electric drives and control report

POWER CONTROL RESEARCH GROUP

“COMPARITIVE EVALUATION OF PULSE WIDTH MODULATION TECHNNIQUES USING THREE PHASE INVERTER“

Prepared & Submitted By A.SREEKANTH(10BEE0001)

KRISHNA TEJA.M(10BEE0204)

Under the Guidance of Prof.UMASHANKAR.S

Owner : Power Control Research Group Ref : PCRG_12_0001Project : COMPARITIVE EVALUATION OF PULSE WIDTH MODULATION

TECHNNIQUES USING THREE PHASE INVERTERVersion : A

Document : PROJECT REPORT Date : 21 APR 13Filename : EDC_PBLREPORT.doc Page : 1/35

CONTENTS

1. INTRODUCTION..............................................................................................................3

2. OBJECTIVES...................................................................................................................4

3. SINUSOIDAL PWM..........................................................................................................43.1 Methodology......................................................................................................43.1.1 Modulation Index of Sinusoidal PWM...........................................................6

4. THIRD HARMONIC INJECTION PWM............................................................................64.1 PRINCIPLE INVOLVED.........................................................................................64.2 METHODOLOGY...................................................................................................7

5. SPACE VECTOR PULSE WIDTH MODULATION.......................................................105.1 PRINCIPLE............................................................................................................105.2 IMPLEMENTATION PROCEDURE OF A TWO-LEVEL SPACE VECTOR

PWM....................................................................................................................175.3 CALCULATION OF TIME DURATIONS T1, T2, T0:............................................185.4 MODULATION INDEX (LINEAR REGION):.........................................................225.5 TYPES OF DIFFERENT SCHEMES....................................................................24

6. SIMULATION RESULTS................................................................................................256.1 SINUSOIDAL PWM..............................................................................................256.2 THIPWM...............................................................................................................276.3 SVPWM................................................................................................................30

7. COMPARISON BETWEEN SPWM, THIPWM, AND SVPWM TECHNIQUES..............32

8. CONCLUSIONS.............................................................................................................33

9. References......................................................................................................................34




ABSTRACT

With advances power electronic devices and various pulse width modulation techniques

have been developed for several applications. For example, PWM based three-phase

voltage source inverters (VSI) convert DC power to AC power with variable voltage

magnitude and variable frequency.

This paper discusses the advantages and drawbacks of three different PWM techniques:

the sinusoidal PWM technique, the third harmonic injection PWM technique and the space

vector PWM technique. These three methods are compared by discussing their method of

implementation.

The matlab simulation results show that both the third harmonic injection PWM and

sinusoidal PWM techniques have lower total harmonic distortion than the SPWM technique.

The THIPWM and SVPWM techniques in the under-modulation region can both increase the

fundamental output voltage by 15.5% over the SPWM technique.

1. INTRODUCTION

Pulse-width modulation (PWM) is a technique where the duty ratio of a pulsating

waveform is controlled by another input waveform. The intersections between the

reference voltage waveform and the carrier waveform give the opening and closing times of

the switches.

Pulse width modulation (PWM) as it applies to motor control is a way of delivering

energy through a succession of pulses rather than a continuously varying (analog) signal.

By increasing or decreasing pulse width, the controller regulates energy flow to the motor

shaft. The motor’s own inductance acts like a filter, storing energy during the on cycle while

releasing it at a rate corresponding to the input or reference signal.

There is no single PWM method that is the best suited for all applications and with

advances in solid-state power electronic devices and microprocessors, various pulse width

modulation techniques have been developed for industrial applications. For these reasons,

the PWM techniques have been the subject of intensive research since 40 years.




2. OBJECTIVES

Comparison of PWM techniques and discussing about their merits and demerits.

Simulation of the mentioned PWM techniques.

3. SINUSOIDAL PWM

3.1 Methodology

In the sinusoidal PWM method, a sinusoidal control signal vA is compared with a high-

frequency triangular waveform vT to generate the inverter switch gating signals. The frequency of VT

establishes the inverter switching frequency fc. The magnitude and frequency of the sinusoidal signal

are controllable, but the triangular signal magnitude and frequency are kept constant. The sinusoidal

control signal VA modulates the switch duty ratio, and its frequency f is the desired fundamental

frequency of the inverter. For the three-phase generation, the same VT is compared with three

sinusoidal control voltages VA, VB, and VC, which are 120° out of phase, with respect to each other, to

produce a balanced output.

A six-step inverter is composed of six switches S1 through S6 with each phase output

connected to the middle of each inverter. When the sinusoidal waveform is greater than the triangular

waveform, the upper switch is turned on and the lower switch is turned off. Similarly, when the

sinusoidal waveform is less than the triangular waveform, the upper switch is off and the lower

switch is on. Depending on the switching states, either the positive or negative half DC bus voltage

is applied to each phaseSwitches are controlled in pairs (S1, S4), (S2, S5), and (S3, S6).When one

switch in a pair is closed, the other switch is open. In practice, there has to be a blanking pulse




between the changes of control signals for the switches in a pair to ensure that there is no short circuit

in the inverter. This is necessary, because practical switches take finite time to turn on and turn off.

The logic for switch control signals is

◦ S1 is ON when VA>VT S4 is ON when VA<VT

◦ S3 is ON when Vb>VT S6 is ON when Vb<VT

◦ S5 is ON when VC>VT S2 is ON when VC<VT.

Three-Phase Sinusoidal PWM: a). Reference Voltages (a, b, c) and TriangularWave b). Vao, c) Vbo, d) Vco e) Line-to-Line Voltages

The inverter line-to-line voltages are obtained from the pole voltages as:

VAB = Vao − Vbo

VBC = Vbo – Vco

VCA = Vco − Vao.




3.1.1 Modulation Index of Sinusoidal PWM

The modulation index is defined as the ratio of the magnitude of output voltage generated by

SPWM to the fundamental peak value of the maximum square wave. The Fourier series expansion of

a symmetrical square wave voltage with a peak magnitude of Vdc/2 has a fundamental of magnitude

2Vdc/π. The maximum of the output voltage generated by the SPWM method is Vdc/2.

Hence modulation index of sinusoidal pwm method is

Where VPW M is the maximum output voltage generated by a SPWM and Vmax−six step is the

fundamental peak value of a square wave.

4. THIRD HARMONIC INJECTION PWM

This method is also called as sine + 3rd harmonic method since a suitable amount of third

harmonic signal is added to the sinusoidal modulating signal of fundamental frequency.

2.1 PRINCIPLE INVOLVED

The sinusoidal PWM is the simplest modulation scheme to understand but it is unable to

fully utilize the available DC bus supply voltage. Due to this problem, the third-harmonic-

injection pulse-width modulation (THIPWM) technique was developed to improve the

inverter performance.

The Sine+3rd harmonic PWM technique is a modification of the SPWM technique

wherein deliberately some amount of third harmonic voltage is introduced in the pole voltage

waveform. Accordingly a suitable amount of third harmonic signal is added to the sinusoidal

modulating signal of fundamental frequency. Now, the resultant waveform (modified

modulating signal) is compared with the high frequency triangular carrier waveform. The

comparator output is used for controlling the inverter switches exactly as in SPWM inverter.

However the third harmonic component of pole voltage will not appear in the load phase and

line voltages. The advantage of adding small amount of third harmonic in the modulating

waveform is that it brings down the peak magnitude of the resultant modulating waveform.

The modified modulating waveform appears more flat topped than its fundamental




component. Thus if the fundamental sinusoidal modulating wave had a peak magnitude

equal to the peak magnitude of the triangular carrier wave the addition of small percentage

of 3rd harmonic to the fundamental wave causes the peak magnitude of the combined

signal to become lower than triangle wave’s peak magnitude.

2.2 METHODOLOGY

Consider a waveform consisting of a fundamental component with the addition of a triple

frequency term:

y = sin θ + A sin 3θ (2.1)

Where θ = ωt and A is a parameter to be optimized while keeping the maximum amplitude of y (t)

under unity. The maximum value of y (t) is found by setting its derivative with respect to θ equal to

zero.

Hence,

(2.2)

(*cos2θ is actually cos2 θ)

The maximum and minimum of the waveform therefore occur at

= 0 (2.3)

And (2.4)

Which yield, respectively, sin θ = 1 (2.5)

And

(2.6)

The peak value of y can be found by substituting the values obtained for sin θ in (2.5) and (2.6) into

(2.1)

Equation (2.1) becomes




y = (1 + 3A) sin θ − 4A sin3 θ (2.8)

Substituting the values in (2.5) and (2.6), for sinθ we have

Y = 1-A (2.9)

i.e.

(2.10)

Where y^ peak value of Y

The optimum value for A is that value which minimizes y and can be found by differentiating

(2.10) for y with respect to A and equating the result to zero.

Then, Equation (2.10) becomes,

Therefore A can be -1/3 or + 1/6

From Equation (2.9), we can see that the negative value of A makes y greater than unity. Therefore,

the only valid solution for A is 1/6 and the required waveform is

y = sin θ + A sin 3θ

From Equation (2.3), yields θ = π /2.Substituting the value of 1/6 for A in (2.4)

gives cos θ = 1/2, i.e., θ = π /3, 2π /3, etc. All triple harmonics pass through zero at these values

of θ. If we substitute the values of θ = nπ /3 in (2.13), then we have a maximum amplitude of

at these angles

In Figure 2.4, it is shown that the addition of a third harmonic with a peak magnitude of one

sixth to the modulation waveform has the effect of reducing the peak value of the output waveform by

a factor of without changing the amplitude of the fundamental. It is possible to increase the

amplitude of the modulating waveform by a factor K, so that the full output voltage range of the




inverter is again utilized. If the modulating waveform is expressed as

y = K (sin θ + A sin 3θ)

Hence

K =

It implies that the addition of this third harmonic produces a 15.5% increase in the amplitude

of the fundamental of the phase voltages

Injecting a third harmonic component to the fundamental component gives the following

modulating waveforms for the three-phase




Reference Voltages (a, b, c), Triangular Waveforms (VT), and Output Voltage(Vao, Vbo, Vco).

3. SPACE VECTOR PULSE WIDTH MODULATION

3.1 PRINCIPLE One more method for increasing the output voltage about that of the SPWM technique i

the space vector PWM technique. Compared to third harmonic injection method, the two methods

have similar results but their methods of executing are differ largely. In the SVPWM technique, the

duty cycles are calculated rather than derived through comparison as in sinusoidal method. The

SVPWM technique can increase the fundamental component by up to 27.39% that of sinusoidal

method. The fundamental voltage can be increased up to a square wave mode where a modulation

index of unity is reached.

SVPWM is accomplished by rotating a reference vector around the state diagram, which is




composed of six basic non-zero vectors forming a hexagon. A circle can be inscribed inside it which

corresponds to sinusoidal operation. The area inside the inscribed circle is called the linear

modulation region or under-modulation region, and the area between the inside circle and outside

circle of the hexagon is called the nonlinear modulation region or over-modulation region. The

method of operation of linear and nonlinear modulation regions depend on the modulation index,

which indirectly reflects on the inverter utilization capability.

Under-modulation and Over-modulation Regions in Space Vector Representation

A three-phase mathematical system can be represented by a space vector. For example, given

a set of three-phase voltages, a space vector can be defined by

Where VA (t), Vb (t), and VC (t) are three sinusoidal voltages of the same amplitude and

frequency but with ±120o phase shifts. At any given time magnitude is constant. As time increases,

the angle of the space vector increases, causing the vector to rotate with a frequency equal to that

of the sinusoidal waveforms. In the space-vector modulation, a three-phase inverter can have eight

switching states where the inverter has six active states (1-6) and two zero states (0 and 7).

A typical two-level inverter has 6 power switches (labelled S1 to S6) that generate three-

phase voltage outputs. The six switching power devices can be constructed using power BJTs,

GTOs, IGBTs, etc. depending on the application. When an upper transistor is switched on, the




corresponding lower transistor is switched off. Therefore, the ON and OFF states of the upper

transistors S1, S3, S5 can be used to determine the current output voltage. The ON and OFF states

of the lower power devices are complementary to the upper ones. Two switches on the same leg

cannot be closed or opened at the same time. The basic principle of SVPWM is based on the eight

switch combinations of a three- phase inverter. The switch combinations can be represented as

binary codes that correspond to the top switches S1, S3, and S5 of the inverter.

The basic principle of SVPWM is based on the eight switch combinations of a three- phase

inverter. The switch combinations can be represented as binary codes that correspond to the top

switches S1, S3, and S5 of the inverter as shown in Fig. Each Switching circuit generates three

independent pole voltages Vao, Vbo, and Vco, which are the inverter output voltages with respect

to the mid-terminal of the DC source marked as ‘O’ on the same figure. These voltages are also

called pole voltages.




Fig: Eight Switching Configuration of a Three-Phase Inverter

The pole voltages that can be produced are either Vdc/2 or −Vdc/2. For example, when switches

S1, S6, and S2 are closed, the corresponding pole voltages are Vao = Vdc/2, Vbo = −Vdc/2, and

Vco = −Vdc/2. This state is denoted as (1, 0, 0) and, according to Equation (3.1), may be

depicted as the space vector

→−

V (t) = [Vdce j0]. Repeating the same procedure, we can find the remaining active

and non-active states. There are eight possible inverter states that can generate eight space

vectors. These are given by the complex vector expressions:




The reference voltage vector →−

V re f rotates in space at an angular velocity

ω = 2π f, where f is the fundamental frequency of the inverter output voltage. When the reference

voltage vector passes through each sector, different sets of switches in Table 3.1 will be turned

on or off. As a result, when the reference voltage vector rotates through one revolution in space, the

inverter output varies one electrical cycle over time. The inverter output frequency coincides with the

rotating speed of the reference voltage vector. The zero vectors (→−

V 0 and →−

V 7) and active

vectors (→−

V 1 to →−

V 6) do not move in space. They are referred to as stationary vectors. When

the upper or lower transistor of a phase is ON, the switching signal of that phase is ‘1’ or ‘-1’, and

when an upper or lower transistor is OFF, then the switching signal is ‘0’. The eight combinations and

the derived output line-to-line and phase voltages in terms of the DC supply voltage are:




Choosing the neutral point n and the output phase voltages of the inverter depend on the relationship

between the switching variables [S1; S3; S5] hence the DC voltage as follows:

Hence by solving above equations we get




The space vector can be also represented in another reference frame with two orthogonal axes

(α and β). We assume that α axis is aligned in the horizontal direction and that the β axis is

vertical. Then the abc three-phase voltage vector given in above equation can be transformed into a

vector with α β coordinates. The α β vector is used to find the sector of α β plane in which the

reference voltage vector lies. The phase voltages corresponding to the eight combinations of

switching patterns can be mapped into α β coordinates.

Equating real and imaginary parts we get,




|The values of Vα and Vβ are called α and β components of the space vector, and the last

column in Table 3.3 shows the reference space vector. The voltages Vα and Vβ become the inputs

for dwelling time calculations in the space vector PWM and are used to compute the scalar

magnitude of the reference voltage →−

V Re f

The magnitude of the reference vector is:

The phase angle is evaluated from

3.2 IMPLEMENTATION PROCEDURE OF A TWO-LEVEL SPACE VECTOR PWM

The procedure for implementing a two-level space vector PWM can be summarized as follows:

1. Calculate the angle θ and reference voltage vector →−

V ref b a s e d on the input voltage

components.

2. Calculate the modulation index and determine if it is in the over-modulation region.

3. Find the sector in which →−

V re f l i e s , and the adjacent space vectors of →−

V k and →−

V k+1

based on the sector angle θ.

4. Find the time intervals Ta and Tb and T0 based on Ts, and the angle θ. (For over- modulation,

find Ta0, T 0 and T 0 is zero.)

5. Determine the modulation times for the different switching states.




Flow Diagram for SVPWM Implementation

3.3 CALCULATION OF TIME DURATIONS T1, T2, T0: T1 and T2 denote the required on-time of the active-state vectors V k and V k+1

during each sample period, and k is the sector number denoting the reference location.T0 is the time

interval for zero vector location.

Space Vectors of Three-Phase Bridge Inverter

To = Ts-(T1+T2)

Volt-sec along α-axis:

V1T1+ (V2cos60o) T2=Vs*Tscosα …… (1)

Volt-sec along β-axis:




0+ (V2sin60o) T2 = Vs*Tssinα …… (2)

Solving (1) and (2) lv1l = lv2l=Vdc

In a sector

Varies between 60o

To = Ts-(T1+T2)

Average values:

[- ]

[T1+T2]

[-T1+T2]

[-T1-T2]

Average values in sector 1:

[T1+T2]




Substituting T1, T2 values above equation

VBO (avg) = Vssin (α-30)

VCO (avg) = -VAO (avg)

SVPWM using the sampled reference phase amplitude

Sector 1:




Substituting above equations we get

T1 = TAS-TBS

Similarly T2 is given as

T2 = TBS-TCS

VALUES OF T0, T1, T2 FOR ALL SECTORS:

SECTOR T1 T2

1 2Ts-(T1+T2) TAS-TBS TBS-TCS

2

2Ts-(T1+T2) TAS-TCS TBS-TAS




3 2Ts-(T1+T2) TBS-TCS TCS-TAS

4 2Ts-(T1+T2) TBS-TAS TCS-TAS

5 2Ts-(T1+T2) TCS-TAS TAS-TBS

6 2Ts-(T1+T2) TCS-TBS TAS-TCS

Switching Patterns of Six Sectors

3.4 MODULATION INDEX (LINEAR REGION):In the linear region, the rotating reference vector always remains within the hexagon. The largest

output voltage magnitude is the radius of the largest circle that can be inscribed within the

hexagon. This means that the linear region ends when the reference voltage is equal to the radius of

the circle inscribed within the hexagon.




From Fourier analysis we can write

The ratio between the reference vector →−

V re f and the fundamental peak value of the square phase

voltage wave (2Vdc/π) is called the modulation index. Therefore in linear region modulation index

can be expressed as

In this case the maximum modulation index is obtained when →−

V re f equals the radius of the

inscribed circle. Hence

Therefore,




3.5 TYPES OF DIFFERENT SCHEMESThere are two modes of operation available for the PWM waveform. They are symmetric and

asymmetric pulse width modulation. The pulse of an asymmetric edge aligned signal always has the

same side aligned with one end of each pulse width modulation period. On the other hand, the pulse

of symmetric signals is always symmetric with respect to the centre of each PWM period. The

symmetrical PWM signal is often preferred because it has the lowest total harmonic distortion

(THD). There are different schemes in space vector pulse width modulation and they are based on

their repeating duty distribution.

Switching is achieved by applying a zero state vector followed by two adjacent active state

vectors in a half switching period. The next half of the switching period is the mirror image of the first

half. In order to reduce the switching loss of the power components of the inverter, it is required that

at each time only one bridge arm is switched. The switching sequence for all sectors are shown below:




When modulation index exceeds 90.7% then the SPVWM falls into over modulated region or

nonlinear region.

4. SIMULATION RESULTS

4.1 SINUSOIDAL PWMSPWM is very popular and easy to implement using comparators. The SPWM

Simulink system model is built in Fig. It has the following blocks: (1) Sinusoidal wave

generators, (2) High-frequency triangular wave generator, and (3) comparators.




(circuit diagram)

The SPWM technique treats each modulating voltage as a separate entity that is

compared to the common carrier triangular waveform. A three-phase voltage set (VA, VB,

and VC) of variable amplitude is compared in three separate comparators with a common

triangular carrier waveform of fixed amplitude as shown in the same figure. The output

(Vao, Vbo, and Vco) of the comparators form the control signals for the three legs of the

inverter composed of the switch pairs (S1; S4), (S3; S6), and (S5; S2), respectively. From

these switching signals and the DC bus voltage, PWM phase-to-neutral voltages (Van,

Vbn, and Vcn) are obtained.




4.2 THIPWMThe THIPWM Simulink system model is the same as that of the SPWM system

except for the modulating waveform voltages, which are generated by injected the third-

harmonic components and line voltages are as follows:

(here the circuit diagram remains same except where a third harmonic is added to the

input)




Circuit diagram:




4.3 SVPWM

(Circuit diagram)

(Control signals)




(Space vectors of two phase voltages)

(SPACE VECTOR TRAJECTORY)




(Line voltages)

5. COMPARISON BETWEEN SPWM, THIPWM, AND SVPWM TECHNIQUES

The simulation studies confirmed that the THIPWM and SVPWM technique have a

better DC bus voltage utilization than SPWM. As seen in Fig, the smaller circle represents

the operating region of the SPWM technique and the larger inscribed circle represents the

operating region of the SVPWM technique in the under-modulation region.

In SPWM, the maximum modulation index is 78.55%, the maximum output

fundamental is 0.5 VDC, and the maximum amplitude of the line-to-line voltage is VDC/2.

The line-to-line voltage of SVPWM is then increased by about:




6. CONCLUSIONSThis report has evaluated three different PWM techniques, namely SPWM,

THIPWM, and SVPWM (in the linear modulation region). The contributions of the report

are as follows:

The report has provided a thorough review of the each techniques with a special focus on the

operation of SVPWM in the under-modulation.

In this report, Simulink models for all three techniques have been developed and tested in the

MATLAB/Simulink environment.

As seen from the simulation results, SVPWM and THIPWM have a superior

performance compared to SPWM, especially in the over-modulation region of SVPWM. The

SPWM technique is very popular for industrial converters. It is the easiest modulation scheme

to understand and implement. This technique can be used in single-phase and three-phase

Inverters. The THIPWM technique operates by adding a third harmonic component to

the sinusoidal modulating wave. It is possible to increase the fundamental by about 15:5%

and, hence, allow a better utilization of the DC power supply.

The SVPWM technique can only be applied to a three-phase inverter and it increases the

overall system efficiency. The SVPWM is used for controlling the switching of the machine

side converter. Advantages of this method include a higher modulation index, lower

switching losses, and less harmonic distortion compared to SPWM. SVPWM research has

been widespread in recent years making it one of the most popular methods for three-phase




inverters because it has a higher fundamental voltage output than SPWM for the same DC bus

voltage. The SVPWM is significantly better than SPWM by approximately 15:5%. However,

the SVPWM technique is complex in implementation, especially in the over-modulation

region.

7. REFERENCES [1]. B.K. Bose. Modern Power Electrics and AC Drives. Prentice-Hall, Inc., 2002.

[2]. K.V. Kumar, P.A. Michael, J.P. John and S.S. Kumar, “Simulation and Comparison of

SPWM and SVPWM control for Three Phase Inverter,” Asian Research Publishing

Network, Vol. 5, No. 7, pp. 61-74, July 2010

[3]. Analysis of pulse width modulation techniques for ac/dc line- side converters

Michal KNAPCZYKF Krzysztof PIEŃKOWSKIF 2006

[4]. K. Zhou and D. Wang, “Relationship between Space-Vector Modulation and Three-

Phase Carrier-Based PWM: A Comprehensive Analysis,” IEEE Transactions on

Industrial Electronics, Vol. 49, No. 1, pp. 186-196, February 2002.

[5]. W.F. Zhang and Y.H. Yu, “Comparison of Three SVPWM Strategies,” Journal of

Electronic Science and Technology of China, Vol. 5, No. 3, pp. 283-287, September

2007.

[6]. J.Y. Lee, and Y.Y. Sun, “A New SPWM Inverter with Minimum Filter Requirement,”

International Journal of Electronics, Vol. 64, No. 5, pp. 815-826, 1988.

[7]. Math Works, 2010, Sim Power Systems, User’s Guide.




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