d2Ibr_dV2
- d2Ibr_dV2(Ybr, V, mu, vcart)
d2Ibr_dV2()
- Computes 2nd derivatives of complex branch current w.r.t. voltage.The derivatives can be take with respect to polar or cartesian coordinates of voltage, depending on the 4th argument. [HAA, HAV, HVA, HVV] = D2IBR_DV2(YBR, V, MU) [HAA, HAV, HVA, HVV] = D2IBR_DV2(YBR, V, MU, 0) Returns 4 matrices containing the partial derivatives w.r.t. voltage angle and magnitude of the product of a vector MU with the 1st partial derivatives of the complex branch currents. [HRR, HRI, HIR, HII] = D2IBR_DV2(YBR, V, MU, 1) Returns 4 matrices (all zeros) containing the partial derivatives w.r.t. real and imaginary part of complex voltage of the product of a vector MU with the 1st partial derivatives of the complex branch currents. Takes sparse branch admittance matrix YBR, voltage vector V and nl x 1 vector of multipliers MU. Output matrices are sparse. Examples: [Ybus, Yf, Yt] = makeYbus(baseMVA, bus, branch); Ybr = Yf; [Haa, Hav, Hva, Hvv] = d2Ibr_dV2(Ybr, V, mu); Here the output matrices correspond to: Haa = d/dVa (dIbr_dVa.' * mu) Hav = d/dVm (dIbr_dVa.' * mu) Hva = d/dVa (dIbr_dVm.' * mu) Hvv = d/dVm (dIbr_dVm.' * mu) [Hrr, Hri, Hir, Hii] = d2Ibr_dV2(Ybr, V, mu, 1); Here the output matrices correspond to: Hrr = d/dVr (dIbr_dVr.' * mu) Hri = d/dVi (dIbr_dVr.' * mu) Hir = d/dVr (dIbr_dVi.' * mu) Hii = d/dVi (dIbr_dVi.' * mu)
For more details on the derivations behind the derivative code used in MATPOWER 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. [Online]. Available: https://matpower.org/docs/TN2-OPF-Derivatives.pdf doi: 10.5281/zenodo.3237866 [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