Robust multiobjective control method for power sharing among distributed energy resources in islanded microgrids with unbalanced and nonlinear loads Sasan Gholami a,⇑ , Sajeeb Saha b , Mohammad Aldeen a a The University of Melbourne, Australia b Deakin University, Australia article info Article history: Received 21 February 2017 Received in revised form 14 June 2017 Accepted 17 July 2017 Keywords: Distributed energy resources Harmonically polluted loads Islanded microgrid Multiobjective control Power sharing Unbalanced loads abstract This paper proposes a robust control method for power sharing among dispatchable electronically- coupled distributed energy resources (DERs) in an autonomous microgrid. The DER units operate in par- allel to meet the total aggregated load demand. The aggregated load is assumed to be uncertain, unbal- anced and/or nonlinear, thus it is considered as a source of unmodeled dynamics. The main objective of this paper is to design an H 1 robust controller to enable tracking reference commands of the voltages at the output of the DERs in the presence of unmodeled dynamics. In addition, the H 1 control design prob- lem is combined with other control methods, such as constrained optimal control and regional pole placement, to achieve an optimal control objective, and to improve transient response. The optimal con- troller is achieved by minimizing an upper bound on H 2 performance. The regional pole placement is achieved by defining a linear matrix inequalities (LMI) region. This multiobjective H 2 /H 1 problem, com- bined with regional pole placement are expressed as a set of LMIs, and solved by using standard convex optimization algorithms. To show the effectiveness of the proposed method in maintaining the desired voltage at the DER outputs, in presence of unbalanced and nonlinear loads, simulation results are pro- vided for a single DER unit, and the performance of the proposed control strategy is compared with three different controller strategies. Power sharing among multi DER units in autonomous networks is then demonstrated through digital time-domain simulation studies using MATLAB/SimPowerSystems Toolbox. Ó 2017 Elsevier Ltd. All rights reserved. 1. Introduction Autonomous power grids are viable means of electrifying remote communities due to the infeasible interconnection with the main power network and/or economic reasons. The common choice for supply of electricity in these remote communities has been fossil-fuel generation [1]. Recently, integration of renewable generation technologies has become a preferred option for eco- nomical, technical, and environmental reasons. An acceptable alternative for integrating distributed energy resources (DERs) are microgrids [2]. A microgrid can be defined as a cluster of DER units, energy storage units and (local) loads that can be controlled as a single integrated control system. A microgrid may operate in grid- connected or islanded modes [3]. Most modern DER units use volt- age source converters (VSCs), which acts as an interface between the energy source and AC grid, and hence a substantial amount of research has been alloted to control of converter-based DER units, in particular control of islanded-mode microgrids [4–11]. It is well-known that converter dynamics are highly nonlinear, due to switching action (and also due to possible saturation of pulse width modulation (PWM) signals), however, the model usu- ally used to design control strategies is a linearized model about an operating point. Linearized models allow for simpler and lower cost linear controllers compared to nonlinear models. Linear mod- els commonly neglect high frequency ripples (which is valid because the switching frequency is relatively much higher than the system dynamics [12]). Regardless of the type of model used, in most cases, a load connected to a DER system might be topolog- ically unknown or structurally uncertain. Although the load cur- rent can be measured, the load dynamics may be nonlinear and in some cases (e.g. a rectifier unit) difficult to model. In order to take into account the overall system uncertainties or unmodeled nonlinearities, robust control of electronically-coupled DER units has been investigated [11,13–16]. http://dx.doi.org/10.1016/j.ijepes.2017.07.012 0142-0615/Ó 2017 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: gholami.sasan@gmail.com (S. Gholami). Electrical Power and Energy Systems 94 (2018) 321–338 Contents lists available at ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes