Influence of the Maximum Flow Ramping Rates on the Water Value

Abstract

This paper presents a study on the influence of maximum ramping rates (ρ) on the water values of a real hydropower plant. For this purpose, a master-slave algorithm, based on stochastic dynamic programming (SDP) and mixed integer linear programming (MILP), is used. The master module, based on SDP, has a 1-year planning period with weekly time steps and considers 3 state variables: stored volume of water in the reservoir at the beginning of each week; weekly water inflow; and average weekly energy price. The slave module, based on MILP, has a 1-week planning period with hourly time steps and considers: maximum legal and minimum technical storage capacities; maximum and minimum technical stored volumes for power generation; maximum and minimum flows released through the hydro units, the bottom outlets and the spillways according to the stored volume; one different power-discharge piecewise linear non-concave curve, as a function of the initial and estimated final stored volumes; start-up and shut-down costs of the hydro units; wear and tear costs of the hydro units caused by power variations; hourly evaporation losses according to the stored volume; hourly water inflows and energy prices; and up and down ρ. The results indicate that the water values of the hydropower plant are very sensitive to the presence of ρ; especially during the months with low water inflows. Water values decrease quadratically when increasing ρ.