# Real-Time Wave Energy Converter Control Using Instantaneous Frequency
## 5 Results  
### Comparison of CWR  
Table 4 presents the CWR percentages for different estimation methods and control schemes. The simulation results shown in Figure 13 provide insight into the comparative performance of different frequency estimation methods. Notably, the CHT-based control strategy demonstrates a more stable cumulative energy accumulation, suggesting improved consistency in energy capture over the observed period. On the other hand, both the PLL and NCHT methods are associated with higher instantaneous peak powers, which, while occasionally yielding more instantaneous absorbed power, introduce greater variability in the energy harvesting process. The time points at which significant divergence in cumulative energy occurs are under further investigation, aiming to better understand the transient dynamics introduced by different estimation techniques. \begin{table}
\begin{tabular}{l c c} \hline
**Tuning Strategy** & **Mean CWR \%** & **Standard Deviation** \\ \hline Fixed & 24.8 & 2.37 \\ NCHT & 25.93 (+4.6) & 2.45 \\ PLL & 25.02 (+0.9) & 2.84 \\ CHT & 27.42 (+10.6) & 2.69 \\ \hline \end{tabular}
\end{table} 
Table 4: Statistical summary of CWR comparison across different estimation methods and control schemes. Higher values indicate more efficient energy absorption. The percent increase over the baseline fixed parameter case is given in parentheses. \begin{table}
\begin{tabular}{l l} \hline
**Parameter** & **Value/Description** \\ \hline Number of simulations & 1000 iterations \\ Simulation duration & 20 min per run \\ Time step & 0.1 s \\ Computational platform & MacBook Pro 16\({}^{\prime\prime}\) (2021), Apple M1 Pro, MATLAB R2024b \\ Wave spectrum & JONSWAP spectrum \\ Peak enhancement factor (\(\gamma\)) & 3.3 \\ Significant wave height (\(H_{s}\)) & 2.4 m \\ Peak period (\(T_{p}\)) & 9 s \\ Phase distribution & Uniformly random in probability domain \\ Excitation force estimation & Convolution with IRF from WAMIT data \\ \hline \end{tabular}
\end{table} 
Table 3: Summary of iteration setup for statistical performance analysis. During this study, multiple parameter sweep tests were conducted using the RM3 SS model. First, the estimation parameters were varied, including the median filter window sizes for the CHT method and the cross-over frequencies of the PLL loop filter, while maintaining a fixed phase margin of 60 degrees. Second, the saturation block window sizes were adjusted, with the lower saturation limit set to \(0.01\times f_{p}\), where \(f_{p}\) denotes the dominant peak frequency of the incoming wave spectrum. It was observed that setting the upper saturation limit to \(1.2\times f_{p}\) while maintaining the lower limit at \(0.01\times f_{p}\) yielded the best performance for the PLL technique. However, for the NCHT and CHT methods, allowing an unbounded upper limit, while keeping the same lower limit as in the PLL setup, resulted in higher energy capture. All sweep tests were conducted with the goal of maximizing the CWR. An important observation from these tests is that the NRMSE of the frequency estimation is not directly correlated with the performance of the PTO control when using the PLL technique. In contrast, the CHT method showed the best performance when the median window size was set at the value corresponding to the minimum NRMSE for Case 1 and Case 2, as presented earlier, which is approximately 4.5% of the total estimation window size and is close to the average half-cycle of the dominant wave. Increasing the median window size beyond this point, while improving smoothing of the frequency estimate, consistently led to a reduction in CWR. Similarly, for the PLL, decreasing the cross-over frequency toward \(f_{p}\) resulted in lower NRMSE values; however, it only improved the CWR up to the level achieved by the fixed PTO control technique. These findings highlight that minimizing estimation error alone is insufficient for maximizing WEC performance--timely adaptation to changing wave conditions is equally, if not more, important.