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Voltage Vector Diagram

A graphical representation in the α−β\alpha-\beta plane showing the instantaneous output voltage vector V⃗out\vec{V}_{out} relative to the fundamental frequency components and the DC bus voltage.
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The statement of the theorem

Define the instantaneous output voltage vector V⃗out(t)\vec{V}_{out}(t) in the stationary α−β\alpha-\beta coordinate system. The vector is decomposed into components relative to the fundamental frequency ω\omega and the DC bus voltage VdcV_{dc}: V⃗out(t)=Vdc⋅(cos⁡(ωt)sin⁡(ωt))+V⃗ripple(t) \vec{V}_{out}(t) = V_{dc} \cdot \begin{pmatrix} \cos(\omega t) \\ \sin(\omega t) \end{pmatrix} + \vec{V}_{ripple}(t) The vector magnitude ∣V⃗out∣|\vec{V}_{out}| represents the instantaneous output voltage, and its projection onto the α−β\alpha-\beta plane is the key metric for modulation analysis.