Chapter 14 permanent magnet AC motor drives

541

14.1. INTRODUCTION

There are a great variety of permanent-magnet ac motor drive confi gurations. Generally,

these may be described by the block diagram in Figure 14.1-1 . Therein, the permanent￾magnet ac drive is seen to consist of four main parts, a power converter, a permanent￾magnet ac machine ( PMAM ), sensors, and a control algorithm. The power converter

transforms power from the source (such as the local utility or a dc supply bus) to the

proper form to drive the PMAM, which, in turn, converts electrical energy to mechani￾cal energy. One of the salient features of the permanent-magnet ac drive is the rotor

position sensor (or at least an estimator or observer). Based on the rotor position, and

a command signal(s), which may be a torque command, voltage command, speed

command, and so on, the control algorithms determine the gate signal to each semi￾conductor in the power electronic converter.

In this chapter, the converter connected to the machine will be assumed to be a

fully controlled three-phase bridge converter, as discussed in Chapter 12 . Because we

will primarily be considering motor operation, we will refer to this converter as an

inverter throughout this chapter.

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.

PERMANENT-MAGNET AC

MOTOR DRIVES

14

542 PERMANENT-MAGNET AC MOTOR DRIVES

The structure of the control algorithms determines the type of permanent-magnet

ac motor drive, of which there are two main classes, voltage-source-based drives and

current-regulated drives. Both voltage-source and current-regulated drives may be

used with PMAMs with either sinusoidal or nonsinusoidal back emf waveforms.

Machines with sinusoidal back emfs may be controlled so as to achieve nearly con￾stant torque; however, machines with a nonsinusoidal back emf may be less expensive

to manufacture. The discussion in this chapter will focus on the machines with sinu￾soidal back emfs; for information on the nonsinusoidal drives, the reader is referred

to References 1–3 .

In this chapter, a variety of voltage-source and current-regulated drives featuring

machines with sinusoidal back emf waveforms will be analyzed. For each drive con￾sidered, computer simulations will be used to demonstrate performance. Next, average￾value models for each drive are set forth, along with a corresponding linearized model

for control synthesis. Using these models, the steady-state, transient, and dynamic

performance of each drive confi guration considered will be set forth. Design examples

will be used to illustrate the performance of the drive in the context of a control

system.

14.2. VOLTAGE-SOURCE INVERTER DRIVES

Figure 14.2-1 illustrates a voltage-source-modulated inverter-based permanent-magnet

ac motor drive. Here, voltage-source inverter refers to an inverter being controlled by

a voltage-source modulation strategy (six-stepped, six-step modulated, sine-triangle

modulated, etc.). Power is supplied from the utility through a transformer, which is

depicted as an equivalent voltage behind inductance. The transformer output is recti￾fi ed using a semi-controlled three-phase bridge converter, as discussed in Chapter 11 .

Since this converter is operated as a rectifi er (i.e., converting power from the ac

system to the dc system), it will be simply referred to as a rectifi er herein. The rectifi er

output is connected to the dc link fi lter, which may be simply an LC fi lter ( L dc , C dc ),

but which may include a stabilizing fi lter ( L st , r st , C st ) as well. The fi ltered rectifi er

output is used as a dc voltage source for the inverter, which drives the PMAM. This

voltage is commonly referred to as the dc link voltage. As can be seen, rotor position

is an input to the controller. Based on rotor position and other inputs, the controller

determines the switching states of each of the inverter semiconductors. The command

signal to the controller may be quite varied depending on the structure of the controls

Figure 14.1-1. Permanent-magnet ac motor drive.

Electrical

System

Command

Signal

Power

Converter

Control

PM

AM

Mechanical

System

Sensors

EQUIVALENCE OF VOLTAGE-SOURCE INVERTERS TO AN IDEALIZED SOURCE 543

in the system in which the drive will be embedded; it will often be a torque command.

Other inputs to the control algorithms may include rotor speed and dc link voltage.

Other outputs may include gate signals to the rectifi er thyristors if the rectifi er is

phase-controlled.

Variables of particular interest in Figure 14.2-1 include the utility supply voltage,

v au , v bu , and v cu , the utility current into the rectifi er i au , i bu , and i cu , the rectifi er output

voltage, v r , the rectifi er current, i r , the stabilizing fi lter current i st , the stabilizing fi lter

capacitor voltage v st , the inverter voltage v dc , the inverter current i dc , the three-phase

currents into the machine i as , i bs , and i cs , and the machine line-to-neutral voltages v as ,

v bs , and v cs .

Even within the context of the basic system shown in Figure 14.2-1 , there are many

possibilities for control, depending on whether or not the rectifi er is phase-controlled

and the details of the inverter modulation strategy. Regardless of the control strategy,

it is possible to relate the operation of the converter back to the idealized machine

analysis set forth in Chapter 4 , which will be the starting point for our investigation

into voltage-source inverter fed permanent-magnet ac motor drive systems.

14.3. EQUIVALENCE OF VOLTAGE-SOURCE INVERTERS TO

AN IDEALIZED SOURCE

Voltage-source inverters are inverters with a voltage-source modulator. In order to make

use of our analysis of the PMAM set forth in Chapter 4 when the voltage source is an

inverter rather than an ideal source, it is necessary to relate the voltage-source inverter

to an ideal source. This relationship is a function of the type of modulation strategy

used. In this section, the equivalence of six-stepped, six-step-modulated, sine triangle￾modulated, extended-sine triangle-modulated, or space-vector-modulated inverter to an

idealized source is established.

Figure 14.2-1. Permanent-magnet ac motor drive circuit.

Ldc i

r

Lst

rst

Cst

v C dc dc

vbu

vcu

vau

Lc

Control

Algorithms

Other Inputs

Other Outputs

T1 – T6

Command Signals

Utility / Transformer Rectifier DC Link Inverter Permanent Magnet AC Machine

Sensor

θr

vbs

vcs

vas

i

cs

i

as

i

bs

i

dc

+

-

-

+

+

-

vr

vst

+

-

+

-

+

+

+

- -

-

+

-

T1 T2 T3

T4 T5 T6

544 PERMANENT-MAGNET AC MOTOR DRIVES

The six-stepped inverter-based permanent-magnet ac motor drive is the simplest

of all the strategies to be considered in terms of generating the signals required to

control the inverter. It is based on the use of relatively inexpensive Hall effect rotor

position sensors. For this reason, the six-stepped inverter drive is a relatively low-cost

drive. Furthermore, since the frequency of the switching of the semiconductors corre￾sponds to the frequency of the machine, fast semiconductor switching is not important,

and switching losses will be negligible. However, the inverter does produce consider￾able harmonic content, which will result in increased machine losses.

In the six-stepped inverter, the on/off status of each of the semiconductors is

directly tied to electrical rotor position, which is accomplished through the use of the

Hall effect sensors. These sensors are confi gured to have a logical 1 output when they

are under a south magnetic pole and a logic 0 when they are under a north magnetic

pole of the permanent magnet, and are arranged on the stator of the PMAM as illustrated

in Figure 14.3-1 , where ϕh denotes the position of the Hall effect sensors. The logical

output of sensors H1, H2, and H3 are equal to the gate signals for T1, T2, and T3,

respectively, so that the gating signals are as indicated in Figure 14.3-2 . The gate signals

T4, T5, and T6 are the logical complements of T1, T2, and T3, respectively.

Comparing the gating signals shown in Figure 14.3-2 with those illustrated in the

generic discussion of six-step operation in Chapter 12 (see Fig. 12.3-1 ), it can be seen

that the two sets of waveforms are identical provided the converter angle θc is related

to rotor position and the Hall effect position by

θ θφ c rh = + (14.3-1)

In Section 12.3 , expressions for the average-value of the q - and d- axis voltages in the

converter reference frame were derived. Taking these expressions as dynamic

averages,

v v ˆ ˆ qs

c = dc

2

π

(14.3-2)

Figure 14.3-1. Electrical diagram of a permanent-magnet ac machine.

bs-axis

as-axis

θr

cs-axis

S

N

as

as

bs

bs

cs

cs

H2

H3

φh H1

φh

φh

′

′ ′