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

1. The Inadequacy of the Single-Phase Gaze

The three-phase machine is one entity. Its state is a rotating complex number. Unbalance, harmonics, and switching states (inverters) become geometric loci, not case-by-case trigonometric expansions. The drive —the control algorithm—does not need to

$$\vec{x}_s = \frac{2}{3} \left( x_a + a x_b + a^2 x_c \right)$$ The drive —the control algorithm—does not need to

“The space vector is not a mathematical trick. It is the machine’s own memory of what it is.” The drive —the control algorithm—does not need to

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.

where $a = e^{j2\pi/3}$. The factor $2/3$ ensures that the magnitude of $\vec{x}_s$ equals the peak amplitude of a balanced sinusoidal phase quantity.