Hybrid Enhanced Lagrangian Relaxation and Quadratic Programming for Hydrothermal Scheduling

This article proposes a hybrid enhanced Lagrangian relaxation and quadratic programming (hybrid LRQP) for hydrothermal scheduling. Hybrid LRQP minimizes the total production cost subject to power balance, spinning reserve, generation limit, minimum up and down time, generation ramp limit, on/off line minimum level, transmission line, limited fuel, environmental, water discharge and water balance constraints. The proposed solution method solves hydrothermal scheduling problem using two coordination procedures. In the first procedure, enhanced Lagrangian relaxation (ELR) is used to find the base feasible schedule of all thermal generation system excluding hydro power plants and relaxing transmission line constraints. ELR is enhanced by new initialization and adaptive Lagrangian multipliers to speedup the convergence. In the second procedure, economic dispatch by quadratic programming, thermal unit decommitment and hydro unit commitment are carried out. The proposed 24-hour economic dispatch could easily consider generation ramp rate limit, and time coupling constraints such as limited fuel supply, environmental, water discharge, and water balance constraints. Hybrid LRQP is tested on hydrothermal system with 17 thermal, 2 hydro and 2 pumped storage hydro plants, and IEEE 24 bus reliability test system. Test results indicate that hybrid LRQP could obtain better solutions than those obtained from augmented hopfield network and augmented Lagrangian relaxation.