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Abstract

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.

Unit commitment problem in renewable integrated environment with storage: A review

“…They have been largely used for testing effectiveness of various solution methodologies deployed for solving UCP. 131 Some other test systems including ISO New England (ISO-NE), MISO, WECC-240 system, CAISO system, [132][133][134][135] and other real-world systems [136][137][138][139][140][141] and other real-world systems have also been investigated as test systems for solving UCP.…”

Modeling and Solution Techniques Used for Hydro Generation Scheduling

“…However, this method usually engenders solution to be moderately infeasible since the linking constraints are scarcely satisfied with the first solutions [1]. The Lagrange decomposition algorithm is also suitable for dealing with the hydrothermal scheduling problem with uncertainty in load [110].…”

The Linear Formulation of Thermal Unit Commitment Problem with Uncertainties through a Computational Mixed Integer

“…In (11) the rates of ramp-up and start-up and in (13) the shutdown ramp rates both constrained the k j p while (12) represents the constraints in which ramp-down limits are enforced on the power output. In [21] the spinning reserve contribution of each unit in each period is precisely modeled which is extended by formulation (9)- (13)…”