“Nonlinear observer for hydropower system”

Authors: Liubomyr Vytvytskyi, Roshan Sharma and Bernt Lie,
Affiliation: University of South-Eastern Norway
Reference: 2019, Vol 40, No 3, pp. 133-142.

Keywords: State estimation, reduced order nonlinear observer, hydropower model

Abstract: Estimation of unmeasured states plays an essential role in the design of control systems as well as for monitoring of hydropower plants. The standard Kalman filter gives the optimum state estimates for linear systems. However, this optimality is not relevant for nonlinear models and a choice between stochastic and deterministic approaches is not so obvious in this case. Thus the application of a nonlinear observer in a hydropower system is of interest here as an alternative to the widely used extended Kalman filter. This paper provides a study and design of a reduced order nonlinear observer to estimate the states of a hydropower system. Implementation of the nonlinear observer is done in OpenModelica and added to our in-house hydropower Modelica library --- OpenHPL, where different models for hydropower systems are assembled. Simulations and analysis of the designed observer are done in Python using a Python API for operating OpenModelica simulations.

PDF PDF (1496 Kb)        DOI: 10.4173/mic.2019.3.1

References:
[1] Anderson, B. D.O. and Moore, J.B. (1979). Anderson, B, D.O. and Moore, J.B. Optimal Filtering. Prentice-Hall, Englewood Cliffs, NJ. .
[2] Andrieu, V. and Praly, L. (2006). Andrieu, V, and Praly, L. On the Existence of a Kazantzis--Kravaris/Luenberger Observer. SIAM J. Control and Optimization. 45(2):432--456. doi:10.1137/040617066
[3] El-Farra, N., Mhaskar, P., and Christofides, P.D. (2005). El-Farra, N, , Mhaskar, P., and Christofides, P.D. Output feedback control of switched nonlinear systems using multiple Lyapunov functions. Proceedings of the 2005, American Control Conference., 2005. 6:3792--3799. .
[4] Kravaris, C., Sotiropoulos, V., Georgiou, C., Kazantzis, N., Xiao, M., and Krener, A.J. (2007). Kravaris, C, , Sotiropoulos, V., Georgiou, C., Kazantzis, N., Xiao, M., and Krener, A.J. Nonlinear observer design for state and disturbance estimation. Systems & Control Letters. 56(11):730 -- 735. doi:10.1016/j.sysconle.2007.05.001
[5] Krener, A.J. and Isidori, A. (1983). Krener, A, J. and Isidori, A. Linearization by output injection and nonlinear observers. Systems & Control Letters. 3(1):47 -- 52. doi:10.1016/0167-6911(83)90037-3
[6] Lie, B., Bajracharya, S., Mengist, A., Buffoni, L., Kumar, A., Sjolund, M., Asghar, A., Pop, A., and Fritzson, P. (2016). Lie, B, , Bajracharya, S., Mengist, A., Buffoni, L., Kumar, A., Sjolund, M., Asghar, A., Pop, A., and Fritzson, P. API for Accessing OpenModelica Models From Python. In Proceedings of the EuroSim 2016, Oulu, Finland. 2016. .
[7] Luenberger, D.G. (1964). Luenberger, D, G. Observing the State of a Linear System. IEEE Transactions on Military Electronics. 8:74--80. doi:10.1109/TME.1964.4323124
[8] Simon, D. (2006). Simon, D, Optimal State Estimation: Kalman, H-Infinity, and Nonlinear Approaches. John Wiley & Sons. .
[9] Smith, M.C. (1995). Smith, M, C. The general problem of the stability of motion: Translated and Edited by A. T. Fuller. Taylor and Francis, 1992. Automatica. 31:353--354. doi:10.1016/0005-1098(95)90022-5
[10] Splavska, V., Vytvytskyi, L., and Lie, B. (2017). Splavska, V, , Vytvytskyi, L., and Lie, B. Hydropower Systems: Comparison of Mechanistic and Table Look-up Turbine Models. In Proceedings of the 58th Conference on Simulation and Modelling (SIMS 58) Reykjavik, Iceland, September 25th--27th, 2017, 138. Linkoping University Electronic Press, Linkopings Universitet, pages 368--373. doi:10.3384/ecp17138368
[11] Vytvytskyi, L. and Lie, B. (2017). Vytvytskyi, L, and Lie, B. Comparison of elastic vs. inelastic penstock model using OpenModelica. In Proceedings of the 58th Conference on Simulation and Modelling (SIMS 58) Reykjavik, Iceland, September 25th--27th, 2017, 138. Linkoping University Electronic Press, Linkopings Universitet, pages 20--28. doi:10.3384/ecp1713820
[12] Vytvytskyi, L. and Lie, B. (2018). Vytvytskyi, L, and Lie, B. Linearization for Analysis of a Hydropower Model using Python API for OpenModelica. In Proceedings of the 59th Conference on Simulation and Modelling (SIMS 59) Oslo, Norway, September 26th--28th, 2018, 153. Linkoping University Electronic Press, Linkopings Universitet, pages 216--221, 2018. doi:10.3384/ecp18153216
[13] Vytvytskyi, L. and Lie, B. (2018). Vytvytskyi, L, and Lie, B. Mechanistic model for Francis turbines in OpenModelica. IFAC-PapersOnLine, 2018. 51(2):103 -- 108. doi:10.1016/j.ifacol.2018.03.018


BibTeX:
@article{MIC-2019-3-1,
  title={{Nonlinear observer for hydropower system}},
  author={Vytvytskyi, Liubomyr and Sharma, Roshan and Lie, Bernt},
  journal={Modeling, Identification and Control},
  volume={40},
  number={3},
  pages={133--142},
  year={2019},
  doi={10.4173/mic.2019.3.1},
  publisher={Norwegian Society of Automatic Control}
};