Energy Flow Calculation Method for Multi-Energy Systems: A Matrix Approach Considering Alternative Gas Injection and Dynamic Flow Direction
The steady-state energy flow calculation (EFC) of multi-energy systems (MESs) is a fundamental foundation for MES planning and operation. However, most of the existing MES models are designed case-specifically, making them incapable of modelling diverse scenarios. Moreover, since it involves initial...
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MDPI AG
2025-04-01
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| author | Jianzhang Wu Jianyong Zheng Fei Mei Shuai Wang Ruilin Xu Kai Li |
| author_facet | Jianzhang Wu Jianyong Zheng Fei Mei Shuai Wang Ruilin Xu Kai Li |
| author_sort | Jianzhang Wu |
| collection | DOAJ |
| description | The steady-state energy flow calculation (EFC) of multi-energy systems (MESs) is a fundamental foundation for MES planning and operation. However, most of the existing MES models are designed case-specifically, making them incapable of modelling diverse scenarios. Moreover, since it involves initial value setting, the convergence of the Newton–Raphson (NR) method to solve the EFC problem of MESs is often unsatisfactory. To tackle these problems, a matrix-based EFC method of MESs is proposed in this paper. The universal matrix formulations of heat and gas subnetworks are first constructed, where the injection of alternative gas sources and the effect of gas compressibility factor on the MES state are both considered. Due to the uncertainty of gas flow direction during the NR iteration process, the gas composition tracking equations are modified to avoid ill conditions. The Jacobian matrices for the constructed subnetwork models are then derived and expressed in matrix form. On this basis, the unified NR strategy is adopted to solve the constructed models. Finally, the performance of the proposed method is verified through case studies. The results demonstrate that the proposed models can accurately capture the MES operating state and achieve significant improvements in convergence and computational efficiency compared to traditional models. |
| format | Article |
| id | doaj-art-4fdbcd7c50a5413cbac65279cabb73ed |
| institution | DOAJ |
| issn | 2076-3417 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj-art-4fdbcd7c50a5413cbac65279cabb73ed2025-08-20T02:59:11ZengMDPI AGApplied Sciences2076-34172025-04-01159481510.3390/app15094815Energy Flow Calculation Method for Multi-Energy Systems: A Matrix Approach Considering Alternative Gas Injection and Dynamic Flow DirectionJianzhang Wu0Jianyong Zheng1Fei Mei2Shuai Wang3Ruilin Xu4Kai Li5School of Electrical Engineering, Southeast University, Nanjing 210096, ChinaSchool of Electrical Engineering, Southeast University, Nanjing 210096, ChinaCollege of Energy and Electrical Engineering, Hohai University, Nanjing 211100, ChinaSchool of Electrical Engineering, Southeast University, Nanjing 210096, ChinaSchool of Electrical Engineering, Southeast University, Nanjing 210096, ChinaSchool of Electrical Engineering, Southeast University, Nanjing 210096, ChinaThe steady-state energy flow calculation (EFC) of multi-energy systems (MESs) is a fundamental foundation for MES planning and operation. However, most of the existing MES models are designed case-specifically, making them incapable of modelling diverse scenarios. Moreover, since it involves initial value setting, the convergence of the Newton–Raphson (NR) method to solve the EFC problem of MESs is often unsatisfactory. To tackle these problems, a matrix-based EFC method of MESs is proposed in this paper. The universal matrix formulations of heat and gas subnetworks are first constructed, where the injection of alternative gas sources and the effect of gas compressibility factor on the MES state are both considered. Due to the uncertainty of gas flow direction during the NR iteration process, the gas composition tracking equations are modified to avoid ill conditions. The Jacobian matrices for the constructed subnetwork models are then derived and expressed in matrix form. On this basis, the unified NR strategy is adopted to solve the constructed models. Finally, the performance of the proposed method is verified through case studies. The results demonstrate that the proposed models can accurately capture the MES operating state and achieve significant improvements in convergence and computational efficiency compared to traditional models.https://www.mdpi.com/2076-3417/15/9/4815multi-energy systemmatrix-based modelalternative gas injectionenergy flow calculationJacobian matrix |
| spellingShingle | Jianzhang Wu Jianyong Zheng Fei Mei Shuai Wang Ruilin Xu Kai Li Energy Flow Calculation Method for Multi-Energy Systems: A Matrix Approach Considering Alternative Gas Injection and Dynamic Flow Direction Applied Sciences multi-energy system matrix-based model alternative gas injection energy flow calculation Jacobian matrix |
| title | Energy Flow Calculation Method for Multi-Energy Systems: A Matrix Approach Considering Alternative Gas Injection and Dynamic Flow Direction |
| title_full | Energy Flow Calculation Method for Multi-Energy Systems: A Matrix Approach Considering Alternative Gas Injection and Dynamic Flow Direction |
| title_fullStr | Energy Flow Calculation Method for Multi-Energy Systems: A Matrix Approach Considering Alternative Gas Injection and Dynamic Flow Direction |
| title_full_unstemmed | Energy Flow Calculation Method for Multi-Energy Systems: A Matrix Approach Considering Alternative Gas Injection and Dynamic Flow Direction |
| title_short | Energy Flow Calculation Method for Multi-Energy Systems: A Matrix Approach Considering Alternative Gas Injection and Dynamic Flow Direction |
| title_sort | energy flow calculation method for multi energy systems a matrix approach considering alternative gas injection and dynamic flow direction |
| topic | multi-energy system matrix-based model alternative gas injection energy flow calculation Jacobian matrix |
| url | https://www.mdpi.com/2076-3417/15/9/4815 |
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