pwrs.core.d2Sbr_dV2#

pwrs.core.d2Sbr_dV2.d2Sbr_dV2(Cbr, Ybr, V, mu, vcart=0, nargout=1)[source]#

Return 2nd derivatives of complex branch power flows.

Computes the Hessian blocks of mu' * Sbr(V) for a branch-end power flow expression defined by connection matrix Cbr and admittance matrix Ybr.

Parameters:

  • Cbr (array_like) – Zero-based endpoint bus indices for the constrained branch rows.

  • Ybr (sparse matrix) – Branch admittance matrix for the corresponding terminal.

  • V (array_like) – Complex bus voltage vector.

  • mu (array_like) – Multiplier vector for the selected branch-end flow equations.

  • vcart (int or bool, optional) – Voltage coordinate flag. Use polar coordinates when false and cartesian coordinates when true.

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

Returns:

Hessian blocks (H11, H12, H21, H22) for the selected voltage coordinate system, or just H11 when nargout == 1.

Return type:

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

pwrs.core.d2Sbr_dV2.d2Sbr_dV2_full(Cbr, Ybr, V, mu, vcart=0)[source]#

Return all four complex branch-power Hessian blocks.