# Optimal Configuration of Integrated Energy System Based on Energy-Conversion Interface
## 4 Case Analysis
### Campus Energy-Conversion-Interface Model  
According to the energy-conversion modeling method described in Section 2.2, the P2G device is a primary conversion device, and the gas turbine (GT), internal combustion engine (ICE), and gas boiler (GB) are secondary conversion devices. The electric refrigerator (EC), absorption chiller (AC), electric-heat pump (HP), waste-heat boiler (WB), and electric storage (ES) are tertiary conversion devices. Cold storage (CS) and thermal storage (TS) are quaternary conversion devices. Due to the particularity of the energy-storage devices, the equation containing the remaining conversion devices is first deduced, and then the energy-storage device is specially treated. What should be pointed out is that, since power grid supply and electrical load are treated as two different forms of energy, it is assumed that there is a primary conversion device with an efficiency of 1 between power grid and electrical load. The block matrix of energy-distribution matrix **A** corresponding to the branch connection characteristic matrix is shown in Equation (23) and satisfies the equality constraint of Equation (8). \[\left\{ \begin{array}{l}\textbf{A}_{\text{I}}=\left[\begin{array}{cccc} \alpha_{11}&0&0\\ \alpha_{21}&0&0\end{array}\right]\\ \textbf{A}_{\text{II}}=\left[\begin{array}{cccccc}0&\alpha_{32}&0&0&\alpha_ {35}\\ 0&\alpha_{42}&0&0&\alpha_{45}\\ 0&0&\alpha_{53}&0&0\end{array}\right]\\ \textbf{A}_{\text{III}}=\left[\begin{array}{cccccc}\alpha_{61}&0&0&0&0& \alpha_{66}&0&0\\ \alpha_{71}&0&0&0&0&\alpha_{76}&0&0\\ 0&0&0&0&0&0&\alpha_{87}&0\\ 0&0&0&0&0&0&\alpha_{97}&0\end{array}\right]\\ \textbf{A}_{\text{IV}}=\left[\begin{array}{cccccc}0&0&0&\alpha_{10,4}&0&0&0&0& 0&0&0\\ 0&0&0&0&0&0&0&\alpha_{11,9}&0&\alpha_{11,11}&0\\ 0&0&0&0&0&0&0&\alpha_{12,8}&0&\alpha_{12,10}&0&\alpha_{12,12}\end{array}\right] \end{array} \right. \tag{23}\]  
Mentioned herein are various types of gas turbines and internal-combustion engines. Assuming that there are \(n\) unit models, the operating characteristics of the gas turbine and internal-combustion engine can be expressed as:  
\[\left[ \begin{array}{c}P_{e}\\ P_{th}\end{array} \right]=\left[ \begin{array}{cccc}\eta_{e,1}&\eta_{e,2}& \cdots&\eta_{e,n}\\ \eta_{th,1}&\eta_{th,2}&\cdots&\eta_{th,n}\end{array} \right]\left[ \begin{array} []{c}\alpha_{1}\\ \alpha_{2}\\ \vdots\\ \alpha_{n}\end{array} \right]E_{air}=\left[ \begin{array}{c}\eta_{e}\\ \eta_{th}\end{array} \right]E_{air} \tag{24}\]  
Figure 7: Schematic diagram of the optimal configuration of a campus ECI. The efficiency matrix of the energy-conversion devices at all levels is given by Equations (25)-(27). \[\mathbf{H}_{\mathrm{I}}=\mathrm{diag}(1,\eta_{\mathrm{P2G}}) \tag{25}\]  
\[\mathbf{H}_{\mathrm{II}}=\left[ \begin{array}{cc}\eta_{e}&0\\ \eta_{th}&0\\ 0&\eta_{\mathrm{GB}}\end{array} \right] \tag{26}\]  
\[\mathbf{H}_{\mathrm{III}}=\mathrm{diag}(\eta_{\mathrm{EC}},\eta_{\mathrm{HP}}, \eta_{\mathrm{AC}},\eta_{\mathrm{WB}}) \tag{27}\]  
Energy-storage devices are handled with the load in this paper. After passing through the energy-conversion device, when energy appears in a form corresponding to the load, there are two energy-transmission paths, direct supply to load or storage. The relationship between energy input and load can be shown as Equation (28), and expressed in matrix form as Equation (29):  
\[L_{i}=(1-X_{i}\alpha_{s,i})E_{in,i}+Y_{i}\beta_{s,i}E_{s,i} \tag{28}\]  
\[\mathbf{L}=(1-\mathbf{XA_{s}})\mathbf{E_{in}+YB_{s}E_{s}} \tag{29}\]  
The values of \(X_{i}\) and \(Y_{i}\) may be 0 or 1, satisfying \(X_{i}+Y_{i}=1\). Matrix \(\mathbf{X}=\mathrm{diag}(X_{1},X_{2},\ldots X_{n})\), \(\mathbf{Y}=\mathrm{diag}(Y_{1},Y_{2},\ldots Y_{n})\), where \(n\) is the number of energy forms of the load.