In this paper, a data-driven based Real-time Stability Metric (RSM) is proposed to evaluate the stability in Solid State Transformer (SST)-based modern distribution systems based on nonlinear time series analysis. This approach brings two main advantages to the analysis. First, the time series dataset is obtained from the terminal measurement; therefore, linearization is not necessarily needed as opposed to linear approaches. Second, fast dynamics in the system can be captured by an appropriate time resolution in data acquisition and it facilitates the proposed stability analysis capable in real-time. In this study, three Solid State Transformers are considered in a microgrid as the test system. Stability is evaluated by real-time determination of Lyapunov exponents through a real-time processor coordinated with the microgrid.