Modeling and Analysis with Induction Generators, 3rd Edition

193

9

Vector Control for

Induction Generators

9.1 SCOPE OF THIS CHAPTER

Vector control is the foundation of modern high-performance drives. It is also

known as decoupling, orthogonal, or transvector control. Vector control techniques

can be classied according to their method of nding the instantaneous position

of the machine ux, which can be either (1) the indirect or feedforward method or

(2) the direct or feedback method. This chapter will discuss eld orientation—the

calculation of stator current components for decoupling of torque and ux—while

laying out the principles for rotor ux– and stator ux–oriented control approaches

for induction generator systems. A discussion of parameter sensitivity, detuning, sen-

sorless systems, PWM generation, and signal processing issues can be found in the

available technical literature.

9.2 VECTOR CONTROL FOR INDUCTION GENERATORS

The induction machine has several advantages: size, weight, rotor inertia, maximum

speed capability, efciency, and cost. However, induction machines are difcult to

control because being polyphase electromagnetic systems they have a nonlinear and

highly interactive multivariable control structure. The technique of eld-oriented or

vector control permits an algebraic transformation that converts the dynamic struc-

ture of the AC machine into that of a separately excited decoupled control structure

with independent control of ux and torque.

The principles of eld orientation originated in West Germany in the work of

Hasse

1

and Blaschke

2

at the technical universities of Darmstadt and Braunschweig

and in the laboratories of Siemens AG. Varieties of other derived implementation

methods are now available, but two major classes are very important and will be dis-

cussed in this chapter: direct control and indirect control. Both approaches calculate

the online instantaneous magnitude and position of either the stator or the rotor ux

vector by imposing alignment of the machine current vector to obtain decoupled

control. Therefore, a very broad and acceptable classication of vector control is

based on the procedure used to determine the ux vector.

Even though Hasse proposed electromagnetic ux sensors, currently direct vector

control (DVC) is based on the estimation through state observers of the ux position.

The technique proposed by Blaschke is still very popular and depends on feedfor-

ward calculation of the ux position with a crucial dependence on the rotor electri-

cal time constant, which may vary with temperature, frequency, and saturation, as

will be discussed in this chapter. The principles of vector control can be employed

194 Modeling and Analysis with Induction Generators

for control of instantaneous active and reactive power. Therefore, it is probably fair

to say that the modern p–q instantaneous power theory has also evolved from the

vector control theory.

3

If a totally symmetrical and three-phase balanced induction

machine is used, a d–q transformation is used to decouple time-variant parameters,

helping to lay out the principles of vector control.

9.3 AXIS TRANSFORMATION

The following discussion draws on voltage transformation, but other variables like

ux and current are also similarly transformed. Figure 9.1 shows a physical distribu-

tion of the three stationary axes a

s

, b

s

, and c

s

, 120° apart from each other, symbol-

izing concentrated stator windings of an induction machine. Cartesian axes are also

portrayed in Figure 9.1, where q

s

is a horizontal axis aligned with phase a

s

, and a

vertical axis rotated by −90° is indicated in the gure by d

s

. Three-phase voltages

varying in time along the axes a

s

, b

s

, and c

s

can be algebraically transformed onto

two-phase voltages varying in time along the axes d

s

and q

s

.

3–5

This transformation is indicated by Equation 9.1. The inverse of such a transfor-

mation can be taken by assuming that the zero sequence

v

os

s

is equal to zero for a bal-

anced system and Equation 9.2 is valid for the inverse transformation. Equation9.1

takes a two-phase quadrature system and transforms it to three phase, while

Equation9.2 takes a three-phase system and converts it to a two-phase quadrature

system. Figure 9.2 shows simplied block diagrams representing transformations of

this kind commonly used for vector control block diagrams:

v

v

v

v

v

as

bs

cs

qs

s

d

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

=− −

−

⎡

⎣

⎢

⎢

⎢

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎥

⎥

⎥

101

1

2

3

2

1

1

2

3

2

1

ss

s

os

s

v

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

(9.1)

a

s

b

s

120°

c

s

d

s

q

s

FIGURE 9.1 Physical distribution of three stationary axes and a quadrature stationary axis.