pwrs.core.d2Abr_dV2#

pwrs.core.d2Abr_dV2.d2Abr_dV2(d2F_dV2, dF_dV1, dF_dV2, F, V, mu, nargout=1)[source]#

Return 2nd derivatives of squared branch flow magnitudes.

Given first- and second-derivative data for a branch flow quantity F(V), computes the Hessian blocks of the corresponding squared magnitude expression used in OPF flow-limit constraints.

Parameters:

  • d2F_dV2 (callable) – Function returning the four Hessian blocks of mu' * F(V).

  • dF_dV1 (sparse matrix) – First derivative of F with respect to the first voltage block.

  • dF_dV2 (sparse matrix) – First derivative of F with respect to the second voltage block.

  • F (array_like) – Complex branch flow vector.

  • V (array_like) – Complex bus voltage vector.

  • mu (array_like) – Multiplier vector for the branch flow limit terms.

  • nargout (int, optional) – MATLAB compatibility flag controlling how many Hessian blocks are returned.

Returns:

Real Hessian blocks (H11, H12, H21, H22) for the squared flow expression, or just H11 when nargout == 1.

Return type:

scipy.sparse.csc_matrix or tuple of scipy.sparse.csc_matrix

pwrs.core.d2Abr_dV2.d2Abr_dV2_full(d2F_dV2, dF_dV1, dF_dV2, F, V, mu)[source]#

Return all four Hessian blocks.