# Topology and Control Strategy of PV MVDC Grid-Connected Converter with LVRT Capability
## 3 Control Strategy of the Converter
### Current Control Strategy with Active Damping
#### 3.2.2 Adding Active Damping in the Converter  
As described in 3.1, inductor series resistance is an effective way to increase damping of the control system. In order to add damping without additional loss, an active damping method based on state variable feedback is derived from the passive damping method.  
Figure 11: Small-signal model in buck mode.  
Figure 12: The bode waveform of current loop gain.  
Figure 13a is the current control loop with a series resistance \(R\) to the inductor \(L_{o}\). \(v_{R}(s)\) is the resistance voltage. Through equivalent transformation, Figure 13a is transformed into Figure 13b.  
Comparing with Figure 13a, the resistance voltage feedback point is moved to the output of the current regulator \(G_{i}(s)\). At the same time, the current sampling point is moved forward to the position of capacitor current \(i_{c}(s)\). The capacitor current is the feedback variable, and the feedback signal is the product of the feedback variable and the feedback function. By subtracting this feedback signal from the duty ratio, the current control loop in Figure 13b could achieve the same effect as series resistance.  
The feedback function \(H_{ic}\)-can be simplified by substituting the transfer function of \(G_{id}(s)\):  
\[H_{ic}=\frac{R}{G_{id}(s)L_{o}s}=\frac{RL_{in}}{L_{o}V_{in}} \tag{36}\]  
The feedback function of the capacitor current is a proportion link, as shown in Equation (36). There is no integral and differential link in the equation, which greatly simplifies the control strategy. Because the control objects are integral link in both modes, the feedback function of the capacitor current is a proportion link for buck mode too. The control equivalent circuit diagram is shown in Figure 14. Then, the active damping control by capacitor current feedback is achieved. System damping can be controlled by adjusting \(R\).  
Figure 14: Equivalent control diagram with output capacitor current feedback.  
Figure 13: Block diagram of output current closed-loop control with LCR filter.  
The transfer function of loop gain in Figure 14 is derived as:  
\[T_{A}(s)=\frac{C_{i}(s)C_{id}(s)}{L\text{Cs}^{2}+R\text{Cs}+1} \tag{37}\]  
Substitute Equation (31) into Equation (37), then  
\[T_{A}(s)=\frac{V_{in}}{L_{in}s}\frac{G_{i}(s)}{L_{o}C_{o}s^{2}+R\text{C}_{o}s+1} \tag{38}\]  
\[\xi=\frac{R}{2}\sqrt{\frac{C_{o}}{L_{o}}} \tag{39}\]  
\[\omega_{r}=\sqrt{\frac{1}{L_{o}C_{o}}} \tag{40}\]  
where \(\xi\) is the damping coefficient and \(\omega_{r}\) is the resonance angular frequency of transfer. Function (38). In order to achieve proper damping without reducing the response speed, the value of the damping coefficient \(\xi\) is generally designed as 0.707. The appropriate active damping value \(K_{R}\) can be obtained by Formula (41):  
\[K_{R}=2\xi\sqrt{\frac{L_{o}}{C_{o}}} \tag{41}\]  
Figure 15 is the bode curve of current control loop before compensation. _Ta1_ is the loop gain in Equation (34). _Ta2_ is the loop gain in Equation (38). The resonance point is eliminated in _Ta2_. Figure 16 shows the loop gain with PI compensation. PI compensators \(K_{P}=0.01\), \(K_{I}=0.002\) are implemented in the current loop. The gain margin is 12.8 dB, phase margin is 56.4\({}^{\circ}\).  
Figure 15: Loop gain before compensation.