VECTOR OR FIELD ORIENTED CONTROL

INDUCTION GENERATORS

D- Q Modeling And Vector Control of Induction Generator

2.4 VECTOR OR FIELD ORIENTED CONTROL

Page 46 And the torque equation for generator can be given as

^m

m turbine

e B

dt J d T

T _{+ =} ω ₊ ω

(2.28)

where T_L=load torque, T_turbine = turbine torque, J=rotor inertia, ω_m=mechanical speed =2/p ω_r ,

ω_r = is the electrical speed of the rotor and P= pole pares of the machine.

The expression for the developed torque can be derived as e P

(

Ψdmiqs Ψqmids

)

T = −

2 2

3

P

(

Ψdsiqs Ψqsids

)

−

=2 2

3

= P

(

Ψdriqr −Ψqridr

)

2 2

3

^{= P}

(

^{Ψdmiqr −Ψqmidr}

)

2 2

3

^{= PLm}

(

^{iqsidr −idsiqr}

)

2 2

3 (2.29)

Equations (2.26), (2.27),(2.28) and (2.29) give the complete model of the electro-mechanical dynamics of an induction machine in synchronous frame.

Page 47 of dc machine-like performance, vector control is also known as decoupling, orthogonal, or transvector control. Vector control is applicable to both induction and synchronous machine drives.

Consider the separately excited dc machine as shown in Figure 2.5. The developed torque is given by

f a t

e K I I

T =

(2.30) where I^a = armature current and I^f =field current. The construction of dc machine is such that the field flux Ψf produced by current I is perpendicular to the armature flux ^f Ψa, which is produced by armature current I . These space vectors, which are stationary in space are ^a orthogonal or decoupled in nature. This means that when torque is controlled by controlling the currentI^a, the flux Ψf is not affected.

DC machine-like performance can also be extended to an induction motor if the machine control is considered in a synchronously rotating reference frame (d^e−q^e), where the sinusoidal variables appear as dc quantities in steady state. Figure 2.6 shows the induction machine with the inverter and vector control with the two control current inputs, i and ^*_ds iqs^* ⋅With vector control, i is analogous to field current ds I and ^f i is analogous to armature current _qs I of a dc machine. ^a Therefore, the torque equation can be expressed as

qs r t

e K Ψ i

T = ˆ

(2.31) or

qs ds t

e K i i

T =

(2.32) The dc machine like performance is only possible if the i is aligned in the direction of _ds Ψˆr and

i is established perpendicular to it. This means that when qs i is controlled, it affects the actual _qs^*

i current only, but does not affect the flux qs

flux only and does not affect the

Figure 2.5

Figure 2.6

2.4.1 EQUIVALENT CIRCUIT AND PHASOR DIAGRAM Consider the d^e−q^e

condition as shown in Figure 2.7 which makes the rotor flux Ψ expressed as

where i_ds= magnetizing component of stator current flowing through the inductance torque component of stator current flowin

phasor diagrams in d^e−q^e frame with peak value of sinusoids and air gap voltage

current only, but does not affect the flux Ψˆr_. Similarly, when i_ds^* is controlled, it controls the flux only and does not affect the i component of current. _qs

Figure 2.5 Separately excited dc machine

Figure 2.6 Vector-controlled induction machine

.1 EQUIVALENT CIRCUIT AND PHASOR DIAGRAM

equivalent circuit diagram of induction machine

condition as shown in Figure 2.7. The rotor leakage inductance Llr is neglected for simplicity, Ψˆr the same as the air gap flux Ψˆm. The stator current

2

ˆ 2

qs

s ids i

I = +

= magnetizing component of stator current flowing through the inductance torque component of stator current flowing in the rotor circuit. Figure 2.8

frame with peak value of sinusoids and air gap voltage

Page 48 is controlled, it controls the

rcuit diagram of induction machine under steady state is neglected for simplicity, . The stator current Iˆs ^{can be}

(2.33)

= magnetizing component of stator current flowing through the inductance Lm and i = _qs 8 and Figure 2.9 shows frame with peak value of sinusoids and air gap voltage Vˆ aligned on _m

the q axis. The in-phase or torque component of current ^e

the air gap, whereas the reactive or flux component of current power. Figure 2.8 indicates an inc

torque while maintaining the flux flux by reducing the i component._ds

Figure 2.7

Figure 2.8 Steady-state phasor diagram with increase of torque component of current phase or torque component of current i contributes the active power across _qs the air gap, whereas the reactive or flux component of current i contributes only reactive _ds indicates an increase of the i component of stator current to increase the _qs torque while maintaining the flux Ψr constant, whereas Figure 2.9 indicates a weakening of the

component.

Complex (qds) equivalent circuit in steady state

state phasor diagram with increase of torque component of current

Page 49 contributes the active power across contributes only reactive component of stator current to increase the indicates a weakening of the

Complex (qds) equivalent circuit in steady state

state phasor diagram with increase of torque component of current

Page 50 Figure 2.9 Steady-state phasor diagram with increase of flux component of current

2.4.2 PRINCIPLE OF VECTOR CONTROL

The fundamental of vector control implementation can be explained with the help of Figure 2.10, where the machine model is represented in a synchronously rotating reference frame. The inverter is omitted from the figure, assuming that it has unity current gain, that is,

Figure 2.10 Vector control implementation principle with machine d^e−q^e model d_e-q_e

to d_s-q_s

d_s-q_s to a-b-c

a-b-c to d_s-q_s

d_s-q_s to d_e-q_e

Machine d_e-q_e model

*

iqs ^s*

iqs

* s

ids ^ia*

*

ib

*

ic

ia

ib

ic

s

ids s

iqs

i ^ds iqs

θe

cos sinθ_e cosθ_e sinθ_e

i ^ds

iqs

Ψr

ω_e

Inverse

transformation Transformation

Control Machine

*

ids

Page 51

it generates currents i ,_a i , and _b i as dictated by the corresponding command currents _c i , _a^* i , _b^* and i from the controller. A machine model with internal conversion is shown on the right. The _c^* machine terminal phase currentsi , _a i , and _b i are converted to _c i and ds^s i components by _qs^s

Φ Φ/ 2

3 transformation. These are then converted to synchronously rotating frame by the unit vector components cosθ_e and sinθ_e before applying them to the d^e−q^e machine model as shown. The controller makes two stages of inverse transformation, so that the control currents i _ds^* and i correspond to the machine currents i^*_qs ds and iqs respectively. In addition, the unit vector assures correct alignment of i current with the flux vector _ds Ψr and i_qs perpendicular to it.

There are essentially two general methods of vector control. One, called the direct or feedback method, was invented by Blaschke and the other known as the indirect or feed-forward method was invented by Hasse. These two methods are different essentially by how the unit vector is generated for the control.