## 4 A Two-Stage Optimal Scheduling Model for Wind-PV-Thermal-Storage System
### Day-Ahead Optimal Scheduling Model
#### 4.1.2 Economy Scheduling Objective Function  
The optimal scheduling strategy is the joint operation of thermal power plants and renewable energy power plants. The objective function is to minimize the operating cost of the system:  
\[F_{1}=\sum_{t=1}^{T}(f_{\text{G},t}+f_{\text{GO},t}+f_{\text{E},t}+f_{\text{ DR},t}) \tag{12}\]  
where \(f_{\text{G},t}\), \(f_{\text{GO},t}\), \(f_{\text{E},t}\), \(f_{\text{DR},t}\) are the generation cost and dispatching cost of multiple power sources, the charging and discharging cost of energy storage stations, and the dispatching cost of demand response at time \(t\). The first item is the power operation cost, including the operation and dispatching cost of thermal units, and the operation and maintenance cost of renewable energy generators. \[f_{\text{G},t}=f_{\text{F},t}+f_{\text{W},t}+f_{\text{PV},t} \tag{13}\]  
where \(f_{\text{F},t}\), \(f_{\text{W},t}\), \(f_{\text{PV},t}\) are respectively thermal power unit operating cost, wind power, and photovoltaic power generation operation and maintenance cost in each period. * The Operating Cost of Thermal Power Units  
Due to the large-scale renewable energy with volatility into the grid, the climbing number and start times of traditional thermal power units increase. Therefore, the cost of deep peak adjustment cannot be ignored. According to the characteristics of the steam turbine, the heat rate will be higher, and the unit life loss will be bigger when the load of the steam turbine is lower. The cost of deep peak adjustment [24] includes coal consumption cost of unit operation and unit loss cost during severe peak load regulation. Thermal power units can be divided into normal operation state and deep peak regulation state during operation. The thermal power unit operation cost is:  
\[f_{\text{F},t}=\sum_{i=1}^{N_{\text{F}}}\Bigl{[}u_{\text{F},i,t}\,\Bigl{(}a_{ i}P_{\text{F},i,t}^{2}+b_{i}P_{\text{F},i,t}+c_{i}+w_{\text{cost},t}\Bigr{)} \Bigr{]} \tag{14}\]  
where \(u_{\text{F},i,t}\) is the start-stop variable of the thermal power unit and the value is 1 or 0, \(P_{\text{F},i,t}\) is the output of the \(i\)-th thermal unit, \(a_{i}\), \(b_{i}\), \(c_{i}\) are the fuel cost coefficients of the \(i\)-th thermal unit in normal operation. When the thermal unit is severe peak load regulation state, the thermal stress of the rotor is too large to cause unit loss cost and \(w_{\text{cost},i}\) is the additional operating cost of deep peak adjustment, and the calculation formula is:  
\[w_{\text{cost},i}=\left\{ \begin{array}{cc}0&P_{\text{F},i}\leq\alpha P_{ \text{F},i,\text{max}}\\ \frac{\chi C_{\text{unit}}}{2N_{t}\left(P_{\text{F},i}\right)}&\text{other}\end{array} \right. \tag{15}\]  
where \(\alpha\) represents the boundary of the low-load state, and usually is 0.6, \(\chi\) is the actual operating loss coefficient of the thermal power unit, \(N_{t}(P_{\text{F},i})\) is the cycle times of rotor cracking, which is determined by the low cycle fatigue characteristics of rotor material, and \(C_{\text{unit}}\) is unit purchase cost. \(\bullet\) Operation and Maintenance Cost of Renewable Energy  
Wind and photovoltaic power generation do not consume fuel, but the randomness and volatility of wind and light will affect the normal operation of the unit and generate a certain operation and maintenance cost, which can be approximately expressed as the linear function of unit generating power [25]. \[f_{\text{W},t}=\sum_{j=1}^{N_{\text{W}}}P_{\text{W},\,j,t}\rho_{\text{W},j} \tag{16}\]  
\[f_{\text{PV},t}=\sum_{k=1}^{N_{\text{PV}}}P_{\text{PV},k}t\rho_{\text{PV},k} \tag{17}\]  
where \(N_{\text{W}}\)\(N_{\text{PV}}\) are the number of wind power units and PV power units, \(\rho_{\text{W},j}\), \(\rho_{\text{PV},k}\) are the operation and maintenance cost coefficient of the wind farm and PV station, \(P_{\text{W},\,j,t}\), \(P_{\text{PV},k,t}\) are the restricted active power output of wind farm and photovoltaic at time \(t\) respectively.