An aggregation‐disaggregation approach to long‐term reservoir management

Abstract

Abstract. The problem is to find the monthly operating policy of Hydro-Qudbec'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 river 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. IntroductionThis paper tackles the problem of determining a monthly releasing policy for Hydro-Qufibec's 26 seasonal and interannual reservoirs over a period of several years. The objective is to find a policy that maximizes the utility's profits while respecting all constraints. The policy must absolutely take into account the random behavior of the reservoir inflows, since these cannot be predicted long in advance and since they vary widely throughout the year. Ideally, the randomness of electricity demand should also be taken into account, but since a probability distribution cannot be obtained for future demand, we suppose that demand is known for the whole period and equal to the most probable scenario.The problem is not stationary, even though the inflows are on an annual basis, because electricity demand increases every year and new power plants must periodically be added to meet it. Whatever the investments made, however, we cannot, in a stochastic environment, guarantee that demand will be met all the time. At best, we can guarantee that demand will be met with a certain probability. The choice of a probability is not obvious, though, because it must take into account, on the one hand, the investment that will have to be made to meet it and, on the other, the losses incurred by the customers when demand is not met. Rather than trying to determine this probability, Hydro-Qufibec has chosen to build, from information gathered from its customers, a curve representing the economic and social costs of a shortage in terms of the number of gigawatt hours (GWh) not supplied in a month. This shortage cost curve is used in our model to penalize shortages.Copyright 1998 by the American Geophysical Union. Paper number 98WR02608.00...

Aggregation Methods for Modelling Hydropower and Its Implications for a Highly Decarbonised Energy System in Europe

“…To aggregate the reservoirs of a hydro system, it suffices to convert the water stored at each plant into its at-site and downstream generating capability and to sum over all plants. As this concept has been well established, e.g., in [12,15,18], the following part describes the conversion coefficients with a crucial level of implementational detail becoming necessary when not only dealing with serially linked hydro systems.…”

“…It is suggested in [18] to assume that the water always takes the downstream path which maximises the potential energy. However, this paradigm can lead to significant overestimations, e.g., of the energy inflow, while building the equivalent model.…”

“…In [18], a hierarchical procedure based marginal values is used to disaggregate the hydropower production among the aggregated rivers of a 26 reservoir system. With that in mind, the disaggregation task is of lower priority in this context, particularly when long-term analyses are carried out, see Section 1.2.…”

Detailed long‐term hydro‐thermal scheduling for expansion planning in the Nordic power system

“…Applied methodologies for solving the high-dimensionality LTHTS problem traditionally rely on aggregation-disaggregation techniques, such as in [3][4][5][6]. That is, the physical reservoirs are represented by aggregate equivalents when computing the strategy, and then the operation is simulated on the detailed system using the obtained strategy.…”

Afluências agregadas na programação dinâmica estocástica aplicada ao planejamento da operação energética

“…Com base nestes trabalhos e idéias, novas aplicações e utilizações foram propostas. Sistemas hidrotérmicos maiores foram simulados através de pocessos de agregação e desagregação [41], [42] e [43]. Foram também utilizadas interpolações do tipo "spline" cúbica para se fazer aproximações das funções de custos [44].…”