AD2S105

REV. 0

–5–

THEORY OF OPERATION

A fundamental requirement for high quality induction motor

drives is that the magnitude and position of the rotating air-gap

rotor flux be known. This is normally carried out by measuring

the rotor position via a position sensor and establishing a rotor

oriented reference frame.

To generate a flux component in the rotor, stator current is ap-

plied. A build-up of rotor flux is concluded which must be

rotor flux. The rotor flux current component is the magnetizing

Torque is generated by applying a current component which is

perpendicular to the magnetizing current. This current is nor-

To orient and control both the torque and flux stator current

vectors, a coordinate transformation is carried out to establish a

new reference frame related to the rotor. This complex calcula-

tion is carried out by the AD2S105.

To expand upon the vector operator a description of a single

vector rotation is of assistance. If it is considered that the

moduli of a vector is OP and that through the movement of ro-

tor position by

, we require the new position of this vector it

can be deduced as follows:

Let original vector OP = A (Cos

+ jSIN ) where A is a

constant;

if

OQ = OP e

j

(1)

and: e

j

= Cos

+ jSin

OQ = A (Cos ( + ) + jSin ( +

))

= A [Cos

Cos

φ – Sin Sin φ + jSin Cos φ + jCos Sin φ]

= A [(Cos

+ jSin ) (Cos

+ jSin

)]

(2)

θ

φ

θ + φ

Q

P

O

a

d

Figure 1. Vector Rotation in Polar Coordinate

j 2

π

3

and a

j 4

π

3

. This can be re-

placed by rectangular coordinates as

(3)

phase stator winding which establishes the same magnitude of

MMF in a three-phase system. These inputs can be seen after

the three-phase to two-phase transformation in the AD2S105

block diagram. Equation (3) therefore represents a three-phase

to two-phase conversion.

To relate these stator current to the reference frame the rotor

currents assume the same rectangular coordinates, but are now

rotated by the operator e

+ jSin

.

Here the term vector rotator comes into play where the stator

current vector can be represented in rotor-based coordinates or

vice versa.

The AD2S105 uses e

j

as the core operator. In terms of the

ponents as follows:

j

e

j

= Cos

+ jSin

+ jSin

)

The output from the AD2S105 takes the form of:

The matrix equation is:

Sin

Cos

and it is shown in Figure 2.

I

ds

I

qs

I

I

φ

e

j

φ

Figure 2. AD2S105 Vector Rotation Operation

DIGITAL

φ

LATCH

3

φ TO 2φ

TRANSFORMATION

LATCH

LATCH

SINE AND

COSINE

MULTIPLIER

(DAC)

SINE AND

COSINE

MULTIPLIER

(DAC)

PARK

COS

θ COSθ + 120° COSθ + 240° SINθ

INPUT CLARK

COS (

θ + φ)

SIN (

θ + φ)

Figure 3. Converter Operation Diagram