# Energy Bus-Based Matrix Modeling and Optimal Scheduling for Integrated Energy Systems
## 1 Introduction
[22] presented a comprehensive input-output matrix approach to model a small-scale trigen system, considering the interactions among the plant components and energy networks. [PERSON] et al. [23] used conversion matrices, including the dispatch factors and component efficiencies, to describe the energy conversion and transfer processes of the CCHP system. [PERSON] et al. [24] proposed a day-ahead scheduling optimization method for a park-level electricity-heat coupled IES, considering a flexible supply. [PERSON] et al. [25] established day-ahead scheduling and real-time scheduling models for the CCHP microgrid and adopted scheduling schemes with different time scales in the real-time scheduling of cooling and electricity, seeking to address the fluctuations in renewable energy resources (RESs) and user loads. [PERSON] et al. [26] proposed a novel two-stage coordinated control approach for CCHP energy management, including an economic dispatching stage (EDS) and a real-time adjusting stage (RTAS), in which the RTAS is used to adjust the scheme of the EDS to tackle power fluctuations. [PERSON] et al. [27] proposed an online optimal scheduling approach based on model predictive control for CCHP microgrids, which can compensate for prediction errors in the RESs and loads. [PERSON] et al. [28] developed a hybrid time-scale energy management approach for IESs, which was composed of a day-ahead robust optimal scheduling model and an intraday rolling model. [PERSON] et al. [29] presented the multi-time-scale optimization of IESs based on distributed model predictive control, which improved the economic performance of the system's operation. [PERSON] et al. [30] proposed a multi-time-scale scheduling approach for IESs considering the uncertainty of the RESs and loads, achieving low-carbon and economical supply-demand matching. [PERSON] et al. [31] presented a multi-time-scale optimization dispatch model for an IES, considering a demand response mechanism. [PERSON] et al. [32]constructed a multi-time-scale optimization model with day-ahead, intraday, and real-time scheduling based on a dynamic EH model, improving the accuracy of the system's operation significantly. In the abovementioned research works, the models of the IES or EH are formulated based on steady-state balances of the energy flows, and the optimal scheduling problems include a day-ahead scheduling stage and a real-time scheduling stage. Due to the fluctuations in the RESs and loads, stochastic optimization methods are used in the day-ahead scheduling stage, while real-time scheduling mainly focuses on how to follow the variations. However, the different energy flows have different time-scale characteristics. For example, the electricity flow can reach a steady state in several seconds, but the heat flow needs several minutes or even an hour. In [25], the real-time scheduling method uses different cycle times to address the multi-time-scale characteristics. In other methods, the multi-time-scale characteristics are somewhat disregarded, leading to an inability to characterize the dynamic differences between electricity, heat, and gas. These methods are not able to achieve optimal real-time scheduling for the cooling or heat flow. To resolve this issue, this paper proposes an energy bus-based matrix-modeling method and a coordinated scheduling strategy for the IES. The steady- and transient-state balances of the energy flows are formulated using the matrix-modeling method, whose parameters are fitted with data from experiments and the literature. To address the fluctuations in the RESs and loads, the coordinated scheduling strategy consists of two components: day-ahead optimization and rolling optimization. Day-ahead optimization uses the steady-state model and multiple scenarios concerning the RES and load forecast data. Rolling optimization is based on the transient-state model, aiming to achieve the optimal real-time scheduling of the energy flows, because the transient model can clearly reflect the multi-time-scale characteristics.