# Piezoelectric Energy Harvesting Prediction and Efficient Management for Industrial Wireless Sensor
## 4 Efficient Management of Harvested Energy
### Management of the Harvested Energy  
Equation (12) offers three possibilities of slaving the performance of the node to the energy harvested. These are the size \(b\) of the data in the payload and the IWS's transmission range. The third possibility is the transmission frequency in the case of a duty cycle adaptation strategy. Assuming that all the energy harvested is dedicated to the operation of the IWS (i.e., we consider an ideal case of a lossless harvesting circuit), the energy management module will then work as shown in Figure 15 below. Figure 14: Node energy dissipation versus transmission range for b = 512 bits. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value and Ref** \\ \hline Path loss exponent & \(n\) & 3 or 4 [61] \\ LoRa transmitter/receiver frequency & \(f_{\text{LoRa}}\) & 2.4 GHz [60] \\ LoRa SX1280 transceiver sensitivity & \(S_{R}\) & \(-99\) dBm [60] \\ Spreading Factor & SF & \(5-12\)[60] \\ Bandwidth & \(BW\) & \([203;406;812;1625]\) kHz [60] \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameter values for IWS energy cost estimation. As shown in this figure, the objective is to transmit the maximum amount of data at the end of the cycle for a known measurement cycle time and distance. This first scenario makes it possible to reduce the length of the queue of data stored in the sensor [62]. In the second case, it is considered that the transmission of a data size is fixed in advance at the greatest possible distance; this strategy would be suitable for fairly dense mesh networks and minimize transmission delays due to multi-hop communications [63]. The duty cycle strategy is the third case dealt with; it applies when the data size and transmission range are previously defined. To simplify writing, for maximizing the data size, the used protocol will be abbreviated as MDSP. It will be a question for the PMM to use all of the harvested energy (estimated by the PHEV) during the current cycle to transmit data at the end of the cycle. Regarding the harvested energy stored during the measurement cycle, it is designated by \(E_{H}\) and is defined as follows:  
\[E_{H}\ =\ \int\limits_{t}^{t+T}p_{\text{PHEV}}(\tau)\cdot d\tau \tag{13}\]  
where \(T\) is the duration of a cycle, \(p_{\text{PHEV}}\) is the harvestable power during the current measurement cycle; the PHEV predicts it, and \(t\) is the instant marking the start of the current cycle. The problem of optimizing energy management by the PMM is then the problem P1 formulated as follows:  
\[\min_{b,d}(E_{H}\ -\ E_{WS}(b,d))\ \text{s.t. }\left\{ \begin{array}{l}E_{H_{i}} \ -\ E_{WS}\ \geq\ 0\\ b\ \geq\ 0\ ;d\ \geq\ 0\end{array} \right. \tag{14}\]  
This problem boils down to minimizing the residual energy of the IWS at the end of each cycle while preventing it from going through a value less than 0. The node's actual residual energy at the end of each measurement cycle, considering its accumulated energy, is defined as follow:  
\[E_{\text{residual}}\ =\ E_{H}\ -\ E_{WS}(b,d)\ \ +\ \int\limits_{t}^{t+T}(p_{ \text{real}}\ -\ p_{\text{PHEV}})(\tau)\cdot d\tau\]  
where \(p_{\text{real}}\) is the power actually accumulated during the measurement cycle; the other parameters of the equation are defined as previously. For data size analysis, it is assumed that the network is deployed at a fixed distance, \(d\) from the base station. The measurement cycle is one minute, corresponding to the initial sampling of the vibration data. Figure 16 shows the operational flowchart of the PMM. Figure 15: Proposed methods for efficient energy management of the harvested energy. In Figure 16, \(E_{min}\) is the minimum energy required to transmit a bit. At the start of the cycle, the range of data variations is defined, and the ranged and the duration \(\Delta T\) of the cycle; \(nT\) represents the number of samples taken during the month. The operation of PMM comes down to transmitting as much data as possible at the end of the cycle under the basis of the energy harvested during the cycle.