1 results about "Cartesian product" patented technology

This invention discloses a real-time power grid state estimation method based on non-Euclidean geometry. The method maps voltage phase angles to a compact manifold, constructing a hybrid state space consisting of the Euclidean space of voltage amplitudes and the Cartesian product of the compact manifold of phase angles. The state is then mapped to the tangent space for prediction and covariance propagation via logarithmic mapping, and then back to the manifold via exponential mapping. An innovation vector on the manifold is calculated, and a periodic normalization function is used to process the phase angle measurement residuals, performing state correction in the manifold space. Furthermore, topology sensing is performed based on simplex theory, detecting topology events through Betti numbers and adaptively adjusting filters. Based on the estimated state, a continuous reactive power control optimization problem is solved in the tangent space, and a smooth, bounded control quantity is obtained through Lie exponential mapping. This invention fundamentally solves the phase angle jump problem, achieving millisecond-level real-time state estimation and significantly improving estimation accuracy and adaptability to topology changes.