Q8Industrial Electronics

(a) Speed Control of DC Series Motor Using Single Phase Full Converter

A single-phase full converter (a fully-controlled bridge of four thyristors, T1-T4) can supply a DC series motor's armature and field winding (connected in series, as is characteristic of series motor construction) from an AC supply, with the average output DC voltage controlled by adjusting the thyristors' common firing angle α.

Operation: during the positive half-cycle of the AC supply, thyristors T1 and T4 are gated (turned on) at a delay angle α measured from the natural zero-crossing of the supply voltage, connecting the supply across the motor in one polarity; during the negative half-cycle, T2 and T3 are gated at the corresponding point, reconnecting the supply across the motor in the same output polarity (since the bridge configuration inverts the negative half-cycle to maintain a consistent output direction), giving a rectified, phase-controlled output. For continuous conduction (ensured in practice by the motor's own armature/field inductance, which is generally large enough in a series motor to maintain continuous current except at very light load or very large α), the average output (and hence motor armature) voltage is given by the standard full-converter relation Vo=(2Vm/π)cos α, allowing the motor's average applied voltage — and hence its speed, since a series motor's speed is approximately proportional to applied voltage divided by the square root of torque/armature current for a given operating condition — to be smoothly controlled by adjusting the common firing angle α of all four thyristors.

Voltage and current waveforms: the output voltage waveform for continuous conduction consists of a series of Vm sin θ segments beginning at each firing instant (θ=α, π+α, 2π+α, ...) and continuing until the next thyristor pair is fired at the subsequent zero-crossing-plus-α point, giving a characteristic 'chopped sinusoid' output voltage waveform with a mean value set by α, while the armature current waveform, smoothed by the substantial series inductance of the armature and field windings, remains continuous and relatively smooth (ripple superimposed on a DC average level) throughout the conduction cycle, in contrast to the more sharply-varying output voltage waveform, this smoothing effect of motor inductance being essential to achieving good speed and torque regulation quality from a phase-controlled single-phase supply.

Discontinuous Conduction in Series Motor Drive

At large firing angles α, at light load (low armature current demand), or in machines with comparatively low armature/field inductance, the current supplied to the series motor by the full converter can fall to zero before the next thyristor pair is fired, placing the drive in discontinuous conduction — in this condition, the motor's back-EMF (proportional, for a series motor, to both armature current and flux, and hence itself dependent on the load condition) is directly impressed across the still-blocked converter output during the current-zero interval, causing the output voltage waveform to depart from the ideal continuous-conduction chopped-sinusoid shape and rise above the value predicted by Vo=(2Vm/π)cos α for the same firing angle. Discontinuous conduction in a series-motor converter drive is generally undesirable from a control standpoint, since it introduces a nonlinear, load-dependent relationship between firing angle and motor speed (complicating closed-loop speed control), increases torque pulsation and associated mechanical vibration/noise, and increases the peak-to-average current ratio for a given average torque — for this reason, industrial series-motor converter drives are commonly fitted with an additional series smoothing inductor (beyond the motor's own winding inductance) specifically to extend the continuous-conduction operating range down to as low a load current and as large a firing angle as practically possible.

Chopper-Based Series Motor Control as an Alternative

As an alternative to phase-controlled AC-fed converter control, a DC series motor already supplied from a fixed DC source (such as a battery, third-rail, or DC catenary supply, as in traction applications) is commonly speed-controlled instead using a DC chopper connected between the fixed DC source and the series-connected armature/field winding, exactly analogous to the step-down chopper principle described in an earlier answer, with the chopper's duty cycle D directly setting the average voltage (and hence approximate speed) applied to the motor via Vo=D×Vd. Chopper-based control avoids the AC-side power-factor and harmonic-injection penalties associated with phase-controlled converter operation (discussed in relation to the bridge rectifier problem earlier in this paper), gives smoother, more continuous torque control at a typically higher switching/chopping frequency than the AC line frequency allows, and is therefore the standard speed-control method used in DC traction (locomotive, tramway, and battery-electric vehicle) series-motor applications supplied from a fixed DC source, whereas the AC-line-fed full-converter method described in part (a) is used specifically where the available supply is AC and direct rectification with phase control is the natural means of deriving a controllable DC output.

(b) Four-Quadrant Operation of a DC-DC Chopper

A basic single-switch step-down (buck) chopper, as discussed in an earlier answer, can only deliver positive output voltage and positive (unidirectional) output current, restricting its operation to the first quadrant of the torque-speed (or voltage-current) plane — corresponding only to forward motoring operation of a connected DC motor. To achieve full four-quadrant operation — forward motoring (Quadrant I: positive voltage, positive current), forward regenerative braking (Quadrant II: positive voltage, negative current), reverse motoring (Quadrant III: negative voltage, negative current), and reverse regenerative braking (Quadrant IV: negative voltage, positive current) — a full H-bridge (also called a Class E) chopper configuration is used, comprising four controllable switches (each with an anti-parallel diode) arranged in an H-bridge pattern identical in topology to the inverter H-bridge discussed elsewhere in this paper, but operated with DC-chopper-style PWM switching rather than simple square-wave inverter switching.

By appropriately selecting which pair(s) of switches are actively modulated (via PWM) at any given time, and which pair provide the freewheeling/return current path via their anti-parallel diodes, the H-bridge chopper can apply either polarity of average voltage across the motor armature (allowing both forward and reverse motoring direction), while also allowing current to flow in either direction through the armature independent of the applied voltage polarity (enabling regenerative braking operation, in which the motor, acting temporarily as a generator during deceleration, returns energy back to the DC source rather than dissipating it as heat) — this bidirectional voltage and current capability, achieved purely through appropriate switch-pair selection and timing within the same four-switch H-bridge hardware, is what constitutes genuine four-quadrant chopper operation, making the H-bridge (Class E) chopper the standard power-electronic building block for high-performance, reversible, regenerative DC motor drive applications such as electric traction, robotics, and servo-positioning systems where rapid, energy-efficient reversal of both speed direction and torque direction is routinely required.

Mode-by-Mode Switch State Table for Four-Quadrant Operation

Labeling the four H-bridge switches S1, S2 (upper legs) and S3, S4 (lower legs), with the motor armature connected between the two leg midpoints (as in the inverter H-bridge topology shown elsewhere in this paper), the four quadrants of operation are obtained by the following switch-pair operating patterns:

• Quadrant I - Forward motoring (+V, +I): S1 and S4 are the actively PWM-modulated pair (chopping the DC source across the armature in the forward polarity); S2, S3 remain off, with their anti-parallel diodes providing the freewheeling path during the modulated pair's off-intervals. Power flows from source to motor.
• Quadrant II - Forward regenerative braking (+V, -I): with the motor still spinning in the forward direction (generating a forward-polarity back-EMF) but decelerating, S3 is held on (or PWM-modulated) while S1 and S4 are held off; the motor's back-EMF drives current backward through S3 and the anti-parallel diode of S2, returning energy to the DC source through this diode/switch pair rather than the source driving the motor.
• Quadrant III - Reverse motoring (-V, -I): S2 and S3 become the actively modulated pair (chopping the DC source across the armature in the reverse polarity); S1, S4 remain off, with their anti-parallel diodes providing the freewheeling path. Power again flows from source to motor, but with reversed armature polarity, giving reverse-direction rotation.
• Quadrant IV - Reverse regenerative braking (-V, +I): with the motor spinning in reverse but decelerating, S1 is held on (or modulated) while S2 and S3 are held off; the reverse-rotation back-EMF drives current through S1 and the anti-parallel diode of S4, again returning energy to the source.

This mode-by-mode pattern illustrates that the same four physical switches and their four anti-parallel diodes are reused across all four quadrants purely by changing which switch(es) are actively gated at a given time, with the presently-inactive switches' diodes automatically providing whichever freewheeling or energy-return path each quadrant requires — no additional power devices or contactor-based polarity-reversal hardware are needed, which is the central practical advantage of the four-quadrant H-bridge chopper over simpler unidirectional chopper topologies for reversible, regenerative DC drive applications.