An Optimal Linear Quadratic Regulator in Closed Loop with Boost Converter for Current Photovoltaic Application

Abstract

In this paper, a steady-state output power oscillation problem is overcome using the indirect control mode based-Perturb and Observe (P&O) implementation algorithm. This can be ensured through controlling the duty cycle input of the DC-DC boost converter using the proposed Linear Quadratic Regulator (LQR) controller. Their parameters are optimized using the Grasshopper Optimization Algorithm (GOA) where a good tracking behavior of a desired Maximum Power Point (MPP) can be guaranteed for various sudden changes in weather conditions such as absolute temperature and solar irradiance. The desired performances and robustness of the closed-loop system can be achieved by the two following stages. In the first stage, the standard P&O algorithm based-direct control mode generates a reference current perturbation using both existing electrical power and measured PV current. Accordingly, a current error perturbation is provided through the discrepancy between reference and measured currents. In the second stage, the previous current error provided in the inner control-loop is mitigated as much as possible using the stabilized LQR controller. The current control-loop problem is addressed with a detailed analysis technique of averaging and linearization, in which the linearization of actual PV-boost converter system around the desired MPP allows determining the corresponding linear plant-model. This leads to well optimize the LQR controller parameters. The performance and robustness provided by the P&O algorithm based-indirect duty cycle control are shown for sudden changes in solar irradiance and absolute temperature as well as in a wide variation of the resistive load.