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The real-time simulation of active distribution networks (ADNs) can provide an accurate insight into transient behaviours, but faces challenges in simulation efficiency and flexibility brought by larger system scales and wider time-scale ranges. This paper presents an asynchronous multi-rate (AMR) method and design for the real-time simulation of large-scale ADNs. In the proposed method, the entire ADN was decoupled into different subsystems according to accuracy requirements, and optimized time-steps were allocated to each subsystem to realize a fully distributed simulation. This not only alleviated the time-step coordination problem existing in multi-rate real-time simulations, but also enhanced the flexible expansion capabilities of the real-time simulator. To realize the AMR real-time simulation, a multi-rate interfacing method, synchronization mechanism, and data communication strategy are proposed in this paper, and their hardware design is also presented in detail. A modified IEEE 123-node system with photovoltaics and wind turbine generators was simulated on a 3 field-programmable gate arrays (FPGAs)-based AMR real-time simulator. The real-time results were captured by the oscilloscope and verified with PSCAD/EMTDC, which demonstrated the superiority in simulation flexibility and accuracy compared with the synchronous multi-rate (SMR) method.