# A Fast, Decentralized, Self-Aligned Carrier Method for Multicellular Converters +
## 3 Proposed Decentralized Self-Aligned Carrier Method
### Proposed Decentralized Self-Aligned Phase-Shifted Carrier Method  
This proposed method is named as decentralized self-aligned PS carriers (DSA-PSC), and its principle is shown graphically in Figure 4. In this method, the (\(n\)\(-\)1)th cell sends to the next \(n\)th cell the information of its angle (\(\theta_{n-1}\)), its index number (\(i_{n-1}\)), and the total number of activated cells of the converter (\(N_{total}\)). Then, each cell controller determines  
Figure 3: Analysis of convergence for a six-carriers system, (**a**) carrier phase; (**b**) inter-carrier phase-shift.  
the elementary phase-angle (\(\Delta\theta_{\textit{base}}\)) and updates its own phase-angle (\(\theta_{n}\)) based on the received information by using the Equations (4)-(7) as follows:  
\[i_{n}^{k+1}=i_{n-1}^{k}+1;n\in[1,2,\ldots N] \tag{4}\]  
\[\left\{\begin{array}{l}N_{total\_1}^{k+1}=i_{N}^{k}\\ N_{total\_n}^{k+1}=N_{total\_(n-1)}^{k};n\in[2,\ldots N]\end{array}\right. \tag{5}\]  
\[\Delta\theta_{\textit{base}}^{k+1}=\frac{360^{\circ}}{N_{total}^{k}} \tag{6}\]  
\[\theta_{n}^{k+1}=mod\Big{(}\theta_{n-1}^{k}+\Delta\theta_{\textit{base}}^{k},360\Big{)} \tag{7}\]  
The indexing rule is simple; in cell \(n\), at time step \(k\), the index number \(i_{n-1}^{k}\) of cell \(n-1\) (named as count_in) is read and augmented by one and assigned as count_out (\(i_{n}^{k+1}\)), and this sequence is applied to all cells. Since the indexing communication line is an open loop chain, the cell at the open point has the index value \(i_{1}^{k}\) because the previous number read is zero (no information). The information count_out of last cell is recognized as the total number of activated cells in series, and it can be transmitted to all the cells via the numbering communication link (Figure 5).  
Moreover, each cell transfers to its neighboring cell the information of referenced voltage (\(V_{\textit{rf}}\)).  
Figure 4: Proposed update rule of phase-angle of carriers in decentralized self-aligned phase-shift (PS) carriers (DSA-PSC) method, (**a**) update rule principle; (**b**) phase-shifted carriers.  
Figure 5: Connection between each cell controller with the proposed DSA-PSC method.  
In Figure 5, the cell with index of zero is used as a master cell controller, which is, different from other cells, responsible for providing duty-cycle and clock synchronization for the rest of the system.  
If a cell is indicated as a master cell controller, then the \(V_{\prime\prime}\) pin function is not used. The synchronous clock pulse frequency from the master cell controller is transmitted to all cells in the system.  
The inputs and the outputs of a cell model are described in Table 1.  
The flowchart algorithm of the proposed DSA-PSC method is shown in Figure 6. If a cell has to be removed from the converter, i.e., deactivated, the bypassing of a cell is realized using an enable bit (\(EN\)).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Input** & & **Output** \\ \hline EN & Enable & & \\ \hline \hline \multirow{2}{*}{eta\_base} & \(\theta_{n-1}^{k}\) & send\_teta & \(\theta_{n}^{k}\) \\ \hline count\_in & Index from cell \(n-1\), \(i_{n-1}^{k}\) & count\_out & Index from cell \(n\), \(i_{n}^{k}\) \\ \hline \multirow{2}{*}{number\_in} & Received total number from & & Transmitted total number to \\  & previous cells \(N_{total}^{k}\) & number\_out & next cell \(N_{total}^{k}\) \\ \hline \multirow{2}{*}{Vrf\_in} & Received signal reference & & Transmitted signal reference \\  & voltage from previous cell & & voltage to next cell \\ \hline \multirow{2}{*}{clk\_in} & Received synchronous clock & & Transmitted synchronous \\  & pulse from master cell & & clock pulse to other cell \\ \hline \hline \end{tabular}
\end{table}
Table 1: Input and output of cell model in DSA-PSC method.  
Figure 6: Algorithm flowchart of the proposed DSA-PSC method.