## 5 Conclusions
& The negative flexible power for BES \\ \(P_{best,n,flex+}\) & The positive flexible power for BES \\ \(P_{gas,t,n,flex-}\) & The negative flexible power for gas tank \\ \(P_{gas,t,n,flex+}\) & The positive flexible power for gas tank \\ \(Pheat_{t,n,flex-}\) & The negative flexible power for gas tank \\ \(Pheat_{t,n,flex+}\) & The positive flexible power for gas tank \\ \(PCHP_{t,n,flex-}\) & The negative flexible power for CHP \\ \(PCHP_{t,n,flex+}\) & The positive flexible power for CHP \\ \(P2G_{t,n,flex-}\) & The negative flexible power for P2G \\ \(P_{WT,t,n}\), \(P_{PVT,t,n}\), \(P_{goo}\) & The output of wind, solar, geothermal \\ \(P_{mm}\), \(Q_{mm}\) & The active and reactive power \\ \(p_{n,g}/p_{n,d}\), \(q_{n,g}/q_{n,d}\) & The active and reactive generation/demand \\ \(pr_{n,flex}\) & The flexibility potential pricing of aggregator \\ \(Q_{gas}\) & The conversion coefficient of gas \\ \(r_{mm}\), \(x_{mm}\) & The line resistance and reactance \\ \(SOC_{i,t,n}\) & The optimal SOC of \(i\) \\ \(SOC_{i,n,max}\) & The maximum SOC of \(i\) in aggregator \(n\) \\ \(SOC_{i,n,min}\) & The minimum SOC of \(i\) in aggregator \(n\) \\ \(SOC_{i,min}\), \(SOC_{i,max}\) & The maximum and minimum SOC of \(i\) \\ \(SOC_{i,t}\) & The state of charge of \(i\) \\ \(T_{max}\), \(T_{min}\) & The maximum and minimum temperature of flexible load \\ \(T_{out}\) & The outside temperature \\ \(U_{n}\), \(U_{0}\) & The voltage magnitude at bus \(n\), slack bus \\ \(\mu_{bay,t}\), \(h_{shell,t}\) & Buying and selling electricity price \\ \(\eta_{e,CHP}\) & Electrical conversion efficiency of CHP \\ \(\eta_{h,CHP}\) & Heat conversion efficiency of CHP \\ \(\mu_{BES}\) & Battery degradation coefficient \\ \(a_{CHP,t,n}\) & The ON/OFF state of CHP \\ \(a_{P2G,t,n}\) & The ON/OFF state of P2G \\ \(\alpha_{1}\), \(\alpha_{2}\) & The coefficients of temperature \\ \(\eta_{ch}\), \(\eta_{dis}\) & The charging and discharging efficiency of BES \\ \(\eta_{w}\) & The loss rate of heat storage tank \\ \(\lambda_{t,n,flex}\) & The number of flexible timestep \\ \(\lambda bs_{t,n,flex-}\) & The negative flexible timestep for BES \\ \(\lambda bs_{t,n,flex+}\) & The positive flexible timestep for BES \\ \(\lambda gas_{t,n,flex-}\) & The negative flexible timestep for gas storage tank \\ \(\lambda gas_{t,n,flex+}\) & The positive flexible timestep for gas storage tank \\ \(\lambda haet_{t,n,flex-}\) & The negative flexible timestep for heat storage tank \\ \(\lambda chtp_{t,n,flex-}\) & The negative flexible timestep for CHP \\ \(\lambda CHP_{t,n,flex-}\) & The positive flexible timestep for P2G \\ \(\lambda P2G_{t,n,flex+}\) & The positive flexible timestep for P2G \\ \(P_{WT,t,n}\), \(P_{PVT,t,n}\), \(P_{goo}\) & The output of wind, solar, geothermal \\ \(P_{mm}\), \(Q_{mm}\) & The active and reactive power \\ \(p_{n,g}/p_{n,d}\) & \(q_{n,g}/q_{n,d}\) \\ \(pr_{n,flex}\) & The flexibility potential pricing of aggregator \\ \(Q_{gas}\) & The conversion coefficient of gas \\ \(r_{mm}\), \(x_{mm}\) & The line resistance and reactance \\ \(SOC_{i,t,n}\) & The optimal SOC of \(i\) \\ \(SOC_{i,n,max}\) & The maximum SOC of \(i\) in aggregator \(n\) \\ \(SOC_{i,n,min}\) & The minimum SOC of \(i\) in aggregator \(n\) \\ \(SOC_{i,min}\), \(SOC_{i,max}\) & The maximum and minimum SOC of \(i\) \\ \(SOC_{i,t}\) & The state of charge of \(i\) \\ \(T_{max}\), \(T_{min}\) & The maximum and minimum temperature of flexible load \\ \(T_{out}\) & The outside temperature \\ \(U_{n}\), \(U_{0}\) & The voltage magnitude at bus \(n\), slack bus \\ \(\mu_{bay,t}\), \(h_{shell,t}\) & Buying and selling electricity price \\ \(\eta_{e,CHP}\) & Electrical conversion efficiency of CHP \\ \(\eta_{h,CHP}\) & Heat conversion efficiency of CHP \\ \(\mu_{BES}\) & Battery degradation coefficient \\ \(a_{CHP,t,n}\) & The ON/OFF state of CHP \\ \(a_{P2G,t,n}\) & The ON/OFF state of P2G \\ \(\alpha_{1}\), \(\alpha_{2}\) & The coefficients of temperature \\ \(\eta_{ch}\), \(\eta_{dis}\) & The charging and discharging efficiency of BES \\ \(\eta_{w}\) & The loss rate of heat storage tank \\ \(\lambda_{t,n,flex}\) & The number of flexible timestep \\ \(\lambda bs_{t,n,flex-}\) & The negative flexible timestep for BES \\ \(\lambda bs_{t,n,flex+}\) & The positive flexible timestep for BES \\ \(\lambda gas_{t,n,flex-}\) & The negative flexible timestep for gas storage tank \\ \(\lambda gas_{t,n,flex+}\) & The positive flexible timestep for gas storage tank \\ \(\lambda haet