# Sensorless Current Pulsation Compensation in a Hybrid Energy Storage
## 2 DC Link Pulsation in an Energy Storage Application
\begin{bmatrix}\cos( \varnothing^{+})\\ \sin(\varnothing^{+})\end{bmatrix} }+I^{-}\cos(\varnothing^{-}) \begin{bmatrix} \cos(2\omega t)\\ -\sin(2\omega t)\end{bmatrix} +I^{-}\sin(\varnothing^{-}) \begin{bmatrix}\sin(2 \omega t)\\ \cos(2\omega t)\end{bmatrix}  \tag{6}\]  
\[i_{dq}{}^{-}= \begin{bmatrix}\overline{i_{d}{}^{-}}\\ \overline{i_{q}{}^{-}}\end{bmatrix} + \begin{bmatrix}\widetilde{i_{d}{}^{-}}\\ \overline{i_{q}{}^{-}}\end{bmatrix} =\overline{I^{+} \begin{bmatrix}\cos( \varnothing^{-})\\ \sin(\varnothing^{-})\end{bmatrix} }+I^{-}\cos(\varnothing^{+}) \begin{bmatrix} \cos(2\omega t)\\ -\sin(2\omega t)\end{bmatrix} +I^{-}\sin(\varnothing^{+}) \begin{bmatrix}\sin(2 \omega t)\\ \cos(2\omega t)\end{bmatrix}  \tag{7}\]  
the positive sequence, Equation (6) is directly related to DC link pulsation, which is linked by voltage gain of the converter \(k\):  
\[i_{dc}=k\overline{\left[\overline{q}{}^{+}\right]}+k\overline{\left[ \widetilde{i_{d}{}^{+}}\right]}=kI^{+}\cos(\varnothing^{+})-kI^{-}\cos( \varnothing^{-})\cos(2\omega t)+kI^{-}\sin(\varnothing^{-})\sin(2\omega t) \tag{8}\]  
Figure 3: A three-level, three-phase, four-wire inverter with a split DC link and an active balancer. this calculated current is used to extract the pulsation value and is further passed as a current reference signal for the compensator, creating a sensorless compensation loop. The compensation circuit, which can take over the AC component of the DC link current, is presented in Figure 4. A three-level T-NPC inverter is connected to the grid via an LCL filter. The DC link of the inverter is connected through an isolated DC/DC dual-active bridge converter (DAB1) to a lithium-ion energy storage and to the compensator-- another dual-active bridge converter (DAB2), connected to the capacitor bank. The goal is to generate a sinewave with a phase opposite of the DC link pulsation current using the DC/DC converter DAB2. The dual active bridge converter was chosen for this application due to its high dynamics and large voltage gain [13]. The sensorless loop in this application is achieved by replacing the main current measurement (I\({}_{\text{DC}}\)) with calculations based on the symmetrical decomposition of the inverter output currents. Both DAB converters are still operating in sensored mode, with their respective internal current loops based on current sensors, and further reduction of the number of the sensors is possible by implementing a sensorless loop on the internal DC/DC converter level [14; 15]. For analysis, the dual active bridge topology can be simplified into two high-frequency voltage sources connected with the leakage inductance L\({}_{\text{lk}}\), which generate square voltage waves (_Vp_ and _Vs_). The power flow is controlled by shifting the phase \(\varphi\) between those generated voltages (Figure 5). It is also common to describe phase shift as D, where D = \(\varphi\)/\(\pi\). When the voltage _Vp_ leads the voltage _Vs_, the power is transferred from the input to the output of the converter; when the voltage _Vp_ lags the voltage _Vs_, the power is transferred from the output to the input. There is no need for separate algorithms when changing the direction of the power flow, which is desired for this application. The dynamics of a dual active bridge topology depend mostly on two contributors: input and output filters, and the leakage inductance L\({}_{\text{lk}}\) of the medium frequency transformer. This makes modeling the converter problematic, as the leakage inductance operates with dynamics several orders of magnitude higher than the output filters. In [16], several modeling methods are compared against one another, with negligible differences between results mostly noticeable towards the high-frequency range. Based on those findings, for this application, the reduced order model was selected to describe the dynamics of the DAB converter. This approach ignores the dynamics of leakage inductance and uses the average values of the switching currents.