loss sensitivity formulas by adjoint networks

this paper presents a new set of formulas for computing power system loss sensitivities with respect to power system parameters. they are derived in the context of tellegen’s theorem and the concept of adjoint networks. the formulas are explicit, showing the combination of the power network quantities and the adjoint networks quantities. the formulas deal with branch-related and node-related parameters with equal ease. data and numerical results for the adjoint quantities and for the sensitivities are presented.