## 3 Methodology
### Energy Model  
In the proposed scheme, a CH is selected based on energy availability, considering both data collection and energy received through WPT. The network operates in rounds, defined by the time it takes for the sink node to traverse the entire network. Data collection is dynamically adjusted by monitoring both available and consumed energy during each round. This subsection details the energy model used to calculate a node's available energy [13; 14; 25]. Solar energy is harnessed and utilized by the sensor nodes in this method. However, solar energy is subject to fluctuations and cannot be collected at night, necessitating a smart energy usage plan. To ensure the efficient and consistent utilization of solar energy over time, this study employs an energy allocation technique that evenly distributes available energy for each round among the sensor nodes if the allocated power to a node is \(P_{al}\) for a single round and the available power is \(P_{av}\), which equals to \(P_{al}\). Furthermore, the sink node has the capability to supply extra energy to the helper nodes. If the total power the sink node can provide to other nodes is \(P_{charge}\), and this power is distributed equally among all helper nodes (\(m\)), then each helper node receives the power of \(P_{charge}/m\). This additional power is added to the node's power \(P_{al}\). In simple terms, the power available to a node for one round, \(P_{av}\), is determined as follows:  
\[P_{av}=\left\{P_{al}+\frac{\eta P_{charge}}{m}\begin{array}{l}\text{for helper head node}\\ P_{al} \begin{array}{l}\text{otherwise}\end{array} \right. \tag{1}\]where \(m\) is the number of helper nodes and \(\eta\) represents the efficiency of WPT. The power used by the sensor node can be categorized into two parts, power spent on the transmission and reception of data, and power used for essential operational tasks. Consequently, the total power consumption for the node during one round is as follows:  
\[P_{Con}=P_{tx}+P_{rx}+P_{idle} \tag{2}\]  
where \(P_{tx}\) is the power needed for data transmission, \(P_{rx}\) is the power needed for data reception, and \(P_{idle}\) is the power used for basic operations. Among these, \(P_{rx}\) and \(P_{idle}\) remain constant in each round, while \(P_{tx}\) can fluctuate based on the quantity of data being transmitted and the transmission distance. This relationship is expressed as follows:  
\[P_{tx}=sP_{1}d^{\beta} \tag{3}\]  
where \(\beta\) represents the path loss exponent, \(P_{1}\) is the energy needed to send 1 bit of data over a 1 m distance, \(d\) stands for the node transmission distance, and \(s\) denotes the size of the data being transmitted. Since the node's energy consumption is directly linked to \(s\), as mentioned in Equation (3), \(s\) should be adapted based on \(P_{av}\) to optimize energy efficiency, all while ensuring that the sensor node's power reserves are not depleted. The UAV has a specific route it follows, as shown in Figure 2, visiting each helper node to gather data and provide energy. This process entails power consumption for its movement and data collection. Furthermore, when the UAV visits each helper node, it uses a short-range power transfer method, incurring power costs for takeoff and landing, as well as additional power consumption during hover time, primarily due to the time spent on recharging. If there are \(m\) helper nodes, this sequence of data collection, power delivery during takeoff and landing, and recharging occurs \(m\) times. Accordingly, the UAV energy model can be written as follows:  
\[P_{UAV}=P_{travel}+m(P_{TL}+P_{d\_coll})+P_{charge}+P_{idle} \tag{4}\]  
where \(P_{travel}\) is the consumed energy during UAV travel, \(P_{TL}\) represents the consumed energy during takeoff and landing processes, \(P_{d\_coll}\) is the consumed energy during data gathering process, and \(P_{charge}\) is the provide energy to the helper nodes. As the sink node follows a predetermined path in each round, the power consumed for its movement remains the same.