# Hybrid Energy Routing Approach for Energy Internet
## 7 Simulation and Results
### Results of the Proposed Energy Routing Approach
#### Case 4 analysis: multi-source consumer

Table 14: Energy profile of the system producers and consumers in the case of a multi-source consumer. Figure 10: Optimization results of case 3 (\(\alpha=0.5\)): (a) energy-efficient path from \(D4\) (\(ER_{13}\)) to \(D7\) (\(ER_{17}\)); (b) energy efficient path from \(D2\) (\(ER_{9}\)) to \(D3\) (\(ER_{10}\)). As shown in Table 15, the fitness value of \(S_{1}\) is larger than the fitness value of \(S_{2}\). Thus, \(ER_{4}\) chooses the set \(S_{2}\) with the power and paths allocation shown in Figure 11:  
\[\left\{ \begin{array}{rcl}p_{D5}&=&11.9928\,\mathrm{kw}&path(D5:D1):&15\to 11 \to 10\to\ 4\\ p_{D6}&=&10.0072\,\mathrm{kw}&path(D6:D1):&16\to 14\to 1\to 3\to 2\to 5\to\ 4 \end{array} \right.\]  
Tables 17-19 show the variation of \(\alpha\) and its affect on the results of _EPSOA_. Figure 12 shows the convergence of the _EPSOA_ in the two sets. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & \multicolumn{4}{c}{**Simulation Parameters**} \\ \hline IACO-ERP & Population size & Iteration number & \(\alpha\) (Equation (28)) & \(\beta\) \\ \cline{2-5}  & 10 & 5 & 1 & 1 \\ \hline _EPSOA_ & Population size & Iteration number & C1 & C2 \\ \cline{2-5}  & 20 & 10 & 2 & 2 \\ \hline \end{tabular}
\end{table} 
Table 16: IACO-BERP and _EPSOA_ simulation parameters. Figure 11: Optimization results of case 4 (\(\alpha=0.5\)). \begin{table}
\begin{tabular}{c c c c c c c c c c c} \multicolumn{7}{c}{_D2_} & \multicolumn{7}{c}{_D6_} \\ \hline
**a** & **Energy Amount** & **Cost** & **Cost** & **Efficient Path** & **Power Loss** & **Fitness Value** & **Energy Amount** & **Cost** & **Efficient Path** & **Power Loss** & **Fitness** \\
**a** & **(low)** & **(USD(N=1))** & **Efficient Path** & **Power Loss** & **Fitness Value** & **Guay** & **(USD(N=1))** & **Efficient Path** & **Power Loss** & **Fitness** \\
0 & 7 & 0.49 & \(9-1-3-2-5-4\) & 0  
_Case 5 analysis: 30 nodes system structure_  
The 30-node (ERs) system was used for further study to validate the efficacy of the proposed energy routing approach on a more complex system, as shown in Figure 13. Tables 20 and 21 show the power lines and ERs parameters used for system in Figure 13. In this system, there are two mono-source consumers, one multi-source consumer and four surplus-energy prosumers. Table 22 displays their energy profile including their cost, power and required transmission time. \begin{table}
\begin{tabular}{l l l} \hline \(\alpha\) & \(Fitness_{S_{1}}\) & \(Fitness_{S_{2}}\) \\ \hline
0 & 1.165 & 1.081 \\
0.1 & 1.21087 & 1.129274 \\
0.2 & 1.25674 & 1.169371 \\
0.3 & 1.30261 & 1.181103 \\
0.4 & 1.34849 & 1.192835 \\
0.5 & 1.39436 & 1.204567 \\
0.6 & 1.43817 & 1.21629 \\
0.7 & 1.47959 & 1.228031 \\
0.8 & 1.52086 & 1.240071 \\
0.9 & 1.56223 & 1.2518 \\
1 & 1.60355 & 1.262795 \\ \hline \end{tabular}
\end{table} 
Table 19: Set fitness. Figure 12: _EPSOA_ convergence (\(\alpha=0.5\)): (**a**) For \(S_{1}\); (**b**) for \(S_{2}\). In case 1 in Table 22, the transmission time of the different consumers does not have an overlapping time. Thus, the different energy transactions will not affect each other during the selection of the minimum energy loss transmission path. Table 23 illustrates the optimization results of the proposed approach with \(\alpha=0.5\). The constructed pairs with the transmission paths that all energy routing constraints such as the power loss and capacity constraints. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline \multirow{2}{*}{**ER**} & \multirow{2}{*}{\ \begin{tabular}{l} **Interface** \\ **Capacity (kw)** \\ \end{tabular}  } & \multirow{2}{*}{**Conversion**} & \multirow{2}{*}{**ER**} & \multirow{2}{*}{ \begin{tabular}{l} **Interface** \\ **Capacity (kw)** \\ \end{tabular}  } & \multirow{2}{*}{**Conversion**} \\  & & & & & **Efficiency (_eff_)** \\ \hline \(R_{1}\) & 30 & 1 & \(R_{16}\) & 19 & 0.97 \\ \(R_{2}\) & 35 & 0.98 & \(R_  
However, in case 2 in Table 22, there is an overlapping time between the transmission time of consumers.