Tellegen's theorem and power systems-new load flow equations, new solution methods

The exact steady-state response of a power system to perturbations has always been evaluated by solving the corresponding load-flow equations. New equations are proposed for evaluating the exact response of the power system to arbitrary perturbations. These equations are not derived from the system and nodal equations, as the conventional load-flow equations are; rather, they are derived from a well-known form of Tellegen's equation. It is shown that the adjoint network information commonly computed for first-order sensitivity analysis is sufficient for the computation of the coefficients to be used on these new equations. The problem of the existence of a solution is addressed, and special solution formulas for the case of network perturbations are developed. A complete numerical example is presented to illustrate the results.>