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Vector Control Strategy for IPMSM Drive

Literature Review

2.2 Vector Control Strategy for IPMSM Drive

The vector control means the control of both magnitude and phase angle of either the motor voltage or current or both instead of their magnitudes only. As mentioned earlier, the vector control technique is one of the most effective techniques for in high performance AC motors drives. In the case of the permanent magnet synchronous motor (PMSM), the torque eqn. (2.3) has two terms: the first term represents the magnet

torque produced by the permanent magnet flux m and the torque producing current component iq; the second term represents the reluctance torque produced by the complex interaction of inductances Ld and Lq and also the currents id and iq. The excitation voltage due to permanent magnets, and the values of the inductances Ld and Lq undergo significant variations in an interior type permanent magnet motor under different steady state and dynamic loading conditions [9,33]. Thus, the complexity of the control of the IPMSM drive arises due to the nonlinear nature of the torque eqn.

(2.3). In order to operate the motor in a vector control scheme avoiding the complexity, id is set to zero. Then the torque equation becomes linear and is given by,

Te = 3P

2 ψmiq=Ktiq

(2.5)

where, the constant Kt=3P 2 ψm

. Using phasor notations and taking the d-axis as a reference phasor, the steady-state phase voltage Va can be derived from the steady-state d-q axis voltage eqn. (2.1) and (2.2) as,

V

a

= v

d

+ j v

q

= R

s

I

a

ω

s

L

q

i

q

+ j ω

s

L

d

i

d

+ j ω

s

ψ

m (2.6)

where, the phase current,

I

a

= i

d

+ j i

q (2.7)

In the case of the IPM motor, the d-axis current is negative and it demagnetizes the main flux provided by the permanent magnets.

(a)

d-axis q-axis

id m Ia iq

Lqiq o Ldid

-s Lqiq -jsLdid jsm IaRs

Va vq

vd

d-axis q-axis

m Ia

o Lqiq

-sLqiq jsm

IaRs Va vq

vd

According to eqns. (2.6) and (2.7) the basic vector diagram of IPMSM is shown in Fig.

2.2 (a). The vector control scheme can be clearly understood by this vector diagram. It is shown in the vector diagram that the stator current, Ia, can be controlled by controlling the d- and q-axis current components. In the vector control scheme, when id

is set to zero then all the flux linkages are oriented in the d-axis as shown in Fig. 2.2 (b).

After setting id = 0, eqn. (2.3) shows that the torque is a function of only the quadrature axis current component, iq and hence a constant torque can be obtained by ensuring iq

constant.

(b)

Fig. 2.2 Basic vector diagram of IPMSM: (a) general; (b) modified with id = 0.

+ r*

Current Controller

Vector rotator

Speed Controller VB

d/dt ia* ib* ic*

r iq* id*

ia ib

- r ic

IPMSM Position sensor PWM Inverter

Base drive circuit

r

f(iq*, r)

The closed-loop vector control of voltage source inverter (VSI) fed IPMSM drive is shown in Fig. 2.3. In this figure VB is the DC bus voltage for the inverter, which supplies AC voltage to the motor with variable frequency and magnitude. The IPMSM drive consists of the current controller and the speed controller. The speed controller generates the torque command and hence the q-axis current command iq* from the error between the command speed and the actual speed. As mentioned earlier, in the vector control scheme traditionally, the d-axis command current id* is set to zero to simplify the nonlinear dynamic model. If the flux control is needed the id should be calculated based on some flux control algorithm

Fig. 2.3. Block diagram of the closed loop vector control of IPMSM drive.

of the IPMSM. The command phase currents ia*, ib* and ic* are generated from the d,q axis command currents using inverse Park’s transformation given in Eqn. (2.8) [34].

The current controller forces the load current to follow the command current as closely as possible and hence forces the motor to follow the command speed due to the feedback control. Therefore, in order to operate the motor in a vector control scheme the feedback quantities will be the rotor angular position and the actual motor currents. In the control scheme, the torque is maintained constant up to the rated speed, which is also called the constant flux or the constant voltage to frequency ratio (V/f) control technique.

[ i a ¿ ¿ ][ i b ¿ ¿ ] ¿

¿ ¿ ¿

(2.8)

The (V/f) is maintained constant by using PWM operation of the VSI. The designs of the speed controller, current controller and voltage source inverter to perform their specific functions are given in the following sub-sections.

2.2.1 Speed Controller

The speed controller processes the speed error (r) between command and actual speeds and generates the command q-axis current (iq*). The small change in speed r

produces a corresponding change in torque Te and taking the load torque TL as a constant, the motor dynamic Eqn.(2.4) becomes,

ΔTe=Jmd

(

Δωr

)

dt +BmΔωr

(2.9) Integrating Eqn.(2.9) gives us the total change of torque as,

T

e

=K

t

i

q

= J

m

Δω

r

+ B

m

0t

Δω

r

( τ )

(2.10) According to Eqn. (2.10), a proportional-integral (PI) algorithm can be used for the speed controller which may be written as,

i

q¿

= K

p

Δω

r

+ K

i

0t

Δω

r

( τ )

(2.11)

r = r*-r (2.12) where, Kp is the proportional constant, Ki is the integral constant and r is the speed error between the command speed, r* and the actual motor speed, r.

For discrete-time representation, Eqn. (2.11) can be differentiated and written in discrete-time domain, respectively as,

di

¿q

dt = K

p

dΔω

r

dt + K

i

Δω

r

(2.13)

i

q¿

(k ) = i

q¿

(k −1) + K

p

[ Δω

r

( k ) − Δω

r

(k − 1) ] + K

i

T

s

Δω

r

(k )

(2.14) where, iq* (k) is the present sample of command torque, iq*(k-1) is the past sample of command torque, r(k) is the present sample of speed error and r(k-1) is the past sample of speed error and Ts is the sampling period.

2.2.2 Current Controller and Voltage Source Inverter

The current controller is used to force the motor currents to follow the command currents and hence forces the motor to follow the command speed due to the feedback control. The outputs of the current controller are the pulse width modulated (PWM) signals for the insulated gate bipolar resistor (IGBT) inverter switches. The voltage source inverter (VSI) converts fixed DC voltage to a variable AC voltage for the motor so that it can follow command speed with the required load. The current control principle and PWM generation for the VSI can be found in [35].