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# Svpwm

## on Nov 26, 2012

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## SvpwmPresentation Transcript

• Introduction: Principle of Space Vector PWM  Treats the sinusoidal voltage as a constant amplitude vector rotating at constant frequency. Coordinate Transformation ( abc reference frame to the stationary d-q frame) : A three-phase voltage vector is transformed into a vector in the stationary d-q coordinate frame which represents the spatial vector sum of the three-phase voltage.  This PWM technique approximates the reference voltage Vref by a combination of the eight switching patterns (V0 to V7).  The vectors (V1 to V6) divide the plane into six sectors (each sector: 60 degrees).  Vref is generated by two adjacent non-zero vectors and two zero vectors.
• PWM – Voltage Source InverterOpen loop voltage control VSI AC vref PWM motorClosed loop current-control AC iref PWM VSI motor if/back
• PWM – Voltage Source InverterPWM – single phase Vdc dc vc vPulse width tri vc modulator qq
• PWM – Voltage Source InverterPWM – extended to 3-phase → Sinusoidal PWM Va* Pulse width modulator Vb* Pulse width modulator Vc* Pulse width modulator
• PWM METHODS Output voltages of three-phase inverter where, upper transistors: S1, S3, S5 lower transistors: S4, S6, S2 switching variable vector: a, b, c
•  The eight inverter voltage vectors (V0 to V7)
•  The eight combinations, phase voltages and output line to line voltages
•  Basic switching vectors and Sectors  6 active vectors (V1,V2, V3, V4, V5, V6)  Axes of a hexagonal  DC link voltage is supplied to the load  Each sector (1 to 6): 60 degrees 2 zero vectors (V0, V7)  At origin  No voltage is supplied to the load Fig. Basic switching vectors and sectors.
• 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: x = ( x a ( t ) + ax b ( t ) + a 2 x c ( t ) ) 2 3 a = ej2π/3 = cos(2π/3) + jsin(2π/3) a2 = ej4π/3 = cos(4π/3) + jsin(4π/3)x – can be a voltage, current or flux and does not necessarily has to be sinusoidal
• Space Vector Modulation v = ( v a ( t ) + av b ( t ) + a 2 v c ( t ) ) 2 x x ax x 3Let’s consider 3-phase sinusoidal voltage: va(t) = Vmsin(ωt) vb(t) = Vmsin(ωt - 120o) vc(t) = Vmsin(ωt + 120o)
• Space Vector Modulation v = ( v a ( t ) + av b ( t ) + a 2 v c ( t ) ) 2 3 Let’s consider 3-phase sinusoidal voltage:At t=t1, ωt = (3/5)π (= 108o)va = 0.9511(Vm)vb = -0.208(Vm)vc = -0.743(Vm) t=t1
• Space Vector Modulation v = ( v a ( t ) + av b ( t ) + a 2 v c ( t ) ) 2 3 Let’s consider 3-phase sinusoidal voltage: bAt t=t1, ωt = (3/5)π (= 108o)va = 0.9511(Vm) avb = -0.208(Vm)vc = -0.743(Vm) c
• Three phase quantities vary sinusoidally with time (frequency f) ⇒ space vector rotates at 2πf, magnitude Vm
• Space Vector Modulation S1 S3 S5 + va - Vdc a + vb - b + vc - n c S4 S6 S2 N We want va, vb and vc to followva* v*a, v*b and v*cvb* S1, S2, ….S6vc*
• Space Vector Modulation S1 S3 S5 + va - Vdc a + vb - b + vc - n c S4 S6 S2 van = vaN + vNn N vbn = vbN + vNnFrom the definition of space vector: vcn = vcN + vNn v = ( v a ( t ) + av b ( t ) + a 2 v c ( t ) ) 2 3
• Space Vector Modulation =0 2 ( v = v aN + av bN + a 2 v cN + v Nn (1 + a + a 2 ) 3 )vaN = VdcSa, vaN = VdcSb, vaN = VdcSa, Sa, Sb, Sc = 1 or 0 2 ( v = Vdc S a + aS b + a 2 S c 3 ) v = ( v a ( t ) + av b ( t ) + a 2 v c ( t ) ) 2 3
• 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 2 ( v = Vdc S a + aS b + a 2 S c 3 ) Sector 6 [001] V5 Sector 5 [101] V6
• Conversion from 3 phases to 2 phases : For Sector 1,Three-phase line modulating signals (VC)abc = [VCaVCbVCc]Tcan be represented by the represented by the complex vector VC = [VC]αβ = [VCaVCb]Tby means of the following transformation: VC α = 2/3 . [vCa - 0.5(vCb + vCc )] VC β = √3/3 . (vCb - vCc)
• Space Vector Modulation Reference voltage is sampled at regular interval, T Within sampling period, vref is synthesized using adjacent vectors and zero vectorsIf T is sampling period, 110 V1 is applied for T1, V2 V2 is applied for T2 Sector 1Zero voltage is applied for therest of the sampling period, T2 V2 T 0 = T − T 1− T 2 T Where, 100 T1 = Ts.|Vc|. Sin (π/3 - θ) T1 V1 T2 = Ts.|Vc|. Sin (θ) V1 T
• Space Vector ModulationReference voltage is sampled at regular interval, TWithin sampling period, vref is synthesized using adjacent vectors andzero vectors T0/2 T1 T2 T0/2 V0 V1 V2 V7If T is sampling period, V1 is applied for T1, va V2 is applied for T2 vbZero voltage is applied for therest 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 vref1 T 1  To T1 T2 T7  ∫T 0 T 0 ∫ 0 ∫ 0 ∫ v ref dt =  v 0 dt + v 1dt + v 2 dt + v 7 dt  0  ∫v ref ⋅ T = v o ⋅ To + v 1 ⋅ T1 + v 2 ⋅ T2 + v 7 ⋅ T7 2 2v ref ⋅ T = To ⋅ 0 + Vd ⋅ T1 + Vd (cos 60o + j sin 60o )T2 + T7 ⋅ 0 3 3 2 2v ref ⋅ T = Vd ⋅ T1 + Vd (cos 60o + j sin 60o )T2 3 3
• Space Vector Modulation q T = T1 + T2 + T0,7 110 V2 Sector 1 v ref ⋅ = v ref ( cos α − j sin α ) α 100 2 2 V1 dv ref ⋅ T = Vd ⋅ T1 + Vd (cos 60o + j sin 60 )T2 o 3 3
• Space Vector Modulation 2 2v ref ⋅ T = Vd ⋅ T1 + Vd (cos 60o + j sin 60o )T2 3 3 2 1 1T v ref cos α = Vd T1 + Vd T2 T v ref sin α = Vd T2 3 3 3Solving for T1, T2 and T0,7 gives:T1= 3/2 m[ (T/√3) cos α - (1/3)T sin α ]T2= mT sin α where, M= Vref/ (Vd/ √3)
•  Comparison of Sine PWM and Space Vector PWM Fig. Locus comparison of maximum linear control voltage in Sine PWM and SV PWM.
•  Comparison of Sine PWM and Space Vector PWM a o b c vao Vdc/2 For m = 1, amplitude of fundamental for vao is Vdc/2∴amplitude of line-line = 3 Vdc 2 -Vdc/2
•  Comparison of Sine PWM and Space Vector PWM  Space Vector PWM generates less harmonic distortion in the output voltage or currents in comparison with sine PWM  Space Vector PWM provides more efficient use of supply voltage in comparison with sine PWM  Sine PWM : Locus of the reference vector is the inside of a circle with radius of 1/2 V dc  Space Vector PWM : Locus of the reference vector is the inside of a circle with radius of 1/√3 Vdc ∴ Voltage Utilization: Space Vector PWM = 2/√3 or (1.1547) times of Sine PWM, i.e. 15.47% more utilization of voltage.
• Space Vector ModulationComparison between SVM and SPWMSVM 1We know max possible phase voltage without overmodulation is Vdc 3 ∴amplitude of line-line = Vdc 3 Vdc − Vdc 2 ≈ 15.47% Line-line voltage increased by: x100 3 Vdc 2
• 1. Power Electronics: Circuits, Devices and Applications by M. H. Rashid, 3rd edition,Pearson2. Power Electronics: Converters, Applications and Devices by Mohan, Undeland andRobbins, Wiley student edition3. Power Electronics Handbook: M.H. Rashid, Web edition4. Modern Power Electronics And Ac Drives: B.K. Bose5. Extended Report on AC drive control, IEEE : Issa Batarseh6. Space vector modulation: Google, Wikipedia ; for figures.