**6. Conclusions**

Large-scale wind power penetration has increased the potential insecurity risk of interarea power exchange. Therefore, rapid and accurate security assessment for inter-corridors is imperative. Towards this end, this paper proposes a learning-aided method for fast TTC calculation. The TTC calculation is firstly modeled as transient stability constrained optimal power flow. Then, to reduce the complexity of the TSCOPF model, DBN-based learning-aided transient stability assessment is introduced to surrogate high-dimensional and time-consuming time-domain constraints. In the end, the Jacobian and Hessian matrix of the trained learning-aided model is derived; thereby, nonlinear programming is allowed to solve the learning-aided TSCOPF model efficiently.

The result of the case study demonstrates that the learning-aided model can achieve TSA with higher accuracy and generalization. Moreover, the learning-aided TSCOPF model proposed in this paper can obtain more accurate TTC values than RPF, sensitivity-based, and direct data-driven methods. This is because the proposed method can both take into account the fidelity and efficiency of physics- and data-driven modeling by combining the learning-aided model with the OPF. And compared with the heuristic search of RPF, the OPF model can search the extreme operating point more accurately. On the other hand, due to the use of the learning-aided model to surrogate the time-consuming TSA, it has higher computational efficiency than other physics-driven methods, which means that it can be applied online after sufficient offline training. Besides, the proposed method is not limited to TTC-oriented research. Because of its high compatibility with other static or dynamic models, it can be extended to other index calculations in the power system that require a large amount of computation but require high efficiency. Other advanced machine learning algorithms will be used to achieve better calculation performance in our future work. And, it would also be meaningful to optimize and control the TTC.

**Author Contributions:** Conceptualization, G.Q. and J.L.; methodology, G.Q. and J.L.; software, J.L.; validation, J.L.; formal analysis, J.L.; resources, Y.L.; data curation, J.L.; writing—original draft preparation, J.L.; writing—review and editing, G.Q. and Y.L.; visualization, J.L.; supervision, Y.L.; project administration, X.S.; funding acquisition, Y.L. and X.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
