Proceedings of the Tomsk Order of the Red Banner of Labor Polytechnic Institute named after S. M. Kirov

Vol. 153　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1965

AC CONVERTER WITH TIME-PULSE MODULATION

A. I. ZAITSEV, M. A. ZHITKOV, A. I. SAPOZHNIKOV

(Recommended by the scientific seminar of the Electromechanical Faculty)

Systems based on the use of the frequency method of regulation are the most advanced systems for automated AC electric drives. One of the principal questions in creating such systems is the choice of the type of device for frequency conversion, as well as the choice and calculation of the voltage-regulation system.

At present, various kinds of electric-machine frequency converters, ionic and semiconductor frequency converters are used as devices for frequency conversion; the extent of their application is determined by the combination of properties inherent in a given frequency converter. Thus [1], systems of electric-machine frequency converters, which make it possible to obtain a sinusoidal voltage with a smoothly varying frequency in the ranges 0–50 Hz and 20–100 Hz, have substantial disadvantages:

1. A large number of electrical machines. The installed power reaches 2–5 times the power of the actuating motor.
2. Low efficiency—0.5–0.7.
3. Difficulty of commutation.

Static ionic and semiconductor frequency converters are practically inertialess and have a high efficiency—0.85. However, a number of disadvantages—the large number of ionic and semiconductor devices, the complexity of the control circuits, and the difficulty of obtaining low frequencies—limit the wide application of such frequency converters. In addition, at the output of ionic and semiconductor frequency converters there are voltages and currents of nonsinusoidal form.

A comparison of the technical characteristics of various frequency converters makes it possible to conclude that eliminating the disadvantages inherent in semiconductor frequency converters, even with a sufficiently complex control circuit, makes them the most promising.

In the present work, the possibility is investigated of obtaining, from a semiconductor frequency converter, a sinusoidal form of output voltage and current in the frequency range 0–200 Hz.

In the technique of continuous-discrete conversion [2], the process of representing a continuous signal \(x(t)\) is carried out by its quantiza-

by level and time. Quantization by level and time is a process in which a continuously varying quantity is replaced by discrete levels, nearest to the values of the continuous quantity at discrete instants of time.

The process of representing a continuous signal \(x=\sin \omega t\) by a quantized signal \(x_k(t)\) with a constant quantization step is shown in Fig. 1.

Fig. 1.

Here \(h_x\) and \(h_t\) are, respectively, the quantization steps by level and by time. It is seen from Fig. 1 that the quantized signal \(x_k(t)\) is the sum of the quantization areas, which for a symmetric signal may be written as

\[ x_k(t)=2nh_xh_t+\sum_{i=1}^{n-1}2s_{ikv}, \tag{1} \]

where \(s_{ikv}=ih_xh_t\) is the area corresponding to the \(i\)-th quantization step by level;

\(n\) is the number of quantization steps by level.

However, the area corresponding to the first quantization step in time over the interval \(t_1-t_0\), equal to \(s_{1kv}=h_xh_t\), can be obtained in a shorter time \(t_i=t'_1-t_0\), at the quantization level \(k=nh_x\). Similar conclusions may be drawn for any numbered quantization step in time. Then the quantized signal \(x_k(t)\) may be represented by the set of pulses shown in Fig. 2, from which it is evident that quantization by level is in this case replaced by quantization according to the relative duration of the pulse within each time-quantization step.

Fig. 2.

Equating the areas \(s_{\mathrm{kv}}\) and \(s'_{\mathrm{kv}}\), we find the pulse duration at each quantization step.

\[ \begin{aligned} s_{\mathrm{kv}1} &= s'_{\mathrm{kv}1} & h_x h_t &= n h_x \cdot t_{u1} \\ s_{\mathrm{kv}2} &= s'_{\mathrm{kv}2} & 2h_x h_t &= n h_x \cdot t_{u2} \\ &\cdots & &\cdots \\ s_{\mathrm{kv}n} &= s'_{\mathrm{kv}n} & n h_x h_t &= n h_x \cdot t_{un} \\ s_{\mathrm{kv}(n+1)} &= s'_{\mathrm{kv}(n-1)} & (n+1)h_x h_t &= (n-1)h_x \cdot t_{u(n+1)} \end{aligned} \]

Hence:

\[ t_{u1}=\frac{h_t}{n}; \qquad t_{u2}=\frac{2h_t}{n}\ .\ .\ .\ .\ .,\qquad t_{un}=\frac{nh_t}{n}; \qquad t_{u(n+1)}=\frac{(n-1)h_t}{n}. \]

Denoting the relative pulse duration by “\(\tau\),” one may write:

\[ \tau=\frac{t_u}{h_t}, \]

where:

\[ \tau_1=\frac{1}{n};\quad \tau_2=\frac{2}{n}\ .\ .\ .\ .\ .,\quad \tau_n=1;\quad \tau_{n+1}=\frac{n-1}{n}; \]

Thus, the continuous input signal \(x=\sin \omega t\) is converted into a sequence of pulses whose duty factor varies in accordance with the variation of the input signal. If the resulting pulse sequence is applied to a load whose electrical time constant is greater than the time-quantization step, then a current will flow in the circuit that repeats the form of the input signal. A device forming pulses of variable duty factor can be constructed as a scanning system implementing time-pulse modulation (TPM).

The sweep conversion in the present case is described by the following operational scheme:

\[ \begin{gathered} s(t)=ct\\ \downarrow\\ x(t)\longrightarrow H\longrightarrow i(t), \end{gathered} \]

where \(x(t)\) is a continuous sine function to be converted,

\(s(t)=ct\) is a cyclic sweep function,

\[ c=\frac{ds}{dt} \]

is the derivative of the function \(s(t)\) with respect to time,

\(H\) is a comparison circuit,

\(i(t)\) is a pulse function representing the result of the conversion as a sequence of discrete samples “\(x\)” on the time scale.

According to this operational scheme, a converter of direct voltage into alternating voltage was developed at the Department of EPPT.

The functional diagram of one phase of the converter is shown in Fig. 3.

Fig. 3.

A continuous reference input signal of sinusoidal form and of the required frequency is supplied from the setting generator ZG to one of the inputs of the comparison circuit. To the other input of the comparison circuit are applied the pulses of the sawtooth-voltage generator GPN, which is the main synchronizing element of the circuit and sets the quantization step in time.

At the trailing edge of the “sawtooth” pulse, control pulses \(UI_1\) are generated, which determine the beginning of the time interval proportional to the reference voltage.

At the instant when the instantaneous values of the “sawtooth” voltage and of the reference voltage coincide, the comparison circuit generates a pulse \(UI_2\), which determines the end of the time interval.

The relative duration of the formed time interval in each quantization step will be equal to the value of the sine of the angle corresponding to the instant of coincidence. This regularity can be verified by a simple construction. The half-wave switching block-

of the VPK, is a sign device and forms “gate” pulses whose duration is equal to a half-period of the input voltage. During each “gate” pulse, the control pulses UI\(_1\) are applied to the flip-flop that commutates that half of the power stage which forms the current half-wave of the reference voltage.

The negative half-wave is inverted. This makes it possible to form both half-waves of the sinusoidal voltage using a single comparison circuit.

The power stage of the converter is constructed analogously to conventional inverters according to a single-phase circuit. Circuit solutions for the individual elements are considered below.

The source of the sawtooth voltage is a sawtooth-voltage generator with a simple integrating circuit, Fig. 4. The amplitude of the sawtooth voltage is determined by the potential of point “b.” When capacitance \(C\) is being charged, at the moment when the potentials of points “a” and “b” become equal, the amplitude comparator assembled on thyratron PP\(_2\) operates, starting two switches PP\(_1\), PP\(_3\).

Fig. 4.

The switch on thyratron PP\(_1\) provides discharge of the integrating capacitance. Control pulses UI\(_1\) are taken from the collector of thyratron PP\(_3\).

The principal advantage of this circuit is its simplicity, the short recovery time, and the possibility of separate regulation of the amplitude and frequency of the “sawtooth.”

The comparison circuit is a diode-regenerative comparator [3], to the inputs of which sawtooth and sinusoidal voltages are applied. The natural oscillation frequency of the comparator must be higher than the switching frequency, i.e., the sawtooth frequency.

This ensures reliable operation of the null organ over a wide temperature range.

The schematic diagram of the half-wave switching unit is shown in Fig. 5. The sign of the half-wave of the sinusoidal voltage is monitored by a blocking oscillator assembled on thyratron PP\(_1\). During the negati-

…half-wave blocking oscillator operates in a self-oscillating mode at a frequency of 25–50 kHz and starts triode \(PP_2\), at whose collector an envelope signal is obtained with a time constant of the collector load \(C_3 R_6\) greater than the period of the starting pulses. From the collectors of triodes \(PP_3\) and \(PP_4\), “gate” pulses are taken, their phase shifted by \(180^\circ\), and their duration equal to the half-period of the sinusoidal voltage.

Fig. 5.
(Schematic labels visible in the figure include: Output 1, Output 2, \(-12\text{ V}\), \(0\), \(+4\text{ V}\), \(UI_1\).)

Coincidence circuits assembled on diodes \(D_3, D_4\) and \(D_5, D_6\) ensure the passage of \(UI_1\) pulses to that output where a negative “gate” pulse is present.

Thus, the converter circuit is built using identical elements and devices operating in switching mode, which increases the reliability of the circuit and simplifies its adjustment.

An advantage of the proposed converter is the production of pulses whose duty factor varies from 0 to 1 during each half-wave. This makes it possible to regulate the depth of modulation in

Fig. 6.

within a range that provides a change in the amplitude of the output voltage by 50% while preserving a waveform close to sinusoidal. This circuit is universal in the sense that it makes it possible to regulate separately the frequency and the amplitude of the output voltage. Any generator of sinusoidal oscillations based on semiconductor devices, ensuring amplitude constancy in the specified frequency range, may be used as the reference device.

Using a low-power three-phase collector generator as the reference device, it is possible to construct a three-phase converter with time-pulse modulation, providing a sinusoidal form of current and voltage.

Fig. 6 presents oscillograms of the output current and voltage of a single-phase converter operating with a two-phase asynchronous motor.

REFERENCES

1. M. Z. Khamudkhanov. Frequency control of an asynchronous electric drive. Publishing House of the Academy of Sciences of the Uzbek SSR, 1959.

2. E. A. Drozdov, A. P. Pyatibratov. Automatic conversion and coding of information. Sov. Radio Publishing House, Moscow, 1964.

3. A. M. Tishchenko, B. M. Lebedev. Calculation and design of transistor pulse devices. Sov. Radio Publishing House, Moscow, 1964.