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Abstract-- A fast algorithm for three-level space
vector pulse wide modulation (SVPWM) in neutral
point clamped (NPC) inverters based on traditional
three-level sinusoidal pulse wide modulation (SPWM)
is proposed. The acting time relation of each state in
each phase is got by deeply researching the
similarities and differences of three-level SPWM and
SVPWM. This algorithm can realize all kinds of statesequences easily, it does not need to do trigonometric
function, irrational operation and coordinate
transformation, it just needs ordinary arithmetic,
therefore the calculation is very simple and the result
is much more accurate. The fast algorithm can be
easily implemented on microprocessor and the
executing speed is faster than the conventional three-
level SVPWM algorithm.
Index Terms-- fast algorithm, three-level SVPWM,
acting time relation, state sequences.
I. INTRODUCTION
Since the development of power electronics, many
kinds of PWM technologies have been used in power
electronic circuits, SPWM and SVPWM are two mostly
used schemes of them [1].
SPWM uses triangular carrier to compare with
sinusoidal wave to get pulse signals, it realizes easily, yetthe voltage utilization is low. SVPWM can obviously
reduce the current harmonic component and raise the
utilization ratio of the power, however, in traditional
SVPWM, nonlinear operation is needed to be carried out,
such as the sine and arctan function etc, these operations
will influence the control speed of the system. In three-level NPC inverters, the simplified or fast algorithm of
three-level SVPWM is attracting more and more attention,due to the complexity of three-level SVPWM[2][3][4].
Some simplifications to SVPWM algorithms have
already been proposed in literatures[4][5][6][7][8][9][10],
yet some of these algorithms still have to use look-uptables to pick out the switching state vectors which
compose the reference vector, some of them can not
change the switching state sequences easily. In this paper,
a fast algorithm for three-level SVPWM in NPC inverters
is discussed, it is very fast and simple to implement,
further more, it can realize different state sequences
easily, therefore it can be used in many differentsituations.
II. FAST ALGORITHM FORTHREE-LEVEL SVPWM
A. Traditional three-level SPWM
Fig.1 shows the schematic diagram of three-level
SPWM in regular sampling method. There are two
carriers in three-level SPWM, in one switch period, if thereference voltage is larger than zero, the reference
compares with the upper carrier, otherwise, it compares
with the lower carrier. From Fig.1, it is clear that in
traditional three-level SPWM, there are two states in eachphase and the wave form of each phase is symmetrical
per switch cycle, so, totally, in a three-phase system,
there are six commutations per switch cycle.
Fig.1 Schematic diagram of three-level SPWM
B. Conventional three-level SVPWM
222
111
000
211
100
210121
010
122
011
112
001
212
101
200
220120020
021
022
012
002 102 202
201
221
110210221
110
211
100
200
222
111
000
1
2
3
S ec . 1 Se c. 2 Sec. 3 Se c. 4 S ec . 5 Sec. 6
Sec. 1
Tri.1: 000-100-110-111-211-221-222
Tri.2: 100-110-210-211-221
Tri.3: 100-110-210-211
Tri.4: 110-210-211-221
220
4V
refV
ref
Fig.2 Schematic diagram of three-level SVPWM
In three-level SVPWM, when using the nearest three
vectors (NTV) to compose the reference vector, as in the
most commonly used SVPWM schemes, firstly, ittransforms three phase reference voltage into the space
A Fast Algorithm for Three-level SVPWM in
NPC Inverters Based on Traditional Three-level
SPWMLI Ning, WANG Yue, JIANG Yingwei and WANG Zhaoan
Xian Jiaotong University, China
xjtulining1983@yahoo.com.cn
2010 2nd IEEE International Symposium on Power Electronics for Distributed Generation Systems
978-1-4244-5670-3/10/$26.00 2010 IEEE 53
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reference vectorVref, secondly, it identifies the sector and
triangle in which the reference vector falls, as shown in
Fig. 2. After the triangle is identified, a look-up table
with as many entries as the number of triangles is used to
find the vectors to be used. Then the SVPWM algorithm
carries several calculations to obtain the duty ratios of
those vectors, at last, it decides the switching statesequences and transforms switching state into gate pulses.
Fig.3 shows some commonly used state sequences of
three-level SVPWM. In the six sequences, SVPWM1 isan asymmetrical sequence, it uses two zero switching
states, there are six communications per switching cycle.
SVPWM2 uses symmetrical sequence to get low THD,
there are also two zero switching states, therefore the
numbers of commutations per switching cycle is six, too.
SVPWM3 and SVPWM4 are used to reduce switching
loss, in SVPWM3, it use zero switching state
alternatively in adjacent switching cycle, the sequence is
asymmetrical in one switching cycle, yet its symmetrical
in every two cycle, the switching loss in this sequence is
a half of SVPWM1, SVPWM4 uses a zero switchingstate in one switching cycle, the reduction of switching
loss in this sequence is one third of SVPWM1. SVPWM5
is similar to SVPWM4, yet the sequence is symmetrical.In SVPWM6, it chooses a zero switching state to avoid
switching the phase with the highest current, another
advantage of this sequence is that it can reduce the
switching loss up to 50%.
SVPWM1 SVPWM2
SVPWM3 SVPWM4
SVPWM5 SVPWM6
Fig.3 6 kinds of commonly used state sequences
C. Derivation of Fast Algorithm
(1) Acting times of each state in SPWM and SVPWM
According to the triangular relationship in Fig.1, when
regular sampling method is used, the acting time of each
state in each phase can be calculated in equ.(1). In the
equation, Va*, Vb* and Vc* are the sampling values of three
phase references in a switch period, Vdc is the DC voltage,
Ts is the switching time, Tga2 (Tgb2, Tgc2), Tga1 (Tgb1, Tgc1)and Tga0 (Tgb0, Tgc0) are the acting times of each state in
three phases.
* *
2 1
* *
2 1
* *
1 0
0 0 2
; (1 )/ 2 / 2
; (1 )/ 2 / 2
(1 ;/ 2 / 2
0
a aga s ga s
dc dc
b bgb s gb s
dc dc
c c
gc s gc sdc dc
ga gb gc
V VT T T T
V V
V VT T T T
V V
V VT T T T
V V
T T T
= =
= = = + =
= = =
(1)
where Va*>0, Vb
*>0, Vc
*
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* * * * * *
2 1
* * * * *
2 1
[(2 1) ( 1) ] ; (1 ) [(2 1) ( 1) ]/ 2 / 2 / 2 / 2 / 2 / 2
[(2 1) ( 1) ] ; 1 [(2 1) (/ 2 / 2 / 2 / 2 / 2
a a c a a ca s s a s s
dc dc dc dc dc dc
b a c b ab s s b s
dc dc dc dc dc
V V V V V V T T k k k T T T k k k T
V V V V V V
V V V V V T T k k k T T T k k k
V V V V V
= + + = +
= + + = +
*
* * * * * *
1 0
0 0 2
1) ]/ 2
(1 [(2 1) ( 1) ] ; [(2 1) ( 1) ]/ 2 / 2 / 2 / 2 / 2 / 2
0
cs
dc
c a c c a cc s s c s s
dc dc dc dc dc dc
a b c
VT
V
V V V V V V T T k k k T T T k k k T
V V V V V V
T T T
= + + + = +
= = =
(2)
where kis the time ratio of the redundant switching states,221 221 110
/( )k T T T = + .
In Sec.I, if the reference vectorVreffalls into the othertriangles, for instant, Vref falls into triangle 2, the total
redundant switching states is 2, while in triangle 1, this
number becomes 4, if only one redundant switching state
which is not the states of zero vector is used in a switch
cycle, table I can be got. In triangle 1 and 2, there are two
switching state sequences, in triangle 3 and 4, there are
only one switching state sequence. In table I, TxSP11(TxSP12), TxSP21 (TxSP22), TxSP3 and TxSP4 are the acting time
of switching state sequences in each triangle if the PWMstrategy is SPWM, while TxSV11 (TxSV12), TxSV21 (TxSV22),
TxSV3 and TxSV4 are the acting time of switching statesequences in each triangle if the PWM strategy is
SVPWM, Tgx is the acting time of each state in each
phase, Tz11 (Tz12), Tz21 (Tz22) and Tz3,4 are the time
differences between SPWM and SVPWM in different
triangles and different switching state sequences. They
are all three rows one line vectors and their values are
different in the positive and negative situation. Tx is a
three rows three lines constant vector, it also has two
different values in positive and negative situation.
TABLEI
ACTING TIME RELATION OF EACH STATE IN SEC.I BETWEEN SPWM AND SVPWMTriangle No. Switching state Seq. Sign ofVx
* Acting time( SPWM) Acting time( SVPWM)
1 100-110-111-211 Va*>0>Vb
*>Vc*
11 ( , , )xSP gx xT T T x a b c= = 11 11[ ]xSV gx z xT T T T = +
1 110-111-211-221 Va*>Vb
*>0>Vc*
12 ( , , )xSP gx xT T T x a b c= = 12 12[ ]xSV gx z xT T T T = +
2 100-110-111-211 Va*>0>Vb
*>Vc*
21 ( , , )xSP gx xT T T x a b c= = 21 21[ ]xSV gx z xT T T T = +
2 110-111-211-221 Va*>Vb
*>0>Vc*
22 ( , , )xSP gx xT T T x a b c= = 22 22[ ]xSV gx z xT T T T = +
3 100-200-210-211 Va*>0>Vb
*>Vc*
3 ( , , )xSP gx xT T T x a b c= = 3 3,4[ ]xSV gx z xT T T T = +
4 110-210-220-221 Va*>Vb
*>0>Vc*
4 ( , , )xSP gx xT T T x a b c= = 4 3,4[ ]xSV gx z xT T T T = +
where2
1
0
gx
gx gx
gx
T
T T
T
=
,1 0 0
0 1 0
0 0 0
xT
=
(Vx*>0),
0 0 0
0 1 0
0 0 1
xT
=
(Vx*0),
* *
11
0
( ( 1) ) 1/ 2 / 2
1
b cz s
dc dc
V VT k k T
V V
= +
(Vx*0),
* *
12
0
( ( 1) ) 1/ 2 / 2
1
c bz s
dc dc
V VT k k T
V V
= +
(Vx*0),
* *
21
0
[ ( 1) ( 1)] 1/ 2 / 2
1
b cz s
dc dc
V VT k k k T
V V
= + + +
(Vx*0),
* *
22
0
[ ( 1) ] 1/ 2 / 2
1
a bz s
dc dc
V VT k k k T
V V
= + +
(Vx*0),
* *
3,4
0
[ ( 1) (2 1)] 1/ 2 / 2
1
a cz s
dc dc
V VT k k k T
V V
= + +
(Vx*
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traditional SPWM is shown in table II. The time with SV
in the subscript is the acting time of fast algorithm, while
the time with SP in the subscript is the acting time of
traditional SPWM.
TABLEII
ACTING TIME RELATION OF EACH STATE BETWEEN SPWM AND FAST ALGORITHM
Triangle No. Acting time relation
1
[ ]
[ ]
*
1 1 1 1 mid max*
1 1 0 ( 0)
[ ] , [ ( 1) ] 0 1 1 ( 0)
T
x
xSV xSP z x z s T
x
V
T T T T T kv k v T V
>
= + = +
= + = +
= + = +
= + = +
= + = +
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