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A Comprehensive Analysis of Space Vector Pulse Width Modulation for 3-phase Voltage Source Inverter (VSI)

Lalit Vidyarthy and K. P. Singh

ABSTRACT: In recent times, developments in power electronics and semiconductor technology have lead improvements in power electronics systems. Hence, different circuit configurations namely multilevel inverters (MLI) have become popular and significant interest by researchers are given on them. Variable voltage and frequency supply for ac drives can be consistently obtained from a three-phase voltage source inverter (VSI). A number of Pulse width modulation (PWM) schemes are used to obtain variable voltage and frequency supply. The most widely used PWM schemes for three-phase VSI are carrier-based sinusoidal PWM (SPWM) and space vector PWM (SVPWM). There is an increasing trend of using space vector PWM (SVPWM) because of their easier digital realization and better dc bus utilization. This paper presents the performance study of a Space Vector PWM based three-phase Voltage Source Inverter. Also this paper focuses on step by step development of MATLAB/SIMULINK model of SVPWM. Initially the model of a three-phase VSI is discussed based on space vector representation. Subsequently he simulation model of SVPWM is obtained using MATLAB/SIMULINK. Simulation results are obtained using MATLAB/Simulink environment for effectiveness of the study. Further new control approach for the three phase inverters based on a variety of techniques has been developed.

Keywords: Multilevel Inverters (MLI), Voltage Source Inverter (VSI), Space Vector Pulse Width Modulation (SVPWM), Sinusoidal Pulse Width Modulation (SPWM), Matlab, Simulink.

1. Introduction

Three phase voltage-fed PWM inverters are recently showing increasing popularity for multi-megawatt industrial drive applications. The main reasons for this popularity are easy distribution of large voltage between the series devices and the enhancement of the harmonic quality at the output as compared to a two level inverter. In the lower end of power, GTO devices are being replaced by IGBTs because of their rapid evolution in voltage and current ratings and higher switching frequency. The Space Vector Pulse Width Modulation of a three level inverter provides the additional benefit of superior harmonic quality and larger under-modulation range that extends the modulation factor to 90.7% from the conventional value of 78.5% in Sinusoidal Pulse Width Modulation.

2. Space Vector PWM Space Vector Modulation (SVM) method was initially developed as vector approach to pulse-width modulation (PWM) for three-phase inverters (Fig. 1). This method limits space vectors to be applied according to region where the output voltage vector is placed. The determination of switching instants may be achieved using space vector modulation method based on the representation of switching vectors in α-β plane. Space Vector Modulation increases the

output potential of Sinusoidal PWM (SPWM) without distorting output voltage waveform; and prevents unnecessary switching.

Fig. 1: Basic Three-Phase Voltage-Source Converter circuit connected to Power Supply

Research Scholar and Associate Professor, Department of Electrical Engineering,

MMM Engineering College, Gorakhpur, Uttar Pradesh, India

Corresponding Author: l.vidyarthi@gmail.com

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3. REALIZATION OF SPACE VECTOR PWM

The topology of a three-leg voltage source inverter is shown in Fig. 2. Because of the constraint that the input lines must never be shorted and the output current must always be continuous a voltage source inverter can assume only eight distinct topologies. These topologies are shown in Fig. 3. Six out of these eight topologies produce a non-zero output voltage and are known as non-zero switching states and the remaining two topologies produce zero output voltage and are known as zero switching states.

Fig. 2: Topology of a three-leg voltage source inverter

Fig. 3: switching states topologies of a voltage source inverter

3.1 Voltage Space Vectors

Space vector modulation (SVM) for three-leg VSI is based on the representation of the three phase quantities as vectors in a two-dimensional (α-β)plane. This is illustrated here for the sake of completeness. Considering topology 1 of Fig. 3, which is repeated in Fig. 4(a) we see that the line voltages Vab, Vbc, and Vca are given by

Vab = Vg

Vbc = 0

Vca = Vg…..................................(1)

This can be represented in the (α-β) plane as shown in Fig. 4(b), where voltages Vab, Vbc, and Vca are three line voltage vectors displaced 120⁰ in space. The effective voltage vector generated by this topology is represented as V1 (pnn) in Fig. 4(b). Here the notation “pnn” refers to the three legs/phases a, b, c being either connected to the positive dc rail (p) or to the negative dc rail (n). Thus “pnn” corresponds to “phase a”

being connected to the positive dc rail and phases b and c being connected to the negative dc rail.

Fig. 4(a): Topology 1-V1 (pnn) of a voltage source inverter

Fig. 4(b): Representation of topology 1 in the (α-β) plane

Proceeding on similar lines the six non-zero voltage vectors (V1 - V6) can be shown to assume the positions shown in Fig. 5. The tips of these vectors form a regular hexagon (dotted line in Fig. 5). We define the area enclosed by two adjacent vectors, within the hexagon, as a sector. Thus there are six sectors numbered 1 - 6 in Fig. 5.

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Fig. 5: Non-zero voltage vectors in the (α-β) plane

Considering the last two topologies of Fig. 3 which are repeated in Fig. 6(a) for the sake of convenience we see that the output line voltages generated by this topology are given by

Vab = 0

Vbc = 0

Vca = 0 …………....…….…….. (2)

These are represented as vectors which have zero magnitude and hence are referred to as zero-switching state vectors or zero voltage vectors. They assume the position at origin in the (α-β)plane as shown in Fig. 4(b). The vectors V1-V8 are called the switching state vectors (SSVs).

Fig. 6(a): Zero output voltage topologies

Fig. 6(b): Representation of the zero voltage vectors in the

(α β) plane

3.2 Space Vector Modulation The desired three phase voltages at the output of the inverter could be represented by an equivalent vector V rotating in the counter clock wise direction as shown in Fig. 7(a). The magnitude of this vector is related to the magnitude of the output voltage (Fig. 7(b)) and the time this vector takes to complete one revolution is the same as the fundamental time period of the output voltage.

Fig. 7(a): Output voltage vector in the (α β) plane

Fig. 7(b): Output line voltages in time domain Let us consider the situation when the desired line-to-line output voltage vector V is in sector 1 as shown in Fig. 8. This vector could be synthesized by the pulse-width modulation (PWM) of the two adjacent SSV’s V1 (pnn) and V2 (ppn), the duty cycle of each being d1 and d2, respectively, and the zero vector [V7 (nnn) / V8 (ppp)] of duty cycle d0:

d1 V1 + d2 V2 = V = m Vgejè.............................. (3) d1 + d2 + d0 = 1……………………………….. (4)

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Where, 0 ≤ m ≤0.866 is the modulation index. This would correspond to a maximum line-to-line voltage of 1.0Vg, which is 15% more than conventional sinusoidal PWM as shown.

Fig. 8: Synthesis of the required output voltage vector in sector 1

All SVM schemes and most of the other PWM algorithms use Eqns. (3) and (4) for the output voltage synthesis. The modulation algorithms that use non-adjacent SSV’s have been

shown to produce higher THD and/or switching losses and are not analyzed here, although some of them, e.g. hysteresis, can be very simple to implement and can provide faster transient response. The duty cycles d1, d2, and d0, are uniquely determined from Eqns. (3) and (4) , the only difference between PWM schemes that use adjacent vectors is the choice of the zero vector(s) and the sequence in which the vectors are applied within the switching cycle. The degrees of freedom we have in the choice of a given modulation algorithms are: 1) The choice of the zero vector; whether we would like to use V 7(ppp) or V8 (nnn) or both, 2) Sequencing of the vectors and 3) Splitting of the duty cycles of the vectors without introducing additional commutations. 4. SIMULATION AND ANALYSIS The simulation and analysis for Space Vector Modulation based Voltage source inverter (VSI) has been done on MATLAB 7.10 (R2010a) using Simulation modelling.

4.1 Open Loop Speed Control of an Induction Motor using constant V/Hz Principle and SVPWM Technique

Fig. 9: Model for Open loop speed control of an induction motor using a space vector PWM modulator

Fig. 10: FFT analysis of stator phase voltage waveform

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Fig. 11: Response of stator voltage Vab and stator current Ia versus time

Fig. 12: Response of Speed (in rpm) of rotor, stator voltage (Vab), Freq and Torque (Te) of the Induction Motor versus time

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4.2. Three-phase two level PWM voltage source motors

Fig. 13: Model for three-phase two level PWM voltage source motors

Fig. 14: FFT analysis of stator phase voltage waveform

Fig. 15: Response of Vab Inverter and Vab Load versus time 5. RESULT The FFT Analysis and output waveforms from Simulation modelling are shown below.

6. CONCLUSION The above discussion shows that Space Vector PWM technique is better as compared to other pulse width modulation technique sin many aspects such as high Modulation Index, 15% more output voltage, less current and torque harmonics. However, despite of all the mentioned advantages that SVPWM technique enjoys over any other PWM technique, SVPWM algorithm used in three-level inverters is more complex because of large number of inverter switching states. Hence it is seen that there is a certain trade off that exists while using SVPWM for inverters for Adjustable Speed Drive Operations.

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7. ACKNOWLEDGMENT I would like to thank the Department of Electrical Engineering, MMM Engineering College, Gorakhpur for extending all the facilities for caring out this work. 8. REFERENCES

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