4. the internal resistance of the power source is neglected;
5. iron losses caused by the pulsating current are negligibly small.

According to [3, 4], the equations for the change of the field current in the form of mixed lattice functions have the form:

\[ i[n_1\varepsilon]=\frac{U}{R}+ \left[ \frac{Ue^{-\beta(1-\gamma)}(1-e^{-\beta\gamma})(1-e^{-\beta n})}{R(1-e^{-\beta})} -\frac{U}{R} \right]e^{-\beta\varepsilon} \]

\[ 0 \leq \varepsilon \leq \gamma. \tag{1} \]

\[ i[n_1\varepsilon]= \left\{ \frac{U}{R}+ \left[ \frac{Ue^{-\beta(1-\gamma)}(1-e^{-\beta\gamma})(1-e^{-\beta n})}{R(1-e^{-\beta})} -\frac{U}{R} \right]e^{-\beta\gamma} \right\}\cdot e^{-\beta(\varepsilon-\gamma)}, \]

\[ \gamma \leq \varepsilon \leq 1. \tag{2} \]

In these equations

\[ \beta=\frac{T}{T_{\mathrm{в}}}; \qquad T_{\mathrm{в}}=\frac{L}{R}, \]

where \(R\) and \(L\) are the active resistance and inductance of the field winding.

From equations (1) and (2), the maximum and minimum steady-state values of the currents can be determined.

\[ i_{\max}=\frac{U(1-e^{-\beta\gamma})}{R(1-e^{-\beta})} \tag{3} \]

\[ i_{\min}=\frac{U(1-e^{-\beta\gamma})e^{-\beta(1-\gamma)}}{R(1-e^{-\beta})}. \tag{4} \]

The current ripple factor, characterizing the ratio of the maximum steady-state current to the minimum steady-state current, is equal to

\[ \chi = e^{\beta(1-\gamma)} . \tag{5} \]

The full amplitude of the current pulsations in the steady-state regime is

\[ \Delta i = i_{\max} - i_{\min} = \frac{U\left(1-e^{-\beta\gamma}\right)\left[1-e^{-\beta(1-\gamma)}\right]} {R\left(1-e^{-\beta}\right)} \tag{6} \]

From the equation obtained it is seen that the amplitude of the current pulsations, for a given value of \(\gamma\), depends only on the parameters of the circuit itself and on the switching frequency of the thyristor.

When the amplitude of the current pulsations is small, the process of establishment of the current in the field winding is characterized by a smooth component.

The equation of the smooth component may be represented in the form [3, 4]

\[ i_{\mathrm{av}}(t)=\frac{U\gamma}{R}\left(1-e^{-\frac{t}{T_{\mathrm{v}}}}\right). \tag{7} \]

When the generator operates on the linear portion of the magnetization curve, the dependence of the emf on the field current is linear; then the equation of the smooth component of the emf, determined by the smooth component of the field current, will have the form

\[ E_{\mathrm{av}}(t)=E_{\mathrm{st}}\left(1-e^{-\frac{t}{T_{\mathrm{v}}}}\right), \tag{8} \]

where

\[ E_{\mathrm{st}}=kU \]

\(k\) is a constant quantity determined by the angle of inclination of the no-load characteristic to the abscissa axis.

In order to reduce current pulsations, as well as oscillations of the generator emf, the commutation frequency of the thyristors, for a given current-pulsation coefficient and relative on-time, is determined as

\[ T=\frac{\ln \chi}{1-\gamma}\,T_{\mathrm{v}}, \tag{9} \]

where \(\chi\) is the current-pulsation coefficient.

Pulse automatic-control systems for the excitation of electric machines using thyristors with artificial current commutation in the power circuit have been developed and are being investigated at the Department of Electric Drive Automation of the Tomsk Polytechnic Institute. The systems have proved to be fast-acting, possessing high tracking accuracy and high quality of regulation.

REFERENCES

1. M. G. Chilikin, I. I. Petrov, B. B. Voronetskii. New directions in the development of automated electric drive. Elektrichestvo, 1965, No. 3.

2. A. I. Zaitsev, V. N. Mishin, A. A. Kuvshinov. Pulse speed control in drives based on the “controlled discrete converter–motor (UDP-D) with artificial commutation” system.
   Means of automation of electric drive. Reports to the IV All-Union Conference on Automatic Drive, VNIIEM, 1964.

3. A. P. Zaitsev. Development and investigation of certain pulse devices for controlling electric machines. Dissertation, TPI, 1964.

4. Ya. Z. Tsypkin. Theory of Linear Pulse Systems. Fizmatgiz, 1963.