*2.3. Mixed-Integer Second-Order Cone Programming (MISOCP) Model*

After the introduction of SOCP approximations and linearization of the OLTC transformer model, the complete set of equations used in this model is represented as follows:

1. By introducing (9) into (1), the objective function is given as:

$$\text{Minimize } \sum\_{i \in \mathbb{B}^{\mathsf{T}}, s \in \mathcal{S}} P\_{\text{Ii}, \text{s}} - \sum\_{i \in \text{DI}, j \in \text{DI}^{\text{task}}\_i, s \in \mathcal{S}} \mathbf{P}\_{i \mid s}^{\text{DI}, \text{inst}} + \sum\_{(ij) \in \text{IV}, s \in \mathcal{S}} r\_{ij} \cdot \mathbf{L}\_{ij, \text{s}} \tag{18}$$

subject to:

