An MILP model for the static transmission expansion planning problem including HVAC/HVDC links, security constraints and power losses with a reduced search space

This paper presents a mixed-integer linear programming (MILP) model to solve the transmission network expansion planning (TNEP) problem, considering HVDC and HVAC proposals with security constraints and the system operation cost. The use of an MILP model guarantees convergence to optimality by using existing classical optimization methods. The operation cost is associated with the cost of transmission losses in the system. In this model, the HVDC lines can be either monopolar or bipolar type. Due to the size and complexity of the problem, a new method to reduce the search space solution is proposed, taking into account line losses, HVDC links, and contingencies. The set of HVDC lines in the proposal may use either line-commutated converters or voltage source converters. The model was implemented using the AMPL modeling language and solved using the CPLEX commercial solver. The Southern Brazilian electrical system was used to demonstrate the effectiveness of the proposed MILP model; tests were performed for cases with and without HVDC links, and with and without the system operation cost. The results show high quality solutions, and high performance when the search space reduction methodology (SSRM) is used. The computational time with the SSRM (the study case with HVDC and operation cost) was reduced by 85.9% with respect to the case that uses the complete search space, and also, the optimal solution was found. The importance of including the operation cost as an objective to be minimized is shown. The cost of losses is reduced by 55.7% when comparing the cases with and without the cost of operation included in the objective function and with HVDC lines as proposals.