High power factor correction circuits with space vector and hysteresis control methods

ELSEVIER

Electric Power Systems Research 43 (1997) 207-214

ELI[C'I'RIC POW|R SWST|ff'l$ RIS|flRgH

High power factor correction circuits with space vector and hysteresis control methods Bor-Ren Lin *, Deng-Ping Wu Power Electronics Research Laboratory, Department of Electrical Engineering, National Yunlin Institute of Technology, I23 Unwersity Road, Section 3. Touliu, Yunlin 640, Taiwan, ROC

Received 18 March 1997

Abstract This paper presents a new topology of the three-phase ac to dc converter. Only three ac switches are required to perform the power factor correction. The series connection of the two output capacitors is adapted to employ the high dc output voltage. A space vector modulation strategy is used to control two of the three ac switches at any time, hence the switching numbers can be reduced. The addition of a hysteresis current control technique can simplify the hardware circuit and reduce the cost. Furthermore the input current can be made to follow any desired waveform. Finally, simulation and experimental results are presented to verify the characteristics of unity power factor and sinusoidal input current. © 1997 Elsevier Science S.A. Keywords: High power: Correction circuits; Space vector; Hysteresis

1. Introduction Due to the increase of nonlinear loads in utility systems, the quality of power has attracted much attention in recent years. The low power factor and large harmonic line currents generated by uncontrolled rectifies are well-known problems that can lead to voltage distortion, and increase losses in the transmission and distribution lines [1]. To overcome these problems, active current waveshaping techniques have been developed to provide nearly sinusoidal source current [1-5]. A m o n g the various current control techniques, hysteresis current control [5] is the simplest and most extensively used method used to follow any desired waveform. However, the hysteresis current control has its disadvantages, i.e. the switching frequency is not constant and the frequency tends to be very high for heavy loads. The space vector modulation strategy has been mentioned in [6,7]. It can reduce the switching numbers in each interval. However, a high speed microprocessor is required to implement this technique. Recently, the application in a three-phase power factor correction * Corresponding author. Tel.: + 886 5 5342601, ext. 4259; fax: + 886 5 5312065; e-mail: [email protected] 0378-7796/97/$17.00 © 1997 Elsevier Science S.A. All rights reserved. PII S0378-7796(97)0 11 82-6

with strategy combing space vector modulation and hysteresis current control was presented in [8]. N o microprocessor was used and the switching numbers can be reduced in each interval, but three ac switches and six diodes and a high stress capacitor are necessary in the application of high dc voltage. A new three-phase ac to dc converter has been proposed in [9]. High dc voltage can be achieved easily. However, four switches should be used. In this paper, a new topology of the three-phase ac to dc converter is proposed. Only three ac switches are required to perform the characteristics of unity power factor and sinusoidal input current. By using the strategy combing space vector modulation and hysteresis current control, the switching numbers can be reduced. Simulation and experimental results verify the control strategy.

2. Operation principle Fig. 1 shows the power circuit of the proposed three-phase ac to dc converter. It consists of three boost inductors in the input lines, four diodes, three ac switches which are placed before the bridge rectifier, and two series-connected capacitors. In the hysteresis

B.-R. Lin, D.-P.

208

Wu ,,"Electric Power

current control, the supply currents ia, ib, ic are tightly controlled by the reference currents i~f~, i~fb, ir~t'~, respectively. The switch is turned off when the inductor current rises to the value i~ef+ Ai, where Ai is the hysteresis band limit. Contrary, when the inductor current falls to the value i ~ f - A i , the switch is turned on. According to the signs of the three-phase voltage, one can divide six intervals within a period as shown in Fig. 2. In interval I, the switch Sca is set normally open. When the switches S~b and Sbc are turned off, i~ and ib are across the diodes D1 and D4, respectively. The corresponding equivalent circuit is shown in Fig. 3(a). If S~b is turned on, a reverse voltage equal to vd (Fig. 3(d)) or V~l +/)¢2 (Fig. 3(b)) forces the diode D1 to be opened. Similarly a reverse voltage equal to /)~2 forces the diode D4 to be opened when Sbc is turned on. F r o m the switching states of Sab and Sb~ in interval I, four equivalent circuits can be obtained as shown in Fig. 3. The state space differential equation for Fig. 3(a) can be given as: di~ L ~ = e~ - / ) ~ 1

Systems Research 43 (1997) 207-214

%,

J , I

(1) (2)

The voltage Dcn can be obtained by adding Eq. (1), Eq. (2), and Eq. (3) together. /)o. = 0

L ~- = e~ -/)¢~

(3)

d/)~ Vo C--~-=ia--- ~

(4)

dt

ib

X=

[il

i2 a

/)0

(5)

(6)

e~ + e b -t- e~ = 0

(7)

AI=

If we assume that the two capacitors are equivalent and the switching frequency is fast compared to the line frequency, the capacitor voltages are 1)0 ['cl = /)c2 = - -

/)cl

(11)

Vc2]T

e~]x

L 0 0 0

L0

R

i3

eb

Z=

ic = 0

(12)

0 L 0 0

0 0 C 0

-0 0 0

0 0 0

0 0 0

1

0

0

0

-1

0

(13) CA -1 0 0

0 1 0 1

1

R

R

1

1

R

R

(14)

(8)

2

B=

L )---1

(10)

where

F o r a balanced three-phase system without neural line, the current and voltage have the following relationship. i a q- i b q-

(9)

The general form of the state equation can be given as follows

U=[e

di~

/

Fig. 2. Six intervals in a voltage period.

Z X = MiX-k- B U --/)¢~

dib L ~ - = e b q- Vc2 - - Vcn

C d/)c2 =

vV

.III

"

Sab)

a

p + I

1 D3

D4

i

R . ] Vo <. } _

4o÷i

C J-Vc2

Fig. 1. T h e p r o p o s e d three-phase ac to dc converter

[;°il 0 0

1 0

(15)

0 0

To fit the space vector modulation, one can represent three-phase voltage as a space vector. ~* = /)an -~ /)bn

~O2rc/3~_ Ucn ~4n/3

Since van =/)o/2, Vbn = vector becomes

(16)

/)O/2, and /)c, = 0, the space

B.-R. Lin. D.-P. Wu//Eleetric Power Systems Research 43 (1997)207214

?

= %/'0 5U

(17)

~ 1 l~z/'6

209

where

2 Similarly, one can obtain the state equations and corresponding space vectors in Fig. 3(b-d).In Fig. 3(b): Zf(=

A2X + BU

iT+

D

Z~

A2=

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1 R

R

1

1

R

R

c

+

'

VO

-1

-1

0

% _

(a)

1

0

UO

L~OeJ2rG~3 _~ DO eJ4rG/3

6

6

3

1

2 3 1

~')0 47t,'3

(18)

(19)

=~-e

In Fig. 3(c): Z X = A3X-4- B U

.2:............ ::;:..........~

I Y+

where n

i

~t'b

R: 'vo

2

0

o

o

5

o

0

o

o

1 ~

o

0

o

o

1 5

o

0

0

1

1

1

R

R

1

1

R

R

-

C

A3=

Co) D

;:)~

0

12

'

n

L

0

0

÷

b-.....................

'

(20)

Vo ~"

Z .............. 5:: ..............

(c)

--

UO

DO eJ2ze/3 __ VO eJ4rG~3

UO

3

6

2

6

(21)

In Fig. 3(d): Z)(= A4X-t- BU

where : ................%; .............iL-;-• i:L!-~ z2~, ~v_e,

L ~b

.....

Im m4

E ........... %E .............

0 0 0

0 0 0

0

0

0

0

(d) Fig. 3. Equivalent circuits in interval I (a)S~b. SB~ off (b)S.b on, Sbc off (c)S~b off, Sb~ on (d)Sab, Sbc on.

-0 0 0

9=0

0

0

0 0 0

0 0 0 1

1

R

R

1

1

R

R.

(22)

(23)

210

B.-R. Lin, D.-P. Wu /'Electric Power Systems Research 43 (1997) 207 214

Table 1 The space vectors in each interval Interval

Normally open switch

Conducting switches (diodes)

Van

Vbn

V~,I

Space vector

I

S~.

S~b, Sb~

0

0

0

0

D l, $1~ gab , D4 D 1, D4

vo/3 -- 0o/6

- Vo/6

- 0o/6 vo/3 0

0o/2 vo ei41r/3/2 0

II

III

IV

Sbc

Sab

S~

0o/'2

-- Vo/2 0

DI, D4 DI, S,,b S~, D4

0 %/2 0o/6 vo/6

0o/2 0o/6 - vo/3

0 0 -00/3 0o,6

Sea, SI,c D 1, Sl×.

0 0o/3

0 -- 00/6

0 -- Vo/6

DI, D2 Sca, D2

00/6

0o/6 0o/3

-- 0o/3 - 00/6

Sab,Sbc

0 %/6

0 - 0o/3 0 0o/6

0 vo ~ / 3 / 2

-- 0o/3

0 vo/6 Vo/2 Vo/6

Sea, gab

0

0

0

0

D3, D2 S¢~, D2 D3, S~,b

- 00,"2

%/'2

0

- vo/6 - Vo/6

00/3 - 00/6

- 0o/6 vo/3

.v/30o eJsa"6,/2 vo eJ2~r,'3/2 v o 44"'3/2

Sca, Sbc

0

0

--vo/3 - %/6

0 0o/6 - %/6

0

D3, Sb~ D3, D4 S ~ , D4

0o/6

- 0o/3

Sca, Sab

S~b, D2 D3,D2 D3, Sb~ g

Vl

Sbc

Sab

-- %/6

- Vo/6

-- 0o/2

\/'3 Vo ej i 1~/6/2 V/'3Voeil lrr/6/2 vo eiS-/3/2 Voei='3/2 0

Vo/2 % ei~/3/2 vo e321r'3/2

w/30o eJS~z/6/2 vo ~ / 2

0o/6

vo ed~/2

Vo/3 0o/6

v o eJ4r~/~/2 v o eJ5~/3/2

m

T h e s w i t c h i n g states in the o t h e r i n t e r v a l c a n be a n a lyzed in the s a m e way. T h e c o r r e s p o n d i n g space vectors in each i n t e r v a l are s u m m a r i z e d in T a b l e 1.

3. M o d u l a t i o n s t r a t e g y

T h e m a i n p u r p o s e o f a space v e c t o r m o d u l a t i o n strategy is to g e n e r a t e a s y n t h e t i c a l c u r r e n t v e c t o r w i t h the s m a l l e s t e r r o r f r o m the reference c u r r e n t vector. T o u n d e r s t a n d the m o d u l a t i o n p r i n c i p l e , o n e c a n r e p r e s e n t t h r e e - p h a s e c u r r e n t as a space v e c t o r ~ . A circle d i v i d i n g i n t o six i n t e r v a l s a c c o r d i n g to Fig. 2 c a n be o b t a i n e d as s h o w n in Fig. 4. F r o m T a b l e 1,

x//3v0eJll=/6/'2, a n d s h o w n in__Fig. 5. I n each i n t e r v a l , the r o t a t i n g space v e c t o r V r i S s y n t h e s i z e d b y the s w i t c h i n g state vectors, a n d V r is s y n c h r o n o u s with the space v e c t o r o f the c o m m a n d c u r r e n t . F o r e x a m pie in the i n t e r v a l III, Vr (Fig. 6(a)) c a n be s y n t h e sized as Vr = d~ Vt + ~ V 2 + doVo

(24)

w h e r e d~, d2, a n d d o are the d u t y - c y c l e s o f V ~ , V 2, a n d V o, respectively. I n the o t h e r c i r c u m s t a n c e , Vr (Fig. 6(b)) c a n be s y n t h e s i z e d as

V6

Fig. 4. The corresponding locations of the six intervals.

m

the space v e c t o r s are defined as follows: Vo = 0, V 1 = Vo_j2, V2 = Vo ei"'3,"2, V---~= Vo ei2"/3/2, ;V4 = . J 3 V o ~ s " ' 6 / 2 , Vs u 0 eJr~/2, V6 u eJ4~r'3/2 V 7 p0 eJ5~."3/2, V 8

V7

m

VII

Fig. 5. The space vectors according to the switching states.

211

B.-R. Lin, D.-P. Wu /'Electric Power Systems Research 43 (I997) 207 214

_ -~

Vr D'~'3

V6

V7

'V'8

(a)

V6

V7

V8

(b) Fig. 6. The vector synthesis in interval III.

(25)

V~ = d2V2 + d3V3 + doV0

m

F r o m above discussion, the rotating space vector V~ can be synt__hesized by the switching state vectors Vo,_V ~, V2, and V3. Similarly, the rotating space vector V, in other intervals can be synthesized by the proper switching state vectors.

When the switch Sab conducts, the corresponding equation is dija ea = 3L T + eb

(28)

The current rises from irefa- Ai to irefa + Ai within the transit time At~ and Eq. (28) can be rewritten as

G = 3 L ~2Ai +eb 4. Control scheme

(29)

Then Aq can be obtained as

To determine the reference current values, the analysis method of the local average is used. when S~ is off, the presented converter can be represented as Fig. 7. Furthermore, Fig. 7 can be separated into two individual circuits as shown in Fig. 8. In the hysteresis current control, the supply current ia is controlled within a region between i~f~ + Ai and iref~-- Ai as shown in Fig. 9 where iref, is the c o m m a n d current and Ai is the hysteresis band limit. The local average current /~ is defined as fo~tl il~ dt

i~t-~ At,. ila -- A~-t£ ~ 2 2 ~ AAt II+ ~

6L. Ai Atl - - e a --

(30)

e b

When the switch Sab is off, the equivalent circuit equation is ea=3L

-}- v0 + e b

(31)

the current falls from irefa+ Ai to irefa- Ai within the transit time At 2 and Eq. (31) can be further rewritten as i2a

(26)

L

C/2

0.5Vo

Similarly, the local average current /2~ is defined as V

irefa At2

~2R P

(27)

""

12a -- Aq + At2

+

T o. vo

(a) 2L

DI

C/2

8a Vo

1% Sb¢)l D~

I

I

w

Fig. 7. The equivalent circuit of the presented converter when S~, off.

c,, 70.5vo (b) Fig. 8. Equivalent circuit when Sea off (a) a-phase (b) c-phase.

212

B.-R. Lin, D.-P. Wu /Electric Power Systems Research 43 (1997) 207-214

i.

.~

e c --

t2c-

I refa + A i

= e," irefa q- e¢' irefc -1- eb( -- irefa -- iref,:)

i refa -- A i i

(37)

The total instantaneous dc power, Pdc, is Pao = Vo' ~ + 0.5Vo' ~

i r~fa

Atl

eb .

0.5Vo Irefc

= e," irefa q- eo- irefc q- ebirelb

L

vt

At2

(38)

In the balance three-phase system, the three-phase voltage and reference current are

(a)

ea = ~/~ V sin w t eb = w/2V sin(wt -- 120 °) e~ = x/"2V sin(wt + 120 °)

(39)

r-

irefa = X/2I sin w t irefb = ,,//2I sin(wt -- 120 °)

L

vt Atl

At2

ir~f¢ = x / 2 I sin(wt + 120)

{b)

(40)

Substituting Eq. (39) and Eq. (40) into Eq. (38), reults in

12a

(41)

Pdc = 3 V I = Pa~

On the other hand, the input power is equal to the load power. T h e reference current Iref can be obtained as Ir~f = - Atl

At2

(c) Fig. 9. (a) The supply current and the command current within a switching period, (b) instantaneous current waveform of i~a, (C) instantaneous current wavefoma of i2a' - 2Ai

ea = 3L ~

+ v0 + eb

(42)

3VR

~t

(32)

W h e n the load changes, the reference current can be adjusted by the o u t p u t voltage regulator. Fig. 10 shows the schematic d i a g r a m of the p r o p o s e d system. The three-phase voltage triggers the reference sinusoidal signal generator, then a w)ltage with fixed amplitude will be sent to the multiplier. The regulator is used to c o m p e n s a t e output dc voltage and filter the 360 Hz ripple. The signs of the three-phase voltage and the

The time At 2 based on Eq. (32) is 6L" Ai

At 2 --

v0 - (e~ - eb)

PWM

converter

(33)

substituting Eq. (30) and Eq. (33) into Eq. (26) and Eq. (27), one obtains

Vref

switt-h~

4-

declslon

.~ /la

--

v0 - (e, - eb) . Irefa v0

.--

e a -- e b .

12a - -

-

-

/refa

Vo

(34)

aeg~ao,

(35)

Using the similarly analysis, one can obtain the c phase current in Fig. 8(b) as

slnmaldal

signal

7

Multiplier

"~

generator

.llc =

0.5Vo - (ec - eb) . trefc 0.5

L~O

(36)

Fig. 10. Block diagram of the control scheme.

213

B.-R. Lin, D.-P. Wu /Electric Power Systems Research 43 (1997) 207-214

Table 2 States of switches Sab, Sbc, and S~, in accordance with the signs of three-phase voltages (S~, Sb, So) and the outputs of the hysteresis comparators (ha, h b, he)

(+,--, (+, -, ( + , +, ( - , +, (--, +, (-,-,

+) -) --)

-) +) +)

(0,0,0)

(0,0,1)

(0,1,0)

(0,1,1)

(1,O,O)

(1,0,1)

(l,l,O)

(1,1,1)

(0,0,0) (1,0,]) (0,0,0) (1,1,0) (0,0,0) (0,1,1)

(0,1,0) (1,0,0) (0,0,0) (1,0,0) (0,0,1) (O,l,l)

(0,0,0) (0,0,1) (0,1,0) (1,1,0) (1,0,0,) (0,0,1)

(0,1,0) (0,0,0) (0,1,0) (1,O,O) (1,0,1) (0,0,1)

(1,0,0,) (1,0,1) (0,0,1) (O,l,O) (0,0,0) (0,1,0)

(1,1,0) (1,0,0) (0,0,1) (0,0,0) (0,0,l) (0,1,0)

(1,0,0,) (0,0,1) (0,1,1) (0, l,O) (1,0,0) (0,0,0)

(1,1,0) (0,0,0) (0,1,1) (0,0,0) ( 1,0,1) (0,0,0,)

outputs of the hysteresis comparators are sent to the switching decision circuit. Table 2 list the inputs and the respective outputs of the decision circuit.

5. Simulation and experimental results To prove the proposed control scheme, computer simulations with the following parameters are performed.

line voltage = 220 V, L = 20 mH, Ro = 400 12,

C 1=

C2

= 2200 gF Fig. ll(a) shows the simulation results of the threephase current ia(t), ib(t), and ijt). A balance three-phase current with nearly sinusoidal wave can be obtained from this simulation. Fig. l l(b) shows the simulation results of ia(t) and ea(t). The phase voltage and current

+: ~7,:1 ~/d

lia,. I !b !

\

il

"

I/ici

/:,

', _AtAJ A: A !

,

i

I !

,

-l~J~

I

1

I- . . . . . . . . . . . . . . . . . . . . . . . . . .

Os

,~. . . . . . . . . . . . . . . . . .

~Omm

.m

't'lm

(a)

(a) ;HI=2~hV r.,H2=5~IV AC P,]I ACfl~ kll

5~5/d

ia~.~\lea:

F\

/

5'00 ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l

],-tA

][ A

/][ "-,?.~a, +

4lw

\/

"i . . . . . . . . . . . . . . . . . .

lhxt

lTms

(b) Fig. 11. Simulation waveforms: (a) three-phase input current; (b) phase voltage and phase current.

(b) Fig. 12. Experimental waveforms: (a) three-phase source current [ia, ib, ic: 10 A/div]; (b) single-phase source voltage and current [ea: 50V/div; i,: 10 A/div].

214

B.-R. Lin, D.-P. Wu / Electric Power Systems Research 43 (1997)207-214

are in phase with n e a r u n i t y power factor. The o u t p u t voltage can be m a i n t a i n e d at a c o n s t a n t value by the voltage regulator. Fig. 12(a) a n d 12(b) show the experim e n t a l results for the three-phase source c u r r e n t a n d near u n i t y power factor between source voltage a n d source current. E x p e r i m e n t a l results show that the proposed control algorithm can effectively o b t a i n high power factor.

6. Conclusions I n this paper a new topology of the three-phase ac to dc converter is proposed. By using the c o n t r o l strategy c o m b i n i n g space vector m o d u l a t i o n a n d hysteresis current control, the switching n u m b e r s can be reduced a n d the i n p u t c u r r e n t can be m a d e to follow a n y desired waveform. F i n a l l y the characteristics of c o n s t a n t dc voltage a n d the sinusoidal i n p u t currents with u n i t y power factor are investigated in the c o m p u t e r simulation a n d experimental test.

References [1] E.H. lsmail, R. Erickson, Single-switch three-phase low harmonic rectifiers, IEEE Trans. PE 11 (2) (1996) 338 346. [2] X. Wang, B.-T. Ooi, Real-time multi-DSP control of three-phase current-source unity power factor PWM rectifier, PESC (1992) 1376-1383. [3] E. Wernekinck, A. Kawamura, R. Hoft, A high frequency AC/DC converter with unity power factor and minimum harmonic distortion, IEEE Trans. PE 6 (3) (1991) 364 370. [4] A.W. Green, J.T. Boys, G.F. Gates, 3.-Phase voltage source reversible rectifier, lEE Proc. B135 (6) (1988) 362-370. [5] M.S. Dawande, V.R. Kanetkar, G.K. Dubey, Three-phase switch mode rectifier with hysteresis current control, IEEE Trans. PE 11 (3) (1996) 466-47t. [6] C. Cuadros, D. Borojevic, S. Gataric, V. Vlatkovic and F.C. Lee, Space vector modulated zero-voltage transition three-phase AC to DC bidirectional converter, IEEE PESC (1994) 16-23. [7] K. Yurugi, K. Muneto, H. Yonemori, M. Nakaoka, New spacevector controlled soft-switching three-pha~e PWM AC/DC converter with unity power factor and sinusoidal line current shaping functions, IEEE INTELEC (1992) 286-293. [8] R.J. Tu, C.L. Chen, A new three-phase space-vector-modulated power factor corrector, IEEE APEC (1994) 725 730. [9] M.C. Jiang, C.T. Pan, L.S. Yang, An economic three-phase current-forced reversible AC to DC converter, IEEE TENCON (1993) 526-530.