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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

[email protected]

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*


2 100-110-111-211 Va*>0>Vb

*>Vc*


2 110-111-211-221 Va*>Vb

*>0>Vc*


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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05545828