# Monitoring System of Transmission Line in Mountainous Area Based on LPWAN
## 4 Experiment and Simulation Analysis
### Working Mode Selection  
In the multi-objective particle swarm optimization, the delay model and energy consumption model are optimized as individuals, and the maximum delay and bottleneck energy are still used as the embodiment of the delay model and energy consumption model. The simulation platform can be established by MATLAB 2016a software to calculate the optimal solution set. The parameter  
Figure 7: Relationship between the maximum delay and bottleneck energy consumption. setting of the MATLAB algorithm is shown in Table 2, in which zero-ductility transition (ZDT) and Deb, Thiele, Laumanns and Zitzler(DTLZ) are standard test functions. After the system delay and energy consumption are brought in, the following solution set diagram is obtained:  
As shown in Figure 8, there was a contradiction between the delay model and the energy consumption model. It can also be seen that the maximum delay was inversely proportional to the bottleneck energy. However, there was no single objective optimization in the multi-objective particle swarm optimization. It is necessary to weigh the delay and energy consumption and find the optimal solution set in line with the objective function. Through the optimization of the delay model and energy consumption model, the red circle is the required optimal solution set. It can be seen from Figure 8 that the system delay is inversely proportional to the system energy consumption. In order to find the parameters suitable for the proposed three working modes in the optimal solution set of system delay and energy consumption, it is necessary to evaluate the communication revenue of the system. Therefore, this paper used the indirect constraint optimization method to construct the objective function by introducing the weight \(\omega\). The revenue function can be expressed as:  
\[Q(x_{k})=\sqrt{\omega D(x_{k})^{2}+(1-\omega)E(x_{k})^{2}}\quad k\in N \tag{27}\]  
In order to analyze the influence of weight \(\omega\) in monitoring mode, early warning mode, and maintenance mode on the optimal solution set of the multi-objective particle swarm optimization algorithm, this paper used sx1272 calculator UI simulation software to change the network parameters, maximum delay, and bottleneck energy under different \(\omega\). The results are shown in Table 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{2}{c}{**Population Size**} & \multicolumn{2}{c}{**Maximum Number of Iterations**} \\ \cline{2-5}  & **ZDT** & **DTLZ** & **ZDT** & **DTLZ** \\ \hline Multi objective particle swarm optimization algorithm & 100 & 100 & 100 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental parameter settings. Figure 8: Solution set of multi-objective particle swarm optimization. According to the requirements of smart grid communication performance in [42], the data transmission period under monitoring mode can be set to 5 min. From the experimental results in Table 2, we can obtain the lowest system energy consumption that the system can achieve when the communication quality is met when \(\omega=0.2\). Therefore, it is defined that the system works in the monitoring mode when \(\omega=0.2\). Similarly, the system revenue function \(Q(x_{k})\) reaches the maximum value when \(\omega=0.5\), so it is defined that the system works in the early warning mode when \(\omega=0.5\). The system delay reaches the minimum value at \(\omega=0.9\), so it is defined that the system works in maintenance mode when \(\omega=0.9\). After the definition of working mode is completed, the system delay and energy consumption of each working mode are brought into Equation (11) to get the system networking mode under different working modes. In this paper, the OMNeT++(5.0, Simulcraft, NYC) network simulation tool was used to simulate the transmission network of transmission lines. The results are shown in Figure 9.  
It can be seen from Figure 9 that when \(\omega=0.2\), the system gives priority to energy consumption constraints.