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Space Vectors & Transformations
Space-vector construction, reference frames and abc, alpha-beta and dq transformations.
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1 Motion of space vectors in a 3-phase excitation system (GIF)
Description: Space vector representation of the mmf distribution in an AC machine created by balanced positive-sequence three-phase sinusoidal currents. Each of the ABC ( R G B ) space vectors pulsates along its respective axis. The resultant vector (in black), of 1.5 magnitude, rotates at the excitation frequency.
Motion of space vectors in a 3-phase excitation system
2 Space vector decomposition in the synchronous dq frame (GIF)
Description: This demo animates the motion of space vectors under balanced sinusoidal conditions, appearing as constant amplitude vectors rotating at the excitation frequency. The components depend on the choice of reference frame. In the stationary αβ frame, the components are time varying representing two-phase sinusoidal signals at stator frequency. In the rotating synchronous dq frame, the dq components are constant whose values depend on the orientation of the space vectors with respect to the dq axes. The state vectors I s (stator current) and λ r (rotor flux linkage) are shown in the common dq synchronous frame. When the d_axis is aligned with the rotor field --a process referred to as field orientation--, λ rq = 0 and the torque is expressed as T e = k 1 i sd i sq. The current i sd is the field component and i sq is the torque component of the stator current space vector I s.
Space vector decomposition in the synchronous dq frame — view 1Space vector decomposition in the synchronous dq frame — view 2
3 Sinusoidal mmf distributions and corresponding space vector representations (GIF)
Description: The sinusoidal space distributions of mmf created by balanced 3-phase sinusoidal currents are shown on the right for the three phases and for their algebraic sum. On the left, the corresponding space vector representations of the effects of each phase are shown together with their vector addition producing the resulting rotating space vector.
Sinusoidal mmf distributions and corresponding space vector representations
4 Space vectors for a balanced 3-phase signal (GIF)
Description: This animation shows the motion of space vectors for the case of a balanced three-phase sinusoidal signal: f A = cos( ωt ), f B = cos ( ωt -α), f C = cos ( ωt+α ) where α = 2π/3. The corresponding space vector is obtained from f R = ( f A + γ f B + γ 2 f C ) = 1.5e jωt where γ = e jα.
Space vectors for a balanced 3-phase signal
5 dq windings in ac machines (GeoGebra)
Description: Explore dq windings in ac machines.
Loading animation…
6 dq windings, current space vectors, reference frames (GeoGebra)
Description: Explore dq windings, current space vectors, reference frames.
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