Probabilistic Power Flow Estimation in Power Grids Considering Generator Frequency Regulation Constraints Based on Unscented Transformation

To address active power fluctuations in power grids induced by high renewable energy penetration and overcome the limitations of existing probabilistic power flow (PPF) methods that ignore generator frequency regulation constraints, this paper proposes a segmented stochastic power flow modeling method and an efficient analytical framework that incorporates the actions and capacity constraints of regulation units. Firstly, a dual dynamic piecewise linear power injection model is established based on “frequency deviation interval stratification and unit limit-reaching sequence ordering,” clarifying the hierarchical activation sequence of “loads first, followed by conventional units, and finally automatic generation control (AGC) units” along with the coupled adjustment logic upon reaching limits, thereby accurately reflecting the actual frequency regulation process. Subsequently, this model is integrated with the State-Independent Linearized Power Flow (DLPF) model to develop a segmented stochastic power flow framework. For the first time, a deep integration of unscented transformation (UT) and regulation-aware power allocation is achieved, coupled with the Nataf transformation to handle correlations among random variables, forming an analytical framework that balances accuracy and computational efficiency. Case studies on the New England 39-bus system demonstrate that the proposed method yields results highly consistent with those of Monte Carlo simulations while significantly enhancing computational efficiency. The DLPF model is validated to be applicable under scenarios where voltage remains within 0.95–1.05 p.u., and line transmission power does not exceed 85% of rated capacity, exhibiting strong robustness against parameter fluctuations and capacity variations. Furthermore, the method reveals voltage distribution patterns in wind-integrated power systems, providing reliable support for operational risk assessment in grids with high shares of renewable energy.