## 5 Results
### Step Change of Load  
The time responses to the step change of \(\Delta P_{\text{L}i}\) are shown in Figures 11-13. In Figure 11 (left), it is clear that the frequency deviations \(\Delta f_{i}\) in all three CAs appeared following a step change of \(\Delta P_{\text{L}i}\) that was applied. After the first step change, \(\Delta f_{1}\) and \(\Delta f_{2}\) were negative due to the positive step change of \(\Delta P_{\text{L}i}\), whereas \(\Delta f_{3}\) was positive due to the negative step change of \(\Delta P_{\text{L}i}\). Note that after the second step change, the signs were opposite. The primary frequency control decreased \(|\Delta f_{i}|\) in about 15-25 s after the step change of \(\Delta P_{\text{L}i}\); then, LFC decreased \(|\Delta f_{i}|\) slowly. The results show that the impact of the INP and CBRR on \(\Delta f_{i}\) is not significant. The impact of the INP and CBRR is shown more obviously in Figures 11 (right) and 12 (left). In all three CAs, the values of \(ACE_{i}\), \(\Delta P_{\text{S}ci}\) and \(\Delta P_{\text{e}i}\) were decreased with the INP and CBRR. Furthermore, the INP and CBRR clearly increased \(\Delta P_{i}\), due to the increased tie-line power flow between the CAs. The signs of \(P_{\text{d}i}\) and \(P_{\text{c}ori}\) are opposite, as shown in Figure 12 (right). A 2 s time delay is seen, due to SH with \(T_{\text{s}}\) = 2 s. Note that the time responses of \(P_{\text{d}i}\) and \(P_{\text{c}ori}\) were already described in Section 2.4 and Figure 7b, where the same case was performed. The time responses \(ACE_{i}\) and \(\Delta P_{\text{S}ci}\) with and without the \(P_{\text{c}ori}\) adjustment function are shown in Figure 13. Without the \(P_{\text{c}ori}\) adjustment, \(ACE_{i}\) was increased and \(\Delta P_{\text{S}ci}\) was undesirably increased, due to switching between the INP and the CBRR, which caused undesirable \(\Delta P_{\text{c}ori}\) sign changes. Clearly, in all three CAs, the values of \(ACE_{i}\) and \(\Delta P_{\text{S}ci}\) were decreased with the \(P_{\text{c}ori}\) adjustment. Note that, in Figure 13, the same example is performed as described in Section 4.2.1 and shown in Figures 11 and 12. The difference can \begin{table}
\begin{tabular}{c c c} \hline \(\mu_{\text{L}1}\) [pu-103] & \(\mu_{\text{L}2}\) [pu-103] & \(\mu_{\text{L}3}\) [pu-103] \\ \hline \(-\)2.501 & 29.526 & \(-\)0.693 \\ \hline \(\sigma_{\text{L}1}\) [pu-103] & \(\sigma_{\text{L}2}\) [pu-103] & \(\sigma_{\text{L}3}\) [pu-103] \\ \hline
74.891 & 76.890 & 78.827 \\ \hline \(\rho_{\text{L}12}\) & \(\rho_{\text{L}23}\) & \(\rho_{\text{L}31}\) \\ \hline \(-\)0.056 & 0.059 & 0.004 \\ \hline \end{tabular}
\end{table} 
Table 2: Statistical parameters of random loads. Both mechanisms reduce the \(|\mu_{\text{RoCoFi}+}|\) and \(|\mu_{\text{RoCoFi}-}|\), with the reduction being most pronounced when both mechanisms operate simultaneously according to Table 3. However, there are no unambiguous conclusions as to which mechanism reduces \(|\mu_{\text{RoCoFi}+}|\) and \(|\mu_{\text{RoCoFi}-}|\) more, and, in most cases, it is the INP. When both mechanisms operate simultaneously, \(|\mu_{\text{PsG}+}|\) and \(|\mu_{\text{PsG}-}|\) are greatly reduced according to Table 3. However, the results of the separate operation of the mechanisms show that the impact of INP is greater than the impact of CBRR. This is expected, as the CBRR only activates the RRs in the cooperating CAs. Moreover, the reduction of \(|\sigma_{\text{PsG}+}|\) and \(|\sigma_{\text{PsG}-}|\) is most noticeable when both mechanisms operate simultaneously. However, the results of the separate operation of the mechanisms show that the impact of the INP is greater than the impact of the CBRR. The conclusions for \(|\Delta W_{\text{e}+}|\) and \(|\Delta W_{\text{e}-}|\) are similar to \(|\mu_{\text{PsG}+}|\) and \(|\mu_{\text{PsG}-}|\) according to Table 4, which is expected, as this indicator describes the response of the control units.