American Institute of Mathematical Sciences

Advanced
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

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

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G. B. Dantzig, Linear programming under uncertainty,, Management Science, 50 (2004), 1764.   Google Scholar

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J. Dupačová, N. Gröwe-Kuska and W. Römisch, Scenario reduction in stochastic programming,, Mathematical Programming, 95 (2003), 493.  doi: 10.1007/s10107-002-0331-0.  Google Scholar

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C. C. Carøe and R. Schultz, Dual decomposition in stochastic integer programming,, Operations Research Letters, 24 (1997), 37.  doi: 10.1016/S0167-6377(98)00050-9.  Google Scholar

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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).   Google Scholar

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N. Gröwe-Kuska, H. Heitsch, and W. Römisch, Scenario reduction and scenario tree construction for power management problems,, in Power Tech Conference Proceedings, 3 (2003).   Google Scholar

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W. E. Hart, C. Laird, J. P. Watson and D. L. Woodruff, Pyomo - Optimization Modeling in Python,, Springer, (2012).   Google Scholar

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N. Hatziargyriou, H. Asano, R. Iravani and C. Marnay, Microgrids,, Power and Energy Magazine, 5 (2007), 78.   Google Scholar

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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.  doi: 10.3934/naco.2012.2.695.  Google Scholar

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H. Jiayi, J. Chuanwen and X. Rong, A review on distributed energy resources and microgrid,, Renewable and Sustainable Energy Reviews, 12 (2008), 2472.   Google Scholar

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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.   Google Scholar

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M. Kaut and S. W. Wallace, Evaluation of scenario-generation methods for stochastic programming,, Pacific Journal of Optimization, 3 (2007), 257.   Google Scholar

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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), 472.   Google Scholar

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S. Mitra, A white paper on scenario generation for stochastic programming,, White paper, (2006).   Google Scholar

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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.   Google Scholar

[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.   Google Scholar

[28]

R. T. Rockafellar and R. J. B. Wets, Scenarios and policy aggregation in optimization under uncertainty,, Math. Oper. Res., 16 (1991), 119.  doi: 10.1287/moor.16.1.119.  Google Scholar

[29]

M. Riis and R. Schultz, Applying the minimum risk criterion in stochastic recourse programs,, Computational Optimization and Applications, 24 (2003), 267.  doi: 10.1023/A:1021862109131.  Google Scholar

[30]

W. Römisch, Scenario generation,, in Wiley Encyclopedia of Operations Research and Management Science, (2011).   Google Scholar

[31]

C. Sagastizábal, Divide to conquer: decomposition methods for energy optimization,, Math. Program., 134 (2012), 187.  doi: 10.1007/s10107-012-0570-7.  Google Scholar

[32]

A. Shapiro, D. Dentcheva and A. Ruszczyński, Lectures on Stochastic Programming. Modeling and Theory,, MPS/SIAM Series on Optimization, (2009).  doi: 10.1137/1.9780898718751.  Google Scholar

[33]

W. Su, J. Wang and J. Roh, Stochastic energy scheduling in microgrids with intermittent renewable energy resources,, Smart Grid, 99 (2013), 1.   Google Scholar

[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.  doi: 10.1007/s10287-010-0125-4.  Google Scholar

[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.  doi: 10.1007/s12532-012-0036-1.  Google Scholar

[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).   Google Scholar

show all references

References:
[1]

, Cbc (Coin-or Branch and Cut) Solver,, Available from: , ().   Google Scholar

[2]

, Embest Technology Co.,LTD,, Available from: , ().   Google Scholar

[3]

, Microgrids at Berkeley Lab,, Available from: , ().   Google Scholar

[4]

, Raspberry Pi Embedded Computer,, Available from: , ().   Google Scholar

[5]

, Sun blade 1000 and sun blade 2000 product notes,, Available from: , (): 19127.   Google Scholar

[6]

, Lithium-ion batteries - The bubble bursts,'' Case study Roland Berger Strategy Consultants,, 2012. Available from: , ().   Google Scholar

[7]

, Medium-term renewable energy market report 2013,, Report of International Energy Agency, (2013).   Google Scholar

[8]

W. Bernhart, Powertrain 2020. The Li-Ion Battery Value Chain - Trends and implications, Case study Roland Berger Strategy Consultants,, 2011. Available from: , ().   Google Scholar

[9]

J. R. Birge and F. Louveaux, Introduction to Stochastic Programming,, Springer series in operations research and financial engineering, (2011).  doi: 10.1007/978-1-4614-0237-4.  Google Scholar

[10]

P. Bishnoi, W. Klein, R. Kuntschke, R. Speh and M. W. Waszak, A Disruptive Approach for a Green Field Smart Grid Installation,, in, (2012).   Google Scholar

[11]

B. Burger, Electricity Production From Solar and Wind in Germany in 2013,, Technical report, (2013).   Google Scholar

[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.   Google Scholar

[13]

G. B. Dantzig, Linear programming under uncertainty,, Management Science, 50 (2004), 1764.   Google Scholar

[14]

J. Dupačová, N. Gröwe-Kuska and W. Römisch, Scenario reduction in stochastic programming,, Mathematical Programming, 95 (2003), 493.  doi: 10.1007/s10107-002-0331-0.  Google Scholar

[15]

C. C. Carøe and R. Schultz, Dual decomposition in stochastic integer programming,, Operations Research Letters, 24 (1997), 37.  doi: 10.1016/S0167-6377(98)00050-9.  Google Scholar

[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).   Google Scholar

[17]

N. Gröwe-Kuska, H. Heitsch, and W. Römisch, Scenario reduction and scenario tree construction for power management problems,, in Power Tech Conference Proceedings, 3 (2003).   Google Scholar

[18]

W. E. Hart, C. Laird, J. P. Watson and D. L. Woodruff, Pyomo - Optimization Modeling in Python,, Springer, (2012).   Google Scholar

[19]

N. Hatziargyriou, H. Asano, R. Iravani and C. Marnay, Microgrids,, Power and Energy Magazine, 5 (2007), 78.   Google Scholar

[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.  doi: 10.3934/naco.2012.2.695.  Google Scholar

[21]

H. Jiayi, J. Chuanwen and X. Rong, A review on distributed energy resources and microgrid,, Renewable and Sustainable Energy Reviews, 12 (2008), 2472.   Google Scholar

[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.   Google Scholar

[23]

M. Kaut and S. W. Wallace, Evaluation of scenario-generation methods for stochastic programming,, Pacific Journal of Optimization, 3 (2007), 257.   Google Scholar

[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), 472.   Google Scholar

[25]

S. Mitra, A white paper on scenario generation for stochastic programming,, White paper, (2006).   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[28]

R. T. Rockafellar and R. J. B. Wets, Scenarios and policy aggregation in optimization under uncertainty,, Math. Oper. Res., 16 (1991), 119.  doi: 10.1287/moor.16.1.119.  Google Scholar

[29]

M. Riis and R. Schultz, Applying the minimum risk criterion in stochastic recourse programs,, Computational Optimization and Applications, 24 (2003), 267.  doi: 10.1023/A:1021862109131.  Google Scholar

[30]

W. Römisch, Scenario generation,, in Wiley Encyclopedia of Operations Research and Management Science, (2011).   Google Scholar

[31]

C. Sagastizábal, Divide to conquer: decomposition methods for energy optimization,, Math. Program., 134 (2012), 187.  doi: 10.1007/s10107-012-0570-7.  Google Scholar

[32]

A. Shapiro, D. Dentcheva and A. Ruszczyński, Lectures on Stochastic Programming. Modeling and Theory,, MPS/SIAM Series on Optimization, (2009).  doi: 10.1137/1.9780898718751.  Google Scholar

[33]

W. Su, J. Wang and J. Roh, Stochastic energy scheduling in microgrids with intermittent renewable energy resources,, Smart Grid, 99 (2013), 1.   Google Scholar

[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.  doi: 10.1007/s10287-010-0125-4.  Google Scholar

[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.  doi: 10.1007/s12532-012-0036-1.  Google Scholar

[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).   Google Scholar

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