A distributed MILP framework to coordinate restoration of transmission and distribution systems under imperfect communication

• A novel coordinated T&DS restoration model is formulated by introducing nodal reserve into coupling constraints. • A novel piecewise-based method is put forward to deal with non-convex bilinear terms. • A primal decomposition-based distributed MILP framework is developed to solve the coordinated T&DS restoration problem. • A strategy is proposed to encounter communication failure through filling missing exchanged information. This paper proposes a novel distributed framework to restore transmission and distribution systems (T&DS) under imperfect communication. First of all, nodal reserve is introduced into the power exchange constraint, thereby making the coordination between transmission systems (TS) and distribution systems (DS) more efficiently to achieve. However, the above formulation undermines the convexity of the model since constraints regarding reserve response involve bi-linear terms. In this regard, a novel linearization method, with guaranteed accuracy and limited complexity, is proposed to reformulate the coordinated model into a mixed-integer linear programming problem. To solve this problem, a primal decomposition-based distributed framework is developed. Then, this paper takes imperfect communication into consideration and adopts data prediction methods to encounter this kind of issue. We theoretically prove that the distributed framework is guaranteed to converge under imperfect communication with the proposed strategy. Finally, the effectiveness and scalability of the proposed framework are verified by numerical experiments.