## 7 Power Consumption Models  
### Sensor Node Power Consumption Model  
The life span of sensor nodes is the time that lapsed from the first transmission until the sensor nodes lose their sensing capability. The life span of a WSN relies on the current consumed by each node in the network. The power consumption of sensor nodes depends on the number of components. In this study, the sensor nodes include air temperature and humidity sensors embedded into the DHT11 sensor, a soil moisture sensor, the Atmega 328p microcontroller as a standalone system for reducing power consumption, and the XBee S2C wireless protocol. Among the sensor nodes, XBee S2C is considered the main power consumer [51]. When the consumption values of these components are added, the total current consumption of the sensor node can be expressed as Equation (2):  
\[I_{SN}=\ I_{Soil}+\ I_{DHT}+I_{Atmega}+I_{XBee\ S2C}, \tag{2}\]  
where \(I_{Soil}\) is the current consumed by the soil moisture sensor, \(I_{DHT}\) is the current consumed by the air temperature and humidity sensors, \(I_{XBee\ S2C}\) is the current consumption of the XBee S2C wireless technology, and \(I_{Atmega}\) is the current consumed by the Atmega 328p microcontroller. The measurements of each sensor node component were achieved by using a storage oscilloscope (MCP Lab Electronics/DQ7042C) and a digital multimeter (MCP Lab Electronics/MT8045) to evaluate the current consumption of the sensor node. Therefore, the current drawn by the sensor node is presented for two cases. The first case, which is a conventional operation (i.e., without a sleep/wake scheme or any power reduction technique), is formulated in Equation (2). The second case, which involves a sleep/wake scheme, can be expressed in terms of average current consumption, as presented in Equations (3)-(7):  
\[I_{Soil\_age}=\text{DC}\ \times\ I_{Soil\_active}+(1-\text{DC})\ \times\ I_{Soil\_sleep}, \tag{3}\]  
\[I_{DHT\_age}=\text{DC}\ \times\ I_{DHT\_active}+(1-\text{DC})\ \times\ I_{DHT\_sleep}, \tag{4}\]  
\[I_{ATmega\_agg}=\text{DC}\ \times\ I_{ATmega\_active}+(1-\text{DC})\ \times\ I_{ATmega\_sleep}, \tag{5}\]  
\[I_{XBee\ S2C\_avg}=\text{DC}\ \times\ I_{XBee\ S2C\_active}+(1-\text{DC})\ \times\ I_{XBee\ S2C\_sleep}, \tag{6}\]  
\[I_{SN\_agg}=I_{Soil\_agg}+I_{DHT\_agg}\ +I_{ATmega\_agg}\ +I_{XBee\ S2C\_avg}\, \tag{7}\]  
Figure 6: Timing diagram of the sleep/wake scheme of the sensor and router nodes. where \(I_{avg}\) is the average current consumption of each sensor node component. DC is the proposed duty cycle of the sensor node, which provides an effective method for achieving energy efficiency and can be computed using the ratio of the active time to the total time (\(t_{active}\)/\(T_{total}\)). DC is configured to 2.222 \(\times\)\(10^{-3}\) to reduce the power consumption of the sensor node, where the active time is 2 s, the sleep time is 898 s, and the total time is 15 min (900 s). \(I_{active}\) and \(I_{sleep}\) are the active and sleep current consumption of each component of the sensor node. The overall power consumption of the sensor nodes (\(I_{SN\_total}\)) without t sleep/wake scheme can be expressed as Equation (8);  
\[I_{SN\_total}=\sum_{1}^{n}I_{SN_{n}}\, \tag{8}\]  
where \(I_{SN_{n}}\) is the current consumption of each sensor node. In addition, \(n\) is the number of sensor nodes, and \(n=16\) in the current work. Given that DC is equal in each sensor node, the total current consumption (\(I_{SN\_avg\_total}\)) of the sensor nodes can be calculated based on Equation (9):  
\[I_{SN\_avg\_total}=\sum_{1}^{n}I_{SN_{n}\_avg}\, \tag{9}\]  
where \(I_{SN_{n}\_avg}\) is the average current consumption of each sensor node that is modeled in Equation (7). The average power consumption (\(P_{avg\_SN}\)) of a sensor node can be calculated by multiplying the average current consumption with the supply voltage of the sensor node (i.e., 2 \(\times\) 3.7 V = 7.4 V), as shown in Equation (10).