Decoupled piecewise linear power flow and its application to under voltage load shedding

Various optimizations in power systems based on the AC power flow model are inherently mixed-integer nonlinear programming (MINLP) problems. Piecewise linear power flow models can handle nonlinearities and meanwhile ensure a high accuracy. Then, the MINLP problem can be turned into a tractable mixed-integer linear programming (MILP) problem. However, piecewise linearization also introduces a heavy computational burden because of the incorporation of a large number of binary variables especially for large systems. To achieve a better trade off between approximation accuracy and computational efficiency, this paper proposes a model called decoupled piecewise linear power flow (DPWLPF) for transmission systems. The P-Q decoupling characteristic is used to ease the evaluation of the piecewise cosine functions in the power flow equations. Therefore, in optimizations, the coupling between variables is reduced. Moreover, an under voltage load shedding (UVLS) approach based on DPWLPF is presented. Case studies are conducted for benchmark systems. The results show that the DPWLPF facilitates the solution of optimal power flow (OPF) and UVLS problems much better than conventional piecewise models. And DPWLPF still enhances the approximation accuracy by using the decoupled piecewise modeling.