Maximum power point tracking in photovoltaic systems using indirect adaptive fuzzy robust controller

Abstract

A photovoltaic system is used to produce energy that is dependent on environmental conditions such as irradiance, temperature, and the load attached to it. Due to the nonlinear characteristics, parameter uncertainties and load disturbance of photovoltaic (PV) systems and the problem of low efficiency due to the variation of environmental conditions, the maximum power point tracking method is required to extract the maximum power from the PV system. So, in this paper a novel indirect adaptive fuzzy fractional-order sliding mode is proposed to tackle this challenge. This method is based on a two-loop method. The first loop is designed to seek the maximum power point, and the second loop is designed to track the maximum power point. At first, a novel fractional-order sliding surface is proposed. Then, chattering in control signal is removed using a continuous function. In this paper, an indirect adaptive fuzzy system is used to estimate the unknown function of the system and adaptation laws are obtained based on the Lyapunov theory. The performance of the photovoltaic system is investigated by applying the proposed method, conventional sliding mode controller, integral sliding mode controller and backstepping sliding mode controller. Simulation results indicate the effectiveness of the proposed method.

Appendix: Proof of Theorem 1

The Lyapunov function is considered as follows:

$$ V = \frac{1}{2}s^{2} $$

(80)

Taking the time derivative of (80) gives:

$$ \dot{V} = s\dot{s} $$

(81)

By using (20) and (21), the above equation can be written as:

$$ \dot{V} = s\left( { - \delta {\text{sign}}\left( s \right)} \right) = - \,\delta \left| s \right| \le 0 $$

(82)

Based on the value $\delta$ > 0, Eq. (82) is always semi-negative and the closed-loop system is stable. Also, using (82), the reaching time to the sliding surface is obtained as follows:

$$ s\dot{s} \le - \delta \left| s \right| \to s\frac{{{\text{d}}s}}{{{\text{d}}t}} \le - \delta \left| s \right| $$

(83)

$$ \mathop \int \limits_{s\left( 0 \right)}^{0} \frac{s}{\left| s \right|}{\text{d}}s \le \mathop \int \limits_{0}^{{t_{r} }} - \delta {\text{d}}t \to t_{{\text{r}}} \le \frac{{\left| {s\left( 0 \right)} \right|}}{\delta } $$

(84)