Some Issues in the Design of Electric Drives Based on the MUS-D System

M. A. Borovikov
(Presented by the scientific seminar of the Electromechanical Faculty)

At present, domestic industry has mastered series of high-quality power magnetic amplifiers; therefore, the design problem of a drive based on the system “self-saturating magnetic amplifier—DC motor” (MUS-D) no longer includes the design of the magnetic amplifier, as had been assumed somewhat earlier [1]. The design of a drive should now be understood as the selection of ready-made series-produced electrical machines and apparatus and their arrangement in order to ensure the specified technical characteristics.

In each specific case, the structure of the electric drive is determined by the requirements imposed on it with respect to the control range, speed of response, accuracy, etc. Therefore, the selection of certain drive elements, mainly the control elements, has a specific character. But such questions as the selection of the motor and of the magnetic amplifier for supplying it are common in all cases. In addition, extensive practical experience in constructing various automatic-control systems makes it possible to make the task of synthesizing the drive structure concrete.

The aim of the present work is to substantiate a method for selecting the motor and magnetic amplifier when designing the MUS-D system, as well as to solve questions concerning the selection of control elements for a specified drive structure.

Selection of the Motor

A feature of motor operation when it is supplied from magnetic amplifiers according to the circuits of Fig. 1 is the increased heating caused by pulsations of the armature current. If, as is customary in the classical theory of electric drive, it is assumed that heating is determined by the average losses, then the increase in overheating—and consequently also in the motor power when it is selected—can be taken into account by the armature-current form factor

\[ K_{\mathrm{f}a}=\frac{I_{a\mathrm{f}}}{I_a}, \tag{1} \]

where \(I_{a\mathrm{f}}\), \(I_a\) are, respectively, the effective (root-mean-square) and average values of the armature current.

Fig. 1.

The selection of a motor from the heating conditions, when \(K_{f\mathrm{ya}}\) is known, can be carried out in the following order:

1. From the load diagram, the equivalent torque of the motor is determined:

\[ M_{\mathrm{e}}=\sqrt{\frac{\sum M_i^{2} t_i}{\sum \gamma_i t_i}}, \tag{2} \]

where \(M_i\) is the value of the torque that the motor must develop during time \(t_i\) in the regulating cycle;

\(\gamma_i\) is a coefficient taking into account the deterioration of the motor cooling conditions when operating at reduced speeds.

1. From the equivalent torque, the “equivalent” average motor current is found:

\[ I_{\mathrm{ya\,e}}=\frac{M_{\mathrm{e}}}{C_M}. \tag{3} \]

1. The equivalent rms motor current \(I_{\mathrm{ya\,ef}}\), which determines its heating, is found:

\[ I_{\mathrm{ya\,ef}}=K_{f\mathrm{ya}} I_{\mathrm{ya\,e}}. \tag{4} \]

The condition for the correctness of the motor selection is taken to be

\[ I_{\mathrm{ya\,nom}} > K_{f\mathrm{ya}} I_{\mathrm{ya}}. \tag{5} \]

The current form factor \(K_{f\mathrm{ya}}\) is a complex function of the relative motor speed \(v\), the armature-circuit parameter \(\tg \varphi\), and the relative value of the armature current. Expressions for determining it can be obtained only under considerable idealization, as was done in [1]. In real cases the values of \(K_{f\mathrm{ya}}\) vary within comparatively small limits: when the motor is supplied from a single-phase amplifier, \(K_{f\mathrm{ya}}\) in the region of rated loads is, on average, within \(1.25 \div 1.3\) (see Fig. 2); when supplied from a three-phase amplifier, \(K_{f\mathrm{ya}} = 1.01 \div 1.04\) for variations of \(v\) and \(\tg \varphi\) (see Fig. 3). Analogous same

Fig. 2.

Fig. 3.

results are given in works by other authors [2, 3]. Therefore the use of expression (5) presents no difficulty.

As a rule, the procedure indicated above is carried out after a preliminary selection of the motor.

Selection of magnetic amplifiers

In drives with a power of up to 1 kW it is advisable to use single-phase amplifiers, whose advantage is the smaller number of component elements (cores, valves) in comparison with three-phase ones. At powers above 1 kW it is recommended to use three-phase amplifiers, which ensure better utilization of the materials incorporated in them, an increased efficiency, smaller pulsations of the output voltage, uniform loading of all phases of the supply network, etc.

The selection of magnetic amplifiers must be made according to the permissible current of the working windings and according to the voltage of the supply network. Selection by current is made from the following expressions: for a single-phase amplifier

\[ I_{p\text{nom}} \geq \frac{K_{fya} I_{ya\text{nom}}}{\sqrt{2}}, \tag{6} \]

for a three-phase amplifier

\[ I_{p\text{nom}} \geq \frac{K_{fya} I_{ya\text{nom}}}{\sqrt{3}} . \tag{7} \]

Since the data sheets for magnetic amplifiers [4] do not give the currents of the working windings, it is more often necessary to select the MA according to the average load current. The selection condition in both cases will then have the form

\[ I_n \geq I_{ya\text{nom}}, \tag{8} \]

where \(I_n\) is the catalog value of the MA load current.

When condition (8) is fulfilled, there is no danger of overheating of the working windings under motor load, since the catalog data are compiled for operation of the amplifier on an active load, when \(K_{fya}\) has values greater than in the presence of inductance in the load circuit, which is always possessed by the motor armature.

The voltage for which the magnetic amplifier should be selected can be determined on the basis of the equations of the mechanical characteristics of the motor derived in works [5, 6]. For a system with a single-phase amplifier (Fig. 1a) we have:

\[ U_c \geq \frac{\pi \left(c_E n_{\text{nom}} + I_{ya\text{nom}} r_{ya} K_z\right)} {2\sqrt{2}\left[1-\left(\frac{\beta_y}{2\xi}\right)_{\min}\right]} . \tag{9} \]

For a system with a three-phase amplifier (Fig. 1b), the line supply voltage must be determined in accordance with the expression:

\[ U_l \geq \frac{\pi \left(c_E n_{\text{nom}} + I_{ya\text{nom}} r_{ya} K_z\right)} {3\sqrt{2}\left[1-\left(\frac{\beta_y}{2\xi}\right)_{\min}\right]} , \tag{10} \]

where

\[ \beta_y = \frac{\Delta B}{B_s} \]

is the relative increment of induction in the cores during the working or control half-periods;

\[ \xi = \frac{U_m 10^8}{\omega W_p S B_s} \]
is the modulation coefficient of the cores at no load [7].

As analysis of real systems shows, the values \((\beta_y/2\xi)_{\min}\) and \((\beta_y,\xi)_{\min}\) in both cases do not reach values below 0.3 at the nominal value of the current in the control circuit. Substituting 0.3 into these expressions, we obtain:

for a single-phase MU

\[ U_c > 1.58 \left(c_E n_{\mathrm{nom}} + I_{\mathrm{я}} r_{\mathrm{я}} K_z\right), \tag{11} \]

for a three-phase one

\[ U_\ell > 1.05 \left(c_E n_{\mathrm{nom}} + I_{\mathrm{я}} r_{\mathrm{я}} K_z\right). \tag{12} \]

When selenium rectifiers are used for magnetic amplifiers, the voltage value in both cases must be increased by \(1/2\,E_v\). The reserve factor \(K_z\), which accounts for the resistance of the MU working windings, the valves, and the influence of the residual inductance \(L_s\), may be taken approximately equal to 2.5–3.

In those cases where the motor speed is regulated not from 0, but from some value \(n_{\min}\), the voltage for which the amplifier should be selected can be reduced by a factor of \(\xi_{\max}\). For a single-phase amplifier this value [7] is determined from the expression

\[ \xi_{\max} = \frac{1}{ \sqrt{ 1-\left(\frac{c_E n_{\min}}{U_m}\right)^2 -\frac{c_E n_{\min}}{U_m} \left( \frac{\pi}{2} -\arcsin \frac{c_E n_{\min}}{U_m} \right) } }. \tag{13} \]

For a three-phase MU, the value of \(\xi_{\max}\) can be found from the corresponding equation for \(\beta_y\) (see [6]) by substituting into it \(\Delta B = 2B_s\) and \(E = c_E n_{\min}\):

\[ \xi_{\max} = \frac{1}{ 1-\frac{c_E n_{\min}}{U_m}\,\frac{\pi}{3} }. \tag{14} \]

The value of the voltage \(U_m\) in (13) and (14) should, as before, be determined from the corresponding expressions (9) and (10).

Selection of Valves

The selection of the semiconductor valves of the MU rectifier bridge is made according to the average operating current and the maximum reverse voltage. The average current through the valves of a single-phase MU is determined by the expression

\[ I_{\mathrm{av}} \approx \frac{1}{2} I_{\mathrm{я\,nom}}, \tag{15} \]

for a three-phase one

\[ I_{\mathrm{av}} \approx \frac{1}{3} I_{\mathrm{я\,nom}}. \tag{16} \]

The maximum reverse voltage on the valves at full saturation of the amplifier cores is equal to the amplitude value of the line voltage

\[ U_{\mathrm{rev}} = U_m. \tag{17} \]

In real cases complete saturation of the cores cannot be achieved; therefore, in the working windings during the negative half-periods of the supply voltage an emf is always induced, which is subtracted from the reverse voltage on the valve. On the average, the maximum value of the reverse voltage is thereby reduced by 15–20% for iron-silicon amplifiers, i.e.,

\[ U_{vsb} \geq 0.85\,U_m . \tag{18} \]

The choice of the shunting valve \(B_{sh}\), in order to eliminate instability of the drive according to the circuit of Fig. 16 at low speeds [8], is made on the basis of the expression:

\[ I_{v.l.} > I_{a\,nom}\left(\frac{3\alpha_{s\,max}}{\pi}-1\right). \tag{19} \]

The value of the maximum firing angle \(\alpha_{s\,max}\) can be found [8] as a function of the specified values \(\gamma_{min}\) and \(I_{a\,max}\). The reverse voltage on the valve \(B_{sh}\) is equal to the maximum armature voltage

\[ U_{vsh} \geq U_{a\,max}. \tag{20} \]

If the supply voltage of the amplifier has been selected in accordance with (12), then expression (20) may be written as follows:

\[ U_{vsh} \geq 0.8U_m . \tag{21} \]

On the choice of the intermediate amplifier

The need to choose an intermediate amplifier is determined by the requirements that the drive must satisfy with respect to the control range, stiffness of characteristics, and starting properties. These same requirements determine the choice of the system structure. As experience shows, when it is required to provide a control range of up to 50:1, systems without speed feedback may be used, but only with voltage and current feedbacks (for example, according to the circuit of Fig. 4). As the intermediate amplifier it is also very convenient to choose a magnetic amplifier \(MU_2\); the use of an intermediate magnetic amplifier does not lead to any great complication of the system or to a noticeable decrease in its reliability, does not cause special difficulties in matching it with the input of the power amplifier \(MU_1\), and, moreover, makes it possible to sum a large number of control signals.

The choice of the intermediate amplifier for the circuit of Fig. 4 may be made by means of the equation of the mechanical characteristic derived for the linearized system [9].

Let the specified value of the steepness of the motor characteristic be \(s\):

\[ s=\frac{\Delta n}{\Delta I_a}\,\frac{I_{a\,nom}}{n_{nom}} . \tag{22} \]

From the equation of the mechanical characteristic of the motor in the circuit of Fig. 4 (see [9]) we obtain:

\[ s=\left[ R_e-\frac{K_{sb.n}\left(\beta+R_{MU}\right)} {K_{sb.ts}R_y} \right]\frac{1}{R_{nom}-r_a}, \tag{23} \]

where

\[ R_{nom}=\frac{U_{nom}}{I_{a\,nom}} \]

is the rated resistance of the motor;

Figure 4.

\(R_{y2}\) — total resistance of the control circuit of \(MU_2\) in the circuit of Fig. 4;
\(K_{\mathrm{tot}} = K_1 \cdot K_2\) — overall gain coefficient of the drive;
\(K_1\) — gain coefficient of \(MU_1\), V/A;
\(K_2\) — gain coefficient of \(MU_2\);
\(\beta\) — coefficient of positive current feedback.

Expression (23) makes it possible, from known values of \(s\) and \(\beta\), to find the value of \(K_{\mathrm{tot}}\) for any part of the motor speed range:

\[ K_{\mathrm{tot}} = \frac{\left[ R_{\mathrm{e}} - s\left(R_{\mathrm{nom}} - r_{\mathrm{a}}\right)\right] R_{y2}} {\beta - R_{\mathrm{a}} + s\left(R_{\mathrm{nom}} - r_{\mathrm{a}}\right)}, \tag{24} \]

where \(R_{\mathrm{a}}\) is the armature resistance in the actual circuit (it may differ from \(r_{\mathrm{a}}\) when additional resistances are introduced).

From the value found for \(K_{\mathrm{tot}}\) and the known \(K_1\), the gain coefficient of the intermediate amplifier \(K_2\) can be found; according to it, the characteristic is selected and then the amplifier itself is chosen. Then, using the refined values of \(K_1\) and \(K_2\), by the method described in [9], it is necessary to check whether the drive satisfies the specified requirements.

Sometimes, instead of the concept of the “steepness” of the characteristic, the concept of the “stability of operation at a specified speed” is used; it is determined by the ratio of the change in speed to the specified speed for a given change in motor load.

\[ \delta = \left(\frac{\Delta n}{n}\right)_{\Delta I_{\mathrm{a}}=\mathrm{const}} \tag{25} \]

If the jump in the motor load is taken equal to the rated armature current, \(\Delta I_a = I_{a\,\mathrm{nom}}\), then the relationship between the slope of the characteristic and the stability will be determined by the expression

\[ S=\delta \nu_0 , \tag{26} \]

where \(\nu_0=\dfrac{n}{n_{\mathrm{nom}}}\) is the relative value of the specified speed.

Selection of the Motor Current-Limiting Circuit

Without an intermediate amplifier, it is not possible to provide contactless current limiting of the motor in the MUS-D system, since, owing to a small increment of the armature current from the cutoff current \(I_{\mathrm{cut}}\) to the stall current \(I_{\mathrm{st}}\), a signal must be obtained that is comparable in power with the signal from the voltage-setting source. Moreover, this signal must be fed into the common comparison circuit, since the MU can have only two control windings (as in the PMU-M drive).

Using an intermediate magnetic amplifier having several control windings, the problem of current limiting can be solved comparatively simply.

The most widely used current-limiting circuit (Fig. 5a) can be calculated with the aid of the expression:

\[ \frac{\left[U_p-I_{up}(r_a-\beta)\right]w_y}{R_{y2}} = \frac{(I_{up}-I_{\mathrm{cut}})\,r_p\,w_{to}}{r_{to}+R_{\mathrm{av}}}, \tag{27} \]

where

\[ R_{\mathrm{av}}=\frac{R_a\cdot R_b}{R_a+R_b} \]

is the resistance of the comparison-voltage potentiometer;

\(r_{to}\) is the resistance of the current-limiting winding.

The comparison voltage is selected as follows:

\[ U_{\mathrm{av}}\frac{R_a}{R_a+R_b}=I_{\mathrm{cut}}\,r_p . \tag{28} \]

It is not always possible to select the parameters of the current-limiting unit in accordance with expression (27), since the magnitude of the control m.m.f. proves to be very large. Some relief is provided by the use of a series nonlinear resistance with a barretter characteristic, which makes it possible to limit the current in the control winding.

If it is impossible to select the required barretter, current limitation in the control winding \(MU_2\) can be ensured by connecting, in parallel with the control winding, a nonlinear element with the characteristic of a stabilovolt, for example a silicon stabilitron. Selenium rectifiers in the forward direction also have a similar characteristic. The number and type of washers are selected on the basis of the following considerations: 1. The current-limiting valve must “open” when the current in the MU control winding is close to the saturation current (see Fig. 3 [9]), that is,

\[ E_{v\,to}=I_{y\,\max}\,r_y . \tag{29} \]

1. The valve must be designed for the current

\[ I_{to}\geq \frac{U_n}{R_{y2}}-I_{y\,\max}. \tag{30} \]

Fig. 5.

It should be noted that the use of the valve shifts the control characteristic of \(MU_2\) somewhat to the right, owing to the unidirectional flow of the even-harmonic currents. This shift can be eliminated by an appropriate choice of the amplifier bias.

The change in the form of the control characteristic when \(B_{\mathrm{to}}\) is switched on is very small.

The circuit of Fig. 5a can be modified somewhat if, instead of

a silicon Zener diode should be used as the reference-voltage source. When low-power Zener diodes are used (current up to 35 mA), it is necessary to employ a special current-limiting amplifier, which can successfully be made on a single semiconductor triode. The current-limiting circuit takes the form shown in Fig. 5b. If Zener diodes for higher currents are available, the additional triode can be dispensed with.

The parameters of the current-limiting circuit in Fig. 5b may be calculated on the basis of the following expression:

\[ \frac{(I_{\mathrm{up}}-I_{\mathrm{cut}})\, r_{\mathrm{sh}}\, a\, w_{\mathrm{to}}} {R_{\mathrm{in}}(1-a)} = (1.1 \div 1.2) I_{y\,\max} w_y , \tag{31} \]

where \(a\) is the current gain of the semiconductor triode in the common-base circuit;

\[ R_{\mathrm{in}} = r_{\mathrm{pos}} + r_b + r_e \left( \frac{a}{1-a} + 1 \right) \]

is the input resistance of the semiconductor triode;

\(w_{\mathrm{to}}\) is the number of turns of the current-limiting winding;

\(I_{\mathrm{up}}, I_{\mathrm{cut}}\) are, respectively, the values of the motor locking current and cutoff current.

The silicon diode and the resistance \(r_{\mathrm{sh}}\) are selected on the basis of the expression

\[ I_{\mathrm{cut}} r_{\mathrm{sh}} \ge U_{\mathrm{st}}, \tag{32} \]

where \(U_{\mathrm{st}}\) is the diode stabilization voltage.

Use of the circuit in Fig. 5b makes it possible effectively to limit the motor currents under steady-state conditions, to obtain a good starting diagram, and to bring the MUS-D system, in terms of starting properties, close to the most advanced electric-drive systems. To ensure stable operation of the MUS-D system in the current-limiting mode, it is necessary to include a forcing element in the delayed current-feedback circuit, that is, to shunt \(r_{\mathrm{pos}}\) in the circuit of Fig. 5a with a capacitance (possibly an electrolytic one).

Stable operation of the system according to the circuit of Fig. 4 before the current-limiting unit comes into action is ensured by the use of flexible feedback encompassing the intermediate amplifier, and by the inclusion of a series integrating element (shunting the winding \(w_{\mathrm{to}}\) and \(B_{\mathrm{to}}\) with a capacitance). The parameters of the correcting elements may be calculated by any known methods of automatic-control theory after appropriate linearization of the system and determination of the parameters that govern its dynamic behavior [10].

References

1. M. A. Boyarchenkov. Some problems in the use of a single-phase self-saturating magnetic amplifier for controlling a direct-current electric drive. Elektrichestvo, No. 8, 1963.

2. A. Ya. Petrovskii, Ya. B. Rozman. Adjustable Electric Drive with Magnetic Amplifiers. Energiya Publishing House, 1964.

3. F. Kümmel. Verhalten von Magnetverstärkern bei Motorbelastung. ETZ-A, Bd. 8, No. 11, 1959.

4. Magnetic amplifiers UMP and blocks of intermediate magnetic amplifiers BO. Information No. 42 (630), TsINTIEP.

5. M. A. Borovikov. Calculation of characteristics of a direct-current motor, regu-

… controlled by means of a single-phase magnetic amplifier with self-saturation. Interuniversity collection on problems of production automation. Novosibirsk, 1964.

1. M. A. Borovikov. Operation of a three-phase magnetic amplifier with self-saturation on the armature of a separately excited DC motor. Proceedings of the Fourth All-Union Conference on Automated Electric Drive. Energiya Publishing House, 1965.

2. M. A. Boyarchenkov, M. A. Rozenblat. Operation of a magnetic amplifier with counter-e.m.f. Automation and Remote Control, vol. XXIII, No. 1, 1962.

3. M. A. Borovikov. Features of the operation of a three-phase magnetic amplifier on the armature of a DC motor at low speeds. Proceedings of TPI, vol. 153, 1965.

4. M. A. Borovikov. Calculation of motor characteristics in automated MUS-D systems by the method of linearization of the magnetic amplifier. Proceedings of TPI, vol. 153, 1965.

5. M. A. Borovikov. Dynamics of an electric drive based on the single-phase magnetic-amplifier—motor system. Proceedings of Higher Educational Institutions: Electromechanics, No. 2, 1965.