## 3 Results
### Case II. Application with a Frequency Modulation \(m_{f}=48\)  
Another example was developed with a higher carrier frequency \(f_{c}\) to apply the algorithm to a more realistic scenario. In the SPWM technique, the harmonics will be displaced to the harmonic corresponding to the frequency modulation \(m_{f}\); with \(m_{f}=48\), the harmonics will be displaced to harmonic 49. A small passive LC filter can eliminate the harmonics in this range. Therefore, the THD will reduce considerably complying with IEEE 519 standard. Therefore, a new scenario has been proposed that simulates a more rigorous situation aligned with current standards, where the proposed technique's response to a higher number of harmonics is thoroughly evaluated. This new case has been specifically designed to comply with the requirements established by the IEEE 519 standard, which establishes rigorous limits for harmonics present in electrical systems. According to the standard, the main objective of this additional analysis is to verify the technique's ability to maintain the THD within acceptable limits even when considering harmonics up to number 50. To achieve this goal, a detailed analysis of the switching angles and the resulting signal has been carried out, ensuring that the requirements established by the regulations are met. It is important to highlight that the main focus of this new case is to ensure that the THD remains within the acceptable limits set by the regulations, even considering a higher number of harmonics. The specifications for this case are the follows:  
Table 4 shows the main specifications illustrated in Fig. 1 and the proposed number of samples \(N\)s. Table 5 shows the rest of the parameters to be calculated from the specifications of Table 4. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Source voltage & \(V_{dc}\) & 180 V \\ Triangular amplitude & \(A_{t}\) & 1 \\ Sine amplitude & \(A_{s}\) & 0.9 \\ Carrier frequency & \(f_{c}\) & 2880 Hz \\ Output frequency & \(f_{o}\) & 60 Hz \\ Number of samples & \(N_{s}\) & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Initial parameters. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Equation** & **Value** \\ \hline Frequency modulation & \(m_{f}\) & \(m_{f}=\frac{f_{c}}{f_{c}}\) & 48 Hz \\ Triangular pulses per half-cycle & \(p_{t}\) & \(p_{t}=\frac{m_{f}}{2}\) & 24 \\ No. per half-cycle & \(p\) & \(p=p_{t}-1\) & 23 \\ Modulation index & \(M\) & \(M=\frac{A_{t}}{A_{t}}\) & 0.9 \\ No. of angles \(\frac{1}{4}\) wave & \(N_{a}\) & \(N_{a}=\frac{p_{t}}{2}\) & 12 \\ Triangular signal period & \(t_{p}\) & \(t_{p}=\frac{1}{f_{c}}\) & 347.2 μs \\ Sample range & \(dm\) & \(dm=\frac{t}{2}\) & 173.6 μs \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Important calculated parameters. The results and detailed analysis for this new case are presented below. The technique's effectiveness will be evaluated in a more demanding context and closer to real operating conditions. The algorithm was modified to calculate the angles corresponding to the new case, ensuring that the output would not present harmonics before harmonic 50, as previously mentioned. As a result of this adaptation, the specific angles for this case were obtained, which are detailed in Table A2 in Appendix A. The data presented in Table A2 illustrate an increase in the required angles to generate harmonics on the sides of the 50 th harmonic (23 angles were obtained). The corresponding signal generated by these angles is depicted in Figure 9, providing evidence of the algorithm's efficiency in determining the angles necessary for this new case. As mentioned, assessing the signal's harmonic content is relevant because it introduces more angles and pulses, ultimately affecting the total harmonic distortion (THD) and harmonic values.