Power electronics

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This article in its original form was written by Bimal K. Bose (University of Tennessee, Knoxville) in 2014.

Introduction

This article gives a brief historical review of the evolution of power electronics over the past 100-plus years. It includes electrical machines, mercury-arc rectifiers, gas tube electronics, MAs, power semiconductor devices, converter circuits, and motor drives. Wherever possible it gives the name of the inventor and the year of invention for important technologies. It is important to note, however, that inventions are generally developed by a number of contributors working over a period of time. The history of power electronics is so vast that it is impossible to review it within a few pages. More information is available in the references.

Power electronics is a technology that deals with the conversion and control of electrical power with high-efficiency switching mode electronic devices for a wide range of applications. These include as dc and ac power supplies, electrochemical processes, heating and lighting control, electronic welding, power line volt–ampere reactive (VAR) and harmonic compensators, high-voltage dc (HVdc) systems, flexible ac transmission systems, photovoltaic and fuel cell power conversion, high-frequency (HF) heating, and motor drives. We can define the 21st century as the golden age of power electronics applications after the technology evolution stabilized in the latter part of the past century with major innovations.

Power electronics is ushering in a new kind of industrial revolution because of its important role in energy conservation, renewable energy systems, bulk utility energy storage, and electric and hybrid vehicles, in addition to its traditional roles in industrial automation and high-efficiency energy systems. It has emerged as the high-tech frontier in power engineering. From current trends, it is evident that power electronics will play a significant role in solving our climate change (or global warming) problems, which are so important.

Power electronics has recently emerged as a complex and multidisciplinary technology after the last several decades of technology evolution made possible by the relentless efforts of so many university scientists and engineers in the industry. The technology embraces the areas of power semiconductor devices, converter circuits, electrical machines, drives, advanced control techniques, computer-aided design and simulation, digital signal processors (DSPs), and field-programmable gate arrays (FPGAs), as well as artificial intelligence (AI) techniques.

The history of power electronics goes back more than 100 years. It began at the dawn of the 20th century with the invention of the mercury-arc rectifier[1] by the American inventor Peter Cooper Hewitt, beginning what is called the “classical era” of power electronics. However, even before the classical era started, many power conversion and control functions were possible using rotating electrical machines, which have a longer history.

Electrical Machines

The advent of electrical machines[2] in the 19th century and the commercial availability of electrical power around the same time began the so-called electrical revolution. This followed the industrial revolution in the 18th century, The commercial wound-rotor induction motor (WRIM) was invented by Nikola Tesla in 1888 using the rotating magnetic field with polyphase stator winding that was invented by Italian scientist Galileo Ferraris in 1885. The cage-type induction motor (IM) was invented by German engineer Mikhail Dolivo-Dobrovolsky in 1889. The history of dc and synchronous machines is older. Although Michael Faraday introduced the dc disk generator (1831), a dc motor was patented by the American inventor Thomas Davenport (1837) and was commercially used from 1892. Polyphase alternators were commercially available around 1891. The concept of a switched reluctance machine (SRM) was known in Europe in the early 1830s, but as it was an electronic machine, the idea did not go far until the advent of self-commutated devices in the 1980s.

The duality of the motoring and generating functions of a machine was well known after its invention. The commercial dc and ac power generation and distribution were promoted after the invention of machines. For example, dc distribution was set up in New York City in 1882 mainly for street car dc motor drives and the incandescent carbon filament lamps (1879) developed by Thomas Edison. However, ac transmission at a higher voltage and longer distance was promoted by Nikola Tesla and was first erected between Buffalo and New York by Westinghouse Electric Corporation (1886). Those were the exciting days in the history of the electrical revolution.

Although rotating machines could be used for power conversion in the pre-power electronics era (the late 19th century), they were heavy, noisy, and the efficiency was poor. A dc generator coupled to a synchronous motor (SM) or an IM could convert ac to dc power, where dc voltage could be varied by controlling the generator field current. Similarly, a dc motor could be coupled to an alternator to convert dc to ac power, where the output frequency and voltage could be varied by motor speed variation with field current and alternator dc excitation, respectively. The ac-ac power conversion at a constant frequency and variable voltage was possible by coupling an alternator with an IM or an SM, where the alternator dc excitation was varied. Generating the variable-frequency supply required for ac motor speed control was not easy in the early days.

How could you control the speed of the dc and ac motors that were so important for the processing industries? Controlling the speed of a dc motor was somewhat straightforward and was done by varying the supply voltage and motor field current. However, ac motors were generally used for constant-speed applications. The historic Ward Leonard method of dc motor speed control was introduced in 1891 for industrial applications. In this scheme, the variable dc voltage for the motor was generated by an IM dc generator set by controlling the generator field current. In the constant-torque region, the dc voltage was controlled at a constant motor field current, whereas the motor field current was weakened at higher speed in the constant-power region. The four-quadrant speed control was easily possible by reversing the dc supply voltage and motor field current. The speed control of the ac motor was more difficult help of power electronics.

For a wound rotor IM (WRIM), the rotor winding terminals could be brought out by the slip rings and brushes, and an external rheostat could control the speed, although efficiency is very poor in such a scheme. Changing the number of stator poles is the simple principle for ac motor speed control, but the complexity and discrete steps of speed control could not favor this scheme. German inventors introduced two methods of WRIM speed control with slip energy recovery by the cascaded connection of machines, which are known as the Kramer drive (1906) and the Scherbius drive (1907). In the former method, the slip energy (at slip frequency) drives a rotary converter that converts ac to dc and drives a dc motor mounted on the WRIM shaft. The feedback of the slip energy on the drive shaft improves the system efficiency. In the Scherbius drive, the slip energy drives an ac commutator motor, and an alternator coupled to its shaft recovers the slip energy and feeds back to the supply mains. Both systems were very expensive. Both the Kramer and Scherbius drives are extensively used today, but the auxiliary machines are replaced by power electronics. For completeness, the Schrage motor drive (1914) invented in Germany, which replaces all the auxiliary machines at the cost of complexity of motor construction, should be mentioned. It is basically an inside-out WRIM with an auxiliary rotor winding with commutators and brushes that inject voltage on the secondary stator winding to control the motor speed.

Power Electronics in the Classical Era: Mercury-Arc Rectifiers

The history of power electronics began with the invention of the glass-bulb pool-cathode mercury-arc rectifier[1] by the American inventor Peter Cooper Hewitt in 1902. While experimenting with the mercury vapor lamp, which he patented in 1901, he found that current flows in one direction only, from anode to cathode, thus giving rectifying action. Multi-anode tubes with a single pool cathode could be built to provide single and multiphase, half-wave, diode rectifier operation with the appropriate connection of transformers on the ac side. The limited amount of dc voltage control was possible by tap-changing transformers. The rectifiers found immediate applications in battery charging and electrochemical processes such as Al reduction, electroplating, and chemical gas production. The first dc distribution line (1905) with the mercury-arc rectifiers was constructed in Schenectady, New York, and used for lighting incandescent lamps. Hewitt later modified glass bulbs with steel tanks (1909) for higher power and improved reliability with water cooling that further promoted the rectifier applications. The introduction of grid control by Irving Langmuir (1914) in mercury-arc rectifiers ushered in a new era that further boosted their applications. The rectifier circuit could also be operated as a line-commutated inverter by retarding the firing angle. Photo of Mercury arc rectifier

Most phase-controlled thyristor converter circuits used today were born in this classical era of power electronics evolution. In 1930 the New York City subway installed a 3,000-kW grid-controlled rectifier for traction dc motor drives. In 1931, German railways introduced mercury-arc cycloconverters (CCVs) that converted three-phase 50 Hz to single-phase 16 2/3 Hz for universal motor traction drives.

Joseph Slepian of Westinghouse invented the ignitron tube in 1933. It is a single-anode, pool-cathode metal-case gas tube, where an igniter with phase control initiates the conduction. The ignitron tube could be designed to handle high power at high voltage. The single-anode structure of the ignitron tube permitted inverse-parallel operation for ac voltage control for applications such as welding and heating control as well as bridge converter configurations popular in railway and steel mill dc drives, and SM speed control, which has used dc-link load-commutated inverters (LCI) late 1930s.

Ignitron converters were also used in HVdc transmission systems in the 1950s until high-power thyristor converters replaced them in the 1970s. The first HVdc transmission system was installed in Gotland, Sweden, in 1954. The diode bridge converter configurations (known as Graetz circuits) were invented much earlier (1897) by the German physicist Leo Graetz using electrolytic rectifiers.

Power Electronics in the Classical Era: Hot-Cathode Gas Tube Rectifiers

The thyratron, or hot-cathode glass bulb gas tube rectifier, was invented by GE (1926) for low-to-medium power applications. Functionally, it is similar to a grid-controlled mercury-arc tube. Instead of a pool cathode, the thyratron tube used a dry cathode thermionic emission heated by a filament similar to a vacuum triode, which was widely used in those days.

The tube was filled with mercury vapor; the ionization of this vapor decreased the anode-to-cathode conduction drop (for higher efficiency), which was lower than that of mercury-arc tube. The grid bias with phase-shift controlled conduction is similar to the pool cathode tube. The modern thyristor or silicon-controlled rectifier (SCR), which is functionally similar, derives its name from the thyratron. The diode version of the thyratron was known as the phanotron. One interesting application of the phanotron was in the Kramer drive, where the phanotron bridge replaced the rotary converter (1938) for slip power rectification. Thyratrons were popular for commercial dc motor drives, where the power requirement was low. Ernst F. W. Alexanderson, the famous engineer at GE Corporate Research and Development (GE-CRD) in Schenectady, installed a thyratron CCV drive in 1934 for a wound-field SM (WFSM) drive (400 hp) for speed control of induced draft fans in the Logan power station. This was the first variable-frequency ac installation in history.

Power Electronics in the Classical Era: Magnetic Amplifiers

Functionally, a magnetic amplifier (MA) is similar to a mercury-arc or thyratron rectifier. Today it uses a high-permeability saturable reactor magnetic core with materials such as Permalloy, Supermalloy, Deltamax, and Supermendur. A control winding with dc current resets the core flux, whereas the power winding sets the core flux to saturate at a “firing angle” and apply power to the load. The phase-controlled ac power could be converted to variable dc with the help of a diode rectifier. In the early days, MAs used copper oxide (1930) and selenium rectifiers (1940) until germanium and silicon rectifiers became available in the 1950s. Copper oxide and selenium rectifiers were bulky leakage current. The traditional MAs used series or parallel circuit configuration. The advantages of MAs are their ruggedness and reliability, but the disadvantages are their increased size and weight. Germany was the leader in MA technology and applied it extensively in military technologies during World War II, such as in naval ship gun control and V-2 rocket control.[3]

Alexanderson was, however, the pioneer in MA applications. He applied MA to radio-frequency telephony (1912), where he designed an HF alternator and used MAs to modulate the power for radio telephony. In 1916, he designed a 70-kW HF alternator (up to 100 kHz) at GE-CRD to establish a radio link with Europe. Even today, MAs are used to control the lights of the GE logo on top of Building 37 in Schenectady, where Alexanderson used to work. The MA dc motor drives were competitors of the thyratron dc drives and popular for use in adverse environments.

Robert Ramey invented the fast half-cycle response MA in 1951, which found extensive applications particularly in low-power dc motor speed control, servo amplifiers, logic and timer circuits, oscillators (such as the Royer oscillator), and telemetry encoding circuits. Copper oxide and selenium applications for signal processing proved extremely important when modern semiconductor-based control electronics was in its infancy.

Power Electronics in the Modern Era: Power Semiconductor Devices

The modern solid-state electronics revolution began with the invention of transistors in 1948 by Bardeen, Brattain, and Shockley of Bell Laboratories. While Bardeen and Brattain invented the point contact transistor, Shockley invented the junction transistor. Although solid-state electronics originally started with Ge, it gradually transformed using with Si as its base. The modern solid-state power electronics revolution[4][5][6][7] (often called the second electronics revolution) started with the invention of the p-n-p-n Si transistor in 1956 by Moll, Tanenbaum, Goldey, and Holonyak at Bell Laboratories, and GE introduced the thyristor (or SCR) to the commercial market in 1958. Thyristors reigned supreme for two decades (1960–1980), even with the present popularity for high-power LCI drive applications.

The word thyristor comes from the word "thyratron" because of the analogy of operation. Power diodes, both germanium and silicon, became available in the mid-1950s. Starting originally with the phase-controlled thyristor, gradually other power devices emerged. The integrated antiparallel thyristor (TRIAC) was invented by GE in 1958 for ac power control. The gate turn-off thyristor (GTO) was invented by GE in 1958, but in the 1980s several Japanese companies introduced high-power GTOs. Bipolar junction transistors (BJTs) and field-effect transistors were known from the beginning of the solid-state era, but power MOSFETs and bipolar junction transistors (BJTs, used as bipolar power transistors, BPTs) appeared on the market in the late 1970s.

Currently, both GTOs and BPTs are obsolete devices, but power MOSFETs have become universally popular for low-voltage HF applications. The invention of the insulated-gate bipolar transistor (IGBT or IGT) in 1983 by GE-CRD and its commercial introduction in 1985 were significant milestones in the history of power semiconductors. Jayant Baliga was the inventor of the IGBT. However, initially, it had a thyristor-like latching problem and, therefore, was defined as an insulated-gate rectifier. Akio Nakagawa solved this latching problem (1984), and this helped the commercialization of the IGBT.

Today, the IGBT is the most important device for medium-to-high power applications. Several other devices, including the static induction transistor, the static induction thyristor, the MOS-controlled thyristor (MCT), the injection-enhanced gate transistor, and the MOS turn-off thyristor, were developed in the laboratory in the 1970s and 1980s but did not ultimately see the daylight. Particularly for MCT development, the U.S. government spent a fortune, but it ultimately went to waste. The high-power, integrated gate-commutated thyristor (IGCT) was introduced by ABB in 1997. Currently, it is a competitor to the high-power IGBT, but it is gradually losing the race. Although silicon has been the basic raw material for current power devices, large-bandgap materials, such as SiC, GaN, and ultimately diamond (in synthetic thin-film form), are showing great promise. SiC devices, such as the Schottky barrier diode (1200 V/50 A), the power MOSFET (1200-V/100-A half-bridge module), and the JBS diode (600 V/20 A), are already on the market, and the p-i-n diode (10 kV) and IGBT (15 kV) will be introduced in the future. There are many challenges in researching large-bandgap power devices.

Fortunately, in parallel with the power semiconductor evolution, microelectronics technology was advancing quickly and the corresponding material processing and fabrication techniques, packaging, device characterization, modeling, and simulation techniques contributed to the successful evolution of so many advanced power devices, their higher voltage and current ratings, and the improvement of their performance characteristics. Gradually, microelectronics-based devices, such as microcomputers/DSPs and application-specified integrated circuit (ASIC)/FPGA chips, became the backbone control.

Power Converters

Most of the thyristor phase-controlled line and load-commutated converters, commonly used today, were introduced in the era of classical power electronics. The disadvantages of line-side phase control are a lagging displacement power factor (DPF) and lower-order line harmonics. The IEEE regulated harmonics with Standard IEEE-519 (1981), whereas Europe adopted the IEC-61000 standard, which was introduced in the 1990s. The current-fed dc link converters became very popular for multi-MW WFSM drives from the 1980s. The initial start-up method of the motor (building sufficient CEMF for load commutation) by the dc-link current interruption method was proposed by Rolf Müller et al. of Papst-Motoren (1979) and is popular even today. For a lagging DPF load (such as IM), the inverter required forced commutation. The auto-sequential current inverter (ASCI) using forced commutation was proposed by Kenneth Phillips of Louis Allis Co. in 1971. This topology became obsolete with the advent of modern self-commutated devices. The thyristor phase-controlled CCVs (with line commutation), were very popular from 1960 until 1995, when multilevel converters made them obsolete. The traditional CCVs used the blocking method, but Toshiba introduced the circulating current method in the 1980s to control the line DPF. The dual converter for a four-quadrant dc motor drive was popular long before that.

The advent of thyristors initiated the evolution of the dc-link voltage-fed class of thyristor inverters for general industrial applications,[8][9][10][11][12][13] particularly for IM drives. The voltage-fed converter topology is the most popular today and will possibly become universal in the future. A diode rectifier (Graetz bridge) usually supplies the dc link, and a force-commutated thyristor bridge inverter was the usual configuration. From the 1960s, the era of the thyristor forced commutation techniques started, and William McMurray of GE-CRD was the pioneer in this area. He invented techniques,[14] known as the McMurray inverter (1961), the McMurray-Bedford inverter (1961), ac switched commutation (1980), and so on, which will remain as the most outstanding contributions in the history of power electronics. Self-commutated devices, such as power MOSFETs, BPTs, GTOs, IGBTs, and IGCTs, began appearing in the 1980s and replaced the majority of thyristor inverters.

The voltage-fed inverters (VFIs) originally introduced with square (or six-stepped) wave output had a rich harmonic content. Therefore, the pulse width modulation (PWM) technique was used to control the harmonics as well as the output voltage. Fred Turnbull of GE-CRD invented the selected harmonic elimination PWM in 1963, which was later generalized by H. S. Patel and Richard Hoft of GE-CRD (1973) and optimized by Giovanni Indri and Giuseppe Buja of the University of Padua (1977). However, the sinusoidal PWM technique, invented by Arnold Schonung and Herbert Stemmler of Brown Boveri (1964), found widespread applications. Since motor drives mostly required current control, Allen Plunkett of GE-CRD developed the hysteresis-band (HB) sinusoidal current control in 1979. This was improved to the adaptive HB method by Bimal Bose (1989) to reduce the harmonic content. The space vector PWM (SVM) technique for isolated neutral load, based on the space vector theory of machines, was invented by Gerhard Pfaff, Alois Weschta, and Albert Wick in 1982. The SVM, although very complex, is now widely used. The front-end diode rectifier was gradually replaced by the PWM rectifier (the same as inverter topology), which allowed for four-quadrant drive capability and sinusoidal line current at any desired DPF. High-power GTO converters could be operated in multistepped mode because of the low switching frequency. The PWM rectifier operation modes allowed for the introduction of the static VAR compensator. Current-fed self-commutated GTO converters for high-power applications that required a capacitor bank on ac side were introduced in the 1980s. The performance of this type of dc-link dual PWM converter system is similar to that of the voltage-fed converter system.

A class of ac-ac converters, called matrix converters or direct PWM frequency converters, was introduced by Marco G. B. Venturini (they are often called Venturini converters) in 1980 using inverse-parallel ac switches. My invention, an inverse-series transistor ac switch (1973), is now universally used in matrix converters. This converter topology has received a lot of attention in the literature, but so far, there have been very few industrial applications. Soft-switched dc-ac power conversion for ac motor drives was proposed by Deepakraj Divan of the University of Wisconsin (1985) and subsequent researchers, but hardly saw any daylight. However, soft-switched, HF link, power conversion has been popular for use in low-power dc-dc converters since the early 1980s.

For high-voltage, high-power voltage-fed converter applications, Akira Nabae et al. at Nagaoka University of Technology invented the neutral-point clamped (NPC) multilevel converter in 1980 that found widespread applications in the 1990s and recently ousted the traditional thyristor CCVs. Gradually, the number of levels of the converter increased, and other types, such as the cascaded H-bridge or half-bridge and flying capacitor types, were introduced. Currently, the NPC topology is the one most commonly used.

Motor Drives

The area of motor drives[15][16][17] is intimately related with power electronics, and it followed the evolution of devices and converters along with the PWM, computer simulation, and DSP techniques. The WRIM slip power control and load-commutated WFSM drives, introduced early in the classical era, have been discussed previously. Historically, however, ac machines were popular in constant-speed applications. During the thyristor age from the 1960s through the 1980s, variable-speed ac drives technology advanced at a rapid rate. Early in the thyristor age, variable-voltage constant-frequency IM drives were introduced using three-phase, anti-parallel thyristor, voltage controllers, and Derek Paice (1964) of Westinghouse was the pioneer in this area.

The so-called Nola speed controller proposed by NASA in the late 1970s is essentially the same type of drive. However, it has the disadvantages of loss of torque at low voltage, poor efficiency, and line and load harmonics. The solid-state IM starter often uses this technique. The introduction of the McMurray inverter and the McMurray-Bedford inverter using thyristors essentially started the revolution for variable-frequency motor drives. With a variable-frequency, variable-voltage, sinusoidal power supply from a dc-link voltage source PWM inverter, rated machine torque was always available and the machine had no harmonic problems. The dc link voltage could be generated from the line either with a diode or a PWM rectifier. This simple open-loop volts/hertz control technique became extremely popular and is commonly used today. To prevent the speed and flux drift of open-loop volts/hertz control and improve the stability problem, closed-loop speed control with slip and flux regulation was used in the 1970s and early 1980s. Current-fed thyristor and GTO converters for IM drives were promoted during the same period. The advent of modern self-commutated devices considerably improved the performance of VFI drives.

The introduction of vector or field-oriented control brought a renaissance in the history of high-performance ac drives. Karl Hasse at the Technical Universit of Darmstadt (1969) introduced the indirect vector control, whereas the direct vector control was introduced by Felix Blaschke of Siemens (1972). The vector control and estimation depended on synchronous reference frame, de – qe, and stationary reference frame, ds – qs, dynamic models of the machine. The de – qe model was originally introduced by Park (1929) for synchronous machines and was later extended to IM by Gabriel Kron of GE-CRD, whereas the ds – qs model of IM was introduced by H. C. Stanley (1938). Because of the control complexity, vector control has been applied in industry since the 1980s in microcomputer/DSP control.

After Intel invented the microcomputer in 1971, the technology started advancing dramatically with the introduction of the TMS320 family in the 1980s by Texas Instruments. Recently, the powerful ASICs/FPGAs along with DSPs are almost universal in the control of power electronics systems. In 1985, Isao Takahashi of Nagaoka University of Technology invented an advanced scalar control technique called direct torque control or direct torque and flux control, which was to some extent close to vector control in performance. Gradually, other advanced control techniques, such as model-referencing adaptive control, sensorless vector control, and model predictive control, emerged. Currently, AI techniques, particularly fuzzy and artificial neural networks, are advancing the frontier of power electronics. Most control techniques developed for IM drives were also applicable to SM drives. However, the interest in SRM drives is fading after the surge of literature during the 1980s and 1990s.

References

  1. 1.0 1.1 C. C. Harskind and M. M. Morack Eds., A History of Mercury-Arc Rectifiers in North America (Piscataway, NJ: IEEE Press, 1987)
  2. E. L. Owen, “Power Electronics and Rotating Machines—Past, Present and Future,” in Proc. Power Electronics Specialists Conf., June 1984, p. 3–11
  3. T. J. Wilson, “The Evolution of Power Electronics,” in Proc. Int. Symp. Industrial Electronics, Xian, China, May 1992, vol. 1, p. 1–9.
  4. B. K. Bose, “Power Electronics—an Emerging Technology,” IEEE Trans. Industrial Electronics 36, no. 3, p. 403–412, Aug. 1989.
  5. B. K. Bose, “The Past, Present and Future of power electronics,” IEEE Industrial Electron. Magazine 3, no. 2, p. 7–14, 2009.
  6. B. K. Bose, “Power Electronics and Motor Drives—Recent Progress and Perspective,” IEEE Trans. Industrial Electronics 56, no. 2, p. 581–588, Feb. 2009.
  7. W. McMurray, “Power Electronics in the 1990s,” in Proc. IEEE Industrial Electronics Society Conf. Record, 1990, p. 839–843.
  8. B. K. Bose, ed., Adjustable Speed AC Drive Systems (New York, NY: IEEE Press, 1981).
  9. B. K. Bose, Modern Power Electronics and AC Drives (Upper Saddle River, NJ: Prentice-Hall, 2001).
  10. B. K. Bose, Power Electronics and Motor Drives—Advances and Trends (Burlington, MA: Academic Press, 2006).
  11. B. K. Bose, “Power Electronics—A Technology Review,” Proc. IEEE 80, no. 8, p. 1301–1334, Aug. 1992.
  12. B. K. Bose, “Power Electronics and Motion Control Technology: Status and Recent Trends,” IEEE Trans. Industrial Applications 29, Oct. 1993.
  13. B. K. Bose, “Global Energy Scenario and Impact of Power Electronics in 21st century,” IEEE Trans. Industrial Electronics 60, no. 7, p. 2638–2651, July 2013.
  14. B. D. Bedford and R. G. Hoft, Principles of Inverter Circuits (New York: Wiley, 1964).
  15. T. M. Jahns and E. L. Owen, “AC adjustable-speed drives at the millennium: How did we get here?” IEEE Trans. Power Electronics 16, no. 1, p. 17–25, Jan. 2001.
  16. E. L. Owen, M. M. Morack, and C. C. Herskind, “AC Adjustable Speed Drives with Electronic Power Converters—the Early Days,” IEEE Trans. Industrial Applications 20, no. 2, pp. 298–308, Mar./Apr. 1984.
  17. A. O. Staub and E. L. Owen, “Solid-state Motor Controllers,” IEEE Trans. Industrial Applications 22, no. 6, pp. 1113–1120, Nov./Dec. 1986.

Acknowledgments

The author would like to thank Thomas Lipo of the University of Wisconsin, Madison; Giuseppe Buja of University of Padova, Italy; and Barry Brusso of S&C Electric Company, United States, for their help in writing this article.

Further Reading