  The Jacobian matrix is the core part of power flow analysis, which is the
basis for power system planning and operations. This paper estimates the
Jacobian matrix in high dimensional space. Firstly, theoretical analysis and
model-based calculation of the Jacobian matrix are introduced to obtain the
benchmark value. Then, the estimation algorithms based on least-squared errors
and the deviation estimation based on the neural network are studied in detail,
including the theories, equations, derivations, codes, advantages and
disadvantages, and application scenes. The proposed algorithms are data-driven
and sensitive to up-to-date topology parameters and state variables. The
efforts are validate by comparing the results to benchmark values.
