# Leveraging Energy Harvesting and Wake-Up Receivers for Long-Term Wireless Sensor Networks
## 3 Energy Management for an Energy-Harvesting Sensor Node
### EBC Design
As most applications do not perform well under strong variations of the allocated energy budget, choosing \(\Delta e_{B}\) requires a compromise between the reactiveness of the EBC and the variability of the allocated energy budget. Indeed, choosing a high value of \(\Delta e_{B}\) leads to high reactiveness of the EM, but at the cost of strong variations of the energy budget, which may not be suitable for many applications. On the other hand, choosing low values of \(\Delta e_{B}\) leads to the low reactiveness of the EM and smooth energy budget variations. Therefore, the choice of \(\Delta e_{B}\) depends on both the energy source and application requirements. Four scenarios can be considered from Figure 2 and are detailed thereafter. Risk of saturation (R7-8-9):  
A risk of saturation occurs when \(e_{R}>E_{ENI}^{up}\). To avoid the waste of energy by the overflow of the energy storage device, the EBC increases the energy budget until the residual energy decreases to bring it to a value belonging to the ENI. Energy neutral interval (R4-5-6):  
If the amount of residual energy belongs to the ENI, the EBC goal is to keep the node in the ENO-MAX state. The ENO-MAX state is achieved when the residual energy is kept constant with regard to time, and the EBC thus corrects the energy budget regarding the sign of \(\Delta e_{R}\) to keep the node in the ENO-MAX state. Figure 2: Energy storage levels and rule base used to compute \(\delta e_{B}\). ENI, Energy Neutral Interval. (**a**) Energy storage device levels. (**b**) Rule base used to compute \(\delta e_{B}\). Charging state (R3):  
The node is considered to be in the charging state when \(e_{R}<E_{ENI}^{down}\) and \(\Delta e_{R}\) is positive. The node is thus re-filling its energy stock. In these conditions, the goal of the EBC is to keep the residual energy increasing for the amount of stored energy to be greater than or equal to \(E_{S}\), i.e., for the residual energy to reach the ENI in a reasonable time, while allocating a high enough energy budget to ensure a good quality of service. A trade-off must be made between the charging time and the quality of service. Indeed, at one extreme, a conservative policy is to allocate the minimal energy budget while the energy storage device is not fully charged, leading to a quick refill of the storage device at the cost of a low quality of service during the charging phase. On the other hand, allocating almost all the harvested energy will lead to a slow charging rate, but to a good quality of service, regarding the currently-available environmental energy, during the charging phase. As the choice of an appropriate strategy is dependent on the application, a tunable strategy is proposed. The energy budget correction \(\delta e_{B}\) is set to a value proportional to the residual energy variation \(\Delta e_{R}\), and the proportionality factor is a function of \(e_{R}\) denoted by \(\mu_{C}\left(e_{R}\right)\)[30]:  
\[\mu_{C}\left(e_{R}\right)=M_{C}\left(1-\left(1-\frac{e_{R}-E_{R}^{fail}}{E_{ ENI}^{down}-E_{R}^{fail}}\right)^{K_{C}}\right). \tag{3}\]  
where \(M_{C}\) and \(K_{C}\) are positive parameters allowing the tuning of the charging strategy. \(\mu_{C}\) increases with \(e_{R}\), as the more energy is stored, the less conservative we need to be. While \(M_{C}\) sets the maximum value of the proportionality factor, \(K_{C}\) sets the growth rate of \(\mu_{C}\). If \(K_{C}=1\), \(\delta e_{B}\) increases linearly with \(e_{R}\). For values of \(K_{C}\) lower than one, the growth rate increases when the residual energy increases, while for values of \(K_{C}\) higher than one, the growth rate decreases when \(e_{R}\) increases. Discharging state (R1-2):  
The node is considered to be in the discharging state when \(e_{R}<E_{ENI}^{down}\) and \(\Delta e_{R}\) is negative. The node is thus using its energy stock. In this scenario, a trade-off must be made between the allocated energy budget and the lifetime of the node, i.e., the time it can last before running into a power outage.