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Single-phase Phase-shift Full-bridge

Photovoltaic Inverter with IntegratedMagneticsYing Jiang

a , Fei Gao

a & Junmin Pan

a

a

Department of Electrical Engineering , Shanghai Jiao TongUniversity , Shanghai, P.R. China

Published online: 26 May 2010.

To cite this article: Ying Jiang , Fei Gao & Junmin Pan (2010) Single-phase Phase-shift Full-bridge

Photovoltaic Inverter with Integrated Magnetics, Electric Power Components and Systems, 38:7,

832-850, DOI: 10.1080/15325000903489751

To link to this article: http://dx.doi.org/10.1080/15325000903489751

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Electric Power Components and Systems, 38:832–850, 2010

Copyright © Taylor & Francis Group, LLC

ISSN: 1532-5008 print/1532-5016 online

DOI: 10.1080/15325000903489751

Single-phase Phase-shift Full-bridge PhotovoltaicInverter with Integrated Magnetics

YING JIANG,1 FEI GAO,1 and JUNMIN PAN1

1Department of Electrical Engineering, Shanghai Jiao Tong University,

Shanghai, P.R. China

Abstract A single-phase phase-shift full-bridge photovoltaic inverter with integrated

magnetics is proposed. In the DC/DC stage, the inductor and transformer are inte-

grated into one magnetic core; then the number of magnetic components is reduced,and soft switching is achieved by the integrated magnetics. First, the coupling co-efficients expression of integrated magnetics is analyzed; then, based on coupling

coefficients expression, the mode analysis is done. Second, a comparison is madeof the zero-voltage switching range when different coupling coefficients are adopted.

Also, the design of integrated magnetics is analyzed. In the DC/AC stage, an SPWM control is adopted, and the sinusoidal output voltage is achieved. The inverter achieves

high efficiency and compact structure. Finally a 100-W prototype inverter is made and the experimental results are given to verify the analysis.

Keywords integrated magnetics, coupling coefficient, phase-shift full-bridge circuit,photovoltaic inverter, zero-voltage switching range

1. Introduction

Single-phase photovoltaic (PV) systems are widely used in PV applications [1–7], which

include the possibility of easily enlarging the system and the opportunity to become a

“plug and-play” device. The PV inverter, which is the main component of a PV system,

always includes a DC/DC stage and a DC/AC stage, and the main challenge is that the

DC/DC stage has a high conversion ratio to lift the low input voltage from the PV panel

and high efficiency to reduce the cost.

A traditional phase-shift full-bridge (PSFB) circuit is usually used as a step-down

DC/DC converter due to its advantages such as simple structure and zero-voltage switch-ing (ZVS) [8–11]. However, when the PSFB converter is used as a step-up DC/DC stage

in a PV inverter, it has a problem with the leakage inductor that mainly comes from

the transformer primary winding achieving full ZVS operation. The methods in previous

literature [12, 13] that make the leakage inductor of the transformer a resonant inductor

are unsuitable for the DC/DC stage in a PV inverter. An external inductor can be added as

a resonant inductor to achieve the ZVS operation, but it increases the number of magnetic

components, thereby decreasing the power density.

Received 7 April 2009; accepted 15 November 2009.

Address correspondence to Dr. Ying Jiang and Prof. Junmin Pan, Department of ElectricalEngineering, Shanghai Jiao Tong University, Shanghai 200240, P.R. China. E-mail: [email protected], [email protected]

832

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Single-phase Phase-shift Full-bridge PV Inverter 833

In the modern power electronics industry, the demand for integrated magnetics has

become much stronger. The integrated magnetics appear in different forms such as

coupled inductors, integrated transformers (two or more transformers sharing a com-

mon magnetic core), and an integrated inductor and transformer [14–22]. By using

integrated magnetics, the number of magnetic components can be reduced, and a con-

trolled coupling between magnetic components is sometimes required to achieve special

functions such as removing current/voltage ripples or reducing voltage/current stress.

In this article, the PSFB circuit with integrated magnetics for the DC/DC stage in

a PV inverter is proposed. The external resonant inductor and transformer are integrated

into one magnetic core to reduce the number of magnetic components, and the coupling

between resonant inductor and transformer is designed to achieve ZVS operation. In the

DC/AC stage, a full-bridge circuit with classical sine pulse width modulation (SPWM)

control is adopted to give the sinusoidal output voltage.

The article first studies the DC/DC stage in detail. The external resonant inductor and

transformer are integrated into one magnetic core. The coupling coefficients expression

of integrated magnetics is analyzed, and then, according to the coupling coefficientsexpression, the operation and key features of the individual modes of the DC/DC stage

are discussed. Also, the analyses of the ZVS range when different coupling coefficients are

adopted and the design of integrated magnetics are achieved. Second, the DC/AC stage

with the classical SPWM control is introduced. Finally, the experimental results of a

100-W inverter with 50-Hz, 220-V AC output are provided to confirm the theoretical

analysis.

2. Main Circuit of Single-phase PV Inverter withIntegrated Magnetics

Figure 1 shows the single-phase PV system configuration. In Figure 1, the maximum

power point tracker (MPPT) circuit makes sure that the output of the PV panel operates

in the maximum power point, the battery is then charged and the PV inverter inverts

the low DC voltage ratios of the battery into the AC voltage of the load. This article

researches the PV inverter, which lifts the 43–53 V DC of the battery into 380 V DC

in the DC/DC stage and then generates 220 V AC in the DC/AC stage. Figure 2(a)

shows the single-phase PV inverter with discrete magnetic, and Figure 2(b) shows the

proposed single-phase PV inverter with integrated magnetics, where the inductor and

transformer are integrated into one magnetic core. In Figure 2(b), several assumptions

are made:

1. Switches S 1–4 and Q1–4 are ideal; S 1–4 includes parasitic capacitors (C oss1 DC oss2 D C oss3 D C oss4 D C oss ) and internal diodes (D1 D D2 D D3 D D4).

Figure 1. Single-phase PV system configuration.

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834 Y. Jiang et al.

Figure 2. (a) PV inverter with discrete magnetics and (b) proposed PV inverter with integrated

magnetics.

2. The transformer T winding is in the middle leg, and the inductor Lr winding

divided into two parts in left and right legs.

3. The input voltage V in is the output of the battery, V DC is the voltage of the DC/DC

stage,V o is the output of the PV inverter, and Ro is the AC load.

4. A voltage-doubler is ideal; rectifier capacitors C r1 and C r 2 are identical; each

voltage is V DC =2; and Dr1 and Dr 2 are rectifier diodes.

3. Operation Principle of DC/DC Stage withIntegrated Magnetics

3.1. Coupling Coefficients Expression of Integrated Magnetics

In order to analyze the operation of the DC/DC stage in a PV inverter, the expression of integrated magnetics should be achieved. Integrated magnetics are shown in Figure 3. In

Figure 3, transformer T includes primary side T P and secondary side T S in the middle

leg. LP and LS are self-inductors of T P andT S , and inductor Lr is divided into two

parts, Lr1 and Lr 2, which are in the left and right legs, respectively. <1, <2, and <3

are the magnetic resistances in the left, right, and middle leg, respectively. N P , N S ,

N Lr1, and N Lr2 are, respectively, the number of turns of T P winding, T S winding, Lr1

winding, and Lr 2 winding. T , Lr1, and Lr2 are, respectively, the fluxes generated by

the transformer winding, Lr1 winding, and Lr 2 winding. 1, 2, and c are the total

fluxes in the left, right, and middle leg, respectively. B1, B2, and Bc are the flux densities

in left, right, and middle leg, respectively. V

P , V

S , V

Lr1, and V

Lr 2 are, respectively, thevoltages of T P , T S , Lr1, and Lr 2. iP , iS , iLr1, and iLr2 are, respectively, the currents of

T P , T S , Lr1, and Lr 2. Based on the magnetic circuit in Figure 3(b), T , Lr1, and Lr2

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Figure 3. (a) Integrated magnetic and (b) magnetic circuit.

can be represented as follows:

8̂̂̂ˆ̂̂̂<ˆ̂ˆ̂̂̂̂:

T D N P iP N S iS

<3 C <1==<2

D .N P iP N S iS /.<1 C <2/

<1<2 C <1<3 C <2<3

Lr1 D N Lr1iLr1

<1 C <2==<3

D N Lr1iLr1.<2 C <3/

<1<2 C <1<3 C <2<3

Lr2 D N Lr1iLr2

<2

C <1==

<3

D N Lr2 iLr2 .<1 C <3/

<1

<2

C <1

<3

C <2

<3

: (1)

According to Eq. (1), the expressions between the voltages V Lr1, V Lr2 , V P , andV S

and the fluxes in each leg 1, 2, and c can be represented as8̂̂ˆ̂̂̂̂̂ˆ̂̂̂̂<ˆ̂̂̂̂̂̂̂̂̂̂ˆ̂:

V Lr1 D N Lr1

d1

dt D N Lr1

d

dt

Lr1 T

<2

<1 C <2

C Lr 2

<3

<1 C <3

V Lr 2 D N Lr 2

d2

dt D N Lr2

d

dt

Lr 2 C T

<1

<1 C <2

C Lr1

<3

<2 C <3

V P

DN P

dc

dt DN P

d

dtT

Lr1

<2

<2 C <3 CLr2

<1

<1 C <3

V S D N S

dc

dtD N S

d

dt

T Lr1

<2

<2 C <3

C Lr2

<1

<1 C <3

: (2)

Since the voltage of Lr can be achieved as V Lr D V Lr1 CV Lr2 and iLr D iLr1 D iLr2 ,

then according to Eqs. (1) and (2), V Lr , V P , and V S can be represented as

0B@

V Lr

V P

V S

1CA D

0B@

Lr M PLr M SLr

M PLr LP

M PS

M SLr M PS LS

1CA

0

BBBBBB@

d iLr

dt

d iP

dtd iS

dt

1

CCCCCCA; (3)

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836 Y. Jiang et al.

where 8̂

ˆ̂̂̂̂̂̂̂̂̂̂̂̂̂̂ˆ̂̂̂̂̂<ˆ̂̂̂̂̂ˆ̂̂̂̂ˆ̂̂̂

ˆ̂̂̂̂̂̂:

M PLr D N P .N Lr2<1 N Lr1<2/

<1<2 C <1<3 C <1<3

;

M SLr D N S .N Lr1

<2

N Lr2

<1/

<1<2 C <1<3 C <1<3

LP DN 2P .<1 C <2/

<1<2 C <1<3 C <1<3

;

LS D N 2S .<1 C <2/

<1<2 C <1<3 C <1<3

Lr D N 2Lr1.<2 C <3/ C N 2Lr2 .<1 C <3/ C 2N Lr1N Lr2<3

<1<2 C <1<3 C <1<3

;

M PS

D N P N S .<1 C <2/

<1<2 C <1<3 C <1<3

: (4)

According to Eqs. (3) and (4), the coupling coefficients can be represented as

8̂̂̂ˆ̂̂̂̂̂ˆ̂̂̂̂ˆ̂̂ˆ̂̂<̂̂̂̂̂̂ˆ̂̂̂̂ˆ̂̂̂̂̂ˆ̂̂:

kPS D M PS p

LP LS

D 1

kLP D M PLrp

Lr LP

D N Lr2<1 N Lr1<2

q N 2

Lr1

.<

2

C <3/

CN 2

Lr2

.<

1

C <3/

C2N Lr1N Lr2

<3 .

<1

C <2/

kLS D M SLrp

Lr LS

D N Lr1<2 N Lr2<1q N 2Lr1.<2 C <3/ C N 2Lr2 .<1 C <3/ C 2N Lr1N Lr2<3

.<1 C <2/

; (5)

where kLP , kLS ; and kPS are the coupling coefficients between Lr and T P , Lr and T S ,

and T P and T S , respectively.

In this article, in order to design conveniently, the air gaps of the EE magnetic core

are the same. Then <1 D <2 D 2<3 D 2<0, where <0 is the gap magnetic resistance of middle leg. Therefore, the Eq. (5) can be simplified as

8̂̂̂ˆ̂̂̂̂<̂ˆ̂̂̂̂̂

ˆ̂̂:

kPS D 1

kLP D N Lr2 N Lr1q

3N 2Lr1 C 3N 2Lr2 C 2N Lr1N Lr 2

kLS D N Lr1 N Lr2

q 3N 2Lr1 C 3N 2Lr2 C 2N Lr1N Lr2

: (6)

According to Eq. (6), kLS D kLP can be obtained, and k D kLS D kLP can be

defined, then coupling coefficient k can be adjusted by N Lr1 and N Lr2. According to the

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different values of k, the coupling method of integrated magnetics can be divided into

two kinds: 0 k 1 and 1 k 0.

Based on Eqs. (3) and (6), the coupling coefficients expression of integrated

magnetics can be represented as

0B@

V Lr

V P

V S

1CA D

0B@

Lr kp

Lr LP kp

Lr LS

kp

Lr LP LP p LP LS

kp

Lr LS p LP LS LS

1CA

0BBBBBB@

d iLr

dt

d iP

dt

d iS

dt

1CCCCCCA

: (7)

Therefore, the coupling coefficients expression of integrated magnetics is achieved as in

Eq. (7), where LP , LS , and Lr can be adjusted by the number of turns and air gaps, as

shown in Eq. (4), and k can be adjusted by N Lr1 and N Lr2, as shown in Eq. (6).

3.2. Mode Analysis of DC/DC Stage with Integrated Magnetics

According to the coupling coefficients expression of integrated magnetics in Eq. (7), the

mode analysis of the DC/DC stage can be done. The operating waveforms of the DC/DC

stage in the steady state are shown in Figure 4; each switching period is subdivided into

six modes, and their topological states are shown in Figure 5.

Mode 1 .t0 t t1/. The input power is transferred to the secondary side through S 1and S 4. Dr1 is turned on, and C r1 is charged by iDr1.t/ and iDr1.t/ D iS .t/. Therefore,

Figure 4. Operating waveforms of the DC/DC stage.

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F i g u

r e

5 . E q u i v a l e n t c i r c u i t s o f t h e p r

o p o s e d c o n v e r t e r f o r m o d e a n a l y s i s : ( a ) M o d e 1 ,

( b ) M o d e 2 ,

( c ) M o d e 3 ,

( d ) M o d e 4 ,

( e ) M o d e 5 , a n

d ( f ) M o d e 6 .

838

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voltage V DC =2 is reflected on the secondary side of T , that is, V S D V DC =2. Lr is

in series with the transformer primary side, that is, iP .t/ D iLr .t/ and V Lr C V P D V in.

The expression of integrated magnetics can be represented as

V in

V DC =2

!D

Lr C LP 2kp Lr LP kp Lr LS p LP LS

kp

Lr LS p

LP LS LS

!0BB@d iP

dt

d iS

dt

1CCA : (8)

According to Eq. (8), the primary current iP .t/ can be achieved as

iP .t/ D iP .t0 / C LS V in C .kp

Lr LS p

LP LS /V DC =2

.1 k2/LS Lr

.t t0/: (9)

Mode 2 .t1

t

t2/. When S 1 is turned off, C oss1 and C oss3 are charged and discharged

by resonance with Lr , respectively, that is, V Lr C V P D vcoss3. The expression of integrated magnetics iP .t/ and the voltage of C oss1 and C oss3 can be represented as

follows:

vcoss3

V DC =2

!D

Lr C LP 2kp

Lr LP kp

Lr LS p

LP LS

kp

Lr LS p

LP LS LS

!0BB@d iP

dt

d iS

dt

1CCA ; (10)

8̂̂<̂̂:

iP .t/ D iP .t1/ cos !.t t1/

vcoss1.t/ D iP .t1/ Z sin !.t t1/

vcoss3.t/ D V in iP .t1/ Z sin !.t t1/

; (11)

where 8̂̂̂<̂ˆˆ̂̂:

! D 1p 2C oss .1 k2/Lr

Z Ds

.1 k2/Lr

2C oss

: (12)

Mode 3 .t2 t t3/. The voltage of C oss3 is discharged to zero, the anti-paralleled diode

D3 of switch S 3 is turned on naturally, that is, V Lr C V P D 0; S 3 can then be turned on

to achieve ZVS. The expression of integrated magnetics and iP .t/ can be represented as

follows:

0

V DC =2

!D

Lr C LP 2kp

Lr LP kp

Lr LS p

LP LS

kp

Lr LS p

LP LS LS

!0BB@d iP

dt

d iS

dt

1CCA ; (13)

iP .t/ D iP .t2/ C

kp Lr LS p LP LS

V DC =2

.1 k2/LS Lr

.t t2/: (14)

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840 Y. Jiang et al.

Mode 4 .t3 t t4/. S 4 is turned off, C oss2 and C oss4 are discharged and charged by

resonance with Lr , respectively, that is, V Lr CV P D vcoss4.The expression of integrated

magnetics iP .t/ and the voltage of C oss2 and C oss4 can be represented as follows:

vcoss4

V DC =2

!D

Lr C LP 2kp Lr LP kp Lr LS p LP LS

kp

Lr LS p

LP LS LS

!0BB@d i

P dt

d iS

dt

1CCA ; (15)

8̂̂<ˆ̂:

iP .t/ D iP .t3/ cos !.t t3/

vcoss4.t/ D iP .t3/ Z sin !.t t3/

vcoss2.t/ D V in iP .t3 / Z sin !.t t3/

; (16)

where ! and Z are the same as in Eq. (12).

Mode 5 .t4 t t5/. The voltage of C oss2 is discharged to zero, the anti-paralleled

diode D2 of switch S 2 is turned on naturally, that is, V Lr C V P D V in. S 2 can then

be turned on to achieve ZVS. The expression of integrated magnetics and iP .t/ can be

represented as follows:

V in

V DC =2

!D

Lr C LP 2kp

Lr LP kp

Lr LS p

LP LS

kp

Lr LS p

LP LS LS

!0

BB@

d iP

dt

d iS

dt

1

CCA; (17)

iP .t/ D iP .t4/ C LS V in C .kp

Lr LS p

LP LS /V DC =2

.1 k2/LS Lr

.t t4/: (18)

Mode 6 .t5 t t6/. The primary current iP .t/ goes though S 2 and S 3, C r 2 is charged

by iDr 2.t/; therefore, the voltage V DC =2 is reflected on the secondary side of T , and the

analysis is similar that of Mode 1. From Mode 6, another circle is begun that is similar

to Modes 1 to 5, analyzed above.

When integrated magnetics are adopted, according to the mode analysis, it can be

seen that primary current iP .t/ is influenced by coupling coefficient k. Therefore, k canbe designed to meet the demand for the ZVS range.

3.3. Comparison of ZVS Range with Different Coupling Coefficient

In order to analyze the ZVS range, the waveform of primary current iP is analyzed. In

Figure 3, compared with Mode 3 (t2 t t3) and Mode 5 (t4 t t5), the charging and

discharging time of primary current iP in Mode 2 (t1 t t2) and Mode 4 (t3 t t4)

are much shorter and can be omitted. Therefore, the waveform of primary current iP is

simplified, as shown in Figure 6. In order to analyze conveniently, the primary current

iP .t/ can be represented as

iP .t/ D A C B.k/t: (19)

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Figure 6. Waveform of primary current.

According to Eqs. (9), (14), and (18), the slope of iP .t/ is B.k/, shown in Table 1,

and it can be seen that B.k/ is influenced by k. When t0 t t1, jB.k/0k1j jB.k/1k0j, it means that iP .t/0k1 increases more rapidly than iP .t/1k0 ; the av-

erage current I av.0k1/ is larger than I av.1k0/, and, based on the power conservation,

average current I av can be represented as

I av D V 2oV inRo

D V 2 DC

2V inRo

: (20)

Therefore, when 0 k 1, the PV inverter can transmit more power and lift higher

voltage, that is, V DC.0k1/ V DC .1k0/.

When t1

t

t3

, j

B.k/0k1j j

B.k/1k0j

, it means that iP

.t/0k1

decreases

more slowly than iP .t/1k0 , and since the anti-paralleled diode of the leading switch

is on, the ZVS of the leading switch is achieved. When t3 t T , the anti-paralleled

diode of the lagging switch is on, and the ZVS of lagging switch is achieved; since

jB.k/0k1j jB.k/1k0j, iP .t/0k1 decreases more slowly than iP .t/1k0 , and

the ZVS range (0 k 1) for the lagging switch is wider than the ZVS range (1 k 0).

3.4. Design of Integrated Magnetics

The flux distribution is shown in Figure 7. When t0

t

t5, the secondary side of

the transformer connects with C r1, meaning that voltage V DC =2 is reflected on thesecondary side. It can then be obtained that

V S D V P

N S

N P

D V DC

2 D N S

dc

dt ; t0 t t5: (21)

Therefore, the maximum flux density of the middle leg Bc;max can be obtained by

Bc;max D c;max

Ac

D V DC

4Ac N S

T; (22)

where T

D t

5 t

0,

c;max is the maximum value of

c, A

c is the cross-section area of the middle leg, and Ac and N s are selected to make sure that Bc is not more than Bc;max

to prevent magnetic saturation.

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T a b l e 1

C o m p a r i s o n o f t h e s l o p e B . k / o f p r i m a r y c u r r e n t

B . k

/ 0 k 1

B . k / 1 k 0

C o m p a r i s o n

t 0 t

t 1

L s V i n

C . j k j p L r L

S

p L P L S / V D C = 2

. 1 k

2 / L s L R

L S V i n C . j k j p L r L S

p L P L S / V D C = 2

. 1 k 2 / L s L R

j B . k / 0 k 1 j

j B . k / 1 k 0 j

t 1 t

t 3

. p L P L S

j k j p L

r L S / V D C = 2

. 1 k 2 / L s L R

. p

L P

L S

C j k j p L r L S V D C = 2

. 1 k 2 / L s L R

j B . k / 0 k 1 j

j B . k / 1 k 0 j

t 3 t

T

L s V i n

C . p L P

L s

j k j p L r L s V D C = 2

. 1 k 2 / L s L R

L s V i n C . p L P L S

C j k j p L r L S /

V D C = 2

. 1 k 2 / L s L R

j B . k / 0 k 1 j

j B . k / 1 k 0 j

842

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Figure 7. Flux distribution.

In Mode 1 (t0 t t1) and the former mode (t 00 t t0) before Mode 1,

8̂̂<ˆ̂:

V Lr D V in C V P D N Lr1

d1

dtC N Lr 2

d2

dt; t 00 t t0

V Lr D V in V P D N Lr1

d1

dt C N Lr2

d2

dt ; t0 t t1

: (23)

At t1, the maximum value of 1 is achieved. According to Eqs. (20) and (22) and

2 D 1 C c , the maximum flux density of the left leg B1;max can be obtained as

B1;max D 1;max

A1

D 1A1.N Lr1 C N Lr 2/

V in C V DC N P V DC N Lr2

2N S

Don1

C

V in V DC N P C V DC N Lr2

2N S

Don2

; (24)

where Don1T D t0 t 00, and Don2T D t1 t0, 1;max is the maximum value of 1; A1 is

the cross-section area of the left leg.

At t0, the maximum value of 2 is achieved, and the maximum flux density of left

leg B2;max can be obtained as

B2;max D 1.t0/ C c;max

A2

D 1

A2.N Lr1 C N Lr2 /

V in C V DC N P V DC N Lr 2

2N S

Don1 C V DC

4A2N S

T: (25)

For the EE magnetic core, Ac D 2A1 D 2A2. Therefore, the magnetic core of

integrated magnetics can be selected according to Eqs. (22), (24), and (25) to prevent

magnetic saturation.

Based on the formula in Eq. (4),

s LS

LP

Ds

N 2S

N 2P

D N T ; (26)

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844 Y. Jiang et al.

where N T is transformer turns ratio, and N T can be selected approximately according to

the demand conversional ratio. Then according to Eqs. (4) and (23), LS and LP can be

achieved.

According to the ZVS range (shown in Figure 6),

I P .t3/.1 k2/Lr

V in C .1=nT kp

Lr =LS /V DC =2D T t3 D tZV S ; (27)

where I P .t3/ is the average current of iP .t/ when t3 t T . Then, according to

Eq. (27), Lr can be selected to meet the demand for ZVS range tZV S .

4. DC/AC Stage

The waveforms of the DC/AC stage are shown in Figure 8. Q1 and Q2 are controlled by

a high-frequency SPWM signal, and Q3 and Q4 are controlled by a line frequency square

wave signal. Filtered by the LC circuit, the V DC and the output V o can be represented as

follows:

V o D mV DC sin !t; (28)

where m is the modulation ratio ! D 2f (f D 50 Hz).

5. Experimental Results

The parameters of integrated magnetics are shown as follows: A ferrite EE42/21/20 core

(PHILIPS Company, Holland) is selected, air gaps with 0.3 mm are placed in three legs,the cross-section area of the center leg is 233 mm 2, N P D 13, N S D 58, N Lr1 D 6,

N Lr2 D 0, Lr D 14 uH, Lp D 148 uH, Ls D 2:9 mH, and k D 0:445. Voltage-doubler

capacitors are 0.1 uF, filter circuit parameters of the DC/AC stage are Lf D 1 mH and

C f D 100 uF, the input voltage of the battery is 43 V DC–53 V DC, and the controller

is the DSP2812 (TI Company, USA). Based on the designed parameters, a 100-kHz,

Figure 8. Operating waveforms of the DC/AC stage.

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100-W inverter with 50-Hz, 220-V AC output is constructed. When Don2 D 0:7, the

input voltage of the battery is 48 V DC.

The key experimental waveforms of the DC/DC stage are shown in Figures 9(a)–

9(e). Figure 9(a) shows the waveforms of V AB . When the input power is transmitted in

the inverter, V AB

is 48 V; when the anti-parallel diode of the leading switch is on, V ABbecomes zero, and the leading switches can achieve ZVS. Figures 9(b) and 9(c) show

the waveforms of primary current iP and the lagging switch voltage. It can be seen that

primary current iP is continuous, and the lagging switch can achieve ZVS. When gate

signalV GS is on, the voltage of switch V DS has already been zero, and the lagging switch

then achieves ZVS. Figures 9(d) and 9(e) show the waveforms of V S and voltages V C r1

and V C r 2 of voltage-doubler capacitors C r1 and C r 2. When V C r1 is charged, V S equates

to V C r1, and when V C r 2 is charged, V S equates to V C r 2. Since V DC D V C r1 C V C r 2,

the output voltage V DC doubled the V S , and then V DC D 190 V DC C 190 V DC D380 V DC.

In order to compare the ZVS range when different magnetics are adopted in the

DC/DC stage, the experimental waveforms of iP are shown in Figures 10(a) and 10(b).The input voltage, magnetic core EE42/21/20, N P and N S , air gaps, and load are

unchanged as above except for N Lr1 and N Lr2. In Figure 10(a), N Lr1 D N Lr 2 D 0,

meaning the Lr winding is not placed. It is obvious that only the leakage inductance

of the transformer is not enough to achieve soft switching, causing the oscillation of iP ;

the leading switch and lagging switch both operate in hard switching. Therefore, it is

necessary to add an external inductor to achieve ZVS. In Figure 10(b), N Lr1 D 0 and

N Lr2 D 6, k D 0:474; it can be seen that primary current iP is near discontinuous,

and it is difficult to achieve the ZVS of lagging switch. On the other hand, the change

of the slope of iP agrees well with the theoretical analysis, which is shown in Table 1,

and the average current of iP .t/0k1 (Figure 9(b)) is larger than that of iP .t/1k0

(Figure 10(b)). Therefore, when 0 k 1, the PV inverter can transmit more power,

the output voltage is higher, which means that the conversional ratio of the DC/DC stage

is higher.

The key experimental waveforms of the DC/AC stage are shown in Figures 11(a)–

11(c). Figure 11(a) shows the driving singles for Q1 and Q2 and the SPWM control,

where a frequency of 20 kHz is adopted. Figure 11(b) shows the driving singles for Q3

and Q4 and the square wave control, where a frequency of 50 Hz is adopted. Figure 11(c)

shows a 220-V AC output V o, and at a rated condition, the total harmonic distortion

(THD) is 5%. A comparison of the conversional ratio of the DC/DC stage (V DC =V in)

and the efficiency of the proposed inverter is shown in Figure 12. It can be seen that

when 0 k 1, the conversional ratio of the DC/DC stage (V DC = V in) and the efficiencyare higher, and the efficiency is about 87% at a rated condition.

6. Conclusion

A single-phase PSFB PV inverter with integrated magnetics is proposed. In the DC/DC

stage, integrated magnetics is adopted due to the following reasons: (1) since the external

inductor and transformer are integrated into one magnetic core, the number of magnetic

components is reduced; (2) when the coupling coefficient k is selected as 0 k 1,

the wider ZVS range and the higher conversional ratio of the DC/DC stage (V DC =V in)

are achieved. In the DC/AC stage, SPWM control is adopted and the AC output isachieved. The experimental results of a 100-W prototype inverter have been presented.

The efficiency of the proposed inverter obtained is about 87% at a rated condition.

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846 Y. Jiang et al.

(a)

(b)

(c)

Figure 9. Experimental waveforms of DC/DC stage: (a) V AB , (b) iP , (c) lagging switch, (d) V S ,

and (e) voltage-doubler. (continued )

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(d)

(e)

Figure 9. (Continued ).

Figure 10. Experimental waveforms of ip: (a) without Lr winding and (b) k D 0:474.

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848 Y. Jiang et al.

(a)

(b)

(c)

Figure 11. Experimental waveforms of DC/AC stage: (a) driving singles for Q1 and Q2,

(b) driving singles for Q3 and Q4, and (c) output voltage V o.

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Figure 12. Comparison of conversional ratio of DC/DC stage (V DC =V in) and efficiency: (a) con-

versional ratio of DC/DC stage (V DC =V in) and (b) efficiency.

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