Package pypower :: Module d2ASbr_dV2
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Module d2ASbr_dV2

source code

Computes 2nd derivatives of |complex power flow|**2 w.r.t. V.

Functions [hide private]
 
d2ASbr_dV2(dSbr_dVa, dSbr_dVm, Sbr, Cbr, Ybr, V, lam)
Computes 2nd derivatives of |complex power flow|**2 w.r.t.
source code
Variables [hide private]
  __package__ = 'pypower'
Function Details [hide private]

d2ASbr_dV2(dSbr_dVa, dSbr_dVm, Sbr, Cbr, Ybr, V, lam)

source code 

Computes 2nd derivatives of |complex power flow|**2 w.r.t. V.

Returns 4 matrices containing the partial derivatives w.r.t. voltage angle and magnitude of the product of a vector lam with the 1st partial derivatives of the square of the magnitude of branch complex power flows. Takes sparse first derivative matrices of complex flow, complex flow vector, sparse connection matrix Cbr, sparse branch admittance matrix Ybr, voltage vector V and nl x 1 vector of multipliers lam. Output matrices are sparse.

For more details on the derivations behind the derivative code used in PYPOWER information, see:

[TN2] R. D. Zimmerman, "AC Power Flows, Generalized OPF Costs and their Derivatives using Complex Matrix Notation", MATPOWER Technical Note 2, February 2010. http://www.pserc.cornell.edu/matpower/TN2-OPF-Derivatives.pdf

See Also: dSbr_dV

Authors:
Ray Zimmerman (PSERC Cornell), Richard Lincoln