Book summary “Power electronics”: summary

Introduction

You face the complex challenge of converting and controlling electrical energy with maximum efficiency and minimal thermal loss in modern industrial systems. Traditional linear regulation wastes vast amounts of energy as heat, rendering it obsolete for high-power applications. You must master solid-state devices and advanced topologies to process electrical power seamlessly across diverse voltage levels and frequencies.

Power electronics controls the flow and conversion of electrical energy at high power levels using semiconductor switches operated with high efficiency.

M. H. Rashid provides a comprehensive framework for understanding this discipline through five detailed sections. You will explore semiconductor switch characteristics, rectifier technologies, DC-DC and DC-AC conversion, AC-AC control methods, and industrial motor drives.

You can answer these fundamental questions by studying the text:

• How do semiconductor devices operate as lossless switches?
• What mechanisms improve power quality and reduce harmonics?
• How do converters regulate DC and AC voltage levels?
• Which control methods ensure stability in power systems?
• Where are power electronics applied in renewable energy and motor drives?

1. Semiconductor Switches and Characteristics

Power electronics focuses on electronic circuits designed to control the flow and conversion of electrical energy at power levels much higher than individual device ratings. You achieve high efficiency by using circuit elements primarily as lossless switches rather than linear dissipative components. An ideal switch has zero voltage drop when on and carries any current, and blocks all current without voltage drop when off, resulting in zero power dissipation.

Power electronics achieves high efficiency by utilizing semiconductor devices as lossless switches rather than linear dissipative components, obeying Kirchhoff laws and thermal limits.

A commercial 100 W audio amplifier uses transistors to dissipate full power in linear mode, whereas power electronic devices act as switches to handle significantly higher power levels relative to their ratings. A 2N2222A transistor provides a 0.5 W rated power dissipation and a 24 W power handling rating. An MTW20N50 transistor provides a 250 W rated power dissipation and a 10 kW power handling rating. A typical American household loses electric power only a few minutes a year, meaning energy is available 99.999% of the time, setting a high benchmark for converter reliability.

The Efficiency Objective and Switch Matrix

Converters with $m$ inputs and $n$ outputs can be organized as an $m \times n$ switch matrix, including an H-bridge as a $2 \times 2$ switch matrix. A power converter's switch matrix must strictly obey Kirchhoff's voltage and current laws to avoid catastrophic short-circuits or open-circuit arcs. Restricted switches define specific current and voltage direction capabilities, categorized into diodes, BJTs, FETs, IGBTs, SCRs, and GTOs. A switching function $q(t)$ takes binary discrete values of 0 and 1 when a switch is on and off, characterized by duty ratio, frequency, and time delay or phase.

Power Diodes and Thyristors

The power diode functions as a fundamental static switch that automatically permits current flow in one direction and blocks it in the other without requiring a control terminal. Practical silicon diodes exhibit a forward threshold voltage below 1 V, incremental resistance, small leakage current, and reverse recovery characteristics. You find thermal resistance between 0.1 and 1 C/W for stud mounted diodes. Bipolar-type devices suffer from thermal runaway where increased conduction causes more heat at room temperature defined as 25 C.

Manufacturers specify repetitive peak inverse voltage and nonrepetitive peak inverse voltage. You must follow specific engineering checks:

• Evaluate actual circuit currents using calculation, simulation, or measurement.
• Check average, rms, and peak current values against datasheet maximums.
• Select a diode with a voltage rating incorporating an appropriate safety factor.

A safety factor of 1.5 helps calculate the repetitive peak inverse voltage. Snubber circuits use a parallel resistor and capacitor to protect diodes from overvoltage spikes and high dv/dt rates. The thickness of the high-resistivity n-base region with a phosphorus impurity concentration of $10^{14} \text{ cm}^{-3}$ and a thickness of 10s to 100s of mm dictates forward-blocking voltage capabilities. Voltage ratings above 1 kV switch much more slowly than 100 V devices.

Thyristors are bistable switches that latch into conduction upon receiving a gate signal and remain on even after the gate signal is removed through regenerative action. Cathode shorts provide a resistive shunt path with a lumped shunt resistance value measured from gate to cathode of 1 to 15 O. This structure improves the critical rate of rise of off-state voltage and prevents false triggering, though it causes a loss of cathode area of 5 to 20%. Gate turn-off thyristors can be turned off via a negative gate signal with a turn-off gain range of 6 to 15. The gate-commutated thyristor achieves turn-off gate current rate of rise values of 7000 A/ms and a low charge storage time of 1 ms. MOS-controlled thyristors integrate 200,000 cells in newer devices with a total active area of $0.38 \text{ cm}^2$ for devices rated at 1000 V and 75 A.

Transistors and Advanced Devices

Choosing between a BJT and a MOSFET depends on a crossover voltage range of 250 to 1000 V and a crossover frequency range of 20 to 100 kHz. Industrial applications require blocking voltages of 1-2 kV and conduction currents of 200-500 A with switching speeds of 10-100 ns. Switching regulators achieve significantly higher efficiency than linear regulators.

Four circuits taking power from a 24-V dc source to deliver 12-V dc to a 6-ohm resistive load illustrate the difference. A voltage divider achieves 50% efficiency, a Zener regulator achieves 45.5% efficiency, and a switching circuit achieves 96% efficiency. Bipolar junction transistors are susceptible to second breakdown and thermal runaway. You must apply operational rules:

• Keep power dissipation under control.
• Use a controlled rate of change of base current during turn-off.
• Use protective snubber circuitry.
• Position the switching trajectory within the safe operating area boundaries.

The Baker's clamp uses antisaturation diodes with a forward bias voltage of 0.7 V for diodes D2 and D3 to prevent deep saturation and reduce storage time. The power MOSFET operates as a voltage-controlled unipolar device with a vertical channel structure. It achieves a switching frequency limit of 1 MHz, a voltage power rating of 600 V, and a current rating of 40 A. Parasitic capacitances, particularly the gate-to-drain capacitance multiplied by the Miller effect, limit the frequency response and switching speeds.

2. Rectifiers and Power Quality

Line-commutated and force-commutated rectifiers convert AC to DC, requiring advanced PWM topologies and harmonic filters to achieve unity power factor.

Diode and Thyristor Rectifiers

Single-phase full-wave rectifiers achieve double the dc output voltage and significantly higher transformer utilization factors compared to half-wave rectifiers. Half-wave rectifiers suffer from poor transformer utilization factors and direct current components that can saturate transformer cores, restricting their use to small current applications. Full-wave center-tapped and bridge rectifiers eliminate core saturation and improve rectification efficiency. The half-wave variant yields a dc output voltage of 0.318 Vm, a rectification ratio of 40.5%, and a transformer utilization factor of 0.286. Bridge rectifiers reach a dc output voltage of 0.636 Vm, an 81% rectification ratio, and a transformer utilization factor of 0.81.

For power outputs above 15 kW, three-phase star, inter-star, double-star, and bridge rectifiers are employed. Three-phase bridge rectifiers are widely used for high power because their output ripple is low and the ripple frequency is six times the input frequency. This bridge produces a dc output voltage of 2.34 times rms phase voltage and an output ripple voltage of 4.2%.

Inductor-input and capacitor-input DC filters smooth out rectifier output voltage, with inductor-input filters being preferred in high-power applications due to lower current form factors. Large inductors maintain steady output current and reduce ripple voltage dependent on ripple frequency and load resistance. Critical inductance formulas define the minimum inductance required to prevent the current from becoming discontinuous.

Inrush current during initial connection of a rectifier to a supply can be extremely high because filtering capacitors have zero initial charge, requiring careful limiting. The worst case occurs when the rectifier is connected at the supply's maximum voltage. Equivalent resistance from transformer windings and filtering capacitors usually limits this current, but off-line switch-mode supplies omit transformers and require an added inrush resistor.

A single-phase bridge rectifier connected to a 120-V 60-Hz source with an IFSM rating of 150 A for 8.3 ms uses a 1.13-ohm inrush limiting resistor.

You must follow these rules when protecting diode circuits:

• Ensure the Maximum Allowable Surge Current IFSM rating of the employed diodes is higher than the calculated worst-case inrush current.
• Add an inrush resistor in series when transformer resistance is absent to control the surge current.

High-frequency converters demand diodes with fast switching speeds, specifically short reverse and forward recovery times, to prevent excessive ringing and power dissipation. Reverse recovery time is when a conducting diode recovers to a blocking state upon sudden voltage reversal. A long reverse recovery creates a temporary short circuit, large reverse current, and severe ringing. Schottky diodes offer the shortest recovery times but suffer from low reverse breakdown voltage and large leakage current, where 200 V marks the normal upper limit for reverse breakdown voltage.

You should apply these practices for high-frequency diode selection:

• Use Schottky diodes for low-voltage, high-frequency applications due to fast speed and low forward drop.
• Use ultra-fast diodes if Schottky limits of low reverse breakdown voltage or high leakage current apply.
• Select reverse breakdown-voltage ratings 10% to 20% higher than the worst-case expected reverse voltage.

Single-phase and three-phase line-commutated controlled rectifiers use thyristors with variable firing angles to regulate the average load voltage and power flow. Delaying the firing pulse by an angle alpha measured from the natural conduction point controls the load voltage. When firing angles exceed 90 degrees, average dc voltage becomes negative, allowing the converter to operate in the inverting mode and feed power back to the supply.

Line inductance prevents instantaneous current commutation between thyristors, causing a commutation overlap angle during which all involved thyristors conduct simultaneously. During the commutation interval, source inductance causes the line current to change gradually, which reduces the average load voltage. Both an increase in line inductance or load current increases the commutation angle.

You must apply these steps for controlled thyristors:

• Delay the firing pulse by angle alpha from the zero crossing point of the supply voltage to control the average load voltage.
• Ensure the extinction angle satisfies safety limits to prevent commutation failure and destructive currents.
• Calculate the commutation angle using line inductance, supply peak voltage, and load current values.
• Verify that the extinction angle exceeds the product of supply frequency and thyristor turn-off time to avoid commutation failure.

Harmonic Reduction and PWM Rectifiers

Nonsinusoidal input currents in classic line-commutated rectifiers generate severe harmonic distortion, which degrades the power factor and causes transformer and conductor overloads. Phase-controlled and capacitive-filtered rectifiers draw non-linear, highly distorted input currents rich in harmonics. This results in poor power factor and violates international standards unless active correction or filtering is employed. A single-phase rectifier with a capacitive filter exhibits a total harmonic distortion of current THDi equal to 197% and a very low power factor of 0.45.

The single-phase boost rectifier uses active transistor switching and inductor control to shape the input current into a sinusoid that is in phase with the source voltage, achieving unity power factor.

By operating a boost switch with hysteresis or PWM control, the input current follows a sinusoidal reference. The output dc voltage must exceed the peak source voltage to maintain continuous control over the inductor current and eliminate low-order harmonics. A single-phase boost rectifier achieves a total harmonic distortion of 4.96% and a power factor of 0.99, easily complying with international harmonic standards.

You should configure boost rectifiers carefully:

• Measure input current harmonics and compare against standard limits like IEC 1000-3-2 Class D.
• Incorporate active power factor correction topologies for equipment drawing active power under 600 W.
• Set the output dc voltage to be at least 10% higher than the peak value of the source voltage.
• Employ a proportional-integral voltage controller combined with a current hysteresis controller to shape the inductor current reference.

3. DC-DC and DC-AC Power Conversion

DC-DC converters step voltage levels up or down using PWM and soft-switching, while inverters synthesize AC outputs via sinusoidal pulsewidth modulation and space vector techniques.

DC-DC Converters and Luo-Converters

The step-down buck converter steps a dc input voltage down to a lower average output voltage using a controlled switch, diode, filter inductor, and filter capacitor. In continuous conduction mode, the inductor current never falls to zero during the switching cycle. The dc voltage transfer function equals the duty ratio D, meaning the output voltage is proportional to the duty ratio and smaller than the input voltage.

You can use transformer versions of buck converters to gain galvanic isolation and high-frequency operation. Isolated topologies include the forward converter, push-pull converter, half-bridge converter, and full-bridge converter.

The step-up boost converter increases input voltage but requires a larger filter capacitor due to discontinuous output current. Fang Lin Luo developed nine series of converters using the voltage-lift technique to overcome parasitic element effects and increase voltage-transfer gain.

Using these circuits, you can convert a 24-V input source-voltage into a 1000-V output load-voltage, which has been applied in insulation testing.

Inverters and Soft-Switching Topologies

Single-phase half-bridge voltage source inverters use sinusoidal pulsewidth modulation to synthesize ac output voltages from a split dc voltage link. The sinusoidal pulsewidth modulation compares a modulating sinusoidal signal against a high-frequency triangular carrier. Full-bridge voltage source inverters double the output voltage range and can use unipolar PWM to shift harmonics to higher frequencies.

Space-vector modulation approximates the reference line-voltage vector using adjacent non-zero space vectors and zero vectors during each sampling period. Voltage-source inverters can operate in a regenerative mode where power flows from the ac load back to the dc bus.

Electrical shovels in mining companies have repetitive working cycles where 15 percent of the energy is sent back into the dc bus.

Soft-switched converters utilize resonance in a controlled manner just before and during turn-on and turn-off processes to create zero-voltage or zero-current switching conditions. This eliminates transient spikes and reduces switching losses, enabling operation at very high frequencies from 500 kHz to several megahertz.

Resonant dc link inverters create periodic zero-voltage instants by forcing the dc link voltage to oscillate at high frequency, enabling zero-voltage switching.

A 50-kVA drive system achieved an operating frequency in the range of 60 to 100 kHz with an energy efficiency of 97 percent using an active-clamped resonant link inverter.

4. AC-AC Converters and Control Methods

AC-AC controllers, cycloconverters, and matrix converters adjust voltages and frequencies directly, while state-space averaging, sliding-mode control, and AI techniques govern converter stability.

AC-AC Converters and Controllers

AC voltage controllers vary the root-mean-square voltage across a load at constant frequency using phase control under natural commutation or on-off control under forced commutation. Phase control utilizes inverse-parallel SCRs or Triacs where the firing angle determines the power flow by conducting load current for a chosen period of each input voltage cycle. Integral cycle control turns switches on for a number of integral cycles and off for others, eliminating radio frequency interference but risking subharmonic generation.

Grid-controlled mercury-arc rectifiers were installed in Germany in the 1930s to obtain a 16 2/3-Hz single-phase supply for ac series traction motors from a three-phase 50-Hz system.

Cycloconverters act as direct ac-ac frequency changers with bidirectional power flow, synthesizing lower frequency output waveforms from higher frequency ac supplies without intermediate dc links. Naturally commutated cycloconverters use SCRs and operate via phase modulation of firing angles. They are limited to an output frequency that is a fraction of the input frequency to avoid subharmonics, and suffer from poor input displacement and power factor at low output voltages.

Matrix converters provide direct three-phase to three-phase power conversion using nine bidirectional switches, achieving sinusoidal input and output waveforms with controllable input power factor. As an evolution of force-commutated cycloconverters, matrix converters eliminate the need for dc link reactive components, allowing compact designs and bidirectional power flow. However, they are restricted by an inherent voltage transfer ratio limit of 0.866, complex control strategies, and the requirement that switches must never short-circuit the supply lines or open-circuit inductive loads.

Advanced Control Systems

State-space averaging and linearization provide an analytical foundation for applying linear control techniques to power converters. By combining switched state-space equations across conduction subintervals and assuming small ripples and slow variations, a continuous time-invariant state-space averaged model is derived. The approximation is valid when the maximum absolute eigenvalue magnitude multiplied by the switching period is much less than one.

Sliding-mode control of variable structure systems forces state trajectories to slide along a prescribed state-space trajectory, yielding inherent robustness and system order reduction. By exploiting the natural on-off switching of power semiconductors, the control action acts like a just-in-time management paradigm. The system order is reduced by the number of independent restrictions imposed by the sliding surface, transforming the control problem into a first-order problem based on the time derivative of the sliding surface.

Fuzzy logic controllers use heuristic human knowledge and linguistic variables to control power converters without requiring exact mathematical models. Fuzzy logic controllers consist of fuzzification, a rule base, an inference engine using min-max operators, and defuzzification via methods like center of area. You can apply these rules for tuning:

• Define input variables such as output error and error change, and output variables like duty cycle or reference current.
• Perform fuzzification by converting crisp inputs into linguistic values using membership functions.
• Apply linguistic control rules through a min-max inference engine.
• Convert the resulting fuzzy set into a crisp control action using the center of area defuzzification method.

5. Industrial Applications and Motor Drives

Power electronics optimizes industrial motor drives, renewable energy sources, HVDC transmission, automotive power architectures, and power quality conditioning.

Motor Drives and Control

Electric variable-speed drive systems optimize industrial processes and yield substantial energy savings in centrifugal applications. Affinity laws for centrifugal fans and pumps make input power proportional to the cube of motor speed. You can achieve dramatic energy reductions at lower flow volumes.

The payback period for a 50 kW fan or pump VSD operating 2000 hours per year is estimated at 1.9 years at 75% speed and 1.23 years at 50% speed. Equipment cost reaches 5.5 thousand pounds at a power cost of 0.05 pounds per kilowatt.

Nonsinusoidal waveforms generated by fast switching devices cause increased motor losses, insulation stress, and supply pollution. A 6-pulse bridge generates 5th and 7th harmonic orders at levels of 63% and 52%.

PWM VSI drives generate high voltage rise rates that cause severe electrical stress and premature motor insulation failure. High dV/dt values lead to partial discharges in motor winding voids and voltage doubling effects when you use long cables. You can employ specific techniques to reduce these effects:

• Output Line Reactor: increases rise time but may increase overshoot duration if cable is too long.
• Sine-Wave Filter: filters carrier frequency for sinusoidal output, best for standard/old motors.
• PWM (dV/dt) Filter: reduces dV/dt to safe levels for custom high-performance drives.
• RC Filter at Motor Terminals: capacitor acts as short circuit for high-frequency components.
• Common-Mode Reactor: reduces peak value of leakage current.

Renewable Energy, HVDC, and Automotive Systems

High-voltage direct current transmission provides economic and technical advantages over AC for bulk power transfer over long distances. The breakeven distance for overhead AC versus DC transmission lines ranges from 500 to 800 km. For cable transmission systems, the breakeven distance is 50 km.

Automotive systems require robust power electronics to manage severe environmental conditions and complex loads. Conventional Lundell alternator efficiency ranges from 40% to 60%, and power capability is limited to 3 kW by mechanical stress limits. Multiplexed remote switching architectures significantly reduce weight and complexity in automotive harnesses compared to point-to-point wiring.

A 1994 C-class Mercedes Benz using point-to-point wiring has about 1,000 wires totaling 2 km in length, over 300 connectors, and weighs 36 kg.

Conclusion

Power electronics integrates semiconductor physics, circuit topologies, and digital control algorithms into a single discipline. You must coordinate device switching dynamics, thermal management, and modulation strategies to achieve high energy efficiency.

1. Select semiconductor devices that match your voltage, current, and frequency requirements while respecting thermal limits.
2. Implement pulsewidth modulation and closed-loop control to minimize harmonic distortion and maintain stability.
3. Apply appropriate filtering and soft-switching techniques to reduce electromagnetic interference and switching losses.
4. Design robust thermal and mechanical packaging to ensure long-term reliability under harsh operating conditions.

10 Key Ideas

1. Power electronics achieves high efficiency by utilizing semiconductor devices as lossless switches rather than linear dissipative components, obeying Kirchhoff laws and thermal limits.
2. Line-commutated and force-commutated rectifiers convert AC to DC, requiring advanced PWM topologies and harmonic filters to achieve unity power factor.
3. The single-phase boost rectifier uses active transistor switching and inductor control to shape the input current into a sinusoid that is in phase with the source voltage, achieving unity power factor.
4. DC-DC converters step voltage levels up or down using PWM and soft-switching, while inverters synthesize AC outputs via sinusoidal pulsewidth modulation and space vector techniques.
5. AC-AC controllers, cycloconverters, and matrix converters adjust voltages and frequencies directly, while state-space averaging, sliding-mode control, and AI techniques govern converter stability.
6. Fuzzy logic controllers use heuristic human knowledge and linguistic variables to control power converters without requiring exact mathematical models.
7. Power electronics optimizes industrial motor drives, renewable energy sources, HVDC transmission, automotive power architectures, and power quality conditioning.
8. Affinity laws for centrifugal fans and pumps make input power proportional to the cube of motor speed, allowing you to achieve dramatic energy reductions at lower flow volumes.
9. High-voltage direct current transmission provides economic and technical advantages over AC for bulk power transfer over long distances, with overhead breakeven distances ranging from 500 to 800 km.
10. Multiplexed remote switching architectures significantly reduce weight and complexity in automotive harnesses compared to point-to-point wiring, eliminating thousands of meters of cables and hundreds of connectors.