# A Fast, Decentralized, Self-Aligned Carrier Method for Multicellular Converters +
## 3 Proposed Decentralized Self-Aligned Carrier Method
### Proposed Decentralized Self-Aligned Level-Shifted Carrier Method  
In many applications, multilevel converters are controlled by the level-shifted PWM method. With some modifications, the previous algorithm can also be applied to this converter type, and hereinafter, it is called a decentralized self-aligned level-shifted carriers (DSA-LSC) method.  
In this method, the \((n-1)\)th cell sends to its next \(n\)th cell the information of its cell level (\(A_{n-1,\text{peak}}\)), its index number (\(i_{n-1}\)), and the total number of activated cells (\(N_{total}\)). Then, the \(n\)th cell controller updates its index number (\(i_{n}\)), the total number of cells (\(N_{total}\)) (see Equations (3) and (4)), and its carrier level by using the Formulas (8) and (9) as follows:  
\[\Delta A_{base}^{k+1}=\frac{2}{N_{total}^{k}} \tag{8}\]  
\[A_{n}^{k+1}=A_{n-1}^{k}+\Delta A_{base}^{k} \tag{9}\]  
The indexing rule of cell \(n\) at time step \(k\) and the determination of total number of cells (\(N_{total}\)) shown in Figure 7 are treated similarly as in the DSA-PSC method. The inputs and the outputs of a cell controller in the DSA-LSC method are clarified in the Table 2. The flowchart algorithm of the proposed DSA-LSC method is presented in Figure 8. Figure 9 shows the rule to apply for the carrier level update with DSA-LSC method. Besides, each cell communicates with its neighboring cell and exchanges information of modulation index of referenced voltage (\(V_{rf}\)) and information of reference frequency (\(F_{rf}\)).  
Figure 7: Connection between each cell controller with the proposed decentralized self-aligned level-shifted carriers (DSA-LSC) method.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Input** & \multicolumn{2}{c}{**Output**} \\ \hline EN & Enable & & \\ \hline ampl\_base & \(A_{n-1}^{k}\) & ampl\_min & \(A_{n}^{k}\) \\ \hline count\_in & Index from cell \(n-1\), \(t_{n-1}^{k}\) & count\_out & Index from cell \(n\), \(t_{n}^{k}\) \\ \hline number\_in & Received total number of cells \(N_{total}^{k}\) & number\_out & Transmitted total number of cells to the next cell \(N_{total}^{k}\) \\ \hline \multirow{3}{*}{Vrf\_in} & Received modulation index of referenced voltage from the previous cell & Vrf\_out & Transmitted modulation index of referenced voltage to the next cell \\ \hline \multirow{2}{*}{Frf\_in} & Received referenced frequency from the previous cell & Frf\_out & Transmitted frequency to the next cell \\ \hline \multirow{2}{*}{clk\_in} & Received synchronous clock pulse from the master cell & clk\_out & Transmitted synchronous clock pulse to other cell \\ \hline \hline \end{tabular}
\end{table}
Table 2: Input and output of cell controller with DSA-LSC method.  
Figure 8: Algorithm flowchart of the proposed DSA-LSC method.  
Similar to the case in Figure 5, the cell with an index of zero in Figure 7 is used as a master cell controller, which is, different from other cells, responsible for providing the modulation index of reference voltage, reference frequency, and clock synchronization for the rest of the system.  
If a cell is specified as a master cell controller, then \(V_{\textit{rf}}\) and \(F_{\textit{rf}}\) pin functions are not used. The synchronous clock pulse frequency from the master cell controller is transferred to all cells in the system.