# A Fast, Decentralized, Self-Aligned Carrier Method for Multicellular Converters +
## 4 Simulation Results
### Evaluate the System Configuration Time  
From the cell controller connection of DSA-PSC method and DSA-LSC method, shown accordingly in Figures 5 and 7, it can be seen that, from starting up, both methods reach the steady-state after \(2N\) time steps. Therefore, the configuration time of both methods is:  
\[T_{configuration}=2N\cdot T_{s} \tag{10}\]  
where \(N\) is the number of active cells and \(T_{s}\) is the sampling time.  
Figure 21 compares the configuration time of the conventional method (using modified updating rules in (2) with K = 0.66) to that of the proposed self-aligned phase-shifted carrier method. For estimating its configuration time, the conventional method is simulated with different values of \(N\), and the system is considered as reaching steady-state when the errors of inter-carrier phase-shifts are smaller than \(10^{-4}\) degree (i.e., \(\varepsilon(\Delta\theta_{n,\,n+1})\leq 10^{-4}\) degree). Meanwhile, the configuration time of the proposed DSA-PSC method is estimated directly using (10). From Figure 21, it can be seen that the reduction of configuration time is the key advantage of the proposed DSA-PSC method. The higher the number of cells is, the larger the reduction of time steps of the proposed method to reach the steady-state is.  
To study in detail the configuration process of the conventional method and the proposed method, simulations are conducted for the systems controlled by these methods with different values of cell numbers (\(N\) = 4, 6, and 13). For each value of \(N\), the variation of carrier phases as well as inter-carrier phase-shifts during starting up processes of both control methods are presented in Figures 22 and 23 (for \(N\) = 4), in Figures 24 and 25 (for \(N\) = 6), and in Figures 26 and 27 (for \(N\) = 13). These simulation results confirm the advantage of the proposed DSA-PSC method in terms of lower configuration time and zero inter-carrier phase-shifts relative error, which is summarized in Table 5.  
Figure 21: Configuration time of conventional (modified updating rule) and proposed (DSA-PSC) self-aligned phase-shifted carrier methods.  
Figure 23: The inter-carrier phase-shifts of a converter with four-carriers, startup with (**a**) conventional modified updating rule; (**b**) proposed DSA-PSC.  
Figure 24: Configuration process of a converter with six-carriers, startup with (**a**) conventional modified updating rule; (**b**) proposed DSA-PSC.  
Figure 22: Configuration process of a converter with four-carriers, startup with (**a**) conventional modified updating rule; (**b**) proposed DSA-PSC.  
Figure 27: The inter-carrier phase-shifts of a converter with 13-carriers, startup with (**a**) conventional modified updating rule; (**b**) proposed DSA-PSC.  
Figure 25: The inter-carrier phase-shifts of a converter with six-carriers, startup with (**a**) conventional modified updating rule; (**b**) proposed DSA-PSC.  
Figure 26: Configuration process of a converter with 13-carriers, startup with (**a**) conventional modified updating rule; (**b**) proposed DSA-PSC.  
Moreover, it should be noted that the proposed method can be applied to any number of carriers (\(N\geq 1\)), and it is different from the conventional method, which can be applied only for the system with \(N\geq 3\), as mentioned in Section 2.