## 4 Direct Output Current Control Based on Virtual Voltage Compensation under No Backflow Power
### Proposed VDCC Method  
For the traditional output voltage control, the value of the feedforward compensation is constant, with the result that the PI controller will bear all the burden of adjusting the system for disturbances. In terms of transient response optimization against input voltage or load disturbances, a VDCC method is thus proposed, and its main principle is that the output current is directly controlled to meet the output current requirement.  
Although the transmission power and voltage gain of the LCL-DAB converter are derived respectively as (31) and (32) based on the premise of lossless transmission, power losses cannot be ignored in the actual operation. Therefore, the input and output power are not equal, which means the calculated control variables are less accurate only according to the ideal equations. Moreover, the system parameters also can change varying to the operating conditions such as the inductance of the filter inductor, which also will result in the difference between ideal and required control variables. Therefore, a virtual voltage \(u_{\text{ov}}\) is introduced in the control loop to compensate for the difference, defined as  
\[i_{\text{oref}}=\frac{u_{\text{ov}}}{R} \tag{38}\]  
where \(i_{\text{oref}}\) is the desired output current reference. Given that the resistance of the load is not constant, the instantaneous sampling values of the output voltage and current are utilized to calculate \(R\), i.e.,  
\[R=\frac{u_{\text{o}}}{i_{\text{o}}} \tag{39}\]  
Substituting (39) into (38), the output current reference is derived as (40). Then, the instantaneous output current can be deduced, based on (31), as (41).  
\[i_{\text{oref}}=\frac{u_{\text{ov}}i_{\text{o}}}{u_{\text{o}}} \tag{40}\]  
\[i_{\text{o}}=\frac{8 NU_{\text{in}}\cos^{2}(\pi d_{1})\sin(2\pi d)}{\pi^{2}Z_ {0}} \tag{41}\]  
According to (40) and (41), the actual inner phase shift ratio \(d_{1}\)* corresponding to the virtual output voltage can be derived, expressed as  
\[d_{1}^{*}=\frac{1}{\pi}\cos^{-1}\bigg{[}\frac{k_{\text{f}}u_{\text{ov}}i_{ \text{o}}}{u_{\text{o}}u_{\text{in}}}\bigg{]}^{\frac{1}{2}} \tag{42}\]  
\[k_{\text{f}}=\frac{\pi^{2}Z_{0}}{8N\sin(2\pi D)} \tag{43}\]  
\[\bigg{(}\frac{u_{\text{ov}}i_{\text{o}}}{u_{\text{o}}}\bigg{)}\in\bigg{[}0_{ \text{,}}\frac{8 NU_{\text{in}}}{\pi^{2}Z_{0}}\bigg{]} \tag{44}\]  
where \(k_{\text{f}}\) is a constant expressed as (43) and \(D\) is the estimated outer phase shift ratio. Based on the above analysis, Figure 9 shows the block diagram of the proposed VDCC method. The outer phase shift ratio is estimated based on Section 4.2 to ensure a wide range of no backflow operation, while the PI controller regulates the inner phase shift ratio mainly to make the output voltage follow the reference value. The input voltage \(u_{\text{in}}\), output voltage \(u_{\text{o}}\), and output current \(i_{\text{o}}\) need to be sampled once per cycle. The error between the sampled output voltage and the output voltage reference is calculated by the PI controller, and the output of the controller is set as the virtual voltage \(u_{\text{ov}}\) corresponding to the desired output current. The dynamic response improvement of the utilization of the virtual voltage has been verified in the traditional DAB converter [29; 30]. Notably, the maximal value of the calculated direct output current should be limited according to the maximal output current of the converter, expressed as (44). Then, according to (42), the actual control variable \(d_{1}\)* is calculated to improve the transient response against input voltage or load disturbances.  
Moreover, the introduction of the virtual voltage also can compensate for the difference between the calculated and the actual \(k_{t}\), which can be more flexible compared with the traditional constant feedforward compensation. Finally, the gate signals of the switches are generated according to \(d_{1}\)* and \(D\).