Tertiary Control of Islanded Microgrids Based on a Linearized ACOPF with Losses Compensation

A tertiary control based on linearized AC optimal power flow(OPF) for islanded microgrids is developed. Nonlinear power flow constraints typically make AC OPF problems nonconvex and computationally intractable. To address this concern, a lossless linearized power flow (LPF) for islanded microgrids is proposed that does not assume a fixed slack bus voltage to convexify AC OPFs under some reasonable assumptions. The approximation error of LPF is examined via norm inequality in finite-dimensional vector space. The geometry of the proposed LPF model is then explored and the effect of fixed voltage assumptions on power generation is studied. As OPFs based on lossless power flow cannot limit power losses when minimizing operational cost as an AC OPF does, a linearized AC OPF model that minimizes operational cost and active power losses as the core of the tertiary control is developed. Moreover, a losses compensation algorithm is proposed to supply power losses using dispatchable generators. Case studies demonstrate that the proposed approach provides substantial computational speed improvements with minimal errors compared to a typical AC OPF.