Stochastic programming approach for energy management in electric microgrids

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2014, 4(3): 241-267. doi: 10.3934/naco.2014.4.241

Stochastic programming approach for energy management in electric microgrids

Harald Held ^1, , Gabriela Martinez ^2, and Philipp Emanuel Stelzig ^3,

1.	Siemens AG, Corporate Technology (CT RTC AUC SIM-DE), Otto-Hahn-Ring 6, 81739 Munich
2.	Department of Biological and Environmental Engineering, Cornell University, Ithaca, NY 14853, United States
3.	Siemens Corporate Technology, Otto-Hahn-Ring 6, 81739 Munich, Germany

Received November 2013 Revised September 2014 Published September 2014

Abstract
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Microgrids are smaller, self-contained electricity grids featuring distributed generation (e.g., solar photovoltaic panels, wind turbines, biomass), energy storage technologies, and power system control devices that enable self-coordinated operations. Microgrids can be seen as a key technology for greater integration of renewable energy resources. However, the uncertain nature in power generated by these resources poses challenges to its integration into the electric grid. In this paper, we present a demand-side management stochastic optimization model to operate an isolated microgrid under uncertain power generation and demand.

Keywords: progressive hedging., Stochastic optimization, power flow optimization, smart grid.

Mathematics Subject Classification: Primary: 90C15; Secondary: 90C90, 90C1.

Citation: Harald Held, Gabriela Martinez, Philipp Emanuel Stelzig. Stochastic programming approach for energy management in electric microgrids. Numerical Algebra, Control and Optimization, 2014, 4 (3) : 241-267. doi: 10.3934/naco.2014.4.241

References:

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[7]	, Medium-term renewable energy market report 2013,, Report of International Energy Agency, (2013).
[8]	W. Bernhart, Powertrain 2020. The Li-Ion Battery Value Chain - Trends and implications, Case study Roland Berger Strategy Consultants, 2011. Available from: http://www.rolandberger.com/media/pdf/Roland_Berger_The_Li_Ion_Battery_Value_Chain_20110801.pdf.
[9]	J. R. Birge and F. Louveaux, Introduction to Stochastic Programming, Springer series in operations research and financial engineering, Springer, 2011. doi: 10.1007/978-1-4614-0237-4.
[10]	P. Bishnoi, W. Klein, R. Kuntschke, R. Speh and M. W. Waszak, A Disruptive Approach for a Green Field Smart Grid Installation, in "VDE Kongress 2012 Smart Grid'', 2012.
[11]	B. Burger, Electricity Production From Solar and Wind in Germany in 2013, Technical report, Fraunhofer Institute for Solar Energy Systems ISE, 2013.
[12]	G. Cardoso, M. Stadler, A. Siddiqui, C. Marnay, N. DeForest, A. Barbosa-Póvoa, and P. Ferrão, Microgrid reliability modeling and battery scheduling using stochastic linear programming, Electric Power Systems Research, 103 (2013), 61-69.
[13]	G. B. Dantzig, Linear programming under uncertainty, Management Science, 50 (2004), 1764-1769.
[14]	J. Dupačová, N. Gröwe-Kuska and W. Römisch, Scenario reduction in stochastic programming, Mathematical Programming, 95 (2003), 493-511. doi: 10.1007/s10107-002-0331-0.
[15]	C. C. Carøe and R. Schultz, Dual decomposition in stochastic integer programming, Operations Research Letters, 24 (1997), 37-45. doi: 10.1016/S0167-6377(98)00050-9.
[16]	D. Gade, G. Hackebeil, S. M. Ryan, J. P. Watson, R. J. B. Wets and D. L. Woodruff, Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs, Sandia Technical report, 2013.
[17]	N. Gröwe-Kuska, H. Heitsch, and W. Römisch, Scenario reduction and scenario tree construction for power management problems, in Power Tech Conference Proceedings, 2003 IEEE Bologna, IEEE, 3 (2003), 7-pp.
[18]	W. E. Hart, C. Laird, J. P. Watson and D. L. Woodruff, Pyomo - Optimization Modeling in Python, Springer, 2012.
[19]	N. Hatziargyriou, H. Asano, R. Iravani and C. Marnay, Microgrids, Power and Energy Magazine, 5 (2007), 78-94.
[20]	A. M. Gleixner, H. Held, W. Huang and S. Vigerske, Towards globally optimal operation of water supply networks, Numer. Algebra Control Optim., 2 (2012), 695-711. doi: 10.3934/naco.2012.2.695.
[21]	H. Jiayi, J. Chuanwen and X. Rong, A review on distributed energy resources and microgrid, Renewable and Sustainable Energy Reviews, 12 (2008). 2472-2483.
[22]	J. J. Justo, F. Mwasilu, J. Lee and J. W. Jung, AC-microgrids versus DC-microgrids with distributed energy resources: A review, Renewable and Sustainable Energy Reviews, 24 (2013), 387-405.
[23]	M. Kaut and S. W. Wallace, Evaluation of scenario-generation methods for stochastic programming, Pacific Journal of Optimization, 3 (2007), 257-271.
[24]	G. Martinez, N. Gatsis and G. B. Giannakis, Stochastic programming for energy planning in microgrids with renewables, in Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2013 IEEE 5th International Workshop, IEEE, (2013), 472-475.
[25]	S. Mitra, A white paper on scenario generation for stochastic programming, White paper, 2006.
[26]	T. Niknam, R. Azizipanah-Abarghooee and M. R. Narimani, An efficient scenario-based stochastic programming framework for multi-objective optimal micro-grid operation, Applied Energy, 99 (2012), 455-470.
[27]	A. Parisio and L. Glielmo, Stochastic model predictive control for economic/environmental operation management of microgrids, in 2013 European Control Conference (ECC), (2013), 2014-2019.
[28]	R. T. Rockafellar and R. J. B. Wets, Scenarios and policy aggregation in optimization under uncertainty, Math. Oper. Res., 16 (1991), 119-147. doi: 10.1287/moor.16.1.119.
[29]	M. Riis and R. Schultz, Applying the minimum risk criterion in stochastic recourse programs, Computational Optimization and Applications, 24 (2003), 267-287. doi: 10.1023/A:1021862109131.
[30]	W. Römisch, Scenario generation, in Wiley Encyclopedia of Operations Research and Management Science, Wiley'' 2011.
[31]	C. Sagastizábal, Divide to conquer: decomposition methods for energy optimization, Math. Program., 134 (2012), 187-222. doi: 10.1007/s10107-012-0570-7.
[32]	A. Shapiro, D. Dentcheva and A. Ruszczyński, Lectures on Stochastic Programming. Modeling and Theory, MPS/SIAM Series on Optimization, 9, Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM), Mathematical Programming Society (MPS), Philadelphia, 2009. doi: 10.1137/1.9780898718751.
[33]	W. Su, J. Wang and J. Roh, Stochastic energy scheduling in microgrids with intermittent renewable energy resources, Smart Grid, IEEE Transactions on, 99 (2013), 1-9.
[34]	J. P. Watson and D. L. Woodruff, Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems, Computational Management Science, 8 (2011), 355-370. doi: 10.1007/s10287-010-0125-4.
[35]	J. P. Watson, D. L. Woodruff and W. E. Hart, PySP: modeling and solving stochastic programs in Python, Mathematical Programming Computation, 4 (2012), 109-149. doi: 10.1007/s12532-012-0036-1.
[36]	Y. Zhou, H. Held, W. Klein, K. Majewski, R. Speh, P. E. Stelzig and C. Wincheringer, SoftGrid: A green field approach of future smart grid, in 2nd International Conference on Smart Grids and Green IT Systems (SMARTGREENS 2013), 2013.

show all references

References:

[1]	, Cbc (Coin-or Branch and Cut) Solver, Available from: https://projects.coin-or.org/Cbc.
[2]	, Embest Technology Co.,LTD, Available from: http://www.armkits.com/product/sbc6020.asp.
[3]	, Microgrids at Berkeley Lab, Available from: http://building-microgrid.lbl.gov/.
[4]	, Raspberry Pi Embedded Computer, Available from: http://www.raspberrypi.org/.
[5]	, Sun blade 1000 and sun blade 2000 product notes, Available from: http://docs.oracle.com/cd/E19127-01/blade1000.ws/816-3219-16/816-3219-16.pdf.
[6]	, Lithium-ion batteries - The bubble bursts,'' Case study Roland Berger Strategy Consultants, 2012. Available from: http://www.rolandberger.de/media/pdf/Roland_Berger_Li_Ion_Batteries_Bubble_Bursts_20121019.pdf.
[7]	, Medium-term renewable energy market report 2013,, Report of International Energy Agency, (2013).
[8]	W. Bernhart, Powertrain 2020. The Li-Ion Battery Value Chain - Trends and implications, Case study Roland Berger Strategy Consultants, 2011. Available from: http://www.rolandberger.com/media/pdf/Roland_Berger_The_Li_Ion_Battery_Value_Chain_20110801.pdf.
[9]	J. R. Birge and F. Louveaux, Introduction to Stochastic Programming, Springer series in operations research and financial engineering, Springer, 2011. doi: 10.1007/978-1-4614-0237-4.
[10]	P. Bishnoi, W. Klein, R. Kuntschke, R. Speh and M. W. Waszak, A Disruptive Approach for a Green Field Smart Grid Installation, in "VDE Kongress 2012 Smart Grid'', 2012.
[11]	B. Burger, Electricity Production From Solar and Wind in Germany in 2013, Technical report, Fraunhofer Institute for Solar Energy Systems ISE, 2013.
[12]	G. Cardoso, M. Stadler, A. Siddiqui, C. Marnay, N. DeForest, A. Barbosa-Póvoa, and P. Ferrão, Microgrid reliability modeling and battery scheduling using stochastic linear programming, Electric Power Systems Research, 103 (2013), 61-69.
[13]	G. B. Dantzig, Linear programming under uncertainty, Management Science, 50 (2004), 1764-1769.
[14]	J. Dupačová, N. Gröwe-Kuska and W. Römisch, Scenario reduction in stochastic programming, Mathematical Programming, 95 (2003), 493-511. doi: 10.1007/s10107-002-0331-0.
[15]	C. C. Carøe and R. Schultz, Dual decomposition in stochastic integer programming, Operations Research Letters, 24 (1997), 37-45. doi: 10.1016/S0167-6377(98)00050-9.
[16]	D. Gade, G. Hackebeil, S. M. Ryan, J. P. Watson, R. J. B. Wets and D. L. Woodruff, Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs, Sandia Technical report, 2013.
[17]	N. Gröwe-Kuska, H. Heitsch, and W. Römisch, Scenario reduction and scenario tree construction for power management problems, in Power Tech Conference Proceedings, 2003 IEEE Bologna, IEEE, 3 (2003), 7-pp.
[18]	W. E. Hart, C. Laird, J. P. Watson and D. L. Woodruff, Pyomo - Optimization Modeling in Python, Springer, 2012.
[19]	N. Hatziargyriou, H. Asano, R. Iravani and C. Marnay, Microgrids, Power and Energy Magazine, 5 (2007), 78-94.
[20]	A. M. Gleixner, H. Held, W. Huang and S. Vigerske, Towards globally optimal operation of water supply networks, Numer. Algebra Control Optim., 2 (2012), 695-711. doi: 10.3934/naco.2012.2.695.
[21]	H. Jiayi, J. Chuanwen and X. Rong, A review on distributed energy resources and microgrid, Renewable and Sustainable Energy Reviews, 12 (2008). 2472-2483.
[22]	J. J. Justo, F. Mwasilu, J. Lee and J. W. Jung, AC-microgrids versus DC-microgrids with distributed energy resources: A review, Renewable and Sustainable Energy Reviews, 24 (2013), 387-405.
[23]	M. Kaut and S. W. Wallace, Evaluation of scenario-generation methods for stochastic programming, Pacific Journal of Optimization, 3 (2007), 257-271.
[24]	G. Martinez, N. Gatsis and G. B. Giannakis, Stochastic programming for energy planning in microgrids with renewables, in Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2013 IEEE 5th International Workshop, IEEE, (2013), 472-475.
[25]	S. Mitra, A white paper on scenario generation for stochastic programming, White paper, 2006.
[26]	T. Niknam, R. Azizipanah-Abarghooee and M. R. Narimani, An efficient scenario-based stochastic programming framework for multi-objective optimal micro-grid operation, Applied Energy, 99 (2012), 455-470.
[27]	A. Parisio and L. Glielmo, Stochastic model predictive control for economic/environmental operation management of microgrids, in 2013 European Control Conference (ECC), (2013), 2014-2019.
[28]	R. T. Rockafellar and R. J. B. Wets, Scenarios and policy aggregation in optimization under uncertainty, Math. Oper. Res., 16 (1991), 119-147. doi: 10.1287/moor.16.1.119.
[29]	M. Riis and R. Schultz, Applying the minimum risk criterion in stochastic recourse programs, Computational Optimization and Applications, 24 (2003), 267-287. doi: 10.1023/A:1021862109131.
[30]	W. Römisch, Scenario generation, in Wiley Encyclopedia of Operations Research and Management Science, Wiley'' 2011.
[31]	C. Sagastizábal, Divide to conquer: decomposition methods for energy optimization, Math. Program., 134 (2012), 187-222. doi: 10.1007/s10107-012-0570-7.
[32]	A. Shapiro, D. Dentcheva and A. Ruszczyński, Lectures on Stochastic Programming. Modeling and Theory, MPS/SIAM Series on Optimization, 9, Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM), Mathematical Programming Society (MPS), Philadelphia, 2009. doi: 10.1137/1.9780898718751.
[33]	W. Su, J. Wang and J. Roh, Stochastic energy scheduling in microgrids with intermittent renewable energy resources, Smart Grid, IEEE Transactions on, 99 (2013), 1-9.
[34]	J. P. Watson and D. L. Woodruff, Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems, Computational Management Science, 8 (2011), 355-370. doi: 10.1007/s10287-010-0125-4.
[35]	J. P. Watson, D. L. Woodruff and W. E. Hart, PySP: modeling and solving stochastic programs in Python, Mathematical Programming Computation, 4 (2012), 109-149. doi: 10.1007/s12532-012-0036-1.
[36]	Y. Zhou, H. Held, W. Klein, K. Majewski, R. Speh, P. E. Stelzig and C. Wincheringer, SoftGrid: A green field approach of future smart grid, in 2nd International Conference on Smart Grids and Green IT Systems (SMARTGREENS 2013), 2013.

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