Complete adjoint-based incremental power flow equations

This paper derives a new complete set of incremental power flow equations based on adjoint networks and Tellegen's theorem. The adjoint networks model the power system passive network, the loads or PQ buses, the generators or PV buses, and the reference bus. The adjoint solutions are used as coefficients to the new equations. The new equations are exact. The power system can be submitted to changes in network configuration, changes in loads, and changes in the values specified for generation. The equations presented in this paper relate those changes with the corresponding changes in voltages. A five-node system example chosen so as to illustrate some specific details of the adjoint-based power flow solution allows the replication of final and intermediate results by the reader. The performance of the equations for a realist transmission network is also presented.