Unit commitment problem in electrical power production

The unit commitment problem (UC) in electrical power production is a large family of mathematical optimization problems where the production of a set of electrical generators is coordinated in order to achieve some common target, usually either match the energy demand at minimum cost or maximize revenues from energy production. This is necessary because it is difficult to store electrical energy on a scale comparable with normal consumption; hence, each (substantial) variation in the consumption must be matched by a corresponding variation of the production.

Coordinating generation units is a difficult task for a number of reasons:

Because the relevant details of the electrical system greatly vary worldwide, there are many variants of the UC problem, which are often very difficult to solve. This is also so because, since some units require quite a long time (many hours) to start up or shut down, the decisions need be taken well in advance (usually, the day before), which implies that these problems have to be solved within tight time limits (several minutes to a few hours). UC is therefore one of the fundamental problems in power system management and simulation. It has been studied for many years,[1][2] and still is one of the most significant energy optimization problems. Recent surveys on the subject[3][4] count many hundreds of scientific articles devoted to the problem. Furthermore, several commercial products comprise specific modules for solving UC,[5] or are even entirely devoted to its solution.[6]

Elements of unit commitment problems

There are many different UC problems, as the electrical system is structured and governed differently across the world. Common elements are:

The decisions that have to be taken usually comprise:

While the above features are usually present, there are many combinations and many different cases. Among these we mention:

Management objectives

The objectives of UC depend on the aims of the actor for which it is solved. For a MO, this is basically to minimize energy production costs while satisfying the demand; reliability and emissions are usually treated as constraints. In a free-market regime, the aim is rather to maximize energy production profits, i.e., the difference between revenues (due to selling energy) and costs (due to producing it). If the GenCo is a price maker, i.e., is has sufficient size to influence market prices, it may in principle perform strategic bidding[11] in order to improve its profits. This means bidding its production at high cost so as to raise market prices, losing market share but retaining some because, essentially, there is not enough generation capacity. For some regions this may be due to the fact that there is not enough grid network capacity to import energy from nearby regions with available generation capacity.[12] While the electrical markets are highly regulated in order to, among other things, rule out such behavior, large producers can still benefit from simultaneously optimizing the bids of all their units to take into account their combined effect on market prices.[13] On the contrary, price takers can simply optimize each generator independently, as, not having a significant impact on prices, the corresponding decisions are not correlated.[14]

Types of production units

In the context of UC, generating units are usually classified as:

Electrical grid models

There are three different ways in which the energy grid is represented within a UC:

When the full AC model is used, UC actually incorporates the optimal power flow problem, which is already a nonconvex nonlinear problem.

Recently, the traditional "passive" view of the energy grid in UC has been challenged. In a fixed electrical network currents cannot be routed, their behavior being entirely dictated by nodal power injection: the only way to modify the network load is therefore to change nodal demand or production, for which there is limited scope. However, a somewhat counter-intuitive consequence of Kirchhoff laws is that interrupting a line (maybe even a congested one) causes a global re-routing of electrical energy and may therefore improve grid performances. This has led to defining the Optimal Transmission Switching problem,[10] whereby some of the lines of the grid can be dynamically opened and closed across the time horizon. Incorporating this feature in the UC problem makes it difficult to solve even with the DC approximation, even more so with the full AC model[22]

Uncertainty in unit commitment problems

A troubling consequence of the fact that UC needs be solved well in advance to the actual operations is that the future state of the system is not known exactly, and therefore needs be estimated. This used to be a relatively minor problem when the uncertainty in the system was only due to variation of users' demand, which on aggregate can be forecasted quite effectively,[23][24] and occurrence of lines or generators faults, which can be dealt with by well established rules (spinning reserve). However, in recent years the production from intermittent renewable production sources has significantly increased. This has, in turn, very significantly increased the impact of uncertainty in the system, so that ignoring it (as traditionally done by taking average point estimates) risks significant cost increases.[21] This had made it necessary to resort to appropriate mathematical modeling techniques to properly take uncertainty into account, such as:

The combination of the (already, many) traditional forms of UC problems with the several (old and) new forms of uncertainty gives rise to the even larger family of Uncertain Unit Commitment[4] (UUC) problems, which are currently at the frontier of applied and methodological research.

References

  1. C.J. Baldwin, K.M. Dale, R.F. Dittrich. A study of the economic shutdown of generating units in daily dispatch. Transactions of the American Institute of Electrical Engineers Power Apparatus and Systems, Part III, 78(4):1272–1282, 1959.
  2. J.F. Bard. Short-term scheduling of thermal-electric generators using Lagrangian relaxation. Operations Research 1338 36(5):765–766, 1988.
  3. N.P. Padhy. Unit commitment – a bibliographical survey, IEEE Transaction On Power Systems 19(2):1196–1205, 2004.
  4. 1 2 M. Tahanan, W. van Ackooij, A. Frangioni, F. Lacalandra. Large-scale Unit Commitment under uncertainty, 4OR 13(2), 115–171, 2015.
  5. PLEXOS® Integrated Energy Model
  6. Power optimization
  7. M. Shahidehpour, H. Yamin, and Z. Li. Market Operations in Electric Power Systems: Forecasting, Scheduling, and Risk Management, Wiley-IEEE Press, 2002.
  8. C. Harris. Electricity markets: Pricing, structures and Economics, volume 565 of The Wiley Finance Series. John Wiley and Sons, 2011.
  9. A.J. Conejo and F.J. Prieto. Mathematical programming and electricity markets, TOP 9(1):1–53, 2001.
  10. 1 2 E.B. Fisher, R.P. O'Neill, M.C. Ferris. Optimal transmission switching, IEEE Transactions on Power Systems 23(3):1346–1355, 2008.
  11. A.K. David, F. Wen. Strategic bidding in competitive electricity markets: a literature survey In Proceedings IEEE PES Summer Meeting 4, 2168–2173, 2001.
  12. T. Peng and K. Tomsovic. Congestion influence on bidding strategies in an electricity market, IEEE Transactions on Power Systems 18(3):1054–1061, August 2003.
  13. A.J. Conejo, J. Contreras, J.M. Arroyo, S. de la Torre. Optimal response of an oligopolistic generating company to a competitive pool-based electric power market, IEEE Transactions on Power Systems 17(2):424–430, 2002.
  14. J.M. Arroyo, A.J. Conejo. Optimal response of a thermal unit to an electricity spot market, IEEE Transactions on Power Systems 15(3):1098–1104, 2000.
  15. J. Batut and A. Renaud. Daily scheduling with transmission constraints: A new class of algorithms, IEEE Transactions on Power Systems 7(3):982–989, 1992.
  16. G. Morales-España, J.M. Latorre, A. Ramos. Tight and Compact MILP Formulation of Start-Up and Shut-Down Ramping in Unit Commitment, IEEE Transactions on Power Systems 28(2), 1288–1296, 2013.
  17. A. Frangioni, C. Gentile. Solving Nonlinear Single-Unit Commitment Problems with Ramping Constraints, Operations Research 54(4), 767–775, 2006.
  18. E.C. Finardi and E.L. Da Silva. Solving the hydro unit commitment problem via dual decomposition and sequential quadratic programming, IEEE Transactions on Power Systems 21(2):835–844, 2006.
  19. F.Y.K. Takigawa, E.L. da Silva, E.C. Finardi, and R.N. Rodrigues. Solving the hydrothermal scheduling problem considering network constraints., Electric Power Systems Research 88:89–97, 2012.
  20. A. Borghetti, C. D’Ambrosio, A. Lodi, S. Martello. A MILP approach for short-term hydro scheduling and unit commitment with head-dependent reservoir, IEEE Transactions on Power Systems 23(3):1115–1124, 2008.
  21. 1 2 A. Keyhani, M.N. Marwali, and M. Dai. Integration of Green and Renewable Energy in Electric Power Systems, Wiley, 2010.
  22. K.W. Hedman, M.C. Ferris, R.P. O’Neill, E.B. Fisher, S.S. Oren. Co-optimization of generation unit commitment and transmission switching with n  1 reliability, IEEE Transactions on Power Systems 25(2):1052–1063, 2010.
  23. E.A. Feinberg, D. Genethliou. Load Forecasting, in Applied Mathematics for Restructured Electric Power Systems, J.H. Chow , F.F. Wu, and J. Momoh eds., Springer, 269–285, 2005
  24. H. Hahn, S. Meyer-Nieberg, S. Pickl. Electric load forecasting methods: Tools for decision making, European Journal of Operational Research 199(3), 902–907, 2009

Vikram Kumar Kamboj, S. K. Bath, J. S. Dhillon, “Solution of non-convex economic load dispatch problem using Grey Wolf Optimizer”, Neural Computing and Applications (ISSN 1433-3058), Vol.25, No. 5, July 2015. DOI: 10.1007/s00521-015-1934-8.

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