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An Investigation on Pruned NNARX Identification Model of Hydropower Plant

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Abstract

The aim of this paper is to determine an accurate nonlinear system model for identification of dynamics. A small hydropower plant connected as single machine infinite bus (SMIB) system is considered in the study. It is modeled by a neural network configured as a feedforward multilayer perceptron neural network (MLPNN). An investigation is conducted on various NN structures to determine the optimally pruned neural network nonlinear autoregressive with exogenous signal (NNARX) identification model. The structure selection is based on validation tests performed on these network models. The proposed structure identifies the model characteristics, which represent the dynamics of a power plant accurately. The results show an improved performance in identification of power plant dynamics by optimal brain surgeon (OBS) pruned network as compared to un-pruned (i.e., fully connected) network.

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Abbreviations

m :

mechanical torque

m l :

load torque

w 0 :

base angular speed (377.16 rad/s)

w :

rotor angular speed (p.u.)

δl :

load angle (rad)

D :

damping torque

T a :

mechanical time constant

e′ q :

internal transient voltage in the q-axis (p.u.)

V t :

terminal voltage (p.u.)

x d :

d-axis synchronous reactance (p.u.)

x′ d :

d-axis transient reactance (p.u.)

r e +jx e :

transmission line impedance (p.u.)

x q :

q-axis synchronous reactance (p.u.)

K A, K E :

voltage regulator gains

T A, T E :

voltage regulator time constants

K F, T F :

stabilizing transformer gain, time constant

K 1–K 6 :

constants of the linearized model of synchronous machine

P e , Q e :

active and reactive power output from synchronous machine

V f :

stabilizing transformer voltage

E FD :

field voltage

V ref :

reference voltage

V a :

regulator voltage

τ ′ d0 :

d-axis open circuit field time constant

References

  1. Narendra KS, Parthasarathy K (1990) Identification and control of dynamical systems using neural networks. IEEE Trans Neural Netw 1:4–27

    Article  Google Scholar 

  2. Osowski S, Siwek K (2002) Regularisation of neural networks for improved load forecasting in the power system. IEE Proc Gener Trans Distrib 149:340–344

    Article  Google Scholar 

  3. Xu F, Li Y, Cheng Q (1995) Study of the modeling of hydroturbine generating set. In: Proceedings of IEEE/IAS conference on industrial automation and control: emerging technologies, May, 1995, pp 22–27

  4. Chen Q, Xiao Z (2000) Dynamic modeling of hydroturbine generating set. In: Proceedings of IEEE international conference on systems, man, and cybernetics, October, 2000, pp 8–11

  5. Jiang C, Bingwen L, Weiyou C (1996) Nonlinear simulation of hydroturbine governing system based on neural network. In: Proceedings of IEEE international conference on systems, man, and cybernetics, 14–17 October, 1996

  6. Herron J, Wozniak L (1991) A state-space pressure and speed sensing governor for hydrogenerators. IEEE Trans Energy Conversion 6:414–418

    Article  Google Scholar 

  7. Arnautovic DB, Skataric DM (1991) Sub-optimal design of hydro-turbine governors. IEEE Trans Energy Conversion 6:438–444

    Article  Google Scholar 

  8. Abdel-Magid YL, Maamar B, Selim SZ (1997) Power system output feedback stabilizer design via genetic algorithms. In: Proceedings of IEE conference on genetic algorithms in engineering-systems, innovations and applications, 2–4 September, 1997

  9. Venayagamoorthy GK, Harley RG (1999) A continually online trained artificial neural network identifier for a turbogenerator. In: Proceedings of IEEE international electric machines and drives conference (IEMDC’99), 9–12 May, 1999

  10. Cybenko G (1989) Approximations by superpositions of a sigmoidal function. Math Control Signals Syst 2:303–314

    Article  MATH  MathSciNet  Google Scholar 

  11. Funahashi K (1989) On the approximate realization of continuous mappings by neural networks. Neural Netw 2:183–192

    Article  Google Scholar 

  12. Pienaar JD, Bodenstein CP (1998) The identification of nonlinear dynamic systems around operating points using neural networks. In: Proceedings of IEEE international symposium on industrial electronics ISTE' 93, 7–10 July, pp 105–109

  13. Kinser JM (1995) The minimum number of hidden neurons does not necessarily provide the best generalization. http://www.ib3.gmu.edu/kinser/pubs/MinNum.pdf

  14. Lo James T (1999) Statistical method of pruning neural networks. In: Proceedings of international joint conference on neural networks (IJCNN’99), 10–16 July, 1999

  15. Madonado FJ, Manry MT (2000) Optimal pruning of feedforward neural networks based upon the Schmidt procedure. http://www.ee.uta.edu/eeweb/IP/papers/192.pdf

  16. Yan Z, Jian C (1999) Studies on genetic feedforward neural networks and the development of GMNN. In: Proceedings of systems, man and cybernetics (IEEE SMC’99), 12–15 October, 1999

  17. Nørgaad M (2000) Neural network based system identification toolbox, Technical report 00-E-891. Department of Automation, Technical University of Denmark

  18. Chong AZS, Wilcox SJ, Ward J (2001) Prediction of gaseous emissions from a chain grate stroker boiler using neural networks of ARX structure. IEE Proc Sci Meas Technol 148:95–102

    Article  Google Scholar 

  19. Hecht-Nielsen R (1990) Neurocomputing. Addison-Wesley, Reading

    Google Scholar 

  20. Mechaqrane A, Zouak M (2004) A comparison of linear and neural network ARX models applied to a prediction of the indoor temperature of a building. Neural Comput Appl 13:32–37

    Article  Google Scholar 

  21. Chiras N, Evans C, Rees D (2002) Nonlinear gas turbine modeling using feedforward neural networks. In: Proceedings of ASME TORBO EXPO 2002, 3–6 June, 2000

  22. Billings SA, Voon WSF (1986) Correlation based model validity tests for non-linear models. Int J Control 44:235–244

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical Engineering, Royal Bhutan Institute of Technology, Phuentsholing, Bhutan

    Nand Kishor, P. R. Sharma & A. S. Raghuvanshi

Authors
  1. Nand Kishor
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  2. P. R. Sharma
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  3. A. S. Raghuvanshi
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Correspondence to Nand Kishor.

Appendix

Appendix

The plant data are as follows:

S n =131 MVA; V n =13.8 kV; x′′ d =0.330; x′ d =0.360; x d =1.010; x′′ q =0.330; x′ q =0.57; x q =0.57; r a=0.004; τ ′′ d =0.030 s; τ ′ d =2.7 s; τ ′′ d0=0.030 s; τ ′ d0=7.6 s; D=0.0; K E=− 0.17; T A=0.05; T E=0.95; K A=400; K F=0.025; T F=1.0; T w =2.23 s.

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Kishor, N., Sharma, P.R. & Raghuvanshi, A.S. An Investigation on Pruned NNARX Identification Model of Hydropower Plant. Engineering with Computers 21, 272–281 (2006). https://doi.org/10.1007/s00366-006-0016-z

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