# A New Modified Non-Approximative Method for Dynamic Systems Direct Calculation
## 4 Example from the Field of Electrical Engineering--Simulation and Validation
### Modelling given electric circuit
}\) are shown in \[x_{n+1}=F_{\frac{T}{2}}x_{n}+G_{\frac{T}{2}}U_{n}\]0  
\[x_{n+1}=F_{\frac{T}{2}}x_{n}+G_{\frac{T}{2}}U_{n}\]1 Time waveforms during the three half-periods for \(u_{0}=U\sin\Bigl{(}\frac{2\pi}{T}h.k\Bigr{)}\). \[x_{n+1}=F_{\frac{T}{2}}x_{n}+G_{\frac{T}{2}}U_{n}\]2 Time waveforms during the first three half-periods for \(u_{0}=U\sin\Bigl{[}\text{integer}\Bigl{(}\frac{6}{T}h.k\Bigr{)}\frac{\pi}{3}+ \frac{\pi}{6}\Bigr{]}\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(n\) & \(u_{0}\) (V) & \(i_{0}\) (A) & \(i_{1}\) (A) & \(u_{1}\) (V) & \(u_{2}\) (V) & \(i_{2}\) (V) \\ \hline
0 & 100 & 0 & 0 & 0 & 0 & 0 \\
3 & 100 & 49.767638 & 48.853863 & 99.143155 & 48.884855 & 48.884855 \\
33 & 100 & 49.114914 & 49.115914 & 99.950884 & 49.115914 & 49.115914 \\
70 & 100 & 49.114914 & 49.115914 & 99.950884 & 49.115914 & 49.115914 \\ \(\dot{\
u}\) & 100 & 49.114914 & 49.115914 & 99.950884 & 49.115914 & 49.115914 \\ \hline \hline \end{tabular}  
The values of state variables \(i_{0}\), \(i_{1}\), \(u_{1}\), and \(u_{2}\) at discrete time instant \(t=n.t\) are given in Table 10.  
Time circumstances: computation time \(t_{\mathrm{comp}}\) (sec) is shown in Table 11 for the implicit Euler method (Eul\({}^{-1}\)—first line) and the direct non-approximative method DNM (second line).  
\end{table} 
Table 10: Values of state variables \(i_{0}\), \(i_{1}\), \(u_{1}\), and \(u_{2}\) at discrete time instant \(t=n.t\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(n\) & \(u_{0}\) (A) & \(i_{0}\) (A) & \(i_{1}\) (A) & \(u_{1}\) (V) & \(u_{2}\) (V) & \(i_{2}\) (V) \\ \hline
3 & 0 & 17.953706 & 21.332934 & 9.698399 & 22.210402 & 22.210402 \\
33 & 0 & 17.955320 & 21.326385 & 9.296168 & 22.214300 & 22.214300 \\
70 & 0 & 17.955320 & 21.326385 & 9.296168 & 22.214300 & 22.214300 \\ \(\dot{\
u}\) & & 17.955320 & 21.326385 & 9.296168 & 22.214300 & 22.214300 \\ \hline \hline \end{tabular}  
Time circumstances: computation time \(t_{\mathrm{comp}}\) (s) is shown in Table 13 for the implicit Euler method (first line) and direct DNM method (second line).  
\end{table} 
Table 11: Computation time at discrete time instant \(t=n.t\), for \(u_{0}(t)=U=\mathrm{const}\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(n\) & \(u_{0}\) (V) & \(i_{0}\) (A) & \(i_{1}\) (A) & \(u_{1}\) (V) & \(u_{2}\) (V) & \(i_{2}\) (V) \\ \hline  
efficiency (97.26%) was computed using [15; 16] as the ratio of the mean value of active output power to active input power. The time waveforms resulting from the simulation are illustrated in Figure 11. The simulated waveforms exhibit similarities to those obtained in Figure 7 and the values documented in Table 12 when the supply voltage is \(u_{0}(t)=U\text{abs}\left[\sin\left(\frac{2\pi}{T}h.k\right)\right]\). Differences between the waveforms are practically negligible. Overall, the validation case indicates that the proposed simulation method produces results that are highly consistent with experimental results. These findings lend credibility to the proposed simulation method and offer assurance that it may be employed in a range of practical applications. Future studies may investigate more complex rectifiers and examine the potential of this method for optimizing the design and performance of rectifier circuits.