## 3 Analysis of Dispatchability on EGCS
### Evaluation Index of Dispatchability on EGCS
\[F_{\text{P2G}}=\eta_{\text{P2G}}P_{\text{P2G}}-C_{\text{P2G}} \tag{13}\]  
where \(F_{\text{P2G}}\) is the dispatchability of P2G devices. \(\eta_{\text{P2G}}\) is the energy conversion efficiency of P2G devices. \(P_{\text{P2G}}\) is the electric power input to P2G devices. \(C_{\text{P2G}}\) is the natural gas power output by P2G devices. The controllable load and uncontrollable load mentioned in this paper include electric load, gas load, and heat load. Since the studied network is a grid and natural gas network, the heat load is equivalent to electric load and gas load. According to the multi-dimensional attributes of dispatchability and the quantitative analysis of dispatchability of different types of resources, various factors that need to be considered in establishing the EGCS dispatchability indexes can be obtained as shown in Table 1.  
As shown in Table 1, electricity balance and flow balance are the prerequisites for the secure and stable operation of the grid and natural gas network, and they must be met. Therefore, they are regarded as constraint conditions of dispatching model. The ramping rate and energy conversion efficiency of units are inherent characteristics of EGCS dispatchability, which cannot be changed after being put into operation. Therefore, they exist as general parameters in the calculation of dispatchability index or constraints. The value dimension parameters can be used as the objective function of the dispatching model to evaluate the dispatchability of the system from the economic point of view. Most importantly, due to the influence of natural factors and prediction errors, the output of wind turbines and photovoltaic units will be uncertain in time scale. At the same time, the available regulating capacity of conventional units will fluctuate with the switching state on time scale. These factors will directly affect the system's upward and downward ability in the dispatching stage; that is, the factors have a great impact on the system's dispatchability. Moreover, the natural gas network is an inertial system, while the grid is a real-time system. Therefore, this paper uses natural gas system to regulate the power system. Considering the capacity of coordinated dispatching of conventional thermal power units, gas generating units, distributed wind, and photovoltaic units in the 24-h operation phase of EGCS, the random variation of load is also considered. Four dispatchability evaluation indexes are proposed. Index 1: Upward dispatchability under-expectation \(E_{\text{UF}}\), is the expected value of the difference between the upward dispatching backup capacity and the system upward dispatchability demand in the system during the operation cycle. \(E_{\text{UF}}\) reflects the average value of the system's failure to replenish resources when the consumption of dispatching resources increases, and the smaller the value, the better. \[\left\{ \begin{array}{l}E_{\text{UF},t}=\Delta R_{\text{UF},t}\text{Pr}\{R_{ \text{UF},t}<P_{\text{L,net},t+1}-P_{\text{L,net},t}\}\\ \Delta R_{\text{UF},t}=P_{\text{L,net},t+1}-P_{\text{L,net},t}-R_{\text{UF},t} \\ R_{\text{UF},t}=\min\sum\limits_{i=1}^{N_{\text{G}}}(P_{\text{G}}^{i,t,\max}- P_{\text{G}}^{i,t}),\sum\limits_{i=1}^{N_{\text{G}}}P_{\text{G},i}^{i}\cdot \Delta T\end{array} \right\} \tag{14}\]  
where \(R_{\text{UF},t}\) is the upward dispatching backup capacity available for the system in \(t\)th period. \(P_{\text{L,net},t}\) and \(P_{\text{L,net},t+1}\) are, respectively, the net load in \(t\)th and (\(t\)+1)th period. \(N_{\text{G}}\) is the total amount of natural gas units in the system. \(P_{\text{G}}^{i,t,\max}\) is the upper limit of the active power output of the \(i\)th conventional unit in \(t\)th period. \(P_{\text{G}}^{i,t}\) is the actual active output of the \(i\)th conventional unit in \(t\)th period. \(r_{\text{G},i}^{\text{u}}\) is the upward ramping rate of the \(i\)th conventional unit. \(\Delta T\) is the dispatching interval.