Large-scale Unit Commitment under uncertainty

Abstract

The Unit Commitment problem in energy management aims at finding the optimal productions schedule of a set of generation units while meeting various system-wide constraints. It has always been a large-scale, non-convex difficult problem, especially in view of the fact that operational requirements imply that it has to be solved in an unreasonably small time for its size. Recently, the ever increasing capacity for renewable generation has strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex, uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focusing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, also providing entry points to the relevant literature on optimization under uncertainty.

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Acknowledgments

The first author would like to thank Afsaneh Salari and Maryam Arbabzadeh for their input and their intellectual support. The second and third author gratefully acknowledge the support of the Gaspard Monge program for Optimization and Operations Research (PGMO) Project “Consistent Dual Signals and Optimal Primal Solutions”.

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Appendix

Appendix

UC Unit Commitment problem
UUC UC problem under Uncertainty
bUC Basic UC problem (common modeling assumptions)
ED Economic dispatch
GENCO Generation Company
TSO Transmission system operator
MP Monopolistic producer
PE Power exchange
PEM PE manager
OTS Optimal transmission switching
UCOTS UC with OTS
MSG Minimal stable generation
OPF Optimal power flow
ROR Run-of-river hydro unit
\(X_1\) Set of technically feasible production schedules
\(X_2\) Set of system wide constraints
\(\mathcal {T}\) Set of time steps
MILP Mixed-integer linear programming
MIQP Mixed-integer quadratic programming
DP Dynamic programming
SDDP Stochastic dual DP B&B, B&C,
B&P Branch and bound (cut, price, respectively)
AL Augmented Lagrangian
LR Lagrangian relaxation
LD Lagrangian dual
CP Cutting plane
SO Stochastic optimization
SD Scenario decomposition
UD Unit decomposition (also called space decomposition or stochastic decomposition)
RO Robust optimization
CCO Chance-constrained optimization
ICCO Chance-constrained optimization with individual probabilistic constraints
JCCO Chance-constrained optimization with joint probabilistic constraints

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Tahanan, M., van Ackooij, W., Frangioni, A. et al. Large-scale Unit Commitment under uncertainty. 4OR-Q J Oper Res 13, 115–171 (2015). https://doi.org/10.1007/s10288-014-0279-y

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Keywords

  • Unit Commitment
  • Uncertainty
  • Large-scale optimization
  • Survey

Mathematics Subject Classification

  • 90-02
  • 90B30
  • 90C06
  • 90C90