Do unit commitment constraints affect generation expansion planning? A scalable stochastic model

  • Anna SchweleEmail author
  • Jalal Kazempour
  • Pierre Pinson
Original Paper


Due to increasing penetration of stochastic renewable energy sources in electric power systems, the need for flexible resources especially from fast-start conventional generation units (e.g., combined cycle gas turbine plants) is growing. The fast-start conventional units are being operated more frequently in order to respond to the variability and uncertainty of stochastic generation. This raises two important technical questions: as it is common in the literature, is it still an appropriate simplification to ignore the operational unit commitment (UC) constraints of conventional units within the generation expansion planning optimization? And if not, which UC constraint impacts most the expansion planning outcomes? To answer these questions, this paper aims at measuring the planning inefficiency (i.e., the underestimation of need for new generation capacity) caused by ignoring each UC constraint. To this purpose, we develop a centralized network-constrained generation expansion planning model incorporating UC constraints. In particular, we model start-up and shut-down costs, minimum production level and hourly ramping limits of conventional units. Wind power production is considered as the only source of uncertainty, and is modeled through a set of scenarios. A two-stage stochastic programming tool is used, whose first stage determines the long-term expansion and short-term UC decisions over different hours of representative days, while the second stage models the real-time operation for accommodating imbalances arising from wind deviation under different scenarios. Since this problem is potentially hard to solve especially with a large number of representative days and scenarios, a multi-cut Benders’ decomposition algorithm is implemented. The well-functioning of the proposed model and the impact of each UC constraint on planning outcomes are evaluated using an extensive numerical study. In our case studies, the exclusion of ramping constraints from planning optimization causes large error and is the most distorting simplification.


Generation expansion planning (GEP) Unit commitment (UC) constraints Wind power uncertainty Two-stage stochastic programming Mixed-integer linear programming Multi-cut Benders’ decomposition 



We thank Amin Nasri for fruitful discussion about the initial model. We also thank Peter Meibom and David Wozabal for constructive feedback.


  1. 1.
    Belgian Transmission System Operator, Elia, Wind-power generation data. Accessed 1 Apr 2017
  2. 2.
    Energy, transport and environment indicators, Annual report by Statistical Office of the European Union (Eurostat), 2016. Accessed 20 Nov 2018
  3. 3.
    PJM Market, Markets and Operations. Energy Market. Day Ahead Demand Bid. Accessed 1 Apr 2017
  4. 4.
    Batlle, C., Rodilla, P.: An enhanced screening curves method for considering thermal cycling operation costs in generation expansion planning. IEEE Trans. Power Syst. 28(4), 3683–3691 (2013)Google Scholar
  5. 5.
    Benders, J.F.: Partitioning procedures for solving mixed-variables programming problems. Numer. Math. 4(1), 238–252 (1962)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Birge, J.R., Louveaux, F.V.: A multicut algorithm for two-stage stochastic linear programs. Eur. J. Oper. Res. 34(3), 384–392 (1988)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Bruno, S., Ahmed, S., Shapiro, A., Street, A.: Risk neutral and risk averse approaches to multistage renewable investment planning under uncertainty. Eur. J. Oper. Res. 250(3), 979–989 (2016)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Conejo, A.J., Baringo, L., Kazempour, S.J., Siddiqui, A.S.: Investment in Electricity Generation and Transmission: Decision Making Under Uncertainty. Springer, Berlin (2016)Google Scholar
  9. 9.
    Conejo, A.J., Carrión, M., Morales, J.M.: Decision Making Under Uncertainty in Electricity Markets. International Series in Operations Research and Management Science. Springer, New York (2010)zbMATHGoogle Scholar
  10. 10.
    Conejo, A.J., Castillo, E., Minguez, R., García-Bertrand, R.: Decomposition Techniques in Mathematical Programming: Engineering and Science Applications. Springer, Berlin (2006)zbMATHGoogle Scholar
  11. 11.
    Connolly, D., Lund, H., Mathiesen, B.: Smart energy Europe: the technical and economic impact of one potential 100% renewable energy scenario for the European Union. Renew. Sustain. Energy Rev. 60, 1634–1653 (2016)Google Scholar
  12. 12.
    Dehghan, S., Amjady, N., Kazemi, A.: Two-stage robust generation expansion planning: a mixed integer linear programming model. IEEE Trans. Power Syst. 29(2), 584–597 (2014)Google Scholar
  13. 13.
    Flores, J.R., Montagna, J.M., Vecchietti, A.: An optimization approach for long term investments planning in energy. Appl. Energy 122, 162–178 (2014)Google Scholar
  14. 14.
    Flores-Quiroz, A., Palma-Behnke, R., Zakeri, G., Moreno, R.: A column generation approach for solving generation expansion planning problems with high renewable energy penetration. Electr. Power Syst. Res. 136, 232–241 (2016)Google Scholar
  15. 15.
    Gil, J., Caballero, A., Conejo, A.J.: Power cycling: CCGTs: the critical link between the electricity and natural gas markets. IEEE Power Energy Magz. 12(6), 40–48 (2014)Google Scholar
  16. 16.
    Hua, B., Baldick, R., Wang, J.: Representing operational flexibility in generation expansion planning through convex relaxation of unit commitment. IEEE Trans. Power Syst. 33(2), 2272–2281 (2018)Google Scholar
  17. 17.
    Jin, S., Botterud, A., Ryan, S.M.: Temporal versus stochastic granularity in thermal generation capacity planning with wind power. IEEE Trans. Power Syst. 29(5), 2033–2041 (2014)Google Scholar
  18. 18.
    Jin, S., Ryan, S.M., Watson, J.P., Woodruff, D.L.: Modeling and solving a large-scale generation expansion planning problem under uncertainty. Energy Syst. 2(3–4), 209–242 (2011)Google Scholar
  19. 19.
    Johnson, E.P.: The cost of carbon dioxide abatement from state renewable portfolio standards. Resour. Energy Econ. 36(2), 332–350 (2014)Google Scholar
  20. 20.
    de Jonghe, C., Delarue, E., Belmans, R., d’Haeseleer, W.: Determining optimal electricity technology mix with high level of wind power penetration. Appl. Energy 88(6), 2231–2238 (2011)Google Scholar
  21. 21.
    de Jonghe, C., Hobbs, B.F., Belmans, R.: Optimal generation mix with short-term demand response and wind penetration. IEEE Trans. Power Syst. 27(2), 830–839 (2012)Google Scholar
  22. 22.
    Kamalinia, S., Shahidehpour, M.: Generation expansion planning in wind-thermal power systems. IET Gen. Transmission Distrib. 4(8), 940 (2010)Google Scholar
  23. 23.
    Kazempour, J., Hobbs, B.F.: Value of flexible resources, virtual bidding, and self-scheduling in two-settlement electricity markets with wind generation - part II: ISO models and application. IEEE Trans. Power Syst. 33(1), 760–770 (2018)Google Scholar
  24. 24.
    Kazempour, S.J., Conejo, A.J., Ruiz, C.: Strategic generation investment using a complementarity approach. IEEE Trans. Power Syst. 26(2), 940–948 (2011)Google Scholar
  25. 25.
    Koltsaklis, N.E., Georgiadis, M.C.: A multi-period, multi-regional generation expansion planning model incorporating unit commitment constraints. Appl. Energy 158, 310–331 (2015)Google Scholar
  26. 26.
    Koltsaklis, N.E., Liu, P., Georgiadis, M.C.: An integrated stochastic multi-regional long-term energy planning model incorporating autonomous power systems and demand response. Energy 82, 865–888 (2015)Google Scholar
  27. 27.
    Liu, Y., Sioshansi, R., Conejo, A.J.: Hierarchical clustering to find representative operating periods for capacity-expansion modeling. IEEE Trans. Power Syst. 33(3), 3029–3039 (2018)Google Scholar
  28. 28.
    Merrick, J.H.: On representation of temporal variability in electricity capacity planning models. Energy Econ. 59, 261–274 (2016)Google Scholar
  29. 29.
    Morales, J.M., Conejo, A.J., Pérez-Ruiz, J.: Economic valuation of reserves in power systems with high penetration of wind power. IEEE Trans. Power Syst. 24(2), 900–910 (2009)Google Scholar
  30. 30.
    Munoz, F.D., Hobbs, B.F., Watson, J.P.: New bounding and decomposition approaches for MILP investment problems: multi-area transmission and generation planning under policy constraints. Eur. J. Oper. Res. 248(3), 888–898 (2016)MathSciNetzbMATHGoogle Scholar
  31. 31.
    Munoz, F.D., van der Weijde, A.H., Hobbs, B.F., Watson, J.P.: Does risk aversion affect transmission and generation planning? A Western North America case study. Energy Econ. 64, 213–225 (2017)Google Scholar
  32. 32.
    Murphy, F.H., Smeers, Y.: Generation capacity expansion in imperfectly competitive restructured electricity markets. Oper. Res. 53(4), 646–661 (2005)zbMATHGoogle Scholar
  33. 33.
    Murphy, J.: Benders, Nested Benders and Stochastic Programming: An Intuitive Introduction. Cambridge University Engineering Department Technical Report (2013). arxiv:1312.3158
  34. 34.
    Nasri, A., Kazempour, S.J., Conejo, A.J., Ghandhari, M.: Network-constrained AC unit commitment under uncertainty: a Benders decomposition approach. IEEE Trans. Power Syst. 31(1), 412–422 (2016)Google Scholar
  35. 35.
    Nogales, A., Wogrin, S., Centeno, E.: Impact of technical operational details on generation expansion in oligopolistic power markets. IET Gen. Transmission Distrib. 10(9), 2118–2126 (2016)Google Scholar
  36. 36.
    Nweke, C.I., Leanez, F., Drayton, G.R., Kolhe, M.: Benefits of chronological optimization in capacity planning for electricity markets. In: IEEE power system technology (POWERCON), pp. 1–6 (2012)Google Scholar
  37. 37.
    Ordoudis, C., Pinson, P., Morales, J.M., Zugno, M.: An updated version of the IEEE RTS 24-bus system for electricity market and power system operation studies. Technical University of Denmark (2016)Google Scholar
  38. 38.
    Ostrowski, J., Anjos, M.F., Vannelli, A.: Tight mixed integer linear programming formulations for the unit commitment problem. IEEE Trans. Power Syst. 27(1), 39–46 (2012)Google Scholar
  39. 39.
    Palmer, K., Burtraw, D.: Cost-effectiveness of renewable electricity policies. Energy Econ. 27(6), 873–894 (2005)Google Scholar
  40. 40.
    Palmintier, B.: Flexibility in generation planning: Identifying key operating constraints. In: Power systems computation conference (PSCC), 2014, pp. 1–7. IEEE (2014)Google Scholar
  41. 41.
    Palmintier, B., Webster, M.: Impact of unit commitment constraints on generation expansion planning with renewables. In: IEEE power and energy society general meeting, pp. 1–7 (2011)Google Scholar
  42. 42.
    Palmintier, B.S., Webster, M.D.: Impact of operational flexibility on electricity generation planning with renewable and carbon targets. IEEE Trans. Sustain. Energy 7(2), 672–684 (2016)Google Scholar
  43. 43.
    Papavasiliou, A., Oren, S.S., O’Neill, R.P.: Reserve requirements for wind power integration: a scenario-based stochastic programming framework. IEEE Trans. Power Syst. 26(4), 2197–2206 (2011)Google Scholar
  44. 44.
    Pina, A., Silva, C.A., Ferrão, P.: High-resolution modeling framework for planning electricity systems with high penetration of renewables. Appl. Energy 112, 215–223 (2013)Google Scholar
  45. 45.
    Pineda, S., Morales, J.M., Boomsma, T.K.: Impact of forecast errors on expansion planning of power systems with a renewables target. Eur. J. Oper. Res. 248(3), 1113–1122 (2016)MathSciNetzbMATHGoogle Scholar
  46. 46.
    Pinson, P., Mitridati, L., Ordoudis, C., Ostergaard, J.: Towards fully renewable energy systems: experience and trends in Denmark. CSEE J. Power Energy Syst. 3(1), 26–35 (2017)Google Scholar
  47. 47.
    Poncelet, K., Delarue, E., Six, D., Duerinck, J., d’Haeseleer, W.: Impact of the level of temporal and operational detail in energy-system planning models. Appl. Energy 162, 631–643 (2016)Google Scholar
  48. 48.
    Poncelet, K., Höschle, H., Delarue, E., Virag, A., d’Haeseleer, W.: Selecting representative days for capturing the implications of integrating intermittent renewables in generation expansion planning problems. IEEE Trans. Power Syst. 32(3), 1936–1948 (2017)Google Scholar
  49. 49.
    Puga, J.N.: The importance of combined cycle generating plants in integrating large levels of wind power generation. Electr. J. 23(7), 33–44 (2010)Google Scholar
  50. 50.
    Schwele, A., Kazempour, J., Pinson, P.: Electronic companion for paper: do unit commitment constraints affect generation expansion planning? A scalable model (2017).
  51. 51.
    Shortt, A., Kiviluoma, J., O’Malley, M.: Accommodating variability in generation planning. IEEE Trans. Power Syst. 28(1), 158–169 (2013)Google Scholar
  52. 52.
    Shortt, A., O’Malley, M.: Impact of variable generation in generation resource planning models. In: IEEE power and energy society general meeting, pp. 1–6 (2010)Google Scholar
  53. 53.
    Sifuentes, W.S., Vargas, A.: Hydrothermal scheduling using Benders decomposition: accelerating techniques. IEEE Trans. Power Syst. 22(3), 1351–1359 (2007)Google Scholar
  54. 54.
    Singh, K.J., Philpott, A.B., Wood, R.K.: Dantzig-Wolfe decomposition for solving multistage stochastic capacity-planning problems. Oper. Res. 57(5), 1271–1286 (2009)MathSciNetzbMATHGoogle Scholar
  55. 55.
    Skar, C., Doorman, G., Tomasgard, A.: Large-scale power system planning using enhanced Benders decomposition. In: Power systems computation conference (PSCC), pp. 1–7 (2014)Google Scholar
  56. 56.
    Staffell, I., Green, R.: Is there still merit in the merit order stack? The impact of dynamic constraints on optimal plant mix. IEEE Trans. Power Syst. 31(1), 43–53 (2016)Google Scholar
  57. 57.
    Trukhanov, S., Ntaimo, L., Schaefer, A.: Adaptive multicut aggregation for two-stage stochastic linear programs with recourse. Eur. J. Oper. Res. 206(2), 395–406 (2010)zbMATHGoogle Scholar
  58. 58.
    Upton Jr., G.B., Snyder, B.F.: Funding renewable energy: an analysis of renewable portfolio standards. Energy Econ. 66, 205–216 (2017)Google Scholar
  59. 59.
    van Stiphout, A., de Vos, K., Deconinck, G.: The impact of operating reserves on investment planning of renewable power systems. IEEE Trans. Power Syst. 32(1), 378–388 (2017)Google Scholar
  60. 60.
    Villumsen, J.C., Bronmo, G., Philpott, A.B.: Line capacity expansion and transmission switching in power systems with large-scale wind power. IEEE Trans. Power Syst. 28(2), 731–739 (2013)Google Scholar
  61. 61.
    Westner, G., Madlener, R.: Investment in new power generation under uncertainty: benefits of CHP vs. condensing plants in a copula-based analysis. Energy Econ. 34(1), 31–44 (2012)Google Scholar
  62. 62.
    Wolf, C., Koberstein, A.: Dynamic sequencing and cut consolidation for the parallel hybrid-cut nested L-shaped method. Eur. J. Oper. Res. 230(1), 143–156 (2013)MathSciNetzbMATHGoogle Scholar
  63. 63.
    You, F., Grossmann, I.E.: Multicut Benders decomposition algorithm for process supply chain planning under uncertainty. Ann. Oper. Res. 210(1), 191–211 (2013)MathSciNetzbMATHGoogle Scholar
  64. 64.
    Zhang, Q., Cremer, J.L., Grossmann, I.E., Sundaramoorthy, A., Pinto, J.M.: Risk-based integrated production scheduling and electricity procurement for continuous power-intensive processes. Comput. Chem. Eng. 86, 90–105 (2016)Google Scholar
  65. 65.
    Zverovich, V., Fábián, C.I., Ellison, E.F., Mitra, G.: A computational study of a solver system for processing two-stage stochastic LPs with enhanced Benders decomposition. Math. Program. Comput. 4(3), 211–238 (2012)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electrical EngineeringTechnical University of DenmarkKongens LyngbyDenmark

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