A Non-Sampling Time-Domain Simulation Framework for Transient Stability Assessment Under Stochastic Continuous Disturbances

The power system dynamic performance under stochastic continuous disturbances is described using stochastic differential algebraic equations (SDAEs). A critical issue of using the conventional numerical methods for SDAEs resides in that they require numerous samples to calculate the probability distributions of state variables in transient process. To mitigate this issue, this paper proposes a non-sampling time domain simulation (NSTDS) framework, which can directly obtain the probability distributions of state variables at each moment of transient process, and significantly reduce the computational time. Within the proposed NSTDS framework, a Milstein-Euler prediction correction iteration scheme is used, which has a higher convergence order than the conventional iteration schemes. In addition, leveraging the duality theorem on L^p space, a method for computing the probability distributions of random variable functions at each moment is proposed, preventing the curse of dimensionality and applicable to large-scale power systems. Finally, case studies on modified IEEE 39- and 118-bus systems validate the high computational accuracy and efficiency of the proposed NSTDS framework for power system transient stability assessment under stochastic continuous disturbances.