0
Research Papers

Hamiltonian Formulation and Analysis for Transient Dynamics of Multi-Unit Hydropower System

[+] Author and Article Information
Huanhuan Li

Institute of Water Resources
and Hydropower Research,
Northwest A&F University,
Yangling 712100, Shaanxi, China;
Key Laboratory of Agricultural Soil and Water
Engineering in Arid and Semiarid Areas,
Ministry of Education,
Northwest A&F University,
Yangling 712100, Shaanxi, China
e-mail: huanhuanli@nwsuaf.edu.cn

Diyi Chen

Institute of Water Resources
and Hydropower Research,
Northwest A&F University,
Yangling 712100, Shaanxi, China;
Key Laboratory of Agricultural Soil and Water
Engineering in Arid and Semiarid Areas,
Ministry of Education,
Northwest A&F University,
Yangling 712100, Shaanxi, China;
Australasian Joint Research Centre
for Building Information Modelling,
School of Built Environment,
Curtin University,
Perth 6102, WA, Australia
e-mail: diyichen@nwsuaf.edu.cn

Silvia Tolo

Institute for Risk and Uncertainty,
University of Liverpool,
Peach Street, Chadwick Building,
Liverpool L69 7ZF, UK
e-mail: S.Tolo@liverpool.ac.uk

Beibei Xu

Institute of Water Resources
and Hydropower Research,
Northwest A&F University,
Yangling 712100, Shaanxi, China;
Key Laboratory of Agricultural Soil and Water
Engineering in Arid and Semiarid Areas,
Ministry of Education,
Northwest A&F University,
Yangling 712100, Shaanxi, China
e-mail: xubeibei0413@163.com

Edoardo Patelli

Institute for Risk and Uncertainty,
University of Liverpool,
Peach Street, Chadwick Building,
Liverpool L69 7ZF, UK
e-mail: Edoardo.Patelli@liverpool.ac.uk

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 20, 2018; final manuscript received July 7, 2018; published online August 1, 2018. Assoc. Editor: Tsuyoshi Inoue.

J. Comput. Nonlinear Dynam 13(10), 101004 (Aug 01, 2018) (10 pages) Paper No: CND-18-1115; doi: 10.1115/1.4040871 History: Received March 20, 2018; Revised July 07, 2018

This paper focuses on the implementation of a Hamiltonian model of multi-unit hydropower systems (MUHSs). First, a nonlinear mathematical model of the MUHS is established considering the occurrence of water hammer during the transient process. From the point of view of the energy transmission and dissipation of the system, a novel Hamiltonian model of the MUHS is proposed. Moreover, numerical simulations are carried out to further investigate the effectiveness and consistency of the implemented model. Finally, a comparative analysis is performed to validate the proposed approach against existing methods. The results demonstrate that the proposed Hamiltonian function not only reflects the energy change but also describes the complex dynamic evolution of MUHSs in transient processes. It is also found that the transient dynamic behavior of the system is influenced by the coupled effect of common penstock and the interaction of basic system variables. This study provides theoretical basis for the safe and stable operation of hydropower stations during transient processes.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Trivedi, C. , Gogstad, P. J. , and Dahlhaug, O. G. , 2017, “ Investigation of the Unsteady Pressure Pulsations in the Prototype Francis Turbines During Load Variation and Startup,” J. Renew. Sustain. Ener., 9(6), p. 064502.
Wu, Q. Q. , Zhang, L. K. , and Ma, Z. Y. , 2017, “ A Model Establishment and Numerical Simulation of Dynamic Coupled Hydraulic-Mechanical-Electric-Structural System for Hydropower Station,” Nonlinear Dyn., 87(1), pp. 459–474. [CrossRef]
Egusquiza, E. , Valero, C. , Presas, A. , Huang, X. X. , Guardo, A. , and Seidel, U. , 2016, “ Analysis of the Dynamic Response of Pump-Turbine Impellers. Influence of the Rotor,” Mech. Syst. Signal Process., 68–69, pp. 330–341. [CrossRef]
Skjoldan, P. F. , and Bauchau, O. A. , 2011, “ Determination of Modal Parameters in Complex Nonlinear Systems,” ASME J. Comput. Nonlinear Dyn., 6(3), p. 031017. [CrossRef]
Niu, W. J. , Feng, Z. K. , and Cheng, C. T. , 2018, “ Optimization of Variable-Head Hydropower System Operation Considering Power Shortage Aspect With Quadratic Programming and Successive Approximation,” Energy, 143, pp. 1020–1028. [CrossRef]
Balkhair, K. S. , and Rahman, K. U. , 2017, “ Sustainable and Economical Small-Scale and Low-Head Hydropower Generation: A Promising Alternative Potential Solution for Energy Generation at Local and Regional Scale,” Appl. Energy, 188, pp. 378–391. [CrossRef]
Razurel, P. , Gorla, L. , Tron, S. , Niayifar, A. , Crouzy, B. , and Perona, P. , 2018, “ Improving the Ecohydrological and Economic Efficiency of Small Hydropower Plants With Water Diversion,” Adv. Water Resour., 113, pp. 249–259. [CrossRef]
Karney, B. W. , and Simpson, A. R. , 2007, “ In-Line Check Valves for Water Hammer Control,” J. Hydraul. Res., 137(11), pp. 1509–1521.
Li, H. H. , Chen, D. Y. , Zhang, H. , Wang, F. F. , and Ba, D. D. , 2016, “ Nonlinear Modeling and Dynamic Analysis of a Hydro-Turbine Governing System in the Process of Sudden Load Increase Transient,” Mech. Syst. Signal Process., 80, pp. 414–428. [CrossRef]
Laguna, A. J. , 2015, “ Modeling and Analysis of an Offshore Wind Turbine With Fluid Power Transmission for Centralized Electricity Generation,” ASME J. Comput. Nonlinear Dyn., 10(4), p. 041002. [CrossRef]
Xue, H. B. , Zhang, J. Y. , Wang, H. , and Jiang, B. S. , 2018, “ Robust Stability of Switched Interconnected Systems With Time-Varying Delays,” ASME J. Comput. Nonlinear Dyn., 13(2), p. 021004. [CrossRef]
Pavesi, G. , Cavazzini, G. , and Ardizzon, G. , 2016, “ Numerical Analysis of the Transient Behaviour of a Variable Speed Pump-Turbine During a Pumping Power Reduction Scenario,” Energies, 9(7), p. 534. [CrossRef]
Adam, N. J. , De Cesare, G. , Nicolet, C. , Billeter, P. , Angermayr, A. , Valluy, B. , and Schleiss, A. J. , 2018, “ Design of a Throttled Surge Tank for Refurbishment by Increase of Installed Capacity at a High-Head Power Plant,” J. Hydraul. Eng. ASCE, 144(2).
Trivedi, C. , 2018, “ Investigations of Compressible Turbulent Flow in a High-Head Francis Turbine,” ASME J. Fluids Eng., 140(1), p. 011101. [CrossRef]
Xu, B. B. , Chen, D. Y. , Zhang, H. , and Zhou, R. , 2015, “ Dynamic Analysis and Modeling of a Novel Fractional-Order Hydro-Turbine-Generator Unit,” Nonlinear Dyn., 81(3), pp. 1263–1274. [CrossRef]
Chen, Z. , Singh, P. M. , and Choi, Y. D. , 2017, “ Suppression of Unsteady Swirl Flow in the Draft Tube of a Francis Hydro Turbine Model Using J-Groove,” J. Mech. Sci. Technol., 31(12), pp. 5813–5820. [CrossRef]
Meijaard, J. P. , 2014, “ Fluid-Conveying Flexible Pipes Modeled by Large-Deflection Finite Elements in Multibody Systems,” ASME J. Comput. Nonlinear Dyn., 9(1), p. 011008. [CrossRef]
Triki, A. , 2017, “ Water-Hammer Control in Pressurized-Pipe Flow Using a Branched Polymeric Penstock,” J. Pipel. Syst. Eng. Pract., 8(4), p. 04017024. https://ascelibrary.org/doi/abs/10.1061/%28ASCE%29PS.1949-1204.0000277
Yuan, X. H. , Chen, Z. H. , Yuan, Y. B. , Huang, Y. H. , Li, X. S. , and Li, W. W. , 2016, “ Sliding Mode Controller of Hydraulic Generator Regulating System Based on the Input/Output Feedback Linearization Method,” Math. Comput. Simul., 119, pp. 18–34. [CrossRef]
Aradag, S. , Akin, H. , and Celebioglu, K. , 2017, “ CFD Based Design of a 4.3 MW Francis Turbine for Improved Performance at Design and Off-Design Conditions,” J. Mech. Sci. Technol., 31(10), pp. 5041–5049. [CrossRef]
Demirel, G. , Acar, E. , Celebioglu, K. , and Aradag, S. , 2017, “ CFD-Driven Surrogate-Based Multi-Objective Shape Optimization of an Elbow Type Draft Tube,” Int. J. Hydrogen Energy, 42(28), pp. 17601–17610. [CrossRef]
Zhou, L. J. , Liu, M. , Wang, Z. W. , Liu, D. M. , and Zhao, Y. Z. , 2017, “ Numerical Simulation of the Blade Channel Vortices in a Francis Turbine Runner,” Eng. Comput., 34(2), pp. 364–376. [CrossRef]
Teran, L. A. , Larrahondo, F. J. , and Rodriguez, S. A. , 2016, “ Performance Improvement of a 500-kW Francis Turbine Based on CFD,” Renewable Energy, 96, pp. 977–992. [CrossRef]
Antali, M. , Takacs, D. , and Stepan, G. , 2018, “ Experimental Fitting of Rotor Models by Using a Special Three-Node Beam Element,” ASME J. Comput. Nonlinear Dyn., 13(2), p. 021009. [CrossRef]
Ebrahimi, R. , Ghayour, M. , and Khanlo, H. M. , 2017, “ Chaotic Vibration Analysis of a Coaxial Rotor System in Active Magnetic Bearings and Contact With Auxiliary Bearings,” ASME J. Comput. Nonlinear Dyn., 12(3), p. 031012. [CrossRef]
An, X. L. , Pan, L. P. , and Zhang, F. , 2017, “ Analysis of Hydropower Unit Vibration Signals Based on Variational Mode Decomposition,” J. Vib. Control, 23(12), pp. 1938–1953. [CrossRef]
Xu, B. B. , Yan, D. L. , Chen, D. Y. , Gao, X. , and Wu, C. Z. , 2017, “ Sensitivity Analysis of a Pelton Hydropower Station Based on a Novel Approach of Turbine Torque,” Energy Convers. Manage, 148, pp. 785–800. [CrossRef]
Nasselqvist, M. , Gustavsson, R. , and Aidanpaa, J. O. , 2013, “ A Methodology for Protective Vibration Monitoring of Hydropower Units Based on the Mechanical Properties,” ASME J. Dyn. Syst. Meas. Control, 135(4), p. 410071. [CrossRef]
Zhang, L. K. , Ma, Z. Y. , Wu, Q. Q. , and Wang, X. N. , 2016, “ Vibration Analysis of Coupled Bending-Torsional Rotor-Bearing System for Hydraulic Generating Set With Rub-Impact Under Electromagnetic Excitation,” Arch. Appl. Mech., 86(9), pp. 1665–1679. [CrossRef]
Agudelo, C. , Anglada, F. M. , Cucarella, E. Q. , and Moreno, E. G. , 2013, “ Integration of Techniques for Early Fault Detection and Diagnosis for Improving Process Safety: Application to a Fluid Catalytic Cracking Refinery Process,” J. Loss. Prev. Process Ind., 26(4), pp. 660–665. [CrossRef]
Jong, C. G. , and Leu, S. S. , 2013, “ Bayesian-Network-Based Hydro-Power Fault Diagnosis System Development by Fault Tree Transformation,” J. Mar. Sci. Technol.-Taiwan, 21(4), pp. 367–379.
Xia, X. , Ni, W. , and Sang, Y. J. , 2017, “ A Novel Analysis Method for Fault Diagnosis of Hydro-Turbine Governing System,” Proc. Inst. Mech. Eng., Part O, 231(2), pp. 164–171. [CrossRef]
Kang, J. , Zhang, L. B. , and Liang, W. , 2015, “ Fault Diagnosis of Pipeline and Pump Unit Systems Using Status Coupling Analysis,” J. Loss. Prev. Process Ind., 33, pp. 70–76. [CrossRef]
Naz, R. , 2016, “ The Applications of the Partial Hamiltonian Approach to Mechanics and Other Areas,” Int. J. Nonlinear Mech., 86, pp. 1–6. [CrossRef]
Elyseeva, J. , 2016, “ Comparison Theorems for Conjoined Bases of Linear Hamiltonian Differential Systems and the Comparative Index,” J. Math. Anal. Appl., 444(2), pp. 1260–1273. [CrossRef]
Zeng, Y. , Zhang, L. X. , Guo, Y. K. , and Qian, J. , 2015, “ Hamiltonian Stabilization Additional L-2 Adaptive Control and Its Application to Hydro Turbine Generating Sets,” Int. J. Control Autom. Syst., 13(4), pp. 867–876. [CrossRef]
Wang, Y. Z. , and Ge, S. S. , 2008, “ Augmented Hamiltonian Formulation and Energy-Based Control Design of Uncertain Mechanical Systems,” IEEE Trans. Control Syst. Technol., 16(2), pp. 202–213. [CrossRef]
Sun, Y. Z. , Zhang, X. , Shen, T. L. , Jiao, X. H. , and He, S. , 2005, “ Damping Coefficient Compensation of Generator by Novel Nonlinear Excitation Control,” International Power Engineering Conference (IPEC), Singapore, Nov. 29–Dec. 2, pp. 740–746.
Xu, B. B. , Wang, F. F. , Chen, D. Y. , and Zhang, H. , 2016, “ Hamiltonian Modeling of Multi-Hydro-Turbine Governing Systems With Sharing Common Penstock and Dynamic Analyses Under Shock Load,” Energy Convers. Manag., 108, pp. 478–487. [CrossRef]
Shen, Z. Y. , 1998, Hydraulic Turbine Regulation, Water Power Press, Beijing, China.
Ling, D. J. , and Tao, Y. , 2006, “ An Analysis of the Hopf Bifurcation in a Hydroturbine Governing System With Saturation,” IEEE Trans. Energy Convers., 21(2), pp. 512–515. [CrossRef]
Chang, J. S. , 2005, Transients of Hydraulic Machine Installations, Higher Education Press, Beijing, China.
Li, H. H. , Chen, D. Y. , Zhang, H. , Wu, C. Z. , and Wang, X. Y. , 2017, “ Hamiltonian Analysis of a Hydro-Energy Generation System in the Transient of Sudden Load Increasing,” Appl. Energy, 185, pp. 244–253. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Structure diagram of the hydropower system with an individual penstock

Grahic Jump Location
Fig. 2

Penstock system of the MUHS

Grahic Jump Location
Fig. 3

Schematic diagram of the hydro-turbine and hydraulic speed regulation system

Grahic Jump Location
Fig. 4

Hamiltonian responses of the hydropower system with two units in the transient process: (a) responses of the hydro-turbine for unit 1, (b) responses of the generator for unit 1, (c) responses of the hydro-turbine for unit 2, and (d) responses of the generator for unit 2

Grahic Jump Location
Fig. 5

Dynamic behaviors of variables of two units (i = 1, 2) in the transient process: (a) generator rotor speed ω of two units, (b) generator rotor angle δ of two units, and (c) guide vane opening y of two units

Grahic Jump Location
Fig. 6

Comparison of the dynamic behaviors of two units computed with the novel and previous Hamiltonian model. The previous Hamiltonian model comes from Ref. [39]. (a) Hamiltonian function of the hydro-turbine for unit 1 and (b) Hamiltonian function of the hydro-turbine for unit 2.

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In