Abstract
The objective of this study was to develop stochastic optimization tools for determining the best strategy of photovoltaic installations in a campus environment with consideration of uncertainties in load, power generation and system performance. In addition to a risk neutral approach, we used Conditional Value-at-Risk to estimate the risk in our problem. The resulting Mixed Integer Programming models were formulated using a scenario-based approach. To minimize the mismatch between supply and demand, hourly solar resource and electricity demand levels were characterized via refined models. A sample-average approximation (SAA) method was proposed to provide high-quality solutions efficiently. The SAA problems were solved using exact and heuristic methods. A complete numerical study was conducted to examine the performance of the proposed solution methods, identify optimal selection strategies and consider the sensitivity of the solution to varying levels of risk.
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References
Abbey, C., & Joos, G. (2007). Supercapacitor energy storage for wind energy applications. IEEE Transactions on Industry Applications, 43(3), 769–776.
AES. (2015). http://aessolar.com/Resources/battery_info.htm. Accessed October 10, 2016.
Ali, S. M. H. (2015). Optimal photovoltaic size estimation for a campus area considering uncertainties in load, power generation and electricity rates. Thesis. Middle East Technical University.
Bortolini, M., Gamberi, M., & Graziani, A. (2014). Technical and economic design of photovoltaic and battery energy storage system. Energy Conversion and Management, 86, 81–92.
Bower, W. (2002). IEA, International guideline for the certification of photovoltaic system components and grid-connected systems. http://www.iea-pvps.org/index.php?id=9&eID=dam_frontend_push&docID=383. Accessed August 28, 2015
Brown, P. D., Lopes, J. A. P., & Matos, M. A. (2008). Optimization of pumped storage capacity in an isolated power system with large renewable penetration. IEEE Transactions on Power Systems, 23(2), 523–531.
CAE. (2015). http://www.cleanenergyauthority.com/solar-energy-resources/solar-pv-warranty/. Accessed October 10, 2016.
Conejo, A. J., Carrión, M., & Morales, J. M. (2010). Decision making under uncertainty in electricity markets. New York, NY: Springer.
Daud, M. Z., Mohamed, A., Ibrahim, A. A., & Hannan, M. A. (2014). Heuristic optimization of state-of-charge feedback controller parameters for output power dispatch of hybrid photovoltaic/battery energy storage system. Measurement, 49, 15–25.
Ekren, O., & Ekren, B. Y. (2010). Size optimization of a PV/wind hybrid energy conversion system with battery storage using simulated annealing. Applied Energy, 87(2), 592–598.
Elhodeiby, A. S., Metwally, H. M. B., & Farahat, M. A. (2011). Performance analysis of 3.6 KW rooftop grid connected photovoltaic system in Egypt. In International conference on energy systems and technologies (Vol. 11, p. 14).
Erbs, D. G., Klein, S. A., & Duffie, J. A. (1982). Estimation of the diffuse radiation fraction for hourly, daily and monthly-average global radiation. Solar Energy, 28(4), 293–302.
IEA. (2016). https://www.iea.org/topics/renewables/. Accessed October 10, 2016.
Jabr, R. (2005). Robust self-scheduling under price uncertainty using conditional value-at-risk. IEEE Transactions on Power Systems, 20(4), 1852–1858.
Jordan, D. C., & Kurtz, S. R. (2013). Photovoltaic degradation rates—An analytical review. Progress in photovoltaics: Research and Applications, 21(1), 12–29.
Katsigiannis, Y. A., & Georgilakis, P. S. (2008). Optimal sizing of small isolated hybrid power systems using tabu search. Journal of Optoelectronics and Advanced Materials, 10(5), 1241.
Kuznia, L., Zeng, B., Centeno, G., & Miao, Z. (2013). Stochastic optimization for power system configuration with renewable energy in remote areas. Annals of Operations Research, 210(1), 411–432.
Luo, X., Wang, J., Dooner, M., & Clarke, J. (2015). Overview of current development in electrical energy storage technologies and the application potential in power system operation. Applied Energy, 137, 511–536.
Merzifonluoglu, Y. (2015). Impact of risk aversion and backup supplier on sourcing decisions of a firm. International Journal of Production Research, 53(22), 6937–6961.
Miller, S. P., Granata, J. E., & Stein, J. S. (2012). The comparison of three photovoltaic system designs using the photovoltaic reliability and performance model (PV-RPM) (No. SAND2012-10342). Albuquerque, NM: Sandia National Laboratories (SNL-NM).
Ogryczak, W., & Ruszczynski, A. (2002). Dual stochastic dominance and related mean-risk models. SIAM Journal on Optimization, 13(1), 60–78.
Queensland Government. (2015). EPA, Grid-connected photovoltaic systems. http://www.soe-townsville.org/data/Gridconnected_photovoltaic_systems.pdf. Accessed August 28, 2015.
Rezgui, W., Mouss, N. K., Mouss, L. H., Mouss, M. D., Amirat, Y., & Benbouzid, M. (2014). Modeling the PV generator behavior submit to the open-circuit and the short-circuit faults. In Environmental friendly energies and applications (EFEA), 2014 3rd international symposium on (pp. 1–6). IEEE.
Riffonneau, Y., Bacha, S., Barruel, F., & Ploix, S. (2011). Optimal power flow management for grid connected PV systems with batteries. IEEE Transactions on Sustainable Energy, 2(3), 309–320.
Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of risk, 2, 21–42.
Senjyu, T., Hayashi, D., Yona, A., Urasaki, N., & Funabashi, T. (2007). Optimal configuration of power generating systems in isolated island with renewable energy. Renewable Energy, 32, 1917–1933.
Wallace, S. W., & Fleten, S. E. (2003). Stochastic programming models in energy, chap.10. In Ruszczynski and Shapiro A. Handbooks in OR & MS (pp. 637–677).
Zhang, Y., & Giannakis, G. B. (2015). Distributed stochastic market clearing with high-penetration wind power. IEEE Transactions on Power Systems, 31(2), 895–906.
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This work is supported, in part, by the European Commission Marie Curie (PIRG-GA-2010-268455) and European Commission Marie Curie (PIRG-GA-2010-268426) Grants.
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Merzifonluoglu, Y., Uzgoren, E. Photovoltaic power plant design considering multiple uncertainties and risk. Ann Oper Res 262, 153–184 (2018). https://doi.org/10.1007/s10479-017-2557-5
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DOI: https://doi.org/10.1007/s10479-017-2557-5