Abstract
The paper proposes a mathematical model of mixed-integer nonlinear programming (MINLP) to optimize the location and size of shunt capacitors in power distribution grids with distributed generation (DG), considering voltage stability constraints. At the same time, the paper also analyzes the influence of the load models, such as voltage-dependence load (ZIP load) and constant power load, together with DG’s operating power factor on the optimal solution. The objective function of the proposed optimization formulation is minimizing the total expenses, including the capital investment of capacitors and the expense incurred by network energy loss. This MINLP model includes constraints in the current and critical loading conditions, such as the system of power flow equations, nodal voltage limits, branch thermal limits, capacitor-related constraints, and restrictions of minimum security level. The proposed optimization model was evaluated on a modified IEEE 33-node distribution grid using the KNITRO commercial solver with the GAMS programming language. The calculation results show that the voltage stability constraints, load models, and operational power factor of the DG units have an essential influence on the optimal position and capacity of the shunt capacitors.
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