## 2 Proposed Methodology
CSR studies typically include up to the third order contingencies for transmission lines and the fourth order for generation outages, as higher order contingencies have an insignificant impact on the results. The net peak load \(L_{peak,i}\) is first obtained for all the load buses from Equation (5). The LOL at each bus is then obtained for the peak load scenario. This is the maximum loss of load \(LOL_{max,i}\) that can occur at Bus \(i\). The cut-off load point \(L_{COi}\) for Bus \(i\) is then obtained from Equation (6). \[L_{peak,i}=Max\Big{[}\{L_{net,i}(t)\}_{t=1}^{T}\Big{]} \tag{5}\]  
\[L_{COi}=L_{peak,i}-LOL_{max,i} \tag{6}\]  
Figure 1 shows the cut-off load point in the typical net load dataset for a bus sorted in descending order. The load levels greater than \(L_{COi}\) in Figure 1 contribute to the loss of  
load. Since the load loss is sensitive to the system load level, the load data \(L_{mod,i}>L_{COi}\) are therefore modeled as a discrete probability distribution. The dataset \(\text{L}_{\text{net,i}}>L_{COi}\) is grouped into \(N_{L}\) states. A \(N_{L}\)-state discrete probability distribution at Bus \(i\) is obtained from Equation (7). \[(\,L_{i})_{k=1}^{NL}=\{L_{i}(k),\ Prob(L_{i}(k))|k=1,2,\ldots,N_{L}\} \tag{7}\]  
where, \(L_{i}(k)\) is the average value of the load data in kth state, and \(Prob(L_{i}(k))\) is the probability of load lying in the kth state for Bus i. It should be noted that representing the state group by a value less than the peak will result in an optimistic assessment. It should be noted that load curtailments can also occur at load levels below \(L_{COi}\) due to islanding conditions. These conditions, however, do not depend on the system load level and, therefore, the load data \(\text{L}_{\text{mod,i}}<L_{\text{COi}}\) are represented by their average value. The (\(N_{L}+1\))th state of the nodal net load model at Bus i, is therefore \(L_{\,i(N_{L}+1)}=\left\{L_{\,i(N_{L}+1)},\ Prob(N_{L}+1)\right\}\). The nodal net load model at Bus i in the form of the \((\,N_{L}+1)\)-state discrete probability distribution is given in Equations (8) and (9). \[L_{PD,i}=\left\{\left(\,L_{i})_{k=1}^{NL}\,,\ L_{i(N_{L}+1)}\,\right\} \tag{8}\]  
\[L_{i,(N_{L}+1)}=\mu(L_{mod,i})\forall L_{mod,i}<L_{COi}\]  
\[Prob(N_{L}+1)=\frac{|L_{\text{net,i}}(t):L_{COi}\geq L_{\text{net,i}}(t)\geq 0 |}{nT} \tag{9}\]  
and \(\mu\) (.) provides the average value. Equations (1) and (3) establish the supply model, and Equations (7) and (8) the demand model for the \(i\)th bus of the network. An accurate CSR assessment should consider operating conditions including the various wind scenarios and load scenarios. The total number of scenarios, \(NoS\), to consider in the assessment is equal to the number of combinations obtained from Equation (10). \[L_{nod\_i}=\{L_{net,i}(t)\}_{t=1}^{nT}\forall\ L_{net,i}\geq 0 \tag{2}\]0  
A flowchart of the CSR assessment methodology embedded with the proposed models is shown in \[L_{nod\_i}=\{L_{net,i}(t)\}_{t=1}^{nT}\forall\ L_{net,i}\geq 0 \tag{2}\]1 Each operating scenario includes a large number of contingencies. A load flow study is performed to assess the impact of each contingency on the bulk system's ability to supply power to the load points. The corresponding CSR indices are calculated for each scenario after all contingencies within that scenario have been analyzed. This process is then repeated for all the scenarios under consideration. The computation time increases  
\[L_{nod\_i}=\{L_{net,i}(t)\}_{t=1}^{nT}\forall\ L_{net,i}\geq 0 \tag{2}\]2 Multi-state load modeling using load cut-off strategy. proportionally with the increase in the number of scenarios. The overall CSR indices for the system are obtained by summing the expected contributions from each scenario. \[L_{nod\_i}=\{L_{net,i}(t)\}_{t=1}^{nT}\forall\ L_{net,i}\geq 0 \tag{2}\]3 Flowchart for CSR assessment capturing supply–demand variabilities.