Power Quality in Power Systems and Electrical Machines, 2nd Edition

${\overline{H}}^{\left(h\right)}=\left[\begin{array}{l}{\overline{0}}_{2\left(m-1\right)\times 2\left(n-m+1\right)}\hfill \\ ---\hfill & ---\hfill & --------\hfill & --\hfill & ---\hfill & ---\hfill \\ \frac{\partial {\mathrm{G}}_{r,m}^{\left(h\right)}}{\partial {\alpha }_m}\hfill & \frac{\partial {\mathrm{G}}_{r,m}^{\left(h\right)}}{\partial {\beta }_m}\hfill & .\hfill & .\hfill & 0\hfill & 0\hfill \\ \frac{\partial {\mathrm{G}}_{i,m}^{\left(h\right)}}{\partial {\alpha }_m}\hfill & \frac{\partial {\mathrm{G}}_{i,m}^{\left(h\right)}}{\partial {\beta }_m}\hfill & .\hfill & .\hfill & 0\hfill & 0\hfill \\ .\hfill & .\hfill & .\hfill & .\hfill & .\hfill & .\hfill \\ 0\hfill & 0\hfill & .\hfill & .\hfill & \frac{\partial {\mathrm{G}}_{r,n}^{\left(h\right)}}{\partial {\alpha }_n}\hfill & \frac{\partial {\mathrm{G}}_{r,n}^{\left(h\right)}}{\partial {\beta }_n}\hfill \\ 0\hfill & 0\hfill & .\hfill & .\hfill & \frac{\partial {\mathrm{G}}_{i,n}^{\left(h\right)}}{\partial {\alpha }_n}\hfill & \frac{\partial {\mathrm{G}}_{i,n}^{\left(h\right)}}{\partial {\beta }_n}\hfill \end{array}\right]$

  (7-112)

where h = 1, 5, 7, …, L. For h = 1 the entries are zero.

7.4.5 Harmonic Jacobian Entry Formulas Related to Line Currents

Figure 7.15 shows a typical nonlinear bus i of an n bus system. This ith bus is connected to three other buses, m, k, and l. The nonlinear device connected to bus i demands a complex load current ${\tilde{g}}_{\mathrm{load},i}^{\left(h\right)}$ (referred to the nonlinear bus i) at the hth harmonic frequency.

Figure 7.15 ...