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Investigation of Feasible and Marginal Operating Regimes of Electric Power Systems

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Abstract

The paper is devoted to the analysis of the feasibility domain of electric power systems. The problems of calculating feasible and marginal regimes of power systems, analyzing the geometry of the feasibility domain, and generating samples in this region are considered. Parallels are drawn with the works of B.T. Polyak on the analysis of the image of a quadratic map, modification of the Newton method and the development of methods for generating asymptotically uniform samples in areas with complex geometry. Particular attention is paid to Newton’s method with the transversality condition (TENR), its application for constructing a boundary oracle procedure and utilization for generating samples in the power system feasibility domain.

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REFERENCES

  1. Polyak, B., Convexity of Quadratic Transformations and Its Use in Control and Optimization, J. Optim. Theor. Appl., 1998, vol. 99, pp. 553–583.

    Article  MathSciNet  Google Scholar 

  2. Polyak, B., Convexity of Nonlinear Image of a Small Ball with Applications to Optimization, Set-Valued Analysis, 2001, vol. 9, pp. 159–168.

    Article  MathSciNet  Google Scholar 

  3. Polyak, B. and Gryazina, E., Convexity/Nonconvexity Certificates for Power Flow Analysis, Advances in Energy System Optimization: Proceedings of the First International Symposium on Energy System Optimization, 2017, pp. 221–230.

  4. Ayuev, B., Davydov, V., and Erokhin, P., Fast and Reliable Method of Searching Power System Marginal States, IEEE Transactions on Power Systems, 2016, vol. 31, no. 6, pp. 4525–4533.

    Article  Google Scholar 

  5. Ali, M., Gryazina, E., Dymarsky, A., and Vorobev, P., Calculating Voltage Feasibility Boundaries for Power System Security Assessment, Int. J. Elect. Power & Energy Syst., 2023, vol. 146, art. no. 108739.

  6. Ali, M., Ali, M.H., Gryazina, E., and Terzija, V., Calculating Multiple Loadability Points in the Power Flow Solution Space, Int. J. Elect. Power & Energy Syst., 2023, vol. 148, art. no. 108915.

  7. Gryazina, E. and Polyak, B., On the Root Invariant Regions Structure for Linear Systems, IFAC Proceedings Volumes, 2005, vol. 38, no. 1, pp. 90–95.

  8. Gryazina, E. and Polyak, B., Stability Regions in the Parameter Space: D-Decomposition Revisited, Automatica, 2006, vol. 42, no. 1, pp. 13–26.

    Article  MathSciNet  Google Scholar 

  9. Polyak, B. and Tremba, A., Sparse Solutions of Optimal Control via Newton Method for Under-Determined Systems, J. Global Optim., 2020, vol. 76, no. 3, pp. 613–623.

    Article  MathSciNet  Google Scholar 

  10. Polyak, B. and Tremba, A., New Versions of Newton Method: Step-Size Choice, Convergence Domain, and Under-Determined Equations, Optim. Method. and Soft., 2020, vol. 35, no. 6, pp. 1272–1303.

    Article  MathSciNet  Google Scholar 

  11. Ali, M., Dymarsky, A., and Turitsyn, K., Transversality Enforced Newton–Raphson Algorithm for Fast Calculation of Maximum Loadability, IET Generat. Transmis. Distribut., 2018, vol. 12, no. 8, pp. 1729–1737.

    Article  Google Scholar 

  12. Ali, M., Gryazina, E., and Turitsyn, K., Fast Calculation of the Transfer Capability Margins, IEEE Milan PowerTech, 2019, pp. 1–6.

    Book  Google Scholar 

  13. Ali, M., Gryazina, E., Khamisov, O., and Sayfutdinov, T., Online Assessment of Voltage Stability Using Newton-Corrector Algorithm, IET Generat. Transmis. Distribut., 2020, vol. 14, no. 19, pp. 4207–4216.

    Article  Google Scholar 

  14. Baluev, D., Ali, M., and Gryazina, E., State of the Art Approach for Comprehensive Power System Security Assessment-Real Case Study, Int. J. Elect. Power & Energy Syst., 2024, vol. 155, art. no. 109594.

  15. Sauer, P.W. and Pai, M.A., Power System Steady-State Stability and the Load-Flow Jacobian, IEEE Transact. Power Syst., 1990, vol. 5, no. 4, pp. 1374–1383.

    Article  Google Scholar 

  16. Tremba, A., Calafiore, G., Dabbene, F., Gryazina, E., Polyak, B., Shcherbakov, P., and Tempo, R., RACT: Randomized Algorithms Control Toolbox for MATLAB, IFAC Proceedings Volumes, 2008, vol. 41, no. 2, pp. 390–395.

  17. Polyak, B. and Gryazina, E., Randomized Methods Based on New Monte Carlo Schemes for Control and Optimization, Ann. Oper. Res., 2011, vol. 189, pp. 343–356.

    Article  MathSciNet  Google Scholar 

  18. Venikov, V.A., Perekhodnye elektromekhanicheskie protsessy v elektricheskikh sistemakh (Transient Electromechanical Processes in Electrical Systems), Moscow: Vyssh. shk., 1985.

  19. Ayuev, B.I., Davydov, V.V., Erohin, P.M., and Nejumin, V.G., Vychislitel’nye modeli potokoraspredeleniya v elektricheskikh sistemakh: monografiya (Computational Models of Power Flow in Electrical Systems: Monograph), Moscow: Flinta, 2008.

    Google Scholar 

  20. Zhdanov, P.S., Voprosy ustoichivosti elektricheskikh sistem (Issues of Stability in Electrical Systems), Moscow: Energiya, 1979.

    Google Scholar 

  21. Idel'chik, V.I., Elektricheskie sistemy i seti (Electrical Systems and Networks), Moscow: Energoatomizdat, 1989.

    Google Scholar 

  22. Diaconis, P., The Markov Chain Monte Carlo Revolution, Bull. Amer. Math. Soc., 2009, vol. 46, no. 2, pp. 179–205.

    Article  MathSciNet  Google Scholar 

  23. Turchin, V.F., On the Computation of Multidimensional Integrals by the Monte-Carlo Method, Theor. Probab. Appl., 1971, vol. 16, no. 4, pp. 720–724.

    Article  Google Scholar 

  24. Smith, R., Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed over Bounded Regions, Oper. Res., 1984, vol. 32, no. 6, pp. 1296–1308.

    Article  MathSciNet  Google Scholar 

  25. Polyak, B. and Shcherbakov, P., Why Does Monte Carlo Fail to Work Properly in High-Dimensional Optimization Problems?, Theor. Probab. Appl., 2017, vol. 173, pp. 612–627.

    MathSciNet  Google Scholar 

  26. Polyak, B. and Gryazina, E., Markov Chain Monte Carlo Method Exploiting Barrier Functions with Applications to Control and Optimization, 2010 IEEE International Symposium on Computer-Aided Control System Design, 2010, pp. 1553–1557.

  27. Gryazina, E. and Polyak, B., Random Sampling: Billiard Walk Algorithm, Eur. J. Oper. Res., 2014, vol. 238, no. 2, pp. 497–504.

    Article  MathSciNet  Google Scholar 

  28. Vittal, V., Martin, D., Chu, R., Fish, J., Giri, J.C., Tang, C.K., Villaseca, F.E., and Farmer, R.G., Transient Stability Test Systems for Direct Stability Methods, IEEE Transact. Power Syst., 1992, vol. 7, no. 1, p. 37.

    Article  Google Scholar 

  29. Working Group, Common Format for Exchange of Solved Load Flow Data, IEEE Transact. Power Apparat. Syst., 1973, no. 6, pp. 1916–1925.

  30. Ali, M., Baluev, D., Ali, M.H., and Gryazina, E., A Novel Open Source Power Systems Computational Toolbox, North American Power Symposium (NAPS), 2021, pp. 1–6.

  31. Lesieutre, B.C. and Hiskens, I.A., Convexity of the Set of Feasible Injections and Revenue Adequacy in FTR Markets, IEEE Transact. Power Syst., 2005, vol. 20, no. 4, pp. 1790–1798.

    Article  Google Scholar 

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Funding

This work was supported by the Russian Science Foundation, project no. 22-19-00773.

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Authors and Affiliations

  1. Skolkovo Institute of Science and Technology, Moscow, Russia

    E. N. Gryazina & D. Y. Baluev

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  1. E. N. Gryazina
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  2. D. Y. Baluev
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Correspondence to E. N. Gryazina or D. Y. Baluev.

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This paper was recommended for publication by P.S. Shcherbakov, a member of the Editorial Board

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Gryazina, E.N., Baluev, D.Y. Investigation of Feasible and Marginal Operating Regimes of Electric Power Systems. Autom Remote Control 85, 461–471 (2024). https://doi.org/10.1134/S0005117924050059

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