# Sensorless Current Pulsation Compensation in a Hybrid Energy Storage
## 3 Implementation and Experimental Verification
### Pulsation Compensator Analysis  
The pulsation compensator was designed as an isolated DC/DC dual-active bridge converter, based on the SiC MOSFET transistors Infineon FF11 MR12W1M1_B11. The PR compensation algorithm, tuned for 100 Hz pulsation, was implemented on a Texas Instruments F28379D Delfino microcontroller. Both the AC/DC converter controller and the compensator controller were linked by the SPI protocol. All the main parameters of the converter are presented in Table 1.  
The resonant controller was implemented in a two-pole, two-zero controller structure, with coefficients calculated as in Equations (16)-(21):  
\[B_{0}=\frac{4K_{H}\Delta T\omega_{nH}}{\Delta T^{2}\omega_{0}{}^{2}+4\omega_{ nH}\Delta T+4} \tag{16}\]  
\[B_{1}\ =1 \tag{17}\]  
\[B_{2}=\frac{-4K_{H}\Delta T\omega_{nH}}{\Delta T^{2}\omega_{0}{}^{2}+4\omega_{ nH}\Delta T+4} \tag{18}\]  
\[A_{0}\ =1 \tag{19}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Compensator power & 10.0 kW \\ Switching frequency & 100 kHz \\ Control loop frequency & 10 kHz \\ Resonant frequency & 100 Hz \\ Resonant gain & 14.5 [-] \\ Input voltage & 750 V \\ Output voltage & 70 V \\ Compensator output capacitance & 90 mF \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Key compensator parameters. Figure 8: Evaluation of the implementation of the current pulsation extraction. \[A_{1}=\frac{-(2\Delta T^{2}{\omega_{0}}^{2}-8)}{\Delta T^{2}{\omega_{0}}^{2}+4 \omega_{nH}\Delta T+4} \tag{20}\]  
\[A_{2}=\frac{-(\Delta T^{2}{\omega_{0}}^{2}-4\omega_{nH}\Delta T+4)}{\Delta T^{2}{ \omega_{0}}^{2}+4\omega_{nH}\Delta T+4} \tag{21}\]  
the pulsation compensator was evaluated using disturbance injection to perform frequency domain analysis. Additionally, step responses were recorded. The disturbance injection was performed in three stages: proportional-resonant controller analysis, open loop dual active bridge converter analysis, and closed loop analysis of the compensator (Figure 9). The Rohde-Schwarz RTB 2004 2.5 Gs/s oscilloscope was used as a disturbance injector for the frequency domain analysis. In the case of the PR controller analysis, the controller was implemented in the microcontroller in a closed loop, with its own output feeding the feedback input. Additionally, the controller output was connected to the microcontroller's digital-to-analog output and connected back to the oscilloscope as disturbance injector feedback. The reference signal was provided by the disturbance injector. A frequency sweep was performed in the range from 10 Hz to 1 kHz. The results are presented in Figure 10a. Next, the DAB converter was analyzed in an open loop. To do this, the disturbance injector was connected to the analog-to-digital converter of the microcontroller driving the DAB converter. Then, the analog value was recalculated and fed directly into the phase output of the converter. This time, the input current of the converter (I\({}_{\text{dab}}\)) was used as disturbance injector feedback. A frequency sweep was performed in the range from 10 Hz to 1 kHz. The results are presented in Figure 10b. Finally, the compensator was tested in the closed loop. The reference signal was passed to the compensator via SPI from the 3p-4w inverter. The input current was connected to the analog-to-digital converter of the microcontroller along with the disturbance injector, and the input current of the converter was used as disturbance injector feedback. A frequency sweep was performed in the range from 10 Hz to 1 kHz. The results are presented in Figure 10c. It can be observed that in the tested range, the DAB converter has a constant gain and does not introduce any delays, which confirms claims from Equations (13) and (14) for the low-frequency signals. Towards the 1 kHz frequency, the phase shift increases\(-\)this is caused by the test frequency approaching the ADC conversion sampling frequency, and the controller execution frequency (both at 10 kHz). In addition to the frequency domain analysis, step responses of the compensator were observed.