## Unit Commitment

Update: May 19, 2017

The short-term Unit Commitment (UC) problem in hydro-thermal power generation systems requires to optimally operate a set of hydro (possibly cascade connected) and thermal generating units, over a given time horizon (typically one day or one week), in order to satisfy a forecasted energy demand at minimum total cost. The generating units are subject to some technical restrictions, depending on their type and characteristics; for hydro units typical constraints concern the discharge rate, spillage limits, reservoir storage and effect on downstream units. As for the thermal units, they must usually satisfy minimum up- and down-time constraints and upper and lower bounds over the produced power when the unit is operational, ramp rate constraints limiting the increase or decrease of generated power from one period to the next, and others. Both thermal and hydro units have nonlinear behavior. For instance, in thermal units the fuel cost is usually taken as quadratic in the generated energy abd the start-up cost is a nonlinear (reverse exponential, but with options for "banking") function of the time between the shutdown and the subsequent startup. For hydro units, the generated energy is a complex nonlinear nonseparable function of the turbined water and the water head. Hence, UC is in general a (potentially, nonconvex) Mixed-Integer Nonlinear Problem. Since decisions have to be taken well in advance of actual operations, it is also in general uncertain [TWFL15] because some parameters influencing the decisions (energy demand, production from renewables, natural inflows in the water basins, ...) are can only be estimated with potentially large errors. For a more detailed description of the problem you can check the WikipediA page.

### Deterministic Unit Commitment

We have developed a generator of determinisitc UC problems that strives to produce "realistic" instances. The generator produces a generating set with "small", "medium" and "large" thermal units in realistic proportions; the characteristics of each unit are then randomly generated within a set of realistic parameters, depending on the type of the unit. The generator has been used for testing several approaches to the solution of UC-related problems, see the bibliography section.

The original C++ generator is available at the OR-Library. A more advanced version, allowing XML output and with a manual, can be found here (184Kb, .tgz); please read the accluded Manual for information about compilation, usage and format of the produced instances.

A more advanced generator, taking into account ramping constraints, is currently under development. For the time being, we distribute a set of ramp-constrained thermal and hydro-thermal instances that we have used to test the approaches; they are available both here (508Kb, .zip) and at the OR-Library. The format of the instances is described in the file Format.pdf, distributed together with the instances. The new generator will also be distributed, when ready.

### Stochastic Unit Commitment

This is a distribution of five stochastic hydro-thermal UC instances generated by Murilo Reolon Scuzziato to realistically represent a typical Brazilian case, where hydro production is predominant. Due to the significant size of the corresponding mathematical formulations, decomposition techniques are typically necessary in order to get solutions [ScFF17]. The structure of the instances is quite complex, and described in this document. The instances themselves can be downloaded here.

### Bibliography

[Betal01] A. Borghetti, A. Frangioni, F. Lacalandra, A. Lodi, S. Martello, C.A. Nucci, A. Trebbi "Lagrangian Relaxation and Tabu Search Approaches for the Unit Commitment Problem" Proceedings IEEE 2001 Powerteck Porto Conference, J.T. Saraiva and M.A. Matos editors, Vol. 3, Paper n. PSO5-397, 2001

[BFLN03] A. Borghetti, A. Frangioni, F. Lacalandra and C.A. Nucci "Lagrangian Heuristics Based on Disaggregated Bundle Methods for Hydrothermal Unit Commitment" IEEE Transactions on Power Systems, 18(1), p. 313 - 323, 2003

[BFLNP03] A. Borghetti, A. Frangioni, F. Lacalandra, C.A. Nucci, P. Pelacchi "Using of a cost-based Unit Commitment algorithm to assist bidding strategy decisions" Proceedings IEEE 2003 Powerteck Bologna Conference, A. Borghetti, C.A. Nucci and M. Paolone editors, Paper n. 547, 2003

[FrGe06a] A. Frangioni, C. Gentile "Perspective Cuts for a class of convex 0-1 Mixed Integer Programs" Mathematical Programming 106(2), p. 225 - 236, 2006

[FrGe06b] A. Frangioni, C. Gentile "Solving nonlinear single-unit commitment problems with ramping constraints" Operations Research 54(4), p. 767 - 775, 2006

[FrGL08] A. Frangioni, C. Gentile, F. Lacalandra "Solving Unit Commitment Problems with General Ramp Contraints" International Journal of Electrical Power and Energy Systems 30, 316–326, 2008

[FrGL09] A. Frangioni, C. Gentile, F. Lacalandra "Tighter Approximated MILP Formulations for Unit Commitment Problems" IEEE Transactions on Power Systems 24(1), 105–113, 2009

[FrGL11] A. Frangioni, C. Gentile, F. Lacalandra "Sequential Lagrangian-MILP Approaches for Unit Commitment Problems" International Journal of Electrical Power and Energy Systems 33, 585–593, 2011

[ScFF17] M.R. Scuzziato, E.C. Finardi, A. Frangioni "Different Decomposition Strategies to Solve Stochastic Hydrothermal Unit Commitment Problems" Technical Report, Dipartimento di Informatica, Università di Pisa 2017

[TWFL15] M. Tahanan, W. van Ackooij, A. Frangioni, F. Lacalandra "Large-scale Unit Commitment under uncertainty" 4OR 13(2), 115—171, 2015