Hybrid Linear and Nonlinear Programming Model for Hydropower Reservoir Optimization

Linear and nonlinear optimization models are common in hydropower reservoir modeling to aid system operators and planners. Different modeling techniques have their advantages and shortcomings. Linear optimization models are faster but less accurate, and nonlinear models are slower with better system representation. A hybrid linear and nonlinear hydropower energy reservoir optimization (HERO) model is introduced, where a hybrid optimization model sequentially solves the overall nonlinear hydropower optimization problem first with a faster-running linear programming (LP) approximation to improve an initial solution for a nonlinear programming (NLP) solution to significantly reduce NLP iterations and run time. The hybrid model is applied to six hydropower plants of California, with capacities of 13.5 to 714 MW. LP and NLP decisions are compared, and run time benchmarks of the LP, NLP, and hybrid LP-NLP models with different numbers of decision variables are presented. The hybrid model reduces the NLP run time by 79% to 88%, depending on model size, but still requires much more run time than the LP solution. For short-term operations with good inflow and energy price forecasts, where accuracy matters more and uncertainties are modest, the hybrid LP-NLP model has advantages. For long-term hydropower planning and management with many more decision variables and greater inflow uncertainty, the LP model, with its greater speed and sensitivity analysis, or stochastic models, representing some uncertainties, will often be preferred.