7 Modulation Strategies Michael Giesselmann Texas Tech University Hossein Salehfar 7.1 7.2 7.3 PWM Signals with DC Average • PWM Signals for AC Output University of North Dakota Hamid A Toliyat 7.4 Texas A&M University Tahmid Ur Rahman Texas A&M University Introduction Six-Step Modulation Pulse Width Modulation 7.5 7.6 7.7 Third Harmonic Injection for Voltage Boost of SPWM Signals Generation of PWM Signals Using Microcontrollers and DSPs Voltage Source–Based Current Regulation Hysteresis Feedback Control Introduction • Principles of the Hysteresis Feedback Control Circuits • Design Procedure • Experimental Results • Conclusions 7.8 Space-Vector Pulse Width Modulation How the SVPWM Works • Implementation • Switching Signals 7.1 Introduction Michael Giesselmann In this chapter, modulation techniques for power electronics circuits are discussed Modulation techniques are strategies to control the state of switches in these circuits Switch mode is preferred to linear operation since switches ideally not dissipate any power in either the ON or OFF state Depending on the switches that are being used, it may only be possible to control the turn on instants However, most modern power semiconductors such as IGBTs can be turned on and off tens of thousands of times per second on command In parallel with the development of these modern power semiconductors, new modulation techniques have emerged In the following sections, a number of modulation techniques along with their advantages and disadvantages will be discussed Most figures have been generated using MathCAD® 2000 [1] The examples for the digital modulation techniques and the voltage source–based current control techniques have been generated using PSpice®[2] References MathCAD® 2000 Professional, MathSoft Engineering & Education, Inc., 101 Main Street, Cambridge, MA 02142-1521, http://www.mathsoft.com PSpice® Documentation, 555 River Oaks Parkway, San Jose, CA 95134, U.S.A.; (408)-943-1234; http://pcb.cadence.com/ © 2002 by CRC Press LLC 7.2 Six-Step Modulation Michael Giesselmann Six-step modulation represents an early technique to control a three-phase inverter Six-step modulation uses a sequence of six switching patterns for the three phase legs of a full-bridge inverter to generate a full cycle of three-phase voltages A switch pair connected between the positive DC bus and the negative DC bus represents a phase leg The output terminal is the midpoint of the two switches Only one switch of a phase leg may be turned on at any given time to prevent a short circuit between the DC buses One state of the inverter leg represents the case when the upper switch is turned on whereas the opposite state is represented by the lower switch being turned on If each phase leg has these two states, the inverter has = possible switching states Six of these states are active states, whereas the two states in which either all of the upper or all of the lower switches are turned on are called zero states, because the line-to-line output voltage is zero in these cases The six discrete switching patterns for six-step modulation are shown in Fig 7.1a to f For clarity, free-wheeling diodes have been omitted After the switching pattern shown in Fig 7.1f, the cycle begins anew with the switching pattern shown in Fig 7.1a Note that in subsequent patterns, only a single inverter leg changes states The switching patterns shown in Fig 7.1a to f represent the following inverter states in the following order: • • • • • • Positive peak of Phase A Negative peak of Phase C Positive peak of Phase B Negative peak of Phase A Positive peak of Phase C Negative peak of Phase B The aforementioned inverter states are equally spaced in a circle with 60° of phase shift between them This is illustrated in Fig 7.2 The hexagon in Fig 7.2 represents the trace of a voltage vector around a circle for six-step modulation This scheme could be extended to space vector modulation, if the voltage vector would not make discrete 60° steps, but would alternate at high speed between two adjacent states The switching control would be such that the average time spend in the previous state is gradually decreasing, whereas the average time spent in the next state is gradually increasing Also by inserting zero states, the magnitude of the output voltage could be controlled Figure 7.3 shows the phase to neutral waveform of one inverter leg for six-step operation if the neutral point is considered the midpoint between the positive and negative bus The resulting line-to-line output voltage is shown in Fig 7.4 This waveform is closer to a sinusoid than the phase to neutral voltage but it still has a considerable amount of harmonics Figure 7.5 shows the spectrum of the line-to-line voltage for six-step operation normalized to the fundamental frequency The lowest harmonic component is the 5th harmonic The advantages of six-step modulation are the simplicity of the procedure and the ability to use slowswitching, high-power devices like GTOs However, the harmonic content of the output voltage and the inability to control the magnitude of the output voltage are serious drawbacks Because of these drawbacks and due to the recent advances in high-power IGBT technology, this modulation scheme is today seldom considered for new designs 7.3 Pulse Width Modulation Michael Giesselmann Pulse width modulation (PWM) is the method of choice to control modern power electronics circuits The basic idea is to control the duty cycle of a switch such that a load sees a controllable average voltage To achieve this, the switching frequency (repetition frequency for the PWM signal) is chosen high enough that the load cannot follow the individual switching events Switching, rather than linear operation of the © 2002 by CRC Press LLC FIGURE 7.1 (a) GTO inverter indicating conducting switches for step in six step sequence (b) GTO inverter indicating conducting switches for step in six-step sequence (c) GTO inverter indicating conducting switches for step in six-step sequence (d) GTO inverter indicating conducting switches for step in six-step sequence (e) GTO inverter indicating conducting switches for step in six-step sequence (Continued) © 2002 by CRC Press LLC GTO3 GTO1 C B A GTO6 (f) FIGURE 7.1 (Continued.) (f) GTO inverter indicating conducting switches for step in six-step sequence FIGURE 7.2 Graphical representation of the vector positions of the inverter states in a circle for six-step modulation FIGURE 7.3 Phase to neutral waveform of the inverter for six-step operation © 2002 by CRC Press LLC FIGURE 7.4 Line-to-line waveform of the inverter for six-step operation FIGURE 7.5 Spectrum of the line-to-line voltage for six-step operation normalized to the fundamental frequency power semiconductors, is of course done to maximize the efficiency because the power dissipation in a switch is ideally zero in both states In a typical case, the switching events are just a “blur” to the load, which reacts only to the average state of the switch PWM Signals with DC Average There are a number of different methods to generate periodic rectangular waveforms with varying duty cycle A standard method is the so-called carrier-based PWM technique, which compares a control signal with a triangular (or sawtooth shaped) waveform Figure 7.6 shows an example of a triangular waveform with 10-kHz repetition (switching) frequency By comparing this signal with a reference level, which can vary between and V, a PWM signal with a duty cycle between and 100% is generated Because of the triangular carrier, the relation between the reference level and the resulting duty cycle is linear Figure 7.7 shows an example where a PWM signal with 80% duty cycle is created This method works very well for duty cycles in the range from 5% up to 95% as shown in Figs 7.8 and 7.9 However, if the reference signal exceeds 100% or falls below 0%, the resulting PWM signal would be always on or always off, respectively This is called overmodulation This regime must be avoided by proper conditioning of the control signal In addition, for control signals resulting in PWM signals with duty cycle values as high as 99% or as low as 1%, the switch may never fully reach the opposite state and spend an undue amount of time in transitions Therefore, it is typically recommended to limit the control signal to a range, which avoids overmodulation as well as extremely narrow pulses © 2002 by CRC Press LLC FIGURE 7.6 Triangular carrier wave for PWM modulation with a duty cycle between and 100% FIGURE 7.7 Triangular carrier wave and PWM signal for 80% duty cycle FIGURE 7.8 Triangular carrier wave and PWM signal for 95% duty cycle © 2002 by CRC Press LLC FIGURE 7.9 FIGURE 7.10 Triangular carrier wave and PWM signal for 5% duty cycle Spectrum of a PWM signal with 25% duty cycle The spectrum of a typical PWM signal with 25% duty cycle with a switching frequency of 10 kHz is shown in Fig 7.10 The DC magnitude of 25% is clearly visible The harmonics are multiples of the carrier frequency The lowest harmonic is located at 10 kHz This spectrum might look dramatic, especially in comparison with Fig 7.5, but the reader should be reminded that, due to the switching speed of modern power semiconductors, the carrier frequency can be chosen sufficiently high that the harmonics can be easily filtered with capacitors and inductors of small size PWM Signals for AC Output In addition to a DC reference signal, any other waveform could be used as the modulation signal as long as the highest frequency of its AC components are at least an order of magnitude less than the frequency of the carrier signal Figure 7.11 shows an example of a carrier waveform, which is symmetrical with respect to the zero level To generate a sinusoidal output voltage for an inverter, which is often desired, this carrier can be modulated with a sinusoidal reference signal An example is shown in Fig 7.12 Note that for clarity, the ratio between the carrier frequency and the frequency of the modulation signal is lower than recommended for actual implementation The resulting sinusoidal PWM (SPWM) voltage drives one phase leg of an inverter If the voltage level is +1, the upper switch is on, and vice versa After filtering out the switching frequency components, the resulting output voltage has the shape and frequency of the modulation signal For the remaining phase legs, the same technique, with reference signals © 2002 by CRC Press LLC FIGURE 7.11 Triangular carrier wave AC modulation FIGURE 7.12 Illustration of the generation of sinusoidal PWM (SPWM) signals that are phase shifted by 120 and 240°, is used The amplitude of the output voltage can be controlled by varying the ratio between the peak of the modulation signal and the peak of the carrier wave If the amplitude of the modulation signal exceeds the amplitude of the carrier, overmodulation occurs and the shape of the fundamental of the output voltage deviates from the modulation signal To appreciate the spectral content of sinusoidal PWM signals, a 20-kHz triangular carrier has been modulated with a 500-Hz sinusoid with an amplitude of 80% of the carrier signal The resulting SPWM signal is shown in Fig 7.13 The spectrum of this PWM signal is shown in Fig 7.14 The fundamental with an amplitude of 0.8 is located at 500 Hz The harmonics are grouped around multiples of the carrier frequency [1] It should be pointed out that this modulation scheme is far superior to the six-step technique described earlier, because the difference between the switching frequency and the fundamental is much larger Therefore, the carrier frequency components can be easily removed with LC filters of small size [2] In addition, the amplitude of the output voltage can be controlled simply by varying the amplitude ratio between the modulation signal and the carrier If six-step modulation is used, the DC bus voltage would have to be controlled in order to control the amplitude of the output voltage © 2002 by CRC Press LLC 20-kHz carrier modulated with 500 Hz 0.5 SPWM(t) Sin(t) 0.5 0.2 0.4 0.6 0.8 t ms FIGURE 7.13 20-kHz carrier modulated with 500 Hz FIGURE 7.14 Spectrum of the SPWM signal shown in Fig 7.13 1.2 1.4 1.6 1.8 References Mohan, N., Undeland, T., and Robbins, W., Power Electronics: Converters, Applications, and Design, 2nd ed., John Wiley & Sons, New York, 1995 Von Jouanne, A., Rendusara, D., Enjeti, P., and Gray, W., Filtering techniques to minimize the effect of long motor leads on PWM inverter fed AC motor drive systems, IEEE Trans Ind Appl., July/Aug., 919–926, 1996 7.4 Third Harmonic Injection for Voltage Boost of SPWM Signals Michael Giesselmann It can be shown (Mohan et al.[1], p 105) that if a three-phase input voltage is rectified using a standard three-phase rectifier, the resulting DC voltage is equal to 1.35 times the rms value of the AC line–line input voltage If this DC voltage is used to feed a three-phase inverter using the SPWM modulation technique described above, the theoretical maximum AC line–line output voltage is only 82.7% of the AC line–line input voltage feeding the rectifier (Mohan et al.[1], p 228) To boost the output voltage without resorting to overmodulation, the third harmonic of the fundamental frequency can be added to the modulation signal Figure 7.15 shows an example, where a third harmonic with an amplitude of 21.1% has been added to the fundamental modulation signal © 2002 by CRC Press LLC FIGURE 7.15 Sinusoidal modulation signal with and without added 3rd harmonic FIGURE 7.16 Line-to-line signal showing the voltage boost obtained by 3rd harmonic injection The amplitude of the fundamental has been increased to 112% in this example It can be seen, that the peak amplitude of the resulting signal does not exceed the amplitude of the pure sinusoid with 100% amplitude By inspection of Fig 7.15 it is easy to see that the voltage–time integral will be higher if a 3rd harmonic is added to the reference signal for the phase to neutral voltage This voltage boost beyond the previously mentioned value of 82.7% is very desirable, to retrofit induction motors with adjustable speed drives in existing installations The 3rd harmonic components exactly cancel each other in the line-to-line voltages of the inverter This is because the phase shift of the fundamental signals is 120° and therefore the phase shift of the 3rd harmonic is × 120 = 360° Therefore, the 3rd harmonic voltages precisely cancel and result in a pure sinusoidal output voltage being applied to the motor This is shown in Fig 7.16, which illustrates the voltage boost that is obtained © 2002 by CRC Press LLC ... loop arrangement [1] However, most power electronics converters are circuits with controllable voltage output To achieve current control, the voltage of the power electronics converter can be controlled... W., Power Electronics: Converters, Applications, and Design, 2nd ed., John Wiley & Sons, New York, 1995 7.5 Generation of PWM Signals Using Microcontrollers and DSPs Michael Giesselmann Modern power. .. compact size, and low cost, switching power supplies continue to gain popularity Switching power supplies could be as high as three times more efficient than linear power supplies and in some cases