© 2002 by CRC Press LLC

7

Modulation Strategies

7.1 Introduction
7.2 Six-Step Modulation
7.3 Pulse Width Modulation

PWM Signals with DC Average • PWM Signals for
AC Output

7.4 Third Harmonic Injection for Voltage Boost
of SPWM Signals
7.5 Generation of PWM Signals Using Microcontrollers
and DSPs
7.6 Voltage Source–Based Current Regulation
7.7 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

Texas A&M University

Tahmid Ur Rahman

Texas A&M University

© 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
2

3
=

8 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

The advantages of six-step modulation are the simplicity of the procedure and the ability to use slow-
switching, 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 1 in six step sequence. (b) GTO inverter
indicating conducting switches for step 2 in six-step sequence. (c) GTO inverter indicating conducting switches for
step 3 in six-step sequence. (d) GTO inverter indicating conducting switches for step 4 in six-step sequence. (e) GTO
inverter indicating conducting switches for step 5 in six-step sequence. (Continued)

© 2002 by CRC Press LLC

FIGURE 7.1

(Continued.) (f) GTO inverter indicating conducting switches for step 6 in six-step sequence.


vary between 0 and 1 V, a PWM signal with a duty cycle between 0 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.

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.

© 2002 by CRC Press LLC

FIGURE 7.6

Triangular carrier wave for PWM modulation with a duty cycle between 0 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 5% duty cycle.

FIGURE 7.10

Spectrum of a PWM signal with 25% duty cycle.

© 2002 by CRC Press LLC

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 mod-
ulated 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.

FIGURE 7.11


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.

FIGURE 7.13

20-kHz carrier modulated with 500 Hz.

FIGURE 7.14

Spectrum of the SPWM signal shown in Fig. 7.13.
1
0.5
0
0.5
1
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
t
ms
SPWM(t)
Sin(t)
20-kHz carrier modulated with 500 Hz

© 2002 by CRC Press LLC

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

Line-to-line signal showing the voltage boost obtained by 3rd harmonic injection.

© 2002 by CRC Press LLC

Reference

1. Mohan, N., Undeland, T., and Robbins, 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 electronics controllers are rapidly moving toward digital implementation. Typical solu-
tions consist of microcontrollers or DSPs. In addition, coprocessors, such as the ADMC200/201 from
Analog Devices, are available that are specifically designed to support inverter control. Most of the
processors, such as the 68HC12B32 from Motorola, that are commonly used to control power electronics
have built-in hardware support for PWM generation. Figure 7.17 shows the basic principle of their digital
PWM generation.
For clarity, the circuit shown in Fig. 7.17 has only 4-bit resolution for the duty cycle of the generated
PWM signals, resulting in only 16 discrete duty cycles. In actual applications, 8 to 12 bits of resolution
is typical. In Fig. 7.17, a digital counter (74163) counts from zero to its maximum value and repeats the
cycle afterward. The count is continuously compared with a digital value representing the duty cycle
using a hardware comparator (7485). The PWM signal is available on the output of the comparator.
Figure 7.18 shows the simulation results from the example circuit shown in Fig. 7.17. The duty cycle in

resolution of the duty cycle is decreased for a given clock speed. It is often important to make the correct
trade-off between the switching frequency and the resolution.
The advantage of hardware support for PWM generation is that the processor typically only needs to
access any registers if the duty cycle is to be changed, since the period is typically only initialized once
upon program start-up. It should also be mentioned that the duty cycle registers are typically “double-
buffered,” meaning that an update of a duty cycle does not need to be synchronized with the current
state of the counter. In double-buffered systems, the new duty cycle will only be chosen once the previous
period is completed to avoid truncated PWM signals. If necessary, a software override can disable this
feature.

7.6 Voltage Source–Based Current Regulation

Michael Giesselmann

In motor drive applications, it is often desired to control directly the input current of the motor to control
the torque. DC control also limits dynamics resulting from the electrical characteristics of the machine.
Controlling the torque provides direct control over the angular acceleration, which is essential for precise
motion control. Current control is typically performed in the innermost loop of a cascaded feedback
control 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
in such a way, that the desired current is obtained. Several methods can be used to achieve this:
• A feedback control loop, typically using a PI controller can be used control the current.
• The necessary voltage can be calculated in real time and applied to the motor.
• The necessary voltage for fast transients can be calculated in real time and applied to the motor
and the residual error can be corrected by a PI controller.
Examples illustrating each of the schemes are described in the following. Figure 7.19 shows an example
of a DC motor in which the current is controlled by adjusting the applied voltage using a PI controller
such that the current follows the desired trajectory. The result is presented in Fig. 7.20, which shows that
the current indeed follows the desired value at all times.
Sometimes even better results and higher loop bandwidth can be obtained if known information about


FIGURE 7.22

Voltage source–based current control using a feedforward approach.
Voltage loop equation
Equivalent Capacitance
Voltage loop equation
V
s

= R
rot
⋅
I
rot
+ L
rot
⋅
− I
rot
+ K
m
⋅
ω
d
dt
V
s

= R

2
1
2
C
eq
=

J
⋅
=
ω
2
E
2
J
K
m
1
C
eq
2

© 2002 by CRC Press LLC

of the motor. An example for this approach is shown in Fig. 7.24. Again, the results are identical to the
ones shown in Fig. 7.20.

Reference

1. Mohan, N.,