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Review of stochastic optimization methods for smart grid

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Abstract

This paper presents various approaches used by researchers for handling the uncertainties involved in renewable energy sources, load demands, etc. It gives an idea about stochastic programming (SP) and discusses the formulations given by different researchers for objective functions such as cost, loss, generation expansion, and voltage/V control with various conventional and advanced methods. Besides, it gives a brief idea about SP and its applications and discusses different variants of SP such as recourse model, chance constrained programming, sample average approximation, and risk aversion. Moreover, it includes the application of these variants in various power systems. Furthermore, it also includes the general mathematical form of expression for these variants and discusses the mathematical description of the problem and modeling of the system. This review of different optimization techniques will be helpful for smart grid development including renewable energy resources (RERs).

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References

  1. Pimentel D, Herz M, Glickstein M, Zimmerman M, Allen R, Becker K, Evans J, Hussain B, Sarsfeld R, Grosfeld A, Seidel T. Renewable energy: current and potential issues. Bioscience, 2002, 52(12): 1111–1120

    Article  Google Scholar 

  2. Ochoa L F, Harrison G P. Minimizing energy losses: optimal accommodation and smart operation of renewable distributed generation. IEEE Transactions on Power Systems, 2011, 26(1): 198–205

    Article  Google Scholar 

  3. Pepermans G, Driesen J, Haeseldonckx D, D’haeseleer W, Belmans R. Distributed generation: definition, benefits and issues. Energy Policy, 2005, 33(6): 787–798

    Article  Google Scholar 

  4. Rasmussen C N. Energy storage for improvement of wind power characteristics. IEEE Trondheim Powertech, 2011: 1–8

    Google Scholar 

  5. Jabr R A, Pal B C. Intermittent wind generation in optimal power flow dispatching. IET Generation, Transmission & Distribution, 2009, 3(1): 66–74

    Article  Google Scholar 

  6. PSERC Executive Committee. “Challenges in integrating renewable technologies into an electric power system” white paper, April 2010

    Google Scholar 

  7. Amarnath R V, Ramana N V. State of art in optimal power flow solution methodologies. Journal of Theoretical and Applied Information Technology, 2011, 30(2): 128–154

    Google Scholar 

  8. Selvi V, Umarani R. Comparative analysis of ant colony and particle swarm optimization techniques. International Journal of Computers and Applications, 2010, 5(4): 1–6

    Article  Google Scholar 

  9. AlRashidi M R, El-Hawary M E. A survey of particle swarm optimization applications in electric power systems. IEEE Transactions on Evolutionary Computation, 2009, 13(4): 913–918

    Article  Google Scholar 

  10. Momoh J A, Adapa R, El-Hawary M E. A review of selected optimal power flow literature to 1993. I. Nonlinear and quadratic programming approaches. IEEE Transactions on Power Systems, 1999, 14(1): 96–104

    Article  Google Scholar 

  11. Monticelli A, Pereira M V F, Granville S. Security constrained optimal power flow with post-contingency corrective rescheduling. IEEE Transaction on Power System, 1987, pwrs-2:1(1): 175–180

    Article  Google Scholar 

  12. Stott B, Alsac O, Monticelli A. Security analysis and optimization. Proceedings of the IEEE, 1987, 75(12): 1623–1644

    Article  Google Scholar 

  13. Birge J R, Louveaux F. Introduction to Stochastic Programming. New York: Springer-Verlag, 1997

    MATH  Google Scholar 

  14. Allan R N, Da Silva A M L, Burchett R C. Evaluation methods and accuracy in probabilistic load flow solutions. IEEE Transactions on Power Apparatus & Systems, 1981, PAS-100(5): 2539–2546

    Google Scholar 

  15. Chandy K M, Low S H, Topcu U, Xu H. A simple optimal power flow model with energy storage. 49th IEEE Conference on Decision and Control, 2011: 58(8) 1051–1057

    Google Scholar 

  16. Yau T, Walker L, Graham H, Gupta A. Effects of battery storage devices on power system dispatch. IEEE Transactions on Power Apparatus & Systems, 1981, PAS-100(1): 375–383

    Google Scholar 

  17. Su W, Wang J, Roh J. Stochastic energy scheduling in microgrids with intermittent renewable energy resources. IEEE Transactions on Smart Grid, 2013, 5(4): 1876–1883

    Article  Google Scholar 

  18. Liu G, Xu Y, Tomsovic K. Bidding strategy for microgrid in dayahead market based on hybrid stochastic/robust optimization. IEEE Transactions on Smart Grid, 2016, 7(1): 227–237

    Article  Google Scholar 

  19. Nikmehr N, Najafi-Ravadanegh S. Probabilistic optimal power dispatch in multi-microgrids using heuristic algorithms. In: Smart Grid Conference, Tehran, 2014: 1–6

    Google Scholar 

  20. Liang H, Zhuang W. Stochastic modeling and optimization in a microgrid: a survey. Energies, 2014, 7(4): 2027–2050

    Article  Google Scholar 

  21. Niknam T. Abarghooee R A, Narimani M R. An efficient scenariobased stochastic programming framework for multi-objective optimal micro-grid operation. Applied Energy, 2012, 99(6): 455–470

    Article  Google Scholar 

  22. Falsafi H, Zakariazadeh A, Jadid S. The role of demand response in single and multi-objective wind-thermal generation scheduling: a stochastic programming. Energy, 2014, 64(1): 853–867

    Article  Google Scholar 

  23. Khazali A, Kalantar M. A stochastic–probabilistic energy and reserve market clearing scheme for smart power systems with plugin electrical vehicles. Energy Conversion and Management, 2015,105: 1046–1058

    Article  Google Scholar 

  24. Yu Z, Jia L, Murphy-Hoye M C, Pratt A, Tong L. Modeling and stochastic control for home energy management. IEEE Transactions on Smart Grid, 2012, 4(4): 2244–2255

    Article  Google Scholar 

  25. Romero-Ruiz J, Pérez-Ruiz J, Martin S, Aguado J A, De la Torre S. Probabilistic congestion management using EVs in a smart grid with intermittent renewable generation. Electric Power Systems Research, 2016, 137: 155–162

    Article  Google Scholar 

  26. Ringler P, Keles D, Fichtner W. Agent-based modelling and simulation of smart electricity grids and markets: a literature review. Renewable & Sustainable Energy Reviews, 2016, 57: 205–215

    Article  Google Scholar 

  27. Koohi-Kamali S, Rahim N A, Mokhlis H, Tyagi V V. Photovoltaic electricity generator dynamic modeling methods for smart grid applications: a review. Renewable & Sustainable Energy Reviews, 2016, 57(C): 131–172

    Article  Google Scholar 

  28. Soroudi A. Robust optimization based self scheduling of hydrothermal Genco in smart grids. Energy, 2013, 61(6): 262–271

    Article  Google Scholar 

  29. Parhoudeh S, Baziar A, Mazareie A, Kavousi-Fard A. A novel stochastic framework based on fuzzy cloud theory for modeling uncertainty in the micro-grids. International Journal of Electrical Power & Energy. 2016, 80: 73–80

    Article  Google Scholar 

  30. Siddaiah R, Saini R P. A review on planning, configurations, modeling and optimization techniques of hybrid renewable energy systems for off grid applications. Renewable & Sustainable Energy Reviews, 2016, 58: 376–396

    Article  Google Scholar 

  31. Mohammadi S, Mohammadi A. Stochastic scenario-based model and investigating size of battery energy storage and thermal energy storage for micro-grid. International Journal of Electrical Power & Energy System, 2014, 61: 531–546

    Article  Google Scholar 

  32. Soares J, Vale Z. Stochastic optimization of distributed energy resources in smart grids. 2015, http://sites.ieee.org/psace-mho/files/ 2015/07/01_15PESGM2908.pdf

    Google Scholar 

  33. Chiang H D. Stochastic security-constrained AC optimal power flow solver for large power networks with renewable. 2015, http:// sites.ieee.org/psace-mho/files/2015/07/05_15PESGM2914.pdf

    Google Scholar 

  34. Miranda V. Electric vehicles in smart grids: a hybrid Benders/EPSO solver for stochastic reservoir optimization. 2015, http://sites.ieee. org/psace-mho/files/2015/07/06_15PESGM2910.pdf

    Google Scholar 

  35. Mohan V, Singh J G, Ongsakul W, Unni A C, Sasidharan N. Stochastic effects of renewable energy and loads on optimizing microgrid market benefits. Procedia Technology, 2015, 21: 15–23

    Article  Google Scholar 

  36. Reka S S, Ramesh V. Demand side management scheme in smart grid with cloud computing approach using stochastic dynamic programming. Perspectives in Science, 2016

    Google Scholar 

  37. Sobu A, Wu G. Optimal operation planning method for isolated micro grid considering uncertainties of renewable power generations and load demand. In: 2012 IEEE PES Innovative Smart Grid Technologies-Asia, Tianjin, 2012: 1–6

    Google Scholar 

  38. Küster T, Lützenberger M, Voß M, Freund D, Albayrak S. Applying heuristics and stochastic optimization for load-responsive charging in a smart grid architecture. In: 2014 IEEE PES Innovative Smart Grid Technologies Conference Europe, Istanbul, 2014: 1–6

    Google Scholar 

  39. Zhu Z, Lambotharan S, Chin W H, Fan Z. A stochastic optimization approach to aggregated electric vehicles charging in smart grids. In: 2014 IEEE Innovative Smart Grid Technologies-Asia, Kuala Lumpur, 2014: 51–56

    Chapter  Google Scholar 

  40. Tan J, Wang L. A stochastic model for quantifying the impact of PHEVs on a residential distribution grid. In: IEEE International Conference on Cyber Technology in Automation, Control and Intelligent Systems, Nanjing, 2013: 120–125

    Google Scholar 

  41. Haghi H V, Qu Z, Lotfifard S. Analytics-based optimization for smart grid operations. In: IEEE International Workshop on Intelligent Energy Systems, San Diego, 2014: 58–63

    Google Scholar 

  42. Venayagamoorthy G K. Dynamic, stochastic, computational, and scalable technologies for smart grids. IEEE Computational Intelligence Magazine, 2011, 6(3): 22–35

    Article  Google Scholar 

  43. Gong C, Wang X, Xu W, Tajer A. Distributed real-time energy scheduling in smart grid: stochastic model and fast optimization. IEEE Transactions on Smart Grid, 2013, 4(3): 1476–1489

    Article  Google Scholar 

  44. Momoh J A. Adaptive Stochastic Optimization Techniques with Applications. Boca Raton: CRC Press, 2015

    Book  MATH  Google Scholar 

  45. Alguacil N, Conejo A J. Multiperiod optimal power flow using benders decomposition. IEEE Transactions on Power Systems, 2000, 15(1): 196–201

    Article  Google Scholar 

  46. Sortomme E, El-Sharkawi M A. Optimal power flow for a system of microgrids with controllable loads and battery storage. Power Systems Conference & Exposition, 2009, 107(1): 1–5

    Google Scholar 

  47. Delson J K, Shahidehpour S M. Linear programming applications to power system economics, planning and operations. IEEE Transactions on Power Systems, 1992, 7(3): 1155–1163

    Article  Google Scholar 

  48. Hashemi-Dezaki H, Hamzeh M, Askarian-Abyaneh H, Haeri-Khiavi H. Risk management of smart grids based on managed charging of PHEVs and vehicle-to-grid strategy using Monte Carlo simulation. Energy Conversion and Management, 2015, 100: 262–276

    Article  Google Scholar 

  49. Arnold U, Yildiz Ö. Economic risk analysis of decentralized renewable energy infrastructures—a Monte Carlo simulation approach. Renewable Energy, 2015, 77: 227–239

    Article  Google Scholar 

  50. Pereira E J S, Pinho J T, Galhardo M A B, Macêdo W N. Methodology of risk analysis by Monte Carlo method applied to power generation with renewable energy. Renewable Energy, 2014, 69(3): 347–355

    Article  Google Scholar 

  51. Rosenblueth E. Point estimates for probability moments. Proceedings of the National Academy of Science of the United States of America, 1975, 72(10): 3812–3814

    Article  MathSciNet  MATH  Google Scholar 

  52. Rosenblueth E. Two-point estimates in probability. Applied Mathematical Modelling, 1981, 5(5): 329–335

    Article  MathSciNet  MATH  Google Scholar 

  53. Morales J M, Pérez-Ruiz J. Point estimate schemes to solve the probabilistic power flow. IEEE Transactions on Power Systems, 2007, 22(4): 1594–1601

    Article  Google Scholar 

  54. Verbic G, Canizares C A. Probabilistic optimal power flow in electricity markets based on a two-point estimate method. IEEE Transactions on Power Systems, 2006, 21(4): 1883–1893

    Article  Google Scholar 

  55. Surender Reddy S, Bijwe P R, Abhyankar A R. Optimal posturing in day-ahead market clearing for uncertainties considering anticipated real-time adjustment costs. IEEE Systems Journal, 2015, 9(1): 177–190

    Article  Google Scholar 

  56. Reddy S S, Momoh J A. Realistic and transparent optimum scheduling strategy for hybrid power system. IEEE Transactions on Smart Grid, 2015, 6(6): 1–1

    Article  Google Scholar 

  57. Reddy S S, Bijwe P R, Abhyankar A R. Joint energy and spinning reserve market clearing incorporating wind power and load forecast uncertainties. IEEE Systems Journal, 2015, 9(1): 152–164

    Article  Google Scholar 

  58. Geidl M, Andersson G. A modeling and optimization approach for multiple energy carrier power flow. Power Technology, IEEE Russia, 2005, 38(16): 1–7

    Google Scholar 

  59. Momoh J A, Surender Reddy S. Review of optimization techniques for renewable energy resources. IEEE Symposium on Power Electronics and Machines for Wind and Water Applications, Milwaukee, WI, 2014

    Google Scholar 

  60. Momoh J A, Reddy S S, Baxi Y. Stochastic Voltage/Var control with load variation. In: 2014 IEEEPES General Meeting Conference & Exposition, National Harbor, MD (Washington, DC Metro Area), 2014

    Google Scholar 

  61. Momoh J A, Baxi Y, Idubor A O. Frame work for real time optimal power flow using real time measurement tools and techniques. In: North American Power Symposium, Boston, 2011, 1–7

    Google Scholar 

  62. Wei H, Sasaki H, Kubokawa J, Yokoyama R. An interior point nonlinear programming for optimal power flow problems with a novel data structure. IEEE Transactions on Power Systems Pwrs, 1998, 47(3): 14–18

    Google Scholar 

  63. Alguacil N, Conejo A J. Multi period optimal power flow using benders decomposition. IEEE Transactions on Power Systems, 2000, 15(1): 196–201

    Article  Google Scholar 

  64. Todorovski M. Rajičic D. An initialization procedure in solving optimal power flow by genetic algorithm. IEEE Transactions on Power Systems, 2006, 21(2): 480–487

    Article  Google Scholar 

  65. Torres G, Quintana V H. An interior point method for nonlinear optimal power flow using voltage rectangular coordinates. IEEE Transactions on Power Systems, 1998, 13(4): 1211–1218

    Article  Google Scholar 

  66. Jabr R A. Optimal power flow using an extended conic quadratic formulation. IEEE Transactions on Power Systems Pwrs, 2008, 23 (3): 1000–1008

    Article  Google Scholar 

  67. Li Y, McCalley J D. Decomposed SCOPF for improving efficiency. IEEE Transactions on Power Systems Pwrs, 2009, 24(1): 494–495

    Article  Google Scholar 

  68. Vovos P N, Harrison G P, Wallace A R, Bialek J W. Optimal power flow as a tool for fault level-constrained network capacity analysis. IEEE Transactions on Power Systems, 2005, 20(2): 734–741

    Article  Google Scholar 

  69. Moon G H, Wi Y M, Lee K, Joo S K. Fault current constrained decentralized optimal power flow incorporating superconducting fault current limiter (SFCL). IEEE Transactions on Applied Superconductivity, 2011, 21(3): 2157–2160

    Article  Google Scholar 

  70. Verbič G. Cañizares C A. Probabilistic optimal power flow in electricity markets based on a two-point estimate method. IEEE Transactions on Power Systems, 2006, 21(4): 1883–1893

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Railroad and Electrical Engineering, Woosong University, Woosong, Republic of Korea

    S. Surender Reddy

  2. School of Engineering, Central University of Karnataka, Karnataka, India

    Vuddanti Sandeep

  3. Department of Railroad and Civil Engineering, Woosong University, Woosong, Republic of Korea

    Chan-Mook Jung

Authors
  1. S. Surender Reddy
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  2. Vuddanti Sandeep
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  3. Chan-Mook Jung
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Correspondence to Chan-Mook Jung.

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Reddy, S.S., Sandeep, V. & Jung, CM. Review of stochastic optimization methods for smart grid. Front. Energy 11, 197–209 (2017). https://doi.org/10.1007/s11708-017-0457-7

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