# Design and Optimization of Piezoelectric-Powered Portable UV-LED Water Disinfection System
## 3 Modeling of the System
### Piezoelectric Energy Harvesting System  
Vibrations are quite typical in energy harvesting. The piezoelectric energy harvester is naturally capable of transforming mechanical energy, such as vibrations, into electrical energy [21, 22]. Various piezoelectric energy harvesters have been developed [23, 24, 25]. Piezoelectric energy harvesters are quite appropriate for portability, and thus for environmentally friendly (eco-friendly) applications. Therefore, the proposed system uses a piezoelectric energy harvester. It is simply composed of piezoelectric blocks, a full-wave bridge rectifier, and a supercapacitor. This structure can also be evaluated by using more complex electronic components such as over-voltage protection circuit, IC full-wave bridge rectifier, filters, etc. However, the presented version of the electrical system is quite functional and available. In the system, the piezoelectric blocks are subjected to mechanical pressure while the moving block moves up and down with user shaking. In every hit of the moving block, the piezoelectric materials generate certain amounts of AC signal [26]. Next, the AC signal is rectified by a full-wave bridge rectifier (with two additional diodes for reverse voltage), and the DC signal is stored in the supercapacitor. The supercapacitor must operate in a wide range of temperatures, and it should have a high charge-discharge efficiency as well as long lifetime [27]. In this regard, the supercapacitors which are classified in IEC/EN 62391-1 Class 2 as an energy storage component could be an appropriate choice for piezoelectric energy harvesting application. Here, the minimum voltage (\(V_{S}\)) and energy capacity (\(E_{S}\)) of the supercapacitor can be determined with respect to the optimization result. After a short examination on relevant piezoelectric materials in the market, _Navy Type II PZT_ circular shape ceramics (\(PZT\) ceramic) were found to be quite appropriate for this system [28]. Therefore, the following model uses the specifications of this ceramic. The thickness (\(h_{3}\)) and the diameter (\(R_{PZT}\)) of the \(PZT\) ceramics can be used in modeling of the system (Figure 4). Moreover, the number of \(PZT\) ceramic (\(N\)) to be used as well as the shake frequency (\(f_{s}\)) should be taken into account. The shake frequency (\(f_{s}\)) in the acceleration tests was around 6 Hz. However, the size and weight of the smartphone and water bottle pair may be slightly smaller than the targeted size of the system. Then the range of the shake frequency must be a little bit smaller. Overall, Table 2 lists the range of the parameters for the piezoelectric harvesting system. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value/Range** \\ \hline Shake acceleration & \(25\leq\alpha\leq 35\) m/s\({}^{2}\) \\ Height of the moving block & \(0.06\leq h_{1}\leq 0.1\) m \\ Outer radius of moving block & \(r_{1}=0.036\) m \\ Inner radius of moving block & \(0.031\leq r_{2}\leq 0.035\) m \\ Floor radius of the drinking glass & \(r_{3}=0.03\) m \\ Density of the block constituent (steel alloy 3D filament) & \(\rho=3500\) kg/m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical System Parameters. Figure 4: The diameter and thickness of the lead–zirconate–titanate (\(PZT\)) ceramic. Mathematical modeling of a piezoelectric energy harvester was already developed in [29]. Following the derivations along with lower frequency operation of the proposed system, the output (mechanical) power of the piezoelectric energy harvester can be simplified to  
\[P=m\zeta\ V_{S}{}^{2}\bigg{(}\frac{w_{s}}{w_{n}}\bigg{)}w_{s}^{3} \tag{5}\]  
where \(\zeta\) is the transducer damping factor, \(w_{n}\) is the resonant angular frequency, \(w_{s}\) is the shaking angular frequency (\(2\pi f_{s}\)), \(V_{S}\) is the amplitude of the sinusoidal shaking (in voltage) [30].