4402 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS–I: REGULAR PAPERS, VOL. 66, NO. 11, NOVEMBER 2019 Complementarity Model of a Photovoltaic Power Electronic System With Model Predictive Control Rodrigo Morfin-Magaña , J. Jesus Rico-Melgoza, Member, IEEE, Fernando Ornelas-Tellez , Member, IEEE, and Francesco Vasca Abstract— The modeling and control problem for a grid-connected photovoltaic (PV) power electronic system, which includes a dc/dc boost converter, an inverter and a filter are con- sidered. A linear complementarity (LC) dynamic model of the PV system allows the design of a model predictive controller (MPC). Dynamic models of the subsystems are obtained and merged in order to represent the whole PV system in a compact and comprehensive LC model, which is valid for all operating modes of power converters and PV cells involved in the energy con- version process. A finite-control-set MPC problem is formulated as a mixed-integer quadratic program subject to the dynamic LC model and pulse width modulators. The minimization of an objective function aimed at tracking dc voltage and grid current references provides directly the commands for the switches of the boost converter and inverter. Numerical results show the effectiveness of the proposed strategy for maximum power point tracking and synchronization to the grid under dynamic scenarios characterized by variations of the solar irradiance. Index Terms— Power system modeling, photovoltaic systems, predictive control, complementarity model, pulse width modula- tion converters. I. I NTRODUCTION E LECTRIC power distribution systems are continuously expanding and increasing their flexibility. The integra- tion of photovoltaic (PV) generation systems into the power grid demands not only modern power electronic equipment, but also state-of-the-art techniques that through modelling and control design would ensure the compatibility of these renewable resources with the existing electric power system. Model predictive control (MPC) has been shown to be an effective technique for the regulation of power converters in many application fields [1] and, more recently, has been also applied for the maximum power point tracking (MPPT) in photovoltaic (PV) power electronic systems [2], [3]. MPC techniques for power converters can be divided into two main classes: continuous-control-set MPC (CCS-MPC) and finite-control-set MPC (FCS-MPC). In CCS-MPC the Manuscript received March 22, 2019; revised June 11, 2019; accepted June 16, 2019. Date of publication July 10, 2019; date of current version October 30, 2019. This work was supported by CONACYT, Mexico, under Project CB-222760 and under Grant 401242. This paper was recommended by Associate Editor G. Russo. (Corresponding author: Rodrigo Morfin-Magaña.) R. Morfin-Magaña, J. J. Rico-Melgoza, and F. Ornelas-Tellez are with the Faculty of Electrical Engineering, Universidad Michoacana de San Nicolás de Hidalgo, Morelia 58030, Mexico (e-mail: rodrigo.morfin@gmail.com). F. Vasca is with the Department of Engineering, University of Sannio, 82100 Benevento, Italy (e-mail: francesco.vasca@unisannio.it). Color versions of one or more of the figures in this article are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCSI.2019.2923978 output of the predictive controller provides the continuous modulation signals which are transformed into the switches commands employing suitable modulators, e.g., pulse width modulation (PWM). The sampling rate of the CCS-MPC is usually chosen as the modulation period and the prediction over one or more periods is obtained by exploiting averaged models of the converters involved in the PV system [4], [5]. CCS-MPC have been applied to different converter topolo- gies for PV applications, e.g. Z-source inverter [6], [7] and DC/DC boost converter with three-phase inverter [8]. Prac- tical operative scenarios of grid-connected power converters usually determine the converter to operate in continuous and discontinuous conduction modes, which contributes to the dif- ficulties for determining a proper averaged model valid for all operating conditions. Indeed, MPC requires the prediction of the system state whose evolution depends on the sequence of configurations of the circuit which are not directly controllable in many situations, such as for the conducting and blocking states of the diodes [9]. In FCS-MPC for PV power electronic systems the predictive controller selects at each sampling time the optimal configura- tion to be implemented in the next period by choosing among the finite set of possibilities corresponding to the combinations of the switches states in the prediction horizon [10]. FCS-MPC too suffers from the problem of possible occurrence of dis- continuous conduction modes within the sampling period(s) characterizing the time interval chosen for the prediction. FCS-MPC for MPPT has been applied for PV systems with flyback DC/DC converters [11], [12] which have been also adopted for energy harvesting architectures [13], boost DC/DC converter [14], multilevel converters [15]. In order to detect the different modes of the converters within a fixed control period, for the integration of the dynamic model within the prediction horizon one could use a sampling period smaller than the control period [16]. A similar idea is used in our paper where the MPC problem is solved by considering linear complementarity (LC) models which pro- vide a very intuitive and circuit-based procedural framework for constructing the power converters model. Indeed, a first relevant contribution of this paper is the complete modelling of the PV generation system in a compact LC model, which includes the power converters together with the nonlinear pho- tovoltaic cell based on its equivalent circuit. This confirms the capabilities of LC models for representing in a comprehensive way the dynamic behaviors of nonlinear switched circuits used 1549-8328 © 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.