Advanced Science and Technology Letters
Vol.138 (ISI 2016), pp.215-219
http://dx.doi.org/10.14257/astl.2016.138.43
Harmonic Frequency Spectrum Customization Method
to Random Space Vector Pulse Width Modulation
Guoqiang Chen and Jianli Kang
School of M echanical 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, M onte Carlo, maximum
harmonic amplitude, random variable
1
Introduction
The undesirable harmonic inevitably results fro m 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 amp litudes, which makes the case more serious . Therefore, the rando m SVPWM
strategy has been studied to suppress the large amp litude harmon ics [4,5,7, 9,12]. The
spectrum characteristic of the rando m SVPWM strategy is extremely co mplicated due
to the random variable , so it is difficu lt to accurately predict the maximu m amplitude
that is a key index to assess the performance of the modulation strategy . In this paper,
an algorith m based on the Monte Carlo method is proposed to optimize and customize
the frequency spectrum of the rando m SVPWM strategy . Furthermore the maximu m
amp litude can be customized. The key steps are presented. Finally, the proposed
algorithm is verified through several examples.
2
Random SVPWM Technology
The 8 b asic space vecto rs are sho wn in Fig .1 (a) fo r the classic t wo -lev el
inv erter. Fo r an arb it rary vo ltag e vecto r, fo r exa mp le U s res id ing in th e first
sextan t, the on -state du rat ion t ime T1 , T2 and T0 are d etermined b y the
id ent ical vo lt -secon d balance in th e s witch in g period Ts .The co mmon ly used 7-
ISSN: 2287-1233 ASTL
Copyright © 2016 SERSC
Advanced Science and Technology Letters
Vol.138 (ISI 2016)
segment SVPWM pattern SVPWM strategy is shown in Fig .1(b ). The rat io o f
 t1  t7  to t4 , th e rat io o f t1 to t7 , the rat io o f t2 to t6 and th e rat io o f t3
to t5 are controlled by 4 random variables
in the random strategy.
A
B
C
U 2 (110)
U 3 (010)
β
A
B
C
2
3
U 4 (011)
1
U 0 (000)

U 7 (111)
TU
1 1
4
0
1
1
1
1
1
0
T2U 2
B
0
0
1
1
1
0
0
C
0
0
0
1
0
0
0
U1 (100)
α
6
5
A
B
C
A
A
B
C
TsU s
A
B
C
U 5 (001)
t
t
1
R1T00
t
2
R2T1
t
4T07
(1-R0)T0
3
R3T2
a) Basic space vectors
t
6
(1-R2)T1
Ts
U 6 (101)
A
B
C
t
5
(1-R3)T2
t
7
(1-R1)T00
(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
T0 . If there are N switching periods Ts in a period T0 , the switching signal x(t )
in Fig.2 can be decomposed into the sum of N square wave signals.
Tbi
xi(t)
Tei
Twi
t
0
tbi
(i-1)Ts
tei
1
2
3
4
5
Ts
Ts
Ts
Ts
Ts
x(t)
...
iTs
i
i+1
i+2
Ts
Ts
Ts
N
Ts
Ts
T0
Fig. 2. Periodic rectangular pulse signal in the fundamental and switching periods
N
x(t )   xi (t )
(1)
i 1
The i-th square wave signal xi (t ) in a period T0 is given by
216
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Advanced Science and Technology Letters
Vol.138 (ISI 2016)
t   i  1 Ts  Tb or t  iTs  Te

0
(2)
xi (t )  
 i  1 Ts  Tb  t  iTs  Te

1
Therefore the harmonic coefficients ck (k  1, 2,3, ) for xi (t ) can be expressed as
N
j
i 1
kT00
ck   cki 
4
e
N
-jk0 tei
 e-jk0tbi
i 1

(3)
Harmonic Peak Customization Algorithm
Based on the accurate theoretical harmonic spectrum (that can be expediently g iven
by Equation 3)), the harmonic amp litudes and the maximu m amp litude can be
computed using Equation (3). A harmonic amp litude customization and optimizat ion
algorith m (using the Monte Carlo method) is proposed to aid in selecting the random
numbers. The algorithm is shown in Fig.3.
Start
Set the loop variable q to 1
Generate random numbers
Compute the duration time varaibles
Compute the coefficients using Eq.(3)
q+1->q
Compute the amplitudes A k using Eq.(3)
Replaced by
Compute the maximum amplitude Amaxq
Is Ak
greater than the
set amplitude
function?
Store the maximum amplitude Amaxq
Is Amaxq greater than the
set maximum amplitude?
Yes
Yes
q<Q?
No
No
Yes
No
End
Fig.3.
Harmonic Amplitude Customization Algorithm
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217
Advanced Science and Technology Letters
Vol.138 (ISI 2016)
4
Examples and Results
The DC bus voltage U DC is 100V, the fundamental wave frequency is 60Hz, and the
switching frequency is 2160Hz. The maximu m harmon ic amp litudes of the line A B
voltage are computed using Equation (3) and the proposed algorithm for the
deterministic symmetrical 7-seg ment 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 maximu m harmon ic amplitudes are shown in Fig.4. It should be noticed that
the computation accuracy based on the Monte Carlo method highly depends on the
maximu m iterat ion number. So me valuable findings can be made fro m the results.
The random SVPWM strategy has outstanding effects on suppressing the maximu m
harmonic amp litude/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 maximu m amp litude is shown
in Fig.4, the customizat ion procedure can be accomplished within 5000 iterations
based on the proposed algorithm.
Magnitude of Harmonic
(of Udc/2)
0.5
Deterministic SVPWM
RZDPWM
RPPPWM
HRPWM
0.4
0.3
Customization function
0.2
0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Modulation Index
0.8
0.9
1
1.1
Fig. 4. M aximum 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 algorith m has several advantages. Firstly, the algorith m is
based on the assumption that the random variab le is imp lemented by the periodical
pseudorandom nu mber, which is consistent with the practical applicat ion. In addition,
the algorith m is highly convenient and feasible. Finally, the algorith m is proved
efficient. However, the harmonic characteristic is ext remely comp licated for the
random SVPWM with the arb itrary frequency. Our future study will work on this task.
218
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Advanced Science and Technology Letters
Vol.138 (ISI 2016)
Acknowledg ments. 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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