Proceedings of the Tomsk Polytechnic Institute named after S. M. Kirov, awarded the Order of the October Revolution and the Order of the Red Banner of Labor

Vol. 192　　　　　　　　　　　　　　　　　　　　　　　　　　　　1975

CHARACTERISTICS AND STRUCTURE OF OUTPUT-VOLTAGE REGULATION SYSTEMS FOR A CLASS OF STATIC CONVERTERS

S. I. Volkov, I. F. Kalinin

(Presented by the scientific-technical seminar of the Department of Electrical Equipment)

For supplying various low-power alternating-current receivers, semiconductor converters have begun to be used instead of rotating ones. Converters of this type are, as a rule, regulated or stabilized. To evaluate the principal characteristic of alternating-current sources—the accuracy of regulation of the output voltage of static converters—there are no generally accepted methods, since the latter depends on a whole series of factors: the set-point voltage, \(U_z\), the input voltage, \(U_{\mathrm{in}}\), the load current, \(I_{\mathrm{n}}\), the ambient temperature and the elements of the regulator itself, etc. The influence of changes in the setting voltage, input voltage, and load current (voltage) is characterized by the static error of the open-loop regulation system

\[ \Delta U = \left( \frac{\Delta U_z}{U_z} + \frac{\Delta U_{\mathrm{in}}}{U_{\mathrm{in}}} + \frac{\Delta U_{\mathrm{n}}}{U_{\mathrm{n}}} \right)100\%, \]

where \(U_z\), \(U_{\mathrm{in}}\), \(U_{\mathrm{n}}\) are the nominal values of the setting voltage, input voltage, and load voltage, respectively;

\(\Delta U_z\), \(\Delta U_{\mathrm{in}}\), \(\Delta U_{\mathrm{n}}\) are the corresponding changes in the setting voltage and in the input and load voltages.

The principal parameter of stabilized alternating-current power supplies is the stabilization coefficient

\[ K_{\mathrm{s}} = \frac{ \dfrac{\Delta U_{\mathrm{in}}}{U_{\mathrm{in}}} + \dfrac{\Delta U_{\mathrm{n}}(I_{\mathrm{n}})}{U_{\mathrm{n}}} }{ \dfrac{\Delta U_{\mathrm{out}}}{U_{\mathrm{out}}} }, \]

where \(U_{\mathrm{out}}\) and \(\Delta U_{\mathrm{out}}\) are the nominal value and the range of variation of the output voltage.

The stabilization coefficient is a dimensionless quantity that determines how many times smaller the relative change of the output voltage is than the relative disturbance of the action. It should be borne in mind that the stabilization coefficient determines the stability of the output voltage in those cases when the stabilizer circuit does not

possesses inertia. In most stabilizer circuits of static converters there are inertial elements (filters, chokes, transformers). Such stabilizers transmit rapid changes in the supply voltage and other disturbing effects. The properties of such stabilizer circuits can be characterized by the stabilization coefficient only in the case where, under the conditions of variation, they must maintain the average value of the voltage, while surges of the supply voltage and other disturbances are of no substantial importance. For stabilizers of static converters, the concept of the stabilization coefficient also loses its meaning because the latter is so large that the instability of the output voltage does not depend on a number of other factors.

Very important characteristics of regulators of static converters are the dynamic parameters: the time constant ($t_{\mathrm{p}}$), the time for response to a step change ($t_1$), the amount of overshoot ($\sigma$), the dynamic accuracy ($\delta$), and the degree of stability ($\eta$) of the automatic regulation system under stepwise changes in the supply voltage, the load current, and other disturbing effects. Thus, in calculating and studying voltage regulators of static converters, the following must be specified:

nominal output power, $S_{\mathrm{vn}}$;

frequency of the output voltage, $f_{\mathrm{nom.}},\ \mathrm{Hz}$;

nominal value of the output voltage $U_{2N}$ in voltage stabilization, or the range of variation $U_{2\max},\ U_{2\min}$ in voltage regulation;

nominal and limiting values of the primary voltage, $U_{1N},\ U_{1\max},\ U_{1\min}$;

accuracy of maintaining the output voltage, in %, relative to the nominal voltage value;

limiting values of the power factor and load resistance;

permissible distortion factor of the waveform of the output-voltage curve;

quality parameters of the transient process;

ambient temperature.

In addition, it is necessary to take into account the duration of operation of the regulator and the conditions of its cooling.

Output-voltage regulators of static converters can be classified according to various features: by purpose, by operating principle, by the type of controlled quantity, by accuracy and regulation power, by the method of regulation, and by the way in which they act on the converter.

By purpose, one may distinguish regulators for stabilized and regulated static converters. The former are intended for supplying various receivers with stabilized voltage; the latter, for supplying a voltage regulated according to an arbitrary law. In addition, it is necessary to distinguish regulators intended for converters with sinusoidal, rectangular, and stepped output-voltage waveforms; for single-ended, push-pull, and bridge converter circuits of single-phase and $m$-phase design.

By operating principle, output-voltage regulators can be divided into regulation circuits based on deviation, regulation circuits based on disturbance, and combined circuits. Regulators that maintain the nominal level of the output voltage (stabilizers) are divided, according to their operating principle, into parametric, compensating, and combined (compensating-parametric). Pa-

Parametric stabilizers are constructed on the basis of nonlinear or controlled elements; moreover, the circuit by which these elements are connected with linear elements is chosen so that, under a substantial change in the supply voltage and the converter load current, the output voltage remains within permissible limits.

Parametric stabilizers belong to open-loop automatic control systems and are capable of providing only low accuracy of voltage stabilization.

In compensation stabilizers, the voltage at the output is compared with a specified value; as a result, an error signal is produced, which is amplified and acts on the stabilizer’s actuating element. Compensation stabilizers are a closed-loop control system and provide high stabilization accuracy.

According to the type of controlled (stabilized) quantity, one distinguishes regulators that maintain, according to a prescribed law, the average, amplitude, or rms value of the voltage at the converter output.

According to regulation accuracy, regulators may conventionally be divided into: low-accuracy (more than 5%), medium-accuracy (from 3 to 5%), high-accuracy (from 1 to 3%), and precision (less than 1%).

According to regulation power, regulators of low, medium, and high power are distinguished.

According to the method of regulation, one distinguishes regulators with amplitude regulation of the converter output voltage, with pulse-width regulation at the fundamental frequency, and with pulse-width regulation at an increased modulation frequency.

In the case of the amplitude method of regulation, a voltage-boosting converter (an active actuating element) or an additional regulating (actuating) element designed for the full load power is used at the input (output) of the converter.

The pulse-width method of regulating the converter output voltage is implemented by means of a special construction of the control circuit for the output stage. The essence of this method consists in changing the duration of the pause between voltage pulses at the load.

According to the method of connecting the actuating element, regulators are distinguished that act on the output, the input, and the starting circuits of the converters’ power amplifier. The first group includes the circuits of amplitude regulators whose actuating elements are various kinds of saturable reactors, transformers, and autotransformers.

Figure 1 shows examples of connecting the actuating elements of regulators that act on the output circuits of converters. The simplest of these is the inclusion, in the line between the input and output of the regulator, of an active controlled resistance (Fig. 1, a). The voltage drop across this resistance is automatically regulated by means of a control signal. Sometimes the regulated resistance is connected into the line through a matching transformer \(T_p\) (Fig. 1, b), which simultaneously also serves as an isolating transformer. Powerful transistors, thyristors, and dc-controlled reactors are used as the regulated resistance.

Figure 1, d shows a circuit for connecting, at the converter output, a voltage-boosting transformer VDTR, the voltage on whose secondary winding is added to (or subtracted from) the converter output voltage.

Widely used circuits of regulators acting on the output circuits of the converter are constructed according to the elementary circuit of Fig. 2, a.

Voltage regulators acting on the supply circuits of the converter are constructed according to the circuit of Fig. 2, b. A powerful transistor operating in the switch mode and controlled by a pulse-width modulator is inserted into the supply circuit of the static converter. The magnitude of the pulsations of the regulated supply voltage depends on the load current and the duty factor. In this case the average supply voltage of the converter is determined by the expression [1]

\[ U_{\mathrm{psr}} = U_p \frac{t_{\mathrm{v}}}{t_{\mathrm{v}} + t_{\mathrm{p}}}, \]

where \(t_{\mathrm{v}}\) is the time of the switch’s on state,
\(t_{\mathrm{p}}\) is the pause time.

Fig. 1. Connection circuits of the actuating elements of regulators acting on the output circuits of the converter.

In the circuit of Fig. 2, c, the regulator adds a voltage boost to the supply voltage of the main source. The supply voltage of the static converter is composed of the input voltage and the voltage-boost component

\[ U_n = U'_n \pm U_{\mathrm{in}}. \]

In Fig. 2, d, the voltage-boost converter is the load of the amplifier, whose pulse duty factor, and consequently the magnitude of the filtered voltage supplying the voltage-boost converter, depend on the signal of the regulator’s setting element. The transistors

Fig. 2. Elementary circuits of automatic control systems for the output voltage of converters: ZG — setting generator; GTN — triangular-voltage generator; GSN — sinusoidal-voltage generator; SP — static converter; IM — pulse modulator; UPT — DC amplifier; UMR — regulator power amplifier; IP — power supply; OP — main converter; VDP — voltage-boost converter; F — filter; I — inverter; FSU — phase-shifting device; \(Z_y\) — controlled reactive impedance.

of the voltage-boost converter are controlled by a rectangular voltage \(U_y\) taken from the additional windings of the transformer of the main converter.

When the voltage is regulated by means of a voltage-boost converter, the output windings of the transformer of the additional converter are connected in series with the output windings of the transformer of the main converter; as a result, the output voltages of the main and additional converters are added,

\[ U_2 = U'_n + U''_n. \]

According to the elementary circuit of Fig. 2, e, voltage regulators with phase-pulse modulation are constructed. In this case the output voltage of the converter \(U_2\) depends on the phase shift of the voltages SP1 and SP2,

\[ U_{2\mathrm{avg}} = \frac{\pi - (\varphi_1 - \varphi_2)}{\pi}\, U_m, \]

where \(\varphi = \varphi_1 - \varphi_2\) is the phase-shift angle of the regulated signal.

The actuator in such control systems is the converter output transformer or a controlled inverter. Simple and reliable regulator circuits that act on the converter output circuits have substantial disadvantages: 1) the great weight and, consequently, significant losses in the steel and copper of the actuator; 2) the difficulty of voltage regulation under small and unbalanced loads; 3) distortion of the output-voltage waveform when the magnetic element is saturated.

Regulator circuits that act on the converter input produce significant pulsations on the side of the power-supply source. When filters are installed on the supply side, the dimensions and weight of the regulator increase. Regulators based on a buck–boost converter are distinguished by large dimensions and weight in comparison with a single regulated converter designed for the full load power.

It should also be noted that the depth of voltage regulation in circuits with various kinds of saturable reactors and transformers is directly dependent on the weight and dimensions of these actuators. The circuit of a phase-pulse regulator has somewhat better characteristics. Such a circuit is considerably simplified when an inverter with feedback is used.

At present, pulse-width and pulse-width-modulation methods for regulating the output voltage of converters are being successfully developed. In these methods, the regulating action is applied through the triggering circuits of the converter power amplifier. The essence of the pulse-width method is regulation of the pulse duration over a half-period.

However, deep voltage regulation by phase and width methods is irrational, since the output voltage contains a significant percentage of harmonics. The use of filters for suppressing harmonic components under deep regulation complicates the converter, increases its weight, and substantially reduces the efficiency of the system.

For a small range of voltage regulation, and also for stabilization of the output voltage, the phase-pulse and width methods of regulation are quite effective: they make it possible to sharply reduce the dimensions and weight of the converter. In addition, the phase-pulse and width methods, when filters are present at the output, make it possible effectively to stabilize the output voltage over a wide range of variation of the supply voltage and the converter load current.

In the pulse-width-modulation method of regulation, the duration of the pause between voltage pulses on the load is varied. This method is based on comparing a symmetrical triangular voltage of the carrier frequency with a reference sinusoidal voltage of the output frequency. As a result, a series of pulses of equal height is formed, whose duration is proportional to the integral of the sinusoid.

Thus, pulse-width modulation of the output voltage according to a sinusoidal law can be carried out with complete elimination of the higher harmonics. This method of action makes it possible to simplify the power section of the converter by combining the functions of conversion and voltage regulation in a single device.

REFERENCES

1. O. I. Khasaev. Transistor Converters of Voltage and Frequency. “Nauka,” Moscow, 1966.

2. Vl. Bunakov and R. G. Gasparov. Semiconductor Voltage and Frequency Regulators for Electrical Machines. “Energiya,” Moscow, 1966.

3. A. M. Bamdas and S. V. Shapiro. Stabilizers with Saturable Transformers. “Energiya,” Moscow, 1965.