# Nonlinear Analysis and Closed-Form Solution for Overhead Line Magnetic Energy Harvester Behavior
## 8 Verification and Experimental Results  
Verification of the theoretical predictions was conducted first by simulation. The theoretical and simulated results for key parameters were found to be in excellent agreement; see Tables 1 and 2. An experimental laboratory prototype OLMEH shown in Figure 1 was constructed by stacking together three pairs of 10H10 C-cores made of silicon steel (EILOR MAGNETIC CORES). The magnetic path length was \(l_{c}=120\) mm, and the total core cross-section was \(Ac=1800\) mm\({}^{2}\). The total number of secondary turns was \(N=40\). The SB256 bridge rectifier was used. To test the performance of the prototype OLMEH, an experimental test bed was constructed, see Figure 8, using two back-to-back connected isolation transformers capable of sustaining a low-side current of up to 200 A rms. The OLMEH line current was regulated using a VARIAC and a high-power resistive load. In Figure 8, the OLMEH is illustrated successfully charging a battery. Magnetic properties of the prototype OLMEH were tested and Froelich coefficients were extracted from the experimental data as mentioned. Figure 8: View of the experimental prototype OLMEH (**a**) and its test bench (**b**). The prototype OLMEH was tested at several line currents and CVL voltage levels. During the experiments, electronic load was used to emulate the voltage sink load. Key waveforms of the OLMEH are shown in Figure 9. Here, the line current was \(I_{1}\) = 100 A rms. The cusp portion of the rectifiers' input voltage waveform, Vin, manifests State 1, whereas the flat portion reveals State 2. Accordingly, the CVL current is zero during State 1, whereas CVL is provided with a pulse of current during State 2. This stands in agreement with the theoretical prediction above. For \(V_{b}\) = 25 V, the measured output power was 49.4 W, see Figure 9a, whereas for \(V_{b}\) = 35 V the output power was 44.6 W, see Figure 9b. Also note that for \(V_{b}\) = 35 V the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**N**} & \multicolumn{2}{c}{**40**} & \multicolumn{2}{c}{**50**} & \multicolumn{2}{c}{**60**} & \multicolumn{2}{c}{**70**} \\  & **Calc** & **Sim** & **Calc** & **Sim** & **Calc** & **Sim** & **Calc** & **Sim** \\ \hline  & 23.16 & 23.25 & 28.95 & 29.5 & 34.75 & 35.2 & 40.54 & 41.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the simulated vs. the calculated borderline voltage \(V_{b}\)* for different turns number N, at line current \(I_{1}\) = 100 A rms. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **I\({}_{\text{1 pk}}\)** \\ **[A]** \\ \end{tabular} } & \multirow{2}{*}{**t\({}_{\text{1 Sim}}\)**} & \multirow{2}{*}{**t\({}_{\text{1 CLa}}\)**} & \multirow{2}{*}{**t\({}_{\text{2 Sim}}\)**} & \multirow{2}{*}{**t\({}_{\text{2 CLa}}\)**} & \multirow{2}{*}{**B\({}_{\text{1 Sim}}\)**} & \multirow{2}{*}{**B\({}_{\text{1 CLa}}\)**} & \multirow{2}{*}{**P\({}_{\text{OSim}}\)**} & \multirow{2}{*}{**P\({}_{\text{OCalc}}\)**} \\  & **[mS]** & **[mS]** & **[mS]** & **[mS]** & **[T]** & **[T]** & **[W]** & **[W]** \\ \hline
50 & \(-1.35\) & \(-1.43\) & 7.05 & 7.07 & \(-1.25\) & \(-1.29\) & 12.87 & 13.08 \\
100 & \(-1.15\) & \(-1.19\) & 8.23 & 8.27 & \(-1.51\) & \(-1.52\) & 33.05 & 33.21 \\
200 & \(-0.92\) & \(-0.93\) & 9.05 & 9.11 & \(-1.66\) & \(-1.67\) & 73.25 & 73.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the simulated vs. the calculated key parameters at different peak line current levels and at a load voltage of \(V_{b}\) = 24 V.  
Figure 9: Typical waveforms of the experimental overhead line energy harvester at: \(I_{1}\) = 100 A rms and \(V_{b}\) = 25 V (**a**); \(I_{1}\) = 100 A and \(V_{b}\) = 35 V (**b**); \(I_{1}\) = 75 A rms and \(V_{b}\) = 23 V (**c**); \(I_{1}\) = 150 A rms and \(V_{b}\) = 23 V (**d**). Vert. scale: \(I_{1}\)—200 A/div; \(V_{in}\)—20 V/div; \(V_{1}\)—2 V/div; \(V_{1}\)—2 V/div; \(I_{in}\)—5 A/div; hor. scale 5 ms/div. duration of State 1 is relatively long and is seen in Figure 9b.