This paper presents a novel method to approximate the nonlinear AC optimalpower flow (OPF) into tractable linear/ quadratic programming (LP/QP) based OPFproblems that can be used for power system planning and operation. We derive alinear power flow approximation and include a convex reformulation of the powerlosses in the form of absolute value functions. We show three ways how we canincorporate this approximation into an LP/QP based OPF problem. The usefulnessof our OPF methods is analyzed for the IEEE test case grids. As a result, theerrors on voltage magnitudes and angles are reasonable, while obtainingnear-optimal results. We find that our methods reduce significantly thecomputational complexity compared to the nonlinear AC-OPF making them a goodchoice for planning purposes.
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