Harmonic Frequency Spectrum Customization Method

to Random Space Vector Pulse Width Modulation

Guoqiang Chen and Jianli Kang

School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo,

454000, China

jz97cgq@163.com

Abstract. The spectrum of the random space vector pulse width modulation

(SVPWM) strategy is extremely complicated due to the random variable. An

algorithm is proposed to optimize and customize the frequency spectrum. The

theoretical spectrum computation method is given firstly. In addition, the key procedure of the proposed algorithm is presented. Finally, several computation

examples verify its convenience and feasibility.

Keywords: Space vector pulse width modulation, Monte Carlo, maximum

harmonic amplitude, random variable

1 Introduction

The undesirable harmonic inevitably results from the space vector pulse width

modulation (SVPWM) strategy in the practical application [1,2], which causes many

problems [3-11]. The deterministic SVPWM strategy presents cluster harmonics with

large amplitudes, which makes the case more serious. Therefore, the random SVPWM

strategy has been studied to suppress the large amplitude harmonics [4,5,7, 9,12]. The

spectrum characteristic of the random SVPWM strategy is extremely complicated due

to the random variable , so it is difficu lt to accurately predict the maximum amplitude

that is a key index to assess the performance of the modulation strategy . In this paper,

an algorithm based on the Monte Carlo method is proposed to optimize and customize

the frequency spectrum of the random SVPWM strategy. Furthermore the maximum

amplitude can be customized. The key steps are presented. Finally, the proposed

algorithm is verified through several examples.

2 Random SVPWM Technology

The 8 basic space vectors are shown in Fig .1 (a) fo r the classic two -level

inverter. For an arb it rary vo ltage vector, fo r exa mple sU res id ing in the first

sextan t, the on-state durat ion t ime 1T , 2T and 0T are determined by the

ident ical vo lt -second balance in the s witch ing period sT .The commonly used 7-

Advanced Science and Technology Letters Vol.138 (ISI 2016), pp.215-219

http://dx.doi.org/10.14257/astl.2016.138.43

ISSN: 2287-1233 ASTL Copyright © 2016 SERSC

segment SVPWM pattern SVPWM strategy is shown in Fig .1(b). The rat io o f

1 7t t to 4t , the rat io o f

1t to 7t , the rat io o f

2t to 6t and the rat io o f

3t

to 5t are controlled by 4 random variables in the random strategy.

1(100)U

2 (110)U3(010)U

4 (011)U

5 (001)U6 (101)U

0 (000)U

7 (111)U 1 1TU

2 2T Uα

β

s sTU

A

B

C

A

B

C

A

B

C

A

B

C

A

B

C

A

B

C

1

2

3

45

6

t1 t2 t3 t4T07 t5 t6 t7

Ts

A

B

C

0

0

0

1

0

0

1

1

0

1

1

1

1

1

0

1

0

0

0

0

0

R1T00 R2T1 R3T2 (1-R0)T0 (1-R3)T2 (1-R2)T1 (1-R1)T00

a) Basic space vectors (b) 7-segment SVPWM pattern in the first sextant

Fig. 1. Vector diagram and vector summation method

3 Harmonic Frequency Spectrum Computation

The three-phase switching signals that control the power switches in the upper arms

of the inverter are periodic . Fig. 2 shows the switching signal of one phase in a period

0T . If there are N switching periods sT in a period

0T , the switching signal ( )x t

in Fig.2 can be decomposed into the sum of N square wave signals.

...Ts Ts Ts Ts Ts Ts Ts Ts Ts Ts

T0

0 ttbi tei

Twi

(i-1)Ts

1 2 3 4 5 i i+1 i+2

iTs

N

x(t)

xi(t)

TeiTbi

Fig. 2. Periodic rectangular pulse signal in the fundamental and switching periods

1

( ) ( )N

i

i

x t x t

(1)

The -thi square wave signal ( )ix t in a period 0T is given by

Advanced Science and Technology Letters Vol.138 (ISI 2016)

216 Copyright © 2016 SERSC

s b s e

s b s e

0 1 or( )

1 1i

t i T T t iT Tx t

i T T t iT T

(2)

Therefore the harmonic coefficients ( 1,2,3, )kc k for ( )ix t can be expressed as

0 e 0 b-j -j

1 10 0

je ei i

N Nk t k t

k ki

i i

c ckT

(3)

4 Harmonic Peak Customization Algorithm

Based on the accurate theoretical harmonic spectrum (that can be expediently g iven

by Equation 3)), the harmonic amplitudes and the maximum amplitude can be

computed using Equation (3). A harmonic amplitude customization and optimizat ion

algorithm (using the Monte Carlo method) is proposed to aid in selecting the random

numbers. The algorithm is shown in Fig.3.

set maximum amplitude?

Start

Set the loop variable q to 1

Compute the duration time varaibles

Compute the coefficients using Eq.(3)

Compute the amplitudes Ak using Eq.(3)

Compute the maximum amplitude Amaxq

Is Amaxq greater than the

End

No

Yes

q<Q? No

Generate random numbers

Yes

Store the maximum amplitude Amaxq

q+1->q

Is Ak

greater than the

set amplitude

function?

NoYes

Replaced by

Fig.3. Harmonic Amplitude Customization Algorithm

Advanced Science and Technology Letters Vol.138 (ISI 2016)

Copyright © 2016 SERSC 217

4 Examples and Results

The DC bus voltage DCU is 100V, the fundamental wave frequency is 60Hz, and the

switching frequency is 2160Hz. The maximum harmonic amplitudes of the line AB

voltage are computed using Equation (3) and the proposed algorithm for the

deterministic symmetrical 7-segment SVPWM strategy, the random zero -vector

distribution SVPWM (RZDPWM), the random pulse position SVPWM (RPPPWM),

the hybrid random SVPWM(HRPWM, the combination of RZDPWM and RPPPWM

schemes ). The iteration number for the Monte Carlo method is 5000.

The maximum harmonic amplitudes are shown in Fig.4. It should be noticed that

the computation accuracy based on the Monte Carlo method highly depends on the

maximum iterat ion number. Some valuable findings can be made from the results.

The random SVPWM strategy has outstanding effects on suppressing the maximum

harmonic amplitude/magnitude. The RZDPWM scheme has excellent performance

for the small modulation index, while RPPPWM scheme has the opposite

characteristic. The HRPWM scheme has excellent performance over the entire linear

modulation range. If the customization function for the maximum amplitude is shown

in Fig.4, the customizat ion procedure can be accomplished within 5000 iterations

based on the proposed algorithm.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.10

0.1

0.2

0.3

0.4

0.5

Ma

gn

itu

de

of

Ha

rmo

nic

(o

f U

dc/2

)

Modulation Index

Deterministic SVPWM RZDPWM RPPPWM HRPWM

Customization function

Fig. 4. Maximum harmonic amplitudes of the line AB voltage for several different strategies

with 5000 iterations

5 Conclusion

A harmonic optimizat ion and customization algorithm is proposed for the random

SVPWM strategy. The algorithm has several advantages. Firstly, the algorithm is

based on the assumption that the random variab le is implemented by the periodical

pseudorandom number, which is consistent with the practical applicat ion. In addition,

the algorithm is highly convenient and feasible. Finally, the algorithm is proved

efficient. However, the harmonic characteristic is ext remely complicated for the

random SVPWM with the arb itrary frequency. Our future study will work on this task.

Advanced Science and Technology Letters Vol.138 (ISI 2016)

218 Copyright © 2016 SERSC

Acknowledgments. This work is supported by National Science Foundation of China

(No. U1304525). The author would like to thank the anonymous reviewers for their

valuable work.

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