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Space Vector Modulation (SVM)

Space Vector Modulation (SVM). Closed loop current-control. AC motor. i ref. PWM. VSI. i f/back. PWM – Voltage Source Inverter. Open loop voltage control. AC motor. VSI. PWM. v ref. + v a -. V dc. a. + v b -. b. + v c -. n. c. N. PWM – Voltage Source Inverter.

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Space Vector Modulation (SVM)

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  1. Space Vector Modulation (SVM)

  2. Closed loop current-control AC motor iref PWM VSI if/back PWM – Voltage Source Inverter Open loop voltage control AC motor VSI PWM vref

  3. + va - Vdc a + vb - b + vc - n c N PWM – Voltage Source Inverter S1 S3 S5 S4 S6 S2 va* Pulse Width Modulation vb* S1, S2, ….S6 vc*

  4. Vdc q vtri vc q Vdc Pulse width modulator vc PWM – Voltage Source Inverter PWM – single phase

  5. Va* Pulse width modulator Vb* Pulse width modulator Vc* Pulse width modulator PWM – Voltage Source Inverter PWM – extended to 3-phase  Sinusoidal PWM

  6. PWM – Voltage Source Inverter SPWM – covered in undergraduate course or PE system (MEP 1532) In MEP 1422 we’ll look at Space Vector Modulation (SVM) – mostly applied in AC drives

  7. Space Vector Modulation 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

  8. Space Vector Modulation

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

  10. Space Vector Modulation 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

  11. b a c Space Vector Modulation 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)

  12. Three phase quantities vary sinusoidally with time (frequency f)  space vector rotates at 2f, magnitude Vm

  13. Space Vector Modulation How could we synthesize sinusoidal voltage using VSI ?

  14. + va - Vdc a + vb - b + vc - n c N va* vb* vc* Space Vector Modulation S1 S3 S5 S4 S6 S2 We want va, vb and vc to follow v*a, v*b and v*c S1, S2, ….S6

  15. + va - Vdc a + vb - b + vc - n c N Space Vector Modulation S1 S3 S5 S4 S6 S2 van = vaN + vNn vbn = vbN + vNn From the definition of space vector: vcn = vcN + vNn

  16. = 0 vaN = VdcSa, vaN = VdcSb, vaN = VdcSa, Sa, Sb, Sc = 1 or 0 Space Vector Modulation

  17. (1/3)Vdc (2/3)Vdc Sector 1 Sector 3 Sector 4 Sector 5 Sector 2 Sector 6 Space Vector Modulation [010] V3 [110] V2 [100] V1 [011] V4 [101] V6 [001] V5

  18. 110 V2 100 V1 Space Vector Modulation Reference voltage is sampled at regular interval, T Within sampling period, vref is synthesized using adjacent vectors and zero vectors If T is sampling period, V1 is applied for T1, Sector 1 V2 is applied for T2 Zero voltage is applied for the rest of the sampling period, T0 = T  T1 T2

  19. T0/2 T1 T2 T0/2 V0 V1 V2 V7 va vb vc T T Vref is sampled Vref is sampled Space Vector Modulation Reference voltage is sampled at regular interval, T Within sampling period, vref is synthesized using adjacent vectors and zero vectors If T is sampling period, V1 is applied for T1, V2 is applied for T2 Zero voltage is applied for the rest of the sampling period, T0 = T  T1 T2

  20. Space Vector Modulation How do we calculate T1, T2, T0 and T7? They are calculated based on volt-second integral of vref

  21. q 110 V2 100 V1 d Space Vector Modulation Sector 1 

  22. where Space Vector Modulation Solving for T1, T2 and T0,7 gives:

  23. a o b c amplitude of line-line = Space Vector Modulation Comparison between SVM and SPWM SPWM vao Vdc/2 For m = 1, amplitude of fundamental for vao is Vdc/2 -Vdc/2

  24.  15% Line-line voltage increased by: Space Vector Modulation Comparison between SVM and SPWM SVM We know max possible phase voltage without overmodulation is amplitude of line-line = Vdc

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