Space Vector Modulation (SVM)

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

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

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

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

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

Space Vector Modulation

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

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

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

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

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

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

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

Space Vector Modulation = 0 Sa, Sb, Sc = 1 or 0 vaN = VdcSa, vbN = VdcSb, vcN = VdcSc,

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

Space Vector Modulation Reference voltage is sampled at regular interval, T Within sampling period, vref is synthesized using adjacent vectors and zero vectors 110 V2 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, 100 V1 T0 = T  T1 T2

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

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

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

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

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

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