The Resolution of the Optimal Reactive Power Dispatch with Continuous and Discrete Variables

This paper presents a strategy for solving the optimal reactive dispatch (ORD) problem with continuous and discrete control variables; the tap ratios of transformers and shunt susceptances of switchable capacitor banks and reactors are the discrete control variables. The discrete control variables are treated as continuous and handled by either a sinusoidal or a polynomial discretisation function. This elaborate modelling of discrete variables results in a modified ORD and, due to the proposed resolution algorithm, it can be efficiently solved by nonlinear programming methods, such as the Generalised Reduced Gradient algorithm. The efficiency and robustness of the proposed modelling are shown for IEEE benchmark test-systems with up to 300 buses. Test results show the success in providing good solutions while attaining directly the discrete values of controls without further approximations.