Robust control of isolated SCIG-based WECS feeding constant power load using adaptive backstepping and fractional order PI methods

Abstract

Designing a control system that is robust against changes in the steady state operating point as well as transient states of the system, especially in the presence of constant power loads, is one of the most important issues in the isolated operation mode of wind energy conversion systems (WECS). In this paper, a robust control structure is proposed for a squirrel cage induction generator-based WECS feeding isolated loads, including constant power loads. The proposed control structure includes two controllers, a flux control system for the machine side converter and a voltage control system for the load side converter. The proposed flux controller is designed based on the adaptive input–output feedback linearization method, and in a new reference frame whose rotation speed at each instant of time is extracted by a cascaded DC voltage regulator based on the fractional order PI method. This regulator maintains the DC-link voltage of the back-to-back converters in the nominal range by controlling the output power of the generator through the speed regulation of the proposed reference frame. The proposed voltage control system includes a voltage regulator based on the adaptive backstepping control method. The proposed controller robustly forces the load voltage magnitude to maintain within its nominal value. The proposed control system is shown to be strong and stable against the presence of constant power load, uncertainties and disturbances. The validity and effectiveness of proposed control structure are demonstrated through simulation studies in the MATLAB^® software environment.

Appendix A

If a definitely positive Lyapunov function is selected as:

$$\begin{aligned} W_\lambda =\frac{1}{2}{{e}_{\lambda }^{2}}+\frac{1}{2{\sqrt{\gamma }}}{{{{{\tilde{R}}_{s}^{2}}}}}, \end{aligned}$$

(37)

by differentiating it with respect to time, it can be expressed that:

$$\begin{aligned} {\frac{d}{dt}}W_\lambda ={{e}_{\lambda }}{\frac{d}{dt}}{{e}_{\lambda }}-\frac{1}{{\sqrt{\gamma }}}{{{\tilde{R}}}_{s}}{\frac{d}{dt}}{{{\hat{R}}}_{s}}. \end{aligned}$$

(38)

Substituting for ${\frac{d}{dt}}{{e}_{\lambda }}$ and ${\frac{d}{dt}}{{{\hat{R}}}_{s}}$ from (18) and (21), and based on control law (19), we can write:

$$\begin{aligned} {\frac{d}{dt}}W_\lambda =-k_\lambda {{e}_{\lambda }^2}\le 0. \end{aligned}$$

(39)

Since the time-derivative of Lyapunov function ${\frac{d}{dt}}W_\lambda$ is semi-definitely negative and uniformly continuous, based on Barbalat’s lemma [34], the designed controller is asymptotically stable and ${e}_{\lambda }$ is converged to zero in a finite time.