Data-Driven Continuous-Time Modeling of Power System Uncertainty Using a Multi-Dimensional Stochastic Differential Equation

This paper proposes a generalized continuous random process modeling framework for imposing any desired probability distribution, autocorrelation and power spectral density of measured data of power system uncertainty by developing a multi-dimension stochastic differential equation (SDE) together with a quadratic output equation. An algorithm for determining appropriate parameters of the proposed SDE model is presented. The effectiveness of derived random modeling scheme is verified by carrying out comparative simulations using actual time series data of wind speed, solar radiation, PJM dynamic regulation, and wind power. The proposed SDE model can be readily integrated in various electrical component models for reliable operation, stability assessment and control of renewable power systems.

Automated summary

This paper proposes a generalized continuous random process modeling framework to impose any desired probability distribution, autocorrelation, and power spectral density on measured data of power system uncertainty. The proposed stochastic differential equation (SDE) model, together with a quadratic output equation, is used and an algorithm for determining appropriate parameters is presented. Comparative simulations using actual time series data show the effectiveness of the derived random modeling scheme for wind speed, solar radiation, PJM dynamic regulation, and wind power. The proposed SDE model can be easily integrated into various electrical component models for reliable operation, stability assessment, and control of renewable power systems.