Tellegen theorem and modelling of power systems-PV buses and nonlinear formulas

Tellegen´s theorem has often been used to derive network sensitivities for a variety of systems, including power systems. Recently, Tellegen´s theorem has been used to derive approximate nonlinear formulas for evaluating the response of a power system to large network perturbations. Those formulas are efficient and yield accurate results, but the efficiency deteriorates dramatically for systems with PV buses. The reason for the deterioration is that the coefficients of the formulas are computed under the assumption of PQ buses; hence, the resulting formulas have to be iteratively corrected. In the paper, approximate noniterative nonlinear formulas are developed which include PV and PQ buses with equal ease. The modelling behind these formulas is presented. It is shown that, whereas a PQ bus leads to a voltage controlled current source, a PV bus leads to a current controlled voltage source. It is also shown that the corresponding adjoint solutions can be obtained by solving a system of linear equations. A complete numerical example is provided to enable the replication of the results