A Systematic Method to Model Power Systems as Stochastic Differential Algebraic Equations

This paper proposes a systematic and general approach to model power systems as continuous stochastic differential-algebraic equations. With this aim, the paper provides a theoretical background on stochastic differential-algebraic equations and justifies the need for stochastic models in power system analysis. Then, the paper describes a general procedure to define stochastic dynamic models. Practical issues related to the numerical integration of the resulting power system model are also discussed. A case study illustrating the proposed approach is provided based on the IEEE 145-bus 50-machine system. The case study also illustrates and compares the reliability of the results obtained using stochastic and conventional probabilistic models.