Part of the International Series In Operations Research & Management Science book series (ISOR, volume 112)

A very basic feature of hydropower operation that has been neglected so far is that inflows to the reservoirs are stochastic variables. Weather is predicted, but as we all know with varying accuracy. The problems this creates for hydropower management are quite obvious. A decision about use of water, i.e., production in the current period and transferring water to the next period, has to be made in the current period while the inflows of the future periods up to the horizon are known only by their predictions. The best we can do in the current period is to formulate an optimal plan by maximising the expectation of the sum of consumer plus producer surpluses. The demand functions themselves may also be influenced by the weather. It is obvious that the need for both space heating and cooling depends on the outside temperature. But the temperature must also be regarded as a stochastic variable. Further real-life stochastic events in the case of a complete electricity system with transmission lines and thermal capacities are transmission capacity being reduced due to transformer accidents, storms blowing down trees on lines, breaking of lines due to icing, etc., and thermal capacities going down due to accidents. Considering windmills the output depends crucially on the wind speed that is stochastic.


Thermal Capacity Demand Function Demand Curve Stochastic Variable Marginal Revenue 
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© Springer Science+Business Media, LLC 2007

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