Energy conservation law and its application for the direct energy method of power system stability

Many papers have contributed to the development of energy functions for power systems. However, there exists limitation in that the conventional energy functions cannot reflect the control effects of the speed governor and exciter efficiently. In this paper, two useful theorems are developed regarding the relationships of the energy integral of generator power versus its phasor current and voltage. With the use of the two theorems, the energy conservation law can be derived to reflect the resistance, flux-decaying effects, saliency with wide adaptability to various detailed generator models including the governor and exciter control loops. By the rigorous mathematical analysis and numerical tests with its application to sample systems, the proposed energy conservation law is proven to be very exact and valid for any kind of generator models including the speed governor and exciter controls