Contents lists available at ScienceDirect Control Engineering Practice journal homepage: www.elsevier.com/locate/conengprac A backstepping high-order sliding mode voltage control strategy for an islanded microgrid with harmonic/interharmonic loads Nima Mahdian Dehkordi a, ⁎ , Nasser Sadati a , Mohsen Hamzeh b a Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran b Department of Electrical Engineering, Shahid Beheshti University, Tehran, Iran ARTICLE INFO Keywords: Backstepping control High-order sliding mode differentiator Interharmonic current Microgrid Unbalanced and nonlinear loads ABSTRACT This paper presents a new nonlinear voltage control strategy based on backstepping control and a high-order sliding mode differentiator for an islanded microgrid. The microgrid consists of multiple distributed generation (DG) units with an arbitrary configuration that can be parametrically uncertain or topologically unknown. The proposed controller robustly regulates the microgrid voltages in the presence of parametric uncertainties, unmodeled dynamics, load imbalances, and nonlinear loads with harmonic/interharmonic currents. In contrast to existing methods, the controller does not need to know the frequency of harmonic and interharmonic current of microgrid loads that lead to the reduction of the steady-state error of the voltage controller in the frequency of unknown harmonics and interharmonics. The MATLAB/SimPowerSystems toolbox has verified the proposed control strategy's performance. 1. Introduction Distributed generation (DG) includes renewable or nonconven- tional energy resources such as wind turbines and photovoltaic arrays. These resources are connected to the grid using power electronic interfacing converters. A microgrid, consisting of DGs and loads in a local area, is an appropriate solution to problems caused by the high penetration of DGs. A microgrid can be operated in both grid- connected and islanded modes. In grid-connected mode, the frequency and voltages of microgrid are imposed by the main grid. In this case, each DG unit controls its own real/reactive power. In the islanded operation of a microgrid, the control techniques used in the grid- connected mode no longer ensure the desired operation of the microgrid (Nikkhajoei & Lasseter, 2009). Hence, after an islanding event, a proper control strategy must be adopted to regulate the frequency and voltages of the microgrid at the point of common coupling (PCC) and manages/shares power between DG units. In stand-alone applications, the main objective of the control system is to regulate the microgrid loads' voltages (e.g., RLC loads, unbalanced loads, and nonlinear loads with harmonic/interharmonic currents) without any performance degradation. According to IEEE standards (IEEE, 2009), the voltage's total harmonic distortion (THD) for sensitive loads should be maintained within 5%. Based on IEEE standards (Gunther, 2002), components with frequencies that are between harmonics are called interharmonics. Interharmonic currents, which are usually presented in the industrial microgrids, have become more significant because of the widespread use of nonlinear loads in such systems. The main sources of interharmonic currents include arcing loads and rapid current changes in equipment and installations; in many cases their amplitude and frequency of harmonics and interharmonics are unknown. Therefore, the improvement of the microgrid power quality through the proper control strategy of converter-based DG units is an issue with high potential for engineer- ing solutions (Cespedes & Sun, 2014). Many control strategies for islanded operation of DGs have been developed in recent years. The best known strategies are the frequency/ real-power and voltage/reactive-power based on the droop control technique for voltage and frequency control of a multi-DG microgrid (Guerrero, Vasquez, Matas, de Vicua, & Castilla, 2011; Majumder, Ledwich, Ghosh, Chakrabarti, & Zare, 2010). Several islanded mode control strategies have been proposed for voltage control of microgrid (Karimi, Davison, & Iravani, 2010; Karimi, Yazdani, & Iravani, 2011). However, existing methods have the following drawbacks: 1. Many control methods are usually synthesized in small-signal equations. Despite its simplicity, small-signal-based controllers lack global stability, which is a necessary requirement in complex networks (Ahmed, Massoud, Finney, & Williams, 2011; Babazadeh & Karimi, 2013; Bahrani, Saeedifard, Karimi, & Rufer, 2013; Hamzeh, Emamian, Karimi, & Mahseredjian, 2016). http://dx.doi.org/10.1016/j.conengprac.2016.10.008 Received 15 April 2016; Received in revised form 17 October 2016; Accepted 18 October 2016 ⁎ Corresponding author. E-mail addresses: mahdian_dehkordi@ee.sharif.edu (N. Mahdian Dehkordi), sadati@sharif.edu (N. Sadati), mo_hamzeh@sbu.ac.ir (M. Hamzeh). Control Engineering Practice 58 (2017) 150–160 0967-0661/ © 2016 Elsevier Ltd. All rights reserved. crossmark