An aggregation-disaggregation approach to long-term reservoir management

The problem is to find the monthly operating policy of Hydro-Quebec's 26 large reservoirs that maximizes the utility's expected profits over a period of several years. The problem is solved in a hierarchical way. First, the optimal operating policy of the whole system, represented by an aggregate model, is found by stochastic dynamic programming (SDP). This gives not only the hydroelectric energy to produce in a month but also, as is very important in a deregulated market, the expected marginal value of the hydroelectric energy produced. At the second level the expected marginal value of the potential energy stored in each liver is determined by solving a SDP problem with two state variables: one for the energy content of the river and the other for the energy content of all the other rivers combined. These marginal values are used afterward to divide the hydroelectric production among the rivers. At the third level the production assigned to each river is distributed between the reservoirs so as to minimize the spillages first, and then the square of the deviations of the reservoir levels from the target level. The targets are adjusted to maximize the expected long-term production of the river. The monthly inflows to the reservoirs are the only random variables in this problem.