A New Second-Order Linear Approximation to AC OPF Managing Flexibility Provision in Smart Grids

AC OPF is a building block in several power system applications and as such spurred a lot of research interest in providing tractable approximated solutions trading off quality and accuracy. In this regard, a novel linear approximation of active and reactive power flows, and longitudinal branch current expression is presented in this work. The proposed approach uses second-order Taylor series expansion of trigonometric terms and models the linear expressions in terms of square of voltage magnitude and voltage angle difference variables which leads to implicit modeling of network losses. Importantly, the developed approach does not rely on the flat-voltage, near-voltage and small angle assumptions. Three variants of the proposed approximation, based on the initial point of linearization (PoL), are incorporated in a fully linear AC OPF framework to procure ancillary services from distributed energy resources (DER). The proposed linear OPF models are evaluated on a modified 34-bus benchmark distribution network against the non-linear AC OPF model. Extensive numerical analysis shows that linearization around a power flow solution in comparison to flat start values leads to highly accurate results in terms of reduced errors values related to the objective function and active and reactive power injections as well as results in the precise determination of DER set-points even under a large deviation from the initial PoL.