Space Vector Modulation(SVM) Technique for PWM Inverter

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Amey Patil (BT11EEE05) Amey Khot (BT11EEE06) Charudatt Awaghate (BT11EEE18) Srikant Pillai (BT11EEE51) Purushotam Kumar (BT11EEE53)

The space vector PWM (SVM) method is an advanced computation-intensive PWM method and is possibly the best method among the all PWM techniques for variable-frequency drive application. Because of its superior performance characteristics, it has been finding wide spread application in recent years.

There are various variations of SVM that result in different quality and computational requirements.

One major benefit is in the reduction of total harmonic distortion (THD) created by the rapid switching inherent to this PWM algorithm.

Pulse widthmodulator

PWM – single phase

PWM – Voltage Source InverterPWM – Voltage Source Inverter

PWM – extended to 3-phase → Sinusoidal PWM

Pulse widthmodulator

PWM – Voltage Source InverterPWM – Voltage Source Inverter

Output voltages of three-phase inverter

Simple 3 phase Inverter

Fig1where, upper transistors: S1, S3, S5

lower transistors: S4, S6, S2

switching variable vector: a, b, c

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)

+ vc -

+ vb -

+ va -

From the definition of space vector:

( ))t(va)t(av)t(v32

ba ++=

• 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.

van = vaN + vNn

vbn = vbN + vNn

vcn = vcN + vNn

Let’s consider 3-phase sinusoidal voltage:

va(t) = Vmsin(ωt)

vb(t) = Vmsin(ωt - 120o)

vc(t) = Vmsin(ωt + 120o)

Vd = Van + Vbn.cos120 + Vcn.cos = Van – 1/2Vbn – 1/2VcnVq = 0 + Vbn.cos30 - Vcn.cos150 = √3/2Vbn -√3/2Vcn

The circuit model of a typical three-phase voltage source PWM inverter is shown in Fig.2

S1 to S6 are the six power switches that shape the output, which are controlled by the switching variables a, a’, b, b’, c and c’.

When an upper transistor is switched on, i.e., when a, b or c is 1, the corresponding lower transistor is switched off, i.e., the corresponding a′, b′ or c’ is 0.

Therefore, the on and off states of the upper transistors S1, S3 and S5 can be used to determine the output voltage.

+ vc -

+ vb -

+ va -

S1, S2, ….S6

We want va, vb and vc to follow v*a, v*b and v*c

Space Vector ModulationSpace Vector Modulation Fig:2Fig:2

Sector 1Sector 3

Sector 4

Sector 5

Sector 2

Sector 6

[100] V1

[110] V2[010] V3

[011] V4

[001] V5 [101] V6

(2/3)Vdc

(1/√3)Vdc

Space Vector Modulation Space Vector Modulation

badc SaaSSV32

Three phase quantities vary sinusoidally with time (frequency f)

⇒ space vector rotates at 2πf, magnitude Vm

Step -1 Determine Vd, Vq, Vref, and angle(alpha) Step -2 Determine time duration T1, T2, T0 Step -3 Determine the switching time of each

transistor (S1 to S6)

T0=T7=0.5Tz Both zero states are used for equal duration

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

Where,T1 = Ts.|Vc|. Sin (π/3 - θ)T2 = Ts.|Vc|. Sin (θ)

Sector 1

Reference voltage is sampled at regular interval, T

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

Vref is sampled Vref is sampled

T2T0/2

Within sampling period, vref is synthesized using adjacent vectors and zero vectors

They are calculated based on volt-second integral of vref

+++= ∫∫∫∫∫ dtvdtvdtvdtv

dtvT1 721o T

772211ooref TvTvTvTvTv ⋅+⋅+⋅+⋅=⋅

0TT)60sinj60(cosV32

0TTv 72oo

d1doref ⋅+++⋅+⋅=⋅

d1dref T)60sinj60(cosV32

Tv ++⋅=⋅

How do we calculate T1, T2, T0 and T7?

Tv ++⋅=⋅

7,021 TTTT ++=

Sector 1

( )α−α=⋅ sinjcosvv refref

Solving for T1, T2 and T0,7 gives:

Tv ++⋅=⋅

2d1dref TV31

cosvT +=α 2dref TV3

1sinvT =α

T1= 3/2 m[ (T/√3) cos α - (1/3)T sin α ]

T2= mT sin α where,M= Vref/ (Vd/ √3)

Basic switching vectors and Sectors

Fig. 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

S1 through S6 are the six power transistors that shape the output voltage. When an upper switch is turned on (i.e., a, b or c is “1”), the corresponding lower switch is turned off (i.e., a', b' or c' is “0”).Eight possible combinations of on and off patterns for the three upper transistors (S1, S3, S5) are possible.

The eight inverter voltage vectors (V 0 to V7)

The eight combinations, phase voltages and output l ine to l ine voltages

Comparison of Sine PWM and Space Vector PWM

Fig. Locus comparison of maximum linear control voltagein Sine PWM and SV PWM.

-Vdc/2

For m = 1, amplitude of fundamental for vao is Vdc/2

∴amplitude of line-line = dcV

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 Vdc

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.

Comparison between SVM and SPWM

We know max possible phase voltage without overmodulation is

∴amplitude of line-line = Vdc

Line-line voltage increased by: 100x

dcdc − ≈ 15.47%

From the simulation results and FFT analysis it is shown that SVPWM generates less harmonics and high output voltage for the modulation index given same for both SPWM and SVPWM techniques.

Compared to SPWM the Total harmonic distortion (THD) and lower order harmonics (LOH) contents are decreased in SVPWM. It is known that the maximum value of the peak-phase voltage that can be obtained from a 3-Ph inverter with Sinusoidal Pulse Width Modulation (SPWM) technique is equal to Vdc/2. It is therefore evident that SVPWM achieves a better DC bus utilization compared to SPWM (by about 15.4%).

SVM offers better harmonic spectrum. Thus this scheme is better than sine-triangle PWM scheme.

Space vector pulse width modulation is new and the best technique which is ruling the world now.

Still a lot of research is going on this svpwm. It should be available with low cost for household

purpose.

1[1]. Hind Djeghloud and Hocine Benalla, “Space Vector Pulse Width Modulation Applied to The Three-Level Voltage Inverter”, 5th International Conference on Technology and Automation ICTA’05, Thessaloniki, Greece, Oct 2010.[2]. Jin-woo Jung, “Space Vector PWM Inverter”, The Ohio State University, February, 2008.[3]. Jae Hyeong Seo; Chang Ho Choi; Dong Seok Hyun, “A New Simplified space-Vector PWM Method for Three-Level Inverters”, IEEE Transactions on Power Electronics, Volume 16, Issue 4, Jul 2010, Pages 545 - 550[4]. Muhammad H.Rashid “Power Electronics Circuits, devices, and Applications”, Prentice-Hall of India Private Limited, Third Edition, 2004.[5]. “the adaptive space vector pwm for four switch three phase inverter fed induction motor with dc – link voltage imbalance” by Hong Hee Lee*, Phan Quoc Dzung**, Le Dinh Khoa**, Le Minh Phuong**, Huynh Tan Thanh***School of Electrical Engineering, University of Ulsan Ulsan, Korea.[6]. P.S.Bimbhra, “Power Electronics”, Khanna publications.[7]. Overview of MATLAB Simulink Http://www.mathworks.com/products/simulink/description/overview.shtml