Adaptive Fuzzy Control Scheme for Variable-Speed Wind Turbines Based on a Doubly-Fed Induction Generator

Abstract

The purpose of this paper is to present a new adaptive fuzzy control scheme for grid-connected variable-speed wind turbines (WT) based on a doubly-fed induction generator (DFIG). The proposed controller simultaneously guarantees two independent control objectives: (1) DFIG torque control allowing the extraction of maximum available power from the wind, and (2) control of the stator reactive power to maintain a desirable power factor according to the grid requirements. Unlike many existing control designs developed for DFIG-based WT, the design of the proposed controller is based on nonlinear coupled models of WT, without attempting approximate linearization. To improve performance in operating conditions, the model uncertainties and the nonlinear functions appearing in the tracking errors dynamics are reasonably approximated by adaptive fuzzy systems. It is mathematically proven that the proposed adaptive fuzzy control scheme can guarantee that all signals of the closed-loop system are uniformly ultimately bounded. Simulation results show that the proposed control scheme has strong robustness against the system parameter variations and unstructured uncertainties.

Appendix

1.1 Sliding Mode Control for DFIG-Based WT

A sliding mode control (SMC) law proposed for DFIG-based WT by Bekakra and Ben Attous (2014) and for Brushless DFIG-based WT by Mahboub et al. (2017) is summarized in this section.

$$ u_{\text{rd}} = u_{\text{rd}}^{\text{eq}} + u_{\text{rd}}^{n} $$

$$ u_{\text{rq}} = u_{\text{rq}}^{\text{eq}} + u_{\text{rq}}^{n} $$

where $u_{\text{rd}}^{\text{eq}} = \left( {\frac{\text{d}}{{{\text{d}}t}}i_{\text{rd{-}ref}} + \frac{{R_{\text{r}} }}{{\sigma L_{\text{r}} }}i_{\text{rd}} - \left( {\omega_{\text{s}} - \omega } \right)i_{\text{rq}} } \right)\sigma$, $u_{\text{rd}}^{n} = k_{\text{d}} {\text{sign}}\left( {e_{\text{d}} } \right)$

$$ u_{\text{rq}}^{\text{eq}} = \left( {\frac{\text{d}}{{{\text{d}}t}}i_{\text{rq{-}ref}} + \frac{1}{\sigma }\left( {\frac{{R_{\text{r}} }}{{L_{\text{r}} }} + \frac{{R_{\text{s}} M^{2} }}{{L_{\text{s}}^{2} L_{\text{r}} }}} \right)i_{\text{rq}} + \left( {\omega_{\text{s}} - \omega } \right)i_{\text{rd}} } \right)\sigma,\quad u_{\text{rq}}^{n} = k_{\text{q}} {\text{sign}}\left( {e_{\text{q}} } \right) $$

with $e_{\text{d}} = i_{\text{rd}} - i_{\text{rd{-}ref}}$ and $e_{\text{q}} = i_{\text{rq}} - i_{\text{rq{-}ref}}$, $k_{\text{d}} > 0$, $k_{\text{q}} > 0$

By setting the d-axis for the Park transformation aligned with stator flux axis. The stator active and reactive powers can be expressed as

$$ P_{\text{s}} = - \frac{{3u_{\text{s}} M}}{{2L_{\text{s}} }}i_{\text{rq}} , $$

$$ Q_{\text{s}} = \frac{{3 u_{\text{s}} }}{{2 L_{\text{s}} }}\left( {\frac{{u_{\text{s}} }}{{\omega_{\text{s}} }} - Mi_{\text{rd}} } \right) $$

Then

$$ i_{\text{rq{-}ref}} = - \frac{{L_{\text{s}} P_{\text{S{-}ref}} }}{{Mu_{\text{s}} }} $$

The stator active power reference is obtained from the MPPT bloc.By setting $Q_{\text{s}} = 0$, we have

$$ i_{\text{rd{-}ref}} = \frac{{u_{\text{s}} }}{{\omega_{\text{s}} M}} $$

Remark 5

To remove the chattering effect omnipresent in the conventional sliding mode control signals, the ${\text{Sign}}\left( . \right)$ function will be replaced by an equivalent smooth function ${\text{Tan}}h\left( . \right)$.

The block diagram of this SMC scheme is illustrated in Fig. 16.

Fig. 16

The SMC scheme of the DFIM-based WT