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Simulation tools play a critical role in the design and test of power systems. In particular, real time simulation is now reliable and constitutes the basis for Hardware in the Loop and Power hardware in the Loop testing techniques. The application of real time simulation and related techniques to power systems is made particularly challenging as it should cover the analysis of stochastic behaviors. In fact, numerous and volatile distributed generation (DG), and end users' dual load-generator behavior are introducing more uncertainties to the conventional power systems. Therefore, it is necessary to consider the uncertainty into the process of real time simulation as well. Methods that require many repetitions, like Monte Carlo, may not be applicable, particularly in Hardware in the Loop experiments with intrinsically long duration, e.g. those involving thermal systems. As a first step, this paper proposes to address this issue combining non-intrusive polynomial chaos theory (NIPCT) with real time simulation. The main goal is to reduce the number of test scenarios, and correspondingly the run-time. The implementation of this approach based on Real Time Digital Simulator (RTDS) and a MATLAB toolbox (NIPC_Tool) is introduced. The method is then demonstrated on a 5-bus system and results are compared with the Monte Carlo approach.