d2Imis_dVdSg
- d2Imis_dVdSg(Cg, V, lam, vcart)
d2Imis_dVdSg()
- Computes 2nd derivatives of current balance w.r.t. V and Sg.The derivatives can be take with respect to polar or cartesian coordinates of voltage, depending on the 4th argument. GSV = D2IMIS_DVDSG(CG, V, LAM) GSV = D2IMIS_DVDSG(CG, V, LAM, 0) Returns a matrix 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 real and reactive power generation. GSV = D2IMIS_DVDSG(CG, V, LAM, 1) Returns a matrix containing the partial derivatives w.r.t. real and imaginary parts of voltage of the product of a vector LAM with the 1st partial derivatives of the real and reactive power generation. Takes the generator connection matrix, complex voltage vector V and nb x 1 vector of multipliers LAM. Output matrices are sparse. Examples: Cg = sparse(gen(:, GEN_BUS), 1:ng, -, nb, ng); Gsv = d2Imis_dVdSg(Cg, V, lam); Here the output matrix corresponds to: Gsv = [ Gpa Gpv; Gqa Gqv ]; Gpa = d/dVa (dImis_dPg.' * lam) Gpv = d/dVm (dImis_dPg.' * lam) Gqa = d/dVa (dImis_dQg.' * lam) Gqv = d/dVm (dImis_dQg.' * lam) [Grr, Gri, Gir, Gii] = d2Imis_dVdSg(Cg, V, lam, 1); Here the output matrices correspond to: Gsv = [ Gpr Gpi; Gqr Gqi ]; Gpr = d/dVr (dImis_dPg.' * lam) Gpi = d/dVi (dImis_dPg.' * lam) Gqr = d/dVr (dImis_dQg.' * lam) Gqi = d/dVi (dImis_dQg.' * lam)
For more details on the derivations behind the derivative code used in MATPOWER, see:
[TN2] R. D. Zimmerman, "AC Power Flows, Generalized OPF Costs and their Derivatives using Complex Matrix Notation", MATPOWER Technical Note 2, February 2010. [Online]. Available: https://matpower.org/docs/TN2-OPF-Derivatives.pdf doi: 10.5281/zenodo.3237866 [TN3] B. Sereeter and R. D. Zimmerman, "Addendum to AC Power Flows and their Derivatives using Complex Matrix Notation: Nodal Current Balance," MATPOWER Technical Note 3, April 2018. [Online]. Available: https://matpower.org/docs/TN3-More-OPF-Derivatives.pdf doi: 10.5281/zenodo.3237900 [TN4] B. Sereeter and R. D. Zimmerman, "AC Power Flows and their Derivatives using Complex Matrix Notation and Cartesian Coordinate Voltages," MATPOWER Technical Note 4, April 2018. [Online]. Available: https://matpower.org/docs/TN4-OPF-Derivatives-Cartesian.pdf doi: 10.5281/zenodo.3237909