IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 54, NO. 5, SEPTEMBER/OCTOBER 2018 4875 Model Predictive Direct Power Control of Three-Phase Grid-Connected Converters With Fuzzy-Based Duty Cycle Modulation Amir Masoud Bozorgi , Student Member, IEEE, Hosein Gholami-Khesht, Mehdi Farasat , Member, IEEE, Shahab Mehraeen , Member, IEEE, and Mohammad Monfared , Senior Member, IEEE Abstract—An improved model predictive direct power control (MPDPC) for three-phase grid-connected converters is proposed. In the proposed method, two voltage vectors are applied during a control period and their duty cycles are determined by a fuzzy logic-based modulator. The inputs to the modulator are the active and reactive power errors and the output is the duty cycle of the first (main) voltage vector. The fuzzy rules are developed based on expert knowledge and the fact that small/large power errors can be compensated by applying the main voltage vector for a small/large portion of the switching period. The candidate voltage vector pairs are examined on a control Lyapunov function and the pair that satisfy the closed-loop stability criteria are selected. The voltage vector pairs are then applied following a proposed switch- ing pattern through which reduced average switching frequency is achieved. Comparative simulation and hardware-in-the-loop stud- ies between the proposed method and a most recently introduced duty cycle-based MPDPC confirm that in addition to lower av- erage switching frequency, better quality currents and active and reactive powers can be achieved under the proposed MPDPC. Index Terms—Control Lyapunov function (CLF), fuzzy logic modulator, model predictive direct power control (MPDPC), switching pattern. I. INTRODUCTION M ODEL predictive direct power control (MPDPC) is a promising control scheme for grid-connected renewable energy systems due to its simple concept and fast dynamics in controlling the power flow between the renewable energy resource and the grid [1], [2]. MPDPC takes advantage of the discrete nature as well as the limited number of available switch- ing states of the power electronics converters. In this method, Manuscript received January 14, 2018; revised April 8, 2018; accepted May 16, 2018. Date of publication May 21, 2018; date of current version September 17, 2018. Paper 2018-IACC-0056.R1, presented at the 2017 Energy Conversion Congress & Exposition, Cincinnati, OH, USA, Oct. 2017, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the In- dustrial Automation and Control Committee of the IEEE Industry Applications Society. This work was supported by Louisiana Board of Regents under Grant 2015-18-RD-A-04. (Corresponding author: Mehdi Farasat.) A. M. Bozorgi, M. Farasat, and S. Mehraeen are with the Division of Electrical and Computer Engineering, Louisiana State University, Baton Rouge, LA 70803 USA (e-mail:, abozor3@lsu.edu; mfarasat@lsu.edu; smehraeen@lsu.edu). H. Gholami-Khesht and M. Monfared are with the Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad 9177948974, Iran (e-mail:, gholami.hosien@yahoo.com; m.monfared@um. ac.ir). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIA.2018.2839660 all possible switching states are examined in each sampling pe- riod and the state that minimizes a predefined cost function is selected and applied to the converter during the next period. The cost function in MPDPC is commonly selected as absolute or squared error of the predicted and the reference powers [3]– [6]. Additional control objectives and constraints can also be included to attain more flexibility. Since in each sampling period the switching state is deter- mined directly based on the cost function value, the switch- ing frequency is variable and the produced currents contain a widespread spectrum of harmonics [7]. This issue is addressed in [8] and [9] by modifying the cost function with adding a discrete digital filter and a nonlinear constraint. In order to reduce the current distortion as well as the power ripple, MPDPC techniques with constant switching frequency (CS-MPDPC) are proposed [10]–[17]. In each sampling period, three voltage vectors (a zero and two active voltage vectors) are selected and applied. Generally, these vectors are selected based on the spatial location of the grid voltage space vector and the least square optimization method is employed to calculate the optimum duty ratio of each voltage vector. An issue that may arise in CS-MPDPC methods is negative duty cycles of the active voltage vectors. As concluded in [14], selecting the voltage vectors based on the sector of the grid voltage space vector may result in negative duty cycles for some load conditions. In such cases, if appropriate measures are not taken, the controller makes the negative duty cycles equal to zero. This in turn results in periodic fluctuations in the controlled active and reactive powers and low-order harmonic content in the currents. This issue is investigated in [14]–[17]. In [14], a CS-MPDPC is proposed based on selecting voltage vectors which may not necessarily be adjacent. Applying such voltage vectors may require more than two switching transitions during a sampling period. This issue complicates the digital implementation and increases the switching losses. To address this issue, selecting the voltage vectors based on the angular position of the inverter reference voltage vector is proposed in [15]. The angular position is obtained by employing a virtual flux observer. In [16], a method for handling negative duty cycles is pro- posed. The cost function is modified in a way that the most appropriate combination of adjacent voltage vectors is selected and applied in each control period. In [17], negative duty cycles 0093-9994 © 2018 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.