Abstract
This paper presents a stochastic mixed integer programming model for a comprehensive hybrid power system design problem, including renewable energy generation, storage device, transmission network, and thermal generators, for remote areas. Given the complexity of the model, we developed a Benders’ decomposition algorithm with two additional types of cutting planes: Pareto-optimal cuts generated using a modified Magnanti-Wong method and cuts generated from a maximum feasible subsystem. Computational results show significant improvement in our ability to solve this type of problem in comparison to a state-of-the-art professional solver. This model and the solution algorithm provide an analytical decision support tool for the hybrid power system design problem.
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References
Abbey, C., & Joos, G. (2009). A stochastic optimization approach to rating of energy storage systems in wind-diesel isolated grids. IEEE Transactions on Power Systems, 24(1), 418–426.
Barton, J. P., & Infield, D. G. (2004). Energy storage and its use with intermittent renewable energy. IEEE Transactions on Energy Conversion, 19(2), 441–448.
Benders, J. F. (2005). Partitioning procedures for solving mixed-variables programming problems. Computational Management Science, 2, 3–19.
Bernal-Agustín, J. L., & Dufo-López, R. (2009). Simulation and optimization of stand-alone hybrid renewable energy systems. Renewable & Sustainable Energy Reviews, 13(8), 2111–2118.
Birge, J. R., & Louveaux, F. (2004). Introduction to stochastic programming. Berlin: Springer.
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.
Côté, G., & Laughton, M. (1984). Large-scale mixed integer programming: Benders-type heuristics. European Journal of Operations Research, 16, 327–333.
Duić, N., & Carvalho, M.d.G. (2004). Increasing renewable energy sources in island energy supply: case study porto santo. Renewable & Sustainable Energy Reviews, 8(4), 383–399.
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.
General Algebraic Modeling System (2012). www.gams.com.
GovTrack (2012). www.govtrack.us/congress/bill.xpd?bill=h111-2454.
Gurobi Optimization (2012). www.gurobi.com.
Karimi, B., Fatemi Ghomi, S. M. T., & Wilson, J. M. (2003). The capacited lot sizing problem: a review of models and algorithms. Omega, 31, 365–378.
Katsigiannis, Y., & Georgilakis, P. (2008). Optimal sizing of small isolated hybrid power systems using tabu search. Journal of Optoelectronics and Advanced Materials, 10(5), 1241–1245.
Magnanti, T. L., & Wong, R. T. (1981). Accelerating Benders’ decomposition: algorithmic enhancement and model selection criteria. Operations Research, 29(3), 464–484.
National Climatic Data Center (2012). www.ncdc.noaa.gov.
National Grid (2012). The Power of Action. www.nationalgrid.com.
Nema, P., Nema, R. K., & Rangnekar, S. (2009). A current and future state of art development of hybrid energy system using wind and PV-solar: a review. Renewable & Sustainable Energy Reviews, 13(8), 2096–2103.
Nemhauser, G., & Wolsey, L. (1988). Integer and combinatorial optimization. New York: Wiley-Interscience.
Nfah, E. M., Ngundam, J. M., & Tchinda, R. (2007). Modelling of solar/diesel/battery hybrid power systems for far-north Cameroon. Renewable Energy, 32(5), 832–844.
Office for National Statistics (2012). www.statistics.gov.uk/CCI/nugget.asp?ID=6.
Papadakos, N. (2008). Practical enhancements to Magnanti-Wong method. Operations Research Letters, 36, 444–449.
Pereira, S., Segurado, R., Costa, A., Pipio, A., & Alves, L. (2009). Energy storage and its use with intermittent renewable energy. Chemical Engineering Transactions, 18, 629–634.
Saharidis, G., & Ierapetritou, M. (2010). Improving Benders’ decomposition using maximum feasible (MFS) cut generation strategy. Computers & Chemical Engineering, 34, 1237–1245.
Saharidis, G., Minoux, M., & Ierapetritou, M. (2010). Accelerating Benders method using covering cut bundle generation. International Transactions in Operational Research, 17, 221–237.
Saharidis, G., Boile, M., & Theofanis, S. (2011). Initialization of the Benders master problem using valid inequalities applied to fixed-charge network problems. Expert Systems With Applications, 38, 6627–6636.
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.
Symbiotics A New Generation of Hydropower (2012). www.symbioticsenergy.com.
Wind Power for Every Home (2012). www.mywindpowersystem.com.
Acknowledgements
The authors wish to thank Mr. Adam Parke and Mr. Gordon Gillette at Tampa Electric Company for their support to this work. Additionally, we would like to thank the anonymous referees for their constructive suggestions which significantly improved the quality of the paper.
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Kuznia, L., Zeng, B., Centeno, G. et al. Stochastic optimization for power system configuration with renewable energy in remote areas. Ann Oper Res 210, 411–432 (2013). https://doi.org/10.1007/s10479-012-1110-9
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DOI: https://doi.org/10.1007/s10479-012-1110-9