Research Papers

Structural Analysis and Control of a Model of Two-Site Electricity and Heat Supply

[+] Author and Article Information
Hikaru Hoshino

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

Yoshihiko Susuki

Department of Electrical and
Information Systems,
Osaka Prefecture University,
1-1 Gakuencho,
Nakaku, Sakai 599-8531, Japan
e-mail: susuki@eis.osakafu-u.ac.jp

T. John Koo

Hong Kong Applied Science and
Technology Research Institute,
2 Science Park East Avenue,
Hong Kong Science Park,
Hong Kong, China
e-mail: johnkoo@astri.org

Takashi Hikihara

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

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received April 8, 2018; final manuscript received April 21, 2019; published online June 3, 2019. Assoc. Editor: Umesh Vaidya.

J. Dyn. Sys., Meas., Control 141(10), 101004 (Jun 03, 2019) (13 pages) Paper No: DS-18-1166; doi: 10.1115/1.4043703 History: Received April 08, 2018; Revised April 21, 2019

This paper introduces a control problem of regulation of energy flows in a two-site electricity and heat supply system, where two combined heat and power (CHP) plants are interconnected via electricity and heat flows. The control problem is motivated by recent development of fast operation of CHP plants to provide ancillary services of power system on the order of tens of seconds to minutes. Due to the physical constraint that the responses of the heat subsystem are not necessary as fast as those of the electric subsystem, the target controlled state is not represented by any isolated equilibrium point, implying that stability of the system is lost in the long-term sense on the order of hours. In this paper, we first prove in the context of nonlinear control theory that the state-space model of the two-site system is nonminimum phase due to nonexistence of isolated equilibrium points of the associated zero dynamics. Instead, we locate a one-dimensional (1D) invariant manifold that represents the target controlled flows completely. Then, by utilizing a virtual output under which the state-space model becomes minimum phase, we synthesize a controller that achieves not only the regulation of energy flows in the short-term regime but also stabilization of an equilibrium point in the long-term regime. Effectiveness of the synthesized controller is established with numerical simulations with a practical set of model parameters.

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Grahic Jump Location
Fig. 1

Schematic diagram of two-site system for electricity and heat supply

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Fig. 2

Energy flow diagram of the two-site system. The arrows show the positive directions of the energy flows.

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Fig. 3

Trajectories of the zero dynamics described by Eq. (10) with a setting of Y1ref and Y2ref such that there exists a set of equilibrium points: Y1ref=1.0 and Y2ref=1.69: (a) responses of the variables η1, η2, η3, η4, (b) projection to (η1, η2, η3) space, and (c) projection to (η2, η3, η4) space

Grahic Jump Location
Fig. 4

Trajectories of the zero dynamics described by Eq. (10) with a setting of Y1ref and Y2ref such that no equilibrium point exists: Y1ref=1.2 and Y2ref=1.69: (a) responses of the variables η1, η2, η3, η4, (b) projection to (η1, η2, η3) space, and (c) projection to (η1, η2, η3) space

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Fig. 5

Block diagram of the proposed controller for the two-site electricity and heat supply

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Fig. 6

Graphical representation of the closed-loop system

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Fig. 7

Numerical simulations for checking assumptions in Theorems 2 and 3 for various Y1ref and Y2ref: (a) singularity conditions of Â(x) and DΦ(x), (b) real parts of eigen values of Q, and (c) real parts of eigen values of Q̂

Grahic Jump Location
Fig. 8

Time responses of (a) output, (b) state, and (c) input variables of the model. The solid lines show the responses with ŷ1,ref=1.2, and the broken lines ŷ1,ref=0.8. (a) Output variables, (b) state variables, and (c) input variables.

Grahic Jump Location
Fig. 9

Time responses of the outputs under the control law (30) with K 0



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