## 3 Analysis of Dispatchability on EGCS
### Evaluation Index of Dispatchability on EGCS
Index 2: Downward dispatchability under-expectation \(E_{\text{DF}}\), is the expected value of the difference between the downward dispatching backup capacity and the system downward dispatchability demand in the system during the operation cycle. \(E_{\text{DF}}\) is reflected that when the resource that consumes \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Spatial Dimension** & **Time Dimension** & **Physical Dimension** & **Value Dimension** \\ \hline Electricity balance & Ramping rate of thermal & Available dispatching capacity & Operation cost of \\ Flow balance & power units & of thermal power units & thermal power units \\ Conversion efficiency of power to gas & Power fluctuation of & wind turbines & Available dispatching capacity & Operation cost of nature \\ Conversion efficiency of power to heat & Power fluctuation of & of nature gas units & gas units \\ Conversion efficiency of gas to heat & photovoltaic units & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Factors to be considered in establishing EGCS dispatchability indexes. dispatchability is reduced, the system cannot cut out the average value of supplied resources due to inertia and other problems, and the smaller the value, the better. \[\left\{ \begin{array}{l}E_{\text{DF},t}=\Delta R_{\text{DF},t}\text{Pr}\{R_{ \text{DF},t}<P_{\text{L,net},t}-P_{\text{L,net},t+1}\}\\ \Delta R_{\text{DF},t}=P_{\text{L,net},t}-P_{\text{L,net},t+1}-R_{\text{DF},t} \\ R_{\text{DF},t}=\min\limits_{i=1}^{N_{\text{C}}}(P_{\text{G}}^{i,t}-P_{\text{ G}}^{i,\text{min}}),\sum\limits_{i=1}^{N_{\text{C}}}P_{\text{G},i}^{\text{d}} \cdot\Delta T\\ \end{array} \right. \tag{15}\]  
where \(R_{\text{DF},t}\) is the downward dispatching backup capacity available for the system in \(t\)th period. \(P_{\text{G}}^{i,t,\min}\) is the lower limit of the active power output of the \(i\)th conventional unit in \(t\)th period. \(P_{\text{G},i}^{\text{d}}\) is the downward ramping rate of the \(i\)th conventional unit. Index 3: Upward dispatchability margin, \(M_{\text{UF}}\), refers to the ratio of the difference between the upward dispatching backup capacity of conventional units and the upward dispatchability requirement of the system and the upward dispatchability requirement of the system during the operation period. \(M_{\text{UF}}\) reflects the adequacy level of dispatching resources that the system can provide when the increase in resources that consume dispatchability; the greater the value, the better. \[\left\{ \begin{array}{l}M_{\text{UF},t}=\frac{R_{\text{UF},t}-F_{\text{UF},t} }{F_{\text{UF},t}}\\ F_{\text{UF},t}=P_{\text{L,net},t+1}-P_{\text{L,net},t}+\sum\limits_{w=1}^{N_{ \text{DG}}}(P_{\text{DG},\text{fc}}^{w,t}-P_{\text{DG}}^{w,t})\\ \end{array} \right. \tag{16}\]  
where \(F_{\text{UF},t}\) is the system's upward dispatchability requirement in \(t\)th period. \(P_{\text{DG},\text{fc}}^{w,t}\) is the predicted output power of the \(w\)th DG unit W in \(t\)th period. \(N_{\text{DG}}\) is the total amount of DG units. \(P_{\text{DG}}^{w,t}\) is the actual output power of the \(w\)th DG unit W in \(t\)th period. Index 4: Downward dispatchability margin \(M_{\text{DF}}\), refers to the ratio of the difference between the downward dispatching backup capacity of conventional units and the downward dispatchability requirement of the system and the downward dispatchability requirement of the system during the operation period. \(M_{\text{DF}}\) reflects the adequacy level of dispatching resources that the system can cut when the decrease in resources that consume dispatchability; the greater the value, the better. \[\left\{ \begin{array}{l}M_{\text{DF},t}=\frac{R_{\text{DF},t}-F_{\text{DF},t} }{F_{\text{DF},t}}\\ F_{\text{DF},t}=P_{\text{L,net},t}-P_{\text{L,net},t+1}+\sum\limits_{w=1}^{N_{ \text{DG}}}(P_{\text{DG}}^{w,t}-P_{\text{DG},\text{fc}}^{w,t})\\ \end{array} \right. \tag{17}\]  
where \(F_{\text{DF},t}\) is the system's downward dispatchability requirement in \(t\)th period. The system operation must satisfy certain reliability.