# 使用基本PWM技术的电压源逆变器的三相电性能分析与仿真 Performance Analysis and Simulation of Th ree Phase Voltage Source Inverter using basic PWM Techniques

【来自IEEE xplore，翻译未经授权，基本是机翻。只是用于学习】

## Abstract:

This paper illustrates use of different Pulse Width Techniques for a three phase voltage source inverter using Matlab Simulink software. These techniques help in reducing harmonic content in power supply as well as in controlling output voltage and frequency. The techniques which we have demonstrated are Multiple PWM, Sinusoidal PWM (SPWM), Trapezoidal PWM, Staircase PWM, 60° PWM and Third Harmonic PWM. Though these techniques are very good at reducing lower order harmonics, effi ciency of an inverter can’t be effectively increased due to the presence of higher order harmonics. To eliminate these harmonics, a fi lter is designed.

## 1. Introduction

Power systems designed to function at the fundamental frequency are prone to unsatisfactory operation and, at times, failure when subjected to voltages and currents that contain harmonics. A harmonic is a component of a periodic wave having a frequency that is an integral multiple of the fundamental power line frequency. Nowadays, a pure sinusoidal wave is a conceptual quantity as harmonics are always present in the periodic wave.

Such distorted sinusoidal waves are generally produced by non linear loads and in inverters1. Reduction of harmonics is important as these have various adverse effects on the power system components. Some of them are discussed1-4: Conductor Overheating-Conductor overheating is a function of square rms current per unit volume of the conductor.

Harmonic currents can cause “skin effect” which increases with frequency. Reduced life of Capacitors- Capacitors are affected by heat rise increases due to power loss .If a capacitor is tuned to one of the characteristic harmonics such as 5th or 7th , overvoltage and resonance can cause dielectric failure . False operations of fuses and circuit breakersHarmonics can cause false operations and trips, damaging or blowing components for no apparent reasons.

Overheating of transformer windings- Transformers have increased iron and copper loses or eddy currents due to stray fl ux losses which cause excessive overheating in the transformer windings. Motors increased hysteresis and eddy current losses in the magnetic core resulting in increase in the operating temperature of the core and the windings surrounding the core. Hence, this paper deals with the reduction of harmonics in inverter output voltage waveforms.

One way to do this is to insert fi lters between the load and the inverter. If the inverter output voltage contains high frequency harmonics, these can be reduced by a low-size fi lter, however for the attenuation of low-frequency harmonics the size of fi lter components increases. The fi lter circuit becomes costly, bulky and in addition, the transient response of the system becomes slow.

This shows that low-frequency harmonics should be reduced by some means other than the fi lter and subsequently high frequency components can be easily attenuated by a low size, low cost fi lter5. Thus in this paper PWM techniques have been used to reduce low frequency harmonics and subsequently, a low pass fi lter is added to fi lter out the high-frequency components.

## 2. PWM Techniques

In these techniques, a fi xed dc input voltage is given to the inverter and a controlled ac output voltage is obtained by adjusting the on and off periods of the inverter components. The on and off periods of the inverter are controlled by different PWM signals. The PWM signals are pulses with fi xed frequency and magnitude and variable pulse width6. Chennai and Vivekanandha College of Technology for women, Th ird International Conference on Sustainable Energy and Intelligent System (seiscon 2012),VCTW, Tiruchengode, Tamilnadu, India on 27-29 December, 2012.

These are generated by mainly two techniques, Triangle comparison based PWM and Space Vector based PWM7. Here, Triangle comparison based PWM is discussed where a triangular carrier wave is compared with a modulating wave of fundamental frequency. The width of the PWM pulses changes from pulse to pulse according to the modulating wave. The frequency of the carrier signal must be much higher than that of the modulating signal, such that the energy delivered to the load depends mostly on the modulating signal6. Advantages of PWM Techniques8:

PWM技术的优势8：

• These are easy to implement and control.
• Lower power dissipation.
• Lower power dissipation.
• Reduction of lower order harmonics
• Filtering requirements are minimized as only higher order harmonics are present
• Hardware implementation is easy as it is compatible with today’s digital microprocessor.
• 这些很容易实现和控制。
• 更低的功耗。
• 更低的功耗。
• 降低低次谐波
• 由于仅存在高次谐波，因此对滤波的要求降至最低
• 硬件实现容易，因为它与当今的数字微处理器兼容。

• They attenuate wanted fundamental component.
• Generation of high frequency components. In this paper the following PWM techniques are presented and the performance of each technique is carried.
• Multiple Pulse Width Modulation.
• Trapezoidal Pulse Width Modulation.
• Staircase Pulse Width Modulation.
• Sinusoidal Pulse Width Modulation (SPWM).
• 60 degree Pulse Width Modulation.
• Third Harmonic Pulse Width Modulation (THPWM).
• 它们减弱了所需的基本成分。
• 产生高频分量。 本文介绍了以下PWM技术，并介绍了每种技术的性能。
• 多脉冲宽度调制。
• 梯形脉宽调制。
• 楼梯脉冲宽度调制。
• 正弦脉冲宽度调制（SPWM）。
• 60度脉冲宽度调制。
• 第三谐波脉宽调制（THPWM）。

【中间还有一些介绍各种PWM，就不放图了。】

## 3. Filter Design

A Harmonic Filter is used for elimination of harmonic distortion in the output waveform. There are various types of fi lters that can be used for this purpose; here a simple constant k type low pass passive fi lter is designed. It is a single T section fi lter as shown in Fig. 7. Designing is done based on formulae derived by image method. The formulae used for calculating the fi lter parameters are10. L = Zo / (ð * fc) and C = 1/(ð *fc *Zo) where, Zo = load impedance and fc = cutoff frequency. For three phases, three single T sections are used, each connected in series with one phase as shown in Fig. 8.

## 4. Simulation Results

The output waveforms and harmonic voltage spectrums of above mentioned techniques are shown below. These are obtained through simulation done by MATLAB Simulink. The data that has been considered is as follows: Modulation index = 0.8 Carrier Frequency = 3 kHz Fundamental Frequency = 50 Hz DC Input Voltage = 400V Cutoff Frequency of fi lter = 1 kHz Resistive Load = 200 ohm The modulation index has been maintained constant for all the PWM technique. The output voltage and the FFT analysis with fi lters and without fi lters for all the techniques are shown in Fig 9 to Fig 13. Finally, the total harmonic distortion and the fundamental voltage for each technique are compared in Table-1 from the simulation result.

【这儿还有一些模拟结果的图也没放】

## 5. Conclusion

After a comparative study of these techniques from the point of view of their harmonics spectrum and total harmonic distortion, it is proven that the techniques SPWM and THPWM have better performances compared to other techniques. Also it has been verifi ed that after the addition of the fi lter, higher order harmonics have been eliminated and THD has been reduced.