Electrical Machines And Drives A Space Vector Theory Approach Monographs In Electrical And Electronic Engineering -

This monograph does not seek to replace the classic texts of Fitzgerald, Leonhard, or Novotny & Lipo. Rather, it aims to re-center the student and practitioner onto the structural invariant : the rotating space vector is the real physical quantity; the three phase windings are merely its projection sensors. From this vantage point, electrical drives become a branch of applied vector calculus, not a catalog of special cases.

1. The Inadequacy of the Single-Phase Gaze This monograph does not seek to replace the

Difference between machine types is merely a matter of flux generation: $\vec{\psi}_s = L_s \vec{i}_s$ (IM), $\vec{\psi}_s = L_s \vec{i} s + \vec{\psi} {PM}$ (PMSM), or $\vec{\psi}_s = L_s \vec{i}_s + L_m \vec{i}_r'$ (DFIM). The drive —the control algorithm—does not need to know the difference beyond the flux linkage map. The space vector theory, first crystallized by Kovacs

The space vector theory, first crystallized by Kovacs and Racz in the 1950s and later refined by Depenbrock, Leonhard, and Vas, offers not merely an alternative method but the canonical language for electromechanical energy conversion in polyphase systems. The space vector theory

$$T_e = \frac{3}{2} p \cdot \text{Im} { \vec{\psi}_s \cdot \vec{i}_s^* } = \frac{3}{2} p (\vec{\psi}_s \times \vec{i}_s)$$

The art of modern drive control (field-oriented control, direct torque control, model predictive control) reduces to selecting, in real time, the inverter switching state that minimizes a cost function of the flux and torque errors. No sinewave mythology required.

$$\vec{x}_s = \frac{2}{3} \left( x_a + a x_b + a^2 x_c \right)$$