MATHEMATICAL PROGRAMMING APPLIED TO POWER SYSTEMS EXPANSION PLANNING WITH PUMPED STORAGE

Power systems expansion planning problem may be decomposed into three separate sub problems,--generation, transmission, and distribution planning. Essentially it is the capacity expansion problem versus dispatching problem. This dissertation discusses the sub-problem of generation expansion planning (capacity expansion planning) that can use pumped hydro-electric storage. The sub-problem of capacity expansion planning can be completely solved without considering the transmission and distribution sub-problems. A multipurpose hydro storage (conventional and pumped hydro plants) is considered which is to meet the needs of irrigation, flood control, and recreation. A linear programming (LP) formulation is developed for power systems expansion planning which incorporates the pumped hydro along with the conventional power plants (hydro, nuclear, thermal, etc.). The pumped hydro will be expected to meet peak demands. The size of the LP model is reduced using the Z-substitute method which results in a reduction of computational time. Next, we consider multiple objectives (flood control, irrigation, recreation) in power systems planning. A goal programming (GP) is developed to analyse the effect of conflecting objectives. Finally we incorporate the uncertainties associated with water inflow to the reservoir. The linear decision rule of the water reservoir planning is introduced to incorporate the randomness of water inflow to the power systems expansion planning. Chance constraint programing is used to reformulate the model. The LP model for power systems expansion planning and the GP model which considers the conflecting objectives are applied to a numerical example to illustrate the usefulness of the models. A typical utility with realistic cost (operating, fixed, and capital costs) and demand data have been used in the example