# Predictive Power Management for Wind Powered Wireless Sensor Node
## 3 System Model
### Power Consumption Model
#### 3.3.2 Energy Consumption of Buck-Boost Converter  
The conduction consumption of this PWM converter is deduced as:  
\[P_{cond\_BuckBoost}=R_{N2}I_{P}^{2}(\frac{t_{1}^{\prime}}{3T_{B-B}})+R_{L2}I_{ P}^{2}(\frac{t_{1}^{\prime}+t_{2}^{\prime}}{3T_{B-B}})+\frac{nV_{t}L_{2}I_{P}^{2}}{2T _{B-B}V_{Out}}[\ln(\frac{I_{P}}{I_{S}})-\frac{1}{2}] \tag{13}\]  
where \(R_{N2}\) is the drain-source on-state resistance of the MOSFET NMOS2, \(I_{P}\) is the peak value of current flowing through inductor \(L2\), \(R_{L2}\) is the parasitic equivalent series resistance of \(L2\), \(t_{1}^{\prime}\) is the time of the inductor current ramps up from zero to peak and \(t_{2}^{\prime}\) is the time of the inductor current ramps down from peak to zero, \(T_{B-B}\) is the converter's working cycle, \(n\) is the ideality factor of the diode \(D2\), \(V_{t}\) is the thermal voltage of \(D2\), and \(I_{S}\) is the reverse bias saturation current of \(D2\).  
As well, the gate-switch power dissipation of Buck-Boost converter is:  
\[P_{Switch2}=V_{SC}\cdot f_{NMOS2}\cdot Q_{SW2} \tag{14}\]  
\(Q_{SW2}\) is the gate charge of NMOS2, \(V_{SC}\) is the input voltage of Buck-Boost converter.  
Almost all manufacturing parameters (i.e., \(R_{N1}\), \(R_{N2}\), \(R_{L1}\), \(R_{L2}\), \(R_{SC}\),..., etc.) can be obtained from the datasheets of every detailed component. Moreover, as can be seen above, power consumption in DC-DC converters is affected by miscellaneous parameters. These are composed of both the manufacturing parameters, which cannot be modified at working time, and load-dependent parameters, such as the output voltage and current of the DC-DC converters, which can be modified by advanced power management techniques to matching the run-time workload. As a matter of convenience, charging/discharging efficiency of the supercapacitor is not considered here. So referring to the method designed in [31], a simplified and synthetic power consumption model can be described as follow:  
\[\begin{array}{ll}P_{D\_System}&=P_{cond\_BuckBoost}+P_{cond\_Boost}+P_{ switch1}+P_{switch2}\\ &=[(\frac{C_{1}}{W_{Bost}}+C_{2})I_{O1}^{2}+C_{3}W_{Boost}+C_{4}]+[(\frac{C_{ 5}}{W_{Bost-Bost}}+C_{6})I_{O2}^{2}+C_{7}W_{Buck-Boost}+C_{8}]\end{array} \tag{15}\]  
where \(I_{O1}\), \(I_{O2}\) are the output currents of each converter, \(W_{Boost}\), \(W_{Buck-Boost}\) are the DC-DC converters' configuration parameters which control a tradeoff between load independent power consumption and load dependent power consumption (e.g., the time interval \(t_{1}\) and the gate width of NMOS1, NMOS2), and \(C_{1}\),..., \(C_{8}\) are constants represent for all the rest manufacture-related parameters. Since TPC module causes a drastic change of workload from one transmission mode to another, then parameters \(W_{Boost}\) and \(W_{Buck-Boost}\) would vary with the specific applications of TPC-enabled EH-WSN system, thus the energy-conversion efficiency changes accordingly. Therefore, an advanced power management incorporates both the energy harvesting and TPC mechanism, which must be researched and designed.