## 6 Simulation and Case Study
### Case Study for Generation and Reserve Schemes
This is because the generation cost of RG is set to be zero. The discrepancy between the forecast and upper limit of RG is determined by its standard deviation. The power vacancy is provided by other SGs. The generation schemes of SGs fluctuate inconsistently with the change of load. The reserve schemes for the IBG unit in MPPT and VSG mode are shown in Figures 14 and 15 From Figure 14, VSG-based RG units participating in system regulation would decrease the requirement of the upward reserve. The upward reserve allocated for RG is zero because the operating point for VSG-RG is set at its upper limit. From the fluctuation properties in each scenario, when the RG unit is under MPPT control, the upward reserve is determined according to the forecast uncertainties of the renewable generation and load. When the RG unit is under VSG control, the upward reserve is determined according to the uncertainty of the load forecast only. The requirement of the total upward reserve in the VSG scenario is identical to that of the original system. By considering N-1 constraints, the upward reserve is equally allocated between SGs. Figure 14: Upward reserve allocated for SGs with RG under MPPT or VSG mode. Figure 13: Generation scheme of RG. When the output of IBG unit 4 is fixed at its output limits, it cannot provide supporting power counteracting frequency dips. If the overall inertia property is insufficient, extra inertial reserves should be considered. The ROCOF can be expressed as  
\[ROCOF=\frac{d\Delta f}{dt}=\frac{\Delta P}{2H} \tag{31}\]  
where \(\Delta P\) is the step change of load, \(H\) is the inertia constant of the IBG unit. In power systems, the typical values of the system inertia constant \(H_{sys}\) and a large step increase of load \(\Delta P_{load}\) are 5 and 3%-5%, respectively [5; 13], then the maximum derivative of frequency (\(ROCOF_{\max}\)) can be obtained. In a synchronous area, the system inertia could be expressed as [36; 39]:  
\[H_{sys}=\sum_{i=1}^{n}\left(H_{i}\frac{S_{i}}{S_{sys}}\right) \tag{32}\]  
where \(i\) is the sequence number of the generation unit. By Equation (32), the required inertia constant \(H_{IBG}\) for the IBG unit (if its inertia property is needed) can be obtained. Therefore, when the overall inertia property is insufficient, the inertia reserve \(\Delta P_{IR}\) can be expressed as  
\[\Delta P_{IR}=2H_{IBG}\cdot ROCOF_{\max} \tag{33}\]  
and the scheduled power \(P_{schedule}\) for the IBG unit can be expressed as  
\[P_{4,t}^{R}\cdot=P_{4,t}^{R}-\Delta P_{IR} \tag{34}\]  
From Figure 15, VSG-based RG participating in system regulation would decrease the need for a downward reserve. Furthermore, the downward reserve allocated for each generation unit is reduced. Based on the fluctuation properties in each scenario, when the RG unit is under MPPT mode, the downward reserve is determined according to the forecast uncertainties of the renewable generation and load. When the RG unit is under VSG mode, the downward reserve is determined according to the uncertainties of the load forecast only. The requirement of the total downward reserve in the VSG scenario is identical to that of the original system. By considering N-1 constraints, the downward reserve is equally allocated between traditional SGs and VSG-RG. Figure 15: Downward reserve allocation for SGs and RG under MPPT or VSG mode. The total operation cost of the two tested scenarios is shown in Table 7, which indicates that there is no significant discrepancy. At every time step, under the VSG control, renewable penetration \(p_{ren}\) can be calculated as [40]:  
\[p_{ren}=\frac{P_{RG}}{L_{served}} \tag{35}\]  
where \(P_{RG}\) is total renewable generation at a certain time step, \(L_{served}\) is the load served in this time step. Then, from Table 8, the maximum renewable penetration is 23.6%. Moreover, scenarios where the renewable generation forecast is halved and doubled while the load remains constant are also considered to see the impacts of different penetration levels on the economic dispatch.