## 6 Simulation and Case Study
### Case Study for Generation and Reserve Schemes  
The proposed approach is tested in two scenarios of RG under MPPT and VSG mode. The economic dispatch model is programmed in MATLAB and solved by Gurobi. Based on the original six-bus three-generator system [38], a renewable unit is added, which is shown in Figure 11. In VSG mode, the RG is denoted as generation unit 4. The system is tested for economic dispatching with six horizons. The predicted renewable generation and load, as well as the upper limit of RG in VSG mode, are shown in Table 4.  
The standard deviation of renewable generation and load are 5% and 1% of the forecast, respectively. The lower limit of renewable generation is 40% of the forecast. The FOR of each generator is 0.01. The cost coefficients for each unit are shown in Table 5. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Horizon** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline Renewable generation (MW) & 59.62 & 60.78 & 70.26 & 72.32 & 75.89 & 82.75 \\ Load (MW) & 370 & 330 & 290 & 260 & 280 & 350 \\ Upper limit in VSG mode (MW) & 50.68 & 51.66 & 59.72 & 61.47 & 64.51 & 70.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Predicted renewable generation and load. Figure 11: Generation scheme of SGs when the IBG is in VSG or MPPT mode. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**IIR** & **PFR** & **SFR** & **TFR** \\ \hline Time scale & Less than 1 s & seconds & Seconds to Mins & Hours-day ahead \\ \hline Activation & ROCOF & Frequency deviation & Frequency deviation last & Optimization \\  & crosses preset deadband & over a preset period & algorithms \\ \hline Reference & ROCOF & Frequency deviation & Frequency deviation & Load reference \\ \hline Control parameter & \(M\) & \(R\) & \(K_{I}\) & \(P_{\textit{refernace}}\) \\ \hline Participants & VSG-PEIs & VSG-PEIs & Dispatchable IBG & Dispatchable IBG \\ \hline Executor & Virtual inertia & Virtual speed governor & Virtual AGC & System operator \\ \hline Energy source & \multicolumn{3}{c}{Kinetic, electrostatic, or chemical, storage, deloading renewable sources} \\ \hline Restoration & The restoration of virtual rotor speed is coupling with the frequency recovery of the system \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Multiple temporal stages of frequency control of VSG-Based PEIs. When the preset LOLP and RSP are set to be 3% and 0.1%, respectively, the reserve requirements (MW) are shown in Table 6.  
From Table 6, in MPPT mode, RG aggravates the total reserve requirement. However, in VSG mode, the overall reserve requirement is reduced, which is equal to the original system (without the integration of RG). The generation schemes for SGs and the IBG unit are shown in Figures 12 and 13. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Horizon**} & \multicolumn{3}{c}{**Requirements of System**} & \multicolumn{2}{c}{**Overall Reserves (MW)**} \\  & **RG Unit in MPPT Mode** & **RG Unit in VSG Mode** \\  & \(R_{t}^{u}\) & \(R_{t}^{d}\) & \(R_{t}^{u}\) & \(R_{t}^{d}\) \\ \hline
1 & 12.91 & 14.254 & 11.88 & 11.1 \\
2 & 12.43 & 13.459 & 10.74 & 9.9 \\
3 & 13.48 & 13.666 & 9.31 & 8.7 \\
4 & 13.59 & 13.361 & 8.35 & 7.8 \\
5 & 14.41 & 14.147 & 8.99 & 8.4 \\
6 & 15.68 & 16.258 & 11.24 & 10.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Requirement for operating reserve capacity. Figure 12: Generation scheme of SGs when the IBG is in VSG or MPPT mode. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Generation Unit**} & \multicolumn{3}{c}{**Cost Coefficients (\$/MW)**} \\  & \(c_{2,i}\) & \(c_{1,i}\) & \(c_{0,i}\) & \(c_{i}^{u}\) & \(c_{i}^{d}\) \\ \hline
1 & 0.00533 & 11.699 & 231.1 & 5.835 & 5.835 \\
2 & 0.00899 & 10.333 & 200 & 5.166 & 5.166 \\
3 & 0.00741 & 10.833 & 240 & 5.417 & 5.417 \\
4 (VSG) & 0 & 0 & 0 & 4 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Generation cost coefficients. From Figures 12 and 13, in MPPT mode, RG output equals the forecast value. In VSG mode, RG output is at its upper limit.