Short Term Scheduling of Hydrothermal Power Systems With Integer Hydro Constraints

The thesis presents models for short term planning (24 hours) of a hyro dominated hydrothermal power system. The purpose of the models is to minimizae the system operation costs to provide a forecasted load and keep enough spinning reserve.This thesis presents models for short term planning (24 hours) of a hydro dominated hydrothermal power system. The purpose of the models is to minimize the system operation cost to provide a forecasted load and keep enough spinning reserve. The thesis focuses on two issues in hydro power modelling. The first issue is the relationship between water discharged and power generated. This relationship is a non-linear and non-convex function. If the plant has several units, the efficiency of the plant will have local maximums, so called local best-efficiency points. The second issue is to take into account the cost of start-ups of hydro units in the planning. The hydro model is mixed-integer. Dischargs are allowed at zero flow, the local best-efficiency points and on the continuous part between the local best-efficiency point with the highest flow and the point with maximum flow. This last continuous part is modelled as a linear function. In order to get data for the start-up cost a survey among the largest power producers in Sweden has been made, where three questions about start-ups of hydro power units has been asked: What causes the costs in the start-up?, How much does a start-up cost? and How do start-ups effect the short-term scheduling strategies of power producers in Sweden? The results show that a fair estimate of the start-up cost is about $3/MW nominal output. For the thermal plants a standard model with polynomial operation cost, start-up costs and ramp-rate constraints has been used. The model also includes the possibilities of purchasing and selling power to forecasted prices. The planning problem is formulated as a mathematical programming problem. The solution technique uses Lagrange relaxation to decompose the problem into subproblems. There will be one subproblem for each hydro and thermal plant. In order to find good feasible solutions a heuristic technique to change the integer variables in the hydro system has been developed. The Lagrange multipliers are updated with the subgradient method. The models are tested in three different load situations; a winter day (heavy load), an autumn day (medium load) and a summer day (light load). The result shows that the method gives near optimal schedules in reasonable computation time in cases with a normal part of the thermal units committed. The assumed start-up cost results in that hydro units almost never are started or stopped for one hour only.QC 20161206