Uncertainty Propagation Through Nonlinear Flows of Grid-Forming Exclusive Power Systems

Ascertaining the transient stability of grid-forming (GFM) exclusive systems under uncertain operating conditions is an emerging problem. This difficulty is addressed here by engineering: (i) an analytic model of GFM power plants for current saturation and (ii) an explicit Runge-Kutta scheme to propagate initial condition uncertainties represented as multivariate polynomial vectors. The propagation scheme builds upon an innovative truncated polynomial multiplication algorithm to prevent polynomial-degree explosion due to such successive operations. Transient stability is ascertained from the calculated polynomials using contraction theory. These contributions are showcased via the modified WSCC 9- and IEEE 39-bus systems.