This paper deals with the problem of alleviating line overloads in a power system by generation rescheduling and load shedding. Mathematical models based on linearized relationships between line currents and state variables, and bus injected powers and state variables are systematically developed to considerthe line overload problem. Two algorithms are described to solve the models in the Newton-Raphson and decoupled load flow programs. The techniques developed can beused to determine the generation rescheduling and load curtailment pattern to alleviate line overloads. The approaches presented in this paper shouldprove useful in system security studies and reliability studies for examining line overload alleviation with minimum computational expense. The analytical results can also serve as an operating guide to the system dispatcher. In a companion paper, the effectiveness of these techniques in alleviating line overloads in several test systems is investigated.
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