Skip to main content
Springer Nature Link
Log in

Renewable Energy Integration: Bayesian Networks for Probabilistic State Estimation

  • Conference paper
  • First Online:
Data Analytics for Renewable Energy Integration. Technologies, Systems and Society (DARE 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11325))

  • 676 Accesses

Abstract

Increased availability of renewable energy sources, along with novel techniques for power flow control, open up a broad range of interesting challenges and opportunities in power flow optimization. This promises reduced power generation costs through better integration of renewable energy generators into the Smart Grid. Unfortunately, renewable generators are fundamentally variable and uncertain. This uncertainty motivates our study of probabilistic state estimation techniques in this paper. Specifically, we use probabilistic graphical models in the form of Bayesian networks to compute probabilities of power system states, thus enabling improved power flow control. Key differences between our probabilistic state estimation results as reported in this paper and similar previous efforts include: our use of Bayesian probabilistic but exact (rather than Monte Carlo) state estimation techniques; auto-generation of Bayesian networks for probabilistic state estimation; integration with corrective Security-Constrained Optimal Power Flow; and application to Distributed Flexible AC Transmission Systems. We present novel models and algorithms for probabilistic state estimation using auto-generated Bayesian networks compiled to junction trees, and report on experimental results that illustrate the scalability of our methods.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    In experiments with different ADAPT configurations and BNs, strong detection and diagnostic performance was achieved. In international diagnostics competitions arranged in 2009 and 2010, this approach had the best results in three out of four competitions in the track that used ADAPT. Please see https://c3.nasa.gov/dashlink/projects/36/ and https://c3.nasa.gov/dashlink/projects/36/ for further details.

  2. 2.

    We assume power flow control devices such as smart wires; please see http://www.smartwiregrid.com/ for details.

  3. 3.

    Details on distributed control techniques for solving DC OPF problems when transmission lines are instrumented with D-FACTS have been presented by Mohammadi, Hug, and Kar [34].

  4. 4.

    The graph definition \(\varvec{G} =(\varvec{U},\varvec{B})\) is found, for example, in an output file produced by the MatPower software, which is used in our experiments in Sect. 5. The MatPower file contains two tables called Bus Data and Branch Data. These tables contain the graph \(\varvec{G} =(\varvec{U},\varvec{B})\) discussed here along with other data utilized by CreateStateEstimator.

  5. 5.

    The junction tree algorithm works for certain hybrid BNs, namely those in which continuous (Gaussian) nodes can have both continuous and discrete parents, but discrete (multinomial) nodes can only have discrete parents.

  6. 6.

    Both relational and functional notation is used for \(\varPhi \). In other words, we say (relationally) \((B,X) \in \varPhi \) when \(\varPhi \) maps (functionally) from B to X.

  7. 7.

    For example, the IEEE 39-bus as discussed elsewhere in this paper has a total of 10 generators (8 conventional generators and 2 wind power generators) and 19 loads. In this case, there are 21 inputs to corrective SCOPF from PSE.

  8. 8.

    The data can be found in the file case39.m in the MatPower package.

  9. 9.

    For our probabilistic parameters we researched several datasets, all of which contained high-frequency data. The dataset that was chosen is from the Bonneville Power Authority (BPA) SCADA system, see http://transmission.bpa.gov/Business/Operations/Wind/default.aspx.

References

  1. Abur, A., Exposito, A.G.: Power System State Estimation: Theory and Implementation, vol. 24. CRC Press, Boca Raton (2004)

    Google Scholar 

  2. Aien, M., Rashidinejad, M., Kouhi, S., Fotuhi-Firuzabad, M., Najafi Ravadanegh, S.: Real time probabilistic power system state estimation. Int. J. Electr. Power Energy Syst. 62, 383–390 (2014)

    Article  Google Scholar 

  3. Andersen, S.K., Olesen, K.G., Jensen, F.V., Jensen, F.: HUGIN–a shell for building Bayesian belief universes for expert systems. In: Proceedings of the Eleventh International Joint Conference on Artificial Intelligence (IJCAI 1989), Detroit, MI, pp. 1080–1085 (1989)

    Google Scholar 

  4. Basak, A., Brinster, I., Ma, X., Mengshoel, O.J.: Accelerating Bayesian network parameter learning using Hadoop and MapReduce. In: Proceedings of the BigMine 2012, Beijing, China (2012)

    Google Scholar 

  5. Bills, G.W.: On-line stability analysis study. Technical report RP 901–1. Electric Power Research Institute (1970)

    Google Scholar 

  6. Borkowska, B.: Probabilistic load flow. IEEE Trans. Power Appar. Syst. PAS–93(3), 752–759 (1974)

    Article  Google Scholar 

  7. Chavira, M., Darwiche, A.: Compiling Bayesian networks using variable elimination. In: Proceedings of the Twentieth International Joint Conference on Artificial Intelligence (IJCAI 2007), Hyderabad, India, pp. 2443–2449 (2007)

    Google Scholar 

  8. Chien, C.F., Chen, S.L., Lin, Y.S.: Using Bayesian network for fault location on distribution feeder. IEEE Trans. Power Deliv. 17, 785–793 (2002)

    Article  Google Scholar 

  9. Cooper, F.G.: The computational complexity of probabilistic inference using Bayesian belief networks. Artif. Intell. 42, 393–405 (1990)

    Article  MathSciNet  Google Scholar 

  10. Darwiche, A.: Recursive conditioning. Artif. Intell. 126(1–2), 5–41 (2001)

    Article  MathSciNet  Google Scholar 

  11. Darwiche, A.: A differential approach to inference in Bayesian networks. J. ACM 50(3), 280–305 (2003)

    Article  MathSciNet  Google Scholar 

  12. Darwiche, A.: Modeling and Reasoning with Bayesian Networks. Cambridge University Press, Cambridge (2009)

    Book  Google Scholar 

  13. Dawid, A.P.: Applications of a general propagation algorithm for probabilistic expert systems. Stat. Comput. 2, 25–36 (1992)

    Article  Google Scholar 

  14. Dechter, R.: Bucket elimination: a unifying framework for reasoning. Artif. Intell. 113(1–2), 41–85 (1999)

    Article  MathSciNet  Google Scholar 

  15. Divan, D., Johal, H.: Distributed FACTS - a new concept for realizing grid power flow control. IEEE Trans. Power Electr. 22(6), 2253–2260 (2007)

    Article  Google Scholar 

  16. Heckerman, D., Geiger, D., Chickering, D.: Learning Bayesian networks: the combination of knowledge and statistical data. Mach. Learn. 20(3), 197–243 (1995)

    MATH  Google Scholar 

  17. Holmström, K.: TOMLAB - an environment for solving optimization problems in MATLAB. In: Proceedings of the Nordic MATLAB Conference, Stockholm, Sweden (1997)

    Google Scholar 

  18. Hu, Y., Kuh, A., Kavcic, A., Nakafuji, D.: Real-time state estimation on micro-grids. In: Proceedings of the 2011 International Joint Conference on Neural Networks, San Jose, CA, pp. 1378–1385 (2011)

    Google Scholar 

  19. Hu, Y., Kuh, A., Yang, T., Kavcic, A.: A belief propagation based power distribution system state estimator. IEEE Comput. Intell. Mag. 6(3), 36–46 (2011)

    Article  Google Scholar 

  20. Hug, G.: Generation cost and system risk trade-off with corrective power flow control. In: Proceedings of the 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton, IL, pp. 1324–1331 (2012)

    Google Scholar 

  21. Hutter, F., Hoos, H.H., Stützle, T.: Efficient stochastic local search for MPE solving. In: Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence (IJCAI 2005), Edinburgh, Scotland, pp. 169–174 (2005)

    Google Scholar 

  22. Jaakkola, T.S., Jordan, M.I.: Variational probabilistic inference and the QMR-DT database. J. Artif. Intell. Res. 10, 291–322 (1999)

    Article  Google Scholar 

  23. Jensen, F.V., Lauritzen, S.L., Olesen, K.G.: Bayesian updating in causal probabilistic networks by local computations. SIAM J. Comput. 4, 269–282 (1990)

    MathSciNet  MATH  Google Scholar 

  24. Kask, K., Dechter, R.: Stochastic local search for Bayesian networks. In: Proceedings of the Seventh International Workshop on Artificial Intelligence and Statistics (AISTATS 1999), Fort Lauderdale, FL (1999)

    Google Scholar 

  25. Koller, D., Friedman, N.: Probabilistic Graphical Methods: Principles and Techniques. MIT Press, Cambridge (2009)

    MATH  Google Scholar 

  26. Lauritzen, S., Spiegelhalter, D.J.: Local computations with probabilities on graphical structures and their application to expert systems (with discussion). J. Roy. Stat. Soc. Ser. B 50(2), 157–224 (1988)

    MATH  Google Scholar 

  27. Lerner, U., Parr, R., Koller, D., Biswas, G.: Bayesian fault detection and diagnosis in dynamic systems. In: Proceedings of the Seventeenth National Conference on Artificial Intelligence (AAAI 2000), pp. 531–537 (2000)

    Google Scholar 

  28. Mengshoel, O.J.: Understanding the scalability of Bayesian network inference using clique tree growth curves. Artif. Intell. 174, 984–1006 (2010)

    Article  MathSciNet  Google Scholar 

  29. Mengshoel, O.J., Chavira, M., Cascio, K., Poll, S., Darwiche, A., Uckun, S.: Probabilistic model-based diagnosis: an electrical power system case study. IEEE Trans. Syst. Man Cybern. Part A: Syst. Hum. 40(5), 874–885 (2010)

    Article  Google Scholar 

  30. Mengshoel, O.J., Darwiche, A., Uckun, S.: Sensor validation using Bayesian networks. In: Proceedings of the 9th International Symposium on Artificial Intelligence, Robotics, and Automation in Space (iSAIRAS 2008) (2008)

    Google Scholar 

  31. Mengshoel, O.J., Wilkins, D.C., Roth, D.: Controlled generation of hard and easy Bayesian networks: impact on maximal clique size in tree clustering. Artif. Intell. 170(16–17), 1137–1174 (2006)

    Article  MathSciNet  Google Scholar 

  32. Mengshoel, O.J.: Understanding the role of noise in stochastic local search: analysis and experiments. Artif. Intell. 172(8), 955–990 (2008)

    Article  MathSciNet  Google Scholar 

  33. Mohammadi, J., Hug, G., Kar, S.: A benders decomposition approach to corrective security constrained OPF with power flow control devices. In: Proceedings of the 2013 IEEE Power Energy Society General Meeting, pp. 1–5 (2013)

    Google Scholar 

  34. Mohammadi, J., Hug, G., Kar, S.: Fully distributed DC-OPF approach for power flow control. In: 2015 IEEE Power Energy Society General Meeting, pp. 1–5 (2015)

    Google Scholar 

  35. Murphy, K.P.: The Bayes net toolbox for MATLAB. Comput. Sci. Stat. 33, 2001 (2001)

    Google Scholar 

  36. Park, J.D., Darwiche, A.: Complexity results and approximation strategies for MAP explanations. JAIR 21, 101–133 (2004)

    Article  MathSciNet  Google Scholar 

  37. Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo (1988)

    MATH  Google Scholar 

  38. Poll, S., et al.: Advanced diagnostics and prognostics testbed. In: Proceedings of the 18th International Workshop on Principles of Diagnosis (DX-07), Nashville, TN, pp. 178–185 (2007)

    Google Scholar 

  39. Ricks, B., Mengshoel, O.J.: Diagnosis for uncertain, dynamic and hybrid domains using Bayesian networks and arithmetic circuits. Int. J. Approx. Reason. 55(5), 1207–1234 (2014)

    Article  Google Scholar 

  40. Roth, D.: On the hardness of approximate reasoning. Artif. Intell. 82, 273–302 (1996)

    Article  MathSciNet  Google Scholar 

  41. Saluja, A., Sundararajan, P., Mengshoel, O.J.: Age-layered expectation maximization for parameter learning in Bayesian networks. In: Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics (AISTATS 2012), La Palma, Spain, pp. 424–435 (2012)

    Google Scholar 

  42. Schenato, L., Barchi, G., Macii, D., Arghandeh, R., Poolla, K., Von Meier, A.: Bayesian linear state estimation using smart meters and PMUs measurements in distribution grids. In: Proceedings of the 2014 IEEE International Conference on Smart Grid Communications, pp. 572–577 (2014)

    Google Scholar 

  43. Schumann, J., et al.: Software health management with Bayesian networks. Innov. Syst. Softw. Eng. 9(4), 271–292 (2013)

    Article  Google Scholar 

  44. Schumann, J., Rozier, K.Y., Reinbacher, T., Mengshoel, O.J., Mbaya, T., Ippolito, C.: Towards real-time, on-board, hardware-supported sensor and software health management for unmanned aerial systems. Int. J. Progn. Health Manag. 6(1), 1–27 (2015)

    Google Scholar 

  45. Shenoy, P.P.: A valuation-based language for expert systems. Int. J. Approx. Reason. 5(3), 383–411 (1989)

    Article  MathSciNet  Google Scholar 

  46. Shimony, E.: Finding MAPs for belief networks is NP-hard. Artif. Intell. 68, 399–410 (1994)

    Article  Google Scholar 

  47. Soliman, W.M., Bahaa El Din, H.S., Wahab, M.A., Mansour, M.: Bayesian networks for fault diagnosis of large power generating stations. In: Proceedings of the 14th International Middle East Power Systems Conference, Cairo, Egypt, pp. 454–459 (2005)

    Google Scholar 

  48. Sundararajan, P.K., Mengshoel, O.J.: A genetic algorithm for learning parameters in Bayesian networks using expectation maximization. In: Proceedings of the Eighth International Conference on Probabilistic Graphical Models (PGM 2016), Lugano, Switzerland, pp. 511–522 (2016)

    Google Scholar 

  49. Weng, Y., Negi, R., Ilic, M.D.: Probabilistic joint state estimation for operational planning. IEEE Trans. Smart Grid PP(99), 1 (2018)

    Article  Google Scholar 

  50. Yongli, Z., Limin, H., Jinling, L.: Bayesian network-based approach for power system fault diagnosis. IEEE Trans. Power Deliv. 21, 634–639 (2006)

    Article  Google Scholar 

  51. Zhang, N.L., Poole, D.: Exploiting causal independence in Bayesian network inference. J. Artif. Intell. Res. 5, 301–328 (1996)

    Article  MathSciNet  Google Scholar 

  52. Zheng, L., Mengshoel, O.J.: Exploring multiple dimensions of parallelism in junction tree message passing. In: Proceedings of the 2013 UAI Application Workshops, pp. 87–96 (2013)

    Google Scholar 

  53. Zheng, L., Mengshoel, O.J.: Optimizing parallel belief propagation in junction trees using regression. In: Proceedings of 19th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD 2013), Chicago, IL (2013)

    Google Scholar 

  54. Zheng, L., Mengshoel, O.J., Chong, J.: Belief propagation by message passing in junction trees: computing each message faster using GPU parallelization. In: Proceedings of the 27th Conference in Uncertainty in Artificial Intelligence (UAI 2011), Barcelona, Spain, pp. 822–830 (2011)

    Google Scholar 

  55. Zimmerman, R.D., Murillo-Sánchez, C.E., Thomas, R.J.: MATPOWER: steady-state operations, planning, and analysis tools for power systems research and education. IEEE Trans. Power Syst. 26(1), 12–19 (2011)

    Article  Google Scholar 

Download references

Acknowledgment

This material is based, in part, upon work supported by ARPA-E. The collaboration with Prof. Gabriela Hug and Javad Mohammadi on the integration of corrective SCOPF and PSE is also acknowledged.

Author information

Authors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, USA

    Ole J. Mengshoel, Priya K. Sundararajan, Erik Reed, Dongzhen Piao & Briana Johnson

Authors
  1. Ole J. Mengshoel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Priya K. Sundararajan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Erik Reed
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dongzhen Piao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Briana Johnson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ole J. Mengshoel .

Editor information

Editors and Affiliations

  1. Masdar Institute (Khalifa University), Abu Dhabi, United Arab Emirates

    Wei Lee Woon

  2. Masdar Institute (Khalifa University), Abu Dhabi, United Arab Emirates

    Zeyar Aung

  3. Autonomous University of Madrid, Madrid, Spain

    Alejandro Catalina Feliú

  4. Massachusetts Institute of Technology, Cambridge, MA, USA

    Stuart Madnick

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Mengshoel, O.J., Sundararajan, P.K., Reed, E., Piao, D., Johnson, B. (2018). Renewable Energy Integration: Bayesian Networks for Probabilistic State Estimation. In: Woon, W., Aung, Z., Catalina Feliú, A., Madnick, S. (eds) Data Analytics for Renewable Energy Integration. Technologies, Systems and Society. DARE 2018. Lecture Notes in Computer Science(), vol 11325. Springer, Cham. https://doi.org/10.1007/978-3-030-04303-2_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-04303-2_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-04302-5

  • Online ISBN: 978-3-030-04303-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics