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Research on Restraint Strategy of Narrow Pulses of Three-level Inverter Shuguang Wei,Minyu Li Department of Control Engineering, Academy of Armored Force Engineering Beijing, China [email protected],[email protected] proposed algorithm is simple and easy to implement, experimental results verify the feasibility of it.

Abstract—Narrow pulses may appear in specific area of space vector diagram. Because of narrow pulses, switching loss and distortion of output current increase. In this paper, the region of narrow pulses in the space vector diagram is obtained. A restraint algorithm of narrow pulses based on space vector optimization allocation is proposed. In the area of narrow pulses, the sequence and the number of space vector is optimized to avoid narrow pulses according to the basic principle of space vector assignment.The proposed strategy is simple and easy to implement. Experimental results verify the feasibility of the proposed algorithm.

II.

Space vector diagram of three-level inverter is shown in Fig. 1.There are six large sectors(I-VI) in the whole diagram and four small regions(1-4) in each sector.The voltage vector can be divided into one zero vector: U0 (PPP, OOO, NNN) and six positive small vectors: U1P (POO), U2P (PPO), U3P (OPO), U4P (OPP), U5P (OOP), U6P (POP) and six negative small vectors: U1N (ONN) U2N (OON), U3N (NON), U4N (NOO), U5N (NNO), U6N (ONO) and six middle vectors: U8 (PON), U10 (OPN), U12 (NPO), U14 (NOP), U16 (ONP), U18 (PNO) and six large vectors: U7 (PNN), U9 (PPN), U11 (NPN), U13 (NPP), U15 (NNP), U17 (PNP) on the basis of magnitude.

Keywords—T-type inverter; narrow pulses; space vector

I.

INTRODUCTION

There are many inherent advantages such as high efficiency,low output harmonics and low electromagnetic interference in three-level inverter.Therefore, it has been widely used in the field of photovoltaic inverter, motor drive and so on[1-4].There is always time delay in the process of turn-on or turn-off. If the minimum width of pulse is less than the sum of delay time of turn-on and turn-off, switching loss and distortion of output current will increase. Many scholars have made a very fruitful research for reducing narrow pulses. The first way is to eliminate or expand narrow pulses directly, which may lead to loss of normal pulse and increase of harmonic content. The second way is to compensate narrow pulses by injecting zero sequence voltage.The algorithm is simple and easy to implement, but it may produce new narrow pulses in the other phase when dealing with a narrow pulses[58]. The third method is to synthesize the reference vector by the non-nearest vectors. Although narrow pulses can be avoided by this method, it will increase the harmonics of output current[9].

ß U10

C U11

III U12

D U13

U3

IV

U4

U2

H

O

U0

E

I-4

U6

U15

U18

Fig. 1. Three-level space vector diagram.

The reference vector is defined as Ur,and the projection of the reference vector on alpha axis and beta axis is defined as UĮ and Uȕ. The length of line AD is defined as 1. The width of narrow pulses is defined as Tmin. Table I shows the duration of voltage vector in different area of sector I[10]. The sequence diagram of vector assignment is shown in Fig.2. TIME OF VECTOR

T0 =Ts ª¬1  ( 3U D  U E ) º¼

978-1-5090-5363-6/17/$31.00 ©2017 IEEE

VI

F

Time of vector

Ts 1  2U E

I

U17 U16 V

c

Area

T1

U8 J

I-2 I-1 Ur I-3 U1 U7 a(¢) UĮ G A

U5

U14

B

U9



TABLE I.

I-2

II

b

In this paper, the region of narrow pulses in space vector diagram is obtained. A restraint algorithm of narrow pulses based on space vector optimization allocation is proposed. In the proposed algorithm, the sequence and the number of space vector is optimized,and then narrow pulses will be avoided.The

I-1

ANALYSIS OF NARROW PULSES DISTRIBUTION

T1 =Ts T2



3U D  U E



Ts ª¬1  ( 3U D  U E ) º¼

430

T2 =2TsU E

T8 =Ts





3U D  U E  1

POO

OOO

OON

0.25T1

0.5T0

0.5T2

POO

PON

OON

I-3

T1

Ts ª¬ 2  ( 3U D  U E ) º¼

I-4

T2

Ts ª¬ 2  ( 3U D  U E ) º¼

ONN

OOO

OON

T7

Ts

T8

bⳌ

OON

PON

POO

aⳌ

0.5T2

0.5T1

(b) PON

PNN

ONN

0.25T1

0.5T8

0.5T7

0.5T1

PPO

PPN

PON

Ts 2U E  1

T9

0.5T0  Tmin  0.5T1  Tmin  0.5T2 ! Tmin ˄6˅

cⳌ

POO



When the reference vector is located near the point of H, the formula ˄6˅is established.

bⳌ 0.5T8

3U D  U E

PNN

PON

POO

There will be narrow pulses in phase a and phase b accoding to Fig. 2(a).

aⳌ bⳌ

As shown in Table II, the region of narrow pulses in other areas could be obtained by the same method.Similiarly we can get the diagram of narrow pulses distribution as shown in Fig. 3.

cⳌ

(c) OON

PON

PPN

PPO

aⳌ

II

b

bⳌ

2TsU E

There will be narrow pulses in phase a and phase b accoding to Fig. 2(a).

(a)

0.25T1



T8

0.5T0 ! Tmin  0.5T1  Tmin  0.5T2  Tmin ˄5˅

0.5T1

ONN

Ts



3U D  U E  1

When the reference vector is located near the point of O, the formula ˄5˅is established.

POO

aⳌ

cⳌ



ß B

0.5T9

0.25T2

0.5T8

0.5T2

cⳌ

(d)

4

III

H

J

Fig. 2. The sequence diagram of vector assignment.

UE

0 ;OB: U E

3U D ;HG: U E

3U D  1 ;AB: U E

0.5 ;GJ: U E

IV

1  3U D ;HJ:

The coordinates of every point in sector I are as follows:

V

Fig. 3. The area of narrow pulses distribution.

3 3 ,0 ˅ ˈ A III.

˄ 2 3 3 ,0˅ˈI˄ 3 2 ,0.5˅ˈB˄ 3 3 ,1˅

The line of OH satisfies the following equation: E



3U D  0 d U D d 3 6



A. The reference vector is located in region I-1 When 0.5T7 ! Tmin  0.5T1  Tmin  0.5T8  Tmin is satisfied,there will be narrow pulses in phase a and phase b. To eliminate narrow pulses,the sequence diagram of vector assignment should be adjusted to Fig. 4(a).

˄1˅

Then the formula ˄ 2 ˅ and ˄ 3 ˅ is also established accoding to Table I.

T0

1  2



3U D Ts , T1

0, T2

THE RESTRAINT STRATEGY OF NARROW PULSE

Taking the case of the reference vector located in sector I as an example, the restraint strategy of narrow pulses could be designed as follows:

The case that the reference vector is located near the line of OH is analysed as an example:

U

a(¢) A

VI

2  3U D .

3 6 ,0.5 ˅ ˈ G ˄

3 G

c

O ˄ 0,0 ˅ ˈ H ˄

1

O

In Fig.1 ,the expressions of boundary line between different regions are as follows: OA: U E

I

2

When 0.5T1  Tmin  0.5T2  Tmin  0.5T0 ! Tmin is satisfied,there will be narrow pulses in phase a and phase b. To eliminate narrow pulses,the sequence diagram of vector assignment should be adjusted to Fig. 4(b).

2 3U D Ts ˄2˅

0  T0  Ts  0  T2  Ts  T1 0 ˄3˅ When the reference vector is located near the line of OH, the formula ˄4˅is established. 0.5T0 ! Tmin  0.5T1  Tmin  0.5T2 ! Tmin ˄4˅

PPO

POO

OOO

OON

0.25T2

0.5T1

0.5T0

0.5T2

aⳌ bⳌ

There will be narrow pulses in phase a and phase b accoding to Fig. 2(a).

cⳌ

(a)

431

OOO

POO

PPO

TABLE II. Area

Location of the reference vector

Range of vector time

Narrow pules appear or not

Near the line of OG

0.5T0 ! Tmin  0.5T1 ! Tmin  0.5T2  Tmin 0.5T0 ! Tmin  0.5T1  Tmin  0.5T2  Tmin 0.5T0  Tmin  0.5T1 ! Tmin  0.5T2  Tmin 0.5T0 ! Tmin  0.5T1  Tmin  0.5T2 ! Tmin 0.5T0  Tmin  0.5T1  Tmin  0.5T2 ! Tmin 0.5T1 ! Tmin  0.5T2 ! Tmin  0.5T0  Tmin 0.5T2 ! Tmin  0.5T8 ! Tmin  0.5T1  Tmin 0.5T1  Tmin  0.5T2 ! Tmin  0.5T8  Tmin 0.5T1  Tmin  T2  Tmin  T8 ! Tmin 0.5 T1 ! Tmin  0.5T2 ! Tmin  0.5T8  Tmin 0.5T1 ! Tmin  0.5T2  Tmin  0.5T8  Tmin 0.5T1 ! Tmin  0.5T8 ! Tmin  0.5T2  Tmin 0.5T7 ! Tmin  0.5T8 ! Tmin  0.5T1  Tmin 0.5T7 ! Tmin  0.5T1  Tmin  0.5T8  Tmin 0.5T8 ! Tmin  0.5T1  Tmin  0.5T7  Tmin 0.5T1 ! Tmin  0.5T7 ! Tmin  0.5T8  Tmin 0.5T1 ! Tmin  0.5T7  Tmin  0.5T8  Tmin 0.5T1 ! Tmin  0.5T8 ! Tmin  0.5T7  Tmin 0.5T8 ! Tmin  0.5T9 ! Tmin  0.5T2  Tmin 0.5T8 ! Tmin  0.5T2  Tmin  0.5T9  Tmin 0.5T9 ! Tmin  0.5T2  Tmin  0.5T8  Tmin 0.5T2 ! Tmin  0.5T8  Tmin  0.5T9  Tmin 0.5T2 ! Tmin  0.5T8  Tmin  0.5T9  Tmin 0.5T2 ! Tmin  0.5T8 ! Tmin  0.5T9  Tmin

No

Near the point of O Near the point of G

I-1

Near the line of OH Near the point of H Near the line of HG Near the line of HJ Near the point of H Near the point of J

I-2

Near the line of HG Near the point of G Near the line of GJ Near the line of AJ Near the point of A Near the point of J

I-3

Near the line of GA Near the point of G Near the line of GJ Near the line of BJ Near the point of J Near the point of B

I-4

Near the line of HB Near the point of H Near the line of HJ

PPP

PPO

TABLE OF NARROW PULSES IN SECTOR I

POO

OOO

POO

PPO

PPP

No Yes Yes No Yes Yes Yes No No No Yes Yes Yes No No No Yes Yes Yes No No No

PPO

POO

PON

0.25T2

0.5T1

0.5T8

OON

PON

POO

PPO

aⳌ

aⳌ bⳌ cⳌ

Yes

0.25T0

0.5T2

0.5T1

0.5T0

0.5T1

0.5T2

bⳌ

0.5T2

cⳌ

0.25T0

(b)

(a) PPO

Fig. 4. The restraint strategy of narrow pulses when Ur.is located in I-1

POO

PON

0.5T1

T8

POO

PPO

aⳌ

B. The reference vector is located in region I-2

bⳌ

When 0.5T1  Tmin  0.5T2 ! Tmin is satisfied,there will be narrow pulses in phase b and phase c.To eliminate narrow pulses,the sequence diagram of vector assignment should be adjusted to Fig. 5(a).

0.5T2

0.5T1

0.5T2

cⳌ

(b) Fig. 5. The restraint strategy of narrow pulses when Ur.is located in I-2

When 0.5T1  Tmin  T2  Tmin  T8 ! Tmin is satisfied, there will be narrow pulses in phase b and phase c.Narrow pulses can not be eliminated completely.The narrow pulses in phase c could be eliminated by the sequence diagram of vector assignment in Fig. 5(b).

C. The reference vector is located in region I-3 When T7 ! Tmin  0.5T1  Tmin is satisfied, there will be narrow pulses in phase a and phase c.Narrow pulses can not be eliminated completely.The narrow pulses in phase a could be eliminated by the sequence diagram of vector assignment in Fig. 6(a).

432

When T8 ! Tmin  0.5T1  Tmin  T7  Tmin is satisfied, there will be narrow pulses in phase a and phase c.Narrow pulses can not be eliminated completely.The narrow pulses in phase c could be eliminated by the sequence diagram of vector assignment in Fig. 6(b). POO

PON

PNN

0.5T8

T7

PON

Fig.8 shows the driving pulse of SVPWM algorithm in sector I. As shown in Fig. 8(a), when the reference vector is close to the point of O, there are narrow pulses in the entire sector I.As shown in Fig. 8(b), when the reference vector is close to the line of OH, narrow pulses appear.As shown in Fig. 8(c), when the reference vector is close to the point of H, narrow pulses appear.As shown in Fig. 8(d), when the reference vector is close to the line of HJ, narrow pulses appear.As shown in Fig. 8(e), when the reference vector is close to the point of J, narrow pulses appear.The simulation results verify the theoretical analysis of the narrow pulses distribution.

POO

aⳌ bⳌ 0.5T1

0.5T8

0.5T1

cⳌ

(a) ONN

PNN

PON

PNN

Fig.9 shows the driving pulse of the proposed narrow pulses restraint algorithm in sector I.It is obvious that narrow pulses can be effectively suppressed in every case.

ONN

aⳌ bⳌ 0.5T1

0.5T7

T8

0.5T7

0.5T1

cⳌ

Sa1 (b)

Sb2

Fig. 6. The restraint strategy of narrow pulses when Ur.is located in I-3

Sc2

D. The reference vector is located in region I-4 When T8 ! Tmin  0.5T2  Tmin is satisfied, there will be narrow pulses in phase a and phase c.Narrow pulses can not be eliminated completely.The narrow pulses in phase a could be eliminated by the sequence diagram of vector assignment in Fig. 7(a).

t/s ˄a˅m=0.05 Sa1 Sb2

When T9 ! Tmin  0.5T2  Tmin  T8  Tmin is satisfied, there will be narrow pulses in phase a and phase c.Narrow pulses can not be eliminated completely.The narrow pulses in phase c could be eliminated by the sequence diagram of vector assignment in Fig. 7(b). PPO

PPN

PON

PPN

Sc2

t/s ˄b˅m=0.35

PPO

Sa1

aⳌ

Sb2

bⳌ 0.5T2

0.5T9

T8

0.5T9

0.5T2

Sc2

cⳌ

(a) OON

PON

PPN

PON

t/s ˄c˅m=0.577

OON

aⳌ bⳌ

Sa1 0.5T2

0.5T8

T9

0.5T8

0.5T2

cⳌ

Sb2 (b)

Sc2

Fig. 7. The restraint strategy of narrow pulses when Ur.is located in I-4

IV.

t/s ˄d˅m=0.8

EXPERIMENT

In order to verify the correctness of the proposed narrow pulses suppression strategy, a prototype of T-type inverter based on DSP28335 is built. 4MBI300VG-120R-50 of Fuji is used to build the main circuit. The load is three phase symmetrical resistance-inductance load.

433

V.

Sa1

CONCLUSIONS

In this paper, the region of narrow pulses in space vector diagram is obtained. A restraint strategy of narrow pulses based on space vector optimization allocation is proposed.In the area of narrow pulses, the sequence of space vector and the number of segments is optimized for avoiding narrow pulses according to the basic principle of vector distribution.The proposed algorithm is simple and easy to implement,and experimental results verify the feasibility of it.

Sb2 Sc2

t/s ˄e˅m=0.99 Fig. 8. The traditional algorithm

ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China under Grant No. 51507190.

Sa1 Sb2

REFERENCES

Sc2

[1]

Mario Schweizer, Johann W.Kolar, “Design and implementation of a highly efficient three-level t-type converter for low-voltage applications,” IEEE Transactions on Power Electronics, vol. 28, issue 2, pp. 899-900, 2013. [2] Mingchen Gu, Peng Xu,Li Zhang,Kai Sun, “A SiC-based t-type threephase three-level grid tied inverter,” 2015 IEEE 10th Conference on Industrial Electronics and Applications, pp. 1116-1120, 2015. [3] Yang Longfei, “Research of energy converter based on three-level Ttype NPC,” Beijing Jiao Tong University, 2013. [4] Xia Lingfang, “Research on the T-type three-level inverter,” NanjingUniversity of Aeronautics and Astronautics, 2014. [5] Bo Baozhong,Liu Weiguo,Su Yanmin, “Study of compensating technique in PWM control for three-level inverters,” Proceedings of the CSEE, vol. 25, issue 10, pp. 61-63, 2005. [6] Bo Baozhong,Liu Weiguo,Luo bing,Su Yanmin, “Study of narrow pulse width compensation technique for three-level inverter,” Electric power Automation Equipment, vol. 24, issue 8, pp. 27-28, 2004. [7] Li Hao, “Study on key technology of high power three-level converter and drive control system of synchronous motor,” China University of mining&technology, 2010. [8] Wang Chenchen,Guan Bo, “A narrow pulse processing method considering neutral-point potential balance problem of diode-clamped three-level inverters,” Transactions of China Electrotechnical Society, vol. 30, issue 19, pp. 138-141, 2015. [9] Liu H LˈCho G H, “Three-level space vector PWM in low index modulation region avoiding narrow pulse problem,” IEEE transactions on power electronics, vol. 5, issue 5, pp. 482-484, 1994. [10] Du Chao, “Study on key technology of high power three-level converter and drive control system of synchronous motor,” China University of mining&technology, 2009.

t/s ˄a˅m=0.05

Sa1 Sb2 Sc2

t/s ˄b˅m=0.35 Sa1 Sb2 Sc2

t/s ˄c˅m=0.577 Sa1 Sb2 Sc2

t/s ˄d˅m=0.8 Sa1 Sb2 Sc2

t/s ˄e˅m=0.99 Fig. 9. The proposed algorithm

434