A Comparative Study of Various PWM Techniques

A Comparative Study of Various PWM Techniques

Shyam Sunder Rai

M Tech (Student), Electrical Engineering, MMMUT,

Gorakhpur, Uttar Pradesh, India

Dr. A. K. Pandey

Associate Professor, Department of Electrical Engineering,

MMMUT, Gorakhpur, Uttar Pradesh, India

Abstract- Pulse-width modulation is the process of modifying the width of the pulses in a pulse train in direct proportion to a small control signal; the greater the control voltage, the wider the resulting pulses become. By using a sinusoid of the desired frequency as the control voltage for a PWM circuit, it is possible to produce a high-power waveform whose average voltage varies sinusoidally in a manner suitable for driving ac motors. This paper presents the MATLAB/Simulink based models of various PWM techniques usually employed.

Keywords: Sinusoidal PWM, Sine Triangle PWM, SVPWM

1. INTRODUCTION

   Present day drive types are the Induction motor drives with voltage source inverters. Also the voltage waveforms of traditional two level inverter fed Induction motor shows that the voltage across the motor contains not only the required fundamental sinusoidal components, but also pulses of voltage i.e. ripple voltage. In a variable speed application of the three phase induction motor, a voltage source inverter is normally used to supply a variable frequency variable voltage supply. A suitable Pulse Width Modulation (PWM) technique is employed to obtain the required output voltage in the line side of the inverter. The various methods for PWM generation can be generally classified into Triangle Comparison based PWM (TCPWM) and Space Vector based PWM (SVPWM).

   In one of the most utilized TCPWM methods i.e. the sine triangle PWM, three phase reference modulating signals are compared against a common triangular carrier to generate the PWM signals for the three phases. The frequency of the carrier signal is very high compared to the

   as voltage reference instead of three phase modulating waves (figure 4.3). The magnitude and frequency of the fundamental component in the line side are controlled respectively, by the magnitude and frequency, of the reference vector.

   The fundamental line side voltage is proportional to the reference magnitude during linear modulation.

   Figure 1: Switching states of inverter in SVPWM

   From figure (1) it is observed that in the SVPWM, there are six non-zero or active states (001,010,011,100,101,110) and two zero states (000,111). Also, the voltage vectors for active states can be located as shown in figure (1), zero vectors being at the origin. Thus we can divide the space into six sectors i.e. from zero to five. Every sector is made up of two active vectors and two zero vectors. In order to

   us

   modulating signal.

   obtain a voltage vector like

   that lies in a sector and is

   The magnitude and frequency of the fundamental component in the line side are controlled by the magnitude and frequency, respectively, of the modulating signal. With sine-triangle PWM, the highest possible peak phase fundamental voltage is 0.5Vdc , where Vdc is the DC bus voltage, in the linear modulation zone. In TCPWM based methods, increasing the reference magnitude beyond a certain level leads to pulse dropping.

2. SPACE VECTOR PULSE WIDTH MODULATION In Space Vector pulse width modulation (SVPWM) methods, a revolving reference voltage vector is provided

   not among the active or zero vectors we make use of the volt-second equality principle. Thus we find that the locus of the complete range of voltages available in the linear SVPWM method is a hexagon. In the space vector based PWM, the peak phase fundamental voltage can be as high as 0.577 Vdc during linear modulation.

   To increase the line side voltage further, the operation of the voltage source inverter (VSI) must be extended into the overmodulation region. The overmodulation region extends up to the six-step mode, which gives the highest possible ac

   dc

   2Vdc or 0.637V

   voltage for a given Vdc i.e. .

   However, in SVPWM methods, an overmodulation algorithm is required for controlling the line-side voltage during overmodulation and to achieve a smooth transition

   If the rated angular velocity of the motor is

   s (2sr )Ts

   T

   sr then,

   from PWM to six-step mode.

   Numerous overmodulation algorithms have been proposed in the literature for space vector modulated inverter. A well known algorithm among these divides the overmodulation zone into two zones, namely zone-I and zone-II [30]. During overmodulation, the fundamental line side voltage

   where s is the actual sampling interval in seconds. In the

   u

   *

   SVM technique, voltage vector s (which is called reference voltage vector) can be obtained as a time average of the adjacent active voltage vectors. This can be

   u*

   and the reference magnitude are not proportional, which is undesirable from the control point of view. The present work explores the possibilities of betterment of the overmodulation region performance by ensuring a linear relationship between the two.

   Reference [54] gives detailed analysis of the different PWM methods and compares them on the basis of higher fundamental voltage content and minimum distortion. In

   [55] and [56] the authors describe the space vector modulation technique of PWM and discuss different variations of the method.

   In SVPWM, one cycle of switching sequence is divided

   explained using figure (4) for the location of 1.

   Figure 3: Three-phase induction motor drive

   s in sector

   into two sub-cycles each of period Ts, a set sub-cycle and a u u

   reset sub-cycle.

   Here we have vectors a = (1 1 0) and b = (0 1 0) as the

   Dynamic control of torque and flux require the ability of

   the PWM scheme to apply the maximum possible voltage vector on the machine. Figure (2) shows that SVM is superior to the conventional sine-triangle method in this regard. Thus the comparison of the two methods is,

   • Carrier based or Sine-triangle method requires separate modulators for every phase and also it does not fully utilize the available DC-link voltage.

   • In the Space vector modulation method (SVM) the reference vector is processed as a whole. It fully utilizes the installed inverter capacity. Also the switching sequence is such that there is minimum number of commutations.

   OA=Linear SVM limit OB=Linear Sine PWM limit

   A

   active vectors which can be switched for times a and b

   in one sub-

   Figure 4: Space vector modulation for different switching combinations of Sa, Sb and Sc

   cycle period s . is the angle of the voltage vector within a sector. One sub-cycle of period s consists of active

   O B C

   voltage vectors switched for times

   a and

   b and zero

   OA 1.15 OB

   vectors switched for 0

   such that,

   s a b 0

   u*

   The maximum voltage vector

   Fig2: Comparison between Sine-Triangle PWM and SVPWM methods

   As the scheme of flux control explained in this proposal is

   magnitude

   s that can be applied in a phase is given as,

   u* (max) 2Vdc

   based upon the principle of SVM, let us try to review the s 3

   basics of SVM and develop equations for switching times.

   We will use normalized time s in the entire analysis. It is therefore necessary to define s .

   For normalizing voltages, the maximum value of the fundamental component during six-step operation is taken

   2 V

   dc

   as base value. This value is .

   Thus the normalized value of DC-link voltage becomes 2 while the normalized magnitude of every switching state voltage vector is,

   2 V

   IV. LINEAR RANGE

   In sine-triangle PWM, a common triangular carrier signal is compared with the three phase modulating sinusoidal signals of required magnitude and frequency to generate PWM signals. The three phase modulating reference signals are given in equation (4.1).

   ua ub

   3 dc

   2 V 3

   mr m cos(wt)

   dc

   The reference voltage can be expressed on the basis of the volt-second (i.e. change of flux) equality as follows,

   my m cos(wt 2 / 3)

   u* u u u

   mb m cos(wt 4 / 3)

   s s a a b b 0 0

   Therefore, the maximum possible volt-second or the maximum possible magnitude of vector displacement

   Figure 7 shows the three phase modulating waveforms with amplitude m = 0.75 and time period T. The triangular carrier signal is also shown along with modulating signal. In this work a half carrier cycle is called as a subcycle Ts.

   s (max)

   in the stator flux vector error that can be

   The triangle carrier signal is shown with low frequency for

   clarity. In practice the frequency of the triangular carrier is

   obtained in a sampling time period is given as

   so high that the reference modulating signal can be

   s

   (max)

   3 s

   assumed to be constant over the given subcycle Ts. The positive peak of the triangular carrier is +1 and the negative peak is -1.

   This vector displacement will be along one of the voltage

   vectors selected for switching in that sampling period.

   An important feature of the space vector modulation method is the sequence of switching. This is done in such a manner that there is minimum number of commutations in a sub-cycle. Considering the switching in sector 1 again, figure (5) shows the switching sequence for minimum number of commutations. Here Sa, Sb and Sc represent the top switches of the inverter legs. A 1 means that this switch is on, while 0 indicates that this switch is off.

   Fig. 7Three phase reference signals for SPWM with m = 0.8.

   The average pole voltage (Vro, Vyo, Vbo) over a given sub- cycle will be 0.5Vdc times of the reference modulating signal as given in equation below.

   Figure 5: On times for switching in sector zero

3. SIMULATED MODEL AND RESULT

Vro Vyo

Vbo

0.5Vdc m cos(wt)

0.5Vdc m cos(wt 2 / 3)

0.5Vdc m cos(wt 4 / 3)

amplitude modulatio

index

Sinusoidal PWM signal

n

(.8)

50Hz sine Wave

Sign

f

pwm

From the average pole voltages the average line to neutral t3 voltages (Vrn, Vyn, Vbn) can be derived. Figure 8 shows t2 modulating signals with m = 0.75 and their corresponding average pole voltages and line to neutral voltages are

shown in Figure 9 and 10. With m = 0.75 the average line

50

signal frequency

15

frequency modulation

pwm1

t1 to neutral voltages are same as the average pole voltages. Figure 10shows the transformed average two phase

Clock

index

-2/pi*asin(sin(2*pi*u(1)*u(2)))

triangular carrier

tri

Figure 6

T

Clock1

voltages Vsa and Vsb, and magnitude and the position of the average voltage vector over a fundamental cycle. Certain average voltage vector is applied in every half-carrier cycle or subcycle. The average voltage vectors applied over different subcycles in a fundamental cycle. The angle between the average voltage vectors in two consecutive cycles is wTs. In this range, the line-side voltage is proportional to m.

CONCLUSION

In Sine PWM, for m 1 (linear zone), the average

voltage vector produced is of uniform magnitude and of uniform angular frequency. In this zone modulation index

(MI) varies from 0 to 0.785. For

1 m

2

and

3

Fig.8Reference modulating signals

2 m 2

3

, the average voltage vector produced is

Fig. 9 Average pole voltages

Fig. 10 Average phase voltages

of non-uniform magnitude and angular frequency is constant or almost constant. The SVPWM method is far better than the sine PWM method in terms of the linearity.

REFERENCES

1. Zhenyu Yu; Arefeen Mohammed and Issa Panahi, A Review of Three PWM Techniques;Texas Instruments; DSP Automotive/Industrial Control Applications

2. Houston; 1997.

3. N. Mohan, T. Undeland, and W. Robbins, Power electronics converters, applications and design, John Wiley, 1985.

4. J. Holtz, Pulsewidth modulation – a survey, IEEE Trans. on Industrial Electronics, vol. 38, no. 5, pp. 410 420, 1992.

5. M. P. Kazmierkowski and G. Buja, Review of direct torque control methods for voltage source inverter-fed induction motors, Industrial Electronics Society, IECON 03. The 29th Annual Conference of the IEEE, November 2003.

6. Russel J. Kerkman, Dave Leggate, Brian J. Seibel, and. Timothy M. Rowan, An Overmodulation Strategy for PWM Voltage Inverters ,Allen-Bradley Co., Standard Drives Business,USA, 1993.

7. J. Holtz, W. Lotzkat, and A. M. Khambadkone, On continuous control of PWM inverters in overmodulation range including six- step, IEEE Transaction on Power Electronics, vol. 8, pp. 546553, 1993