## 4 Case Studies
### Random Disturbances
However, when the scale of the charging station increases, the centralized algorithms mentioned above have some distinct drawbacks, such as low calculation speed and weak optimum searching ability; thus, the 4-16 seconds' time-scale requirement of AGC real-time control is hard to satisfy. However, the cost consensus algorithm still has the advantages of high convergence speed and stable optimization outcome, which represents higher practicability on engineering problems. Compared with other intelligence algorithms, the LP algorithm is a traditional optimization algorithm that can find the only definite optimal solution in the feasible domain, thus the total adjustment cost is the lowest. Besides, PROP adopts the fixed proportional allocation strategy based on the adjustable capacity, which lacks optimization objectives, such that its total adjustment cost is the highest among all the algorithms. Table 4 shows the control performance standard index and total adjustment cost of the Hainan power grid without the participation of EV. The comparison between Tables 3 and 4 shows that, as the batteries of EV have a fast response speed, no climbing constraints, and low frequency regulation delay, the simulation results with EV participating in frequency regulation are better than those without EV. Hence, the participation of EV in AGC power allocation can effectively reduce the regional control deviation and restrain the load fluctuation. Meanwhile, as the time delay of the hydro-power unit is smaller than that of the thermal power unit and the climbing speed is higher, the simulation results are more desirable when the total power instruction \(\Delta P_{\text{EV}\,\Sigma}\) of EV centralized control center is all borne by the hydro-power unit G6 rather than coal-fired unit G3. Besides, this also highlights that the participation of hydro-power in power system frequency regulation is beneficial to improve the CPS index and the economic performance index of the power grid. Figure 7 demonstrates the power tracking and frequency deviation curves (0-3 h) obtained by the cost consensus algorithm under random square wave load disturbance in the Hainan power grid. One can readily find that the total power instruction \(\Delta P_{\text{EV}\,\Sigma}\) issued by the proportional-integral (PI) controller can effectively track the load disturbance, while the actual total output of the unit basically matches the load disturbance. Meanwhile, the frequency deviation of grid caused by the load disturbances can be maintained within a reasonable range, which can also quickly recover to the ideal value. The above results verify the feasibility of the cost consensus algorithm in the allocation of different charging stations. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Scenarios** & **[A/] (Hz)** & **[ACE] (MW)** & **CPS1 (\%)** & **CPS2 (\%)** & **CPS (\%)** & **Cost (10\({}^{3}\) yuan)** \\ \hline Coal-fired unit G3 replaces EV & \(9.8293\times 10^{4}\) & 0.5199 & 199.9753 & 100 & 100 & 11.73 \\ Hydropower generator G6 replaces EV & \(9.3228\times 10^{4}\) & 0.5209 & 199.9762 & 100 & 100 & 11.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: AGC performance indices obtained by different scenarios without electric vehicles (EVs) in the Hainan power grid in July. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & **[A/] (Hz)** & **[ACE] (MW)** & **CPS1 (\%)** & **CPS2 (\%)** & **CPS (\%)** & **Cost (10\({}^{3}\) yuan)** \\ \hline Cost consensus algorithm & \(9.0017\times 10^{4}\) & **0.5176** & **199.9767** & 100 & 100 & 10.94 \\ GA & \(9.0018\times 10^{4}\) & 0.5177 & **199.9767** & 100 & 100 & 10.91 \\ PSO & **0.0014 \(\times 10^{4}\)** & **0.5176** & **199.9767** & 100 & 100 & 10.92 \\ GSO & **9.0014 \(\times 10^{4}\)** & **0.5176** & **1999.9767** & 100 & 100 & 10.89 \\ LP & \(9.2019\times 10^{4}\) & 0.5723 & 199.9747 & 100 & 100 & **10.73** \\ PROP & **9.0014 \(\times 10^{4}\)** & **0.5176** & **199.9767** & 100 & 100 & 10.95 \\ \hline \hline \end{tabular}
\end{table}