# Comprehensive Energy Demand Response Optimization Dispatch Method Based on Carbon Trading
## 5 Optimal Dispatch Model of Integrated Energy Demand Response Based on Carbon Trading
### Restrictions
#### 5.2.2 Integrated Energy System Component Constraints  
(1) Coal-fired unit constraints  
Coal-fired engines mainly meet the constraints of the upper and lower limits of output and the constraints of the ramp rate.  
\[\left\{\begin{array}{l}P_{C,j,min}\leq P_{C,j,t}\leq P_{C,j,max}\\ P_{C,j,downmax}\leq P_{C,j,t}-P_{C,j,t-1}\leq P_{C,j,upmax}\end{array}\right. \tag{33}\]  
where \(P_{C,j,min}\) and \(P_{C,j,max}\) are the minimum and maximum output values of the \(j\)-th coal-fired unit, respectively; \(P_{C,j,downmax}\) and \(P_{C,j,upmax}\) are the maximum down-climbing power and maximum up-climbing power of the \(j\)-th coal-fired unit, respectively; \(P_{C,j,t}\) is the generating power of the \(j\)-th coal-fired unit at time \(t\); and \(P_{C,j,t-1}\) is the generating power of the \(j\)-th coal-fired unit at time \(t-1\).  
(2) Gas turbine constraints  
The gas turbine mainly satisfies the constraints of the upper and lower limits of output, the constraints of the ramp rate, and the constraints of the electric-to-heat ratio.  
\[\left\{\begin{array}{l}P_{C,j,min}\leq P_{C,j,t}\leq P_{C,j,max}\\ \alpha=P_{G,j,t}/H_{G,j,t}\\ P_{G,j,downmax}\leq P_{G,j,t}-P_{G,j,t-1}\leq P_{G,j,upmax}\end{array}\right. \tag{34}\]  
where \(P_{C,j,min}\) and \(P_{C,j,max}\) are the minimum and maximum output values of the \(j\)-th gas turbine, respectively; \(\alpha\) is the electric-thermal ratio of the gas turbine; \(P_{C,j,downmax}\) and \(P_{C,j,upmax}\) are the maximum downhill power and maximum uphill power of the \(j\)-th gas turbine, respectively; \(P_{C,j,t}\) is the power generation of gas turbine \(j\) at time \(t\); \(P_{C,j,t-1}\) is the powergeneration of gas turbine \(j\) at time \(t-1\); and \(H_{G,j,t}\) is the output heat of gas turbine \(j\) at time \(t\).
3. Wind turbine constraints The constraints of the wind turbines mainly satisfy their maximum output constraints. \[0\leq P_{W,j,t}\leq P_{W,j,max}\] (35) where \(P_{W,j,t}\) is the power supply of wind turbine \(j\) at time \(t\), and \(P_{W,j,max}\) represents the predicted output value of the \(j\)-th typhoon generator unit.
4. Photovoltaic unit constraints The constraints of photovoltaic units mainly satisfy their maximum output constraints: \[0\leq P_{P,j,t}\leq P_{P,j,max}\] (36) where \(P_{P,j,t}\) is the generating power of the \(j\)-th photovoltaic unit at time \(t\), and \(P_{P,j,max}\) represents the predicted output value of the \(j\)-th photovoltaic unit.
5. Gas boiler constraints The gas boiler mainly meets the constraints of the upper and lower limits of the output and the constraints of the ramp rate: \[\left\{\begin{array}{l}H_{H,j,min}\leq H_{H,j,t}\leq H_{H,j,max}\\ H_{H,j,downmax}\leq H_{H,j,t}-H_{H,j,t-1}\leq H_{H,j,upmax}\end{array}\right.\] (37) where \(H_{H,j,min}\) and \(H_{H,j,max}\) are the minimum and maximum output values of the \(j\)-th gas boiler, respectively; and \(H_{H,j,downmax}\) and \(H_{H,j,upmax}\) are the maximum down-climbing power and maximum up-climbing power of the \(j\)-th gas boiler, respectively.
6. \(P2G\) device constraints \(P2G\) equipment mainly meets its rated power constraints: \[0\leq P_{P2G,j,t}\leq P_{P2G,j,max}\] (38) where \(P_{P2G,j,t}\) is the input power of the \(j\)-th \(P2G\) device at time \(t\), and \(P_{P2G,j,max}\) is the rated power of the \(P2G\) device.