Recently, we have witnessed the rapid development of techniques on upgrading energy efficiency for wireless sensor networks (WSN). With the improvement of the detection range and the detection intensity, the lifetime of wireless sensor networks (WSN) is still limited by sensor node batteries (BA). Due to the need for wireless sensor network energy optimization, the power supply side has been putting forward higher requirements, and the traditional wireless sensor network with energy supplement has difficulty in meeting this development trend. The game and potential game concepts were introduced to take economics into account. Taking the wireless sensor network (WSN) with photovoltaic (PV) array charging and mobile-charging car (MCC) as an example, a running optimization model based on potential game is proposed, and the existence of Nash equilibrium has been proven. The iterative solution is completed by communication between the players, and the energy utilization rate is effectively improved. This paper verifies that potential game theory can be used to improve the feasibility and efficiency of wireless sensor network energy optimization.

The wireless sensor network is a new emerging network technology composed of sensor nodes with sensing, computing, and communication in a self-organizing manner. The information of the object is perceived by the wireless sensor network through the collection network. It uses multihop as a wireless communication method to transmit the collected and processed information to the base station and finally to the end user. In the power industry, with the in-depth construction of the smart grid, the monitoring of the operational status of the equipment has been put forward in the power generation, transmission, substation, power distribution, power consumption, and other aspects of the power system. The requirement of monitoring appeared in power plants, which is based on wireless sensor networks. The optimization of energy strategy has become the primary consideration for sensor network design in wireless sensor networks, due to insufficient energy supplementation or unpredictable energy supplementation. It is effective to use wireless sensor network technology with multiple charging sources to solve the life-limited problem. In a rechargeable power monitoring sensor network, nodes can be completely free of energy constraints if the nodes can acquire enough energy or the energy of the nodes can be replenished periodically and continuously. However, due to the weather, the supplement of node energy is unpredictable and unreliable, in many solar and wind power applications.

Therefore, this paper believes that the operation of the wireless sensor network needs to be equipped with MCCs in the case of PV supplementation.

Operational optimization is the core approach to efficient energy management. The optimization problem of wireless sensor network energy is a multiobjective collaborative optimization problem, including economic, technical, and environmental factors.

Considering energy saving, the routing protocols are used to reduce the overall energy consumption of wireless sensor network node [

High-energy WSN and sustainable development are the points of consideration in this article. Game theory in wireless sensor networks is mainly used for network coverage [

A revenue model is established for the energy of the heterogeneous wireless sensor network from the perspective of economy

Complex individual constraints are transformed into the strategy space of the players. From the perspective of the game, the potential game model is unified by the individual

The strategy is solved by a distributed method, which fully reflects the individual’s intelligence

The rest of this article is organized as follows: Section II describes the structure of the wireless sensor network and the basic concept of the potential game and determines a uniform revenue function. Section III analyzes the algorithm of wireless sensor network based on potential game and proposes an optimization method. Section IV shows the simulation results. Section V shows the conclusion.

Relying on the laboratory sensor network system, a complete wireless sensor network is established by adding photovoltaic panels, lead-acid BA and MCC. The structure is shown in Figure

Structure of wireless sensor network.

Game theory is a research of mathematical models of strategy interaction between rational decision-makers. It is used in all area of social science, as well as in logic and computer science. At the beginning, it addressed zero-sum games, in which one player’s gains result in losses for the other players. Today, game theory applies to a wide range of behavioral relations and is now an umbrella term for the science of logical decision making in humans, animals, and computers [

In game theory, the Nash equilibrium, named after the late mathematician John Nash, is a proposed solution of a noncooperative game involving two or more players. Each player knows the equilibrium strategies of the other players, and the other player has nothing to gain by changing only their own strategy.

The potential game is such a type of game. As a special form of noncooperative game, it has limited improvement characteristics, which was first proposed by Monderer and Shapely in 1996 [

The potential game [

For the game _{i}^{th} player, ^{-i}^{th} player, the strategy of all players can be expressed as

The Nash equilibrium must exist, if the game model based on the potential game satisfies the three attributes of the potential game. Therefore, we only need to prove that the model is a potential game, and the convergence of the model does not need to be proven again.

This paper will map the wireless sensor network to the three elements of the game. The three elements are the players, the revenue function, and the strategy space. The specific instructions are as follows:

According to Attributes 2 and 3 of the potential game, it is necessary to linearly divide the strategy space (the discrete interval is determined according to the accuracy requirement, and currently, 1 kW/step is recognized) to complete the discretization, making it a limited strategy space and ensuring that the game is a finite game. In addition, because they are heterogeneous, they cannot reciprocate the revenue function in a uniform form. It is necessary to separate the resumed revenue function for each individual and establish a strategy space.

^{2}),

This paper ensures that the battery has sufficient real-time scheduling margin and emergency power support without PV replenishment at night, where

The allowable charge and discharge power of the battery are constantly changing with the state of charge, expressed follows:

The heterogeneity of energy individuals in wireless sensor networks makes no uniform representation of both the income function and the strategy space. Determining the revenue function and finding the potential function is the key to issue potential game modeling. In order to maximize the benefits of each power source in the game process while optimizing the efficiency of the system, consider constructing the potential function as the sum of the benefits of all players, expressed follows:

The wireless sensor network game model established by equation (

From equation (

This paper studies the distributed optimization of wireless sensor network energy supply and chooses the optimization from the utility function of the game. It is a way to match the potential game with the distributed. In the framework of the potential game, it can not only maximize the benefits of players but also optimize the system. This paper’s potential game optimization is mainly divided into the following parts:

determination of strategy space

policy evaluation and decision rules

policy update

power balance

The constraints are different for each player. In order to adapt to the requirements of the game, the constraints must be transformed into the strategy space of the players, simplifying the game model.

The corresponding maximum allowable output power is determined to be calculated by the photovoltaic array according to the power prediction model and environmental parameters. The photovoltaic strategy is the discrete data points within the maximum allowable output power range.

The battery should update the state of charge, and consider the safe operation to determine the charge and discharge power allowed in the next period, and discretize it as the strategy space of the battery player.

The MCC should be considered to prevent overcharging of the battery within the basic power output range, and since the moving distance is negligible compared to the amount of charging, it will be ignored in later simulation.

It is assumed that each player is individually rational; that is, the purpose of each player in the game is to maximize their own benefits. Therefore, it is the most direct way to use the revenue function of the player as the objective function of the strategy evaluation. The decision rule is adopted; that is, the strategy of maximizing the income function is selected as the next strategy. In the discrete strategy space, the players determine the optimal strategy through exhaustive.

After the players determine the optimal strategy, the policy updates are performed in a determined priority order. The PV array player has low operation and maintenance cost, and the photovoltaic energy is renewable energy, so it is updated first. The battery player plays the role of power balance and peak clipping in the sensor energy network, so the policy update sequence is set to the last. The revenue function of MCC is worse than PV, and environmental protection is not as good as PV; therefore, the order of policy updates is PV arrays, MCCs, and batteries. Players are assigned priorities based on the update order, and players can communicate with each other to ensure sequential updates.

Unlike other models, this potential game model must satisfy real-time power-balance constraints. Therefore, the penalty function is used to consider the power-balance constraint, and the power deficiency is set to characterize the degree of constraint satisfaction. The game model after balancing power is still considered a full-potential game model, and the final penalty function term will approach 0, and the resulting Nash equilibrium satisfies the power-balance.

The distributed structure of the players is shown in Figure

The flow chart of game iteration.

Distributed structure of players.

In this algorithm, each player can communicate with each other to understand the decision-making situation of other players, and they have certain autonomy to maximize their own revenue. In the end, under the framework of the potential game, the common goal of optimizing system benefits can be realized.

A simulation was conducted for a wireless sensor network consisting of three groups of PVs, three MCCs, three BA, and three sensor nodes (for the convenience of the example simulation, this paper concludes that the moving time of MCC can be neglected, regardless of charging loss, and the energy of each PV arrays and BA can circulate among the three sensor nodes.) The coefficients of maintenance cost of different equipment are shown in Table

Coefficient of maintenance cost of different equipment.

Equipment type | Maintenance cost ($/kW) |
---|---|

Photovoltaic array | 0.001396 |

Battery pack | 0.026641 |

Mobile-charging car | 0.001998 |

Date of the forecast 48 h.

Photovoltaic array parameters.

Photovoltaic array | Rated power |
---|---|

No. 1 | 2.75 W |

No. 2 | 2.80 W |

No. 3 | 2.85 W |

Total | 8.4 W |

Battery parameters.

Parameters | Numerical value |
---|---|

Total capacity (kW·h) | 0.5 |

Charge and discharge efficiency (%) | 85% |

Initial storage capacity | 0.25 |

SOC_{min} |
0.2 |

Mobile-charging car parameters.

Parameters | Numerical value |
---|---|

Total capacity (kW·h) | 10 |

Movement speed (m/s) | 1.8 |

Power consumption (W) | 25 |

Figure

PV and load output power forecasting.

Through experimental simulation, the potential game optimization results of PVs, MCCs, and BA are shown in Figures

Comparison of optimal power generation and maximal output power of PV.

Battery charge state and 48 h charge and discharge power (the BA are charging while

Battery charge state and 48 h charge and discharge power (without MCT).

Battery charge state and 48 h charge and discharge power (without algorithm).

Output power of sleep strategy and predicted load (maximize energy usage with greedy selection strategies——based on sleep mode switching).

Battery charge state and 48 h charge and discharge power (maximize energy usage with greedy selection strategies——based on sleep mode switching).

From Figures

Figure

Figure

The game result of the MCC player is shown in the spikes of Figure

Figure

Figure

Figures

This paper establishes revenue models for heterogeneous sensor network energy modules and models them according to their respective characteristics from an economic perspective. The photovoltaic, MCC, and battery are mapped into players. The potential function is constructed by the player’s income function, and the potential game model is proven

This paper establishes a unified form of strategy space for the players by transforming the constraints into strategy space

The potential game model is optimized by a distributed method, and the example is verified. The experimental results show that the players composed of PV, MCC, and BA have sufficient autonomy and independent decision-making ability. At the same time, the priority of PV promotes the highest utilization rate of renewable energy. The fast response feature of MCC ensures reliable power supply to the WSN; BA can promote the preservation of excess light energy and maintain the power balance during the game. The experiment proves that the distributed optimization method based on potential game can better protect the battery from overcharging and nondischarging and consume as much renewable energy as possible. The feasibility and effectiveness of the method presented in this paper has been proven

The specific parameters of photovoltaic power generation are based on the test results of electrical engineering laboratory of ZheJiang University in China. The economic parameters of batteries and mobile-charging car used to support the findings of this study are included within the article (Tables

The authors declare that there is no conflict of interest regarding the publication of this paper.

The author would like to thank the support of the Hongqiao Deng in School of Electrical Engineering, Zhejiang University, for photovoltaic panel experimental data and Linxun Liang for the mobile-charging trolley experimental data. This research was funded by the National Natural Science Foundation of China (61202369), Shanghai Technology Innovation Project (17020500900), and “Shuguang Program” sponsored by Shanghai Education Development Foundation and Shanghai Municipal Education Commission (17SG51).