Standalone DC Microgrids as Complementarity Dynamical Systems: Modeling and Applications Arash M. Dizqah a,* , Alireza Maheri a , Krishna Busawon a , Peter Fritzson b a Faculty of Engineering and Environment, Northumbria University, NE1 8ST, Newcastle upon Tyne, UK b PELAB - Programming Env. Lab, Link¨ oping University, SE-581 83, Link¨ oping, Sweden Abstract It is well-known that, due to bimodal operation as well as existent discontinuous differential states of batteries, standalone microgrids belong to the class of hybrid dynamical systems of non-Filippov type. In this work, however, standalone microgrids are presented as complementarity systems (CSs) of the Filippov type which is then used to develop a multivariable nonlinear model predictive control (NMPC)-based load tracking strategy as well as Modelica models for long-term simulation purposes. The developed load tracker strategy is a multi-source maximum power point tracker (MPPT) that also regulate the DC bus voltage at its nominal value with the maximum of ±2.0% error despite substantial demand and supply variations. Keywords: Nonlinear model predictive control (NMPC), Mixed complementarity problem (MCP), Wind energy, Photovoltaic (PV), Lead-acid battery, Modelica, Modeling, Maximum power point tracking (MPPT). 1. Introduction Microgrids are the building blocks of the modern power grids. In fact, the near future distribution grids can be seen as a network of several intercon- nected microgrids which locally generate, consume, and even store energy [1]. Intermittent solar and wind energies, coupled with battery storages, con- tributes to the energy resources for supplying vari- able load demands of the microgrids [2]. Due to some challenges that ac microgrids face with host- ing several distributed energy systems [3, 4], such as the need for synchronization, dc microgrids have gained more popularity particularly for standalone applications in avionic, automotive, or marine in- dustries as well as the remote rural areas [1, 5]. There are various interests in employing nonlinear model predictive control (NMPC) technique [6, 7] to develop coordinated multivariable control strate- gies for the standalone microgrids (e.g. [8, 9]). However, such control strategies require the use of * Corresponding author Email address: arash.moradinegade@northumbria.ac.uk (Arash M. Dizqah ) an adequate mathematical model of the microgrids in order to predict their behavior during the pre- diction horizon. Moreover, in smart grid applica- tions, such a model is needed to simulate the mi- crogrids behavior for at least one day ahead [10]. There are three major considerations that need to be taken into account when developing a mathemat- ical model for the microgrids: i) the algebraic con- straints presented by the PV module, wind turbine, and battery bank; ii) the battery bank as a sub- system with two modes of operation, namely, charg- ing and discharging; and iii) the cycle life of the battery bank as a discontinuous differential state. Algebraic constraints and bimodal operation of battery bank lead to a description of standalone dc microgrids as a set of hybrid differential algebraic equations (hybrid DAEs) [11, 12]. Therefore, the standalone dc microgrids can be represented by an acausal model for the control and simulation pur- poses. Unlike the causal approach, which requires the system being decomposed into a chain of causal interacting blocks consisting of only ordinary dif- ferential equations (ODEs), the acausal modeling is a declarative approach in which individual parts of the model are described as hybrid DAEs [12]. Preprint submitted to Elsevier October 17, 2014 Control Engineering Practice, 2/2015, vol. 35, pp:102-112