# A Study on Wireless Charging for Prolonging the Lifetime of Wireless Sensor Networks
## 8 Simulations
### Result  
The experimental platform is Eclipse Java EE IDE for Web Developers. All simulation results are averaged 100 times. Firstly, we randomly deploy 50 nodes in a 50 m \(\times\) 50 m area. The relevant information of each node is shown in Table 3. According to the theoretical analysis and calculation, the upper and lower limits of the network size are 5 and 71, respectively. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Total energy of MC: \(E_{MC}\) & 10,000 J \\ Power out rate of MC: \(P_{out}\) & 5 J/s \\ Moving consumption of MC: \(C_{MC}\) & 30 J/m \\ Speed of MC: \(v\) & 5 m/s \\ Initial energy of sensor node: \(E_{t}\) & 1000 J \\ Mean and variance of Gaussian distribution & X-N (3, 1) \\ energy consumption rate range of node (mj) & (0, 6) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental parameter setting. Figure 3 shows the effect of different charging schemes on the network lifetime, when the number of nodes increases from 40 to 70 in the 100 m \(\times\) 100 m area. TSPFull is a charging scheme which takes the Hamilton circuit as the charging path and uses the node energy to calculate the charging time. It can be seen that as the number of nodes increases, the network lifetime is gradually shortened. In contrast to Greedy Algorithm, IPCTS has a similar network lifetime as the Greedy one. However, with the network size gradually expanding, the IPCTS's network lifetime is longer than those of the other two charging schemes. This is because of the fact that with the increase of the number of sensor nodes, the Greedy algorithm and TSPFull only charge five nodes, and most of the other nodes do not get an opportunity to charge. Therefore, their lifetime falls faster. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Node ID**} & \multirow{2}{*}{**Coordinate**} & \multicolumn{2}{c}{**Energy**} & \multirow{2}{*}{**Node ID**} & \multirow{2}{*}{**Coordinate**} & \multicolumn{2}{c}{**Energy**} \\  & & **Consumption** & & & **(m)** & **Consumption** \\  & **(m)** & **Rate (mj)** & & & **Rate (mj)** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 3: Node coordinates and energy consumption rate. Figure 3: The effect of different charging times on the network lifetime. Figure 4 also shows the effect of different charging schemes, when the number of nodes increases from 40 to 70 in the 100 m \(\times\) 100 m area. EnLin is a charging scheme which takes the ascending of remaining energy as the charging path of the MC and calculates the charging time of each node using linear programming. TSPLin considers the Hamiltonian circuit as the charging path, and uses linear programming to calculate the charging time of each node. Although the three charging schemes use linear programming to compute the charging time for each sensor node dynamically, they are different in moving path designs. Figure 4 shows that with the increasing number of nodes, the network lifetime of the three charging schemes decreases. The IPCTS considers the remaining energy of node and the length of charging path of MC, and its network lifetime is longer than those of the other two charging schemes. Figure 5 shows the effect of different area size on the network lifetime. The number of nodes is selected to be 40 and 70 in this simulation. As can be seen from Figure 5, with the increase of the area, the network lifetime gradually reduces. This is because that with the increasing area size, the distance between the nodes increases, resulting in an increase in the moving path length of the MC. In addition, the MC consumes more energy on the moving path. Figure 6 shows the effect of different moving speeds of the MC to prolong the network lifetime. The area is 100 m \(\times\) 100 m. In Figure 6, with the moving speed increasing, the network lifetime increases gradually. This is because of the fact that in the case of a constant area size, the reduction of moving time can bring an increase for charging time, and save MC energy consumption.