Chapter 13 induction motor drives

503

13.1.  INTRODUCTION

The objective of this chapter is to explore the use of induction machines in variable￾speed drive systems. Several strategies will be considered herein. The first, volts-per￾hertz control, is designed to accommodate variable-speed commands by using the

inverter to apply a voltage of correct magnitude and frequency so as to approximately

achieve the commanded speed without the use of speed feedback. The second strategy

is constant slip control. In this control, the drive system is designed so as to accept a

torque command input—and therefore speed control requires and additional feedback

loop. Although this strategy requires the use of a speed sensor, it has been shown to be

highly robust with respect to changes in machine parameters and results in high effi￾ciency of both the machine and inverter. One of the disadvantages of this strategy is

that in closed-loop speed-control situations, the response can be somewhat sluggish.

Another strategy considered is field-oriented control. In this method, nearly instanta￾neous control of torque can be obtained. A disadvantage of this strategy is that in its

direct form, the sensor requirements are significant, and in its indirect form, it is sen￾sitive to parameter measurements unless online parameter estimation or other steps are

Analysis of Electric Machinery and Drive Systems, Third Edition. Paul Krause, Oleg Wasynczuk,

Scott Sudhoff, and Steven Pekarek.

© 2013 Institute of Electrical and Electronics Engineers, Inc. Published 2013 by John Wiley & Sons, Inc.

INDUCTION MOTOR DRIVES

13

504 Induction Motor Drives

taken. Another method of controlling torque, called direct torque control (DTC), is also

described, and its performance illustrated by computer traces. Finally, slip energy

recovery systems, such as those used in modern variable-speed wind turbines, are

described.

13.2.  VOLTS-PER-HERTZ CONTROL

Perhaps the simplest and least expensive induction motor drive strategy is constant

volt-per-hertz control. This is a speed control strategy that is based on two observations.

The first of these is that the torque speed characteristic of an induction machine is

normally quite steep in the neighborhood of synchronous speed, and so the electrical

rotor speed will be near to the electrical frequency. Thus, by controlling the frequency,

one can approximately control the speed. The second observation is based on the a￾phase voltage equation, which may be expressed

v r as = + s ai p s a λ s (13.2-1)

For steady-state conditions at mid- to high speeds wherein the flux linkage term domi￾nates the resistive term in the voltage equation, the magnitude of the applied voltage

is related to the magnitude of the stator flux linkage by

Vs e = ω Λs (13.2-2)

which suggests that in order to maintain constant flux linkage (to avoid saturation), the

stator voltage magnitude should be proportional to frequency.

Figure 13.2-1 illustrates one possible implementation of a constant volts-per-hertz

drive. Therein, the speed command, denoted by ωrm

* , acts as input to a slew rate limiter

(SRL), which acts to reduce transients by limiting the rate of change of the speed

command to values between αmin and αmax. The output of the SRL is multiplied by P/2,

where P is the number of poles in order to arrive at the electrical rotor speed command

ωr

*

to which the radian electrical frequency ωe is set. The electrical frequency is then

multiplied by the volts-per-hertz ratio Vb/ωb, where Vb is rated voltage, and ωb is rated

radian frequency in order to form an rms voltage command Vs. The rms voltage

command Vs is then multiplied by 2 in order to obtain a q-axis voltage command vqs

e*

(the voltage is arbitrarily placed in the q-axis). The d-axis voltage command is set to

zero. In a parallel path, the electrical frequency ωe is integrated to determine the posi￾tion of a synchronous reference frame θe. The integration to determine θe is periodically

reset by an integer multiple of 2π in order to keep θe bounded. Together, the q- and

d-axis voltage commands may then be passed to any one of a number of modulation

strategies in order to achieve the commanded voltage as discussed in Chapter 12. The

advantages of this control are that it is simple, and that it is relatively inexpensive by

virtue of being entirely open loop; speed can be controlled (at least to a degree) without

feedback. The principal drawback of this type of control is that because it is open loop,

some measure of error will occur, particularly at low speeds.

Volts-per-Hertz Control 505

Figure 13.2-2 illustrates the steady-state performance of the voltage-per-hertz

drive strategy shown in Figure 13.2-1. In this study, the machine is a 50-hp, four-pole,

1800-rpm, 460-V (line-to-line, rms) with the following parameters: rs = 72.5 mΩ,

Lls = 1.32 mH, LM = 30.1 mH, Llr′ = 1 3. m2 H, rr′ = 41. m3 Ω, and the load torque is

assumed to be of the form

T T L b S rm

rm

bm

= + 



 



 









 0 1 0 9

2

. (ω ) . ω

ω

(13.2-3)

where S(ωrm) is a stiction function that varies from 0 to 1 as ωrm goes from 0 to 0+

.

Figure 13.2-2 illustrates the percent error in speed 100( ) / * * ω ω rm − rm ωrm, normalized

voltage Vs/Vb, normalized current Is/Ib, efficiency η, and normalized air-gap flux linkage

Figure 13.2-1. Elementary volts-per-hertz drive.

Figure 13.2-2. Performance of elementary volts-per-hertz drive.