Optimal Control of Virtual Batteries using Stochastic Linearization

Stochastic Linearization (SL) is a method of linearizing a nonlinearity that, unlike traditional Jacobian linearization that is valid only close to the operating point, uses statistical properties of the input to render the linearization fairly accurate over a wide range of inputs. In this paper, the method of SL is applied to optimally design controllers for an aggregation of distributed energy resources (DERs), called a virtual battery (VB), by taking into account the solar penetration levels, grid parameters, and the VB power limits. Analysis and simulation results show that VB performance can be greatly improved over a baseline design that ignores VB power limits, and that the controllers can be adaptively designed to effectively respond to changes in system parameters. This proves to be a new method for designing controllers to improve the participation of power-constrained VBs.