22-Elec-B8 Power Electronics and Drives · May 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Exams, May 2018 — 16-Elec-B8, Power Electronics and Drives. Open book, three hours, any non-communicating calculator permitted. The paper is in two parts: Part 1 is twenty short-answer items (a) to (t) worth 2.5 points each, and Part 2 is five calculation problems worth 15 points each. The rubric says “attempt all parts” and that the maximum total score of 125 points includes a bonus of 25 points, so a candidate scoring 100 of the 125 available marks has a full paper. Every item and every sub-part is worked below.
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.
These twenty items are definitions, functions and comparison questions; each is answered in prose, in the two or three sentences a 2.5-point item earns. Where a numerical relation makes the point sharper it is quoted, but no item here requires a calculation.
Define the delay angle of phase-controlled rectifier.
The delay (firing) angle α is the angle, measured in electrical degrees of the supply waveform, from the instant at which the thyristor would begin to conduct if it were replaced by an uncontrolled diode — the natural commutation point, which is the supply zero crossing in a single-phase circuit and the crossover of two phase voltages in a polyphase bridge — to the instant the gate pulse is applied and the device actually turns on. It is the converter's one control variable: for continuous conduction the mean output follows $V_{dc}=V_{do}\cos\alpha$, so α sets the dc output between $+V_{do}$ at $\alpha=0$ and $-V_{do}$ at $\alpha=180^\circ$ (inversion).
What is the function of the freewheeling diode in a phase-controlled rectifier?
It is connected directly across the load with its cathode to the positive dc terminal, so it is reverse-biased while the supply drives the load and becomes forward-biased the moment the output voltage tries to go negative. With an inductive load the stored energy $\tfrac12 L i^{2}$ must keep the current flowing; the diode gives that current a closed path around the load instead of forcing it back through the thyristor into the reversed supply. In doing so it clamps the output at about zero (one diode drop) and removes the anode current from the conducting thyristor, which therefore turns off by natural commutation.
What are the advantages of the free-wheeling diode in a rectifier circuit?
Four benefits follow from clamping the output at zero. (i) The negative excursions of the output voltage are removed, so the mean dc voltage is higher for the same firing angle. (ii) The output ripple is reduced and the load current is kept continuous, which avoids the poor speed regulation that discontinuous conduction gives a dc drive. (iii) The input displacement factor improves, because the reactive energy stored in the load inductance is returned to the load rather than pumped back into the supply. (iv) The thyristors are relieved of reverse-recovery stress and their turn-off duty is eased. The price is that the converter can no longer invert, so regenerative braking is lost.
what are the advantages of a GTO over a BJT
The gate turn-off thyristor is a latching four-layer device, so once triggered it stays on with no continuing gate drive, whereas a bipolar transistor needs a base current of roughly $I_C/\beta$ for the whole conduction interval — the GTO's on-state drive power is therefore far lower. Its four-layer structure gives deep conductivity modulation, hence a lower on-state drop at a given rating, and it is available at much higher voltage and current ratings (kilovolt, kiloampere class against hundreds of volts and amperes). It also has a far larger surge-current capability, higher $dv/dt$ and $di/dt$ withstand, and no second-breakdown failure mode. The offset is a large negative gate current pulse to turn off and a slower switching speed.
In power electronic circuits, what does the term commutation mean?
Commutation is the transfer of load current from one conducting device or branch to another, together with the recovery of the outgoing device to its forward-blocking state. For a thyristor that means two conditions must be met in sequence: the anode current has to be reduced below the holding current $I_{H}$, and the device then has to be held under reverse or zero anode voltage for at least its circuit-commutated turn-off time $t_{q}$ so that the stored charge recombines. If the forward voltage returns before $t_{q}$ has elapsed the thyristor re-fires without a gate pulse and the converter fails.
Define the term natural commutation.
Natural (line or supply) commutation is commutation performed by the alternating supply itself: the supply voltage reverses at the end of the half cycle, drives the anode current of the conducting thyristor to zero and then holds the device reverse-biased for the remainder of the half cycle, which comfortably exceeds $t_{q}$ at 50 or 60 Hz. It is the mechanism in every line-fed converter — ac voltage controllers, phase-controlled rectifiers and cycloconverters — and it needs no auxiliary commutating capacitor, inductor or auxiliary thyristor, which is why line-commutated converters remain the cheapest and most robust high-power topology.
What are the two types of AC voltage controllers? which one is preferred and why?
They are integral-cycle (on-off, or burst-firing) control, in which whole cycles of the supply are passed and blocked in a repeating pattern, and phase-angle control, in which a portion of every half cycle is passed by delaying the firing angle. Phase-angle control is the preferred general-purpose choice because it gives smooth, stepless control within each half cycle and hence a fast response, which is what a motor soft starter or a lighting dimmer needs. Integral-cycle control is preferred only for loads with a large thermal time constant, such as resistance furnaces, because switching at the zero crossings produces no harmonics of the supply frequency; against that it generates sub-harmonic flicker and cannot be used on a motor.
Discuss the advantages of AC voltage controllers.
An ac voltage controller is a pair of inverse-parallel thyristors (or a triac) in series with the load, so it is the simplest and cheapest ac-to-ac converter there is: few components, small volume and no dc link. Because it is line-fed it commutates naturally, which removes all forced-commutation circuitry. The switch is either fully on or fully off, so the conversion efficiency is high and the losses are essentially conduction losses. Control is continuous and the response is within one half cycle. These properties make it the standard solution for induction-motor soft starting, lighting dimming, resistance heating, transformer on-load tap changing and static VAR control.
What are the disadvantages of armature resistance control?
Inserting resistance in the armature circuit of a dc motor can only reduce speed below base speed, and it does so by wasting power: the resistor carries the full armature current, so the loss $I_{a}^{2}R_{ext}$ is proportional to the speed reduction and the efficiency falls in the same proportion. Speed regulation becomes poor, since the speed now drops steeply with load. The resistor bank must be rated for full armature current, so it is bulky, expensive and needs forced cooling; contactor-switched steps give stepped rather than continuous control; and there is no regenerative capability. It survives only on intermittent-duty crane and hoist drives where its simplicity outweighs the loss.
What do you understand by constant torque drive and constant power drive?
They are the two operating regions of a variable-speed drive. Below base speed the flux is held at its rated value by raising the terminal voltage in proportion to frequency (or by holding field current constant in a dc machine), so the maximum torque the drive can develop is constant and the output power rises linearly with speed — the constant-torque region. Above base speed the converter has reached its voltage ceiling, so the flux is weakened as $1/f$; the torque capability then falls as $1/\omega$ while the product $T\omega$ stays at the rated value — the constant-power region. Conveyors and hoists are constant-torque loads; spindles, winders and traction drives exploit the constant-power region.
List three methods for starting an induction motor.
(i) Direct-on-line, in which the motor is thrown straight across the supply and draws five to seven times rated current. (ii) Reduced-voltage starting, by star-delta switching, a series stator reactor or resistor, or an autotransformer starter; the starting current falls with the voltage and the starting torque with its square. (iii) A solid-state soft starter, an ac voltage controller that ramps the stator voltage from a chosen pedestal to full voltage over a set time and is then bypassed by a contactor. For a wound-rotor machine, external rotor resistance is a fourth method, and a variable-frequency drive a fifth, both giving high torque at low current.
What are the disadvantages of the stator voltage control method?
Torque varies as the square of the applied voltage, so a large voltage reduction buys only a modest speed change and the useful range is confined to slips below breakdown — that is, a narrow speed range, and even then only with a fan or pump load whose torque falls as $\omega^{2}$. Rotor copper loss is $sP_{g}$, so running at large slip converts a large fraction of the air-gap power into rotor heat: the efficiency collapses and the rotor must be derated or force-ventilated. Phase-angle control at large firing angles also gives a poor input displacement factor, substantial harmonic currents and pulsating torque.
What are the advantages and disadvantages of rotor resistance control?
Advantages: the scheme is simple and cheap, gives smooth speed control below synchronous speed, leaves the breakdown torque unchanged (only the slip at which it occurs moves), and therefore raises the starting torque while simultaneously reducing the starting current — the reason it is standard on crane and hoist drives. Disadvantages: it needs a wound-rotor machine with slip rings and brushes, which cost more and require maintenance; the slip power is dissipated as heat in the external resistors, so efficiency falls in proportion to the speed reduction; speed regulation with load becomes poor; the resistors are bulky; and no operation above synchronous speed is possible.
Is it Possible to Use the same soft starter to start two MV induction motors?
Yes, but only sequentially. In the standard cascade arrangement the starter feeds each machine in turn through its own isolating contactor; when a motor reaches full speed a bypass (run) contactor puts it directly across the line, the isolating contactor opens and the starter is released for the next machine. The conditions are that the starter be rated for the largest motor's starting duty, that the interlocked isolating and bypass contactors carry the medium-voltage rating, that the machines never need to start together, and that the starter's thermal model be allowed to cool between starts, which limits starts per hour. Starting two motors simultaneously through one starter is not sound practice, because the starter cannot control the two torque profiles independently and the lightly loaded machine accelerates first, distorting the current ramp seen by the other.
Define electric drives.
An electric drive is the complete electromechanical system that converts electrical energy into controlled mechanical motion. It comprises the electrical supply, a power-electronic converter, the electric machine, the mechanical transmission and load, and the sensing and control electronics that regulate torque, speed or position. Its defining function is that the converter delivers power to the machine in exactly the form — magnitude, frequency and waveform — that the load duty demands, rather than the fixed form the supply offers.
What is meant by slip power?
Of the air-gap power $P_{g}$ that crosses from stator to rotor in an induction machine, the fraction $(1-s)P_{g}$ is converted to mechanical power and the remaining fraction $sP_{g}$ — the slip power — enters the rotor circuit at slip frequency $sf$. It equals the rotor copper loss $3I_{r}^{2}R_{r}$, and in a cage machine that is all it can ever be. In a wound-rotor machine it appears at the slip rings, where it can be dissipated in external resistance, or intercepted by a converter and returned usefully to the supply or the shaft.
What are the advantages of slip power recovery system?
A slip-power-recovery cascade (static Kramer or static Scherbius) rectifies the slip-ring output and returns the energy to the supply instead of burning it in resistors, so the efficiency stays high across the whole speed range. Decisively, the converter has to handle only the slip power, not the machine rating: a drive that must vary speed over $\pm20\%$ of synchronous needs a converter of roughly 20 per cent rating, which is far cheaper and smaller than a full-rating inverter. Control is smooth and stepless, and the Scherbius form, using a bidirectional converter, allows both sub-synchronous and super-synchronous operation with regeneration. The scheme is standard on large fan, pump and doubly-fed wind-generator drives.
What is meant by V/Hz control?
Constant volts-per-hertz control varies the inverter's output voltage in proportion to its output frequency so that the air-gap flux, $\Phi\approx V/(4.44\,k_{w}Nf)$, is held at its rated value. Because the breakdown torque of an induction machine depends on $(V/f)^{2}$, holding $V/f$ constant keeps the whole torque–slip curve unchanged in shape and simply translates it along the speed axis, so full torque capability is available at every speed below base speed. At low frequency a voltage boost is added to make up for the stator resistance drop, and above base speed the voltage saturates at its ceiling and the drive enters field weakening.
What are the advantages of V/Hz control?
The breakdown torque stays constant over the whole sub-base-speed range, so the machine can deliver rated torque at any speed; the slip at a given load stays small, so rotor loss and hence efficiency are good. It is an open-loop scalar scheme requiring no shaft encoder, which makes it cheap, simple and robust, and one inverter can drive several motors in parallel. Starting is soft, with full starting torque at a fraction of the direct-on-line inrush current, and fan or pump loads yield large energy savings because power falls as the cube of speed. Its limitations are weak torque control at very low frequency and a dynamic response well short of vector control.
What is the difference between a variable frequency drive (VFD) and a variable speed drive (VSD)?
Variable-speed drive is the generic term for any drive whose output speed can be varied, by whatever means: mechanically by belt-and-pulley or a variable-ratio gearbox, hydraulically by a fluid coupling or eddy-current clutch, or electrically by a dc drive, wound-rotor slip control or an inverter. Variable-frequency drive names one specific electrical subset — a power-electronic converter that supplies an ac machine at a controlled frequency, with the voltage varied alongside it to hold the flux. Every VFD is therefore a VSD, but a dc drive, a fluid coupling and a soft-start-plus-slip-control scheme are variable-speed drives that are not variable-frequency drives.
