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.

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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.



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