Derivation of energy conservation law by complex line integral for the direct energy method of power system stability

This paper presents a complex line integral approach to derive an energy conservation law which reflects the resistance, flux-decaying effects, saliency with wide adaptability to various detailed generator models including the governor and exciter control loops. Especially, the previous work has shown that an exact energy conservation law can be derived under the assumption of stator network transients being negligible. In this paper, it is shown that an exact energy conservation law can be derived by using the complex line integral approach without any assumptions. Consequently, the proposed energy conservation law is applicable to power systems adopting any kind of detailed generator model. The stator resistance of the generator can be taken into account in a simple manner. The proposed energy conservation law is tested for several sample systems and the results show its validity