## 6 Simulation Results and Analysis
### Comparison of Network Lifetime  
In this subsection, we compare our method with EBCAG and EBCH. In AEBDC, the network is divided into several virtual concentric annuluses with the same width, which is the same as EBCAG and EBCH. The nodes are organized into uneven clusters in these three methods for balance of energy consumption. It is worth mentioning that in AEBDC, we use wireless charging technology, which is not adopted in EBCAG and EBCH. At present, in most wireless sensor network recharging strategies, it is regarded \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(k=3\), \(n=8\) & \(k=4\), \(n=5\) & \(k=5\), \(n=4\) \\ \hline Total Recharging Efficiency of WCV & 70.19\% & 59.9\% & 57.67\% \\ Percentage of Energy Consumption on Moving & 17.34\% & 21.95\% & 32.21\% \\ Percentage of the Residual Energy after Returning Back to BS & 12.47\% & 18.15\% & 10.12\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Total recharging efficiency and energy distribution of WCV. Figure 12: The recharging efficiency of WCV in each annulus (\(k=3\) and \(n=8\)). that all the nodes are rechargeable. So, the purpose of this kind of recharging schemes is to make the network run stably for a long time, and even there will never be dead nodes. However, the cost of recharging has not been fully taken into account, and some researchers even regard that the nodes can continuously obtain energy. This is obviously not practical. In AEBDC, we mainly focus on energy balance technology in Wireless Sensor Networks. The recharging strategy is only one of the means to improve the energy balance of the whole network. Thus, in the proposed algorithm, the cost on recharging and some other problems (such as the slow recharging speed, the low recharging efficiency, etc.) are fully considered. Only the cluster headers and the candidate cluster headers can be recharged, which keeps their residual energy at the same level as that of the common nodes. Therefore, we do not compare the proposed method with other wireless recharging methods. Figure 13 shows the comparison of the number of alive nodes among EBCH, EBCAG and AEBDC. It is easy to see that, the performance of EBCAG is the worst. The dead nodes begin to appear after about 800 rounds, and a large number of nodes die after about 1500 rounds. However, in EBCH, it is not until at around 1100 rounds that the dead nodes appear, and the network lifetime ends at around 2000 rounds, which shows better performance than EBCAG. With the help of the non-uniform deployment of nodes and the optimal load distribution strategy for the cluster headers, an approximate balance of energy consumption among CHs in the same annulus is realized in EBCH, so the network lifetime of this data collection method is prolonged to a certain extent. However, in EBCH, once the CHs die, other nodes will also die quickly, and thus the network lifetime will rapidly decrease. While in AEBDC, the network is divided into different sizes of annulus-sectors. Then, according to the amount of data that nodes need to send and receive in each annulus-sector, we calculate out the size of each RCCH to balance the network load. At the same time, the collaboration based multiple-hop data forwarding strategy is adopted in each annulus-sector to further reduce the energy consumption of the CHs. With the running of the network, the energy consumption rate of the CHs becomes lower and lower in AEBDC so that the number of alive nodes of it decreases slower than that of EBCH and EBCAG, as shown in Figure 13. That is to say, the energy balance performance of AEBDC is better than other methods. The time when the first node dies is shown in Figure 14. It is easy to see that in EBCAG, no matter how many nodes are deployed in the network, the moment when the first dead node appears is almost unchanged (at about the 800-th round). The reason is that the optimal radius of the cluster is calculated which minimizes the energy consumption of the whole network.