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This paper presents a new method for minimizing transmission line losses and improving voltage profile in a given system by adjusting control variables, i.e., tap position of transformers and reactive power injection of VAR sources. Transmission losses are considered as a function of voltage increments. The control variables and voltage increments are related by a modified Jacobian matrix. Linear Programming (LP) is used to calculate the voltage increments which minimize the transmission losses, and the adjustments of control variables are obtained by a modified Jacobian matrix. Since this method does not need any matrix inversion, it will save computational time and memory space.
Qiu et al. (Thu,) studied this question.