## 2 The TPUMSTSR Under RLV Model
### Internal Operation Model of MCSs
#### 3.3.1 Objective Function  
For a single CS \(i\), the objective function of internal optimized operation is to maximize the total revenue at each time period, denoted as \(f_{i,t}^{\text{A}}\)  
\[\max f_{i,t}^{\text{A}}=\Delta T(\sum\limits_{u\in U_{i}}f_{i,u,t}^{\text{TPU }}+f_{i,t}^{\text{RE}}-C^{\text{GU}}\Big{|}P_{i,t}^{\text{UN}}\Big{|}) \tag{11}\]  
where \(P_{i,t}^{\text{UN}}\) represents the difference between the actual total power generation of the CS and the dispatch requirement, and \(C^{\text{GU}}\) is the penalty factor. The comprehensive power generation revenue of thermal power \(f_{i,u,t}^{\text{TPU}}\) is given by the following equation:  
\[f_{i,u,t}^{\text{TPU}}=f_{i,u,t}^{\text{UB}}+f_{i,u,t}^{\text{UD}}-f_{i,u,t}^{ \text{UU}}-f_{i,u,t}^{\text{UE}}-f_{i,u,t}^{\text{US}}-f_{i,e,t}^{\text{HS}} \tag{12}\]where \(f_{i,u,t}^{\rm UB}\) represents the basic electricity sales revenue of the thermal power unit; \(f_{i,u,t}^{\rm UD}\) represents the compensation revenue from participating in DPR auxiliary services; \(f_{i,u,t}^{\rm UD}\) represents the operational cost of the thermal power unit \(f_{i,u,t}^{\rm UE}\) represents the environmental cost due to pollutant emissions; \(f_{i,u,t}^{\rm US}\) represents the CA for PR auxiliary services; \(f_{i,u,t}^{\rm HS}\) represents the comprehensive operating cost of the MSTS system of the thermal power unit, where \(e\) denotes the index of TPUMSTSR in the single CS and \(E\) represents the set of such units. The total power generation revenue from renewable energy \(f_{i,u,t}^{\rm RE}\) is given as follows:  
\[ \begin{array}{ll}f_{i,t}^{\rm RE}&=C^{\rm WT}P_{i,t}^{\rm WT}+C^{\rm PV}P_{i, t}^{\rm PV}\\ &-C^{\rm RE,D}(P_{i,t}^{\rm WT}-P_{i,t}^{\rm WT}+P_{i,t}^{\rm PV^{*}}-P_{i,t}^ {\rm PV})\\ &-f_{i,t}^{\rm WTS}-f_{i,t}^{\rm PVS}\end{array}  \tag{13}\]  
where \(C^{\rm WT}\) and \(C^{\rm PV}\) denote the unit revenue of wind and PV power generation, respectively; \(C^{\rm RE,D}\) denotes the curtailment cost for wind and PV power; \(P_{i,t}^{\rm WT^{*}}\) and \(P_{i,t}^{\rm PV^{*}}\) denote the maximum possible generation capacity of wind and PV power at time \(t\), respectively; \(P_{i,t}^{\rm WT}\) and \(P_{i,t}^{\rm PV}\) represent the actual generation outputs of wind and PV power at time \(t\), respectively; and \(f_{i,t}^{\rm WTS}\) and \(f_{i,t}^{\rm PVS}\) denote the CA for PR auxiliary services of wind and PV power, respectively. (1) Comprehensive Sales Revenue of Thermal Power Units \(f_{i,u,t}^{\rm UB}+f_{i,u,t}^{\rm UD}\)  
In addition to the basic electricity sales revenue, thermal power units can receive PR auxiliary service compensation when their generation output is below the compensation threshold. Therefore, CSs can leverage their local renewable energy consumption advantages to obtain more PR compensation, thereby increasing overall revenue and enhancing competitiveness. The total electricity sales revenue of a thermal power unit is expressed as the sum of \(f_{i,u,t}^{\rm UB}+f_{i,u,t}^{\rm UD}\). When the unit's power generation exceeds the compensation threshold, the revenue consists only of the basic revenue \(f_{i,u,t}^{\rm UB}\), which can be expressed as follows:  
\[f_{i,u,t}^{\rm UB}=C_{0}P_{i,u,t}^{\rm TPU} \tag{14}\]  
where \(P_{i,u,t}^{\rm TPU}\) represents the electric power generated by thermal power plants for external use and \(C_{0}\) is the basic unit electricity sale price, which the thermal power unit can receive regardless of its generation state. When the unit's power generation is below the compensation threshold, in addition to the basic revenue \(f_{i,u,t}^{\rm UB}\), it also includes DPR auxiliary service compensation revenue \(f_{i,u,t}^{\rm UD}\), given by the following equation:  
\[