NON - LINEAR STOCHASTIC Networks

Power Systems

A rigorous uncertainty quantification theory for non-linear stochastic networks has been developed, addressing a previously underexplored area. Through a complex analytic study of the nonlinear network with respect to stochastic parameters, convergence rates were derived and demonstrated to be of subexponential or algebraic order relative to the dimensionality of random perturbations. Due to the method's high accuracy, sparse grids prove effective for computing low-probability events with high confidence. This approach has been successfully applied to the general power flow problem, with numerical experiments on the complex 39-bus New England power system model under large stochastic loads aligning with the theoretical convergence rates. Notably, this method achieves computational speeds approximately 10⁻¹¹ times faster than the Monte Carlo (MC) method while maintaining equivalent accuracy. This improvement translates to solving problems in hours on a standard desktop computer versus over a million years with traditional MC approaches. While traditional methods have long been used, modern ML-based solutions offer key benefits: processing large datasets, handling high-dimensional data from various sources, achieving higher accuracy, and enabling real-time detection. These capabilities make ML indispensable in data-driven environments where rapid, reliable anomaly identification is critical.