New Elastic Model of Pipe Flow for Stability Analysis of the Governor-Turbine-Hydraulic System
Publication: Journal of Hydraulic Engineering
Volume 137, Issue 10
Abstract
A higher-order elastic model of the flow in long pressurized pipelines is expected to be utilized for stability analysis of the governor-turbine-hydraulic system in hydropower stations. Because traditional elastic models are limited in lower order application because of their difficult decoupling in addition to the rigid model, a new linear elastic model of the flow in pressurized pipelines is derived on the basis of the equations of hydraulic vibration, in which each oscillatory flow with a different order has been obtained with ordinary differential equations in decoupling form. For water conveyance systems with branching pipes or parallel pipes in hydropower stations, the state equations to describe hydraulic characteristics of the governor-turbine-hydraulic system are established with the application of this new elastic model for diversion pipeline flow or tail tunnel flow. The influence of the elastic models with different order on a system’s stability are revealed in detail by two cases that illustrate that an elastic model with proper order should be used for the flow in pressurized pipelines of hydropower stations, according to their length, to improve the accuracy of stability analysis.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The paper was completed within the research projects funded by the National Natural Science Foundation of China under Grant Nos. NNSFC90610027 and NNSFC51079051, and also financially supported by the Fundamental Research Funds for the Central Universities of China.
References
Chaudhry, M. H. (1987). Applied hydraulic transients, 2nd Ed., Van Nostrand Reinhold, New York.
Chaudhry, M. H., and Hussaini, M. Y. (1985). “Second-order accurate explicit finite-difference schemes for waterhammer analysis.” J. Fluids Eng., 107(4), 523–529.
Jaeger, C. (1977). Fluid transients in hydro-electric engineering practice, Blackie and Sons, Glasgow, Scotland.
Karney, B. W. (1984). “Analysis of fluid transients in large distribution networks.” Ph.D. thesis, Univ. of British Columbia, Vancouver, BC, Canada.
Liang, H. Z., Ye, L. Q., and Meng, A. B. (2004). “A new method for calculation of water hammer based on precise model.” Large Electr. Mach. Hydraul. Turbine, (5), 49–52.
Ling, D. J., Tao, Y., and Shen, Z. Y. (2007). “Hopf bifurcation analysis of hydraulic turbine governing systems with elastic water hammer effect.” J. Vib. Eng., 20(4), 374–379.
Makinen, J., Piche, R., and Ellman, A. (2000). “Fluid transmission line modeling using a variation method.” J. Dyn. Syst., Meas., Control, 122(1), 153–162.
Margolis, D. L., and Yang, W. C. (1985). “Bond graph models for fluid networks using model approximation.” J. Dyn. Syst., Meas., Control, 107(3), 169–175.
Philipp, B. L., and Hsu, C. S. (1996). “Discrete system dominance index for model reduction.” Appl. Math. Modell., 20(6), 429–439.
Politano, M., Odgaard, A. J., and Klecan, W. (2007). “Case study: Numerical evaluation of hydraulic transients in a combined sewer overflow tunnel system.” J. Hydraul. Eng., 133(10), 1103–1110.
Souza, O. H., Jr., and Barbieri, N. (1999). “Study of hydraulic transients in hydropower plants through simulation of nonlinear model of penstock and hydraulic turbine model.” IEEE Trans. Power Syst., 14(4), 1269–1272.
Streeter, V. L., and Wylie, E. B. (1967). Fluid transients, McGraw-Hill, New York.
Suo, L. S., and Wylie, E. B. (1989). “Impulse response method for frequency-dependent pipeline transients.” J. Fluids Eng., 111(4), 478–483.
Suo, L. S., and Wylie, E. B. (1990). “Hydraulic transients in rock-bored tunnels.” J. Hydraul. Eng., 116(2), 196–210.
Taniguchi, H., Nagao, T., and Higasa, H. (1992). “Development of a pumped-storage power station model for power system stability study.” Electr. Eng. Jpn., 112(3), 50–62.
Watton, J., and Tadmori, M. J. (1988). “A comparison of techniques for the analysis of transmission line dynamics in electrohydraulic control systems.” Appl. Math. Modell., 12(5), 457–466.
Wylie, E. B., Streeter, V. L., and Suo, L. S. (1993). “Solution by characteristics method; Complex systems with multipipe and nonpipe elements; Concepts of oscillatory flow and resonance; Analysis of oscillatory flow in systems.” Chapters 3, 6, 12, and 13, Fluid transients in systems, Prentice-Hall, Englewood Cliffs, NJ.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 137 • Issue 10 • October 2011
Pages: 1238 - 1247
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Mar 10, 2010
Accepted: Apr 1, 2011
Published online: Apr 4, 2011
Published in print: Oct 1, 2011
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.