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Real-time digital simulation of large power systems requires not only significant computational power but also simpler and accurate models. This paper proposes a new approach for transient simulation of power systems using a robust two-layer network equivalent model and an advanced PC-cluster based parallel real-time simulator. Using a combination of well established fitting and optimization methods, the generated low-order model is of high accuracy compared to its full model over a wide frequency bandwidth. The merits of this method are its robustness in terms of stability and positive-realness, its accuracy at not only transient frequencies but also at dc and power frequency, and its optimal order determination feature. To validate the new method, a realistic large-scale power system - the Alberta interconnected electric system - is simulated in real-time. The real-time electromagnetic transient program is implemented in C++ language using object-oriented programming techniques on the PC-cluster. A time-step of 20 mus has been used for the real-time simulation. The captured oscilloscope results demonstrate excellent accuracy and efficiency of the proposed model in comparison to a full-scale off-line simulation of the original system in the ATP version of EMTP.