ScienceDirect IFAC-PapersOnLine 48-30 (2015) 363–368 ScienceDirect Available online at www.sciencedirect.com 2405-8963 © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2015.12.405 © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Optimal control, islanded microgrids, Kuramoto model, renewable energy. 1. INTRODUCTION A microgrid is an interconnected low voltage group of devices consisting of distributed energy resources (DERs) and loads. It is typically seen by the main grid as a single controllable entity and it connects or disconnects to the main grid on previously defined events and therefore works in grid connected or islanded mode respectively (Hatziar- gyriou et al., 2007). DERs can be either AC resources such as wind turbines or DC resources such as solar panels and, for both cases, AC/AC or DC/AC voltage source inverters are needed to ensure network synchronization. A microgrid may consist of a wind turbine, solar energy resource, storage device and loads connected in a logical bus (or ring) as shown in Figure 1. Microgrids facilitate distributed generation and high penetration of renewable energy sources and hence increase power quality and relia- bility of electric supply (Barker and Herman, 2002). Fault events within the connection with the main grid could lead to an islanded mode of operation (Katiraei et al., 2005). Frequency control is needed in both grid connected and island modes. Control strategies for island modes are dis- cussed in (Peas Lopes et al., 2006) where it was shown that the forced islanding of the microgrid can be per- formed safely under several different power importing and exporting conditions. They also showed that management of storage devices are essential to implement successful control strategies. In this paper we take advantage of the existence of storage devices to provide a desired feasible control flexibility to respond to renewable energy sources that do not have a well predicted power generation behav- ior. In a grid connected mode, the microgrid - depending on the amount of power generated and consumed - acts as either a load when the power consumption within the microgrid exceeds the supply, or as a generator when the supply exceeds the consumption. The latter case is called power penetration where the grid injects power to the main grid (Mathiesen et al., 2011). Although this penetration reduces the overall amount of power needed to be sup- 1 S. Sahyoun and S. M. Djouadi are with the University of Ten- nessee, Knoxville, TN 37996 USA (e-mails: ssahyoun@vols.utk.edu, djouadi@eecs.utk.edu). 2 M. Shankar is with Oak Ridge National Lab, Oak Ridge, TN 37830 USA, he is also a joint faculty member at the University of Tennessee. (e-mail: shankarm@ornl.gov). Fig. 1. Microgrid basic elements plied by the main grid, the fluctuating and intermittent nature of this renewable generation causes variations of power flow that can significantly affect the operation of the electrical grid and causes frequency instabilities (Kroposki et al., 2008). Wind generation for instance is a growing renewable energy resource but a known challenge is to effectively integrate a significant amount of wind power into the power network (Georgilakis, 2008). Figures (2) and (3) show a 24 hours simulation of power consumption and supply for two households that use solar energy resources.The black curve is the amount of power supplied by the main grid, the blue curve is the household consumption while the red curve is the generated power from the solar energy resources. The simulation starts at 12:00 am at night where there is no solar energy generation so the power consumption equals exactly the power supplied by the grid. In the morning, the solar Abstract: For an islanded microgrid modeled by a Kuramoto oscillators nonlinear model, we design the distributed optimal controller using the maximum principle optimization theory. We first quantify synchrony in terms of phases and droop coefficients at the inverters in the microgrid and then we maximize it. We prove that the solution of the distributed optimal control problem exists and we find it. We evaluate performance in a simulation case. S. Sahyoun 1 , S. M. Djouadi 1 , and M. Shankar 2 Optimal Control of Droop Controlled Inverters in Islanded Microgrids