## 3 Multi-Energy Coordination and Optimization Dispatching Strategy of Urban Power Grid
### Integrated Day-Ahead Coordination and Dispatching Model with Large-Scale Intermittent Energy
(4) Unit output and climbing constraints:  
\[\min L\Big{(}Q_{\text{PB}}^{t},Q_{\text{HB}}^{t},Q_{\text{PG}}^{t},Q_{\text{HG }}^{t}\Big{)}=C_{\text{PB}}+C_{\text{PG}}+C_{\text{HB}}+C_{\text{HG}} \tag{1}\]0  
\[\min L\Big{(}Q_{\text{PB}}^{t},Q_{\text{HB}}^{t},Q_{\text{PG}}^{t},Q_{\text{HG }}^{t}\Big{)}=C_{\text{PB}}+C_{\text{PG}}+C_{\text{HB}}+C_{\text{HG}} \tag{1}\]1  
where \(Q_{\text{mmin}}\) and \(Q_{\text{mmax}}\) are respectively the minimum and maximum output of thermal power unit \(g\); \(r_{g,\text{up}}\) is the upward climbing rate of thermal power units \(g\) and \(r_{g,\text{down}}\) is the downward climbing rate of thermal power units \(g\). (5) Most large-capacity electric regenerative boilers are composed of electrode boilers and water storage tanks. Some of the generated heat is used directly for heating, and the other part can be stored in the regenerative device as a movable time load. The heat storage capacity of the heat storage tank should be within its limit, that is:  
\[\min L\Big{(}Q_{\text{PB}}^{t},Q_{\text{HB}}^{t},Q_{\text{PG}}^{t},Q_{\text{HG }}^{t}\Big{)}=C_{\text{PB}}+C_{\text{PG}}+C_{\text{HB}}+C_{\text{HG}} \tag{1}\]2  
where \(Q_{\text{HS}}^{t}\) is the heat storage capacity of the heat storage tank in time period \(t\); \(Q_{\text{HS,max}}\) and \(Q_{\text{HS,min}}\) are respectively the maximum and minimum heat storage capacity of the heat storage tank. (6) Power constraint of electric boilers:  
\[\min L\Big{(}Q_{\text{PB}}^{t},Q_{\text{HB}}^{t},Q_{\text{PG}}^{t},Q_{\text{HG }}^{t}\Big{)}=C_{\text{PB}}+C_{\text{PG}}+C_{\text{HB}}+C_{\text{HG}} \tag{1}\]3  
where \(P_{\text{HS}}^{t}\) is the electric power of the regenerative boiler in time period \(t\); \(P_{\text{HS,max}}\) is the upper limit of power of section regenerative electric boiler. (7) The \(SOC\) (State of Charge) of the energy storage system should also be within the appropriate range, that is:  
\[\min L\Big{(}Q_{\text{PB}}^{t},Q_{\text{HB}}^{t},Q_{\text{PG}}^{t},Q_{\text{HG }}^{t}\Big{)}=C_{\text{PB}}+C_{\text{PG}}+C_{\text{HB}}+C_{\text{HG}} \tag{1}\]4  
where \(SOC_{\rm max}\) and \(SOC_{\rm min}\)are the upper and lower limits of the charged state, respectively. In general, the upper limit is 0.8 and the lower limit is 0.2. (8) The \(SOC\) of the energy storage system after the last time period should be equal to that before the first period of time:  
\[\min L\Big{(}Q_{\text{PB}}^{t},Q_{\text{HB}}^{t},Q_{\text{PG}}^{t},Q_{\text{HG }}^{t}\Big{)}=C_{\text{PB}}+C_{\text{PG}}+C_{\text{HB}}+C_{\text{HG}} \tag{1}\]5  
where \(SOC^{0}\) is the \(SOC\) of the energy storage system at the beginning of the scheduling cycle and \(SOC^{T}\) is the \(SOC\) of the energy storage system at the time of the end of the scheduling cycle. (9) Many devices in urban energy system such as solar power plants, wind farms, PHEVs (plug in hybrid electric vehicle), and HEVs (Hybrid Electric Vehicle) can't get connected to power grid without an AC/DC (Alternating Current/Direct Current) or DC/DC (Direct Current/Direct Current) converter. In order to ensure the stability of grid voltage, the converters are in constant voltage control mode [34]. The output constraint of converters is:  
\[\min L\Big{(}Q_{\text{PB}}^{t},Q_{\text{HB}}^{t},Q_{\text{PG}}^{t},Q_{\text{HG }}^{t}\Big{)}=C_{\text{PB}}+C_{\text{PG}}+C_{\text{HB}}+C_{\text{HG}} \tag{1}\]6  
where \(P^{t}_{con}\) is the output of the converter \(i\); \(P^{t}_{con,\rm min}\) and \(P^{t}_{con,\rm max}\) are the output ranges of the converter \(i\). The power loss of the converter is 1.5% of the output [34].