## 4 Reliability Criteria for IBG Units in VSG Mode  
As the conventional power system is undergoing an evolving transition to a converter-dominated regime, IBG in the future grid will inevitably take the role (regulating the overall energy balance for stability and reliability) of SGs. For the process of electricity generation, every generation unit includes two components: the primary energy input, and electric power generation, as shown in Figure 4.  
If VSG-IBG units participate in secondary and tertiary frequency regulations, persistent power reserves for power increment and decrement counteracting frequency deviations are indispensable. In other words, the capabilities of frequency regulation are determined by the availability of the reserved power input. For renewable energy sources alone (regardless of energy storage accessories), the reserved energy comes from curtailable generation ability. Generally, active power reserves using RG units can be realized through two types of control strategies: (1) the delta control, which deloads RG units by constant percentages or values [36], and (2) the balance control, which controls the RG output through an upper limit [37]. The reserves by the delta control are still stochastic on the basis of meteorological conditions. It is noted that the decisive difference in the primary input between the SGs and the RG units is whether the primary power is dispatchable or stochastic. Inspired by this, in this paper, the uncertainty of renewable generation is eliminated based on a deloading strategy with fixed upper limits. The principle of deloading control with fixed upper limits is shown in Figure 5.  
Figure 4: Comparison between SGs and IBG.  
As the forecast error of RG obeys Gaussian distribution, RG output also obeys Gaussian distribution, whereby the probability density function is \(f(P_{t}^{R})\sim N(P_{t}^{FR},r_{t}{}^{2})\). The upper output limit of renewable generation unit can be set as  
\[P_{t,\text{max}}^{R}=P_{t}^{F}-3r_{t} \tag{12}\]  
which is shown in Figure 6.  
In this way, the property of the generation profile of IBG is modified with fixed upper limits, and the generation uncertainties of the RG units could be eliminated. Consequently, after the transformation, the uncertainty mainly lies in the load disturbances, and the net load forecast error is  
\[\Delta P_{t}^{N}=\Delta P_{t}^{D} \tag{13}\]  
Figure 5: Curtailed IBG with fixed upper generation limit.  
Figure 6: Probability density function of renewable generation.  
The LOLP for a specific period \(t\) in power system with grid-supporting IBG can be expressed as  
\[\begin{array}{l}p_{t}^{LOLP}=\prod\limits_{i=1}^{N}{(1-p_{i}^{\text{FO}})\cdot p \Big{\{}(\Delta P_{t}^{N}-R_{t}^{u})>0\Big{\}}+}\\ \sum\limits_{i=1}^{N}{p_{i}^{\text{FO}}}.\prod\limits_{\begin{array}{l}{N}\\ {j=1}\\ {j\
eq i}\end{array}}^{N}{(1-p_{j}^{\text{FO}})\cdot p\Big{\{}(\Delta P_{t}^{N }+P_{i}^{MAX}-R_{t}^{u})>0\Big{\}}}\\ \end{array} \tag{14}\]  
where \(N\) is the number of generation units, including traditional generators and VSG-IBG units. Renewable generation spillage probability in period \(t\) can be expressed as  
\[p_{t}^{RSP}=p\Big{\{}(\Delta P_{t}^{N}+R_{t}^{d})<0\Big{\}} \tag{15}\]  
where \(R_{t}^{d}\) is the downward reserve at period \(t\), which is provided by both SGs and VSG-IBG.  
Since the RG unit has been modified with a fixed upper output limit at each time period, the SGs and RG are homogeneous in power profile. Therefore, the RG unit could be seen as a virtual SG-based plant, and the economic dispatch including VSG-IBG could be solved.