*3.3. Learning-Aided OPF for TTC Calculation*

The trained learning-aided model is finally forwarded to replace (5)~(6) to mitigate the TTC computational burden. The reformed learning-aided OPF for calculating TTC is given as follows:

$$\begin{array}{l}\text{Maximize (2)}\\\text{s.t. (3)-(4)}\\\Gamma\_{\mathcal{L}} \ge 0, \mathcal{c} \in \mathcal{S}\_{\mathcal{L}}\end{array} \tag{2.3}$$

In Equation (23), steady-state physics remains the same, but dynamics become a data model. This modeling strategy possesses several merits: (1) it remarkably reduces the solving complexity of the full physics version. (2) it preserves physics to decrease adverse effects from significant learning errors. A common way to solve Equation (23) is gradientfree algorithms [26–28]. However, these algorithms characterize cumbersome stochastic search mechanism. A fast-solving algorithm for such physics and data hybrid model is still under exploitation.
