# Day-Ahead Dispatch Model of Electro-Thermal Integrated Energy System with Power to Gas Function
## 3 Electro-Thermal Integrated Energy System with \"P2G Function\"
### Solution Strategy
\begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Definition** \\ \hline \(p_{i,t}^{\text{TU}}\) & Generation output of thermal unit \(i\) at period \(t\). \\ \(p_{i,t}^{\text{CHP}}\) & Generation output of combined heat and power unit \(i\) at period \(t\). \\ \(p_{i,t}^{\text{WT},\text{SC}}\) & Grid-connected output of wind turbine \(i\) at period \(t\). \\ \(h_{i,t}^{\text{CHP}}\) & Heat production output of combined heat and power unit \(i\) at period \(t\). \\ \(h_{i,t}^{\text{CB}}\) & Heat production output of gas-fired boiler \(i\) at period \(t\). \\ \(h_{i,t}^{\text{J},\text{J},\text{J}}\) & Natural gas part of heat production output of gas-fired boiler \(i\) at period \(t\). \\ \(h_{i,t}^{\text{hydrogen}}\) & Hydrogen part of heat production output of gas-fired boiler \(i\) at period \(t\). \\ \(C_{i,t}^{\text{TU}}\) & Standard coal consumption of thermal unit \(i\) at period \(t\). \\ \(C_{i,t}^{\text{CHP}}\) & Standard coal consumption of combined heat and power unit \(i\) at period \(t\). \\ \(C_{i,t}^{\text{GB}}\) & Standard coal consumption of gas-fired boiler \(i\) at period \(t\). \\ \(\lambda^{\text{FU}}\) & Conversion coefficient of standard coal for thermal units. \\ \(\lambda^{\text{CHP}}_{\text{L},\text{HP}}\) & Conversion coefficient of standard coal for the CHPs’ power supply. \\ \(\lambda^{\text{CB}}_{\text{LB}}\) & Conversion coefficient of standard coal for the CHPs’ heat supply. \\ \(\lambda^{\text{load}}_{\text{LB}}\) & Conversion coefficient of standard coal for gas fired boilers. \\ \(p_{i,t}^{\text{Wf},\text{max}}\) & Net active load demand in node \(i\) at period \(t\). \\ \(p_{i,t}^{\text{WT},\text{max}}\) & Maximum generation output of wind turbine \(i\) at period \(t\). \\ \(F_{i,t}^{\text{gas}}\) & Air input of natural gas at period \(t\). \\ \(F_{i,t}^{\text{J},\text{J}}\) & Air input of hydrogen at period \(t\). \\ \(\rho^{\text{gas}}\) & Density of natural gas. \\ \(\rho^{\text{H2}}\) & Density of hydrogen. \\ \(\eta_{\text{F}}\) & Electrokinetic efficiency of electrolyzers. \\ \(g_{\text{H2}}^{\text{H2}}\) & Production of hydrogen per kilowatt hour. \\ \(p_{i,t,t}^{\text{WT},\text{true}}\) & Actual generation output of wind turbine \(i\) at period \(t\). \\ \(\eta_{\text{G}}^{\text{GB},\text{min}}\) & Efficiency of gas-fired boilers. \\ \(h_{i,t}^{\text{GB},\text{min}}\) & \(h_{i,t}^{\text{GB},\text{max}}\) & Maximum/minimum generation output of gas-fired boiler \(i\) at period \(t\). \\ \(p_{i,t}^{\text{CHP},\text{min}}\) & \(p_{i,t}^{\text{CHP},\text{max}}\) & Maximum/minimum generation output of CHP \(i\) at period \(t\). \\ \(h_{i,t}^{\text{EX},\text{J}}\) & Residual heat of the gas displacement. \\ \(\eta_{\text{F}}^{\text{CHP}}\) & Electrical efficiency of combined heat and power units. \\ \(\eta_{\text{L}}\) & Cooling efficiency of combined heat and power units. \\ \(\gamma_{\text{th}}^{\text{CHP}}\) & Thermal efficiency of combined heat and power units. \\ \(\text{COPh}\) & Coefficient of performance. \\ \(\text{RAf}\) & Ramping capability of combined heat and power units. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters and functions. Take the decision variables \(\mathbf{x}\) = (\(x_{1}\), \(x_{2}\),..., \(x_{n}\)) to be solved as \(n\) particles without mass and volume. The position and velocity vectors of the \(i\)th particle of a two-dimensional search space can be represented as \(s_{i}\) = (\(s_{1}\), \(s_{2}\),..., \(s_{n}\)) and \(v_{i}\) = (\(v_{1}\), \(v_{2}\),..., \(v_{n}\)) respectively, After initialization, the particle tries to modify its position using the current velocity and the distance on the basis of the value of the evaluation function. The best previous position of a particle is recorded and represented as _pbest_. If the \(g\)th particle is the best among all particles in the group so far, it is represented as _pbest_ = _gbest_.