# Joint Acquisition Time Design and Sensor Association for Wireless Sensor Networks in Microgrids
## 5 Experiment Simulation
#### Simulation Results  
Figure 3 shows the topology of the WSN and the results of the sensor association by the ATSAO during the first round. In this paper, the number of CHs is set to five. According to the CHs selection algorithm, the CHs are located in the center of the whole cluster, and other sensor nodes are associated with a single CH to transmit data. Figure 4 shows the convergence performance of the algorithms proposed in this paper. It can be seen from the figure that as the number of iterations increases, the objective function value Equation (11) of the algorithms gradually increase. After about six iterations, all algorithms tend to convergence. At this time, the CHs and sensor associations no longer change. In addition, from the value of the objective function after the algorithms converge, it can be seen that the performance gap between the ATSAO proposed in this paper and the Relax-CVX is small. Compared with the GREEDY, the improvement is more significant when the complexity increase is not large. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Variable** & **Parameter** & **Value** \\ \hline S & Distribution area & \(500\times 500\) \\ \(\rho\) & Deployment density of WSN nodes & 250 \\ \(N_{j}^{\max}\) & Maximum access number of CH & 30 \\ \(\sigma\) & Satisfaction coefficient & \(1\times 10^{3}\) \\ \(l\) & Amount of data generated per unit time & 40 bit \\ \(\beta\) & Trade-off parameter & 100 \\ \(p_{c}\) & Data acquisition power & 1 mW \\ \(p_{t}\) & Data transmission power & 20 mW \\ \(\eta\) & Power amplifier efficiency & 0.9 \\ \(\alpha\) & Circuit power & 5 mW \\ \(e_{c}\) & Energy consumption for data receiving & 5 mJ/bit \\ \(E_{DA}\) & Energy cost for data aggregation & 0.5 mJ/bit \\ \(T_{max}\) & Maximum acquisition time & 10 s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 3: Topology of WSN and result of sensor associaton by ATSAO. Figure 5 shows that the residual energy changes of all sensor nodes versus number of iteration rounds. Compared with the LEACH, the algorithms proposed in this paper can effectively reduce the energy consumption of the entire WSN and prolong its lifetime. This is because energy consumption is considered when formulating the objective function of the optimization problem. The sensor association is obtained by solving the proposed optimization problem. Then, we select CHs according to the CHs selection algorithm, and multiple iterations have been carried out. Compared with the LEACH, the proposed algorithms in this paper can obtain a better topology control strategy and effectively reduce the transmission energy consumption of all sensor nodes. The Relax-CVX obtains the upper bound of the optimization problem by relaxing the knapsack problem. Therefore, it obtains the best performance. As for the ATSAO, the distance between the optimal gain and the sub-optimal gain is considered when selecting items to pack into the backpack. Compared with the GREEDY algorithm, which only considers the current optimal choice, the ATSAO can obtain better performance. Although compared to the Relax-CVX, the lifetime of the WSN network using the ATSAO is slightly reduced, the time complexity and computational complexity of the ATSAO are reduced significantly. Therefore, the ATSAO achieves a tradeoff between complexity and performance, which is meaningful for sensor nodes with limited computing capacity. The unreasonable CHs selection and sensor association of LEACH algorithm lead to the maximum energy consumption, and finally lead to the shortest lifetime of the WSN using the LEACH algorithm. Figure 6 shows the change in the number of alive sensor nodes versus the number of iteration rounds. It can be seen that the algorithms proposed in this paper can slow down the death process of nodes. First, the Relax-CVX has the slowest death of sensor nodes, followed by the ATSAO, and the WSN with LEACH has the shortest lifetime.