1.3 The Space Vector Definition
Let phase quantities ( a(t), b(t), c(t) ) satisfy ( a + b + c = 0 ) (no zero sequence). The space vector is defined as
[ \mathbfx_s(t) = \frac23 \left[ a(t) + b(t)e^j2\pi/3 + c(t)e^j4\pi/3 \right] ]
where ( e^j2\pi/3 ) and ( e^j4\pi/3 ) are unit vectors at 120° intervals. The factor ( 2/3 ) preserves amplitude (peak value) of sinusoidal phase quantities. For balanced three-phase currents ( i_a = I_m \cos(\omega t) ), ( i_b = I_m \cos(\omega t - 2\pi/3) ), ( i_c = I_m \cos(\omega t - 4\pi/3) ), the space vector becomes ( \mathbfi_s = I_m e^j\omega t ), a rotating vector of constant magnitude. This compact representation replaces three time-varying signals with one complex function, enabling geometric interpretation of torque and flux.
A significant portion (Chapter 9) treats main flux saturation and cross-saturation (coupling between $d$ and $q$ axes due to saturation). This is critical for high-performance drives. A significant portion (Chapter 9) treats main flux
This is not a beginner's "Motors 101" picture book. As part of the Monographs in Electrical and Electronic Engineering series, this text assumes you know Ohm's law and what a slip ring does. then systematically derive the transformations (Clarke
What it delivers is rigor.
The author (typically associated with the deep academic work from the 1990s/2000s on this topic) builds the entire theory from the ground up using vector notation. You will start with the general theory of electrical machines, then systematically derive the transformations (Clarke, Park) that make control possible. Park) that make control possible.