Specifications of Photovoltaic Pumping Systems in Agriculture

Appendix C

The Induction Machine: Modeling and Control

C.1 Space Vector Notion

The space vector $\overline{x}$ is defined by (Fig. C.1):

$\overline{x}=\frac{2}{3}\left(x_1+a{x}_2+a^2{x}_3\right)$

where

$a=e^{j\frac{2\pi }{3}}$

and

$\{\begin{array}{c}{x}_1=X_1\cos (wt+{\phi }_1)\\ x_2=X_2\cos (wt+{\phi }_2)\\ x_3=X_3\cos (wt+{\phi }_3)\end{array}$ (C.1)

(C.1)

Figure C.1 Schematic representation ...