# Energy Bus-Based Matrix Modeling and Optimal Scheduling for Integrated Energy Systems
## 2 Matrix-Modeling Method  
### IES Structure Based on Energy Bus  
Figure 1 shows the structure and energy flow of a complex IES with various devices. The IES uses the energy from RESs (wind and solar), power, and gas grids and can provide gas, electricity, cooling, and heating for users simultaneously. Any energy flow can be converted into another by using different devices, e.g., a power generation unit (PGU) can consume gas to generate electricity, and an electric chiller can make use of electricity to produce cooling energy. Some energy storage units are also introduced to improve the overall performance of the IES. The existing methods separately analyze and model the balances of the electricity, cooling, and heating, and the modeling processes and results are somewhat complex.  
In this study, an energy bus-based unified modeling method is proposed for the IES. Natural gas, electricity, cooling, and heating are defined as a unified energy vector.  
\[\mathbf{e}=[G\ E\ C\ Q]^{\mathrm{T}} \tag{1}\]  
where \(G\), \(E\), \(C\), and \(Q\) represent natural gas, electricity, cooling, and heating, respectively. Then, the IES can be described by an energy bus-based structure, as shown in Figure 2, in which \(G\), \(E\), \(C\), and \(Q\) are uniformly expressed as an energy vector \(\mathbf{e}\). The balance of the energy vector \(\mathbf{e}\) can be expressed as  
\[\mathbf{e}_{\mathrm{grid}}+\mathbf{e}_{\mathrm{res}}+\mathbf{e}_{\mathrm{pgu,out}}-\mathbf{e}_{ \mathrm{pgu,in}}+\mathbf{e}_{\mathrm{gb,out}}-\mathbf{e}_{\mathrm{gb,in}}+\mathbf{e}_{ \mathrm{ac,out}}-\mathbf{e}_{\mathrm{ac,in}}+\mathbf{e}_{\mathrm{ec,out}}-\mathbf{e}_{ \mathrm{ec,in}}+\mathbf{e}_{\mathrm{s}}=\mathbf{e}_{\mathrm{load}} \tag{2}\]  
Energy purchased from the gas and power grids is classified as the energy vector \(\mathbf{e}_{\mathrm{grid}}\), which is generally a controllable vector. WP and PV are classified as the energy input vector \(\mathbf{e}_{\mathrm{res}}\), whose value needs to be predicted. \(\mathbf{e}_{\mathrm{load}}\) represents the energy output vector of the IES. \(\mathbf{e}_{\mathrm{s}}\) is the charging (\(\mathbf{e}_{\mathrm{s}}<0\)) or discharging (\(\mathbf{e}_{\mathrm{s}}>0\)) vector of the energy storage unit. Its state of charge (SOC) is  
\[\mathbf{e}_{\mathrm{s,soc}}(t+1)=\mathbf{H}_{\mathrm{soc}}\mathbf{e}_{\mathrm{s,soc}}(t)- \mathbf{H}_{\mathrm{s}}\mathbf{e}_{\mathrm{s}}(t) \tag{3}\]  
where \(\mathbf{H}_{\mathrm{s}}\) is the loss coefficient matrix of the charging and discharging processes. The above ports of the energy bus belong to a single energy input or output vector, which fails to  
Figure 1: The structure and energy flow of a complex IES.  
Figure 2: An energy bus-based structure for the IES.  
consider the energy conversion process. Some energy conversion devices or components can acquire any type of energy from the energy bus, and their outputs are injected into the energy bus, e.g., the PGU consumes some gas and returns the converted electricity and heat; the electric chiller inputs some electricity and outputs the corresponding cooling energy. By using an energy bus-based structure, the energy flow analysis can be clarified, which is beneficial in modeling the steady-state and transient-state energy flows of the IES.