# Modular Combined DC-DC Autotransformer for Offshore Wind Power Integration with DC Collection
## 3 MCAT Main Circuit Parameters Selection  
MCAT main circuit parameters consist of MMC main circuit parameters, DC-isolation capacitors, and compensation inductors. As the selection methods of MMC main circuit parameters (e.g., sub-module capacitors, arm inductors, etc.,) have been discussed particularly in [18], this section only focuses on DC-isolation capacitors and compensation inductors. For the sake of clarity of this section, Table 11 with explanations of the abbreviations and symbols used in this section are provided in Appendix A.  
The voltage \(u_{cj}\) of \(C_{j}\) (\(j=1,\,2,\,\ldots,\,M+2N\)) is always composed of the DC offset voltage \(U_{\rm vdcj}\) and the AC voltage \(\Delta t_{cj}\), which is expressed as:  
\[u_{cj}=U_{\rm vdcj}+\Delta u_{cj} \tag{7}\]  
\(U_{\rm vdcj}\) is supposed to be eliminated by the DC-isolation capacitor. The degree of \(\Delta u_{cj}\) fluctuations could affect the stability of the AC side. In this regard, the value of capacitors should be taken as large as possible to reduce the \(\Delta u_{cj}\) fluctuations. On the other hand, DC-isolation capacitors need to be charged by the connected MMCs in the start orfault recovery process of MCAT and excessive value would slow down the charging rate. Therefore, DC-isolation capacitors need to be selected by considering the above two factors.  
Ignoring the power losses in steady-state operation, the active power \(P_{\text{MMC}j}\) and the reactive power \(Q_{\text{MMC}j}\) transmitted by the MMC\({}_{j}\) could be described as:  
\[\left\{\begin{array}{l}P_{\text{MMC}j}=\sqrt{3}U_{\text{vac}j}I_{j}\cos\delta _{j}\\ Q_{\text{MMC}j}=\sqrt{3}U_{\text{vac}j}I_{j}\sin\delta_{j}\end{array}\right. \tag{8}\]  
where \(U_{\text{vac}j}\) is the fundamental RMS (root mean square) L-L (line-line) voltage at MMC\({}_{j}\) valve side, \(I_{j}\) is the fundamental RMS line current at MMC\({}_{j}\) valve side, and \(\delta_{j}\) is the phase angle between \(U_{\text{vac}j}\) and \(I_{j}\). In the steady-state condition, \(U_{\text{vac}}\), \(I\), and \(\delta\) of each MMC are similar. Furthermore, if MMC\({}_{j}\) adopts reactive power control with the reference value 0 pu, \(Q_{\text{MMC}j}\) will be controlled to 0, \(U_{\text{vac}j}\) and \(I_{j}\) will be in the same phase (\(\delta_{j}=0\)). Considering \(\delta_{j}=0\) and ignoring high-order harmonics, \(\Delta U_{\text{cj}}\) is described as:  
\[\Delta U_{\text{cj}}=\frac{I_{j}}{\omega C_{j}}=\frac{P_{\text{MMC}j}}{\sqrt{ 3}U_{\text{vac}j}}\frac{1}{2\pi fC_{j}} \tag{9}\]  
where \(\Delta U_{\text{cj}}\) is the fundamental RMS voltage of \(\Delta u_{\text{cj}}\), \(f\) is the fundamental frequency at the MCAT AC side. The voltage fluctuation rate \(\alpha_{j}\) of \(C_{j}\) is defined as:  
\[\alpha_{j}=\frac{\sqrt{2}\Delta U_{\text{cj}}}{U_{\text{vdc}j}}\times 100\% \tag{10}\]  
where, \(\alpha_{j}\) is the fluctuation ratio of \(u_{\text{cj}}\), and it should be limited within 25% according to engineering experience in [19].  
In (9) and (10), \(U_{\text{vac}}\) of each MMC and \(f\) in the MCAT are similar under the steady-state operation, but \(U_{\text{vdc}}\) and \(P_{\text{MMC}}\) of the LVM are different from those of the HVM. As a result, parameters of DC-isolation capacitors C and compensation inductors \(L\) in HVM and LVM are supposed to be calculated respectively.