Coordinated Economic Operation of Hydrothermal Units with HVDC Link Based on Lagrange Multipliers

Coordinated operation of hydrothermal scheduling with HVDC links considering network constraints becomes a vital issue due to their remote location and recent induction in the existing power system. The nonlinear and complex nature of the problem introduces many variables and constraints which results in a heavy computational burden. A widespread approach for handling these complexities is to reformulate the problem by several linearization methods. In this paper, a Lagrange multipliers-based method is proposed for the solution of hydrothermal economic scheduling including HVDC link. This method solves equality constraint optimization problems. The linear programming approach is embedded with the Lagrange method to consider both equality and inequality constraints. The proposed technique has been used on piecewise linear variables and constraints of the system considering generation, water volume, and line power flow limits. The formulated method efficiently minimizes the operational cost of thermal units and maximizes the utilization of hydro units while meeting all generation, water volume, and the HVDC link constraints. The method was successfully implemented in two scenarios of a case study. In the first scenario, hydrothermal scheduling was performed on the typical network without an HVDC line limit and equal nodal prices were found with minimal thermal generation cost of $278,822.3. In the second scenario, the proposed method optimally dispatches units to meet the HVDC line limit and minimizes thermal generation cost to $279,025.4 while satisfying hydro, thermal, and other operating constraints. Both scenarios are implemented for a 24 h period. The results have been presented to illustrate the performance of the proposed method.