HYDROELECTRIC POWER SYSTEM PLANNING An agency controls the operation of a system consisting of two water reservoirs with one hydroelectric power generation plant attached to each as shown in the Fig. 2.1. The planning horizon for the system is broken into two period. When the reservoir is at full capacity, additional inflowing water is spilled over a spillway. In addition, water can also be released through a spillway as desired for flood purposes. Spilled water does not produce any electricity. Assume that on an average 1 kilo-acre-foot (KAF) of water is converted to 400 megawatt hours (MWh) of electricity by power plant A and 200 MWh by plant B. The capacities of power plants A & B are 60,000 and 35,000 MWh per period. During each period, up to 50,000 MWh of electricity can be sold at $20.00/MWh, and excess power above 50,000 MWh can only be sold for $14.00/MWh. The following table gives additional data on the reservoir operation and inflow in kilo-acre-feet Ca Predicted inflow 2000 1500 Period 1 Period 2 200 130 1200 1900 40 15 800 850 Minimum allowable level Level at the beginning of period 1 Develop a linear programming model for determining the optimal operation policy that will maximize the total revenue from electricity sales. Inflow to A Power Power Spill water Inflow to B Fig. 2.1 Hydroelectric system