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Published byKiara Samford Modified about 1 year ago

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Space Vector Modulation (SVM)

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Open loop voltage control VSI AC motor PWM v ref Closed loop current-control VSI AC motor PWMi ref i f/back PWM – Voltage Source Inverter

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

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v tri V dc q vcvc q Pulse width modulator vcvc PWM – single phase PWM – Voltage Source Inverter

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

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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 PWM – Voltage Source Inverter

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Definition: Space vector representation of a three-phase quantities x a (t), x b (t) and x c (t) with space distribution of 120 o apart is given by: x – can be a voltage, current or flux and does not necessarily has to be sinusoidal a = e j2 /3 = cos(2 /3) + jsin(2 /3) a 2 = e j4 /3 = cos(4 /3) + jsin(4 /3) Space Vector Modulation

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Let’s consider 3-phase sinusoidal voltage: v a (t) = V m sin( t) v b (t) = V m sin( t - 120 o ) v c (t) = V m sin( t + 120 o ) Space Vector Modulation

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Let’s consider 3-phase sinusoidal voltage: t=t 1 At t=t 1, t = (3/5) (= 108 o ) v a = 0.9511(V m ) v b = -0.208(V m ) v c = -0.743(V m ) Space Vector Modulation

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Let’s consider 3-phase sinusoidal voltage: At t=t 1, t = (3/5) (= 108 o ) v a = 0.9511(V m ) v b = -0.208(V m ) v c = -0.743(V m ) b c a Space Vector Modulation

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Three phase quantities vary sinusoidally with time (frequency f) space vector rotates at 2 f, magnitude V m

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

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

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+ v c - + v b - + v a - n N V dc a b c From the definition of space vector: S1 S2 S3 S4 S5 S6 Space Vector Modulation v an = v aN + v Nn v bn = v bN + v Nn v cn = v cN + v Nn

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Space Vector Modulation = 0 S a, S b, S c = 1 or 0v aN = V dc S a, v aN = V dc S b, v aN = V dc S a,

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

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Reference voltage is sampled at regular interval, T Within sampling period, v ref is synthesized using adjacent vectors and zero vectors 100 V1 110 V2 If T is sampling period, V1 is applied for T 1, V2 is applied for T 2 Zero voltage is applied for the rest of the sampling period, T 0 = T T 1 T 2 Sector 1

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Space Vector Modulation Reference voltage is sampled at regular interval, T If T is sampling period, V1 is applied for T 1, V2 is applied for T 2 Zero voltage is applied for the rest of the sampling period, T 0 = T T 1 T 2 T T V ref is sampled V1 T1T1 V2 T2T2 T 0 /2 V0 T 0 /2 V7 vava vbvb vcvc Within sampling period, v ref is synthesized using adjacent vectors and zero vectors

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Space Vector Modulation They are calculated based on volt-second integral of v ref How do we calculate T 1, T 2, T 0 and T 7 ?

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Space Vector Modulation 100 V1 110 V2 Sector 1 q d

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Space Vector Modulation Solving for T 1, T 2 and T 0,7 gives: where

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Space Vector Modulation Comparison between SVM and SPWM SPWM o a b c V dc /2 -V dc /2 v ao For m = 1, amplitude of fundamental for v ao is V dc /2 amplitude of line-line =

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

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