A complex Lagrangian approach with applications to power network sensitivity analysis

The well-known Lagrangian approach, traditionally described in real form, for calculating first-order changes and gradients of functions of interest subject to equality constraints is generalized and applied in a compact complex form. Hence, general complex functions and constraints can be handled directly while maintaining the original complex mode of formulation. The theoretical foundations of the approach are stated. An application to power network sensitivity analysis and gradient evaluation is presented.