# Analysis of PWM Voltage Source Inverters in the overmodulation region.

1. INTRODUCTION

In this paper is analyzed three-phase VSI that is presented in the fig. 1. A VSI used to supply a variable frequency voltage to a three phase AC motor in a variable speed application. A suitable Pulse Width Modulation strategy (Holtz, 1992) is employed to obtain the required output voltage in the inverter. In this paper used two strategies. Sine-triangle PWM, three phase reference modulating signals is compared with triangular carrier to generate the PWM signals. And, SVPWM technology, a revolving reference voltage vector is provided as voltage reference instead of three phase modulating waves (Holmes & Lipo 2003). The magnitude and frequency of the fundamental component in the output inverter are controlled by the magnitude and frequency, respectively of the reference vector. The output voltage is proportional to the reference magnitude during linear modulation. With sine-triangle PWM (Bose, 1986), the highest possible peak phase fundamental voltage is 0.5 Vdc, where Vdc the DC bus voltage in the linear modulation zone, while with strategies space vector based PWM, the peak phase fundamental voltage can be as high as Vdc/3 during linear modulation. To obtain the maximum possible fundamental voltage 2Vdc/[pi], the operation of the VSI must be extended into the overmodulation region. In overmodulation region of the modulator, the reference voltage and the line side voltage are not proportional. In this paper we are focuses on the overmodulation region of the PWM modulator. At steady state, the voltage demanded by the controller has to be applied in the line side in order to achieve the desired control objective. To ensure this, the problem of nonlinearity in the overmodulation zone has to be solved. This is achieved by transforming the reference voltage vector before the PWM calculations (Mohan et al., 1995). Changing of the reference voltage vector before the input of the modulator is termed as 'pre modulation'. The control variables and the fundamental voltage have a non-linear relationship. Inverse of this relationship is used to pre modulate the reference voltage vector (Wang, 2002). Apart from the fundamental component, the inverter output voltage mainly consists of harmonic components at high frequencies during linear modulation.

2. PRINCIPLE OF OPERATION

The topology of a three-phase inverter which is used in this paper is shown in fig. 1. 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 (1).

A(t) = m cos ([omega]t), B(t) = m cos ([omega]t - 2[pi]/3)

C(t) = m cos ([omega]t - 4[pi]/3) (1)

(1)

In linear range, fig. 2 shows the three phase modulating waveforms with amplitude m = 0,8 and time period T. The triangular carrier signal is also shown along with modulating signal. The triangle carrier signal is shown with low frequency. The positive peak of the triangular carrier is +1 and the negative peak is +1. Fig. 2 also illustrates how the relative values of the three phase modulating voltage waveforms are related to the position of the reference voltage space vector in the space vector plane, by identifying the sectors.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

With m=0.8 the average line to neutral voltages are some as the average pole voltages. While, the average voltage vectors applied over different sub cycles in a fundamental cycle are as shown in fig. 3 the angle between the average voltage vectors in two consecutive sub cycles is [omega][T.sub.s].

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

In non-linear range for m>1, say m=1.065 in which the peak of the modulating signals are greater then the peak of the triangular carrier signal. In non linear range (1 [less than or equal to] m [less than or equal to] 2 / [square root of 3]), the average voltage vector has lost the property of uniform magnitude as shown by the non circular portion of the locus of its tip.

[FIGURE 5 OMITTED]

In the rang 2[square root of 3] [less than or equal to] m [less than or equal to] 2, only one of the modulating waves is beyond the positive or the negative peak of the carrier in certain regions of the fundamental cycle, while two of the modulating waves are beyond the peaks of the carrier in other regions.

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

3. CONCLUSION

In this paper, the triangle comparison based PWM techniques are analyzed from space vector perspective. In the above figures, two distinct zones of overmodulation are identified. The first zone starts from the end of linear modulation. In sine triangle PWM strategy, in linear zone for m<1, the average voltage vector produced is of uniform magnitude and uniform angular frequency. In this zone modulation index varies from 0 to 0.785. In overmodulation zone 1 [less than or equal to] m [less than or equal to] 2 / [square root of 3] and 2 / [square root of 3] [less than or equal to] m [less than or equal to] 2, the average voltage vector produced are of non uniform magnitude and angular frequency is constant or almost constant. Index modulation ranging for this zone is from 0.785 to 0.952. While in SVPWM strategy index modulation in this overmodulation zone extends from 0.907 to 0.952. And for m>2 the average voltage vector produced is non uniform magnitude and non uniform angular frequency. While in this zone for the SVPWM strategy, the average voltage vector is not same as the reference voltage vector. In the first zone is shown only a magnitude error between the reference and applied average voltage vector, while in the second zone are shown the both magnitude and angle error between their. Comparison of low order voltage ripple due to different triangle based PWM technique is achieved.

4. REFERENCES

Bose BK. (1986). Power Electronics and AC Drives, NJ,

Englewood Cliffs: Prentice-Hall. Holmes, D. G. & Lipo, T. A (2003). PWM For Power Converters Principles and Pratice, John Wiley & Sons. Inc., Canada

Holtz, J. (1992). Pulse Width modulation--a survey, IEEE Transaction on Industrial Electronics, Volume 39, Page 1194-1214

Mohan, N.; Robbin, W. P. and Undeland, T. (1995). Power Electronics: Converters, Applications, and Design, 2nd ed. New York: Wiley

Wang, F. (2002). Sine-Triangle versus Spae Vector Modulation for Three-Level PWM Voltage Source Inverter, IEEE Trans. On Industry Applications, Vol. 38, No. 2

OSMANAJ, S[abrije]; XHUVANI, A[leksander] *; LIMANI, M[yzafere] & SELIMAJ, R[exhep]