New Method for Battery Sizing in Microgrids by Seeing Battery Autonomy as a Chance Constraint

In this paper, the authors have introduced a two-step method using MILP to size batteries along with DERs in a microgrid. The optimal objectives are to minimize simulation time and total net present cost (TNPC) of the microgrid at minimum unmet deferrable load (UDL) and optimally sizing batteries along with DERs. Therefore, battery size is selected as an optimal variable. It is achieved by seeing battery autonomy (BA) as a chance constraint. In the first-step, the simulations are performed based on random input vectors of batteries, converters (PCS), and DERs, including diesel generators (DGENS) and PV, and results are generated. Then chance constraint is applied to BA, and respective probability indices are calculated. Based on the threshold of probability index of BA, minimized objectives are calculated subject to constraints and presented as a Pareto front of TNPC vs. UDL. In the second-step, based on the highest probability index of BA, another battery-sizes vector is estimated, and simulations are re-performed. Again, the chance constraint is applied to BA, and respective probability indices are calculated. For comparison purposes, another random vector of battery sizes is re-estimated, and the same calculation steps are repeated. Results of both methods are compared, and it is seen that the proposed method outperforms the random vector method in terms of simulation time and minimized TNPC at minimum UDL.