Converter output impedance: overlap
So far we have tacitly assumed that the output voltage from the converter was independent of the current drawn by the motor, and depended only on the delay angle α. In other words we have treated the converter as an ideal voltage source.
In practice the a.c. supply has a finite impedance, and we must therefore expect a volt-drop which depends on the current being drawn by the motor. Perhaps surprisingly, the supply impedance (which is mainly due to inductive leakage reactances in transformers) manifests itself at the output stage of the converter as a supply resistance, so the supply volt-drop (or regulation) is directly proportional to the motor armature current.
It is not appropriate to go into more detail here, but we should note that the effect of the inductive reactance of the supply is to delay the transfer (or commutation) of the current between thyristors; a phenomenon known as overlap. The consequence of overlap is that instead of the output voltage making an abrupt jump at the start of each pulse, there is a short period when two thyristors are conducting simultaneously. During this interval the output voltage is the mean of the voltages of the incoming and outgoing voltages, as shown typically in Figure 4.5.
Figure 4.5 Distortion of converter output voltage waveform caused by rectifier overlap.
It is important for users to be aware that overlap is to be expected, as otherwise they may be alarmed the first time they connect an oscilloscope to the motor terminals. When the drive is connected to a 'stiff' (i.e. low impedance) industrial supply the overlap will only last for perhaps a few microseconds, so the 'notch' shown in Figure 4.5 would be barely visible on an oscilloscope.
Books always exaggerate the width of the overlap for the sake of clarity, as in Figure 4.5: with a 50 or 60 Hz supply, if the overlap lasts for more than say 1 ms, the implication is that the supply system impedance is too high for the size of converter in question, or conversely, the converter is too big for the supply.
Returning to the practical consequences of supply impedance, we simply have to allow for the presence of an extra 'source resistance' in series with the output voltage of the converter. This source resistance is in series with the motor armature resistance, and hence the motor torque"speed curves for each value of α have a somewhat steeper droop than they would if the supply impedance was zero.
Four-quadrant operation and inversion
So far we have looked at the converter as a rectifier, supplying power from the a.c. mains to a d.c. machine running in the positive direction and acting as a motor. As explained in Chapter 3, this is known as one-quadrant operation, by reference to quadrant 1 of the complete torque"speed plane shown in Figure 3.16.
But suppose we want to run the machine as a motor in the opposite direction, with negative speed and torque, i.e. in quadrant 3; how do we do it? And what about operating the machine as a generator, so that power is returned to the a.c. supply, the converter then 'inverting' power rather than rectifying, and the system operating in quadrant 2 or quadrant 4. We need to do this if we want to achieve regenerative braking. Is it possible, and if so how?
The good news is that as we saw in Chapter 3 the d.c. machine is inherently a bidirectional energy converter. If we apply a positive voltage V greater than E, a current flows into the armature and the machine runs as a motor. If we reduce V so that it is less than E, the current, torque and power automatically reverse direction, and the machine acts as a generator, converting mechanical energy (its own kinetic energy in the case of regenerative braking) into electrical energy. And if we want to motor or generate with the reverse direction of rotation, all we have to do is to reverse the polarity of the armature supply. The d.c. machine is inherently a four-quadrant device, but needs a supply which can provide positive or negative voltage, and simultaneously handle either positive or negative current.
This is where we meet a snag: a single thyristor converter can only handle current in one direction, because the thyristors are unidirectional devices. This does not mean that the converter is incapable of returning power to the supply however. The d.c. current can only be positive, but (provided it is a fully controlled converter) the d.c. output voltage can be either positive or negative (see Chapter 2). The power flow can therefore be positive (rectification) or negative (inversion).
For normal motoring where the output voltage is positive (and assuming a fully controlled converter), the delay angle (α) will be up to 90°. (It is common practice for the firing angle corresponding to rated d.c. voltage to be around 20° when the incoming a.c. voltage is normal: if the a.c. voltage falls for any reason, the firing angle can then be further reduced to compensate and allow full d.c. voltage to be maintained.)
Figure 4.6 Average d.c. output voltage from a fully-controlled thyristor converter as a function of the firing angle delay α.
When α is greater than 90°, however, the output voltage is negative, as indicated by equation (2.5), and is shown in Figure 4.6. A single fully controlled converter therefore has the potential for two-quadrant operation, though it has to be admitted that this capability is not easily exploited unless we are prepared to employ reversing switches in the armature or field circuits. This is discussed next.
