Performance Characteristics

This page describes how a separately-excited DC motor can be controlled in closed-loop with a single-phase fully-controlled rectifier supplying dc source to its armature. The operation of a DC motor is described briefly at first.

A symbolic representation of a separately-excited DC motor is shown above. The resistance of the field winding is R_f and its inductance is L_f, whereas the resistance of the armature is R_a and its inductance is L_a. In the description of the motor, the armature reaction effects are ignored. It is justifiable since the motor used has either interpoles or compensating winding to minimize the effects of armature reaction. The field current is described by equation (1). If a steady voltage V_f is applied to the field, the field current settles down to a constant value, as shown in equation (2). When the field current is constant, the flux induced by the field winding remains constant, and usually it is held at its rated value f. If the voltage applied to the armature is v_a, then the differential equation that is to be applied to the armature circuit is shown in equation (3). In steady-state, equation (4) applies. The voltage, e_a, is the back e.m.f. in volts. In a separately-excited DC motor, the back e.m.f is proportional to the product of speed of motor w rad/s and the field f Webers, as shown by equation (5).

In equation (5), K_m is a coefficient and its value depends on the armature winding. If the armature current in steady-state be I_a, then the power P that is supplied to the armature is E_aI_a. This electric power is converted to mechanical power by the armature of the DC motor. Let the torque developed by the armature be T_e, the unit for torque being Nm (Newton-metre). Then power and torque can be related as shown in equation (6). On canceling the common term on both sides, the torque T_e developed by the armature is obtained as presented in equation (7).

If the instantaneous armature current is i_a, then equation (8) applies. Torque has been denoted by T_e in both equations.

The speed of the motor can be controlled by varying V_a and holding V_f constant at its rated value. Then as the voltage applied to the armature is raised, the armature current increases first. As the armature current increases, the torque developed by motor increases and hence the speed of motor increases. The drop across the armature resistance tends to be small and hence the motor speed rises almost proportionately with the voltage applied to the armature. But there is a limit to the voltage that can be applied to the armature and that limit is the rated voltage of the armature voltage. The speed of the motor corresponding to the rated armature voltage and the rated field voltage is its rated speed. Thus the speed of a motor can be varied below its rated speed by controlling the armature voltage. It would be desirable that the motor should be able to develop as high as a torque as possible and hence the voltage rated applied to the field is held at its rated value. Applying higher than the rated voltage to either the field or the armature is not recommended. When the rated voltage is applied to the field, the flux would be near the saturation level in the poles. If a voltage higher than its rated voltage is applied to the field, the flux would saturate and there would not be any significant increase in the torque that the motor can deliver. On the other hand, this would only result in increased losses in the winding. Since the total heat which the DC motor can dissipate is fixed due to its surface area and cooling system, increased losses from the excitation system would mean that the other losses would have to reduce, implying that the armature current cannot be at its rated level and the maximum torque that the motor can deliver may reduce. Increasing the armature voltage above its rated value is not recommended because the insulation of the armature is designed for operation of the motor with the rated voltage applied to its armature. Moreover, the torque that the motor can deliver depends on the armature current and the field current. If the motor is operated continuously, the maximum armature current should not be higher than its rated value. When the armature current and the field voltage are at their rated level, the motor generates the rated torque. Hence the maximum torque the motor can deliver continuously over a long period of time is its rated torque when its speed is varied from a low value to its rated speed. Over this period, 0 < w < w_r, where w_r is its rated speed, the power output is given by:

The maximum torque which the motor can deliver continuously is called T_{e,max cont}. What is being referred to here is the maximum torque the motor can deliver, and not the actual torque the motor delivers. The actual torque the motor delivers depends on the mechanical load connected to its shaft. If the speed of the motor is to be increased beyond its rated value, the voltage applied to the armature can be held at its rated value and the field can be weakened by reducing the voltage applied to it. When the speed of the motor is in this manner, the maximum power that can be supplied to the armature is fixed, since both the voltage applied to the armature and the armature current cannot exceed the rated level over a long period. That means the maximum torque the motor can develop above the rated speed is:

The plots of T_{e,max cont} and the maximum power P_a,max can be plotted as a function of rotor speed as shown below. The rated values of speed, torque and power to the armature have been set equal to unity.

A separately-excited dc motor can be controlled, either by varying the voltage applied to the field winding or by varying the voltage applied to the armature. This page describes how the motor can be controlled by varying the armature voltage and it is assumed that the field is excited by a constant voltage, equaling the rated voltage of the field winding. It means that the discussion to follow assumes that the field current remains steady at its rated value.

 
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