# A Fixed-Point Based Distributed Method for Energy Flow Calculation in Multi-Energy Systems

TL;DR: A fixed-point based distributed method for EFC in an electricity-gas-heating system with quantified superiority over the existing methods in computation time, accuracy and reliability and the information privacy of subsystems can be preserved.

Abstract: Energy flow calculation (EFC) plays an important role in steady-state analysis of multi-energy systems (MESs). However, the independent management of sub-energy systems (subsystems) poses a considerable challenge to solve the high-order nonlinear energy flow model due to the limited information exchange between these subsystems. In this article, a fixed-point based distributed method is proposed for EFC in an electricity-gas-heating system. Firstly, the mathematical modeling of each subsystem with coupling units is introduced. Then, two information exchange structures among subsystems are presented as sequential and parallel structures. Based on the fixed-point theorem, novel distributed sequential and parallel methods for EFC are proposed to calculate energy flow distribution in MESs. In our proposed method, the EFC in subsystems is implemented by the individual system operators, with limited information exchange between subsystems. Therefore, the information privacy of subsystems can be preserved in this solution process. Moreover, the convergence of the proposed method is guaranteed, and the sufficient conditions for the convergence are presented. Lastly, simulations on a MES demonstrate the effectiveness of the proposed method and the quantified superiority over the existing methods in computation time, accuracy and reliability.

## Summary (1 min read)

### Introduction

- 3 method is significantly decreased by decomposing the EFC of MESs into several sub-EFCs in the respective subsystems; 2) effective solution methods for EFC in subsystems, such as HE, can be utilized to accelerate the EFC process; and 3) the distributed method can preserve the autonomy of subsystems and enhance robustness against data loss.
- In Structure (a), the information flows as a loop in a sequential way across the electricity system operator (ESO), gas system operator (GSO) and heating system operator (HSO).
- The contributions of this paper are summarized as follows: 1) According to Structure (a), a novel fixed-point based distributed sequential method is presented.

### II. OVERVIEW OF THE MODELING METHODOLOGY

- The structure of the modeling methods is summarized.
- As shown in Fig.1, the MES is modeled as electricity, gas and heating subsystems with coupling units in Section III.
- Then, the distributed EFC method is proposed to solve the MES model in Section IV.
- Specifically, the additional unknown variables in EFC of subsystems are presented in Section IV-A, and then the loop and radial structures of information exchange among subsystems are designed in Section IV-B.
- Lastly, the effectiveness of the proposed method is demonstrated, and the superiority over other existing method is validated by numerical tests in Section V.

### III. MULTI-ENERGY SYSTEM MODELING

- A MES consists of electricity, gas, and heating subsystems as well as various coupling units, such as combined heat and power (CHPs), gas boilers (GBs) and gas turbines (GTs), are comprehensively modeled.
- The modeling of natural gas system contains nodal gas flow balance equations (3) [20], which are built for all known-injection nodes.
- Personal use is permitted, but republication/redistribution requires IEEE permission.
- In addition to the models of electric compressors and pumps in Eqs. (5)-(6) and (13), an three line model of CHPs is adopted in this paper, which takes into account the changes of the power production at part load operation [27], details are shown in (14)-(17).

### IV. DISTRIBUTED EFC METHOD

- A novel fixed point distributed method for EFC in MESs is presented in this section.
- //www.ieee.org/publications_standards/publications/rights/index.html for more information, also known as See http.
- In general, the proposed method can be adapted to other coupling relationships, which will be discussed in Section IV-G.
- According to Theorem 2, the sufficient conditions for convergence of FPDPM are presented.

### VI. CONCLUSION

- A novel fixed-point based distributed method for the EFC in MESs is proposed in this paper.
- //www.ieee.org/publications_standards/publications/rights/index.html for more information, also known as See http.
- In the natural gas system, with the given (PC es, ϕC hs), the value of Pcomp can be obtained by solving gas models (3)-(6) and (14), and this relationship can be formulated as equations (A8).

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