DFIG based wind energy system is a nonlinear stochastic system and is subjected to many disturbances like faults on the transmission line, parameter perturbations, and variable wind speeds. However, the conventional vector controlled DFIG system is not robust. In order to improve the robustness of conventional vector control, sliding mode control is introduced in the current control loop and accordingly, the control objectives are chosen as:
$$ \underset{t\to {t}_F}{Lt}\left({i}_{dr}-{i}_{dr\_ ref}\right)\to 0 $$
(13)
$$ \underset{t\to {t}_F}{Lt}\left({i}_{qr}-{i}_{qr\_ ref}\right)\to 0 $$
(14)
$$ \underset{t\to {t}_F}{Lt}\left({i}_{dg}-{i}_{dg\_ ref}\right)\to 0 $$
(15)
$$ \underset{t\to {t}_F}{Lt}\left({i}_{qg}-{i}_{qg\_ ref}\right)\to 0 $$
(16)
where tF is a finite time value and idr_ref and iqr_ref are the reference d-axis and q-axis currents.
In the vector controlled DFIG system with stator flux orientation,ψqs = 0and ψds = ψs. Modifying the dynamics given in (1–2) in terms of rotor currents:
$$ \frac{di_{qr}}{dt}=\frac{1}{\sigma {L}_r}\left({V}_{qr}-{R}_r{i}_{qr}-s{\omega}_s{\psi}_{dr}\right) $$
(17)
$$ \frac{di_{dr}}{dt}=\frac{1}{\sigma {L}_r}\left({V}_{dr}-{R}_r{i}_{dr}+s{\omega}_s{\psi}_{qr}\right) $$
(18)
The reference rotor current idr_ref is generated using PI controller by comparing reference and actual active powers while the reference current iqr_ref is generated using another PI controller using terminal voltage error. Now these currents are compared with the actual currents and current errors are generated as given (19) & (20).
$$ {e}_d={i}_{dr}-{i}_{dr\_ ref} $$
(19)
$$ {e}_q={i}_{qr}-{i}_{qr\_ ref} $$
(20)
Because of the features like chattering free, finite time convergence and simplicity in design, current controllers are designed with BFASMC.
For the design of control input in d-axis loop, the sliding surface is selected as:
$$ {\rho}_d={e}_d $$
(21)
Taking the derivative of (21) and from (17), the error dynamics ofρdare given as:
$$ {\dot{\rho}}_d=\frac{1}{\sigma {L}_r}\left({V}_{dr}-{R}_r{i}_{dr}+s{\omega}_s{\psi}_{qr}\right)-{\dot{i}}_{dr\_ ref}+{\varphi}_d $$
(22)
where φd represents unmodelled dynamics and parametric variations.
Now modifying the error dynamics in (22) as:
$$ {\dot{\rho}}_d={u}_d+{\phi}_d $$
(23)
where
$$ {u}_d=\frac{1}{\sigma {L}_r}\left({V}_{dr}-{R}_r{i}_{dr}+s{\omega}_s{\psi}_{qr}\right) $$
(24)
and ϕd is the cumulative disturbance.
From (11), the control input required to stabilize the error in fixed time is given by (25)
$$ {u}_d=-{\widehat{K}}_{dr}\left|{\rho}_d\right|\mathit{\operatorname{sign}}\left({\rho}_d\right) $$
(25)
where
$$ {\widehat{K}}_{dr}=\frac{\left|{\rho}_d\right|}{\Gamma_d-{\rho}_d} $$
(26)
From (24),
$$ {V}_{dr}=\sigma {L}_r{u}_d+{R}_r{i}_{dr}-{\omega}_{sl}{\psi}_{qr} $$
(27)
For the design of control input in q-axis loop, the sliding surface is chosen as:
$$ {\rho}_q={e}_q $$
(28)
Taking the derivative of (28) and from (18),
$$ {\dot{\rho}}_q=\frac{1}{\sigma {L}_r}\left({V}_{qr}-{R}_r{i}_{qr}-{\omega}_{sl}{\psi}_{dr}\right)-{\dot{i}}_{qr\_ ref}+{\varphi}_q $$
(29)
where φq represents unmodelled dynamics and parametric variations.
Let
$$ {u}_q=\frac{1}{\sigma {L}_r}\left({V}_{qr}-{R}_r{i}_{qr}-{\omega}_{sl}{\psi}_{dr}\right) $$
(30)
Modifying error dynamics in (30) as:
$$ {\dot{\rho}}_q={u}_q+{\phi}_q $$
(31)
From (31), the control input required to stabilize the error in fixed time is:
$$ {u}_q=-{\widehat{K}}_{qr}\left|{\rho}_q\right|\mathit{\operatorname{sign}}\left({\rho}_q\right) $$
(32)
where
$$ {\widehat{K}}_{qr}=\frac{\left|{\rho}_q\right|}{\Gamma_q-{\rho}_q} $$
(33)
From (32),
$$ {V}_{qr}=\sigma {L}_r{u}_q+{R}_r{i}_{qr}+{\omega}_{sl}{\psi}_{dr} $$
(34)
The proposed idea of rotor side converter control can be viewed from Fig. 2.
A similar procedure is followed for the design of grid side control as shown in Fig. 3. DC link voltage is compared with the reference voltage and voltage error is given to PI controller which generates the reference current idg_ref. BFASMC is used in the design of the current control.
Remarks: The control parametersΓq,Γdare selected based on the maximum possible current errors eq and ed respectively.