A
Two-Stage Planning Model for Power Scheduling in a Hydro-Thermal System
under Uncertainty
Robert Nürnberg, Werner Römisch
Preprint series: Institut für Mathematik, Humboldt-Universität
zu Berlin (ISSN 0863-0976)
MSC 2000
-
90C15 Stochastic programming
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90C90 Applications of mathematical programming
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90C11 Mixed integer programming
Abstract
A
two-stage stochastic programming model for the short- or mid-term cost-optimal
electric power production planning is developed. We consider the power
generation in a hydro-thermal generation system under uncertainty in demand
(or load) and prices for fuel and delivery contracts. 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 that couple power units. It is assumed that the stochastic
load and price processes are given (or approximated) by a finite number
of realizations (scenarios). Solving the dual by a bundle subgradient method
leads to a successive decomposition into stochastic single 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 primal
problem 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 400.000 binary and 650.000 continuous variables,
and more than 1.300.000 constraints.
Keywords:stochastic
programming, Lagrangian relaxation, unit commitment