## Minimisation of active power losses and number of control adjustments in the optimal reactive dispatch problem

Trade-offs between power system's optimal operational performance and the minimal number of control adjustments necessary to attain a desired operating point make optimal reactive dispatch (ORD) solutions practical to system operators. In this study, a multi-objective ORD model that provides, in terms of weighting factors, trade-offs between minimal active power losses in transmission systems and minimal number of control adjustments in generator voltages, tap ratios and shunt controls is featured. This multi-objective ORD is formulated as a mixed-integer non-linear programming (MINLP) problem, and the proposed resolution methodology is based on translating the original MINLP problem into non-linear programming (NLP) problem deploying a sigmoid function, enabling the use of NLP solvers. Both original MINLP and translated NLP models are implemented in GAMS and numerical tests with IEEE test-systems with up to 300 buses are conducted using DICOPT, KNITRO and CONOPT solvers to validate the proposed ORD model and its resolution methodology. Results demonstrate the relation between active power losses and the number of adjustments in control variables, which is valuable information for operation planning. Another fundamental result is the high computational performance of the method when compared to specialized MINLP solvers.