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Coordination of transmission and distribution power systems is increasingly critical in the context of the ongoing energy transition. However, traditional centralized energy management faces challenges related to privacy and/or sovereignty concerns, leading to growing research interests in distributed approaches. Nevertheless, solving distributed AC optimal power flow (OPF) problems encounters difficulties due to their nonlinearity and nonconvexity, making it challenging for state-of-the-art distributed approaches. To solve this issue, the present paper focuses on investigating the distributed AC OPF problem of generic integrated transmission-distribution (ITD) systems, considering complex grid topology, by employing a new variant of Augmented Lagrangian based Alternating Direction Inexact Newton method (ALADIN). In contrast to the standard ALADIN, we introduce a second-order correction into ALADIN to enhance its numerical robustness and properly convexify distribution subproblems within the ALADIN framework for computing efficiency. Moreover, a rigorous proof shows that the locally quadratic convergence rate can be preserved for solving the resulting distributed nonconvex problems. Extensive numerical simulations with varying problem sizes and grid topologies demonstrate the effectiveness of the proposed algorithm, outperforming state-of-the-art approaches in terms of numerical robustness, convergence speed, and scalability.

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