# Energy Bus-Based Matrix Modeling and Optimal Scheduling for Integrated Energy Systems
## 6 Conclusions  
This study proposes the concept of an energy bus for IESs, defining natural gas, electricity, cooling, and heating as a unified energy vector. Thus, the structure of the IES can be represented as a structural diagram based on the  
On this basis, the steady-state matrix model and transient-state matrix model are built. In the steady-state model, the definitions of the device input vector and energy conversion coefficient matrix are shown first, and then, the equilibrium equation of the gas, electricity, cooling, and heat vectors is established, which can be directly transformed into the standard form of the equation constraints for the optimization problem. As for the transient-state model, considering the difficulty in solving the optimization problem, the first-order inertial time constant matrix is used to represent the dynamic characteristics of the device, and then a method to obtain the transient-state matrix models of the devices is proposed. By using curve fitting and system identification methods, the parameters of the steady-state and transient-state matrix models of typical devices are obtained, and the fitting results are good.  
The steady-state and transient-state matrix models established in this study are applied for day-ahead stochastic optimization and rolling optimization, so as to obtain day-ahead hourly scheduling and an intraday 5 min scheduling correction scheme. The simulation results show that stochastic optimization reduces the total daily cost by 1.48% compared to deterministic optimization when considering the prediction errors of the RESs and loads, highlighting the stronger adaptability of stochastic optimization to prediction errors. Moreover, the standard deviation of the objective value for rolling optimization based on the day-ahead stochastic optimization scheme is reduced by 42.79% compared to that of rolling optimization based on the deterministic optimization scheme, indicating smaller revisions to the devices and stronger adaptability to prediction errors.  
In future work, extending the modeling approach based on the energy bus to interconnected integrated energy networks would be both interesting and useful. Additionally, employing artificial intelligence methods to address multi-time-scale optimization problems will provide further improvements.  
Conceptualization, L.Z. and F.L.; methodology, L.Z. and F.L.; software, L.Z.; validation, L.Z. and F.L.; data curation, L.Z.; writing--original draft preparation, L.Z.; writing--review and editing, F.L.; visualization, L.Z. and F.L.; supervision, F.L.; project administration, F.L.; funding acquisition, F.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number: 62103239.  
The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding author/s.  
This research was supported by the National Natural Science Foundation of China (grant number 62103239).  
The authors declare no conflicts of interest.