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# Unit Commitment under uncertainty

The integration of the production of renewable sources, due to its uncer= tainty, must be adequately addressed to avoid affecting the operational rel= iability of a power system. Unit commitment (UC) is a critical decision pro= cess which consists in an optimization problem to generate the outputs of a= ll the generators to minimize the system cost. Generally, UC decisions are = made once a day, 24 or more hours before the actual operation.

The main principle in operating an electrical system is to cover the dem= and for electricity at all times and under different conditions depending o= n the season, weather and time. The common goal of UC formulations is to mi= nimize the operating cost, while ensuring sufficient reserve to accommodate= real-time realization of uncertainty. The main difference between models i= s the representation of this uncertainty.

The deterministic UC formulation is a traditional solution in which the = net load is modeled using a single forecast for each renewable output and t= he associated uncertainty is managed using ad hoc rules (i.e. the generatin= g units are committed to meeting the deterministic prediction and the uncer= tainty is managed by imposing reserve requirements ). This approach is e= asy to implement in practice, but ad hoc rules do not necessarily adequatel= y reflect uncertainty. For this reason, different approaches are used to ma= nage the UC under uncertainty.

The UC available approaches in literature are:

• Stochastic UC

Stochastic UC is based on probabilistic scenarios. A finite set of scena= rios is generated with assigned weight for each scenario. The basic idea is= to generate a large number of scenarios where each scenario represents a p= ossible realization of the underlying uncertain factors. Stochastic UC is g= enerally formulated as a two-stage problem that determines the generation s= chedule to minimize the expected cost over all of the scenarios respecting = their probabilities. There is a difference between commitment and dispatch = decisions: the first are the same for all the scenarios, the second are dif= ferent for each scenario. The large number of scenarios in the model requir= es high computational demand for simulations. Similar scenarios are aggrega= ted based on, for example, their probability or the cost . The structure= of scenarios can be a number of parallel scenarios in a two-stage problem = or a scenario tree in a multistage problem. Monte Carlo simulation  is o= ften used to populate the scenarios based on probability distribution funct= ions learned from historical data and to generate scenario trees based on s= tochastic processes. However, increasing the number of scenarios may lead t= o small improvements in the solution quality. Thus, Sample Average Approxim= ation (SAA)  can be used to test the convergence of the solution. Scenar= io reduction techniques are used in the literature =E2=80=93. The goa= l is to reduce the number of scenarios without sacrificing their accuracy t= o a large extent.

• Robust UC

In Robust UC formulations a deterministic set of uncertainty is used, in= stead of a probability distribution on the uncertain data. For example, the= two-stage model in  has the first stage which finds the optimal commitm= ent decision, and the second stage which generates the worst case dispatch = cost under a fixed solution from the first stage. The range of uncertainty = is defined by the upper and lower bounds on the net load at each time perio= d. In place of minimizing the total expected cost as in Stochastic UC, Robu= st UC reduces the worst costs to the minimum for all possible results of un= certain parameters. These models produce conservative solutions, but the= y are better from a computational point of view because they can avoid inco= rporating a large number of scenarios. In the power system literature, Robu= st UC models have been used to address uncertainties from net electricity i= njection , wind power availability , demand-side management .

• Interval UC

Interval UC formulations minimize the cost of covering the most probable= load forecast by ensuring feasibility in the uncertainty range that is del= imited with upper and lower bounds as in robust unit commitment formulation= s. The formulation is more efficient than the stochastic unit commitment fo= rmulation: the model can be composed by three scenarios. In particular, the= scenarios are: the central forecast, the upper and lower bounds. The trans= ition constraints are modeled as constraints. The interval unit commitment = can also be formulated as a two stage problem where the optimal solution is= found in the first stage and then tested in the second stage for feasibili= ty. A method is proposed in .

• Hybrid UC

To improve the advantages and reduce disadvantages of the models present= ed in the previous parts, hybrid models have been proposed in the last year= s. Some of these models are unified stochastic and robust unit commitment f= ormulation  and stochastic/interval unit commitment formulation . [= 14] proposes a model able to achieve low expected total cost while ensuring= the system robustness.  proposes a model that applies the stochastic f= ormulation to the initial hours of the optimization horizon and then switch= es to the interval formulation for the remaining hours.

References:

 Y. V. Makarov, C. Loutan, M. Jian, and P. de Mello, "Operational imp= acts of wind generation on California Power Systems," IEEE Trans. Power Sys= t. vol 24, no. 2, pp. 1039-1050, May 2009.

 K. Jurkovic, H. PandZic and I. Kuzle, =E2=80=9CReview on Unit Commit= ment under UncertaintyApproaches=E2=80=9D, MIPRO 2015.

 S. Raychaudhuri, =E2=80=9CIntroduction to Monte Carlo simulation=E2= =80=9D, Proceedings of the 2008 Winter Simulation Conference.

 A. Shapiro, "Sample average approximation.",Encyclopedia of Operatio= ns Research and Management Science, Springer US, 2013. 1350-1355.

 J. Sumaili, H. Keko, V. Miranda, A. Botterud, and J. Wang, =E2=80=9C= Clustering-based wind power scenario reduction technique,=E2=80=9D in Proc.= 17th Power Syst. Computation Conf., Stockholm, Sweden, Aug. 2011, pp. 391= =E2=80=93397.

 J. Dupacova, N. Growe-Kuska, and W. Romisch, =E2=80=9CScenario reduc= tion in stochastic programming: An approach using probability metrics,=E2= =80=9D Math. Programming A, vol. 3, pp. 493=E2=80=93511, 2003.

 N. Growe-Kuska, H. Heitsch, and W. Romisch, =E2=80=9CScenario reduct= ion and scenario tree construction for power management problems,=E2=80=9D = in Proc. IEEE Power Tech. Conf., Bologna, Italy, Jun. 2003, pp. 1=E2=80=937= .

 D. Bertsimas, E. Litvinov, X. A. Sun, Z. Jinye, and T. Tongxin, "Ada= ptive robust optimization for the security constrained unit commitment prob= lem," IEEE Trans. Power Syst., vol. 28, no.1, pp. 52-63, Feb. 2013.

 Q. P. Zheng, J. Wang, A.L. Liu, =E2=80=9CStochastic Optimization for= Unit Commitment =E2=80=93 A Review=E2=80=9D, IEEE Transactions on Power Sy= stems (Vol: 30, Issue: 4, July 2015)

 L. Zhao and B. Zeng, =E2=80=9CRobust unit commitment problem with d= emand response and wind energy,=E2=80=9D in Proc. IEEE Power and Energy Soc= . Gen. Meeting, 2012, pp. 1=E2=80=938.

 R. Jiang, J. Wang, and Y. Guan, =E2=80=9CRobust unit commitment wit= h wind power and pumped storage hydro,=E2=80=9D IEEE Trans. Power Syst., vo= l. 27, no. 2, pp. 800=E2=80=93810, May 2012.

 C. Zhao, J. Wang, J.-P. Watson, and Y. Guan, =E2=80=9CMulti-stage r= obust unit commitment considering wind and demand response uncertainties,= =E2=80=9D IEEE Trans. Power Syst., vol. 28, no. 3, pp. 2708=E2=80=932717, A= ug. 2013.

 X. Sun and C. Fang, "Interval mixed-integer pro ming for daily unit= commitment and dispatch incorporating wind power," in Proc. Power System T= echnolo (POWERCON) 2010, Hangzhou, China, Oct. 2010, pp. 1-6.

 C. Zhao and Y. Guan, "Unified stochastic and robust unit commitment= ," iEEE Trans. Power Syst., vol. 28, no. 3, pp. 3353- 33761, Aug. 2013.

 Y. Dvorkin, H. Pandzic, M. Ortega-Vazquez, and D. S. Kirschen, "A h= ybrid stochastic/interval approach to transmission-constrained unit commitm= ent," iEEE Trans. Power Syst., early access

Contributors:

Allegra De Filippo, Michele Lombardi and Michela Milano, University of B= ologna

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