Research on Unipolar Inverted Sine Carrier PWM Strategies for Three Phase Five Level CMLI

C. R. Balamurugan^{1}^{, *}, S. P. Natarajan^{2}, R. Bensraj^{2}, T. S. Anandhi^{2}

^{1}Department of EEE, Arunai Engineering College, Tiruvannamalai, Tamil nadu, India

^{2}Department of EEE & EIE, Annamalai University, Chidambaram, Tamil nadu, India

Abstract

This paper presents the comparison of various Unipolar Inverted Sine Carrier Pulse Width Modulation (UISCPWM) techniques for the three phase Cascaded Multi Level Inverter (CMLI). Due to switch combination redundancies, there are certain degrees of freedom to generate the multilevel AC (Alternating Current) output voltage. This paper presents the use of Control Freedom Degree (CFD) combination. The effectiveness of the pulse width modulation strategies developed using CFD are demonstrated using simulation. The results indicate that the chosen five level inverter triggered by the developed UISCPSPWM (Unipolar Inverted Sine Carrier Phase Shift Pulse Width Modulation) and UISCVFPWM (Unipolar Inverted Sine Carrier Variable Frequency Pulse Width Modulation) strategy with sine and stepped wave reference and UISCAPODPWM strategy with 60 degree reference exhibits reduced harmonics and UISCCOPWM (Unipolar Inverted Sine Carrier Carrier Overlapping Pulse Width Modulation) provides higher fundamental RMS (Root Mean Square) output voltage for all references. Simulation are performed using MATLAB-SIMULINK.

Keywords

ISCPWM, CMLI, THD, 60 Degree, FF, Unipolar

Received: February 15, 2015

Accepted: March 7, 2015

Published online: March 12, 2015

@ 2015 The Authors. Published by American Institute of Science. This Open Access article is under the CC BY-NC license. http://creativecommons.org/licenses/by-nc/4.0/

Contents

1. Introduction 2. Multilevel Inverter 3. Unipolar Multi Carrier PWM Strategies 3.1. Unipolar Inverted Sine Carrier Phase Disposition PWM (UISCPDPWM) strategy 3.2. Unipolar Inverted Sine Carrier Alternative Phase Opposition and Disposition PWM (UISCAPODPWM) strategy 3.3. Unipolar Inverted Sine Carrier Phase Shift PWM (UISCPSPWM) strategy 3.4. Unipolar Inverted Sine Carrier Carrier Overlapping PWM (UISCCOPWM) strategy 3.5. Unipolar Inverted Sine Carrier Variable Frequency PWM (UISCVFPWM) Strategy 4. Inverted Sine PWM Technique for MLI 5. 60 Degree PWM Reference 6. Stepped Wave Reference 7. Simulation Results 7.1. Simulation Results for Sinusoidal Reference 7.2. Simulation Results for 60 Degree PWM Technique 7.3. Simulation Results for Stepped Wave PWM Technique 8. Conclusion

1. Introduction

The multilevel inverter topology gives the advantages of usage in high power and high voltage application with reduced harmonic distortion without a transformer. The semiconductor devices are not connected in series to for one single high-voltage switch. In which each group of devices contribute to a step in the output voltage waveform. The steps are increased to obtain an almost sinusoidal waveform. The number of switches involved is increased for every level increment. Donald Grahame Holmes and McGrath [1] proposed opportunities for harmonic cancellation with carrier based PWM for two level and multilevel cascaded inverters. Loh et al in [2] introduced synchronization of distributed PWM cascaded multilevel inverter with minimal harmonic distortion and common mode voltage. Mariethoz and Rufer [3] analysed resolution and efficiency improvements for three phase cascaded multilevel inverters. Xianglian Xu et al in [4] proposed phase shift SPWM (Sinusoidal Pulse Width Modulation) technique for cascaded multilevel inverter. Azli and Choong [5] analyzed the performance of a three phase cascaded H-bridge multilevel inverter. Shanthi and Natarajan proposed carrier overlapping PWM methods for single phase cascaded five level inverter [6]. Roozbeh Naderi and Rahomati [7] proposed phase shifted carrier PWM technique for general cascaded inverters. Gierri Waltrich and Barbi [8] introduced three phase cascaded multilevel inverter using power cells. Urmila and Subbarayudu [9] analyzed comparative study of various pulse width modulation techniques. Gierri Waltrich and Barbi [10] introduced also three phase cascaded multilevel inverter with commutation sub-cells. Konstantinou et al [11] proposed harmonic elimination control of a five level DC (Direct Current)-AC cascaded H-bridge hybrid inverter. Farid Khoucha et al [12] proposed comparison of symmetrical and asymmetrical three phase H-bridge multilevel inverter for direct torque control induction motor drives. Simulations are performed using MATLAB-SIMULINK. hhhhhHHarmonic analysis and evaluation of performance measures for various modulation indices have been carried out and presented.

2. Multilevel Inverter

The concept of this inverter is based on connecting H-bridge inverters in series to get a sinusoidal voltage output. The output voltage is the sum of the voltage that is generated by each cell. The number of output voltage levels are 2*n*+1, where *n *is the number of cells. The switching angles can be chosen in such a way that the total harmonic distortion is minimized. One of the advantages of this type of multilevel inverter is that it needs less number of components comparative to the diode clamped or the flying capacitor, so the price and the weight of the inverter is less than that of the two former types. Fig. 1 shows a configuration of the three phase five level cascaded multilevel inverter. A cascaded multilevel inverter consists of a series of H-bridge inverter units. The general function of this inverter is to synthesize a desired voltage from several Separate DC Sources (SDCSs).

The load voltage is equal to the summation of the output voltage of the respective modules that are connected in series. The number of modules (M) which is equal to the number of DC sources required depend on the total number of positive, negative and zero levels (m) of the CMLI. It is usually assumed that m is odd as this would give an integer valued M. In this work, load voltage consists of five levels which include +2V_{DC}, +V_{DC}, 0, -V_{DC} and -2V_{DC }and the number of modules needed is 2. The following equation gives the relation between M and m. Where M= (m-1)/2.

The gate signals for chosen five level cascaded inverter are simulated using MATLAB-SIMULINK. The gate signal generator model developed is tested for various values of modulation index m_{a} and for various PWM strategies. Fig. 2 shows a sample SIMULINK model developed for UISCPD (Unipolar Inverted Sine Carrier Phase Disposition) PWM method. The simulation results presented in this work in the form of the outputs of the chosen MLI are compared and evaluated.

3. Unipolar Multi Carrier PWM Strategies

This paper presents four types of unipolar PWM strategies. The reference in the unipolar strategy may be a rectified sinusoid or two sine references (sine and 180^{0} phase shifted sine) The later is used in this work. The multi carriers are positioned above zero level.

For an m-level inverter using unipolar multi-carrier technique, (m-1)/2 carriers with the same frequency f_{c} and same peak-to-peak amplitude A_{c }are used. The reference waveform has amplitude A_{m} and frequency f_{m} and it is placed at the zero reference. The reference wave is continuously compared with each of the carrier signals. If the reference wave is more than a carrier signal, then the active devices corresponding to that carrier are switched on [10]. Otherwise, the device switches off. The frequency ratio m_{f }is defined in the unipolar PWM strategy as follows:

(1)

In this paper, m_{f} = 40 and m_{a} is varied from 0.6 to 1.

m_{f} is chosen as 40 as a trade off in view of the following reasons:

(i) to reduce switching losses (which may be high at large m_{f})

(ii) to reduce the size of the filter needed for the closed loop control, the filter size being moderate at moderate frequencies.

(iii) to effectively utilise the available dSPACE system for hardware implementation.

3.1. Unipolar Inverted Sine Carrier Phase Disposition PWM (UISCPDPWM) strategy

The principle of the UISCPDPWM strategy is to use several triangular carriers with two modulation waves. For an m-level inverter, (m-1)/2 triangular carriers of the same frequency f_{c} and the same peak-to-peak amplitude A_{c} are disposed so that the bands they occupy are contiguous [10]. The carrier set is placed above the zero reference.

(2)

where n is the number of carriers

Carrier arrangements for five level UISCPDPWM are shown in Fig. 3 for m_{a}=0.8.

3.2. Unipolar Inverted Sine Carrier Alternative Phase Opposition and Disposition PWM (UISCAPODPWM) strategy

Carriers are arranged in such a manner that each carrier is out of phase with its neighbour by 180 degrees (Fig.4).

3.3. Unipolar Inverted Sine Carrier Phase Shift PWM (UISCPSPWM) strategy

The UISCPSPWM uses two carrier signals of same amplitude and frequency which are phase shifted by 90^{0} to one another to generate the five level inverter output voltage. The gate signals for the CMLI are derived by comparison of the carriers with two sinusoidal references. The amplitude modulation index is defined for this strategy as follows:

(3)

Carriers for five level inverter with UISCPSPWM strategy are illustrated in Fig. 5 for ma=0.8.

3.4. Unipolar Inverted Sine Carrier Carrier Overlapping PWM (UISCCOPWM) strategy

The UISCCOPWM has two carriers’ signals of peak-to-peak amplitude A_{c} and they overlap with each other. The gate signals for this strategy are derived by comparing the two overlapping carriers with the two sine references [10]. Fig. 5 shows the carrier arrangements for the chosen MLI with UISCCOPWM strategy.

(4)

3.5. Unipolar Inverted Sine Carrier Variable Frequency PWM (UISCVFPWM) Strategy

The number of switching for upper and lower devices of chosen MLI is much more than that of intermediate switches in PDPWM using constant frequency carriers. In order to equalize the number of switching for all the switches, variable frequency PWM strategy is used as illustrated in Fig. 6.

(6)

4. Inverted Sine PWM Technique for MLI

The inverted sine carrier PWM method uses the conventional sinusoidal reference signal and inverted sine carriers. The control scheme uses an inverted sine carrier that helps to maximize the output voltage for a given modulation index. For an ‘m’ level inverter, (m-1) carrier waves are required for bipolar PWM. The pulses are generated when the amplitude of the modulating signal is greater than that of the carrier signal[12,4].

The advantages of ISCPWM method are:

(i) It has a better spectral quality and a higher fundamental component compared to the conventional sinusoidal PWM without any pulse dropping.

(ii) The ISCPWM strategy enhances the fundamental output voltage particularly at lower modulation index ranges.

(iii) There is reduction in the total harmonic distortion and switching losses.

(iv) The appreciable improvement in the total harmonic distortion in the lower range of modulation index attracts drive applications where low speed operation is required.

(v) To increase the fundamental amplitude in the sinusoidal pulse width modulation the only way is by increasing the modulation index beyond 1 which is called over modulation. Over modulation causes the output voltage to contain many lower order harmonics and also makes the fundamental component Vs modulation index relation non-linear. Inverted sine pulse width modulation technique replaces over modulation.

This paper focuses on inverted sine carrier based sinusoidal PWM strategies and third harmonic injection PWM strategies which have been developed for the chosen three phase cascaded MLI.

5. 60 Degree PWM Reference

This method is almost similar to sinusoidal PWM except that the modulating sine wave is flat topped for a period of 60 degree in each half cycle [11]. 60 degree PWM reference technique is as shown in Fig. 8.

6. Stepped Wave Reference

The stepped wave is not a sampled approximation to the sine wave. It is divided into specified intervals (say 20^{0}) with each interval controlled individually to control magnitude of the fundamental component and to** **eliminate** **specific harmonics. This type of control gives low distortion but higher fundamental amplitude compared with that of normal PWM control [11]. Stepped wave PWM techniques are as shown in Fig. 9.

7. Simulation Results

The cascaded five level inverter is modeled in SIMULINK using power system block set. Switching signals for CMLI are developed using unipolar inverted sine carrier PWM techniques discussed previously. Simulations are performed for different values of m_{a} ranging from 0.6 – 1. The corresponding %THD (Total Harmonic Distortion) values are measured using FFT block and they are shown in Tables 1, 3 and 5. Tables 2, 4 and 6 display the V_{RMS} of fundamental of inverter output for same modulation indices. Figs. 18 - 47 show the simulated output voltages of CMLI and corresponding FFT (Fast Fourier Transform) plots with above strategies but for only one sample value of m_{a} = 0.8. Figs. 10 and 11 are for sine reference. Fig. 10 shows the five level output voltage generated by UISCPDPWM strategy and its FFT plot is shown in Fig. 11. From Fig. 11, it is observed that the UISCPDPWM strategy produces significant 7^{th}, 9^{th}, 31^{st}, 33^{rd} and 37^{th} harmonic energy. It is observed that the UISCAPODPWM produces significant 3^{rd},5^{th}, 9^{th}, 31^{st}, 35^{th}, 37^{th} and 39^{th} harmonic energy. It is also observed that the UISCCOPWM strategy produces no significant/dominant harmonic. It is shown that the UISCPSPWM strategy produces significant 3^{rd}, 5^{th} and 7^{th} harmonic energy. It is also shown that the UISCVFPWM strategy produces significant 7^{th} , 9^{th}, 35^{th} and 39^{th} harmonic energy.

The next two figures show results for 60 degree PWM strategy. Fig. 12 shows the five level output voltage generated by UISCPDPWM (60 degree) strategy and its FFT plot is shown in Fig. 13. From Fig. 13, it is observed that the UISCPDPWM (60 degree) strategy produces significant 3^{rd}, 11^{th}, 27^{th}, 29^{th} and 37^{th} harmonic energy. It is observed that the UISCAPODPWM (60 degree) strategy produces significant 3^{rd}, 5^{th}, 7^{th}, 27^{th}, 31^{st}, 33^{rd} and 35^{th} harmonic energy. It is also observed that the UISCCOPWM (60 degree) strategy produces significant 3^{rd} and 37^{th} harmonic energy. It is shown that the UISCPSPWM (60 degree) strategy produces significant 3^{rd} and 5^{th} harmonic energy. It is also shown that the UISCVFPWM (60 degree) strategy produces significant 3^{rd} and 11^{th} harmonic energy.

The next two figures show results for stepped wave PWM strategy. Fig. 14 shows the five level output voltage generated by UISCPDPWM (stepped wave) strategy and its FFT plot is shown in Fig. 15. From Fig. 15, it is observed that the UISCPDPWM (stepped wave) strategy produces significant 15^{th}, 21^{st}, 23^{rd}, 25^{th}, 31^{st} and 37^{th} harmonic energy. It is observed that the UISCAPODPWM (stepped wave) strategy produces significant 3^{rd}, 5^{th}, 11^{th}, 15^{th}, 19^{th}, 25^{th}, 27^{th}, 29^{th}, 31^{st}, 33^{rd}, 35^{th} and 37^{th} harmonic energy. It is also observed that the UISCCOPWM (stepped wave) strategy produces significant 3^{rd}, 7^{th}, 9^{th}, 21^{st}, 23^{rd}, 25^{th} and 29^{th} harmonic energy. It is displayed that the UISCPSPWM (stepped) strategy produces significant 3^{rd}, 5^{th}, 7^{th}, 21^{st}, 23^{rd} and 25^{th} harmonic energy. It is also observed that the UISCVFPWM (stepped wave) strategy produces significant 3^{rd}, 11^{th}, 15^{th}, 23^{rd}, 25^{th}, 27^{th} and 35^{th} harmonic energy. The following parameter values are used for simulation: V_{DC} =220V and R (load) = 100 ohms.

7.1. Simulation Results for Sinusoidal Reference

7.2. Simulation Results for 60 Degree PWM Technique

7.3. Simulation Results for Stepped Wave PWM Technique

ma | UISCPD | UISCAPOD | UISCCO | UISCPS | UISCVF |

1 | 26.74 | 26.85 | 37.20 | 28.76 | 26.46 |

0.9 | 30.97 | 32.84 | 40.89 | 32.05 | 30.87 |

0.8 | 35.85 | 37.90 | 48.26 | 35.79 | 35.91 |

0.7 | 40.08 | 44.53 | 58.12 | 38.43 | 40.27 |

0.6 | 44.87 | 52.58 | 68.97 | 40.45 | 44.38 |

ma | UISCPD | UISCAPOD | UISCCO | UISCPS | UISCVF |

1 | 328.7 | 322.5 | 342.2 | 338.1 | 328.9 |

0.9 | 304.7 | 295.7 | 325.2 | 318.5 | 304.8 |

0.8 | 279.1 | 268.5 | 301.7 | 296.8 | 278.6 |

0.7 | 249.8 | 234.6 | 275 | 275.1 | 249.5 |

0.6 | 213.6 | 191.7 | 244.3 | 253.7 | 214 |

ma | UISCPD | UISCAPOD | UISCCO | UISCPS | UISCVF |

1 | 25.74 | 24.64 | 33.16 | 28.73 | 25.57 |

0.9 | 31.19 | 29.91 | 36.95 | 32.57 | 31.00 |

0.8 | 34.57 | 34.42 | 40.46 | 38.02 | 34.54 |

0.7 | 39.54 | 39.44 | 51.11 | 39.46 | 39.64 |

0.6 | 42.20 | 43.11 | 61.57 | 43.07 | 42.13 |

ma | UISCPD | UISCAPOD | UISCCO | UISCPS | UISCVF |

1 | 370.6 | 367.7 | 375.3 | 371.6 | 370.6 |

0.9 | 343.2 | 340.8 | 359 | 352.1 | 343.4 |

0.8 | 319.2 | 313.7 | 341.2 | 323.6 | 319.2 |

0.7 | 289.7 | 283.5 | 311.7 | 306.7 | 289.4 |

0.6 | 257.2 | 248.1 | 278.1 | 277.8 | 257.3 |

ma | UISCPD | UISCAPOD | UISCCO | UISCPS | UISCVF |

1 | 21.79 | 23.23 | 36.18 | 26.88 | 22.01 |

0.9 | 29.33 | 32.90 | 40.76 | 30.50 | 29.02 |

0.8 | 35.26 | 38.85 | 43.87 | 34.99 | 34.92 |

0.7 | 39.30 | 43.02 | 54.42 | 36.36 | 39.65 |

0.6 | 42.60 | 56.73 | 65.61 | 38.21 | 42.32 |

ma | UISCPD | UISCAPOD | UISCCO | UISCPS | UISCVF |

1 | 330.3 | 327.2 | 344.7 | 336.6 | 330.9 |

0.9 | 307.1 | 299.5 | 325.6 | 319.2 | 309 |

0.8 | 284.2 | 275.6 | 303.9 | 296.8 | 285.7 |

0.7 | 249 | 239 | 275.9 | 280.7 | 249.9 |

0.6 | 216 | 190.5 | 245.9 | 252.1 | 217.2 |

ma | UISCPD | UISCAPOD | UISCCO | UISCPS | UISCVF |

1 | 1.4140 | 1.4142 | 1.4140 | 1.4140 | 1.4144 |

0.9 | 1.4145 | 1.4139 | 1.4142 | 1.414 | 1.4143 |

0.8 | 1.4145 | 1.4141 | 1.4143 | 1.4140 | 1.4142 |

0.7 | 1.4143 | 1.4143 | 1.4138 | 1.4143 | 1.4144 |

0.6 | 1.4143 | 1.4141 | 1.4142 | 1.4138 | 1.4144 |

ma | UISCPD | UISCAPOD | UISCCO | UISCPS | UISCVF |

1 | 1.4141 | 1.4141 | 1.4140 | 1.4141 | 1.4144 |

0.9 | 1.4143 | 1.4143 | 1.4142 | 1.4140 | 1.4140 |

0.8 | 1.4141 | 1.4144 | 1.4141 | 1.4144 | 1.4144 |

0.7 | 1.4142 | 1.4141 | 1.4141 | 1.4144 | 1.4143 |

0.6 | 1.4144 | 1.4143 | 1.4142 | 1.4143 | 1.4143 |

ma | UISCPD | UISCAPOD | UISCCO | UISCPS | UISCVF |

1 | 1.4144 | 1.4144 | 1.4139 | 1.4144 | 1.4143 |

0.9 | 1.4141 | 1.4143 | 1.4143 | 1.4141 | 1.4142 |

0.8 | 1.4144 | 1.4136 | 1.4139 | 1.4140 | 1.4144 |

0.7 | 1.4140 | 1.4142 | 1.4139 | 1.4139 | 1.4141 |

0.6 | 1.4143 | 1.4141 | 1.4143 | 1.4141 | 1.4139 |

ma | UISCPD | UISCAPOD | UISCCO | UISCPS | UISCVF |

1 | INF | INF | INF | INF | INF |

0.9 | INF | INF | INF | INF | INF |

0.8 | INF | INF | INF | INF | INF |

0.7 | INF | INF | INF | INF | INF |

0.6 | INF | INF | INF | INF | INF |

ma | UISCPD | UISCAPOD | UISCCO | UISCPS | UISCVF |

1 | INF | INF | INF | INF | INF |

0.9 | INF | INF | INF | INF | INF |

0.8 | INF | INF | INF | INF | INF |

0.7 | INF | INF | INF | INF | INF |

0.6 | INF | INF | INF | INF | INF |

ma | UISCPD | UISCAPOD | UISCCO | UISCPS | UISCVF |

1 | INF | INF | INF | INF | INF |

0.9 | INF | INF | INF | INF | INF |

0.8 | INF | INF | INF | INF | INF |

0.7 | INF | INF | INF | INF | INF |

0.6 | INF | INF | INF | INF | INF |

8. Conclusion

It is observed from Tables 1, 3 and 5 that UISCAPODPWM with 60 degree PWM reference provide output with low distortion and UISCPSPWM and UISCVFPWM with sine and stepped wave reference provide output with relatively low distortion. UISCCOPWM with sine, 60 degree and stepped wave references is found to perform better since it provides relatively higher fundamental RMS output voltage (Tables 2, 4 and 6). Tables 7, 8 and 9 provide crest factor and Tables 10, 11 and 12 provide FF for all modulating indices. Depending on the performance measure required in a particular application of chosen MLI based on the output quality appropriate PWM have to be employed.

References

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