# Optimized Charging Scheduling with Single Mobile Charger for Wireless Rechargeable Sensor Networks

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## Abstract

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## 1. Introduction

- (1)
- The effect of the moving speed of the mobile charger:
- (2)
- Previous work failed to neglect the importance of the location of service station:
- (3)
- Non periodic charging problem in WRSN:
- (4)
- How to apply the rest sensor nodes if the residual energy of a part of nodes in the network reaches the threshold.

- (1)
- We propose a new method to determine the optimal location for the service station.
- (2)
- The WRSN is divided into several sub networks. In the premise of ensuring certain coverage, not all sensor nodes in each sub network are selected for the active nodes. When the residual energy of the sensor node for the active nodes is lower than the threshold value, the sensor node stops working and waits for charging.

## 2. Related Models and Problem Statement

#### 2.1. Network and Charging Model

#### 2.2. The Model of Energy Consumption

- (1)
- When $d<{d}_{0}$, the formula for energy consumption is expressed as the following equation.$${E}_{TX}(K,d)=(1+b)K{E}_{elec}+K{\epsilon}_{fs}{d}^{2}({d}^{2}=\mathrm{min}({d}^{2},{d}_{ic}^{2}+{d}_{jc}^{2}))$$
- (2)
- When $d\ge {d}_{0}$, the formula for energy consumption is expressed as the following equation.$${E}_{TX}(k,d)=\{\begin{array}{l}K(1+b){E}_{elec}+K{\epsilon}_{mp}{d}^{4}({d}^{4}=\mathrm{min}({d}^{4},{d}_{ic}^{4}+{d}_{jc}^{4}),{d}_{ic}\ge {d}_{0},{d}_{jc}\ge {d}_{0})\\ K(1+b){E}_{elec}+bK{\epsilon}_{fs}{d}_{ic}^{2}+K{\epsilon}_{mp}{d}_{jc}^{4}({d}^{4}=\mathrm{min}({d}^{4},{d}_{ic}^{2}+{d}_{jc}^{4}),{d}_{ic}<{d}_{0},{d}_{jc}\ge {d}_{0})\\ K(1+b){E}_{elec}+K{\epsilon}_{mp}{d}_{ic}^{4}+bK{\epsilon}_{fs}{d}_{jc}^{2}({d}_{ic}^{4}=\mathrm{min}({d}^{4},{d}_{ic}^{4}+{d}_{jc}^{2}),{d}_{ic}\ge {d}_{0},{d}_{jc}<{d}_{0})\\ K(1+b){E}_{elec}+K{\epsilon}_{mp}{d}^{4}({d}^{4}=\mathrm{min}({d}^{4},{d}_{ic}^{2}+{d}_{jc}^{2}),{d}_{ic}<{d}_{0},{d}_{jc}<{d}_{0})\end{array}$$

#### 2.3. Problem Formulation

## 3. Charging Scheduling Policy

#### 3.1. Location Problem of Service Station

- (1)
- Compute the shortest distance ${d}_{ij},i,j\in [1,{\mathrm{n}}^{\prime}]$ in each sub network $G=({S}^{\prime},{D}^{\prime})$ using Floyd algorithm.
- (2)
- Calculate the distance between each sensor node and its farthest sensor node ${l}_{i}$. ${l}_{i}$ can be expressed as ${l}_{i}=\mathrm{max}\left\{{d}_{ij}\right|1\le j\le {n}^{\prime}\text{}(i=1,2,\cdots {n}^{\prime})\}$.
- (3)
- Find the minimum ${l}_{i}$, that is to say, ${l}_{k}=\mathrm{min}\left\{{l}_{i}\right|1\le i\le {n}^{\prime}\}$.

#### 3.2. The Selection of Active Nodes

#### 3.3. Optimal Path Selection

- (1)
- Use the principle of proximity to determine the division of sub networks;
- (2)
- Determine the position of the mobile charger;
- (3)
- Determine the active nodes and select cluster nodes in each sub network;
- (4)
- Update the active nodes according to the energy consumption of the node, and update the cluster nodes correspondingly;
- (5)
- According to the energy consumption of each sensor node in the sub network and the overall energy consumption in each sub network, the recharging scheduling strategy is determined. In each sub network, the residual energy of the last ${k}_{j}$ active nodes is no less than ${E}_{\mathrm{min}}$ before being charged. It can make full use of the energy of each node;
- (6)
- After finishing the charging nodes, the mobile charger returns to the service station and waits for the next charge.

## 4. Simulation Results

- (1)
- The sensor nodes are fixed.
- (2)
- The sensor nodes send data through single hop or multiple hops.
- (3)
- The sensor nodes know their locations with the help of GPS.
- (4)
- Euclidean distance can be obtained by mobile charger with the help of GPS and location algorithm.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Wang, Q.; Kong, F.; Wang, M.; Wang, H.
Optimized Charging Scheduling with Single Mobile Charger for Wireless Rechargeable Sensor Networks. *Symmetry* **2017**, *9*, 285.
https://doi.org/10.3390/sym9110285

**AMA Style**

Wang Q, Kong F, Wang M, Wang H.
Optimized Charging Scheduling with Single Mobile Charger for Wireless Rechargeable Sensor Networks. *Symmetry*. 2017; 9(11):285.
https://doi.org/10.3390/sym9110285

**Chicago/Turabian Style**

Wang, Qihua, Fanzhi Kong, Meng Wang, and Huaqun Wang.
2017. "Optimized Charging Scheduling with Single Mobile Charger for Wireless Rechargeable Sensor Networks" *Symmetry* 9, no. 11: 285.
https://doi.org/10.3390/sym9110285