My Report

CHB Multilevel Inverters

By Xi Xiaodan

No: 3100104733

Abstract

This project is focused on the goal to investigate carrier based PWM schemes for multilevel cascaded H-bridge

inverters and do some further research about the changes of properties of CHB inverters. The project is divided into

five parts. The first part is to state some basic theories about the CHB multilevel inverter. The second part is to build

a Matlab/Simulink model to simulate the bipolar and unipolar PWM CHB three phase inverter and compare their

results. The third part is to develop a simulation program for a specific seven level CHB inverter, using phase-shifted

and level-shifted mode, and compare the results. The fourth part is to search for the influence of overlap of carrier

waves and different carrier positions to the results of the inverter. And the last part is to search for the effects with

the method of third harmonic injection. Finally, we get the conclusion of the simulations in this project.

Content

Abstract ............................................................................................................................................................... 2

1. Introduction ................................................................................................................................................. 4

2. Basic theory of CHB Multilevel Inverters ................................................................................................... 4

2.1 Circuit of CHB Multilevel Inverters .................................................................................................... 4

2.2 H-Bridge Inverter Cell ......................................................................................................................... 4

2.2.1 Bipolar PWM H-bridge Inverter ......................................................................................................... 4

2.2.2 Unipolar PWM H-bridge Inverter ...................................................................................................... 5

2.3 Carrier-Based PWM Schemes .............................................................................................................. 6

2.3.1 Phase-Shifted Multicarrier Modulation ........................................................................................ 6

2.3.2 Level-Shifted Multicarrier Modulation ........................................................................................ 7

3. H-bridge Inverter Modeling and Simulation ............................................................................................... 7

3.1 H-bridge Inverter Modeling ................................................................................................................. 7

3.2 Simulation Results ............................................................................................................................... 9

3.2.1 Bipolar PWM H-bridge Inverter ......................................................................................................... 9

3.2.2 Unipolar PWM H-bridge Inverter ...................................................................................................... 9

3.3 Conclusions ........................................................................................................................................ 10

4. Multilevel Inverter Modeling and Simulation ........................................................................................... 10

4.1 System Specifications and Modeling ................................................................................................. 10

4.2 Simulation Results ............................................................................................................................. 13

4.2.1 Phase-Shifted Mode .......................................................................................................................... 13

4.2.2 Level-Shifted Mode .......................................................................................................................... 15

4.3 Conclusions ........................................................................................................................................ 18

5. Influence of Some Factors to Level-Shifted Mode.................................................................................... 19

5.1 Influence of Overlap of Carrier Waves in Level-Shifted Mode ......................................................... 19

5.2 Influence of Position of Carrier Waves in Level-Shifted Mode ......................................................... 21

6. Third Harmonic Injection PWM in CHB Multilevel Inverters ................................................................. 23

6.1 Theory of Third Harmonic Injection PWM ....................................................................................... 23

6.2 Conclusion .......................................................................................................................................... 24

7. Conclusions ............................................................................................................................................... 25

References ......................................................................................................................................................... 25

1. Introduction

Cascaded H-bridge (CHB) multilevel inverter is one of the popular converter topologies used in high-power

medium-voltage (MV) drives. It is composed of a multiple units of single-phase H-bridge power cells. The H-

bridge cells are normally connected in cascade on their ac side to achieve medium-voltage operation and low

harmonic distortion. In practice, the number of power cells in a CHB inverter is mainly determined by its operating

voltage and manufacturing cost. The use of identical power cells leads to a modular structure, which is an effective

means for cost reduction. The CHB multilevel inverter requires a number of isolated dc supplies, each of which

feeds an H-bridge power cell. There are mainly two methods of PWM modulation, thus phase-shifted and level-

shifted modulations. This essay will present the simulation results of various circuits of CHB multilevel inverter,

and discuss the effects of carrier waves and third harmonic injection.

2. Basic theory of CHB Multilevel Inverters

2.1 Circuit of CHB Multilevel Inverters

Fig 2.1-1 shows a simplified circuit diagram of a single-phase H-bridge inverter.

Fig2.1-1 Single-phase H-bridge inverter

The inverter dc bus voltage Vd is usually fixed, while its ac output voltage vAB can be adjusted by either bipolar

or unipolar modulation schemes.

2.2 H-Bridge Inverter Cell

2.2.1 Bipolar PWM H-bridge Inverter

Fig 2.2.1-1 shows a set of typical waveforms of the H-bridge inverter with bipolar modulation, where vm is the

sinusoidal modulating wave, vcr is the triangular carrier wave, and vg1 and vg3 are the gate signals for the upper

switches S1 and S3, respectively.

Fig2.2.1-1 Waves and harmonic spectrum of bipolar PWM H-bridge inverter

The harmonic spectrum of the inverter output voltage vAB normalized to its dc voltage Vd is shown in Fig. 7.2-

2b, where VABn is the rms value of the nth-order harmonic voltage. The harmonics appear as sidebands centered

around the frequency modulation index mf and its multiples such as 2mf and 3mf. The voltage harmonics with the

order lower than (mf – 2) are either eliminated or negligibly small.

2.2.2 Unipolar PWM H-bridge Inverter

The unipolar modulation normally requires two sinusoidal modulating waves, vm and vm–, which are of the

same magnitude and frequency but 180° out of phase as shown in Fig 2.2.2-1. The two modulating waves are

compared with a common triangular carrier wave vcr, generating two gating signals, vg1 and vg3, for the upper

switches, S1 and S3, respectively.

Fig2.2.2-1 Waves and harmonic spectrum of unipolar PWM H-bridge inverter

The harmonics of vAB appear as sidebands centered around 2mf and 4mf. The low-order harmonics generated by

the bipolar modulation, such as mf and mf ± 2, are eliminated by the unipolar modulation. The dominant harmonics

are distributed around 2mf.

2.3 Carrier-Based PWM Schemes

The carrier-based modulation schemes for multilevel inverters can be generally classified into two categories:

phase-shifted and level-shifted modulations. Both modulation schemes can be applied to the CHB inverters.

2.3.1 Phase-Shifted Multicarrier Modulation

In the phase-shifted multicarrier modulation, all the triangular carriers have the same frequency and the same

peak-to-peak amplitude, but there is a phase shift between any two adjacent carrier waves, given by:

360 / 1cr m (1.1)

Fig 2.3.1-1 Phase-shifted PWM for seven-level CHB inverters (mf = 3, ma = 0.8, fm = 60Hz, and fcr = 180 Hz)

The inverter phase voltage can be found from

1 2 3AN H H Hv v v v (1.2)

For a seven-level inverter, Vd = 3E. The maximum fundamental-frequency voltage can be found from:

1,max 1.224 0.612 1 1AB d aV V m E for m (1.3)

2.3.2 Level-Shifted Multicarrier Modulation

Similar to the phase-shifted modulation, an m-level CHB inverter using level-shifted multicarrier modulation

scheme requires (m – 1) triangular carriers, all having the same frequency and amplitude. The (m – 1) triangular

carriers are vertically disposed such that the bands they occupy are contiguous.

Fig 2.3.2-1 Level-shifted PWM for a seven-level CHB inverter (mf = 15, ma = 0.8, fm =60 Hz, and fcr = 900 Hz)

3. H-bridge Inverter Modeling and Simulation

3.1 H-bridge Inverter Modeling

We can build the model of three-phase H-bridge inverter in Simulink as follows:

Fig3.1-1 H-bridge inverter model in Simulink

In the model, the sub-system SPWM is shown as follows:

Fig3.1-2 Sub-system SPWM in bipolar mode

Fig3.1-3 Sub-system SPWM in unipolar mode

And the sub-system H is:

Fig3.1-4 Subsystem H

3.2 Simulation Results

3.2.1 Bipolar PWM H-bridge Inverter

We can get the results of bipolar PWM H-bridge inverter with fI =60Hz, ma =0.7, mf =12.0 as follows:

Fig 3.2.1-1 Voltage waveforms vAN, vAB and their harmonic spectrum with fI =60Hz and ma =0.7

3.2.2 Unipolar PWM H-bridge Inverter

We can get the results of unipolar PWM H-bridge inverter with fI =60Hz, ma =0.7, mf =12.0 as follows:

Fig 3.2.2-1 Voltage waveforms vAN, vAB and their harmonic spectrum with fI =60Hz and ma =0.7

3.3 Conclusions

(1) The results show that the bipolar PWM H-bridge inverter is a three level inverter, while the unipolar PWM

H-bridge inverter is a five level inverter.

(2) From the results we can know that: I bipolar PWM mode, the harmonics appear as sidebands centered

around the frequency modulation index mf and its multiples such as 2mf and 3mf. While in unipolar mode, the

harmonics of vAB appear as sidebands centered around 2mf and 4mf. The low-order harmonics generated by the

bipolar modulation, such as mf and mf ± 2, are eliminated by the unipolar modulation. The dominant harmonics are

distributed around 2mf.

(3) From the comparison of bipolar and unipolar PWM H-bridge inverter, we can know that the bipolar PWM

H-bridge inverter has a higher dc bus utilization but also a higher THD of the inverter than unipopar.

4. Multilevel Inverter Modeling and Simulation

4.1 System Specifications and Modeling

The requirements of this project is shown as follows:

Inverter Configuration: Seven-level cascaded H-bridge inverter

Rated Inverter Output Voltage: 2300V (rms fundamental line-to-line voltage)

Rated Inverter Output Power: 2MVA (three phase)

Rated Inverter Output Frequency: 60Hz

DC link voltage of H-bridges: Constant, ripple free. DC voltage: To be determined.

Inverter load: Three-phase balanced RL load with a lagging power factor of 0.9 at the rated frequency of

60Hz.

The inverter has the output with a fundamental line-to-line voltage of 2300V (rms) at the modulation index of

ma = 1.0. So we can calculate the dc link voltage as:

2300626.36

0.612 1 0.612 7 1

olVE V

m

(1.4)

and the load resistance:

2 2

6

/ 3 2300 / 32.645

/ 3 2 10 / 3

ol

load

UR

P

(1.5)

And we can determine the inductance as:

22

0.9 3.40load

load

RL mH

R L

(1.6)

Then we build the model of multilevel CHB inverter as follows:

Fig 3.1-1 Multilevel CHB inverter model in Simulink

In the model, the sub-system SPWM is shown as:

Fig 3.1-2 Sub-system SPWM in phase-shifted mode

Fig 3.1-3 Sub-system SPWM in level-shifted mode

And the sub-system H is shown as:

Fig 3.1-4 Sub-system H

4.2 Simulation Results

4.2.1 Phase-Shifted Mode

The simulation results of the voltage waveforms (vH1, vH2,vH3, vAN and vAB ) and their harmonic spectrums are

shown as follows:

(1) fI =60Hz, ma =1.0, mf =12.0:

Fig 4.2.1-1 Voltage waveforms vH1, vH2,vH3 and their harmonic spectrum with fI =60Hz and ma =1.0

Fig 4.2.1-2 Voltage waveform vAN and its harmonic spectrum with fI =60Hz and ma =1.0

Fig 4.2.1-3 Voltage waveform vAB and its harmonic spectrum with fI =60Hz and ma =1.0

(2) fI =60Hz, ma =0.2, mf =12.0:

Fig 4.2.1-4 Voltage waveforms vH1, vH2,vH3 and their harmonic spectrum with fI =60Hz and ma =0.2

Fig 4.2.1-5 Voltage waveform vAN and its harmonic spectrum with fI =60Hz and ma =0.2

Fig 4.2.1-6 Voltage waveform vAB and its harmonic spectrum with fI =60Hz and ma =0.2

4.2.2 Level-Shifted Mode

The simulation results of the voltage waveforms (vH1, vH2,vH3, vAN and vAB ) and their harmonic spectrums are

shown as follows:

(1) fI =60Hz, ma =1.0, mf =72.0:

Fig 4.2.2-1 Voltage waveforms vH1, vH2,vH3 and their harmonic spectrum with fI =60Hz and ma =1.0

Fig 4.2.2-2 Voltage waveform vAN and its harmonic spectrum with fI =60Hz and ma =1.0

Fig 4.2.2-3 Voltage waveform vAB and its harmonic spectrum with fI =60Hz and ma =1.0

(2) fI =60Hz, ma =1.0, mf =72.0:

Fig 4.2.2-4 Voltage waveforms vH1, vH2,vH3 and their harmonic spectrum with fI =60Hz and ma =0.25

Fig 4.2.2-5 Voltage waveform vAN and its harmonic spectrum with fI =60Hz and ma =0.25

Fig 4.2.2-6 Voltage waveform vAB and its harmonic spectrum with fI =60Hz and ma =0.25

4.3 Conclusions

(1) In phase-shifted mode, when ma=1.0, the harmonics in vH1 appear as sidebands centered around 2mf and its

multiples such as 4mf and 6mf. The harmonic content of vH2 and vH3 is identical to that of vH1.

The inverter phase voltage vAN does not contain any harmonics of the order lower than 4mf, which leads to a

significant reduction in THD. vAN contains triplen harmonics such as (6mf ± 3) and (6mf ± 9).

And the output line to line voltage has a even lower THD, and the rms fundamental line-to-line voltage is:

1 3216 0.707 2273.7 2300ABv V V (1.7)

which means the inverter satisfies the requirement of the project.

(2) In level-shifted mode, when ma=1.0, The output voltages of the H-bridge cells, vH1, vH2, and vH3, are all

different, and the harmonics in them appear as sidebands centered around mf.

The dominant harmonics in vAN and vAB appear as sidebands centered around mf. The inverter phase voltage

contains triplen harmonics, such as mf and mf ± 6, with mf being a dominant harmonic.

The output phase and line to line voltage has lower THDs than that of vH1, vH2 and vH3, and the rms

fundamental line-to-line voltage is:

1 3216 0.707 2273.7 2300ABv V V (1.8)

which means the inverter satisfies the requirement of the project.

(3) When ma is low, such as ma=0.2 and 0.25, the THD of vH1, vH2, vH3,vAN and vAB will all increase, and vAN

changes from seven level to three level, vAB changes from thirteen level to five level, and the dc bus utilization also

decreases.

(4)In phase-shifted and level-shifted mode, the dc bus utilizations are the same, but the former has a higher THD

than the latter, and the harmonic waves are easier to eliminate in phase-shifted mode than in level-shifted mode,

because the former has no harmonics lower than 4mf.

5. Influence of Some Factors to Level-Shifted Mode

5.1 Influence of Overlap of Carrier Waves in Level-Shifted Mode

In Level-Shifted mode, if we make the carrier waves overlapped with each other, for example, if we modify the

carrier waves as follows:

Fig 5.1-1 Overlapped carrier waves in level-shifted mode

Then we can get the simulation results with

Fig 5.1-2 Voltage waveforms vH1, vH2,vH3 and their harmonic spectrum with fI =60Hz and ma =1.0

Fig 5.1-3 Voltage waveform vAN and its harmonic spectrum with fI =60Hz and ma =1.0

Fig 5.1-4 Voltage waveform vAB and its harmonic spectrum with fI =60Hz and ma =1.0

The results show that if the carrier waves are overlapped, the inverter fundamental voltage VAB1 increases from

3216V to 3286V, and the THD also increases from 10.75% to 13.31%, which means that overlapped carrier waves

can result in an improvement of dc bus utilization but also a higher total harmonic distortion to the inverter.

5.2 Influence of Position of Carrier Waves in Level-Shifted Mode

The positions of carrier waves can affect the results of CHB multilevel inverters, and in this part, we change the

positions of carrier waves as follows to search for the influence of it:

Fig 5.2-1 shows three schemes for the level-shifted multicarrier modulation: (a) in-phase disposition (IPD),

where all carriers are in phase; (b) alternative phase opposite disposition (APOD), where all carriers are

alternatively in opposite disposition; and (c) phase opposite disposition (POD), where all carriers above the zero

reference are in phase but in opposition with those below the zero reference. In what follows, only POD modulation

scheme is discussed.

Fig 5.2-1 Three schemes for the level-shifted multicarrier modulation

Fig 5.2-2 POD modulation in level-shifted mode

Fig 5.2-3 Voltage waveforms vH1, vH2,vH3 and their harmonic spectrum with fI =60Hz and ma =1.0

Fig 5.2-4 Voltage waveform vAN and its harmonic spectrum with fI =60Hz and ma =1.0

Fig 5.2-5 Voltage waveform vAB and its harmonic spectrum with fI =60Hz and ma =1.0

The results show that if the carrier positions are changed in POD modulation as Fig 5.2-2 shows, the inverter

fundamental voltage VAB1 increases from 3216V to 3286V, and the THD also increases from 10.75% to 13.31%,

which means that the POD modulation can result in an improvement of dc bus utilization but also a higher total

harmonic distortion to the inverter.

6. Third Harmonic Injection PWM in CHB Multilevel Inverters

6.1 Theory of Third Harmonic Injection PWM

The inverter fundamental voltage VAB1 can be increased by adding a third harmonic component to the three-

phase sinusoidal modulating wave without causing over-modulation. This modulation technique is known as third

harmonic injection PWM.

Fig 6.1-1 The production and wave of the modulating wave with third harmonic injection

Fig 6.1-2 and Fig 6.1-3 shows the comparison of Voltage waveform vAB and its harmonic spectrum without

and with third harmonic injection.

Fig 6.1-2 Voltage waveform vAB and its harmonic spectrum with fI =60Hz and ma =1.0 (without third harmonic injection)

Fig 6.1-3 Voltage waveform vAB and its harmonic spectrum with fI =60Hz and ma =1.0 (with third harmonic injection)

6.2 Conclusion

From the results comparison, we can know that after injecting third harmonic waves into the modulating wave,

the inverter fundamental voltage VAB1 increases from 3216V to 3538V, which means that the third harmonic injection

can raise dc bus utilization of the inverter. But at the same time, the THD of also increases, which is not expexted.

7. Conclusions

In this project, we do some research about CHB multilevel inverters, build a practical model of seven level

inverter, and finish the simulation in Simulink. From the results, we can come to the following conclusions.

Bipolar PWM H-bridge inverter is a three level inverter, while the unipolar PWM H-bridge inverter is a five

level inverter, and bipolar PWM H-bridge inverter has a higher dc bus utilization but also a higher THD of the inverter.

In phase-shifted and level-shifted mode, the dc bus utilizations are the same, but the former has a higher THD than

the latter, and the harmonic waves are easier to eliminate in phase-shifted mode than in level-shifted mode, because

the former has no harmonics lower than 4mf. When ma is low, such as ma=0.2 and 0.25, the THD of vH1, vH2, vH3,vAN

and vAB will all increase, and vAN changes from seven level to three level, vAB changes from thirteen level to five level,

and the dc bus utilization also decreases.

What’s more, we find that overlapped carrier waves can result in an improvement of dc bus utilization but also a

higher total harmonic distortion to the inverter. And the POD modulation can result in an improvement of dc bus

utilization but also a higher total harmonic distortion to the inverter than the IPD modulation. Finally, we find that

through third harmonic injection, the dc bus utilization of the inverter can increase, but the THD of also increases.

References

[1] Bin Wu. High Power Converters and AC Drives. IEEE Press

[2] Penugonda V. V. N. M. Kumar*, P. M. Kishore, R. K. Nema. Simulation Of Cascaded H-Bridge Multilevel

Inverters For PV Applications

[3] 李宋. 采用三次谐波注入法的多电平级联H桥逆变器. 南昌工程学院学报

[4] 叶满园, 李宋, 官二勇. 九电平高压级联逆变器及其电压移位脉宽调制技术. 电网技术