## 5 Case Study  
### Verify the Evaluation Index of Dispatchability on EGCS  
In order to verify the rationality of dispatchability evaluation index, an economic dispatching model as shown in Equation (32) is established for the simple pure power system. \[ \begin{split}\min& F=\sum\limits_{i=1}^{T}\sum \limits_{i=1}^{N_{\text{P}}}\left[a_{i}+b_{i}P_{\text{G}}^{i,t}+c_{i}(P_{\text {G}}^{i,t})^{2}\right]+\sum\limits_{t=1}^{T}c_{\text{F}}E_{\text{F}}^{t}\\ \text{s.t.}&\left(\begin{array}{l}P_{\text{G}}^{i,t+1}-P _{\text{G}}^{i,t}\leq u_{i,t}\cdot r_{\text{G}}^{\alpha},\cdot\Delta T+P_{\text {G}}^{i,\max}(1-u_{i,t})\\ \sum\limits_{i=1}^{N_{\text{P}}}P_{\text{G}}^{i,t}+E_{\text{F}}^{t}-P_{\text{ L}}^{t}=0\\ P_{\text{G}}^{i,\min}\leq P_{\text{G}}^{i}\leq P_{\text{G}}^{i,\max}\\ E_{\text{F}}^{t}\leq E_{\text{F}}^{\max}\end{array}\right.\end{split}  \tag{32}\]  
where \(a_{i}\), \(b_{i}\), and \(c_{i}\) are the operating cost factors of the \(i\)th conventional thermal power unit. \(c_{F}\) is the cost factor of outage loss per unit load. \(E_{\text{F}}^{t}\) is the expected value of the system when the power is insufficient in \(i\)th period. \(E_{\text{F}}^{\max}\) is the maximum allowable load shedding value of the system, indicating the reliability level of the system operation. Based on the above model, the unit's combination of the system at all time periods can be obtained, and the dispatchability capacity and dispatchability requirement for each period of the system can be obtained, thus the system dispatchability margin index \(M_{\text{UF}}\) and \(M_{\text{DF}}\) can be obtained. The dispatchability of the system is analyzed by using the three-machine three-node system as shown in Figure 7. The conventional units related parameters and load data are as shown in Tables 2 and 3. \(\Delta T=1\) h, \(c_{F}=\$1500/\text{M}\).  
Firstly, without considering the reliability level of the system, the above economic dispatching model is solved under the three-machine system. The operating cost of the system is $28,076.9. The \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Unit** & \(P_{\text{G}}^{i,\max}\)**/MW** & \(P_{\text{G}}^{i,\min}\)**/MW** & \(a_{i}\)**/(\$5/MW\({}^{2}\))** & \(b_{j}\)**/(\$5/MW)** & \(c_{i}\)**/\$ & \(r_{\text{G},i}^{\alpha,d}\)**/(MW/min)** \\ \hline
1 & 150 & 50 & 0.0020 & 30 & 500 & 2 \\
2 & 100 & 20 & 0.0025 & 40 & 300 & 1.5 \\
3 & 100 & 10 & 0.0050 & 20 & 100 & 1.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the conventional units. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Period/h** & **1** & **2** & **3** & **4** \\ \hline Load/MW & 80 & 120 & 200 & 150 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Load data. Figure 7: Three-machine three-node system. output and dispatching capacity allocation of each unit in the system are shown in Table 4. Based on this, the dispatchability evaluation index of the system is obtained as shown in Table 5.  
From Tables 4 and 5, the dispatchability margin of the system can be calculated effectively under the premise of satisfying the reliability, and the system economy is optimal. The model has a feasible optimal solution, which can verify the rationality of the index mentioned in this paper. Because system reliability is closely related to dispatchability, this paper takes a single time period as an example to study the impact of reliability on system dispatchability margin when the load is 180 MW. On the basis of the above examples, the reliability level of the system is adjusted, and the dispatchability margin index of the system under a series of reliability levels is obtained. The calculation results are shown in Table 6 and Figure 8. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(\mathbf{E_{\text{F}}^{\text{max}}}\) & \(\mathbf{R_{\text{F}}}\)/MW & \(\mathbf{F_{\text{F}}}\)/MW & \(\mathbf{M_{\text{F}}}\)/\% \\ \hline  
\\ \hline \hline \end{tabular}
\end{table} 
Table 6: Dispatchability margin index of the system under a series of reliability levels.