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An integrated inverter for a single-phase single-stage z source


BULLETIN OF THE POLISH ACADEMY SCIENCES single-stage grid-connected PV system based on Z-source An integrated inverter forOF a single-phase TECHNICAL SCIENCES Vol. 55, No. 3, 2007

An integrated inverter for a single-phase single-stage grid-connected PV system based on Z-source
Z. CHEN, X. ZHANG, and J. PAN*
Department of Electrical Engineering, Shanhai Jiao Tong University, Shanghai 200030, P .R.China

Abstract. An integrated Z-source inverter for the single-phase single-stage grid-connected photovoltaic system is proposed in this paper. The inverter integrates three functional blocks including maximum-power-point-tracking, step-up/down DC-side voltage and output grid-connected current. According to the non-minimum-phase characteristic presented in DC-side and the functional demands of the system, two constant-frequency sliding-mode controllers with integral compensation are proposed to guarantee the system robustness. By using two controllers, the effects caused by the non-minimum-phase characteristic are mitigated. Under the circumstance of that the input voltage or the grid-connected current changes suddenly, the notches/protrusions following the over-shoot/ under-shoot of the DC-bus voltage are eliminated. The quality of grid-connected current is ensured. Also, a small-signal modelling method is employed to analyze the close-loop system. A 300W prototype is built in the laboratory. A solar-array simulator (SAS) is used to verify the systematic responses in the experiment. The correctness and validity of the inverter and proposed control algorithm are proved by simulation and experimental results. Key words: Z-source inverter, single-phase single-stage grid-connected photovoltaic system, sliding-mode controller.

1. Introduction
In the 90's of the last century, the centralized mode is used in the photovoltaic (PV) system. Many parallel solar cell arrays (SCAs) connect the grid by using one inverter. Recently, the decentralized technology that each PV module is less than 500W has been put into use in PV systems [1-3].The technology enhances the flexibility and expansibility of PV grid-connected systems. Most of actual PV grid-connected systems consider only the static characters of the SCAs, not the dynamic stability. In fact, when the irradiance amplitude changes rapidly, especially the irradiance decreases suddenly, the working point of the output voltage and current of the SCAs will be changed simultaneously, and the voltage amplitude will decrease in a sudden manner, which will maybe cause the DC-bus voltage to collapse. The dynamic stability of the PV system in the case of the sudden changes has been studied, and the model of the SCAs is established based on the experimental results [4]. Dr. Wu analyzed the collapse process of the DC-bus voltage in the single-stage PV gridconnected system and proposed a vary-step MPPT method [5]. But even if the method is put into use, the collapse still exists and its range is dependent on the value of the step and the sample-cycle of the MPPT method. Furthermore, in the traditional single-stage system the voltage of the solar-cell must be greater than the peak of the grid voltage to ensure the grid-connected success. The Z-source inverter is a new inverter proposed in 2003 [6]. An impedance-source (Z-source) is used to replace the DC-bus capacitance or inductance so as to overcome the
* e-mail: chen.zongxiang@gmail.com

limitations of the traditional inverters that voltage amplitude can only be boosted or bucked. At the same time, the Z-source network has good flexibilities because its main circuit may be either the voltage-source or the currentsource, so the inverter bridge can be permitted to short or open. The Z-source inverter has been used widely in many realms [6-8]. The transfer function of the Z-source impedance has a right-hand-plane (RHP) zero which can't be eliminated by adjusting the parameters [9,10]. The unstable zero brings an obvious over-shoot and a following notch because of the energy resettling when the input voltage declines rapidly [11]. Many literatures have been focused on the disadvantages. A discrete-time PI controller is used to control the voltage of Z-source capacitors under the circumstances of the slow change of input voltage [12]. A multi-loop closed loop controller is proposed to minimize the effects of non-minimum phase characteristics. But when the input voltage declined suddenly an over-shoot and a following notch of the DC-bus voltage still exists obviously due to the bandwidth limitation of the proposed controller [11], and recovering time to zero state error is about 40ms. This paper presents an integrated single-phase singlestage PV grid-connected inverter based on the Z-source. The inverter has three functional blocks, namely maximum power point tracking (MPPT), voltage boost and current output according to the grid-connected standards. In the proposed system, the constant switching frequency is

Bull. Pol. Ac.: Tech. 55(3) 2007

263

Z. Chen, X. Zhang, And J. Pan

needed because the above-mentioned three functional blocks are realized by controlling four power-switch devices of the inverter bridge logically. Considering the dynamic characteristics of the SCAs, the non-minimum-phase characteristics exhibited in the DC side, the quality of the grid-connected current and the constant-frequency demands, two constant-frequency sliding-mode controllers (SMCs) with the integral compensation based on variable structure theory is proposed in this paper. Usually the reference part is a constant value and its derivative is zero. So the error items can be replaced by state variables in the controllers. In order to use the equivalent control of the SMC directly as the duty cycle control, the integral component of the references' error is introduced to make its derivative still contain reference information. It can also track the error in the sliding surface to ensure the staticstate and dynamic performance of the system [13, 14]. In the sliding mode, the system can't be influenced by the change of systematic parameters and the disturbances. It has strengthened the self-adaptability and robustness. Via the DC-side controller the fast recovery with zero steadystate error is exhibited when the perturbations of the input voltage occur. Especially the following notch/protrusion is eliminated even if the input voltage declines/rises abruptly. Besides, when the grid-connected current decreases/ increases rapidly, the DC-side voltage isn't impacted. The over-shoot/under-shoot of the Z-source-network output voltage doesn't appear. All of these control results ensure the quality of the grid-connected current. Furthermore, a small-signal modelling method is employed to analyze the close-loop system to prove the system stability. A 300W prototype is built in the laboratory. A solar-array simulator (SAS) is used to verify the systematic responses in the experiment. The correctness of the integrated PV gridconnected inverter and the validity of the proposed control algorithm are proved by the simulation and experimental results in this paper.

relation must be obeyed, because all the functional blocks, including MPPT, voltage boost and current output, are realized by controlling four devices of the inverter bridge. The two switches of one phase leg cannot be closed simultaneously while the inverter outputs the current to the grid in order to ensure the quality of the grid-connected current. On the contrary, the grid-connected current cannot be output while the two switches of one phase leg are working in the shoot-through state.

u

uc

u cr u acr

S1 S4 t0 t1 t3 t2 t4

Fig. 2. The Z-source inverter control mode (positive or negative cycle)

2. Operating principle of the single-phase integrated inverter with Z-source
The structure of single-phase PV grid-connected inverter is shown in Fig. 1.
L L11 I Il l1 1
C 1 C 2 Lf

i2
T x

S S1 S4 4 S 1

A unipolar control method is used in the paper [15]. Taking the positive half-cycle, its basic switching mode is shown in Fig. 2, where uacr is an AC-current modulation signal, ucr is a DC-voltage modulation signal to be used to boost DC voltage as desired, and uc is a carrier signal. From Fig. 2, when the instantaneous value ucr>uc> uacr, namely during the time t0 to t1, the switch S1 and S4 both switch off. The inductor current i2 flows through diode D2 (the diode which is paralleled the switch S2 inversely) and S3 which is always open in the positive half-cycle. During the time (t1,t2], uacr is greater than uc, so the switch S1 turns on and the inverter is in the active state that i2 flows through S1 and S3. The next duration is the same as that of (t0,t1]. In the duration of (t3,t4], the instantaneous value uc is greater than those of uc and uacr and the switch S3 is closed. So the inverter is in the shoot-through state. The current i2 flows through D2 and S3 while the power is exchanged between the passive components C1 and L1 (and also between C2 and L2) through S3 and S4 in this state. The simplified operation-mode figure (in positive cycle) is shown in Fig. 3 [16].
L Il1 L 11 I l 1
C1 C2
S1

PV Array

Vin

Vc1
C C i
i

Vc2

Vinv
S S 2 S S 3 2 3

/ vac vv ac v’ ac ac

vs

Lf s4

i2

L I l 2 I2 L 2 2 Fig. 1. Single-phase inverter with Z-source

V in

Vc1

Vc2

Vinv s

Comparing the Z-source inverters with the traditional ones, a shoot-through state that the upper and lower switch devices of any one phase leg are shorten is added besides the zero state and active state. This is the best advantage and feature of the Z-source. Some special switch logical 264

2

s3

vac

vs

L2 II L l 2 l2 2

(a) Bull. Pol. Ac.: Tech. 55(3) 2007

An integrated inverter for a single-phase single-stage grid-connected PV system based on Z-source

Il L1L1 I l1 1
C1 C2
S1

Lf s4

i2

Vc =

Vin + Vinv 2

.

(4)

As to the single-phase inverter, its output voltage is

V in

Vc1

Vc2

Vinv s

2

s3

vac

vs

vac = MVinv = BMVin

(5)

L IIll2 2 L2 2

where M is the modulation index of inverter. Due to the relationship between the shoot-through state and the active state, the maximal value of M cannot exceed 1-d. From Eq. (5), one has

(b)
L L Il1 11 I l 1 C1 C2
S1

vac = BMVin ≤ (1 ? d ) ?
Lf s4

i2

1 Vin = Vc . 1 ? 2d

(6)

So, when the system is connected with the grid, the voltage

Vc must be greater than | vac |peak, otherwise it

V in

V c1

Vc2

Vinv s

2

s3

vac

vs

will cause the current distortion even inverting failure.

3. MPPT design
In order to ensure the SCAs to output maximum power, a P&O MPPT method is introduced in the paper. The control figure is shown in Fig. 4. In Fig. 4, Ik and Vk are the momentary current and voltage respectively and I* and V* are the previous

I 2 Il LL l2 2 2
(c) Fig. 3. The simplified operation modes in positive cycle (a)zero state (t0,t1]& (t2,t3], (b)active state(t1,t2], (c)shoot-through state(t3,t4]

I pv
Vin

M PPT

V

*

+

-

PI

I*

From the symmetry circuits with C1=C2, L1=L2 in Fig. 1, we have the capacitor voltage Vc1=Vc2 and the inductance current Il1=Il2. It is given that the duty cycle of shoot-through state is d during a switching cycle, one has [6]

(a)
sense V k , I k

Vinv =
where

1 Vin = BVin 1 ? 2d 1 1 ? 2d

(1)

?I = ? Ik ? I D ?V = ? Vk ?V D
*

*

B=

(2)
yes

? ? 0 DV =
no
?I D Ik + Vk = ? ? 0 ?V D

yes

1? d Vc = Vin . 1 ? 2d

=0 ? DI ?
no

yes

(3)
yes

no
?I D Ik + Vk > ? ? 0 ?V D

From Eqs.(1) and (3), when the shoot-through state exists, it has two working regions: one is d ∈ [0, 1 ) and

D ?I> ? 0
no
decrease V ref

yes

2

no
increase

V ref

decrease

Vref

increase

Vref

the other is d ∈ ( 1 ,1] . According to Eq. (1), only when 2

d ∈ [0, 1 ) , Vinv>0 is ensured. So the value of d must be 2
limited in the range of d ∈ [0, 1 ) .

* V = ? Vk I* ? = Ik

return

2

Equation (4) is obtained from Eqs. (1) and (2):

(b)

Fig.4. The MPPT controller (a) the controller configuration of the proposed system. (b) Flowchart of the MPPT method Bull. Pol. Ac.: Tech. 55(3) 2007

265

Z. Chen, X. Zhang, And J. Pan

current and voltage respectively while Ipv is the output current of the SCAs. Another control aim of MPPT is to obtain the current controller command I 2 ref
* = I * ? sin ωt , where I

is

obtained from a PI adjustment of the MPPT controller output

i2
Boost converter Based Z source network (DC-DC)
u eq 1 R efer en c e

the grid-connected current. Not only the control destination is reached, but also the control rules are simplified. 4.1. DC side voltage controller. According to Fig. 1, the inverter can be equivalent to a current source (see Fig. 6). Considering Vc1=Vc2=Vc and Il1=Il2=Il, Eq.(7) can be established. In Fig. 5, T is off while T is on and T is on while T is off.

Inverter

Vin

Vin v

(DC-AC )

vac

ue q 2

VC ref

*

Sliding Surface s ?1

Sliding Surface s ?2

? 2 x2 ? Vin ? ? ? x2 + Vin ? ? ? ? ? &1 ? ?x L L u = + ? ? ? ? 1 ?x ? ? &2 ? ? ?2 x1 + I load ? ? x1 ? I load ? ? ? ? C ? ? ? C ? ?
where

(7)

R e fe r en c e

* sin(? I 2r wt ) ef

X = [ x1

x2 ]T = [ I l Vc ]T ;
?1 T switch on u1 = ? ?0 T switch off
. in the DC-side

Fig. 5. Proposed sliding-mode controllers

(shown in Fig. 4a). The detailed description can be seen in the reference [17].

The control aim is to get

* x2 → x2

4. Controller design
Due to the shoot-through state, the DC-bus voltage of Zsource is the high-frequency pulse signal which is difficult to test. The capacitor voltage Vc, which is a constant voltage signal, is easy to test and control. According to Eq. (6), at the same time, the quality of output current can be better by controlling Vc. Because four devices of the inverter bridge must obey some special control logical rules, the paper presents two constant-frequency sliding-mode controllers to control the capacitor voltage of Z-source and the gridconnected current. The control variables of the controller are ucr and uacr, which are obtained from the equivalent control of the SMCs. And these two variables are compared with a high-frequency sawtooth signal to obtain the pulses controlling these devices. It is simple to obey the control rules by using the proposed control methods, meanwhile the advantages of the fast response and robustness of sliding-mode are retained. The grid can be considered as an ideal voltage source. Two unattached close-loop controllers, shown in Fig. 5, are employed to control the voltage of Z-source capacitors and

controller, and based on the two points that error items are replaced by state variables and the integral component of the reference's error is introduced, the sliding surface is chosen as
* σ 1 ( x, t ) = k1 x1 + k 2 x2 + k 3 ∫ ( x2 ? x2 ) dt (k1,k2,k3 ≠ 0) 0 t

where x2 is the reference value of The switching law is chosen as

*

x2 .

(8)

?0 when σ 1 > 0 u1 = ? ?1 when σ 1 ≤ 0
Then Eq. (10) is obtained from Eq. (8)

.

(9)

* &1 ( x, t ) = k1 x &1 + k 2 x &2 + k 3 ( x2 ? x2 σ ) = 0.

(10)

Assume that

?1 if sgn(σ 1 ) = ? ? ?1 if
and substitute (7) into (10):

σ1 > 0 σ1 ≤ 0

(11)

T

L1

I l1
C 1 C2

? ? x2 + Vin ? ? 2 x2 ? Vin ? ? &1 ( x, t ) = k1 ?? σ ? ?+? ? u1 ? + k 2 L L ? ? ? ? ??
V c2
T

Vi n

Vc1

Vin v

I L o ad

?? x1 ? I load 2 ?? ?? C

? ? ?2 x1 + I load ?+? C ? ?

? ? * ? u1 ? + k 3 ( x2 ? x2 ) ? ?

. (12)

The equivalent control can be obtained

Il 2
L2
Fig. 6. Equivalent circuit with controlled DC side voltage

* -k1C(Vin ? x2 ) + k 2L( x1 ? Iload ) + k3LC( x2 ? x2 ) ueq1 = (13) k1C(Vin ? 2x2 ) + k2L(2i1 ? Iload )

where ueq1 is continuous and belongs to [0, 0.5).
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An integrated inverter for a single-phase single-stage grid-connected PV system based on Z-source

Deriving from Eqs.(12) and (9), one has

x dσ ? x * ? lim? 1 === lim? ?k1 2 ? k2 1 + k3 ( x2 ? x2 )? . σ1 →0 dt σ1 →0 ? L C ?
It is reasonable to consider that
* x2 ? x2

u1 =1

lim
(14)

dσ 1 t →∞ dt ? ? ?

σ1 <0

k ?k *? = lim ? 1 x2 ? 2 x1 + x2 ? x2 ? t →∞ C ?L ? > lim x2
t →∞ k1 k Vc min ? 2 I l max > 0 L C

is very small

in the vicinity of the sliding surface. And x1 and x2 is greater than zero according to the limitation of

k1 k Vc min ? 2 Il max > 0 L C

> 0.

(19)

d ∈ [0, 1 ) . 2

Inequality (20) can be confirmed by Eqs. (15), (17), (18) and (19). So, Eq. (8), the sliding-mode surface, is existing and reachable.

If

k1 k Vc min ? 2 I l max > 0 , one has L C
σ 1 →0 ?

lim

dσ 1 |u =1 > 0 . dt 1

&1 < 0 when σ 1 > 0 ?σ ? &1 ≥ 0 when σ 1 ≤ 0 . ?σ
(15)

(20)

The close-loop system on the sliding surface can be obtained with the substitution of (7) into (10).
2 * * ? ?k2x2Iload + k2Vinx1 + k3C(2x2 ? ? 2x2 x2 ? xV in ) 1 in + x2V ? ? &1 ? ? k1 ?x ? ?x ? =? * ?. & ? 2 ? k1(?xV 1 in + Iload x2 ) + k3L(?2x 1 + Iload )(x2 ? x2 ) ? ? k1C(Vin ? 2x2 ) + k2L(2x1 ? Iload ) ? ? ? ?

In the same way Eq. (16) can be obtained

x ?I dσ u1=0 ? V ?x * ? lim+ 1 === lim+ ?k1 in 2 + k2 1 load + k3(x2 ? x2 )?.(16) σ1→0 dt σ1→0 ? L C ?
Equation (3) and the limitation

d ∈ [0, 1 ) 2

Vin ? x2 < 0

is satisfied, and (x1-Iload) is the value of the

(21) By assuming that the right side of Eq. (21) is equal to zero, the stable point of the equation is shown as follows:
* ? I load x2 ? ? x1 ? ? ? ?α I load ? ? x ? = ? Vin ? = ? x* ? . ? 2? ? * ? ? 2 ? ? x2 ?

current ic. In the vicinity of the sliding surface, the value of the voltage x2 is very close to the voltage reference

x

* 2.

So the charging current of the capacitor ic is very small. The inequality (17) can be concluded as follows:

σ1 →0

lim+

dσ 1 |u =0 < 0 , dt 1

(22)

(17)

and the reaching condition is verified as follows. 1) If the representing point (RP) of the system is in the region where

When introducing the perturbation around the operating point, the small-signal state-space equation is obtained as

σ 1 > 0 and on the assumption that the RP

cannot reach the sliding surface, the switch T is always on according to Eq. (9). So, dmin equals to zero and Vin equals to Vc, and Il equals Iload according to Eq. (3). One has

d 1 * ?xi = ( A?xi + B?Vin + C?Iload + D?x2 ) (i = 1,2) (23) Λ dt
where

lim

dσ 1 t →∞ dt

σ1 > 0

I ?I ? ?V + V = lim ? k1 c in + k 2 l load + k 3 t →∞ L C ?

?kV A = ? 2 in ? ?k1Vin

* ? k 2 I load + 2k 3Cx2 ? k 3CVin ? ?, (k1 -2k 3 Lá+k 3L) I load ?

(V

in

* ? * ? x2 = lim k 3 (Vin ? x2 )? ). t →∞ ?

(18)

? α k 2 I laod ? B=? ? ?-k1α I load ? ,
* ? ? k 2 x2 ? C=? * ?, ? k 1 x2 ?

If k3 > 0, then Eq. (18) is minus. 2) If the RP of the system is in the region where

σ1 < 0

and on the assumption that RP cannot reach the sliding surface, the switch T is off and its maximum duty is 0.5 according to the limitation of d ∈ [0, 1 ) . Vc will be infinite

2

? -2k Cx* + k 3CVin ? D=? 3 2 ? ? (2α -1)k 3 LI load ? ,

according to Eq. (3). One has

α = x2 V

*

in

Bull. Pol. Ac.: Tech. 55(3) 2007

267

Z. Chen, X. Zhang, And J. Pan
* Λ = k1C(Vin ? 2 x2 ) + k 2 L(2α ? 1) I load

of paper this derivation is omitted.

. If the poles of matrix A of Eq. (23) are all in the left plane, the close-loop system is stable. So the inequality is concluded as follows.

5. Simulation and experiments
5.1. Simulation analysis. In the paper, the integrated single-phase single-stage grid-connected system is simulated. For simplification, a DC-voltage source replaces the SCAs in the simulation [1]. The static and dynamic simulation of the grid-connected system is presented in the paper. It includes three assumptions: ? Setting that Vdc=VPv, the working voltage of SCAs, is 100VDC and iout, the output AC current, is 2.1A (rms), the voltage and current waveforms are shown in Fig. 8. The figures show the stable characteristic. ? The dynamic characteristic of the voltage control-loop is simulated based on the points, which are rated on condition that VPv=Vdc=100V descend to VPv= Vdc=75V immediately and then back to VPv=Vdc=100V while iout is always 2.1A (rms). The voltage and current waveforms are shown in Fig. 9. ? The dynamic characteristic of the current control-loop is simulated and based on the points, which are rated on condition that iout=2.1A(rms) descend to iout=1.0A(rms) immediately and then back to iout=2.1A(rms). The voltage and current waveforms are shown in Fig. 10. The grid-voltage is 110V (rms) in these assumptions. We can conclude that the grid-connected current has low distortion, power factor is close to 1 and static voltage error of the capacitor of Z-source is small. (The reference value of the capacitor is 180V) from Fig. 8. Figure 9 shows that when sudden changes of input voltage Vin burst, the tracking responses of the voltage of the Z-source are very fast. When the voltage changes from 100V to 75V , it takes about 12ms for the voltage to recover from the transient to the zero static-state error. And when the voltages changes from 75V to 100V , the time is about 8ms. Especially, while the input voltage steps up/down suddenly, the notch/protrusion following the over-shoot/ under-shoot of the Z-source output voltage is eliminated. These entire response features exhibit that the voltage controller has the good characteristics of the static and dynamic state that ensure the quality of the DC-side voltage and the grid-connected current. 200 (V) 6 (A)

? 2 2 * ?CVin (Vin ? 2x2 ) ? Lα ? ?k1 + (k2Vin + 2k3Lα ) + 2k1k2 (2Iload ?1)Vin + 4k1k3 ? ?<0 ? ? * ? ?( ?k1 ? k2Vin + 2k3Lα ) ? ?k1C(Vin ? 2x2 ) + k2LIload ( 2α ?1)? > 0 ? ? k1 V ? k2 I > 0 . (24) c min l max ? ?L C
According to the inequality (24), one can determine the range of the coefficients k1, k2 and k3 and then choose appropriate values by a trade-off. 4.2. AC current-shaper controllers. According to Fig. 1, the equivalent circuit figure with AC-current output is shown in Fig. 7. Its state equation can be obtained as follows.

dx3 1 ′) = (Vdcu2 ? uac dt Lf
where

(25)

x3 = i2 , ?1 S switch on u2 = ? ?0 S switch off
.

The sliding surface

σ2

can be chosen as follows:
t

* σ 2 ( x3 ) = g ( x3 ? x3 ) + ∫ ( x3 ? x3* )dt 0

(26)

where Set

* is the reference value of x3 . x3

?0 when σ 2 > 0 u2 = ? ?1 when σ 2 < 0
and the equivalent control can be obtained from Eq. (26).

(27)

ueq 2 =

* * ′ +Lf x &3 ? x3 )Lf vac ( x3 + gVdc Vdc

.

(28)

The inequality

& 2 ≤ 0 can be proved simply by the σ 2 ?σ
S=1
S

same method from Section 4.1. For the sake of the length

Lf

S=0
V dc

i2

0

0

u ’? ac
-200 50 (ms) 60 70 (a)
Bull. Pol. Ac.: Tech. 55(3) 2007

-6 80 90

Fig. 7. Equivalent circuit with AC current output

268

An integrated inverter for a single-phase single-stage grid-connected PV system based on Z-source

200 (V) V 180

200 (V) 150 100 50 50 (ms) 60 70 (b) 80 90 50 (ms) 100

(b)

160

150 (b)

200

250

300 (V) 200

300 (V) 200 (b)

100 0 50 (ms) 50.1 50.2 (c)
Fig. 8. Static waveforms (a) current and voltage waveforms of the grid (b) voltage waveform of the capacitor of Z-source and its reference (c) output voltage of Z-source

100

50.3

50.4

50.5

0 50 (ms) 100 150 (c)
Fig. 9. Dynamic waveforms while Vdc changes (a) current and voltage waveforms of the grid, (b) voltage waveform of the capacitor of Z-source and input voltage Vdc (c) output voltage of Z-source

200

250

The excellent reference tracking is exhibited in Fig. 10 (a) when the grid-connected current reference changes suddenly. Figures 10 (b) and (c) show that the voltage fluctuates weakly due to the decoupled voltage and current control-loop and the static state and dynamic characteristics of the DC-side voltage. The PV dynamic characteristic is that the working point of the output voltage and current of the SCAs will change at the same time when the irradiance amplitude changes rapidly. In order to make the simulation condition close to the practical condition, an approximative system with the PV dynamic characteristic is simulated. Two simulation conditions are presented as below: ? Set that Vdc=VPv=100V descend to VPv= Vdc=75V and then back to 95V in 20ms (one cycle of the grid) while 6 (A)

i2 decreases from 2.1A(rms) to 1A in the duration.

200 (V)

6 (A)

0

0

-200 50 (ms) 100 150 (a) 200 (V) 150 200

-6 250

200 (V)

0

0 100

-200 50 (ms) 100 150 (a)
Bull. Pol. Ac.: Tech. 55(3) 2007

-6 200 250

50 50 (ms) 100 150 (b) 200 250

269

Z. Chen, X. Zhang, And J. Pan

300 (V) 200

Table 1 Components value of the prototype and parameters of the controllers

100

components value of the prototype

Switch frequency Capacitor C1&C2 Capacitor Cin Inductance L1&L2 Inductance Lf Grid voltage v'ac(rms) Parameter of controller k1 Parameter of controller k2 Parameter of controller k3 Parameters of controllers g

10k Hz 1000?F 1500?F 1.0 mH 12 mH 110 V/50Hz 0.001 0.0015 1 0.002

0 50 (ms) 100 150 (c)
Fig. 10. Dynamic waveforms while i2 changes (a) current and voltage waveforms of the grid, (b) voltage waveform of the capacitor of Z-source and input voltage Vdc (c) output voltage of Z-source

200

250

parameters of the controllers

?

200 (V)

6 (V)

Set that Vdc=VPv=95V rise to VPv= Vdc=120V and then back to 100V in 20ms while i2 increases from 1A(rms) to 2.1A in the duration. In these conditions the voltage and current control-loop operate simultaneously. The
3,0 300 250
= 2, 4 5A

0

0
SAS current, A

2,5 2,0 1,5 1,0 0,5
1 I ph= ,45 A

200 150 100 50 0

I ph

-200 50 (ms)

100

(a)

200

250

-6

200 (V) 150

0 20 40 60 80 100 120 140

Fig. 12. Characteristics of the SAS while Iph=2.5A and 1.25A (Line: I-V curve, dot line: P-V curve)

related waveforms are shown in Fig. 11. 100 5.2. Experiment analysis. To verify the performance of the proposed integral single-phase PV grid-connected system and its control arithmetic, an experimental 100 150 (b) 200 250 300

50 50 (ms) 300 (V) 200

100

0 50 (ms) 100 150 (c) 200 250 250

Fig. 11. Dynamic waveforms while Vdc and i2 changes simultaneous (a) current and voltage waveforms of the grid, (b) voltage waveform of the capacitor of Z-source and input voltage Vd, (c) output voltage of Z-source

Fig. 13. Experimental grid-connected voltage and current while Iph=2.5A. v'ac (Ch1:85V/div), i2 (Ch2: 1.5A/div) (Timebase: 4ms/div) Bull. Pol. Ac.: Tech. 55(3) 2007

270

SAS power, W

An integrated inverter for a single-phase single-stage grid-connected PV system based on Z-source

prototype is set up in the laboratory. The relative components value of the prototype and the parameters of the controllers are tabulated in Table 1. Besides a solararray simulator (SAS) is used instead of the SCAs in the experiments. The SAS can simulate the I-V and P-V characteristic of some SCAs which are shown in Fig. 12.

Fig. 15. Experimental voltage and current waveforms (Iph is changed suddenly from 2.5A to 1.25A.) (a) Vc (Ch1:50V/div), Vin (Ch2:50V/div) ( Timebase: 100ms/div), (b) v'ac (Ch1:170V/div), i2 (Ch2:1.5A/div) (Timebase: 40ms/div)

(b)

(a)

From the figure, the output maximum-power is 250W and the MPP retains 100V , while Iph=2.5A and the output maximum-power is about 119W and the MPP keeps around 95V while Iph=1.25A. Figure 13 shows the waveforms the grid-connected voltage and current while the Iph is equal to 2.5A. From the figure, one concludes that the current has such a low distortion that THD for the optimized controller was calculated to be 3.8% and high power factor is promoted. Next figure shows the voltage waveforms of Z-source, where Fig. 14(a) is Vin and Vc waveform and Fig. 14(b) is the output voltage Vinv waveform of the Z-source while Iph=2.5A. Figure 15 shows the voltage and current waveforms while Iph is changed suddenly from 2.5A to 1.25A. From Fig. 15(a), we can conclude that the voltage of the SAS first falls from 100V (the MPP of Iph=2.5A) to around 75V in about 40ms and then return about 95V(the MPP of Iph=1.25A) because of the MPPT arithmetic. Meanwhile, the grid-connected current also falls but there do not occur any distortions due to the effects of the two sliding controllers, especially the DC-side controller, that ensure the stabilization of the DC-bus voltage.

(b)
Fig.14 Experimental voltage and current waveforms while Iph=2.5A, (a) Vc (Ch1:50V/div), Vin (Ch2:50V/div), (timebase: 10ms/div), (b) Vinv (Ch2:100V/div,timebase: 0.05ms/div)

(a)
Bull. Pol. Ac.: Tech. 55(3) 2007

(a) 271

Z. Chen, X. Zhang, And J. Pan

REFERENCES
[1] B.M.T Ho and H. Shu-Hung Chung, "An integrated inverter with maximum power tracking for grid-connected PV systems", IEEE Trans. Power Electronics 20(4), 953-962 (2005). M. Meinhardt, T. O'Donnell, and et al., "Miniaturized low profile module integrated converter for photovoltaic applications with integrated magnetic components", IEEE Appl. Power Electronics Conf. and Exposition, 305-311 (1999). M. Calais, J. Myrzik, and et al., "Inverters for single-phase grid connected photovoltaic systems-an review", 33rd Annual IEEE Power Electronics Specialists Conf.,1995-2000 (2002). Y.T. Tan, D.S Kirschen, and et al., "A model of PV generation suitable for stability analysis", IEEE Trans. Energy Conversion 19(4), 748-755 (2004). L.B. Wu, Z.M Zhao, and et al. "Modified MPPT strategy applied in single-stage grid-connected photovoltaic system", Proc. Int. Conf. Electrical Machines and Systems, 1027-1030 (2005). F.Z. Peng, "Z-source inverter", IEEE Trans. Industry Applications 39(2), 504-510 (2003). F .Z. Peng, M.S. Shen, and K. Holland, "Application of Z-source inverter for traction drive of fuel cell-battery hybrid electric vehicles", IEEE Trans. Power Electronics 22(3), 1054-1061 (2007). F.Z. Peng, X.M. Yuan, and et al., "Z-source inverter for adjustable speed drives", IEEE Power Electronics Letters 1(2), 33-35 (2003). C.J. Gajanayake, D.M.Vilathgamuwa, and C.L. Poh, "Smallsignal and signal-flow-graph modeling of switched Z-source impedance network", IEEE Power Electronics Letters 3(3), 111-116 (2005). C.L. Poh, D.M. Vilathgamuwa, and C.J. Gajanayake, "Transient modeling and analysis of pulse-width modulated Z-source inverter", IEEE Trans. Power Electronics 22(2), 1498-507 (2007). C.J. Gajanayake, D.M. Vilathgamuwa, and C.L. Poh, "Modeling and design of multi-loop closed loop controller for Z-source inverter for Distributed Generation", IEEE Power Electronics Specialists Conference, 1-7 (2006). J.W. Jung, M. Dai, and A. Keyhani, "Modeling and control of a fuel cell based Z-source converter", IEEE Applied Power Electronics Conference and Exposition, 1112-1118 (2005). J.H. Lee, P .E. Allaire, and et al., "Integral sliding-mode control of a magnetically suspended balance beam: analysis, simulation, and experiment", IEEE/ASME Trans. Mechatronics 6(3), 338-346 (2001). Y. He, and F.L. Luo, "Sliding-mode control for dc-dc converters with constant switching frequency", IEEE Proc.: Control Theory and Application 153(1), 37-45 (2006). C.C. Marouchos, The Switching Function: Analysis of Power Electronic Circuits, The Institution of Electrical Engineering, London, 2006. M.S. Shen and F.Z. Peng, "Operation modes and characteristics of the Z-source inverter with small inductance", Industry Applications Conference, 1253-1260 (2005). Y.C. Kuo, T.J. Liang, and J.F . Chen, "Novel maximum-power-pointtracking controller for photovoltaic energy conversion system", IEEE Trans. Industrial Electronics, 48(3), 594-601 (2001).

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(b)
Fig. 16. Experimental voltage and current waveforms (Iph is changed suddenly from 1.25A to 2.5A.) (a) Vc (Ch1:50V/div), Vin (Ch2:50V/div), (timebase: 100ms/div), (b) v'ac (Ch1:170V/div), i2 (Ch2:1.5A/div), (timebase: 40ms/div) [6] [7]

Figure 16 shows the voltage and current waveforms while Iph is changed suddenly from 1.25A to 2.5A.

[8]

6. Conclusions
The paper studies an integrated single-phase singlestage grid-connected inverter based on the Z-source which has three functional blocks to track the maximum power point, step-up/down voltage and output grid-connected current. According to the non-minimum-phase characteristic of Z-source impedance network and the functional demands of PV grid-connected system, two constant-frequency sliding-mode controllers with integral compensation are proposed to guarantee the system robustness. The effects caused by the non-minimum-phase characteristic are minimized. In the state of that the input voltage or the grid-connected current changes suddenly, any notches/protrusions following the over-shoot/under-shoot of the DC-bus voltage are eliminated. These excellent staticstate and dynamic attributes of the SMCs ensure the quality of the grid-connected current. Furthermore, this method to control the DC-side voltage of the Z-source might also shed a light on other Z-source inverter/rectifier systems. Besides, a small-signal modelling method is employed to analyze the close-loop system to prove the system stability. At last, the simulation and experiment results show the proposed PV grid-connected inverter is feasible and the validity of the proposed control scheme is also confirmed. Acknowledgements. We are grateful to Dr. Huajun Yu, an engineer of Shanghai Power Transmission&Distribution Co. Ltd., for his valued assistance and comments in this study. We also wish to thank Prof. Pengsheng Ye and Dr. Sanbo Pan who give their hands to this study.

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