A complete modeling and simulation of DFIG based wind turbine system using fuzzy logic control

Abstract

The current paper talks about the variable speed wind turbine generation system (WTGS). So, the WTGS is equipped with a doubly-fed induction generator (DFIG) and two bidirectional converters in the rotor open circuit. A vector control (VC) of the rotor side converter (RSC) offers independent regulation of the stator active and reactive power and the optimal rotational speed tracking in the power maximization operating mode. A VC scheme for the grid-side converter (GSC) allows an independent regulation of the active and reactive power to exchange with the grid and sinusoidal supply currents and keeps the DC-link voltage constant. A fuzzy inference system (FIS) is adopted as an alternative of the conventional proportional and integral (PI) controller to reject some uncertainties or disturbance. The performances have been verified using the Matlab/Simulink software.

Key words： wind turbine generation system (WTGS); doubly-fed induction generator (DFIG); maximum power point tracking (MPPT); vector control (VC); fuzzy logic controller (FLC)

Introduction

Doubly-fed induction generator (DFIG) based wind turbine generation system (WTGS),a standard wind power conversion system choice, has been extensively used to get the extreme power conversion efficiency, with reduced capacity of power converters and full controllability of stator powers [ 1], due to their features such as variable speed operation. The stator winding terminals are directly connected to the grid, while the rotor winding terminals are fed via a two bidirectional converters connected in back to back. Between these two converters, there is a DC-link capacitor filter which works as energy storage in order to maintain the DC-link voltage ripple small. The DFIG based WTGS is a dynamical system with highly nonlinear and coupled characteristics, with time-varying and uncertain inputs [ 2]. The objectives of the WTGS controllers depend upon the operating mode defined by wind speed [ 3]. For low wind speed, it has to maximize the captured wind power, while above the rated wind speed it has to limit the generated power and the rotational speed in order to protect the mechanical parts of the WTGS [ 4].

Traditionally, each of the PWM converters is controlled using the VC approaches. One drawback of the VC is that many transformations are involved, and there is also a strong dependence on the stator flux position estimation or measurement. Furthermore, this approach needs exact value of the machine parameters. So, the performance of the VC method is affected by this nonlinear operating condition. The challenge is how to tune the parameters of the traditional PI controllers to get an optimal response around one operation point and struggle with other nonlinear operation points. As all VC methods depend on the assumptions of constant stator voltage and flux to achieve an independent control of stator active and the reactive powers, the performance will be degraded because of voltage dipor grid fault [ 5].

Many research approaches have been adopted to automatically tune the gains of the PI controller, such as the genetic algorithm [ 6] or the particle swarm optimization [ 7]. The artificial intelligence and gain schedule technique have been used to provide optimal response for a varying operation condition [ 8, 9]. Input-output linearization has been proposed to completely decouple the control of the DFIG [ 10].

In this paper, FIS is applied to regulate the DFIG. It replaces the PI controller in the rotor speed, stator active and reactive power control loops. For the DC-link voltage control loop, a fuzzy logic gain tuner (FGT) has been used to update the PI controller in order to get more robust response.

Modeling of wind turbine generation system

The overall structure of the grid connected WTGS is illustrated in Fig. 1.

Fig.1 Overall structure of DFIG based WTGS

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Modeling of wind turbine

WPGS is a device, which can convert wind energy to mechanical energy. The power contained in the wind is given by the kinetic energy of the flowing air mass per unit time [ 11]. That is

(1) P_t={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\pi \rho R_{\mathrm{balde}}^2{v}_w^3{C}_p({\lambda }_{\mathrm{TSR}},\beta ).

The efficiency coefficient C_p (l_TSR, b), as indicated, is a function of the blade angle called the pitch angle, denoted by b, and the tip speed ratio (TSR) denoted by l_TSR. This relationship is presented in Fig. 2.

Fig.2 Efficiency coefficient characteristic versus TSR and pitch angle

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The TSR is the ratio of the linear speed of the blade tip and the wind speed, which is given as

(2) {\lambda }_{\mathrm{TSR}}={\displaystyle \frac{R_{\mathrm{blade}}{\omega }_t}{v_w}}.

One way to get C_p is by using a look up table, while another way is by approximating C_p using a nonlinear function. The second way is more precise and faster in simulation, as given by Eqs. (3) and (4) [ 12].

(3) C_p({\lambda }_{\mathrm{TSR}},\beta )=\mathrm{0.22}\left({\displaystyle \frac{\mathrm{116}}{{\lambda }_i}}-\mathrm{0.4}\beta -\mathrm{5}\right)e^{-\frac{\mathrm{12.5}}{{\lambda }_i}},

(4) {\displaystyle \frac{\mathrm{1}}{{\lambda }_i}}=\left[\left({\displaystyle \frac{\mathrm{1}}{{\lambda }_{\mathrm{TSR}}+\mathrm{0.08}\beta }}\right)-\left({\displaystyle \frac{\mathrm{0.035}}{{\beta }^{\mathrm{3}}+\mathrm{1}}}\right)\right].

When there is a possibility to control TSR, the pitch angle is kept at zero. The extreme efficiency coefficient can approach the Betz limit which is 16/27 [ 13]. The turbine torque is defined as the ratio of the turbine output power to the low shaft speed, and is given by Eq. (5).

(5) T_t={\displaystyle \frac{P_t}{{\omega }_t}}.

Modeling of drive train system

Some authors use the two-mass model [ 14]. In the case in the present paper, the typical one-mass model appears sufficient [ 15], and the dynamic equation of the one-mass drive-train is given in Eq. (6).

(6) {\displaystyle \frac{d}{dt}}{\omega }_m={\displaystyle \frac{\mathrm{1}}{J_{\mathrm{eq}}}}(T_m-T_{\mathrm{em}}-f_{\mathrm{eq}}{\omega }_m).

By neglecting the gearbox losses, the torque and the rotational speed referred to the generator side are given by

T_m={\displaystyle \frac{T_t}{G}}

and

{\omega }_m={\omega }_{t}G.

Modeling of DFIG system

It is assumed that the stator and rotor windings are sinusoidal and symmetric [ 16]. The DFIG model in the arbitrary reference coordinate is expressed in Eq. (7).

(7) \{\begin{array}{l}{\displaystyle \frac{d}{dt}}{\phi }_{sd}=V_{sd}-R_s{i}_{sd}+{\omega }_s{\phi }_{sq},\\ {\displaystyle \frac{d}{dt}}{\phi }_{sq}=V_{sq}-R_s{i}_{sq}-{\omega }_s{\phi }_{sd},\\ {\displaystyle \frac{d}{dt}}{\phi }_{rd}=V_{rd}-R_r{i}_{rd}+({\omega }_s-{\omega }_e){\phi }_{rq},\\ {\displaystyle \frac{d}{dt}}{\phi }_{rq}=V_{rq}-R_r{i}_{rq}-({\omega }_s-{\omega }_e){\phi }_{rd}.\end{array}

The stator and rotor flux is expressed as

(8) \{\begin{array}{l}{\phi }_{sd}=L_s{i}_{sd}+M{i}_{rd},\\ {\phi }_{sq}=L_s{i}_{sq}+M{i}_{rq},\\ {\phi }_{rd}=L_r{i}_{rd}+M{i}_{sd},\\ {\phi }_{rq}=L_r{i}_{rq}+M{i}_{sq},\end{array}

where {\omega }_e=p{\omega }_m is the electrical rotational speed. The electromagnetic torque of the induction machine is given as

(9) T_{\mathrm{em}}=p({\phi }_{sd}{i}_{sq}-{\phi }_{sq}{i}_{sd}).

The stator active and reactive powers are expressed as [ 17]

(10a) P_s=V_{sd}{i}_{sd}+V_{sq}{i}_{sq},

(10b) Q_s=V_{sq}{i}_{sd}-V_{sd}{i}_{sq}.

Modeling of DC bus

Together with the RSC, the DC-link and the GSC form two back-to-back converters (Fig. 1). The DC-link between them is modeled as a pure capacitor. The DC-link voltage is expressed as

(11) V_{\mathrm{DC}}=V_{\mathrm{DC}\mathrm{0}}+{\displaystyle \frac{\mathrm{1}}{C_{\mathrm{DC}}}}{\int }_{\mathrm{0}}^t{i}_{\mathrm{DC}}\mathrm{d}t=V_{\mathrm{DC}\mathrm{0}}+{\displaystyle \frac{\mathrm{1}}{C_{\mathrm{DC}}}}{\displaystyle {\int }_{\mathrm{0}}^t(i_{\mathrm{DC�GSC}}-i_{\mathrm{DC�RSC}})\mathrm{d}t},

where i_DC-GSC and i_DC-RSC are the continuous current coming from, or going to the GSC and the RSC, respectively, and i_DC is the capacitor charging current.

Modeling of grid-filter

The mathematical model of the grid side system is given by Eq. (12).

(12) \{\begin{array}{l}{\displaystyle \frac{d}{dt}}{i}_{fd}={\displaystyle \frac{\mathrm{1}}{L_f}}(V_{gd}-V_{fd}-R_f{i}_{fd}+{\omega }_s{L}_f{i}_{fq}),\\ {\displaystyle \frac{d}{dt}}{i}_{fq}={\displaystyle \frac{\mathrm{1}}{L_f}}(V_{gq}-V_{fq}-R_f{i}_{fq}-{\omega }_s{L}_f{i}_{fd}).\end{array}

The output active and reactive powers of the GSC are expressed as

(13a) P_g=V_{fd}{i}_{fd}+V_{fq}{i}_{fq},

(13b) Q_g=V_{fq}{i}_{fd}-V_{fd}{i}_{fq}.

Vector control of DFIG using RSC

The RSC control has different objectives depending on the stage of operation of the WTGS. Therefore, the three stages of RSC control are to generate voltage at the stator terminals, to synchronize the stator terminals with the grid, connect and produce the required power.

Output power maximization based on fuzzy logic control

Capturing the maximum available power from the wind kinetic energy is the main control goal for the underrated wind velocity conditions. The optimal torque control (indirect speed control) strategy is characterized by its slow dynamic response [ 18]. The TSR method (direct speed control method) gives faster dynamic, but it causes more oscillations in the driving torque and the active power delivered [ 18, 19]. Therefore, the TSR control strategy is adopted in the control system to track the maximum power curve (MPC), as demonstrated in Fig. 3.

(14) P_{t\_\max }={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\pi \rho R_{\mathrm{balde}}^2{v}_w^3{C}_{p\mathrm{.max}}({\lambda }_{\mathrm{TSR}\mathrm{.opt}},\beta )=K_{\mathrm{opt}}{v}_w^{\mathrm{3}}.

The global control scheme of the employed MPPT is displayed in Fig. 4.

Fig.3 Maximum power curve (MPC) of WTGS

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Fig.4 MPPT strategy based on TSR-fuzzy control

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Vector control of the RSC

The VC method based on Park’s transformation provides independent control of active and reactive power. This is similar to the control of a DC machine [ 20]. The stator power thus has to be controlled through rotor currents. It is normally assumed that the voltage drop on the stator resistance is negligible due to its small value [ 21]. The stator flux dynamics is neglected since the stator is connected to the grid and the stator flux is nearly constant [ 22]. By adjusting the d-axis of the reference frame along the stator flux vector position, the next relationships are derived from Eq. (7).

(15) {\phi }_{sd}={\phi }_s=-{\displaystyle \frac{V_{sq}}{{\omega }_s}}={\displaystyle \frac{V_s}{{\omega }_s}}=\mathrm{const,}

(16) {\phi }_{sq}={\displaystyle \frac{V_{sd}}{{\omega }_s}}=\mathrm{0},

where V_s and j_s are the RMS voltage and the rated stator flux, respectively. In such case the next expressions are obtained from Eqs. (8), (15) and (16).

(17) i_{sd}={\displaystyle \frac{V_s}{{\omega }_s{L}_s}}-{\displaystyle \frac{M}{L_s}}{i}_{rd},

(18) i_{sq}=-{\displaystyle \frac{M}{L_s}}{i}_{rq}.

Substituting Eqs. (17) and (18) into Eq. (8) gives

(19) {\phi }_{rd}={\displaystyle \frac{M^{\mathrm{2}}}{L_s}}{i}_{\mathrm{ms}}+\sigma L_r{i}_{rd},

(20) {\phi }_{rq}=\sigma L_r{i}_{rq},

where i_{\mathrm{ms}}={\displaystyle \frac{{\phi }_s}{M}} is the magnetizing current of the DFIG. Substituting Eqs. (15), (16), (17) and (18) into Eqs. (10a) and (10b) gives

(21a) P_s=-{\displaystyle \frac{V_{s}M}{L_s}}{i}_{rq}=K_{\mathrm{ps}}{i}_{rq},

(21b) Q_s={\displaystyle \frac{V_s^2}{{\omega }_s{L}_s}}-{\displaystyle \frac{V_{s}M}{L_s}}{i}_{rd}.

The d- and q-axis components of the rotor currents have to be manipulated in order to regulate the stator reactive and active power, respectively. The current and power control loops are based on the rotor circuit equations of the DFIG (Eq. (22)).

(22) \{\begin{array}{l}{V}_{rd}=R_r{i}_{rd}+\sigma L_r{\displaystyle \frac{d}{dt}}{i}_{rd}-{\omega }_r\sigma L_r{i}_{rq},\\ V_{rq}=R_r{i}_{rq}+\sigma L_r{\displaystyle \frac{d}{dt}}{i}_{rq}+{\omega }_r\left({\displaystyle \frac{M^{\mathrm{2}}}{L_s}}{i}_{\mathrm{ms}}+\sigma L_r{i}_{rd}\right),\end{array}

where {\omega }_r={\omega }_s-{\omega }_e=g{\omega }_s, {\omega }_r is the rotor pulsation and g is the slip. This gives the process model G_r and the compensation terms, for the cross coupling between the d- and q-axis of the rotor current control loops, as given in Eqs. (23) and (24), respectively. V_{rd}^{\text{'}} , V_{rq}^{\text{'}} and V_{rd}^{\mathrm{comp}} , V_{rq}^{\mathrm{comp}} are the controller output voltage and the compensation voltage, respectively.

(23) G_r(s)={\displaystyle \frac{i_{rd}(s)}{V_{rd}^{\text{'}}(s)}}={\displaystyle \frac{i_{rq}(s)}{V_{rq}^{\text{'}}(s)}}={\displaystyle \frac{\mathrm{1}}{R_r+\sigma L_{r}s}},

(24) \{\begin{array}{l}{V}_{rd}^{\mathrm{comp}}(s)=-{\omega }_r\sigma L_r{i}_{rq}(s),\\ V_{rq}^{\mathrm{comp}}(s)={\omega }_r({\displaystyle \frac{M^{\mathrm{2}}}{L_s}}{i}_{\mathrm{ms}}+\sigma L_r{i}_{rd}(s)).\end{array}

The pole-zero cancellation method is used to get the PI controller gains via Eq. (23) [ 23]. The transfer function for the stator active and reactive power is therefore [ 19, 24]

(25) G_{P\mathrm{s}}(s)={\displaystyle \frac{P_s(s)}{i_{rq}(s)}}={\displaystyle \frac{Q_s(s)}{i_{rd}(s)}}={\displaystyle \frac{M}{L_r}}{V}_{sq}.

For an ideal grid, the transfer function G_Ps can be represented by a constant K_P-Ps in the control design. The additional term for the reactive power control (Eq. (21b)) can be compensated in the chain control. The control loop scheme for the stator active power is given in Fig. 5.

Fig.5 Stator active power control structure using FLC

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Fuzzy logic control approach

The FIS has the aptitude to control nonlinear, uncertain and adaptive systems, which gives robust performance for parameter variation [ 9]. FLC does not require any mathematical model of the controlled system. Its rule can be expressed based on series of logic statements. The structure of FLC applied in the speed and stator power control loops is illustrated in Fig. 6 where the input are the error and its derivation (e and de/dt) and the output is the derivation of the command (du/dt). Figure 7(a) depicts the fuzzy sets and the corresponding membership functions (MFs), and Fig. 7(b) shows the surface constructed by the seven MFs. Table 1 is the rules table fuzzy controllers.

Fig.6  Structure of employed FLC

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Fig.7 Membership functions of employed FLC

(a)Inputs and output MFs; (b) surface given by seven MFs

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Tab.1   Ruletable for FLC

de/dt	e/pu
	NB	NM	NS	Z	PS	PM	PB
NB	NB	NB	NB	NB	NM	NS	Z
NM	NB	NB	NB	NM	NS	Z	PS
NS	NB	NB	NM	NS	Z	PS	PM
Z	NB	NM	NS	Z	PS	PM	PB
PS	NM	NS	Z	PS	PM	PB	PB
PM	NS	Z	PS	PM	PB	PB	PB
PB	Z	PS	PM	PB	PB	PB	PB

DC-link voltage control using GSC

The goal of GSC is to hold the DC-bus voltage constant, and to exchange the reactive power with the grid if necessary. At the start-up phase, it is the GSC that has to bring the DC-link voltage to the level required, after which the RSC control can be enacted [ 24].

Vector control of GSC

The d-axis of the reference frame is aligned to the grid voltage vector, which makes the V_gq become zero. The GSC output filter in the AC side is modeled as

(26) \{\begin{array}{l}{V}_{gd}=R_f{i}_{fd}+L_f{\displaystyle \frac{d}{dt}}{i}_{fd}+V_{fd}-L_f{\omega }_s{i}_{fq},\\ \mathrm{0}=R_f{i}_{fq}+L_f{\displaystyle \frac{d}{dt}}{i}_{fq}+V_{fq}+L_f{\omega }_s{i}_{fd}.\end{array}

If the AC filter is lossless, the active power at the grid side and at the output of GSC are the same [ 25, 26]. Thus, the active and reactive slip power become proportional to i_fd and i_fq, respectively,

(27a) P_g=V_{gd}{i}_{fd},

(27b) Q_g=-V_{gd}{i}_{fq}.

Thus, the i_fd and i_fq currents have to be manipulated to control P_g and Q_g powers. Thus, the process of model G_f and the compensation terms are given by Eqs. (28) and (29), respectively, for the cross coupling between the d- and q-axis of the AC current control loops. V_{fd}^{\text{'}} , V_{fq}^{\text{'}} and V_{fd}^{\mathrm{comp}} , V_{fq}^{\mathrm{comp}} are the output of current controllers and the compensation terms, respectively.

(28) G_f(s)={\displaystyle \frac{i_{fd}(s)}{V_{fd}^{\text{'}}(s)}}={\displaystyle \frac{i_{fq}(s)}{V_{fq}^{\text{'}}(s)}}={\displaystyle \frac{\mathrm{1}}{R_f+L_{f}s}},

(29) \{\begin{array}{l}{V}_{fd}^{\mathrm{comp}}(s)=V_{gd}(s)+L_f{\omega }_s{i}_{fq}(s),\\ V_{fq}^{\mathrm{comp}}(s)=-L_f{\omega }_s{i}_{fd}(s).\end{array}

The pole-zero cancellation method is used to get the PI controller gains via Eqs. (29) and (28) [ 23]. By neglecting the GSC loss and considering the voltage oriented to the d-axis, the power exchanged by the GSC is given as [ 27]

(30) {{\displaystyle P}}_g={{\displaystyle V}}_{gd}{{\displaystyle i}}_{fd}={{\displaystyle V}}_{DC}{{\displaystyle i}}_{DC-GSC}.

Also, the PWM technique gives

(31) V_{gd}={\displaystyle \frac{\sqrt{\mathrm{3}}}{\mathrm{2}\sqrt{\mathrm{2}}}}{m}_{\mathrm{GSC}}{V}_{\mathrm{DC}}.

where m_{\mathrm{GSC}} is the modulation index of GSC. By substituting Eq. (31) into Eq. (30), the DC current passing by GSC is

(32) i_{\mathrm{DC-GSC}}={\displaystyle \frac{\sqrt{\mathrm{3}}}{\mathrm{2}\sqrt{\mathrm{2}}}}{m}_{\mathrm{GSC}}{i}_{fd}=K_{i_{\mathrm{DC}}}{i}_{fd},

with respect to the DC currents directions of Fig. 1, the DC-link voltage is given as

(33) V_{\mathrm{DC}}=V_{\mathrm{DC}\mathrm{0}}+{\displaystyle \frac{\mathrm{1}}{C_{\mathrm{DC}}}}{\displaystyle \underset{\mathrm{0}}{\overset{t}{\int }}(K_{i_{\mathrm{DC}}}{i}_{fd}-i_{\mathrm{DC-RSC}})dt}.

Thus, V_DC and Q_g exchanged between GSC and the grid can be controlled through the currents in the d and q-axis, respectively [ 28, 29]. The i_fq* is maintained nil to get a unity power factor in the grid side. The i_fd* is the output of the DC-link voltage control loop, and the V_DC model is based on the DC bus capacitor from Eq. (11), which gives the process model G_DC where i_DC* is the controller output current

(34) G_{\mathrm{DC}}(s)={\displaystyle \frac{V_{\mathrm{DC}}(s)}{i_{\mathrm{DC}}^{*}(s)}}={\displaystyle \frac{\mathrm{1}}{C_{\mathrm{DC}}s}}.

From Eq. (32), i_{fd_ref} can be deduced.

(35) i_{fd}^{*}={\displaystyle \frac{\mathrm{1}}{K_{i_{\mathrm{DC}}}}}(i_{\mathrm{DC\_RSC}}+i_{\mathrm{DC\_ref}}).

The overall control loop scheme for GSC is given in Fig. 8.

Fig.8 Cascade control structure for GSC using FGT

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Adopted FGT controller

The DC-link voltage dynamic depends on the exchanged power through the rotor circuit in different operation mode. Fuzzy rules are used to update the PI gains [ 8]. Input signals are the error and its derivation of the DC-link voltage. The adopted FGT controller is shown in Fig. 9 and the rule tables are listed in Tables 2 and 3 [ 30]. The input/output MFs used in these two FGTs are like the FLC presented in Fig. 7(a).

Fig.9 FGT of the DC-link voltage controller

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Tab.2 Rule table for fuzzy K_p tuner

de/dt	e/pu
	NB	NM	NS	Z	PS	PM	PB
NB	PB	PB	PM	PM	PS	Z	Z
NM	PB	PB	PM	PS	PS	Z	NS
NS	PM	PM	PM	PS	Z	NS	NS
Z	PM	PM	PS	Z	NS	NM	NM
PS	PS	PS	Z	NS	NS	NM	NM
PM	PS	Z	NS	NM	NM	NM	NB
PB	Z	Z	NM	NM	NM	NB	NB

Tab.3 Rule table for fuzzy K_i tuner

de/dt	e/pu
	NB	NM	NS	Z	PS	PM	PB
NB	NB	NB	NM	NM	NS	Z	Z
NM	NB	NB	NM	NS	NS	Z	Z
NS	NB	NM	NS	NS	Z	PS	PM
Z	NB	NM	NS	Z	PS	PM	PB
PS	NM	NS	Z	PS	PS	PM	PB
PM	Z	Z	PS	PS	PM	PB	PB
PB	Z	Z	PS	PM	PM	PB	PB

Simulation results and discussion

The parameters of DFIG are taken from Ref. [ 15]. and mentioned in Tables 4 and 5 in the appendix. The performance of the controlled system with the proposed FLCs is compared to a VC employing a fixed gains PI controller chosen carefully. The simulation objectives are to emulate powerful wind turbulence, and sub and super-synchronous modes of operation are performed. The tracking of references and rejection of disturbances have been presented in Figs. 10, 11, and 12. To verify the robustness of the adopted FLCs against the typical WTGS faults, these different faults are injected separately to the system, and the responses are compared with the those of the PI controller (see Figs. 13, 14).

Power maximization performance

The wind speed rises in steps from the starting speed (2m/s) into the rated speed (12m/s) as presented in Fig. 10(a).The generator speed almost has the same image as the wind speed, as presented in Fig. 10(b). The fuzzy speed control is faster and more efficient than the indirect speed control.

The Fig. 10(c) shows the efficiency coefficient which is maintained at its maximum. This means that the MPPT algorithm is working perfectly. Again, the fuzzy speed control is faster and more effective than the indirect speed control.

The TSR is maintained at its optimum value, as presented in Fig. 10(d).

Fig.10 Rotational speed response in MPPT operating mode

(a) Wind speed profile; (b) rotational speed response; (c) efficiency coefficient; (d) tip speed ratio

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Vector control performance of the DFIG

Figure 11(a) shows the measured stator active and reactive power. The active power follows its reference brought from the speed control loop. It depends on the turbine aerodynamic power. The stator reactive power follows its reference that kept at zero. The FLC has a faster dynamic response, with no overshoot and less steady-state ripple.

Figure 11(b) shows the d and q-axis component of the rotor current. They have the same image as the stator reactive and active power respectively, as denoted in Eq. (21). The FLC is faster and superior in oscillation damping. Figure 11(c) shows the normal and the zoomed waveform of the stator currents and voltages. The stator currents frequency is 50Hz and undergoes the same variation as the wind speed. Figure 11(c) focuses on one phase voltage and current of the stator. There is always a p phase between them, because of the generation mode. Figure 11(d) shows the normal and the zoomed waveform of the currents and the estimated voltages in the rotor circuit. The magnitude and frequency of the currents and the estimated voltages change according to the slip or the generator speed. Figure 11(d) focuses on one phase voltage and current of the rotor circuit. There is almost a 0 phase between them before the 0.3 sin sub-synchronous mode of operation, and p rad phase after 0.5s in super-synchronous mode. Between the 0.3s and the 0.5s the DFIG is in the synchronous mode, thus, the slip and the frequency are zero.

Fig.11 Stator active and reactive powers responses in MPPT operating mode

(a) Stator active and reactive power control; (b) d and q-axis component of the rotor current; (c) stator currents and voltages; (d) rotor currents and voltages

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Vector control performance of the GSC

Figure 12(a) shows a good response achieved in the measured DC-link voltage through the FGT of the classic PI controller, because there is no overshot, no steady-state error and less settling time compared to the conventional PI controller. Figure 12(b) shows the slip powers exchanged between the GSC and the grid. To get a unity power factor in the AC side of the GSC, the reactive power reference is set to nil. The DC-link voltage control loop regards the slip active power of the DFIG as an external disturbance represented by the DC current exchanged between the RSC and the DC bus. The amount and the direction of the slip active power are uncontrolled grandeur; it changes with the generator slip. Figure 12(c) shows the AC side currents of the GSC. Its frequency is maintained equal to the grid voltage frequency which is 50Hz, and its amount changes in accordance with the slip value. Figure 2(c) focuses on the one phase voltage and current of the filter. There is a 0 phase between them before the 0.5s in sub-synchronous mode of operation, and p rad phase after 0.5 s in super-synchronous mode.

Fig.12 DC-link voltage response in MPPT operating mode

(a) DC-link voltage control; (b) slip active and reactive power; (c) AC side currents of the GSC; (d) rotor currents and voltages

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Robustness against parameters deviations

In this test, the proposed FLC is verified against the machine parameters deviations. An increase by 500% in the stator and the rotor resistances and a decrease by 30% in the mutual inductance are introduced simultaneously.

Fig.13 Parameters deviations rejection by using a FLC

(a) Stator active power control; (b) stator reactive power control

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According to Fig. 13, degradation in the performance appears with the conventional PI control. A huge steady-state error appears, and the system loses its stability. On the contrary, the proposed FLC keeps its good performance, free from the influence of the variation of parameters.

Robustness against grid voltage disturbances

The second fault concerns the grid voltage disturbance and distortion. The seventh harmonics is added to the fundamentals of the three phases grid voltage, and a dip by 30% at t = 1.02 s and a swell by 30% at t = 1.1 s are introduced into the fundamental grid voltage profile. A period of 30 ms is regarded as fault time.

Fig.14 Grid voltage disturbance rejection using a FLC

(a) Stator active and reactive power control; (b) DC-link voltage control

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Figure 14(a) shows the stator powers responses. A huge disturbance appears in the PI control. However, FLC keeps its good performance with small influence, especially in reactive power response. Figure 14(b) shows the DC-link voltage response. The classic PI and the intelligent FGT are both affected by the grid voltage dip and swell, but the proposed FGT controller is faster and superior in the oscillation damping, especially in swell voltage fault.

Conclusions

This paper describes a study of the decoupled VC of the DFIG. The VC technique has been applied to both PWM converters. The results show the superiority of the FLCs, strong robustness against the grid disturbances and machine parameter variations. The settling time is reduced considerably, no overshoot happens and oscillations are damped out faster. The FGT together with the well-known PI controller provides an excellent performance in the DC-bus voltage, faster dynamic response with no overshoot. Shorter settling time and no steady-state error are achieved. Besides, a strong robustness against the external disturbances is accomplished, like the bi-directionality of the slip active power and the grid voltage unbalance conditions.

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