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Large-scale Unit Commitment under uncertainty

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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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Authors and Affiliations

  1. Ecole Centrale Paris, Grande Voie des Vignes, Chatenay-Malabry, France

    Milad Tahanan

  2. OSIRIS, EDF R&D, Avenue du Général de Gaulle 1, 92141, Clamart Cedex, France

    Wim van Ackooij

  3. Dipartimento di Informatica, Università di Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy

    Antonio Frangioni

  4. QuanTek S.r.L., Via G. Marconi, 3, 40122, Bologna, Italy

    Fabrizio Lacalandra

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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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