Advanced nonlinear controller of single‐phase shunt active power filter interfacing solar photovoltaic source and electrical power grid

Abstract

This paper addresses the nonlinear controller design and the stability analysis of a shunt active power filter (SAPF) interfacing a solar photovoltaic (PV) system that consists of a couple of PV panels, a single-phase two-stage IGBT half-bridge SAPF and two identical DC link capacitors. We seek for the considered system the fulfillment of three control objectives: (a) extracting the maximum PV power using an appropriate maximum power point tracking (MPPT) algorithm; (b) regulation of the DC link capacitor voltages to the reference provided by the MPPT controller hence ensuring the exchange of power between the PV source and the AC power grid; (c) compensation for reactive power and undesired harmonics caused by the nonlinearity of electronic power loads, that is, performing power factor correction (PFC). The control objectives are achieved using a new two-loop cascaded controller. The Backstepping approach is applied in the inner loop to perform PFC. A filtered proportional-integral (PI) controller is applied in the outer loop to ensure tight regulation of the PV voltage. The MPPT control is implemented using a perturb-and-observe (PO) algorithm. The performance of the closed-loop system under the two-loop control strategy is formally analyzed through the Lyapunov approach applied to the averaged model. Numerical simulations are performed in MATLAB/SimPowerSystems environment to validate the design methodology and to confirm the theoretically predicted performances of the system under the proposed nonlinear controller.average analysis, Lyapunov stability analysis, nonlinear control, power factor correction, shunt active power filter, solar photovoltaic system List of Symbols and Abbreviations: L g , grid inductor; r g , grid resistor; R, load resistor; L, load inductor; C pv , filter capacitor; r f , filter resistor; L f , filter inductor; N s ,N p , number of connected modules in series and in parallel respectively; G, irradiance; T, temperature; μ, binary switching signal; i g , grid current; v go , grid voltage; i f , filtering current; i L , load current; i pv1 , i pv2 , PV output currents; v pv1 , v pv2 , PV output voltages; u, continuous control input; β, external control signal; P pv , PV panels power; v f , inverter output voltage; v g , voltage at point of common coupling; I f , peak value of output filter current; V f , peak value of inverter output voltage; θ 1 , phase of the voltage at point of common coupling; θ 2 , phase of the output filter current; χ, square of the PV voltage; u à , Steady state value of u; V , Lyapunov function candidate; f PWM , switching frequency; Q g , reactive power; T g , grid period; P g , active power; c 1 ,c 2 , c 3 , c 4 , controller parameters; ω g , angular frequency; IC, incremental conductance; IGBT, insulated-gate bipolar transistor; MPP, maximum power point; MPPT, maximum power point tracking; PCC, point of common coupling; PFC, power factor correction; PI, proportional-integral; PO, perturb and observe; PV, photovoltaic; PWM, pulse width modulation principle; SAP...