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.

Many papers have recently 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 govemor and exciter eflticiently. 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 govemor 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 govemor and exciter controls.

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