SIMULATION
AND COMPARISON OF SPWM AND SVPWM CONTROL FOR THREE PHASE INVERTER
ABSTRACT
A voltage source inverter is commonly used to supply a
three-phase induction motor with variable frequency and variable voltage for
variable speed applications. A suitable pulse width modulation (PWM) technique
is employed to obtain the required output voltage in the line side of the
inverter. The different methods for PWM generation can be broadly classified
into Triangle comparison based PWM (TCPWM) and Space Vector based PWM (SVPWM).
In TCPWM methods such as sine-triangle PWM, three phase reference modulating
signals are compared against a common triangular carrier to generate the PWM
signals for the three phases. In SVPWM methods, a revolving reference voltage
vector is provided as voltage reference instead of three phase modulating
waves. The magnitude and frequency of the fundamental component in the line
side are controlled by the magnitude and frequency, respectively, of the
reference vector. The highest possible peak phase fundamental is very less in
sine triangle PWM when compared with space vector PWM. Space Vector Modulation
(SVM) Technique has become the important PWM technique for three phase Voltage
Source Inverters for the control of AC Induction, Brushless DC, Switched
Reluctance and Permanent Magnet Synchronous Motors. The study of space vector
modulation technique reveals that space vector modulation technique utilizes DC
bus voltage more efficiently and generates less harmonic distortion when
compared with Sinusoidal PWM (SPWM) technique. In this paper first a model for
Space vector PWM is made and simulated using MATLAB/SIMULINK software and its
performance is compared with Sinusoidal PWM. The simulation study reveals that
Space vector PWM utilizes dc bus voltage more effectively and generates less
THD when compared with sine PWM.
Keywords: PWM, SVPWM, three phase inverter, total harmonic distortion.
INTRODUCTION
AC drives are more predominant than dc drives. Ac drives
requires high power variable voltage variable frequency supply. The research in
Pulse width modulation schemes has been intensive in the last couple of
decades. PWM techniques have been used to achieve variable voltage and variable
frequency in ac-dc and dc-ac converters. PWM techniques are widely used in
different applications such as variable speed drives (VSD), static frequency
changers (SFC), un-interruptible power supplies (UPS) etc. The main problems
faced by the power electronic design engineers are about the reduction of
harmonic content in inverter circuits. The classical square wave inverter used
in low or medium power applications suffers from a serious disadvantage such as
lower order harmonics in the output voltage. One of the solutions to enhance
the harmonic free environment in high power converters is to use PWM control
techniques. The objective of PWM techniques was to fabricate a sinusoidal AC
output whose magnitude and frequency could both be restricted.
PWM switching strategies not only addresses the primary
issues viz, less THD, effective dc bus utilization etc but also take care of
secondary issues like EMI reduction , switching loss, better spreading of
Harmonics over the spectrum. Real-time method of PWM generation can be broadly
classified into Triangle comparison based PWM (TCPWM) and Space Vector based
PWM (SVPWM).
In TCPWM methods such as sine-triangle PWM, three phase
reference modulating signals are compared against a common triangular carrier
to generate PWM pulses for the three phases. The frequency of the carrier
signal is very high compared to the modulating signal. The magnitude and
frequencies of the fundamental component in the line side are controlled by
changing the magnitude and frequency of the modulating signal. It is simple and
linear between 0% and 78.5% of six step voltage values, which results in poor
voltage utilization. Voltage range has to be extended and harmonics has to be
reduced.
In SVPWM methods, the voltage reference is provided using
a revolving reference vector. In this case magnitude and frequency of the
fundamental component in the line side are controlled by the magnitude and
frequency, respectively, of the reference voltage vector. Space vector
modulation utilizes dc bus voltage more efficiently and generates less harmonic
distortion in a three phase voltage source inverter.
SPACE VECTOR PULSE WIDTH MODULATION
Space Vector Modulation (SVM) was originally
developed as vector approach to Pulse Width Modulation (PWM) for three phase
inverters. It is a more sophisticated technique for generating sine wave that
provides a higher voltage to the motor with lower total harmonic distortion.
The main aim of any modulation technique is to obtain variable output having a
maximum fundamental component with minimum harmonics. Space Vector PWM (SVPWM)
method is an advanced; computation intensive PWM method and possibly the best
techniques for variable frequency drive application.
A space vector PWM
The circuit model of a typical three-phase
voltage source PWM inverter is shown in Figure-1. 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 switch 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 switch S1, S3 and S5 can be used to determine the
output voltage. SVPWM is a different approach from PWM modulation, based on space vector representation of the voltages in the α-β
plane. The α-β components are found by Clark’s transformation. Space Vector PWM
(SVPWM) refers to a special switching sequence of the upper three power
transistors of a three-phase power inverter. It has been shown to generate less
harmonic distortion in the output voltages and/or currents applied to the
phases of an AC motor and to provide more efficient use of dc input voltage.
Because of its superior performance characteristics, it has been finding
widespread application in recent years.
Figure-1. Three phase
voltage source inverter.
SPACE VECTOR CONCEPT
The space vector concept, which is derived from the
rotating field of induction motor, is used for modulating the inverter output
voltage. In this modulation technique the three phase quantities can be
transformed to their equivalent two-phase quantity either in synchronously
rotating frame (or) stationary frame. From these two-phase components, the
reference vector magnitude can be found and used for modulating the inverter
output. The process of obtaining the rotating space vector is explained in the
following section, considering the stationary reference frame. Considering the
stationary reference frame let the three-phase sinusoidal voltage component be,
Va = VmSinωt (1)
Vb = VmSin(ωt-2π/3) (2)
Vc = VmSin(ωt-4π/3) (3)
When this three-phase voltage is applied to
the AC machine it produces a rotating flux in the air gap of the AC machine.
This rotating resultant flux can be represented as single rotating voltage
vector. The magnitude and angle of the rotating vector can be found by means of
Clark’s Transformation as explained below in the stationary reference frame. To
implement the space vector PWM, the voltage equations
in the abc reference frame can be transformed into
the stationary dq reference frame that consists of the horizontal (d) and
vertical (q) axes as depicted in Figure-2. From Figure-2, the relation between
these two reference frames is below =
(4)
Figure-2. The relationship of abc reference
frame and stationary dq reference frame.
and f denotes either a voltage or a current variable.
As described in Figure-2. This transformation
is equivalent to an orthogonal projection of [a b c]t onto
the two-dimensional perpendicular to the vector [1 1 1]t (the
equivalent d-q plane) in a three-dimensional coordinate system. As a result,
six non-zero vectors and two zero vectors are possible. Six non-zero vectors (V1-V6) shape
the axes of a hexagonal as depicted in Figure-3, and supplies power to the
load. The angle between any adjacent two non-zero vectors is 60 degrees.
Meanwhile, two zero vectors (V0 and V7) and are at the origin and
apply zero voltage to the load. The eight vectors are called the basic space
vectors and are denoted by (V0, V1, V2, V3, V4, V5, V6, V7). The
same transformation can be applied to the desired output voltage to get the
desired reference voltage vector,Vref in the d-q plane. The
objective of SVPWM technique is to approximate the reference voltage vector Vref using
the eight switching patterns. One simple method of approximation is to
generate the average output of the inverter in a small period T to be the same
as that of Vref
in the same period
Figure-3. Basic switching,
vectors and sectors.
SWITCHING STATES
Table-1. Switching patterns and output
vectors.
For 180° mode of operation, there exist six switching
states and additionally two more states, which make all three switches of
either upper arms or lower arms ON. To code these eight states in binary
(one-zero representation), it is required to have three bits (23 = 8).
And also, as always upper and lower switches are commutated in complementary
fashion, it is enough to represent the status of either upper or lower arm
switches. In the following discussion, status of the upper bridge switches will
be represented and the lower switches will it’s complementary. Let
"1" denote the switch is ON and "0" denote the switch in
OFF. Table-1 gives the details of different phase and line voltages for the
eight states.
SOFTWARE IMPLEMENTATION OF SVPWM
Space vector PWM can be implemented by the following
steps:
Step-1: Determine,,and
angle(dVqVrefVα).
Step-2: Determine
the time duration,, and 1T2T0T
Step-3: Determine the switching time of each transistor (1S to6S).
Step-1: Determine Vd,Vq,Vref
and angle(a)
From Figure-4,Vd,Vq,Vref
and angle (α) can determined as follows:
(6)
(7)
(8)
(9)
, where f = fundamental frequency.
Figure-4
Voltage space vector and its components in (d,q).
Step-2: Determine the time durationT1,T2 and T0
From
Figure-5 the switching time duration can be calculated
as follows:
Switching
time at sector-1
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
Figure-5. Reference vector as a combination
of adjacent vectors at sector-1.
Step-3: Determine the switching time of each transistor
(S1 TO S6)
(a) Sector 1
(b) Sector 2
(c) Sector 3
(d) Sector 4
(e) Sector 5
(f) Sector 6
Figure-6. Switching pulse pattern for the
three phases in the 6 different sectors.
RESULTS AND DISCUSSIONS
The main aim of any modulation technique is to obtain
variable output having maximum fundamental component with minimum harmonics.
The objective of Pulse Width Modulation techniques is enhancement of
fundamental output voltage and reduction of harmonic content in Three Phase
Voltage Source Inverters. In this paper different PWM techniques are compared
in terms of Total Harmonic Distortion (THD). Simulink Models has been developed
for Sinusoidal PWM (SPWM), Space vector PWM (SVPWM), and Space vector PWM switching
Patterns. Simulation work is carried in MATLAB 7.0/Simulink.
The simulation parameters used are:
Fundamental frequency 50 Hz
Switching frequency 10 kHz
DC voltage 600 Volt
ODE Solver ode23tb
Simulation of SPWM
In Sinusoidal PWM three phase reference modulating
signals are compared against a common triangular carrier to generate the PWM
signals for the three phases. It is simple and linear between 0% and 78.5% of
six step voltage values, which results in poor voltage utilization. Frequency
in conventional SPWM output waves owing to their fixed switching frequencies.
Simulation has been carried out by varying the modulation index between 0 and
1.Finally performance of chaos based SPWM has been compared with SPWM. The
block diagram for Sinusoidal pulse width modulated inverter fed induction motor
is shown in Figure-7. The line voltage and line current are shown in Figures 8
and 9, respectively.
Figure-7. Block
diagram of SPWM inverter fed induction motor.
Figure-8a.
Response of line voltage in SPWM.
Figure-8. Response of line voltage in SPWM.
Figure-9a.
Response of line current in SPWM.
Figure-9b. Response of line current in SPWM.
Figure-10. Response of rotor speed in SPWM.
Figure-11.
Response of torque in SPWM.
Simulation of SVPWM
Space vector PWM is an advanced technique used for
variable frequency drive applications. It utilizes dc bus voltage more
effectively and generates less THD in the Three Phase Voltage Source Inverter.
SVPWM utilize a chaotic changing switching frequency to spread the harmonics
continuously to a wide band area so that the peak harmonics can be reduced
greatly. Simulation has been carried out by varying the modulation index
between 0 and 1. Finally performance of SVPWM has been compared with
conventional Sine PWM.
The Block Diagram of Space Vector Pulse width
modulated inverter fed Induction Motor is shown in Figure-12. The line voltage
and line current are shown in Figures 13 and 14, respectively.
Figure-12. Simulink block
diagram of space vector PWM.
Figure-13. Response of line voltage in SVPWM.
Figure-14.
Response of line current in SVPWM.
Figure-15. Response of rotor speed in SVPWM.
Figure-16.
Response of torque in SVPWM.
Simulation results of SPWM and SVPWM
MODULATION INDEX = 0.4:
(A) SPWM (B) SVPWM
MODULATION INDEX = 0.6:
(A) SPWM (B) SVPWM
MODULATION INDEX = 0.8:
(A) SPWM (B) SVPWM
MODULATION INDEX = 1:
(A) SPWM (B) SVPWM
Table-2. Comparisons between SPWM and SVPWM by varying modulation
index.
CONCLUSIONS
Space vector Modulation Technique has become the most
popular and important PWM technique for Three Phase Voltage Source Inverters
for the control of AC Induction, Brushless DC, Switched Reluctance and
Permanent Magnet Synchronous Motors. In this paper first comparative analysis
of Space Vector PWM with conventional SPWM for a two level Inverter is carried
out. The Simulation study reveals that SVPWM gives 15% enhanced fundamental
output with better quality i.e. lesser THD compared to SPWM.
PWM strategies viz. SPWM and SVPWM are
implemented in MATLAB/SIMULINK software and its performance is compared with
conventional PWM techniques. Owing to their fixed carrier frequencies cfin
conventional PWM strategies, there are cluster harmonics around the multiples
of carrier frequency. PWM strategies viz. Sinusoidal PWM and SVPWM utilize a
changing carrier frequency to spread the harmonics continuously to a wideband
area so that the peak harmonics are reduced greatly.
REFERENCES
(1) Zhenyu Yu, Arefeen Mohammed, Issa Panahi. 1997. A
Review of Three PWM Techniques. Proceedings of the American Control Conference
Albuquerque, New Mexico. pp. 257-261.
(2) D. G. Holmes and T. A. Lipo. 2003. Pulse Width
Modulation for Power Converters: Principles and Practice. M.E. El-Hawary, Ed.
New Jersey: IEEE Press, Wiley- Interscience. pp. 215-313.
(3) T. Erfidan, S. Urugun, Y. Karabag and B. Cakir. 2004.
New Software implementation of the Space Vector Modulation. Proceedings of IEEE
Conference. pp.1113-1115.
(4) D. Rathnakumar, J. Lakshmana Perumal and T.
Srinivasan. 2005. A New software implementation of space vector PWM.
Proceedings of IEEE Southeast conference. pp.131-136.
(5) B. Hariram and N. S. Marimuthu. 2005. Space vector
switching patterns for different applications- A comparative analysis.
Proceedings of IEEE conference. pp. 1444-1449.
(6) Raed H. Ahmad, George G. Karady, Tracy D. Blake,
Peter Pinewski. Comparison of Space Vector Modulation Techniques based on
performance Indexes and Hardware Implementation. Electrical Engg. Department,
Arizona State University.
(7) Wajiha Shireen, Srinivas Vanapalli, Hrishikesh Nene.
2006. A DSP Based SVPWM Control for Utility Interactive Inverters used in
Alternate Energy Systems. IEEE Transactions on Industrial Electronics.
(8) B.K. Bose. 1986. Power electronics and ac
drives. Prentice hall Inc., Englewood Cliffs, New Jersey.
No comments:
Post a Comment