This paper presents a heuristic constructive algorithm (HCA) for optimal capacitor placement on distribution systems. This is a nonlinear mixed integer optimization problem. In the proposed approach, the integer variables are represented using sigmoid function, thus interior point optimal power flow formulation can be applied to obtain sensitivity indexes based on Lagrange multipliers, reactive power, and bus voltage. The methodology is applied to two power distribution systems, and the results are compared with those obtained using a genetic algorithm approach.

This paper presents an optimum power flow (OPF) modeling algorithm that uses the primal-dual interior point technique to determine the best investment strategy in the transmission line expansion problem. In the proposed method, the expansion decision (0 or 1) is mitigated by using a sigmoid function, which is incorporated in the OPF problem through the modified dc power flow equations. The investment decision is taken using a new heuristic model based on good sensitivity produced by the OPF results. Additionally, the transmission power losses are considered in the network model. The proposed methodology has been compared with methods available in the literature, using both a test system and an equivalent of the southeastern Brazilian system.