EFFECT OF SWITCHING TIME IN PULSED DC CONVERTERS ON THE CHARACTERISTICS OF ELECTRIC DRIVES WITH SERIES-WOUND MOTORS

A. I. Sapozhnikov, V. A. Beglarovich

(Presented by the scientific and technical seminar of the Scientific Research Institute of AEM)

Pulsed methods of regulating the rotational speed of electric motors using thyristor converters are finding wide application in electric drives. At present a large number of circuits of thyristor DC voltage converters are known, used for regulating the rotational speed of electric motors supplied from unregulated DC sources. Such systems are of especially great importance in traction electric drives and installations with storage-battery supply.

Since thyristors have a thyratron-type characteristic, devices for artificial commutation are used in DC voltage converters. According to the type of artificial commutation device, DC converters may be divided into two groups. The first group comprises pulsed converters with instantaneous cessation of the supply of energy to the load, as a result of which the average voltage on the load is uniquely determined by the relative on-time $\gamma$. The second group comprises pulsed converters with a finite commutation time, during which energy from the supply source continues to be delivered to the load. As a consequence of this, the minimum value of the average voltage on the load cannot be less than a certain value determined by the parameters of the artificial commutation device and by the magnitude of the load current.

When calculating artificial electromechanical and mechanical characteristics by the methods described in [2], the average voltage on the motor is assumed to be equal to $\gamma U$, which leads to a discrepancy between experimental and calculated characteristics in the case of converters of the second group. In [1] a method is presented for calculating artificial electromechanical characteristics taking into account the finite switching time in converters with one commutation branch (Fig. 1a), and it is shown that $\gamma_k U$ does not uniquely determine the magnitude of the average voltage on the load. This is explained by the fact that the actual on-time $\gamma$ changes substantially depending on the magnitude of the load current $I$ (Fig. 1b), since the recharge time of the commutating capacitor $C_k$ at constant current under a supply voltage $U$ is equal to [1]

\[ t = \frac{2 U C_k}{I}. \tag{1} \]

Fig. 1.

As a result, the external characteristic of the converter and, accordingly, the electromechanical and mechanical characteristics under pulse supply from converters of the second group turn out to be softer.

In the present work, the influence of a pulse converter of the second group on the change in the rotational speed of motors is investigated in comparison with the supply of the same motors from a pulse converter of the first group; that is, a quantitative assessment is given of the influence of the real commutation time on the electromechanical characteristics of an electric drive with a pulse-width power converter.

The parameters of the forced-commutation device are chosen so that the possibility is retained of blocking (turning off) the power thyristor of the converter when the maximum permissible load current flows through it. In the case of motor supply, the selected converter circuit must commutate the starting current of the motor or, in the presence of current limiting, the stall current. In this case, the commutation device provides the power thyristor with time for restoration of its blocking properties [3]

\[ t_{\mathrm{v\,max}} = K_{\mathrm{z}} t_{\mathrm{v\,pas}} = C_{\mathrm{k}} \frac{U}{\lambda I_{\mathrm{n}}}, \tag{2} \]

where

\[ K_{\mathrm{z}} = (1.2 \div 1.5) \]
is the safety factor with respect to recovery time;

\[ t_{\mathrm{v\,pas}} \]
is the rated recovery time of the blocking properties of the power thyristor;

\[ I_{\mathrm{n}} \]
is the rated motor current;

\[ \lambda \]
is the factor of multiplicity of the maximum current relative to the rated current.

Dividing expression (1) by (2) and dividing both sides of the resulting equality by the duration of the commutation period \(T_{\mathrm{k}}\), we obtain an expression for the relative duration of the additional flow

current through the motor by means of forced-commutation devices in converters of the second group, which depends on the magnitude of the load current,

\[ \Delta \gamma(i)=2K_z \cdot t_{\mathrm{on,passp}}\cdot f_k \frac{\lambda}{i}, \tag{3} \]

where

\[ f_k=\frac{1}{T_k} \]

is the commutation frequency;

\[ i=\frac{I}{I_n} \]

is the relative value of the load current.

In an analogous manner one can investigate other circuit variants of converters of the second group and show that in all cases \(\Delta \gamma(i)>0\).

Taking the above into account, the average value of the voltage on the load of converters of the second group, under the condition that the initial voltage on the commutating capacitor is equal to the supply-source voltage and that the load current is continuous, as a result of which a current of constant magnitude equal to the load current flows through the capacitor, is determined by the expression:

\[ U_{\mathrm{avg}}=[\gamma_y+\Delta \gamma(i)]\cdot U . \tag{4} \]

Let us determine the magnitude of the error introduced by neglecting the additional turn-on duration \(\Delta \gamma(i)\) when calculating the electromechanical characteristics. Following the method of [2] and assuming the source voltage to be equal to the nominal voltage, the motor speed in relative units is determined as

\[ \nu_i=\frac{\alpha\gamma-i\rho_e}{\alpha-i}\nu_e, \tag{5} \]

where

\[ \nu_i=\frac{\omega_i}{\omega_n};\quad \nu_e=\frac{\omega_e}{\omega_n} \]

are the relative values of the motor rotational speed, respectively, on the artificial and natural characteristics;

\[ i=\frac{I}{I_n} \]

is the relative value of the armature-circuit current;

\[ \alpha=\frac{U_n}{I_n R_{\mathrm{dv}}} \]

is the ratio of the nominal supply voltage to the nominal voltage drop in the motor circuit;

\[ \rho_e=\frac{R_e}{R_{\mathrm{dv}}} \]

is the relative value of the resistance of the power circuit of the pulsed DC converter–DC motor system, including the internal resistance of the supply source;

here

\[ R_{\mathrm{dv}} \]

is the resistance of the motor armature circuit;

\[ U_n,\ I_n,\ \omega_n \]

are the nominal motor parameters.

In expression (5) we consider \(\gamma\) to consist of two components

\[ \gamma=\gamma_y+\Delta\gamma(i). \]

Then expression (5), with (6) taken into account, is written as

\[ \nu_i=\nu_0+\Delta\nu= \frac{\alpha\gamma_y-i\rho_e}{\alpha-i}\nu_e+ \frac{\alpha\Delta\gamma(i)}{\alpha-i}\nu_e . \tag{7} \]

The speed deviation will be determined by the second term with \(\Delta \gamma(i)\). Taking, as is done in [2], as the reference characteristic the one obtained with an ideal switch and an ideal power supply, determined by the expression

\[ \nu_{\mathrm{e}}=\frac{\alpha \gamma_{y}-i}{\alpha-i}\,\nu_{e}, \tag{8} \]

the relative speed deviation is determined by dividing the second term of expression (7) by the value of the reference speed according to (8) for the same current value and the same value of \(\nu_{e}\)

\[ \frac{\Delta \nu}{\nu_{\mathrm{e}}} = \frac{\alpha \Delta \gamma(i)}{\alpha \gamma_{y}-i}. \tag{9} \]

To generalize the results of the analysis to pulse converters of the second group with any type of thyristors, expression (9), taking (3) into account, is written as

\[ \frac{\Delta \nu}{A\nu_{\mathrm{e}}} = \frac{2\alpha}{(\alpha \gamma_{y}-i)\cdot i}, \tag{10} \]

where \(A=|K_{z}t_{\mathrm{v\,sat}}f_{k}\cdot \lambda\) is a constant quantity for the selected converter circuit.

Fig. 2.

Figure 2 shows dependences constructed from expression (10), characterizing the deviation of the motor speed from the calculated value under idealization of the converter according to expression (8), and making it possible, from the known quantities \(A\), \(\alpha\), \(i\), \(\gamma_{y}\), to determine \(\dfrac{\Delta \nu}{\nu_{\mathrm{e}}}\). Figure 3 shows dependences of the motor speed deviation from the calculated value at load current \(i=0.5\) and supply from a pulse-width converter of the second group (of the type in Fig. 1, a) with the indicated parameters, which determine the value of the constant coefficient \(A=0.042\). The curves of Fig. 3 were obtained from the curves of Fig. 2 by multiplying the ordinate \(\dfrac{\Delta \nu}{A\nu_{\mathrm{e}}}\) for the specified values of \(\gamma_{y}\), \(\alpha\), and \(i\) by the constant coefficient \(A\). For examp-

Fig. 3.

For example, the ordinate of point B in Fig. 3 is equal to
\(\dfrac{\Delta \nu}{A\nu_{\mathrm{e}}}\cdot A = 23 \cdot 0.042 = 0.965\) for
\(\alpha = 4\), \(i = 0.5\), and \(\gamma_y = 0.3\).

From the curves in Figs. 2 and 3 it is evident that neglecting \(\Delta \gamma(i)\) leads to a considerable error in determining the motor speed, especially in the region of small values of the motor load current and small \(\gamma_y\). Thus, at a load current \(i = 0.5\) and \(\gamma_y = 0.3\) (Fig. 3), depending on \(\alpha\), the error in determining the speed under the idealized conditions (8) ranges from 0.6 to 0.95; that is, the actual speed of a motor supplied by a thyristor converter of the second group will be 1.6–1.95 times higher than that calculated by the method of [2] without taking into account the finite commutation time.

Analogous dependences of the speed deviation can also be obtained for the case of motor supply from a frequency-pulse converter [4], in which it is also possible to distinguish a constant component of the voltage-pulse duration and a variable component dependent on the load current and determined by expression (3).

Thus, in order to avoid large errors when calculating the electromechanical and mechanical characteristics of series-wound motors according to (2), supplied from thyristor pulse converters of the second group, it is necessary to take into account the finite commutation time.

REFERENCES

1. B. P. Petrov. External and electromechanical characteristics of a DC traction motor under pulse control. Elektrichestvo, 1971, No. 1.

2. A. I. Sapozhnikov, V. A. Beinarovich, A. I. Alifirov. Electromechanical and mechanical characteristics of a series-wound motor supplied from a TPC. Article in the present collection.

3. M. I. Kraitsberg and E. V. Shikut. Pulse methods for regulating DC circuits using thyristors. Moscow, “Energiya,” 1969.

4. V. E. Rosenfeld, V. V. Shevchenko, V. A. Maiboga, G. P. Dolaberidze. Thyristor control of electric DC rolling stock. Moscow, “Transport,” 1970.