Transmission System Expansion Planning Using a Sigmoid Function to Handle Integer Investment Variables

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.