Investment Planning for Hydro-Thermal Power System Expansion: Stochastic Programming Employing the Dantzig-Wolfe Decomposition Principle (original) (raw)
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Applications of Stochastic Programming, 2005
Economic needs and the ongoing liberalization of European electricity markets stimulate the interest of power utilities in developing models and optimization techniques for the generation and trading of electric power under uncertainty. Utilities participating in deregulated markets observe increasing uncertainty in load (i.e., demand for electric power) and prices for fuel and electricity on spot and contract markets. The mismatched power between actual and predicted demand may be supplied by the power system or by trading activities. The competitive environment forces the utilities to rate alternatives within a few minutes.
Expansion planning under uncertainty for hydrothermal systems with variable resources
International Journal of Electrical Power & Energy Systems, 2018
The significant integration of variable energy resources in power systems requires the consideration of greater operational details in capacity expansion planning processes. In hydrothermal systems, this motivates a more thorough assessment of the flexibility that hydroelectric reservoirs may provide to cope with variability. This work proposes a stochastic programming model for capacity expansion planning that considers representative days with hourly resolution and uncertainty in yearly water inflows. This allows capturing high resolution operational details, such as load and renewable profile chronologies, ramping constraints, and optimal reservoir management. In addition, long-term scenarios in the multi-year scale are included to obtain investment plans that yield reliable operations under extreme conditions, such as water inflow reduction due to climate change. The Progressive Hedging Algorithm is applied to decompose the problem on a long-term scenario basis. Computational experiments on an actual power system show that the use of representative days significantly outperforms traditional load blocks to assess the flexibility that reservoir hydroelectric plants provide to the system, enabling an economic and reliable integration of variable resources. The results also illustrate the impacts of considering extreme long-term scenarios in the obtained investment plans.
Different Decomposition Strategies to Solve Stochastic Hydrothermal Unit Commitment Problems
2017
Solving very-large-scale optimization problems frequently require to decompose them in smaller subproblems, that are iteratively solved to produce useful information. One such approach is the Lagrangian Relaxation (LR), a broad range technique that leads to many different decomposition schemes. The LR supplies a lower bound of the objective function and useful information for heuristics aimed at constructing feasible primal solutions. In this paper, we compare the main LR strategies used so far for Stochastic Hydrothermal Unit Commitment problems, where uncertainty mainly concerns water availability in reservoirs and demand (weather conditions). This problem is customarily modeled as a two-stage mixed-integer optimization problem. We compare different decomposition strategies (unit and scenario schemes) in terms of quality of produced lower bound and running time. The schemes are assessed with various hydrothermal systems, considering different configuration of power plants, in terms of capacity and number of units.
Power management in a hydro-thermal system under uncertainty by Lagrangian relaxation
2002
We present a dynamic multistage stochastic programming model for the cost-optimal generation of electric power in a hydro-thermal system under uncertainty in 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 employ stochastic 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. . 1 2 GR OWE-KUSKA, KIWIEL, NOWAK, R OMISCH, WEGNER costs and constraints, huge dimensions and data uncertainty. The latter aspect mostly concerns uncertainty in electric load forecasts, generator failures, stream ows to hydro reservoirs, and fuel and electricity prices (see for relevant earlier work). The present paper aims at optimizing generation and trading of an electric hydro-thermal based utility under data uncertainty. More specically, we consider a power system comprising thermal units, pumped hydro storage plants and contracts for delivery and purchase. The relevant uncertain data comprise electric load, stream ows to hydro units, and fuel and electricity prices.
Annals of Operations Research, 2000
A dynamic (multi-stage) stochastic programming model for the weekly cost-optimal generation of electric power in a hydro-thermal generation system under uncertain demand (or load) is developed. The model involves a large number of mixed-integer (stochastic) decision variables and constraints linking time periods and operating power units. A stochastic Lagrangian relaxation scheme is designed by assigning (stochastic) multipliers to all constraints coupling power units. It is assumed that the stochastic load process is given (or approximated) by a finite number of realizations (scenarios) in scenario tree form. Solving the dual by a bundle subgradient method leads to a successive decomposition into stochastic single (thermal or hydro) unit subproblems. The stochastic thermal and hydro subproblems are solved by a stochastic dynamic programming technique and by a specific descent algorithm, respectively. A Lagrangian heuristics that provides approximate solutions for the first stage (primal) decisions starting from the optimal (stochastic) multipliers is developed. Numerical results are presented for realistic data from a German power utility and for numbers of scenarios ranging from 5 to 100 and a time horizon of 168 hours. The sizes of the corresponding optimization problems go up to 200 000 binary and 350 000 continuous variables, and more than 500 000 constraints.
Stochastic optimization of a hydro-thermal system including network constraints
IEEE Transactions on Power Systems, 1992
This paper describes a methodology for the optimal scheduling of hydrothermal systems taking into account multiple hydro reservoir characteristics, inflow stochasticity and transmission network represented by a linearized power flow model. The solution algorithm is based on stochastic dual dynamic programming (SDDP), which decomposes the multi-stage stochastic problem into several one stage subproblems. Each subproblem corresponds to a linearized optimal power flow with additional constraints representing the hydro reservoir equations and a piecewise linear approximation of the expected future cost function. Each subproblem is solved by a customized network flow/Dual Simplex algorithm which takes advantage of the network characteristics of the hydro reservoirs and of the transmission system. The application of the methodology is illustrated in a case study with a Brazilian system comprising 44 hydroplants, 11 thermal plants, 463 buses and 834 circuits.