Losses in power systems networks: Development of a generalized loss formula

Abstract

A generalized loss formula (GLF) is developed for the system losses around an operating point. It is a quasi-oscillatory approximation of the exact losses by having the same first and approximately the same second derivatives at the operating point, with respect to three sets of variables: generator powers <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> , generator voltage magnitudes <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> , and transformer tap settings <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> . The numerical results obtained from two test systems demonstrate that the error in the losses given by the GLF, in comparison to the exact losses from a load flow calculation, is relatively small.