Advertisement

Energy Systems

, Volume 9, Issue 2, pp 277–303 | Cite as

SMART-Invest: a stochastic, dynamic planning for optimizing investments in wind, solar, and storage in the presence of fossil fuels. The case of the PJM electricity market

  • Javad Khazaei
  • Warren B. Powell
Original Paper

Abstract

In this paper, we present a stochastic dynamic planning model called SMART-Invest, which is capable of optimizing investment decisions in different electricity generation technologies. SMART-Invest consists of two layers: an optimization outer layer and an operational core layer. The operational model captures hourly variations of wind and solar over an entire year, with detailed modeling of day-ahead commitments, forecast uncertainties and ramping constraints. The outer layer requires optimizing an unknown, non-convex, non-smooth, and expensive-to-evaluate function. We present a stochastic search algorithm with an adaptive stepsize rule that can find the optimal investment decisions quickly and reliably. By properly capturing the marginal cost of investments in wind, solar and storage, we feel that SMART-Invest produces a more realistic picture of an optimal mix of wind, solar and storage, resulting in a tool that can provide more accurate guidance for policy makers.

References

  1. 1.
    Archer, C., Simao, H. P., Kempton, W., Powell, W., Dvorak, M. (2015). The challenge of integrating offshore wind power in the US electric grid. part I: Wind forecast error. Princeton University, Dept. of Operations Research and Financial EngineeringGoogle Scholar
  2. 2.
    Archer, C. L., Jacobson, M. Z.: Supplying baseload power and reducing transmission requirements by interconnecting wind farms. J. Appl. Meteorol. Climatol 46(11), 1701–1717. ISSN:15588424 (2007)Google Scholar
  3. 3.
    Asamov, T., Ruszczyski, A.: Time-consistent approximations of risk-averse multistage stochastic optimization problems. Math. Program (2014). ISSN:0025-5610. doi: 10.1007/s10107-014-0813-x
  4. 4.
    Bazaraa, M.S., Sherali, H.D., Shetty C.M.: Nonlinear programming: theory and algorithms. Wiley, Hoboken, NJ (2013)Google Scholar
  5. 5.
    Becker, S., Frew, B., Andresen, G., Zeyer, T., Schramm, S., Greiner, M., Jacobson, M.: Features of a fully renewable US electricity system: Optimized mixes of wind and solar PV and transmission grid extensions (2014). arXiv preprint arXiv:1402.2833
  6. 6.
    Bertsekas, D.P.: Nonlinear programming. Athena scientific, Belmont (1999)Google Scholar
  7. 7.
    Budischak, C., Sewell, D., Thomson, H., Mach, L., Veron, D.E., Kempton, W.: Cost-minimized combinations of wind power, solar power and electrochemical storage, powering the grid up to 99.9% of the time. J. Power Sour. 225, 60–74 (2013)CrossRefGoogle Scholar
  8. 8.
    Delucchi, M.A., Jacobson, M.Z.: Providing all global energy with wind, water, and solar power, Part II: Reliability, system and transmission costs, and policies. Energy Policy 39(3), 1170–1190 (2011). ISSN:03014215. doi: 10.1016/j.enpol.2010.11.045
  9. 9.
    Ekren, O., Ekren, B.Y.: Size optimization of a PV/wind hybrid energy conversion system with battery storage using simulated annealing. Appl. Energy 87(2), 592–598 (2010). ISSN:03062619. doi: 10.1016/j.apenergy.2009.05.022
  10. 10.
    Gabriel, S.A., Conejo, A.J., Fuller, J.D., Hobbs, B.F., Ruiz, C.: Complementarity modeling in energy markets, vol. 180. Springer Science & Business Media (2012)Google Scholar
  11. 11.
    Jacobson, M.Z., Delucchi, M.A.: Providing all global energy with wind, water, and solar power, Part I: Technologies, energy resources, quantities and areas of infrastructure, and materials. Energy Policy 39(3), 1154–1169 (2011). ISSN:03014215. doi: 10.1016/j.enpol.2010.11.040
  12. 12.
    Jacobson, M.Z., Delucchi, M.A., Ingraffea, A.R., Howarth, R.W., Bazouin, G., Bridgeland, B., Burkart, K., Chang, M., Chowdhury, N., Cook, R., et al.: A roadmap for repowering California for all purposes with wind, water, and sunlight. Energy 73, 875–889 (2014)Google Scholar
  13. 13.
    Jacobson, M.Z., Howarth, R.W., Delucchi, M.A., Scobie, S.R., Barth, J.M., Dvorak, M.J., Klevze, M., Katkhuda, H., Miranda, B., Chowdhury, N.A., et al.: Examining the feasibility of converting New York state‘s all-purpose energy infrastructure to one using wind, water, and sunlight. Energy Policy 57, 585–601 (2013)Google Scholar
  14. 14.
    Kempton, W., Pimenta, F.M., Veron, D.E., Colle, B.A.: Electric power from offshore wind via synoptic-scale interconnection. Proc. Natl. Acad. Sci. 107(16), 7240–7245 (2010)CrossRefGoogle Scholar
  15. 15.
    Nahmmacher, P., Schmid, E., Hirth, L., Knopf, B.: Carpe diem: a novel approach to select representative days for long-term power system modeling. Energy 112, 430–442 (2016)CrossRefGoogle Scholar
  16. 16.
    Philpott, A., de Matos, V., Finardi, E.: On solving multistage stochastic programs with coherent risk measures. Oper. Res. 61(4), 957–970 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Powell, W.B.: Clearing the jungle of stochastic optimization. Informs Tutor. Oper. Res. 2014, 109–137 (2014)Google Scholar
  18. 18.
    Powell, W.B., Meisel, S.: Tutorial on Stochastic Optimization in Energy II : an energy storage illustration. IEEE Trans. Power Syst XX(X), 1–8 (2015)Google Scholar
  19. 19.
    Regis, R.G., Shoemaker, C.A.: Constrained global optimization of expensive black box functions using radial basis functions. J. Glob. Optim. 31(1), 153–171 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Regis, R.G., Shoemaker, C.A.: Improved strategies for radial basis function methods for global optimization. J. Glob. Optim. 37(1), 113–135 (2007)Google Scholar
  21. 21.
    Regis, R.G., Shoemaker, C.A.: A stochastic radial basis function method for the global optimization of expensive functions. Inf. J. Comput. 19(4), 497–509 (2007)Google Scholar
  22. 22.
    Ryan, S.M., Wets, R.J.-B., Woodruff, D.L., Silva-Monroy, C., Watson, J.-P.: Toward scalable, parallel progressive hedging for stochastic unit commitment. In: Power and Energy Society General Meeting (PES), 2013 IEEE, pp. 1–5. IEEE (2013)Google Scholar
  23. 23.
    Simao, H.P., Powell, W., Archer, C., Kempton, W.: The challenge of integrating offshore wind power in the US electric grid. part II: Simulation of electricity market operations. Renew. Energy 103, 418–431 (2017)CrossRefGoogle Scholar
  24. 24.
    Takriti, S., Birge, J.R., Long, E.: A stochastic model for the unit commitment problem. Power Syst. IEEE Trans. 11(3), 1497–1508 (1996)CrossRefGoogle Scholar
  25. 25.
    Wogrin, S., Galbally, D., Ramos, A.: CCGT unit commitment model with first-principle formulation of cycling costs due to fatigue damage. Energy 113, 227–247 (2016)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Operations Research and Financial EngineeringPrinceton UniversityPrincetonUSA

Personalised recommendations