# High Frequency Transformers for Solid-State Transformer Applications
## 4 Simulation Results
### Numerical Simulation Results  
To verify the performance of the scaled transformer model and the ability of the control to adapt, three tests were employed:  
* Test 1--Constant Load: Consider that the system feeds a constant, purely resistive load in the direct power direction and that the load has a power of 50 kVA. By analyzing the waveforms of the voltage represented in Figure 11, it is possible to verify that the control system worked as expected, acting on the phase shift angle so that the voltage at the load terminals assumes the previously established reference value. The value of the phase shift angle depends essentially on the equivalent inductance of the model under study and the value of the current that the load requests, having as a maximum value \(+\Omega/2\). \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(R_{1}\) & 17.01 m\(\Omega\) \\ \hline \(L_{l1}\) & 34.26 \(\mu\)H \\ \hline \(L^{\prime}\)\({}_{2}\) & 10.37 \(\mu\)H \\ \hline \(R^{\prime}\)\({}_{2}\) & 5.30 m\(\Omega\) \\ \hline \(C_{stray}\) & 0.40 nF \\ \hline \(R_{c}\) & 18.55 k\(\Omega\) \\ \hline \(L_{m}\) & 58.70 mH \\ \hline \(C_{add}\) & 1.00 mF \\ \hline \(L_{add}\) & 80.00 mH \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The HFT equivalent parameters. \begin{table}
\begin{tabular}{c c} \hline \hline
**Primary Winding: Litz Wire** \\ \hline \(N\) of Single Conductors & 1368 \\ \hline Construction & \(12\times\left(3\times\frac{38}{0.08}\text{ mm}^{2}\right)\) \\ \hline Equivalent Copper Section & 120 mm\({}^{2}\) \\ \hline \multicolumn{2}{c}{**Secondary Winding: Litz Wire**} \\ \hline \(N\) of Single Conductors & 840 \\ \hline Construction & \(6\times\left(5\times\frac{24}{0.08}\text{ mm}^{2}\right)\) \\ \hline Equivalent Section & 70 mm\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Constitution of the windings. To evaluate the performance of the developed HFT, its performance can be analyzed. Figure 11 represents the average instantaneous power at the primary and secondary terminals. By using the measurement tools integrated in the software, Matlab/Simulink, it is possible to determine the obtained efficiency, having verified a value of 99.5%. Analyzing the obtained efficiency, we conclude that it does not consider the winding resistance variation as a function of frequency and does not account for the skin effect. When the theoretical efficiency is determined without accounting for the skin effect, a theoretical efficiency of 99.4% is obtained. The analysis of the voltage waveform at the transformer terminals will be performed in Test 3. * Test 2--Variable load: Consider that the system is feeding a variable load, purely resistive, in the direct power direction. The initial load presents a power of 25 kVA and, at instant \(t=1\) s the load doubles, resulting in a power of 50 kVA. All the analysis performed for Test 1 is valid for Test 2. The focus of the analysis described below is the impact of varying the value of the load on the system under study. Analyzing Figure 12 it is possible to verify the occurrence of a voltage drop at the load terminals and a consequent controller action to guarantee the reference voltage at the load terminals. The voltage drop is significant, but it should be considered that the instantaneous doubling of the load is an extremely demanding transient for the system. Nevertheless, it is an excellent case to test the good performance of the controller. The shift angle after load variation and stabilization assumes approximately twice the value because the load has also doubled from 25 kVA to 50 kVA. Figure 12 shows the variation of the average instantaneous power at the HFT terminals. Although this is a different test, after the stabilization of the load of 50 kVA, the performance values verified are the same as those in Test 1. When the load assumes a value of 25 kVA, an efficiency in simulation of 99.7% is verified.