A Charging Algorithm for the Wireless Rechargeable Sensor Network with Imperfect Charging Channel and Finite Energy Storage
Abstract
:1. Introduction
1.1. Background and Motivation
1.2. Contribution
1.3. Paper Organization
2. System Model
2.1. Network Model
2.2. Cellular Structure
2.3. Limited Rechargeable Clusters
3. Problem Formulation and Solution
3.1. Problem Analysis
3.2. The Traveling Path Planning
Algorithm 1. The nearest neighbor algorithm. 
Input:$[{x}_{i},{y}_{i}],0\le i\le {N}_{c}$ 
Output: The traveling path of the WCV 

3.3. The Selection of Optimal Charging Nodes
Algorithm 2. Procedure of solution for our problem. 
Input: Twodimensional coordinates of sensor nodes $[{x}_{i},{y}_{i}]$, the distance between each sensor node ${v}_{i}$ in the ${c}_{th}$ priority cluster and the WCV ${d}_{i}$, the number of selected charging nodes ${N}_{c}$, the density of nodes $\rho $, initial energy of each sensor node ${E}_{i,0}$ and the remaining energy ${E}_{i,t}$, the speed of the WCV ${V}_{c}$. 
Output: Energy average waste rate ${P}_{waste}$, the total charging time ${T}_{per}$, the traveling path of the WCV. 

3.4. Extend Node Dynamic Replacement Strategy
4. Simulation Evaluation
4.1. Parameter Setting
4.2. Results and Analysis
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Symbols  Definition 

${E}_{i,0}$  The initial energy level of sensor node ${v}_{i}$ 
${E}_{i,t}$  The residual energy of node ${v}_{i}$ at time 
${E}_{\mathrm{max}}$  The capacity of the sensor node ${v}_{i}$ 
${E}_{\mathrm{min}}$  The minimum energy required by the regular operation 
${\epsilon}_{i,t}$  The energy consumption rate of sensor node ${v}_{i}$ before time $t$ 
${T}_{i,d}$  The charging time of sensor node ${v}_{i}$ 
${T}_{(i1),i}$  The total charging time from sensor node ${v}_{i1}$ to sensor node ${v}_{i}$ 
${T}_{travel(i1\to i)}$  The time spent by the WCV from sensor node ${v}_{i1}$ to sensor node ${v}_{i}$ 
${T}_{per}$  The total charging time during a charging circle 
${V}_{c}$  The speed of the WCV 
N_{c}  The number of selected charging clusters 
${N}_{Rc}$  The number of sensor nodes which send the charging request in the ${c}^{th}$ cluster 
$Num$  The number of clusters which send the charging request 
${T}_{p,\mathrm{max}}$  The maximum time of the WCV in a charging round 
${E}_{ci,t}$  The residual energy of sensor node ${v}_{i}$ in the ${c}^{th}$ cluster at time $t$ 
${B}_{c,\mathrm{max}}$  The capacity of the WCV 
${P}_{i,waste}$  The waste rate of sensor node ${v}_{i}$ 
$\rho $  The density of the sensor node 
Cluster Number  1  2  3  4  5  6  7  8  9  10 

weight  2.24  2.52  1.36  2.16  0.64  1.04  2.84  0.64  1.52  1 
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Tian, M.; Jiao, W.; Liu, J.; Ma, S. A Charging Algorithm for the Wireless Rechargeable Sensor Network with Imperfect Charging Channel and Finite Energy Storage. Sensors 2019, 19, 3887. https://doi.org/10.3390/s19183887
Tian M, Jiao W, Liu J, Ma S. A Charging Algorithm for the Wireless Rechargeable Sensor Network with Imperfect Charging Channel and Finite Energy Storage. Sensors. 2019; 19(18):3887. https://doi.org/10.3390/s19183887
Chicago/Turabian StyleTian, Mengqiu, Wanguo Jiao, Jiaming Liu, and Siyuan Ma. 2019. "A Charging Algorithm for the Wireless Rechargeable Sensor Network with Imperfect Charging Channel and Finite Energy Storage" Sensors 19, no. 18: 3887. https://doi.org/10.3390/s19183887