## 5 Results
### Simulation 2: Input Signal with 5 Spectral Components That Increases to 11 Components at = 0.8 s
Increase to 11 Components at t = 0.8 s  
In the second part of the simulation, the evolution of the system is shown when the input signal varies and transitions from being composed of 5 components to 11 spectral components. Table 7 displays the new components forming the input signal, and Figure 31 illustrates the temporal evolution of the new signal. \begin{table}
\begin{tabular}{c c c c} \hline
**No. Spectral** & **Voltage rms (V)** & **Frequency (Hz)** & **Frequency (Rad/s)** \\
**Component** & & & \\ \hline
1 & 23 & 33.9 & 213 \\
2 & 230 & 51.1 & 321.0707 \\
3 & 46 & 75.15 & 472.1813 \\
4 & 34.5 & 121.75 & 764.9778 \\
5 & 69 & 150.45 & 945.3052 \\
6 & 23 & 214.3 & 1346.4866 \\
7 & 23 & 229 & 1438.8494 \\ \hline \end{tabular}
\end{table} 
Table 7: Harmonic components present in the input signal at the instant t = 800 ms.  
Figure 30: Temporal evolution of the estimation of the value of the frequency of all spectral components inside the input signal. Figure 29: Evolution of the input subharmonic component at 33.9 Hz (blue) and the LKF prediction (red). The input signal changes at t = 0.8 s. As shown in Figure 32, there is a rapid increase in the error produced between the real signal and the signal estimated by the LKF. Figure 33 illustrates the evolution of the input and estimated signals. In response to the increase in estimation error, the method starts again, performing the DFT and applying the algorithms described in Section 4. This leads to a new identification of the number of components in the real signal, and the obtained result is presented in Table 8.  
Figure 34 depicts the evolution of the input signal to the algorithm and the estimation made by the LKF (in red). The estimation of the input signal begins at t = 1 s, which corresponds to the completion of the DFT calculation, implementing the LKF with the number obtained from the spectral components forming the signal. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No. Spectral** & **Voltage rms (V)** & **Frequency (Hz)** & **Frequency (Rad/s)** \\ \hline
8 & 23 & 250.5 & 1573.9379 \\
9 & 23 & 450.7 & 2831.8316 \\
10 & 23 & 497 & 3122.7431 \\
11 & 16.1 & 549 & 3449.4687 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Cont. Figure 31: Evolution of the input signal during the modification of the number of spectral components. Figure 32: LKF estimated signal error. In Figure 35, the evolution of the error signal between the input signal to the algorithm and the estimation made by the LKF (Figure 34, red) is shown. The estimation of the input signal begins at t = 1 s, with the error being higher at the start of the estimation. It is observed that the error signal decreases, reaching a steady state at t = 1.3 s of simulation (300 ms after the estimation begins). Figure 36 provides a closer look at this approximation. It is noteworthy that at t = 1.25 s, the error is less than 0.5% of the value of the main harmonic and less than 1% of that provided by most commercial sensors. \begin{table}
\begin{tabular}{c c c} \hline \hline
**No. Spectral** & **Voltage rms (V)** & **Frequency (Hz)** \\ \hline
1 & 11.26 & 30 \\
2 & 199.4 & 50 \\
3 & 15.14 & 70 \\
4 & 22.55 & 120 \\
5 & 59.74 & 150 \\
6 & 9.851 & 210 \\
7 & 15.87 & 230 \\
8 & 19.91 & 250 \\
9 & 19.91 & 450 \\
10 & 19.57 & 500 \\
11 & 13.93 & 550 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Harmonic components identified in the input signal after the increase of components. Figure 34: LKF estimated signal (red) versus input signal (blue). Figure 33: LKF estimated signal (red) versus input signal (blue). Figure 37: Estimation of the interharmonic spectral component at 214.3 Hz (red) versus real component (blue). Figure 35: LKF estimated signal error. Figure 36: LKF estimated signal error detail. Figure 37: Estimation of the interharmonic spectral component at 214.3 Hz (red) versus real component (blue). Figure 40: Estimation detail of the interharmonic spectral component at 229 Hz (red) versus real component (blue).