# Load Frequency Optimal Active Disturbance Rejection Control of Hybrid Power System
## 4 Experimental Results and Analysis
### The Step-Load Disturbance  
Suppose that the first region is interfered with by a step load disturbance at \(t1=5\) s, \(\Delta P_{L,1}=1\)\(p.u\); \(t2=15\) s, \(\Delta P_{L,2}=2\)\(p.u\) and \(t3=25\) s, \(\Delta P_{L,3}=1.5\)\(p.u\). The response results of the frequency deviation of the three regions are shown in Figures 4-6, respectively. The tie-line power exchanges of the three regions are displayed in Figures 7-9. The optimization results of different methods, such as LQR, ESO-LQR, and the proposed optimal ADRC, which is marked as ADRC-LQR, are also presented. In order to better observe the results of the comparison, the dramatically changed parts have been enlarged in the small images.  
\begin{table}
\begin{tabular}{l l l} \hline
**Description** & **Parameter** & **Value** \\ \hline PVG Gain & \(K_{\text{P0}}\) & 1 \\ Time constant of PVG & \(T_{\text{P0}}\) & 1.8 \\ Pitch actuator gain & \(K_{\text{P1}}\) & 1.25 \\ Time constant of WTG & \(T_{\text{P1}}\) & 6.0 \\ Time constant of WTG & \(T_{\text{P2}}\) & 0.041 \\ Blade characteristic & \(K_{\text{PC}}\) & 0.80 \\ Droop of each WTG unit & \(R_{\omega}\) & 0.024 \\ Load damping coefficient & \(D_{i}\) & 2.0 \\  & \(T_{12}\) & 2.5 \\ Synchronizing torque coefficient & \(T_{13}\) & 5.0 \\  & \(T_{23}\) & 3.8 \\ \hline \end{tabular}
\end{table}
Table 1: The System Parameter Values.  
\begin{table}
\begin{tabular}{l l} \hline
**Parameter** & **Value** \\ \hline \(\alpha_{\text{G4}}\) & 0.52 \\ \(\alpha_{\text{G5}}\) & 0.1 \\ \(\alpha_{\text{G6}}\) & 0.1 \\ \(\alpha_{\text{G7}}\) & 0.1 \\ \(\alpha_{\text{PV2}}\) & 0.18 \\ \hline \end{tabular}
\end{table}
Table 2: The participation Factors for area 1.  
\begin{table}
\begin{tabular}{l l} \hline
**Parameter** & **Value** \\ \hline \(\alpha_{\text{G4}}\) & 0.52 \\ \(\alpha_{\text{G5}}\) & 0.1 \\ \(\alpha_{\text{G6}}\) & 0.1 \\ \(\alpha_{\text{G7}}\) & 0.1 \\ \(\alpha_{\text{PV2}}\) & 0.18 \\ \hline \end{tabular}
\end{table}
Table 3: The participation Factors for area 2.  
Figure 4: Comparison results of frequency deviation in region 1.  
Figure 5: Comparison results of frequency deviation in region 2.  
Figure 6: Comparison results of frequency deviation in region 3.  
In Figure 4, the steady-state error of region 1 is \(1.25\times 10^{-3}\) Hz using the LQR method. The steady-state error is 0 when using the LQR with ESO and the proposed methods. From  
Figure 8: Comparison results of tie-line exchanged power between region 2 and region 3.  
Figure 7: Comparison results of tie-line exchanged power between region 1 and region 2.  
Figure 9: Comparison results of tie-line exchanged power between region 3 and region 1.  
stability in this state. The ADRC-LQR method exhibits convergence approximately 3 s earlier than the LQR-ESO method.  
Regarding the dynamic response, the proposed LFC system, which integrates the ADRC and LQR control methods, demonstrates the capability to efficiently attain the desired set value with minimal occurrence of overshoot and undershoot. This demonstration convincingly showcases the efficacy of the proposed methodology.