# Integrated Energy System Optimization Based on Standardized Matrix Modeling Method
## 4 Results and Analysis
### Simulation Case Study for Operation Optimization  
In order to test the effectiveness of the integrated energy system standardization modeling method and operation optimization method proposed in the paper, a simulation case study, which is described previously [13; 18], is used to validate. The system consists of a back pressure operated CHP equipment, an auxiliary boiler (AB), an absorption refrigeration equipment (CERG), and an electric refrigeration equipment (WARG). The application case is a typical regional cooling, heat, and electricity triple supply system, and the physical structure description of the linear programming model for this integrated energy system is shown in Figure 11.  
The conversion character of each equipment of the system is shown in Table 4.  
Figure 11: A typical regional cooling, heat, and electricity triple supply system. Figure 10: The variation of optimal comprehensive energy efficiency with both \(y\) and \(z\). At this point, the integrated energy system linear programming matrix model (Equation (10)) can be scaled to  
\[\left[ \begin{array}{c}E_{\text{IES}}^{\text{c}}\\ E_{\text{IES}}^{\text{h}}\\ E_{\text{IES}}^{\text{e}}\end{array} \right]=\left[ \begin{array}{c}\eta_{ \text{C}},\eta_{\text{R}},0,0,0\\ 0,-1,\eta_{\text{AB}},\eta_{\text{Q}},0\\ -1,0,0,\eta_{\text{W}},1\end{array} \right]\left[ \begin{array}{c}E_{\text{c} }\\ H_{\text{h}}\\ F_{\text{AB}}\\ F_{\text{CHP}}\\ E_{\text{i}}\end{array} \right] \tag{27}\]  
Among them, the hourly demands for regional end users such as cooling, heat, and electricity are shown in Figure 12.  
In addition, the gas price of natural gas is 40 Euro/MWh and kept constant. The hourly price of external purchased electricity is shown in Figure 13.  
Then, the optimization target is as follows. \[OF=\sum_{t=1}^{24}E_{\text{i,t}}P_{\text{e,t}}+F_{AB,t}P_{\text{g,t}}+F_{CHP,t}P _{\text{g,t}} \tag{28}\]  
The constraints of regional energy supply and demand balance are as follows. \[\eta_{\text{C}}E_{\text{c,t}}+\eta_{\text{R}}H_{\text{h,t}}\geq E_{\text{IES,t}}^ {\text{c}} \tag{29}\]  
\[-H_{\text{h,t}}+\eta_{\text{AB}}F_{\text{AB,t}}+\eta_{\text{Q}}F_{\text{CHP,t} }\geq E_{\text{IES,t}}^{\text{h}} \tag{30}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Type** & **Parameter** & **Capacity/kW** \\ \hline \(1\) & CHP & \(\eta_{\text{w}}=0.3\) & \(120\) \\  & \(\eta_{\text{Q}}=0.4\) & \(160\) \\ \(2\) & AB & \(\eta_{\text{AB}}=0.8\) & \(400\) \\ \(3\) & CERG & \(\eta_{\text{C}}=3\) & \(300\) \\ \(4\) & WARG & \(\eta_{\text{R}}=0.7\) & \(300\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Conversion characteristics of each equipment. Figure 12: The hourly energy demands for regional end users. \[-E_{\mathrm{c,t}}+\eta_{\mathrm{W}}F_{\mathrm{CHP,t}}+E_{\mathrm{i,t}}\geq E_{ \mathrm{IES,t}}^{\mathrm{e}} \tag{31}\]  
The constraints of conversion characteristics of each equipment are as follows. \[0\leq\eta_{AB}F_{\mathrm{AB,t}}\leq 400 \tag{32}\]  
\[0\leq\eta_{\mathrm{Q}}F_{\mathrm{CHP,t}}\leq 160 \tag{33}\]  
\[0\leq\eta_{\mathrm{C}}E_{\mathrm{C,t}}\leq 300 \tag{34}\]  
\[0\leq\eta_{\mathrm{R}}H_{\mathrm{h,t}}\leq 300 \tag{35}\]  
The optimization algorithm of fmincon at MATLAB can be taken as the solver to obtain the hourly operating strategy of the system components; the results can be seen in Figure 14.  
Figure 14 shows the optimal hourly operation strategy of each equipment of the regional system obtained by the proposed integrated energy system standardized matrix modeling method and optimization method. In the 0-6 h phase, due to the lower electricity price, the electricity demand of the regional end users is entirely supplied by the external purchased electricity.