SVPWM
How it works
Step by step: (1) the three-phase reference voltage is transformed into the stationary αβ plane (Clarke transform); in FOC this vector comes from the inverse Park transform. (2) The hexagon sector is identified (one of six, every 60°) in which the reference vector lies. (3) The reference vector is approximated by the two adjacent active vectors plus the zero vectors; their on-times (T1, T2, T0) are computed so their average over the modulation period equals the reference vector. (4) The times are converted into duty cycles for the inverter’s three legs, usually with symmetric placement of the zero vectors, which minimizes switching count and distortion.
Problem solved
Sinusoidal PWM does not fully use the available DC-bus voltage and produces higher current harmonic distortion. SVPWM addresses both: it raises the maximum linear output voltage (in the linear range the phase amplitude reaches Udc/√3 instead of Udc/2) and reduces current ripple and switching losses at the same carrier frequency.
Components
The eight switching states of a two-level inverter: six non-zero active vectors (V1–V6) spaced 60° apart and two zero vectors (V0=000, V7=111).
The active vectors divide the αβ plane into six 60° sectors; sector identification selects which two active vectors to use.
Computation of T1, T2 (active vectors) and T0 (zero vectors) within the modulation period so their weighted average equals the reference vector.
Ordering of the vectors within the period (usually symmetric, splitting the zero vectors) to minimize switching count and harmonic distortion.
Implementation
The dead-time inserted between switching the devices of one leg causes an output voltage error, especially at low speed and low voltage.
Above the linear range (outside the circle inscribed in the hexagon) the reference vector cannot be reproduced faithfully, introducing low-order harmonics.
Incorrect sector identification or missing the computation time window corrupts the switching sequence and current quality.
Evolution
Van der Broeck, Skudelny and Stanke present the analysis and realization of a PWM modulator based on voltage space vectors, establishing the theoretical foundation of SVPWM.
Hyperparameters (configurable axes)
The modulation carrier frequency; a trade-off between current ripple and switching losses.
Ratio of the reference vector amplitude to the radius of the circle inscribed in the hexagon; above the linear range the modulator enters overmodulation.