## 3 Model Development
### Evaluation Process  
To evaluate the RESs accommodation capability and the flexibility potential of TPUs, this paper employs the following indices to analyze the scheduling results:* Accommodation level: Indicates the utilization efficiency of WT, PV, and overall RESs. They are represented \(I_{\text{WT}}^{\text{AL}}\), \(I_{\text{PV}}^{\text{AL}}\), and \(I_{\text{RES}}^{\text{AL}}\), respectively. The accommodation level is calculated as \[\left\{ \begin{array}{l}I_{\text{WT}}^{\text{AL}}=\sum_{t=1}^{T}\frac{P_{t}^{ \text{WT}}}{P_{t}^{\text{WT}*}}\\ I_{\text{PV}}^{\text{AL}}=\sum_{t=1}^{T}\frac{P_{t}^{\text{WT}}}{P_{t}^{ \text{WT}*}}\\ I_{\text{RES}}^{\text{AL}}=\sum_{t=1}^{T}\frac{P_{t}^{\text{WT}}+P_{t}^{ \text{PV}}}{P_{t}^{\text{WT}*}+P_{t}^{\text{WT}*}}\end{array} \right..\] (27)
* Regulation marginals: Denote the total additional available regulation resources of TPUs after accommodating the RESs between two consecutive time steps. The flexibility marginals are differentiated into upward and downward indices corresponding to \(I_{\text{TPU}}^{\text{FM}+}\) and \(I_{\text{TPU}}^{\text{FM}-}\). They are calculated as follows: \[I_{\text{TPU}}^{\text{FM}+}=\frac{\sum_{t=1}^{T-1}I_{\text{TPU},t}^{\text{FM}+ }}{\sum_{t=1}^{T-1}S_{t}^{\text{up}}},\] (28) \[I_{\text{TPU}}^{\text{FM}-}=-\frac{\sum_{t=1}^{T-1}I_{\text{TPU},t}^{\text{ FM}-}}{\sum_{t=1}^{T-1}S_{t}^{\text{dw}}},\] (29) \[I_{\text{TPU},t}^{\text{FM}+}= \begin{cases}\sum_{u=1}^{N_{\text{TPU}}}\left[ P_{u,t}^{\text{TPU},\text{Rup},\text{max}}-\left(P_{u,t+1}^{\text{TPU}}-P_{u,t}^{ \text{TPU}}\right)\right]\Delta t,&\sum_{u=1}^{N_{\text{TPU}}}P_{u,t+1}^{\text {TPU}}-P_{u,t}^{\text{TPU}}\geq 0\\ 0,&\sum_{u=1}^{N_{\text{TPU}}}P_{u,t+1}^{\text{TPU}}-P_{u,t}^{\text{TPU}}<0^{ \prime}\end{cases} \] (30) \[S_{t}^{\text{up}}= \begin{cases}1,&\sum_{u=1}^{N_{\text{TPU}}}P_{u,t+1}^{ \text{TPU}}-P_{u,t}^{\text{TPU}}\geq 0\\ 0,&\sum_{u=1}^{N_{\text{TPU}}}P_{u,t+1}^{\text{TPU}}-P_{u,t}^{\text{TPU}}<0^{ \prime}\end{cases} \] (31) \[I_{\text{TPU},t}^{\text{FM}-}= \begin{cases}\sum_{u=1}^{N_{\text{TPU}}}\left[ P_{u,t}^{\text{TPU},\text{Rdw},\text{max}}-\left(P_{u,t+1}^{\text{TPU}}-P_{u,t}^{ \text{TPU}}\right)\right]\Delta t,&\sum_{u=1}^{N_{\text{TPU}}}P_{u,t+1}^{ \text{TPU}}-P_{u,t}^{\text{TPU}}<0\\ 0,&\sum_{u=1}^{N_{\text{TPU}}}P_{u,t+1}^{\text{TPU}}-P_{u,t}^{\text{TPU}}\geq 0 ^{\prime}\end{cases} \] (32) \[S_{t}^{\text{dw}}= \begin{cases}1,&\sum_{u=1}^{N_{\text{TPU}}}P_{u,t+1}^{ \text{TPU}}-P_{u,t}^{\text{TPU}}<0\\ 0,&\sum_{u=1}^{N_{\text{TPU}}}P_{u,t+1}^{\text{TPU}}-P_{u,t}^{\text{TPU}}\geq 0 ^{\prime}\end{cases} \] (33) \[\left\{ \begin{array}{l}P_{u,t}^{\text{TPU},\text{Rup},\text{max}}=\min \left(P_{u}^{\text{TPU},\text{max}},P_{u,t}^{\text{TPU},\text{Rup}1},P_{u,t}^{ \text{TPU},\text{Rup}2}\right)-P_{u,t}^{\text{TPU}}\\ P_{u,t}^{\text{TPU},\text{Rdw},\text{max}}=\max\left(P_{u}^{\text{TPU},\min},P_{u,t}^{\text{TPU},\text{Rdw}1},P_{u,t}^{\text{TPU},\text{Rdw}2}\right)-P_{u,t}^{ \text{TPU}}\\ P_{u,t}^{\text{TPU},\text{Rup}1}=P_{u,t}^{\text{TPU}}+R_{u}^{\text{IM}}\Delta t \\ P_{u,t}^{\text{TPU},\text{Rup}2}=\frac{R_{u}^{\text{IPU}}}{R_{u}^{\text{IPU}}} \left[P_{u,t}^{\text{TPU}}+R_{u}^{\text{IM}}\Delta t-\left(1-\frac{R_{u}^{ \text{IM}}}{R_{u}^{\text{IM}}}\right)P_{u}^{\text{TPU},\text{Rdn}1}\right]\\ P_{u,t}^{\text{TPU},\text{Rdw}1}=P_{u,t}^{\text{TPU}}-R_{u}^{\text{IM}}\Delta t \\ P_{u,t}^{\text{TPU},\text{Rdw}2}=\frac{R_{u}^{\text{IM}}}{R_{u}^{\text{IM}}}P_{u,t}^{\text{TPU}}-R_{u}^{\text{IM}}\Delta t+\left(1-\frac{R_{u}^{\text{IM}}}{R_ {u}^{\text{IM}}}\right)P_{u}^{\text{TPU},\text{Rdn}2}\end{array} \right.,\] (34) where \(P_{u}^{\text{TPU},\text{Rup},\text{max}}\) and \(P_{u}^{\text{TPU},\text{Rdw},\text{max}}\) represent the maximum upward and downward regulation capabilities of TPU from \(t\) to \(t+1\). \(S_{t}^{\text{up}}=1\) or \(S_{t}^{\text{dw}}=1\) indicates that an upward or downward adjustment has occurred in the TPUs from \(t\) to \(t+1\).