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Research Papers

A Lumped-Parameter Model of Multiscale Dynamics in Steam Supply Systems

[+] Author and Article Information
Hikaru Hoshino

Department of Electrical Engineering,
Kyoto University,
Katsura, Nishikyo,
Kyoto 615-8510, Japan
e-mail: hoshino@dove.kuee.kyoto-u.ac.jp

Yoshihiko Susuki

Department of Electrical Engineering,
Kyoto University,
Katsura, Nishikyo,
Kyoto 615-8510, Japan
e-mail: susuki@ieee.org

Takashi Hikihara

Department of Electrical Engineering,
Kyoto University,
Katsura, Nishikyo,
Kyoto 615-8510, Japan
e-mail: hikihara.takashi.2n@kyoto-u.ac.jp

1Present address: Department of Electrical and Information Systems, Osaka Prefecture University, 1-1 Gakuencho, Nakaku, Sakai, Osaka 599-8531, Japan and JST CREST, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 18, 2016; final manuscript received August 7, 2016; published online September 16, 2016. Assoc. Editor: Stefano Lenci.

J. Comput. Nonlinear Dynam 11(6), 061018 (Sep 16, 2016) (9 pages) Paper No: CND-16-1023; doi: 10.1115/1.4034491 History: Received January 18, 2016; Revised August 07, 2016

This paper focuses on multiscale dynamics occurring in steam supply systems. The dynamics of interest are originally described by a distributed-parameter model for fast steam flows over a pipe network coupled with a lumped-parameter model for slow internal dynamics of boilers. We derive a lumped-parameter model for the dynamics through physically relevant approximations. The derived model is then analyzed theoretically and numerically in terms of existence of normally hyperbolic invariant manifold in the phase space of the model. The existence of the manifold is a dynamical evidence that the derived model preserves the slow–fast dynamics, and suggests a separation principle of short-term and long-term operations of steam supply systems, which is analog to electric power systems. We also quantitatively verify the correctness of the derived model by comparison with brute-force simulation of the original model.

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Figures

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Fig. 1

Overview of steam supply systems with multiple CHP plants that we consider in this paper. It shows an example of three-site system.

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Fig. 2

Schematic diagram of the two-site steam supply. Each block in the figure shows (a) components of the two-site system and (b) components of a boiler.

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Fig. 3

Schematic diagram of the steam transporting pipe l

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Fig. 4

Numerical values of (a) ei(pi) (solid line) and the values of terms on the right-hand side of Eq. (2) and (b) hc(pis(pi)

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Fig. 5

Responses of state variables (p1, p2, u) and heat output rates Qoi′:=msi′hc(pi) from the boilers. The solid lines show the responses of Eq. (14), and the points (×) show the sample plot of responses of Eq. (19). They are initiated by a step changeofthe parameters from (Q1′,Q2′)=(5MJ/s, 5MJ/s ) to. (Q1′,Q2′)=(6MJ/s, 4MJ/s ).

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Fig. 6

Trajectories of the derived model (14) with (Q1′,Q2′)=(6 MJ/s,4 MJ/s). The trajectory starting from the point (p1,p2,u) = (800kPa,800kPa,0m/s) corresponds to the time response presented in Fig. 5 with subsequent long-term response. The trajectory which is parallel to (p1+p2)/2-axis shows an invariant manifold located with direct numerical integration of Eq. (14).

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Fig. 7

Long-term dynamics for the periodic change of the parameter Q′1. Numerical simulation of (a) time responses of the state variables and (b) trajectory in the phase space are shown.

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Fig. 8

Responses of p1, p2, u0:=u(t,0), and uL:=u(t,L) by the original coupled equations. The points (×) show the sequence of time responses of the derived lumped-parameter model (14).

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