## 3 Illustration of the Methodology  
The emerging low-carbon energy system is characterized by an increased penetration of renewable energy sources, which are distributed across various locations in the power network. The application of the proposed methodology is illustrated by integrating a wind farm into the Roy Billinton Test System (RBTS) [22], as shown by Figure 3. Although the example presented for illustration is a relatively small system with a single wind farm, the proposed methodology includes generalized models that can be applied to large complex networks with multiple renewable sources connected to different buses along with increased demand variability anticipated in evolving net-zero emission power systems. The RBTS consists of 11 conventional generators with capacities ranging from 5 MW to 40 MW, totaling 240 MW; and comprises 5 load points with a peak load of 185 MW. The detailed system data are provided in [22,23]. It is assumed that a coal-fired 40 MW unit at Bus 2 is replaced by a 150 MW wind farm at Bus 3, resulting in a 43% wind power penetration to the system. The hourly time-series wind power data obtained for the Swift Current location in Saskatchewan, Canada is used in the study. The availability of wind power is mainly dictated by the wind speed at any point in time. The failure rates of wind turbine, therefore, is ignored in the study. The time-series data for the loads at the different buses are obtained from [23]. The initial step of the methodology is to obtain the time-series net load data at all the buses using Equation (1). Bus 3 is connected to the wind farm and a load. The net load time-series recognizes the cross-correlation between the wind generation and the load connected at Bus 3. Figure 4 illustrates the net load data arranged in the descending order at Bus 3, which shows that a significant amount of wind power is absorbed by the load. The next step is to determine the cut-off load \(L_{CO}\) using Equation (6). The first pass load flow analysis was conducted using the PSS/E software version 34 for the peak load scenario considering contingencies up to the third order. Table 1 shows the load point LOL obtained and the Lco for each load bus. A three-state nodal net load model is obtained using Equations (7) and (9) for all load buses. The model for Bus 3 is shown in Figure 4. The load models for the remaining load buses are similarly obtained. Figure 5 shows the load models for all the load buses. Figure 3: RBTS network. The next step is to develop the net wind generation model at Bus 3. The Sturge's rule, as given by Equation (11), is applied to determine optimal grouping of the available net wind power data,  
\[K=\left\lceil 1+3.3\log_{10}(N)\right\rceil \tag{11}\]  
where K is the optimal number of states to represent N number of total data and \(\left\lceil.\right\rceil\) denotes rounding up to next integer. Using the Sturge's Rule, a 12-state discrete probability distribution of the wind power data is created, and then reduced to four states using the \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Bus 2** & **Bus 3** & **Bus 4** & **Bus 5** & **Bus 6** \\ \hline Peak load (MW) & 20 & 82.45 & 40 & 20 & 20 \\ \hline \(\text{LOL}_{\text{max}}\) (MW) & 10.24 & 42.22 & 20.48 & 10.24 & 10.24 \\ \hline \(\text{L}_{\text{CO}}\) (MW) & 9.76 & 40.23 & 19.52 & 9.76 & 9.76 \\ \hline \end{tabular}
\end{table} 
Table 1: Maximum LOL and LCo for load buses. Figure 4: Probability distribution of multi-state supply–demand model at Bus 3. Figure 5: Per unit load models for all buses of the network. approporting technique described by Equation (12). The four-state net wind generation model for Bus 3 is shown in Figure 4.  
\[ \begin{array}{l}P(C_{j})=\frac{C_{\mathrm{r}}-C_{\mathrm{i}}}{C_{\mathrm{r}}-C _{\mathrm{j}}}*P(C_{i})\\ P(C_{k})=\frac{C_{\mathrm{r}}-C_{\mathrm{j}}}{C_{\mathrm{r}}-C_{\mathrm{j}}}*P(C _{i})\end{array}