# Modular Combined DC-DC Autotransformer for Offshore Wind Power Integration with DC Collection
## 3 MCAT Main Circuit Parameters Selection
### Parameter Calculation of DC-Isolation Capacitors and Compensation Inductors in LVM  
In the LVM, the calculation of DC-isolation capacitors and compensation inductors depend on \(M\), which is discussed as follows:  
1. When \(M=1\), the DC-isolation capacitors and compensation inductors are excluded from the LVM.
2. When \(M=2\), \(4\), \(6\),..., \(\text{MMC}_{\text{L},M/2}\) (and \(\text{MMC}_{\text{L},(M/2)+1}\)) has the lowest DC offset voltage in the LVM, and \(\alpha_{\text{L},M/2}\) (and \(\alpha_{\text{L},(M/2)+1}\)) is largest correspondingly.
3. When \(M=3\), \(5\), \(7\),..., \(\text{MMC}_{\text{L},(M-1)/2}\) (and \(\text{MMC}_{\text{L},(M+3)/2}\)) has the lowest DC offset voltage, and \(\alpha_{\text{L},(M-1)/2}\) (and \(\alpha_{\text{L},(M+3)/2}\)) is largest correspondingly.  
Take case (2) as an example to calculate DC-isolation capacitors and compensation inductors. \(U_{\text{vacL},M/2}\), \(U_{\text{vdcL},M/2}\), and \(P_{\text{MMCL},M/2}\) are expressed as [17]:  
\[u_{\text{vL},\text{M}/2}=u_{\text{vacL},\text{M}/2}+U_{\text{vdcL},\text{M}/2} \tag{18}\]  
\[U_{\text{vacL},M/2}=\frac{1.05U_{\text{dcL},M/2}}{2} \tag{19}\]  
\[U_{\text{vdcL},M/2}=\frac{U_{\text{dcL},M/2}}{2} \tag{20}\]  
\[P_{\text{MMCL},M/2}=\frac{(1-1/k_{\text{dc}})P_{\text{N}}}{M} \tag{21}\]  
where \(u_{\text{vL},M/2}\) is the voltage at MMC \({}_{\text{L},M/2}\) valve side, \(u_{\text{vacL},M/2}\) and \(U_{\text{vdcL},M/2}\) are the AC component and DC component of \(u_{\text{vL},M/2}\). \(U_{\text{vacL},M/2}\) are the fundamental RMS L-L voltage at MMC\({}_{\text{L},M/2}\) valve side, \(U_{\text{dcL},M/2}\) is the DC voltage of MMC\({}_{\text{L},M/2}\). \(P_{\text{MMCL},M/2}\) is the power transmitted by MMC\({}_{\text{L},M/2}\). Substituting these variables into (10), \(C_{\text{L},M/2}\) is described as:  
\[\begin{array}{ll}C_{\text{L},M/2}&=\frac{\sqrt{2}(1-1/k_{\text{dc}})P_{ \text{N}}/M}{\sqrt{3}\times\frac{12}{2}U_{\text{dcL},M/2}2\pi/\text{C}_{\text {L},M/2}}\frac{1}{\frac{U_{\text{dcL},M/2}}{2}}\\ &=0.496\frac{(1-1/k_{\text{dc}})P_{\text{N}}}{M/\alpha_{\text{L},M/2}l_{\text {dcL},M/2}^{2}}\end{array} \tag{22}\]  
where \(\alpha_{\text{L},M/2}\) is the fluctuation ratio of \(u_{\text{CL},M/2}\) of \(C_{\text{L},M/2}\). After specifying \(\alpha_{\text{L},M/2}\), the corresponding value of \(C_{\text{L},M/2}\) could be calculated by (22). The DC-isolation capacitor and the compensation inductor occur in series resonation at resonance frequency \(f\) so that they produce no reactive power. Therefore, the calculation expression of \(L_{\text{L},M/2}\) is:  
\[L_{L,M/2}=\frac{1}{\left(2\pi f\right)^{2}\text{C}_{L,M/2}} \tag{23}\]After obtaining the values of \(C_{\text{L},M/2}\) and \(L_{\text{L},M/2}\), the value of other DC-isolation capacitors in the LVM could be taken as the \(C_{\text{L},M/2}\), so that their \(\alpha\) are smaller than \(\alpha_{\text{L},M/2}\) and \(\alpha_{\text{L},(M/2)+1}\), as mentioned above. The values of other DC-isolation capacitors and compensation inductors in the LVM are described as:  
\[\left\{\begin{array}{l}C_{\text{L},1}=C_{\text{L},2}=\cdots=C_{\text{L},M/2} =\cdots=C_{\text{L},M}\\ L_{\text{L},1}=L_{\text{L},2}=\cdots=L_{\text{L},M/2}=\cdots=L_{\text{L},M} \end{array}\right. \tag{24}\]