High-Order Sliding Mode Control of DFIG-Based Wind Turbines - Wind Turbine Control and Monitoring - page 25

Main Circuit Breaker Main Circuit Breaker

Brake Brake

DFIG DFIG

Gear Gear

Pitch
Drive

Pitch
Drive

Line Coupling
Transformer

Line Coupling
Transformer

Medium Voltage Switchgear Medium Voltage Switchgear

Frequency
Converter

Frequency
Converter

Wind Turbine
Control

Wind Turbine
Control

Fig. 2.3 Schematic diagram of a DFIG-based wind turbine

The control system is usually defined in the synchronous d - q frame fixed to
either the stator voltage or the stator flux. For the proposed control strategy, the
generator dynamic model written in a synchronously rotating frame d - q is given
by Eq. ( 2.5 ).

8
< V sd ¼ R s I sd þ d/ sd

dt x s / sq
V sq ¼ R s I sq þ d/ sq

dt þ x s / sd
V rd ¼ R r I rd þ d/ rd

dt x r / rq
V rq ¼ R r I rq þ d/ rq

dt þ x r / rd
/ sd ¼ L s I sd þ MI rd
/ sq ¼ L s I sq þ MI rq
/ rd ¼ L r I rd þ MI sd
/ rq ¼ L r I rq þ MI sq
T em ¼ pM I rd I sq I rq I sd

ð 2 : 5 Þ

:

where V is the voltage, I is the current, / is the flux, x s is the synchronous, x r is
the angular speed, R is the resistance, L is the inductance, M is the mutual
inductance, T em is the electromagnetic torque, and p is the pole pair number.
For simplification purposes, the q-axis is aligned with the stator voltage and the
stator resistance is neglected. These will lead to Eq. ( 2.6 ).