# Indoor PV Modeling Based on the One-Diode Model
## 3 Results and Discussion  
To determine the available energy at low illumination levels, a 1000 lux illuminance reference characteristic point value from the PV panels is used to translate to other illuminance levels. Both photovoltaic panels are exposed to 1000 lux with different light sources. The measured reference characteristic points are listed in Tables 2 and 3. Using the proposed translation technique, the reference values can be translated to different illuminance levels for various light sources. The model's parameters can then be extracted with the translated characteristic point values as input values. Table 4 shows the extracted model's parameter values at 1000 lux for one of the PV panels. It can be noted that the relatively higher value of \(R_{s}\) is due to the lower fill factor under indoor illumination. [PERSON] [11] and [PERSON]'s [16] works are used for comparison with the proposed model. This is because [PERSON] improved the existing parameter extraction technique. [PERSON]'s results appear promising, with low normalized root mean square deviation error (NRMSE) at low illumination levels. NRMSE is also applied to our proposed model in order to achieve the same benchmark for model accuracy. The NRMSE can be calculated using Equation (22):  
\[\text{NRMSE}(\%)=\frac{100}{I_{sc}}\times\sqrt{\frac{1}{k}\sum_{i=1}^{k}\left( I_{i}^{\text{mod}}-I_{i}^{\text{exp}}\right)^{2}} \tag{22}\]  
where \(I_{i}^{\text{mod}}\) is the model's value, \(I_{i}^{\text{exp}}\) is the experimental value, and \(i\) is the value of a dataset of length \(k\). On the other hand, [PERSON] utilized the iterative thermal voltage to translate the open-circuit voltage, which is frequently employed in existing translation works. The same modeling procedures are applied to both panels at 900, 800, 700, 600 lux, etc. The values are recorded and compared to the experimental values. \begin{table}
\begin{tabular}{c c} \hline \hline
**Extracted Parameter** & **Value** \\ \hline \(a\) & 2.283 \\ \(R_{s}\) (\(\Omega\)) & 188.887 \\ \(R_{p}\) (\(\Omega\)) & 103.883 \\ \(I_{o}\) (\(\mu\)A) & 0.1083 \\ \(I_{ph}\) (\(\mu\)A) & 125.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Extracted parameters for k\(\infty\)b22\(-\)12x1 at 1000 lux. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Characteristic Points at 1000 lux**} & \multicolumn{3}{c}{**Light Source**} \\ \cline{2-3}  & **7 W LED** & **12 W CFL** \\ \hline \(I_{sc}\) (\(\mu\)A) & 125.251 & 123.172 \\ \(V_{oc}\) (V) & 0.414 & 0.408 \\ \(I_{inp}\) (\(\mu\)A) & 102.835 & 100.390 \\ \(V_{mp}\) (V) & 0.293 & 0.287 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Measured average reference characteristic points for k\(\infty\)b22\(-\)12x1 at 1000 lux. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Characteristic Points at 1000 lux**} & \multicolumn{3}{c}{**Light Source**} \\ \cline{2-3}  & **7 W LED** & **12 W CFL** \\ \hline \(I_{sc}\) (\(\mu\)A) & 39.327 & 39.244 \\ \(V_{oc}\) (V) & 0.933 & 0.937 \\ \(I_{mp}\) (\(\mu\)A) & 28.969 & 29.056 \\ \(V_{mp}\) (V) & 0.637 & 0.639 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Measured average reference characteristic points for k\(\infty\)b22\(-\)04x3f at 1000 lux. The generated I-V curves are presented in Figures 11-16. It can be noted that the values of the currents and voltages are very low due to the small size of the PV panels and the low illuminances of 1000 lux and below used in the experiments. For example, the current values in the data sheet [50; 51] are in the order of mA, but these are provided for an irradiance level of 1000 W/m\({}^{2}\), whereas 1000 lux is at least two orders of magnitude less, which results in current values in the order of \(\upmu\)A. Figure 11 shows the I-V curves generated for both panels at 1000 lux; all of the I-V curves fit closely with the experimental values. As the illuminance level decreases, the accuracy of these works decreases. At 800 lux for the kx0b22 \(-\)04x3f panel, the I-V curves near the maximum-power point begin to diverge.