## Space vector representation of three phase signals in stationary and rotating frames

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Space Vector Representation of Three Phase Signals in Stationary and Rotating Frames

Updated 28 Jul 2011

This demonstration illustrates the use of a complex space vector to represent a three-phase signal . It also shows the transformation of the 3-phase signal 'ABC' into an equivalent 2-phase system 'alpha_beta'. The only restriction to the 3-phase signal is that the zero-sequence component is zero i.e. fA+fB+fC=0.
The complex space vector in the stationary frame is defined as
Fs = 2/3 (fA + fB*exp(j2*pi/3) + fC*exp(-2j*pi/3)
whose cartesian components are
fa = Re (Fs)
fb = Im (Fs)
When expressed in a rotating frame at frequency wk, the space vector becomes
Fk = Fs*exp(-jwk*t)
whose cartesian components are
fd = Re(Fk)
fq = Im(Fk)
The inverse transformation from complex space vector back to the 3-phase signal is also demonstrated.
Finally, the real transformations of the ABC components to the components ab (in the stationary frame) and then dq (in the rotating frame) are shown.

### Cite As

Syed Abdul Rahman Kashif (2021). Space vector representation of three phase signals in stationary and rotating frames (https://www.mathworks.com/matlabcentral/fileexchange/32368-space-vector-representation-of-three-phase-signals-in-stationary-and-rotating-frames), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2008b
Compatible with any release
##### Platform Compatibility
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