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 *t*_{F} is a finite time value and *i*_{dr_ref} and *i*_{qr_ref} are the reference d-axis and q-axis currents.

In the vector controlled DFIG system with stator flux orientation,*ψ*_{qs} = 0and *ψ*_{ds} = *ψ*_{s}. 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 *i*_{dr_ref} is generated using PI controller by comparing reference and actual active powers while the reference current *i*_{qr_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 of*ρ*_{d}are 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 *φ*_{d} 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 *ϕ*_{d} 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 *φ*_{q} 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 *i*_{dg_ref}. BFASMC is used in the design of the current control.

*Remarks: The control parameters*Γ_{q}*,*Γ_{d}*are selected based on the maximum possible current errors e*_{q} *and e*_{d} *respectively.*