## 2 The TPUMSTSR Under RLV Model
### Operational Model of TPUMSTSR Under RLVs  
Thermal power units face the dual challenges of reducing carbon emissions and enhancing flexibility. While individual retrofitting technologies (such as MSTS or RLV retrofitting) can partially address these issues, they still have limitations. Integrating MSTS retrofitting with RLV retrofitting can leverage the advantages of both, further improving the PR capability, operational flexibility, and economic efficiency of thermal power units. However, this combined retrofitting approach imposes higher requirements on the operational control of thermal power units, necessitating the establishment of precise mathematical models and consideration of multiple constraints. Figure 2: Schematic diagram of internal energy flow in TPUMSTSR. To further reduce coal consumption and carbon emissions, the MSTS system is first utilized to regulate the unit's output when thermal power units need to adjust their output to meet dispatch requirements. The operational model of the thermal power unit under this scenario can be described by the following mathematical expression [35; 36]:  
\[\left\{ \begin{array}{l}S_{t}^{\rm H}=(1-\eta^{\rm H})S_{t-1}^{\rm H}+(\eta^{ \rm HC}P_{t}^{\rm HC}-\frac{P_{t}^{\rm HD}}{\eta^{\rm HC}})\Delta t\\ S_{t}^{\rm L}=(1-\eta^{\rm L})S_{t-1}^{\rm L}+(\eta^{\rm LC}P_{t}^{\rm LC}- \frac{P_{t}^{\rm HD}}{\eta^{\rm LD}})\Delta t\\ P_{t}^{\rm BURN}+P_{t}^{\rm HD}-P_{t}^{\rm HC}+P_{t}^{\rm LD}-P_{t}^{\rm LC} =P_{t}^{\rm ST}\\ P_{t}^{\rm BURN}=\frac{\eta^{\rm coal}M_{t}^{\rm coal}Q_{t}^{\rm coal}}{ \Delta t}\\ P_{t}^{\rm TPU}=\eta^{\rm ST}P_{t}^{\rm ST}\\ SOC^{\rm min}\leq SOC(t)\leq SOC^{\rm max}\end{array} \right. \tag{1}\]  
where \(S_{t}^{\rm H}\) and \(S_{t}^{\rm L}\) represent the stored heat in the high-temperature and low-temperature thermal storage systems at time \(t\); \(\eta^{\rm H}\) and \(\eta^{\rm L}\) denote the heat loss rates of the high-temperature and low-temperature thermal storage systems, respectively; \(\eta^{\rm HC}\), \(\eta^{\rm HD}\), \(\eta^{\rm LC}\), and \(\eta^{\rm LD}\) represent the thermal efficiencies of the high-temperature and low-temperature systems; \(\eta^{\rm coal}\) is the thermal efficiency of coal combustion; \(M^{\rm coal}\) is the mass of coal consumed at time \(t\); \(Q^{\rm coal}\) is the calorific value of pulverized coal combustion; \(\eta^{\rm ST}\) represents the thermoelectric conversion efficiency; and SOC (state of charge) represents the remaining power of the energy storage system, described as residual heat in the MSTS system, and is specifically described in the constraint conditions of (30). To enhance the PR capability and operational flexibility of thermal power units, RLV adjustment is initiated when the capacity or charging/discharging efficiency of the MSTS system cannot meet the load demand. The primary goal in this scenario is to meet the real-time dispatch requirements of the grid. During the operation of the thermal power unit, the following ramp rate constraint under RLVs must be satisfied [3]:  
\[\left\{\begin{array}{l}\forall P_{t-1}^{\rm BURN}\in P_{a},P_{t}^{\rm min,BURN}\in P_{b},P_{t}^{\rm max,BURN}\in P_{c}\\ \left\{\begin{array}{l}P_{t}^{\rm BURN}\leq r_{c}\Delta t+\frac{r_{c}}{r_{ a}}P_{t-1}^{\rm BURN}-\sum\limits_{x=c}^{a-1}\left(\frac{r_{c}}{r_{x+1}}- \frac{r_{c}}{r_{x}}\right)P_{x}^{\rm PR}\\ P_{t}^{\rm BURN}\geq-r_{b}\Delta T+\frac{r_{b}}{r_{a}}P_{t-1}^{\rm BURN}+ \sum\limits_{x=a}^{b-1}\left(\frac{r_{b}}{r_{x+1}}-\frac{r_{b}}{r_{x}}\right)P _{x}^{\rm PR}\\ \sum\limits_{x=c}^{a-1}\left(\frac{r_{c}}{r_{x+1}}-\frac{r_{c}}{r_{x}}\right)P _{x}^{\rm PR}=0,\forall a=c\\ \sum\limits_{x=a}^{b-1}\left(\frac{r_{b}}{r_{x+1}}-\frac{r_{b}}{r_{x}}\right)P _{Under the existing ancillary service market framework, there are no rules for benefit distribution involving MCSs as primary entities.