## 4 Analysis and Simulation Verification
### Optimization of Multiple Parameters  
When the system stability cannot be satisfied by the optimization of a single parameter, it is necessary to promote system stability through joint adjustment of multiple parameters. To verify the adaptability of the method proposed in this paper to this situation, the control parameters of the VSCs are modified. The control parameters are listed in Table 10. Define the system as system B. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Value** & **Value** & **Value** & **Variation** \\ \hline \(k_{\text{ip1}}\) Parameter & 2.175 \(\times\) 10\({}^{-3}\) & 1.800 \(\times\) 10\({}^{-3}\) & 4.600 \(\times\) 10\({}^{-4}\) & 1.715 \(\times\) 10\({}^{-3}\) \\ Harmonic Content & 32.81\% & 30.68\% & 5.050\% & 27.76\% \\ \hline \(k_{\text{ip2}}\) Parameter & 6.500 \(\times\) 10\({}^{-3}\) & 3.600 \(\times\) 10\({}^{-3}\) & 1.400 \(\times\) 10\({}^{-3}\) & 5.100 \(\times\) 10\({}^{-3}\) \\ Harmonic Content & 32.81\% & 28.03\% & 12.22\% & 20.59\% \\ \hline \(k_{\text{ip3}}\) Parameter & 5.800 \(\times\) 10\({}^{-3}\) & 2.900 \(\times\) 10\({}^{-3}\) & 7.000 \(\times\) 10\({}^{-4}\) & 5.1000 \(\times\) 10\({}^{-3}\) \\ Harmonic Content & 32.81\% & 27.84\% & 8.060\% & 24.75\% \\ \hline \(k_{\text{p1}\text{p1}}\) Parameter & 3.994 & 3.674 & 3.371 & 0.6230 \\ Harmonic Content & 32.81\% & 28.78\% & 27.99\% & 4.820\% \\ \hline \(k_{\text{p1}\text{p2}}\) Parameter & 0.7189 & 0.3994 & 9.590 \(\times\) 10\({}^{-2}\) & 0.6230 \\ Harmonic Content & 32.81\% & 24.98\% & 12.22\% & 20.59\% \\ \hline \(k_{\text{p1}\text{p3}}\) Parameter & 0.6390 & 0.3195 & 1.600 \(\times\) 10\({}^{-2}\) & 0.6230 \\ Harmonic Content & 32.81\% & 24.76\% & 14.02\% & 18.79\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The harmonic content of PCC voltage before and after VSC control parameter modification. Figure 14: PCC voltage waveforms before and after VSC parameter modification: (**a**) \(k_{\text{ip1}}\) parameter modification; (**b**) \(k_{\text{ip2}}\) parameter modification; (**c**) \(k_{\text{ip3}}\) parameter modification; (**d**) \(k_{\text{p1}\text{p1}}\) parameter modification; (**e**) \(k_{\text{p1}\text{p2}}\) parameter modification; (**f**) \(k_{\text{p1}\text{p3}}\) parameter modification. According to Equation (22), the \(g(f)\) function is constructed by obtaining the \(\mathbf{L}\)(s) for the multi-converter grid-tied system, and is plotted in Figure 15. Figure 15 shows the minimum value of the \(g(f)\) is \(-6.446\times 10^{-1}\) less than 0 at point \(M\), indicating the system is unstable. The parameter sensitivity of each VSC parameter under the \(g(f)\) at the point \(M\) is calculated, respectively, according to Equation (25) and presented in Table 3. Sorting parameters based on the magnitude of their sensitivities, the influence of each VSC parameter on system stability is as follows: \(k_{\text{ip2}}>k_{\text{ip3}}>k_{\text{ip1}}>k_{\text{plp2}}>k_{\text{plplp3}}>k_{ \text{plplp1}}\). The same analysis method as in Figure 11 is used to verify the correctness of the parameter sensitivity analysis method. The variation of \(k_{\text{ip1}}\) is \(5.000\times 10^{-4}\) and the variation of other parameters is \(-5.000\times 10^{-4}\). Figure 16 depicts that increasing \(k_{\text{ip1}}\) and decreasing other parameters both bring the Nyquist curves of system B closer to the \((-1,\,\,j0)\) point, and system B stability is improved. According to the degree to which changing parameters makes the Nyquist curves approach \((-1,\,\,j0)\), the ranking of parameters is as follows: \(k_{\text{ip2}}>k_{\text{ip3}}>k_{\text{ip1}}>k_{\text{plplp2}}>k_{\text{plp3}}>k_{ \text{plplp1}}\). This ranking aligns with the result of the parameter sensitivity analysis method. Figure 16: Nyquist curves of system B with different VSC control parameters: (**a**) integrated graph; (**b**) partial enlargement of (**a**); (**c**) partial enlargement of (**b**). Figure 15: Stability evaluation function of system B under initial parameters (in Table 10).