Derivation of P-Q loss sensitivities by angle reference transposition and an application to optimal P-Q generation for minimum cost

In this letter, the reactive power loss sensitivities as well as the active loss sensitivities are derived using the angle reference transposition. Four kinds of power loss sensitivities of all generators, including the slack bus, can be obtained by specifying the angle reference on a load bus that has no generation. As an example application, we show a formula with which these loss sensitivities can be used to derive the optimal P-Q allocation for minimizing the total system operating cost. A simulation is carried out on a sample system, and the results show that these loss sensitivities can also be used to obtain the optimal solutions in power system computations.