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ELECTRIC DRIVES

ELECTRIC DRIVES. SPACE VECTORS Dr. Nik Rumzi Nik Idris Dept. of Energy Conversion, UTM 2013. Space Vector. WHY space vectors?. Representation of 3-phase equations (for 3-phase AC motor) is more compact: only one equations is needed.

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ELECTRIC DRIVES

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  1. ELECTRIC DRIVES SPACE VECTORS Dr. Nik Rumzi Nik Idris Dept. of Energy Conversion, UTM 2013

  2. Space Vector WHY space vectors? Representation of 3-phase equations (for 3-phase AC motor) is more compact: only one equations is needed Space vectors can also be represented in using dand q axes. If windings are transform into d-q phases, magnetic coupling between them is avoided (since they are quadrature) Transformation between frames is conveniently performed using space vectors equations.

  3. Space Vector Definition: Space vector representation of a three-phase quantities xa(t), xb(t) and xc(t) with space distribution of 120o apart is given by: a = ej2/3 = cos(2/3) + jsin(2/3) a2 = ej4/3 = cos(4/3) + jsin(4/3) x – can be a voltage, current or flux and does not necessarily has to be sinusoidal

  4. Space Vector

  5. Space Vector Let’s consider 3-phase sinusoidal voltage: va(t) = Vmsin(t) vb(t) = Vmsin(t - 120o) vc(t) = Vmsin(t + 120o)

  6. Space Vector Let’s consider 3-phase sinusoidal voltage: At t=t1, t = (3/5) (= 108o) va = 0.9511(Vm) vb = -0.208(Vm) vc = -0.743(Vm) t=t1

  7. b a c Space Vector Let’s consider 3-phase sinusoidal voltage: At t=t1, t = (3/5) (= 108o) va = 0.9511(Vm) vb = -0.208(Vm) vc = -0.743(Vm)

  8. Space Vector Let’s consider 3-phase sinusoidal voltage: At t=t1, t = (3/5) (= 108o) va = 0.9511(Vm) vb = -0.208(Vm) vc = -0.743(Vm)

  9. Space Vector Space vector can also be represented in its d-q axis: q θ d

  10. Space Vector If rotates, and vd and vq will oscillate on the stationary d and q axes q qe de d If we define a rotating axes de and qe that rotates synchronously with , then we can write and will appear as DC on this rotating frame

  11. Space Vector is the angle between the stationary and rotating frames q qe de α θ d In rotating reference frame, This is expressed in stationary reference frame

  12. Space Vector is the rotator vector - transforms stationary frame to rotating frame. The transformation can also be written in matrix form:

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