Package pypower :: Module d2Sbus_dV2
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Module d2Sbus_dV2

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Computes 2nd derivatives of power injection w.r.t. voltage.

Functions [hide private]
 
d2Sbus_dV2(Ybus, V, lam)
Computes 2nd derivatives of power injection w.r.t.
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Variables [hide private]
  __package__ = 'pypower'
Function Details [hide private]

d2Sbus_dV2(Ybus, V, lam)

source code 

Computes 2nd derivatives of power injection w.r.t. voltage.

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 complex bus power injections. Takes sparse bus admittance matrix Ybus, voltage vector V and nb 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

Authors:
Ray Zimmerman (PSERC Cornell), Richard Lincoln