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
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, Springer, 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 "VDE Kongress 2012 Smart Grid'', 2012. Google Scholar

[11]

B. Burger, Electricity Production From Solar and Wind in Germany in 2013, Technical report, Fraunhofer Institute for Solar Energy Systems ISE, 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), 61-69. Google Scholar

[13]

G. B. Dantzig, Linear programming under uncertainty, Management Science, 50 (2004), 1764-1769. Google Scholar

[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.  Google Scholar

[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.  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, 2003 IEEE Bologna, IEEE, 3 (2003), 7-pp. 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), 78-94. 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), 695-711. 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). 2472-2483. 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), 387-405. Google Scholar

[23]

M. Kaut and S. W. Wallace, Evaluation of scenario-generation methods for stochastic programming, Pacific Journal of Optimization, 3 (2007), 257-271.  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 IEEE 5th International Workshop, IEEE, (2013), 472-475. 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), 455-470. 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), 2014-2019. Google Scholar

[28]

R. T. Rockafellar and R. J. B. Wets, Scenarios and policy aggregation in optimization under uncertainty, Math. Oper. Res., 16 (1991), 119-147. 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), 267-287. doi: 10.1023/A:1021862109131.  Google Scholar

[30]

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

[31]

C. Sagastizábal, Divide to conquer: decomposition methods for energy optimization, Math. Program., 134 (2012), 187-222. 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, 9, Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM), Mathematical Programming Society (MPS), Philadelphia, 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, IEEE Transactions on, 99 (2013), 1-9. 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), 355-370. 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), 109-149. 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, Springer, 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 "VDE Kongress 2012 Smart Grid'', 2012. Google Scholar

[11]

B. Burger, Electricity Production From Solar and Wind in Germany in 2013, Technical report, Fraunhofer Institute for Solar Energy Systems ISE, 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), 61-69. Google Scholar

[13]

G. B. Dantzig, Linear programming under uncertainty, Management Science, 50 (2004), 1764-1769. Google Scholar

[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.  Google Scholar

[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.  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, 2003 IEEE Bologna, IEEE, 3 (2003), 7-pp. 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), 78-94. 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), 695-711. 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). 2472-2483. 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), 387-405. Google Scholar

[23]

M. Kaut and S. W. Wallace, Evaluation of scenario-generation methods for stochastic programming, Pacific Journal of Optimization, 3 (2007), 257-271.  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 IEEE 5th International Workshop, IEEE, (2013), 472-475. 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), 455-470. 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), 2014-2019. Google Scholar

[28]

R. T. Rockafellar and R. J. B. Wets, Scenarios and policy aggregation in optimization under uncertainty, Math. Oper. Res., 16 (1991), 119-147. 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), 267-287. doi: 10.1023/A:1021862109131.  Google Scholar

[30]

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

[31]

C. Sagastizábal, Divide to conquer: decomposition methods for energy optimization, Math. Program., 134 (2012), 187-222. 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, 9, Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM), Mathematical Programming Society (MPS), Philadelphia, 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, IEEE Transactions on, 99 (2013), 1-9. 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), 355-370. 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), 109-149. 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

[1]

Chuong Van Nguyen, Phuong Huu Hoang, Hyo-Sung Ahn. Distributed optimization algorithms for game of power generation in smart grid. Numerical Algebra, Control & Optimization, 2019, 9 (3) : 327-348. doi: 10.3934/naco.2019022
[2]

Jie Sun, Honglei Xu, Min Zhang. A new interpretation of the progressive hedging algorithm for multistage stochastic minimization problems. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1655-1662. doi: 10.3934/jimo.2019022
[3]

Mohammed Al-Azba, Zhaohui Cen, Yves Remond, Said Ahzi. Air-Conditioner Group Power Control Optimization for PV integrated Micro-grid Peak-shaving. Journal of Industrial & Management Optimization, 2021, 17 (6) : 3165-3181. doi: 10.3934/jimo.2020112
[4]

Radu C. Cascaval, Ciro D'Apice, Maria Pia D'Arienzo, Rosanna Manzo. Flow optimization in vascular networks. Mathematical Biosciences & Engineering, 2017, 14 (3) : 607-624. doi: 10.3934/mbe.2017035
[5]

Zhenhuan Yang, Wei Shen, Yiming Ying, Xiaoming Yuan. Stochastic AUC optimization with general loss. Communications on Pure & Applied Analysis, 2020, 19 (8) : 4191-4212. doi: 10.3934/cpaa.2020188
[6]

Michael Herty, S. Moutari, M. Rascle. Optimization criteria for modelling intersections of vehicular traffic flow. Networks & Heterogeneous Media, 2006, 1 (2) : 275-294. doi: 10.3934/nhm.2006.1.275
[7]

Mohsen Abdolhosseinzadeh, Mir Mohammad Alipour. Design of experiment for tuning parameters of an ant colony optimization method for the constrained shortest Hamiltonian path problem in the grid networks. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 321-332. doi: 10.3934/naco.2020028
[8]

Mingshang Hu. Stochastic global maximum principle for optimization with recursive utilities. Probability, Uncertainty and Quantitative Risk, 2017, 2 (0) : 1-. doi: 10.1186/s41546-017-0014-7
[9]

Feng Bao, Thomas Maier. Stochastic gradient descent algorithm for stochastic optimization in solving analytic continuation problems. Foundations of Data Science, 2020, 2 (1) : 1-17. doi: 10.3934/fods.2020001
[10]

Yeming Dai, Yan Gao, Hongwei Gao, Hongbo Zhu, Lu Li. A real-time pricing scheme considering load uncertainty and price competition in smart grid market. Journal of Industrial & Management Optimization, 2020, 16 (2) : 777-793. doi: 10.3934/jimo.2018178
[11]

Rolf Rannacher. A short course on numerical simulation of viscous flow: Discretization, optimization and stability analysis. Discrete & Continuous Dynamical Systems - S, 2012, 5 (6) : 1147-1194. doi: 10.3934/dcdss.2012.5.1147
[12]

Simone Göttlich, Oliver Kolb, Sebastian Kühn. Optimization for a special class of traffic flow models: Combinatorial and continuous approaches. Networks & Heterogeneous Media, 2014, 9 (2) : 315-334. doi: 10.3934/nhm.2014.9.315
[13]

Ning Lu, Ying Liu. Application of support vector machine model in wind power prediction based on particle swarm optimization. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1267-1276. doi: 10.3934/dcdss.2015.8.1267
[14]

A. Zeblah, Y. Massim, S. Hadjeri, A. Benaissa, H. Hamdaoui. Optimization for series-parallel continuous power systems with buffers under reliability constraints using ant colony. Journal of Industrial & Management Optimization, 2006, 2 (4) : 467-479. doi: 10.3934/jimo.2006.2.467
[15]

Jean-Paul Arnaout, Georges Arnaout, John El Khoury. Simulation and optimization of ant colony optimization algorithm for the stochastic uncapacitated location-allocation problem. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1215-1225. doi: 10.3934/jimo.2016.12.1215
[16]

Ardeshir Ahmadi, Hamed Davari-Ardakani. A multistage stochastic programming framework for cardinality constrained portfolio optimization. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 359-377. doi: 10.3934/naco.2017023
[17]

Haodong Yu, Jie Sun. Robust stochastic optimization with convex risk measures: A discretized subgradient scheme. Journal of Industrial & Management Optimization, 2021, 17 (1) : 81-99. doi: 10.3934/jimo.2019100
[18]

Qiong Liu, Ahmad Reza Rezaei, Kuan Yew Wong, Mohammad Mahdi Azami. Integrated modeling and optimization of material flow and financial flow of supply chain network considering financial ratios. Numerical Algebra, Control & Optimization, 2019, 9 (2) : 113-132. doi: 10.3934/naco.2019009
[19]

Oliver Jenkinson. Ergodic Optimization. Discrete & Continuous Dynamical Systems, 2006, 15 (1) : 197-224. doi: 10.3934/dcds.2006.15.197
[20]

Qun Lin, Antoinette Tordesillas. Towards an optimization theory for deforming dense granular materials: Minimum cost maximum flow solutions. Journal of Industrial & Management Optimization, 2014, 10 (1) : 337-362. doi: 10.3934/jimo.2014.10.337

 Impact Factor: 

Tools

Metrics

  • PDF downloads (66)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences