We can see from Figure 4.2 that as the load torque is reduced, there will come a point where the minima of the current ripple touches the zero-current line, i.e. the current reaches the boundary between continuous and discontinuous current. The load at which this occurs will also depend on the armature inductance, because the higher the inductance the smoother the current (i.e. the less the ripple). Discontinuous current mode is therefore most likely to be encountered in small machines with low inductance (particularly when fed from two-pulse converters) and under light-load or no-load conditions.
Typical armature voltage and current waveforms in the discontinuous mode are shown in Figure 4.3, the armature current consisting of discrete pulses of current that occur only while the armature is connected to the supply, with zero current for the period (represented by θ in Figure 4.3) when none of the thyristors are conducting and the motor is coasting free from the supply.
Figure 4.3 Armature voltage current waveforms for discontinuous-current operation of a d.c. motor supplied from a single-phase fully-controlled thyristor converter, with firing angle of 60°.
The shape of the current waveform can be understood by noting that with resistance neglected, equation (3.7) can be rearranged as
di/dt = (1/L)(V - E) (4:2)
which shows that the rate of change of current (i.e. the gradient of the lower graph in Figure 4.3) is determined by the instantaneous difference between the applied voltage V and the motional e.m.f. E. Values of (V - E) are shown by the vertical hatchings in Figure 4.3, from which it can be seen that if V > E, the current is increasing, while if V <>E, the current is falling. The peak current is thus determined by the area of the upper or lower shaded areas of the upper graph.
The firing angle in Figures 4.2 and 4.3 is the same, at 60°, but the load is less in Figure 4.3 and hence the average current is lower (though, for the sake of the explanation offered below the current axis in Figure 4.3 is expanded as compared with that in Figure 4.2).
It should be clear by comparing these figures that the armature voltage waveforms (solid lines) differ because, in Figure 4.3, the current falls to zero before the next firing pulse arrives and during the period shown as θ the motor floats free, its terminal voltage during this time being simply the motional e.m.f. (E). To simplify Figure 4.3 it has been assumed that the armature resistance is small and that the corresponding volt-drop (IaRa) can be ignored. In this case, the average armature voltage (Vdc) must be equal to the motional e.m.f., because there can be no average voltage across the armature inductance when there is no net change in the current over one pulse: the hatched areas - representing the volt-seconds in the inductor - are therefore equal.
The most important difference between Figures 4.2 and 4.3 is that the average voltage is higher when the current is discontinuous, and hence the speed corresponding to the conditions in Figure 4.3 is higher than in 4.2 despite both having the same firing angle. And whereas in continuous mode a load increase can be met by an increased armature current without affecting the voltage (and hence speed), the situation is very different when the current is discontinuous.
In the latter case, the only way that the average current can increase is when speed (and hence E) falls so that the shaded areas in Figure 4.3 become larger. This means that from the user's viewpoint the behaviour of the motor in discontinuous mode is much worse than in the continuous current mode, because as the load torque is increased, there is a serious drop in speed. The resulting torque-speed curve therefore has a very unwelcome 'droopy' characteristic in the discontinuous current region, as shown in Figure 4.4, and in addition the I2R loss is much higher than it would be with pure d.c.
Under very light or no-load conditions, the pulses of current become virtually non-existent, the shaded areas in Figure 4.3 become very small and the motor speed reaches a point at which the back e.m.f. is equal to the peak of the supply voltage.
It is easy to see that inherent torque-speed curves with sudden discontinuities of the form shown in Figure 4.4 are very undesirable. If for example the firing angle is set to zero and the motor is fully loaded, its
Figure 4.4 Torque-speed curves illustrating the undesirable 'droopy' characteristic associated with discontinuous current. The improved characteristic (shown dotted) corresponds to operation with continuous current.
speed will settle at point A, its average armature voltage and current having their full (rated) values. As the load is reduced, current remaining continuous, there is the expected slight rise in speed, until point B is reached. This is the point at which the current is about to enter the discontinuous phase. Any further reduction in the load torque then produces a wholly disproportionate - not to say frightening - increase in speed, especially if the load is reduced to zero when the speed reaches point C.
There are two ways by which we can improve these inherently poor characteristics. Firstly, we can add extra inductance in series with the armature to further smooth the current waveform and lessen the likelihood of discontinuous current. The effect of adding inductance is shown by the dotted lines in Figure 4.4. And secondly, we can switch from a single-phase converter to a 3-phase converter which produces smoother voltage and current waveforms, as discussed in Chapter 2.
When the converter and motor are incorporated in a closed-loop control the user should be unaware of any shortcomings in the inherent motor/converter characteristics because the control system automatically alters the firing angle to achieve the target speed at all loads. In relation to Figure 4.4, for example, as far as the user is concerned the control system will confine operation to the shaded region, and the fact that the motor is theoretically capable of running unloaded at the high speed corresponding to point C is only of academic interest.
Coming up in Part 2: More on thyristor DC drives, including converter output impedance, four-quadrant operation, single- and double converter reversing drives, and power factor and supply effects.
Printed with permission from Newnes, a division of Elsevier. Copyright 2005. "Electric Motors and Drives" by Austin Hughes. For more information about this title and other similar books, please visit www.elsevierdirect.com.
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