22-Elec-B8 Power Electronics and Drives · December 2019
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examinations, December 2019 — 16-Elec-B8 Power Electronics and Drives. Three hours; closed book with one double-sided aid sheet; an approved Casio or Sharp calculator. Five questions constitute a complete paper and all questions are of equal value, so each carries 20 marks. All a.c. voltages and currents are rms unless noted otherwise; for three-phase circuits voltages are line-to-line and power is total real power unless noted otherwise. Every question is solved below, in the exam's own order.
Reference texts.
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Each part is answered in turn, with the static anode characteristic drawn once because parts (a), (b) and (c) are all read off the same curve.
A thyristor is a four-layer $p$–$n$–$p$–$n$ device, and its static anode characteristic divides into four regions. In the forward blocking region (region 2 on Figure 3.1) the anode is positive with respect to the cathode but no gate signal has been applied; the centre junction $J_2$ is reverse-biased and the device supports the full forward voltage while passing only a small leakage current of the order of milliamperes. If the forward voltage is raised far enough without a gate signal, the device breaks over at $V_{BO}$ and switches to the forward conduction region (region 1), the on-state, in which both outer junctions and the centre junction are forward-biased, the internal two-transistor regeneration has taken hold, and the device behaves as a closed switch with an on-state drop of roughly one to two volts almost independent of current. Between these two lies a short negative-resistance transition, drawn dashed, which is unstable and is traversed in microseconds rather than occupied.
With the anode negative the device is in the reverse blocking region (region 3): junctions $J_1$ and $J_3$ are reverse-biased, the device withstands the reverse voltage, and only reverse leakage flows. Beyond the reverse breakdown voltage $V_{BR}$ the device enters the reverse avalanche region (region 4). It is important to say that region 4 is a rating limit rather than a usable operating mode: avalanche in a conventional SCR is destructive, so the peak repetitive reverse voltage of the device must exceed the worst-case circuit voltage with margin. In normal phase-controlled service the device therefore cycles only between regions 2, 1 and 3.
The gate's role is visible on the same figure. Injecting gate current supplies carriers to the base of the lower transistor, so the sum of the two internal current gains $\alpha_1 + \alpha_2$ reaches unity at a lower anode voltage: the break-over voltage falls as $I_G$ rises, and with sufficient gate drive the device turns on at a few volts. This is why a thyristor in service is fired by its gate and never by break-over.
The latching current $I_L$ is the minimum anode current that must be reached, while the gate pulse is still present, for the thyristor to remain in conduction after the gate signal is removed. Turn-on is a regenerative process that needs time and current to establish itself across the whole cathode area: conduction begins in a small region next to the gate and spreads outwards at a finite plasma-spreading velocity. Until enough of the area is conducting, the internal feedback is not yet self-sustaining, and if the gate drive is withdrawn the device reverts to forward blocking.
The practical consequence is a rule about gate-pulse duration rather than amplitude. With a highly inductive load the anode current rises slowly, so a short gate pulse may end before $I_L$ has been reached and the device will fail to latch — an intermittent, load-dependent misfire that is easily mistaken for a faulty device. The standard remedies are a gate pulse long enough to cover the current rise, a pulse train, or a continuous gate signal for the whole intended conduction interval.
The holding current $I_H$ is the minimum anode current that will keep an already-latched thyristor conducting. If the anode current falls below $I_H$ the regeneration collapses and the device reverts to the forward blocking state, after which it can only be returned to conduction by another gate pulse. Holding current is measured with the gate open, and it is the quantity that governs turn-off, whereas latching current governs turn-on.
The two are related but not equal: $I_L$ is typically two to three times $I_H$, because latching requires the conduction area to have spread whereas holding merely requires it not to have collapsed. Both are small — tens of milliamperes for a device rated at hundreds of amperes — and both fall as junction temperature rises. In a natural-commutation circuit such as the a.c. controller of Question 4, it is the fall of the load current below $I_H$ near the end of each half cycle, not the removal of the gate signal, that turns the device off.
The gate of a thyristor does not hold the device on the way a base current holds a transistor on; it merely delivers the packet of charge that starts the internal regeneration. The trigger condition is therefore an integral rather than a level: the device fires when the charge injected into the gate–cathode junction exceeds a critical value $Q_G$, that is when $\int i_G \, dt \ge Q_G$. Because it is the integral that matters, a short pulse of large amplitude and a long pulse of small amplitude are equally effective provided each delivers the same charge, and manufacturers exploit exactly this by specifying high-amplitude gate pulses of a few microseconds to obtain fast, well-defined and uniform turn-on.
Once the injected charge has driven $\alpha_1 + \alpha_2$ to unity, the regeneration is self-sustaining and the gate loses all control — further gate current changes nothing, and removing the gate signal does not turn the device off. That is the other half of the same statement, and it is why a conventional SCR is also called a semi-controlled or latching switch: the gate commands turn-on only, and turn-off must come from the external circuit, either naturally when the a.c. supply reverses or by forced commutation in a d.c. circuit. Devices that break this limitation — the GTO, the IGCT, and the fully controlled IGBT and MOSFET — are precisely the ones that displaced the SCR in modern drives.
The dominant advantage is efficiency. A thyristor controls the average power delivered to a machine by switching, so the device is either fully on with a drop of one or two volts or fully off with only leakage current; the loss in the controller is a small fraction of the throughput. The alternatives it displaced — armature or rotor rheostats, autotransformers, Ward–Leonard motor generator sets — dissipate the difference between supply and load power as heat, or require a second and third machine to avoid doing so. A rheostat that halves the speed of a d.c. motor at constant torque throws away roughly half the input power; a phase-controlled converter doing the same job wastes a per cent or two.
Beyond efficiency the practical advantages follow from the same solid-state character. Speed is continuously and smoothly adjustable over a wide range by a low-power control signal, since the gate needs only milliwatts to command tens or hundreds of kilowatts. The response is fast — the firing angle can be changed within one half cycle — which makes tight closed-loop speed and current regulation, and hence accurate torque limiting during acceleration, straightforward. There are no moving or wearing parts: no contactors, brushes or commutator segments in the controller, so maintenance is low, there is no arcing, and reliability and service life are high. Equipment is compact, light and quiet relative to rotating or rheostatic alternatives, and it can be enclosed for hazardous or dirty environments. Soft starting comes free: raising the firing angle gradually limits inrush current to a chosen ceiling, which reduces mechanical shock on the driven load and voltage dip on the supply. Finally, a dual or fully controlled converter gives regeneration and four-quadrant operation, returning braking energy to the line instead of burning it in a resistor.
Honesty about the costs belongs in the same answer, because it is what a marker looks for at this level. Phase control draws a non-sinusoidal current rich in low-order harmonics, which causes additional machine heating, torque pulsation at low speed and distortion on the supply; the displacement power factor falls as the firing angle increases, so a lightly loaded drive can present a poor power factor to the utility; and the fast switching generates electromagnetic interference that must be filtered. Canadian installations must meet the harmonic limits of CSA/IEEE 519 and the general requirements of the Canadian Electrical Code, CSA C22.1, so input reactors, filters or a higher pulse number are routine parts of a thyristor drive design rather than optional extras.
Summary of the five parts.
| Part | Answer in one line |
|---|---|
| (a) | Forward blocking, forward conduction (on-state), reverse blocking, and reverse avalanche — the last being a rating limit, not an operating mode |
| (b) | $I_L$: minimum anode current needed while the gate pulse is present for conduction to be self-sustaining once the gate is removed |
| (c) | $I_H$: minimum anode current that keeps a latched device conducting; $I_L \approx 2$–$3\,I_H$ |
| (d) | Firing depends on the injected gate charge $\int i_G\,dt \ge Q_G$, not on a gate current level; after latching the gate loses control |
| (e) | High efficiency, wide smooth speed range, fast response, low control power, no moving parts, soft start, regeneration — at the cost of harmonics, poor displacement power factor and EMI |
