Available Transfer Capability Calculation Using a Smoothing Pointwise Maximum Function

The determination of the available transfer capability (ATC) is formulated as a problem of finding the solution of a system of equations using the pointwise maximum function, which collapses all operating constraints of the system into one equation. The resulting equations are semismooth. The semismooth equations are solved by the use of a smoothing function. Two solution algorithms are presented. One is a smoothing Newton method in which the smoothing parameter is treated as an independent variable. Another one is a smoothing decoupled Newton method, which incorporates the inherent weak-coupling characteristics of power systems into the algorithm and is suitable for solving large scale problems. The convergence of the two algorithms is studied in detail. A numerical example is presented to illustrate the effectiveness of the proposed methods.