# Hybrid Energy Routing Approach for Energy Internet
## 7 Simulation and Results
### Results of the Proposed Energy Routing Approach  
Applying the proposed energy routing approach, a source selection (Section 4) with a non-congestion minimum loss path (Section 5) is constructed for each consumer. _Case 1 analysis: mono-source consumer with non overlapping transmission time_  
In this case, according to Table 10, there are two consumers (_D7_ and _D3_) with two producers (_D2_ and _D4_). The transmission time of the consumers is different, which means it does not have any overlap. Thus, in this case, the pre-existing power through lines is zero and the energy transmission path taken by the first consumer will not affect the second one. Starting with consumer _D7_, using the proposed energy routing mechanism:  
1. _D7_ sends energy request to _ER17_. 2. _ER17_ transfers this request to the broker. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Energy Profile** & \multicolumn{2}{c}{_D2_} & _D3_ & _D4_ & _D7_ \\ \hline \(C/P\) & & \(P\) & \(C\) & \(P\) & \(C\) \\ \(P\) (Kw) & & \(15\) & \(-9\) & \(25\) & \(-12\) \\ cost (USD/Kw.h) & & \(0.068\) & - & \(0.043\) & - \\ \hline \multirow{3}{*}{Transmission Time (h:m)} & Case 1 & \(09\):45-14:00 & \(10\):00\(-12\):00 & \(09\):00\(-14\):00 & \(12\):00\(-14\):00 \\ \cline{2-6}  & Case 2 & \(09\):45-14:00 & \(10\):00\(-12\):00 & \(09\):00\(-12\):00 & \(10\):15-12:15 \\ \cline{1-1} \cline{2-6}  & Case 3 & \(09\):45-14:00 & \(10\):00\(-12\):00 & \(09\):00\(-12\):00 & \(10\):15-12:15 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Energy profile of the system prosumers (\(P\)) and consumers (\(C\)) in different cases. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Instruction** & **Complexity** & **Explanations** \\ \hline \(i\gets 1\) & & O(1) & elementary instruction \\ \(X(i,j)\leftarrow\mathit{Rand}(X(i,j)_{\mathit{min}},X(i,j)_{\mathit{max}})\) & O(k*n) & 2 nested loops \\ while and for \(f_{0}(i)\gets OF(X(i,:),S,c)\) & O(k) & Executed \(k\) times \\ \([f\mathit{omit},\mathit{index}]\leftarrow\mathit{min}(f_{0})\) & O(1) & Elementary instruction \\ \(\mathit{pbest}\gets X\) & O(1) & // \\ \(\mathit{gbest}\gets X(\mathit{index})\) & O(1) & // \\ \(\mathit{ite}\gets 1\) & O(1) & // \\ Update \(V\) & O(\(\mathit{maxit}\)) & One loop while \\ Update \(X\) & \(O(\mathit{maxit}*k*np)\) & 3 nested loops \\ \(X(i,j)\gets X(i,j)+V(i,j)\) & \(O(\mathit{maxit}*k*np)\) & // \\ \(f(i)\leftarrow OF(X(i,:),S,c)\) & \(O(\mathit{maxit}*k)\) & 2 nested loops \\ \(f_{0}(i)\gets f(i)\) & \(O(\mathit{maxit}*k)\) & // \\ \(\mathit{pbest}(i)\gets X(i,:)\) & \(O(\mathit{maxit}*k)\) & // \\ \([f\mathit{min},\mathit{index}]\leftarrow\mathit{min}(f_{0})\) & \(O(\mathit{maxit})\) & One loop while \\ \(\mathit{gbest}\leftarrow\mathit{pbest}(\mathit{index})\) & \(O(\mathit{maxit})\) & // \\ \(\mathit{f0 min}\leftarrow\mathit{fmin}\) & \(O(\mathit{maxit})\) & // \\ \(i\gets i+1\) & \(O(\mathit{maxit})\) & // \\ \hline \hline \end{tabular}
\end{table} 
Table 9: _EPSOA_ complexity: _comp(EPSOA)_. 3. The broker creates a list with the available producers that can provide 12 kw in the corresponding time (10.00-12.00) \(L=\{D2,D4\}\), and sends it to \(ER_{17}\). 4. \(ER_{17}\) starts the execution of the subscriber matching mechanism (Section 4). As we can see, \(D7\) is a mono-source consumer. Thus, for each producer in \(L\) (\(D2\) and \(D4\)), the \(ER_{17}\) calculates the cost and the energy-efficient path to determine the fitness value. The energy-efficient path is given by the execution of IACO-based energy routing protocol (IACO-ERP) described in Section 5. The protocol's first phase allows the \(ER_{17}\) to construct a new graph from the EI graph (Figure 2) by deleting all the lines and routers that cannot transfer 12 kw as shown in Figure 6. This step with the dynamic routing creates a non-congestion minimum loss path. 5. As described in Equation (3), in our approach, the objective was the minimization of the power loss and cost of energy. For that, the value of \(\alpha\) used in the calculation of the fitness value was 0.5.