## 3 Multi-Energy Coordination and Optimization Dispatching Strategy of Urban Power Grid
### Integrated Day-Ahead Coordination and Dispatching Model with Large-Scale Intermittent Energy
(2) Costs for power and heat generation  
\[C_{\text{PG}}=\sum_{i=1}^{m}\sum_{t=1}^{T}\Big{(}a_{i}\Big{(}Q_{\text{PG},i}^{t }\Big{)}^{2}+b_{i}Q_{\text{PG},i}^{t}+c_{i}+C_{\text{Pss},i}\Big{|}u_{\text{HG },i}^{t}-u_{\text{HG},i}^{t-1}\Big{|}\Big{)} \tag{4}\]  
where, \(m\) is the number of power generation equipment, including thermal power generators, gas power generators, renewable energy power generators and other types of equipment. \(Q_{\text{PG},i}^{t}\) is the generation capacity of the \(i\)th power generation equipment in time period \(t\). \(a_{i}\), \(b_{i}\) and \(c_{i}\) are the generation cost coefficients of the \(i\)th generation equipment, and the model is expressed by a quadratic function. \(C_{\text{Pss},i}\) is the starting and stopping cost of the \(i\)th power generation equipment, and for power generation equipment such as renewable energy, its value is 0. \(u_{\text{PG},i}^{t}\) is the starting and stopping state of power generation equipment \(i\) in time period \(t\), and its value of 0 represents the stopping state and 1 represents the starting state. \[C_{\text{HG}}=\sum_{i=1}^{n}\sum_{t=1}^{T}\Big{(}d_{i}\Big{(}Q_{\text{HG},i}^{ t}\Big{)}^{2}+e_{i}Q_{\text{HG},i}^{t}+f_{i}+C_{\text{HSs},i}\Big{|}u_{\text{HG},i}^{t }-u_{\text{HG},i}^{t-1}\Big{|}\Big{)} \tag{5}\]  
where, \(n\) is the number of heating equipment, including micro-gas turbine, heat pump, heat storage boiler, gas boiler and other types of equipment; \(Q_{\text{HG},i}^{t}\) is the calorific value of the \(i\)th heating device at time period \(t\); \(d_{i}\), \(e_{i}\), and \(f_{i}\) are the heating cost coefficients of the \(i\)th heating equipment respectively; \(C_{\text{HSs},i}\) is the starting and stopping cost of the \(i\)th heating equipment; \(u_{\text{HG},i}^{t}\) is the start and stop state of heating equipment \(i\)th in time period \(t\), and its value of 0 represents the stop state and 1 represents the starting state. (2) Model constraintsThe cascade utilization of energy is not considered in the model, but the coupling and complementarity between different energy systems are considered. Therefore, the quasi-steady state model and electrical and thermal energy balance of the equipment are modified as follows. (1) Constraints for the balance of heat and power in any time periods of the system. \[Q_{\text{PB}}^{t}+\sum_{i=1}^{m}Q_{\text{PG},i}^{t}=Q_{\text{PS}}^{t} \tag{6}\]  
\[Q_{\text{HB}}^{t}+\sum_{i=1}^{n}Q_{\text{HG},i}^{t}=Q_{\text{HS}}^{t} \tag{7}\]  
where \(Q_{\text{PS}}^{t}\) is the predicted load power value of the system in time period \(t\); \(Q_{\text{HS}}^{t}\) is the predicted thermal load of the system in time period \(t\); the output of the power storage system under the discharge state is recorded as a negative value. The heat pump and the heat storage boiler are taken as the load of the system in the heat storage state. (2) Considering the full utilization of renewable energy, certain rotation reserve constraints are required. \[\sum_{g\in\text{G}_{\text{G}_{\text{G}}}}I_{g}^{t}*Q_{\text{gmax}}^{t}+\sum_{g \in\text{G}_{\text{min}}}I_{g}^{t}*Q_{g}^{t}+P_{\text{GB}}\geq D^{t}+R^{t} \tag{8}\]  
where \(G_{\text{com}}\)represents all units except renewable energy, \(G_{\text{ren}}\) is wind turbine and PV (photovoltaic), andis rotation reserve demand in \(t\)th period. (3) Line safety constraint:  
\[\left|\sum_{g\in\text{G}_{\text{all}}}\gamma_{gj}Q_{g}^{t}\right|\leq L_{j} \tag{9}\]  
where \(G_{\text{all}}\) is all units, \(\gamma_{gj}\) is the power distribution factor of unit \(g\) output on line \(j\), and \(L_{j}\) is the line flow limit.