# MMCS: Multi-Module Charging Strategy for Increasing the Lifetime of Wireless Rechargeable Sensor Networks

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Related Works

## 3. Multi-Module Charging Strategy

#### 3.1. Problem Definition

_{n}can use Equation (1) to calculate LT

_{n}:

_{n}in WRSNs. Each WCV has two independent batteries: One for moving the vehicle and the other for charging Node

_{n}. When WRSNs run for a while, Node

_{n}needs to be charged. The optimized charging path problem is to improve total lifetime of WRSNs. In addition, there is the problem of how to select urgent nodes as candidate nodes CNs, and charge the CNs efficiently to prolong the lifetime of WRSNs.

_{i,j}represents the distance between the source Node

_{i}and the destination Node

_{j}, and $\frac{{D}_{i,j}}{V}$ represents WCV’s travel time without the time for charging. ED

_{n}represents the energy demand for noden. The travel time considering the time for charging Node

_{n}represents the total travelling time of WCV, as shown in Equation (2):

_{c}and B

_{m}of WCV, and it seeks to minimize T

_{t}and as well as maximize the life time of the WRSNs, as shown in Equations (3) and (4):

#### 3.2. Method Description

_{n}for charging; MMCS has designed two charging scheduling methods based on Dijkstra; and the charging strategy stage is used to calculate the energy demand ED

_{n}of Node

_{n}. The details of all three stages are introduced in this section, and the simulated results are presented in Section 4.

#### 3.2.1. The Stage of Charging Topology

_{n}. However, WCV’s power is limited by the size of its battery; therefore, MMCS was used to design three methods to construct the topology and plan a travel path with reduced cost.

_{n}is categorized into an energy consumption grade (CG). The number of nodes in each CG could be estimated by $E\left(N\right)=\left|N\right|\times \frac{1}{CG}$. Obviously, the first grade consists of death nodes with the highest energy consumption. However, the second grade must also be considered. Therefore, in the MMCS, $\left|CNs\right|=E\left(N\right)\times 2$ is defined to be the number of candidate charging nodes, indicating that MMCS selects $\left|CNs\right|$ nodes with lowest LT

_{n}as CNs.

**Topology construction:**The topology is constructed according to three aspects (distance, energy and lifetime) to establish three modules:

**Distance-based module:**The travel distance of a WCV is limited by its battery capacity. In MMCS, a distance-based topology is designed to plan the shortest travel path. The first node S is the ${\text{Node}}_{n\in CNs}$ with the lowest LT_{n}. Node S then establishes adjacent relations with three ${\text{Node}}_{n\in CNs}$ with the shortest distance to S. The next node is the ${\text{Node}}_{n\in CNs}$ with the shortest path to S. Repeat this process until all the CNs are complete.**Energy/Lifetime-based module:**The energy consumption rate of each ${\text{Node}}_{n\in CNs}$ is different; however, there are different degrees of criticality. Therefore, MMCS utilizes the remainder of energy/lifetime as a basis for establishing the topology. In terms of energy-based topology construction, each ${\text{Node}}_{n\in CNs}$ is first sorted in the ascending order, then the ${\text{Node}}_{n\in CNs}$ is sequentially chosen as Node S, which establishes adjacent relations with three ${\text{Node}}_{n\in CNs}$ with the lowest E_{n}. In lifetime-based construction, ${\text{Node}}_{n\in CNs}$ is selected because of its lifetime.

#### 3.2.2. The Stage of Charging Scheduling

_{m}in one round trip. We believe that the energy consumption due to repeated movements could be reduced if the WCV is able to rescue other CNs on the path to the nodes with the lowest lifetime. Therefore, the MMCS based on the Dijkstra algorithm proposed the best-effort and delay-based modules:

**Best-effort module:**Best effort is a concept used for attempting the rescue of ${\text{Node}}_{n\in CNs}$ which WCV can pass. The best-effort module algorithm is shown in Figure 5. The nodes in ${\text{Node}}_{n\in CNs}$ are first sorted in an ascending order; then, MMCS is used to define the source (SN) as the present location of WCV and its destination (DN) as the location of ${\text{Node}}_{n\in CNs}$ with lowest LT_{n}. Next, the Dijkstra algorithm is executed to determine the shortest path. If SN does not directly connect with the DN, check if B_{c}and B_{m}are sufficient to charge and move to the first relay ${\text{Node}}_{n\in CNs}$ between SN and DN, and then from first relay ${\text{Node}}_{n\in CNs}$ to DN. If energy is sufficient, the first relay ${\text{Node}}_{n\in CNs}$ is defined as the next node to which WCV will move to charge.**Delay-based module:**The concept of best effort only considers the relay station bringing the result of DN. However, the insert relay ${\text{Node}}_{n\in CNs}$ not only affect the DN but also other ${\text{Node}}_{n\in CNs}$ that are subsequent to SN. If a ${\text{Node}}_{n\in CNs}$ subsequent to SN is more critical than relay ${\text{Node}}_{n\in CNs}$, it may lead to node death. Therefore, in the MMCS the delay time is considered instead of the scheduling time, and the delay-based method is proposed. Figure 6 shows the process of delay time.

_{n}. The Dijkstra algorithm is then executed to determine the shortest path. Equation (7) is used to calculate the delay time DT

_{ik}of CNs that are scheduled by ascending values of LT

_{k}, which reduces the time spent on travelling to Node

_{k}. DT

_{ik}implies the time that can be delayed for reaching Node

_{k}. The cumulative total travel time CD

_{ik}is defined by Equation (8), and cumulative total energy demand of sensor nodes CED

_{ik}is shown in Equation (9):

_{c}and B

_{m}are sufficient to charge and move to first relay ${\text{Node}}_{n\in CNs}$ between SN and DN, and from first relay ${\text{Node}}_{n\in CNs}$ to DN. If the energy is sufficient, it is confirmed that no more death nodes are caused by the insert relay ${\text{Node}}_{n\in CNs}$ in the schedule. If there are no dead ${\text{Node}}_{n\in CNs}$, relay ${\text{Node}}_{n\in CNs}$ is defined as the next node that the WCV will move to. Next, the values of LT

_{n}are then updated and resorted after charging ${\text{Node}}_{n\in CNs}$.

_{i}(Node

_{i}→ Node

_{x}→ Node

_{x+}

_{1}→ Node

_{x+}

_{2}→ Node

_{y}→ Node

_{j}). Further, the dotted line represents the process for inserting Node

_{y}between Node

_{i}and Node

_{x}(Node

_{i}→ Node

_{y}→ Node

_{x}→ Node

_{x+}

_{1}→ Node

_{x+}

_{2}→ Node

_{j}). Changing the schedule would mean ${\text{Node}}_{n\in CNs}$ is divided into three cases. In Case 1, ${\text{Node}}_{n\in CNs}$ is scheduled before Node

_{x}. Owing to these nodes being charged, they are not affected by the relay node. In Case 2, ${\text{Node}}_{n\in CNs}$ is scheduled after Node

_{y}. The DT

_{ik}of these nodes are affected by the changing schedule. The change in schedule causes distance variation. However, Node

_{y}represents the relay node, and charging Node

_{y}on the way from Node

_{i}to Node

_{x}can reduce energy consumption. Therefore, when Node

_{y}becomes the relay node, it does not result in an extra death node. In Case 3, ${\text{Node}}_{n\in CNs}$ is scheduled between Node

_{x}and Node

_{y}. The DT

_{ik}of these nodes are affected by the changing schedule. The distance variation can be calculated using Equation (10). If any DT

_{ik}of nodes in Case 3 are shorter than the variation, Node

_{y}would cause a death node. As shown in Equation (11), Node

_{y}is not the most critical node; therefore, the maximum charging time is the minimum delayable time of ${\text{Node}}_{n\in CNs}$ in Case 3.

#### 3.2.3. The Stage of Charging Strategy

_{n}of each node. The MMCS considers E

_{n}and LT

_{n}to develop two charging modules: average energy and average lifetime, respectively.

**Average energy module:**As shown in Equation (12), CNs selected in the charging topology stage are nodes that are more urgent. To enhance CNs to a high-energy level, MMCS uses double CNs (dCNs) as threshold for improving energy. Next, the E_{n}of urgent nodes is enhanced by enhancing energy of nodes with the lowest E_{n}to next higher energy level.$$E{D}_{n}=\frac{{\displaystyle {\sum}_{n\in dCNs}{E}_{n}}}{\left|dCNs\right|}-{E}_{i}$$**Average lifetime module:**As shown in Equation (13), to enhance CNs to a high-energy level, MMCS uses dCNs as threshold for improving energy. The LT_{n}of critical nodes is enhanced by enhancing the energy of nodes with the lowest LT_{n}to next higher lifetime level.$$L{T}_{n}=\left(\frac{{\displaystyle {\sum}_{n\in dCNs}L{T}_{n}}}{\left|dCNs\right|}-L{T}_{n}\right)\times {C}_{R}$$

#### 3.3. An Example of Multi-Module Charging Strategy

## 4. Experimental Results and Analysis

#### 4.1. The Combination Experiment of Multi-Module Charging Strategy

#### 4.2. Result of Return on Investment Analysis of Battery

_{c}and B

_{m}) need to be replaced. Therefore, additional cost is incurred for replacing the group of batteries (B

_{c}and B

_{m}). As shown in Equation (14), the return on investment (ROI) represents the extension in the lifetime achieved using a group of batteries. The results shown in Figure 10 are classified according to the charging strategies. Figure 10a presents the average energy charging strategy, whereas Figure 10b presents the average lifetime charging strategy. The x-axis and y-axis presents the charging topology and the extension in lifetime achieved by using the group of batteries, respectively. Overall, the average lifetime charging strategy provides higher ROI and gives credit to the different ED between nodes.

#### 4.3. Efficiency of Battery

_{m}and B

_{c}. In Figure 11, the x-axis presents the combination of charging topology and charging strategy, the y-axis presents the type of battery, and the z-axis presents the usage efficiency of the battery. The usage efficiency of the battery is calculated by Equation (15). Indeed, the most efficient battery is B

_{c}, which is used in the average lifetime charging strategy. However, there is a great disparity between B

_{m}and B

_{c}in the average lifetime charging strategy. In contrast, it is more balanced between B

_{m}and B

_{c}in the average energy charging strategy. The unbalanced usage efficiency is caused by the oversized battery. It implies that a lot of energy is wasted at B

_{m}and B

_{c}while replacing the group of batteries. This analysis of the results is used to determine the capacity of the battery.

#### 4.4. Extended Lifetime of Wireless Rechargeable Sensor Networks

#### 4.5. Distribution of the Rescued Sensor Nodes

#### 4.6. Comprehensive Comparison

**’s efficiency.**

_{m}#### 4.7. Effect of Variation of the Amount of Charge

#### 4.8. The Analysis of Density

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Wireless sensor network with a WCV using cell centers to find stay points on the traveling path.

**Figure 9.**The combination experiment of MMCS with different charging scheduling module (

**a**) MMCS with the best effort-charging module; (

**b**) MMCS with delay-based charging module; and (

**c**) MMCS with NJNP.

Reference | Focus on | Energy Constraints of WCV ^{1} | Traveling Path (Static/Dynamic) |
---|---|---|---|

Guo et al. (2013) [8] | Traveling path of WCV | No | Static |

Fu et al. (2013) [9] | Traveling path of WCV | No | Static |

Hu et al. (2013) [10] | On-demand mobile charging problem (scheduling) | No | Dynamic |

Xie et al. (2012–2015) [4,5,6,7] | Traveling path of WCV | No | Static |

He et al. (2013–2015) [13,14] | On-demand mobile charging problem (scheduling) | No | Dynamic |

^{1}: The energy constraints of WCV is considered in this work.

Type | Electromagnetic Induction | Coupling Magnetic Resonance | Micro-Wave Conversion | Laser Light Sensor |
---|---|---|---|---|

Theory | Faraday‘s law | Same resonance frequency energy transfer | Electromagnetic wave transfer | Laser and the Solar panels |

Power transmission | W~hundreds of KW | W~hundreds of KW | >100 mW | hundreds of KW |

Transmission distance | <10 cm | 5 m | >10 m | >100 m |

Conversion efficiency | 70% | 50% | 1.6% | 25% |

Advantage | High conversion efficiency | Multiple charging | Radio wave transmission and automatic charging anywhere | Technology matures over long distances |

Parameter | The Definition of Parameter |
---|---|

BS | Base station |

N | Set of all sensor nodes |

CNs | Candidate nodes are the set of nodes selected for charging, $CNs\in N$ |

E_{n} | Energy of sensor node n. $n\in \text{integer}$ |

C_{n} | Energy consumption for sensor node n |

LT_{n} | Rest of the lifetime of sensor node n |

ED_{n} | Energy demand of sensor node n |

B_{m} | Battery for WCV moving |

B_{c} | Battery for WCV charging sensor nodes |

V | Travelling speed of WCV |

C_{M} | Energy consumption of WCV |

R | Charging rate of the sensor nodes |

D_{i,j} | Path distance of Node_{i} to Node_{j} |

T_{t} | Total travelling time of WCV |

CG | Consumption grades of sensor nodes |

CD_{ik} | Cumulative total travel time of WCV from Node_{i} to Node_{k} |

CED_{ik} | Cumulative total time of charging the noden from Node_{i} to Node_{k} |

DT_{ik} | Delay time of Node_{k} |

Parameters | The Value of Parameters | Unit |
---|---|---|

Number of sensor nodes | 5 | - |

Energy consumption for sensor nodes. | 10–20 | J/min |

Battery capacity of the sensor nodes | 15,000 | J |

Charging rate of the sensor nodes. | 20 | J/min |

Parameters | The Value of Parameters | Unit |
---|---|---|

Map scale | 100 × 100 | m^{2} |

Number of sensor nodes | 100 | - |

Energy consumption for sensor nodes | 0.2–1 | J/min |

Battery capacity of the sensor nodes | 15,000 | J |

Charging rate of the sensor nodes. | 6 | J/min |

Energy consumption for WCV | 80 | J/min |

Moving speed of WCV | 1 | m/s |

Battery capacity of the WCV’s battery for moving | 45,000 | J |

Battery capacity of the WCV’s battery for charging | 45,000 | J |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Chang, H.-Y.; Lin, J.-C.; Wu, Y.-F.; Huang, S.-C.
MMCS: Multi-Module Charging Strategy for Increasing the Lifetime of Wireless Rechargeable Sensor Networks. *Energies* **2016**, *9*, 664.
https://doi.org/10.3390/en9090664

**AMA Style**

Chang H-Y, Lin J-C, Wu Y-F, Huang S-C.
MMCS: Multi-Module Charging Strategy for Increasing the Lifetime of Wireless Rechargeable Sensor Networks. *Energies*. 2016; 9(9):664.
https://doi.org/10.3390/en9090664

**Chicago/Turabian Style**

Chang, Hong-Yi, Jia-Chi Lin, Yu-Fong Wu, and Shih-Chang Huang.
2016. "MMCS: Multi-Module Charging Strategy for Increasing the Lifetime of Wireless Rechargeable Sensor Networks" *Energies* 9, no. 9: 664.
https://doi.org/10.3390/en9090664