## 4 System Architecture and Design Procedures
### Perovskite Photovoltaic Energy Harvesting System
Equation (11) can be modified for the perovskite module reverse saturation current, \(I_{s,r,M}\), as follows:  
\[I_{s,r,M}=\frac{I_{sc}}{e^{(\frac{q\times Y_{0}}{I_{sc}+k\times M}I_{p}^{2})}- 1}. \tag{16}\]  
The photon currents of the modules ( \(I_{ph1}\), \(I_{ph2}\),... \(I_{ph_{Xp}}\)) (Figure 6) are identical and equal to the incident light on the unit PSCs \((I_{ph})\), as outlined in (10). Hence, \((I_{ph_{1}}=I_{ph_{2}}=\ \ldots\ =I_{ph_{(X_{p}-1)}}=I_{ph_{X_{p}}}=I_{ph})\). Thus, the perovskite array incident current, \(I_{PH}\), is expressed by (17) or (18). \[I_{PH}=X_{p}\times I_{ph}, \tag{17}\]  
\[I_{PH}=\sum_{k=1}^{X_{p}}I_{ph_{k}}. \tag{18}\]  
The perovskite array's output current \((I_{PSCs})\), illustrated in Figure 8, is expressed as follows:  
\[I_{s,r}=\frac{I_{sc}}{e^{\frac{(r+V_{out})}{(I_{sc}\times A\times I_{p})}}-1}. \tag{11}\]0  
Hence, the current \((I_{P})\) through \(R_{sh}\) is defined by (20). \[I_{s,r}=\frac{I_{sc}}{e^{\frac{(r+V_{out})}{(I_{sc}\times A\times I_{p})}}-1}. \tag{11}\]1  
Hence, the output current for a PSC array, depicted in Figure 8, composed of \(Y_{s}\) cells connected in series and \(X_{p}\) modules in parallel, can be mathematically expressed as follows:  
\[I_{s,r}=\frac{I_{sc}}{e^{\frac{(r+V_{out})}{(I_{sc}\times A\times I_{p})}}-1}. \tag{11}\]2  
In general, Equations (17), (19) and (20) can be adapted for unit cells by setting \(X_{p}=Y_{s}=1\) and for modules by setting \(X_{p}=1\) and \(Y_{s}\
eq 1\). The power generated by PSCs, \(P_{PSCs}\), supplies energy to IoT devices during the operational time (\(t_{PSCs}\)), which is  
\[I_{s,r}=\frac{I_{sc}}{e^{\frac{(r+V_{out})}{(I_{sc}\times A\times I_{p})}}-1}. \tag{11}\]3 PSC array equivalent circuit. the maximum available time (\(t_{m}\)) minus the inactive duration (\(t_{off}\)) when the cell cannot produce electricity due to low light or shading. The electric power (\(P_{PSCs}\)) and total harvested energy (\(E_{PSCs}\)) from a perovskite array can be computed as follows:  
\[I_{s,r}=\frac{I_{sc}}{e^{\frac{(r+V_{out})}{(I_{sc}\times A\times I_{p})}}-1}. \tag{11}\]4  
\[I_{s,r}=\frac{I_{sc}}{e^{\frac{(r+V_{out})}{(I_{sc}\times A\times I_{p})}}-1}. \tag{11}\]5  
The efficiency of a cell, \(\eta_{c}\), is determined using (24), considering key parameters such as open circuit voltage (\(Voc\)), short circuit current (\(I_{sc}\)), input irradiation power (\(P_{in}\)), fill factor (\(FF_{cell}\)), and the current (\(I_{mp}\)) and voltage (\(V_{mp}\)) at the maximum power point (MPP). \[I_{s,r}=\frac{I_{sc}}{e^{\frac{(r+V_{out})}{(I_{sc}\times A\times I_{p})}}-1}. \tag{11}\]6  
\[I_{s,r}=\frac{I_{sc}}{e^{\frac{(r+V_{out})}{(I_{sc}\times A\times I_{p})}}-1}. \tag{11}\]7  
Substituting the expression (25), \(FF_{cell}\), into (24) gives:  
\[I_{s,r}=\frac{I_{sc}}{e^{\frac{(r+V_{out})}{(I_{sc}\times A\times I_{p})}}-1}. \tag{11}\]8  
The efficiency of a PSC array is evaluated using (9), which factors in the efficiencies of individual modules arranged in parallel. Each module's efficiency is determined by multiplying the series-connected cells' efficiencies. The module's efficiency, \(\eta_{M}\), is provided by (27). \[I_{s,r}=\frac{I_{sc}}{e^{\frac{(r+V_{out})}{(I_{sc}\times A\times I_{p})}}-1}. \tag{11}\]9  
In this context, \(\eta_{c1},\eta_{c2},\eta_{c3},\ldots,\eta Y_{s}\) represent the efficiencies of individual PSCs within the module. Since these cells are identical and made from the same material, their efficiencies are equal and denoted as \(\eta_{c}\). Therefore, (27) can be simplified as follows:  
\[I_{d}=I_{s}[e^{(\frac{V_{out}+I_{ppv}\times R_{s}}{A\times V_{T}})}-1], \tag{12}\]0  
The overall efficiency of the entire PSCs system array, \(\eta_{A}\), is as follows:  
\[I_{d}=I_{s}[e^{(\frac{V_{out}+I_{ppv}\times R_{s}}{A\times V_{T}})}-1], \tag{12}\]1  
where \(N\) represents the number of parallel-connected modules, ranging from 1 to \(X_{P}\) (Figure 8).