## 2 The TPUMSTSR Under RLV Model
### Internal Operation Model of MCSs
#### 3.3.2 Constraints  
The constraints of the coordinated operation model within the CS can be categorized into the power balance constraint of the CS, the stepped ramp constraint of thermal power units, and others. 1. Power Balance Constraint of the CS  
The sum of power generation from thermal power units and renewable energy within the CS must meet the power demand of the main grid on the CS, expressed as follows:  
\[P^{\text{L}}_{i,t}=\sum\limits_{u=1}^{U}P^{\text{TPU}}_{i,u,t}+P^{\text{WT}}_ {i,t}+P^{\text{PV}}_{i,t}+P^{\text{UN}}_{i,t} \tag{27}\]  
where \(P^{\text{L}}_{i,t}\) is the power demand of the main grid on the CS during the \(t\) dispatch period, and \(P^{\text{UN}}_{i,t}\) represents the active power imbalance between the total power generation and the dispatch command. 2. Stepped Ramp Constraint of Thermal Power Units  
Thermal power units exhibit different ramp rates under different operating states, known as the stepped ramp characteristic. The feasible power output region between adjacent time periods \(t\) and \(t+1\) is correlated with the stepped ramp characteristics, the output range under different states, and the selection of time scales. For the non-convex stepped ramp constraints of thermal power units, refer to Equation (2). 3. Power Generation Constraints of Thermal Power Units  
The power generation constraints of thermal power units include the upper and lower output limits and the flexible reserve constraints, as follows:  
1. Upper and Lower Output Limits of Thermal Power Units  
The power output of thermal power units during each dispatch period must remain within their allowable output range:  
\[P^{\text{TPU,min}}_{i,u}\leq P^{\text{TPU}}_{i,u,t}\leq P^{\text{TPU,max}}_{i,u} \tag{28}\]
2. Flexible Reserve Constraint of Thermal Power Units  
Thermal power units must reserve a certain amount of spinning reserve during each dispatch period to address uncertainties and power imbalances between generation and load demand during the operation of the CS:  
\[\left\{ \begin{array}{l}P^{\text{TPU}}_{i,u,t}=P^{\text{TPU,B}}_{i,u,t}+P^{ \text{TPU,F}}_{i,u,t}\\ -P^{\text{TPU}}_{i,u}P^{\text{TPU,max}}_{i,u}\Delta T\leq P^{\text{TPU,F}}_{i,u,t}\leq\tau^{\text{TPU}}_{i,u}P^{\text{ITU,max}}_{i,u}\Delta T\end{array} \right. \tag{29}\]where \(P_{i,u,l}^{\rm TPU,B}\) is the predetermined fixed base output of the unit; \(P_{i,u,l}^{\rm TPU,F}\) is the real-time flexible output of the unit to mitigate source and load fluctuations, which can be adjusted within a certain range to track real-time fluctuations; and \(\tau_{i,u}^{\rm TPU}\) is the coefficient of adjustable flexible resources of the unit. Constraints of the MSTS Systems  
The constraints of the molten salt thermal energy storage system include charging/discharging constraints and state-of-charge constraints [35; 36], as follows:  
1 Capacity Constraints of High/Low-Temperature Thermal Storage Systems  
\[\left\{ \begin{array}{l}S_{\rm min}^{\rm H}\leq S_{\rm f}^{\rm H}\leq S_{\rm max }^{\rm H}\\ S_{\rm min}^{\rm L}\leq S_{\rm f}^{\rm L}\leq S_{\rm max}^{\rm L}\end{array} \right. \tag{30}\]  
where \(S_{\rm min}^{\rm H}\) and \(S_{\rm max}^{\rm H}\) represent the minimum and maximum storage capacities of the high-temperature system during period \(t\), respectively; and \(S_{\rm min}^{\rm L}\) and \(S_{\rm max}^{\rm L}\) represent the minimum and maximum storage capacities of the low-temperature system during period \(t\), respectively. 2 State Constraints of High/Low-Temperature Thermal Storage Systems  
\[\left\{