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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DOI: https://doi.org/10.1007/s10288-014-0279-y