We p r e s e n t a dynamic multistage stochastic programming model for the cost-optimal generation of electric power in a hydro-thermal system under uncertainty i n load, in ow to reservoirs and prices for fuel and delivery contracts. The stochastic load process is approximated by a scenario tree obtained by adapting a SARIMA model to historical data, using empirical means and variances of simulated scenarios to construct an initial tree, and reducing it by a scenario deletion procedure based on a suitable probability distance. Our model involves many mixed-integer variables and individual power unit constraints, but relatively few coupling constraints. Hence we e m p l o y s t o c hastic Lagrangian relaxation that assigns stochastic multipliers to the coupling constraints. Solving the Lagrangian dual by a proximal bundle method leads to successive decomposition into single thermal and hydro unit subproblems that are solved by dynamic programming and a specialized descent algorithm, respectively. The optimal stochastic multipliers are used in Lagrangian heuristics to construct approximately optimal rst stage decisions. Numerical results are presented for realistic data from a German power utility, with a time horizon of one week and scenario numbers ranging from 5 to 100. The corresponding optimization problems have up to 200,000 binary and 350,000 continuous variables, and more than 500,000 constraints.
Abstract-We present an applied mathematical model with stochastic input data for mean-risk optimization of electricity portfolios containing electricity futures as well as several components to satisfy a stochastic electricity demand: electricity spot market, two different types of supply contracts offered by a large power producer, and a combined heat and power production facility with limited capacity. Stochasticity enters the model via uncertain electricity demand, heat demand, spot prices, and future prices. The model is set up as a decision support system for a municipal power utility (price taker) and considers a medium term optimization horizon of one year in hourly discretization. The objective is to maximize the expected overall revenue and, simultaneously, to minimize risk in terms of multiperiod risk measures. Such risk measures take into account intermediate cash values in order to avoid uncertainty and liquidity problems at any time. We compare the effect of different multiperiod risk measures taken from the class of polyhedral risk measures which was suggested in our earlier work.
We compare different multiperiod risk measures taken from the class of polyhedral risk measures with respect to the effect they show when used in the objective of a stochastic program. For this purpose, simulation results of a stochastic programming model for optimizing the electricity portfolio of a German municipal power utility are presented and analyzed. This model aims to minimize risk and expected overall cost simultaneously.
We present a mathematical model with stochastic input data for mean-risk optimization of electricity portfolios containing several physical components and energy derivative products. The model is designed for the optimization horizon of one year in hourly discretization. The aim consists in maximizing the mean book value of the portfolio at the end of the optimization horizon and, at the same time, in minimizing the risk of the portfolio decisions. The risk is measured by the conditional value-at-risk and by some multiperiod extension of CVaR, respectively. We present numerical results for a large-scale realistic problem adapted to a municipal power utility and study the effects of varying weighting of risk
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