an integrated inverter with maximum power

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 20, NO. 4, JULY 2005 953

An Integrated Inverter With Maximum PowerTracking for Grid-Connected PV SystemsBilly M. T. Ho, Student Member, IEEE, and Henry Shu-Hung Chung, Senior Member, IEEE

AbstractAn inverter for grid-connected photovoltaic systemsis presented in this paper. It can globally locate the maximumpower point of the panel over wide insolation and feed the solarenergy to the grid. Its structure mainly integrates a previouslydeveloped maximum point tracking method and output currentshaping function into a buck-boost-derived converter and theninverts the shaped current through a grid frequency bridge tothe grid. Instead of having a storage capacitor connecting inparallel with the converter output, series connection is used, sothat the required capacitor voltage rating is lower than that inclassical inverters. Most importantly, the inverter output currentharmonics are less sensitive to the capacitor value. A 30-W labo-ratory prototype has been built. The tracking capability, inversion

efficiency, and large-signal responses at different insolations havebeen investigated. Detailed analysis on the inverter performancehas been performed. The theoretical predictions are verified withthe experimental results.

Index TermsDC/AC power conversion, inverters, photovoltaicsystems.

I. INTRODUCTION

PHOTOVOLTAIC (PV) technology has developed rapidly

over the last two decades from a small scale, specialist

industry supplying the United States space program to a

broadly based global activity [1]. The advancement of power

electronics and semiconductor technologies, the declining costof solar panels, and the favorable incentives in a number of

countries had profound impact on the commercial acceptance

of grid-connected PV systemswhich have been used in peak

shaving, demand reduction, and supply of remote loads [2],

[3]. Apart from the solar panels, the core technology associated

with these systems is a power-conditioning unit (inverter) that

converts the solar output electrically compatible with the utility

grid [4].

Most inverters in the mid 1990s consisted of a central in-

verter of dc power rating above 1 kW. They connect several

solar panel strings in parallel via a dc bus. However, the con-

cept has the drawbacks of causing a complete loss of gener-ation during inverter outage and losses due to the mismatch

of strings [5]. Later, string inverters, which are designed for a

system of one string of panels, were used to lessen the problems

and have become popular nowadays. With further system de-

centralization, concept of AC-module was introduced. Every

solar panel has a module-integrated inverter of power rating

Manuscript received July 17, 2003; revised June 8, 2004. This work was sup-ported by the Research Grants Council, Hong Kong Special Administrative Re-gion, China, under Project CityU 1221/03E.

The authors are with the Department of Electronic Engineering, City Univer-sity of Hong Kong, Hong Kong (e-mail: [email protected]).

Digital Object Identifier 10.1109/TPEL.2005.850906

Fig. 1. Typical structures of grid-connected PV systems. (a) With voltage-fed,

self-commutated inverter switching at high frequency. (b) With current-fed,grid-commutated inverter switching at the grid frequency.

below 500 W mounted on the backside [6][10]. This panel-

inverter integration allows a direct connection to the grid and

provides the highest system flexibility and expandability. It also

offers the possibilities to overcome problems with respect to

high dc voltage level connection, safety, cable losses, and risk

of dc arcs, and to achieve high-energy yield in case of system

suffering from shading effect, due to the lack of mutual influ-

ence among modules operating points.

Typical structures of the AC-module consist of several power

conversion stages (Fig. 1) [9], [10]. The front stage has a max-

imum power point (MPP) tracker for maximizing the outputpower of the panel, because the maximum power drawn from the

panel varies with temperature and insolation [11]. The grid-con-

nected stage uses a full-bridge inverter toward the grid, either

self-commutated with a high switching frequency [Fig. 1(a)], or

grid-commutated at the grid frequency [Fig. 1(b)]. In the former

structure[Fig.1(a)],the panel voltageis firstlyboosted to thegrid

level together with the tracker. The dc/acconversionstage, which

is usually a pulse-width-modulated (PWM) voltage-source

inverter, shapes and inverts the output current. A high-frequency

filter is used to eliminate the high-frequency component at the

inverter output. In the latter structure [Fig. 1(b)], the tracker,

voltage boost, and output current shaping are performed in thefront stage. The full bridge is switched at the grid frequency for

inverting the shaped output current [7], [9], [10].

As the inverter generates grid-conformed ac power, some en-

ergy storage elements, such as the dc-link capacitor and the

panel input capacitor , are used to compensate the difference

between the dc power from the panel and the time-varying in-

stantaneous power absorbed by the grid. They, particularly ,

determine the harmonic quality of the output current. For in-

verters without MPP tracking, is made large for keeping

the panel voltage constant and preventing the 100-Hz or 120-Hz

grid disturbance injecting into the panel. However, although the

terminal voltage is stable, the panel output current may be time

0885-8993/$20.00 2005 IEEE


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954 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 20, NO. 4, JULY 2005

Fig. 2. Circuit schematics of the proposed inverter.

varying or even pulsating that cannot stabilize the panel oper-

ating point. It is thus important to keep both the panel terminal

voltage and output current constant at the MPP [12].

Majority works usually emphasize on researching new

MPP tracker [11] and refining individual converter stage.However, the system complexity is still governed by the mul-

tistage structure, as depicted in Fig. 1. This paper proposes a

buck-boost-derived converter that integrates the functions of the

MPP tracker and current shaper in Fig. 1(b). Low component

count and the use of low-voltage-rating capacitor are the key

advantages of this converter. The output current harmonics

are also less sensitive to the storage capacitor value. Tracking

of the MPP is based on the switching frequency modulation

scheme (SFMS) in [11]. Shaping of the output current is based

on controlling the converters output pulse duration such that its

average value is proportional to the required current reference

in each switching cycle [13]. A 30-W laboratory prototypehas been built. The tracking capability, inversion efficiency,

and large-signal responses at different insolation have been

investigated. Detailed analysis on the inverter performance has

been performed. The theoretical predictions are verified with

the experimental results.

II. OPERATING PRINCIPLES OF THE INVERTER

A. Description of the Inverters Operations

Fig. 2 shows the circuit schematics of the inverter consisting

of two stages. The first stage is a buck-boost-derived converter

operating in discontinuous conduction mode. It is formed by

, , , and for tracking the MPP of the panel andshaping the output current . The input filter formed by and

is used to smooth the panel output current. The MPP tracking

method in [11] is used. Its technique is to perturb the switching

frequency of and compare the ac component and the average

value of the panel voltage to control the duty cycle of . The

MPP can be globally located over wide insolation.When is on, and are off. stores energy. When

is off, both and are on. The energy stored in and

will transfer to the output. will be switched off when the

integrated value of is larger than that of the required output

current in a switching period .

acts as a buffer that temporarily stores panel energy and

transfers it to the output in a switching cycle. If the panel power

output is higher than the power absorbed by the grid in one

cycle, the energy remaining in after switching off will

transfer to through and . Since the average voltage

across will be shown to be equal to half of the peak output

ac voltage , it is used to regulate , and so . Thus,the series connection of and in transferring energy to

the grid provides the advantages of shaping the current and re-

ducing the voltage stress on .

The second stage is a grid frequency inverter formed by

switches , , , and . and are switched on

in the positive half cycle of the grid voltage, whilst and

are switched on in the negative half cycle of the grid

voltage. For the output filter section, is used to absorb the

current difference between and the currents through

and when and are on. and have

the resonant frequency at the switching frequency of for

keeping the line-frequency and attenuating the high-frequency

voltage components across and . is used to filter thehigh frequency current components going out to the grid. The


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HO AND CHUNG: INTEGRATED INVERTER 955

Fig. 3. Relationships among v , i , v , p , and p .

transformer is used to adjust the voltage level between the

inverter output and the grid voltage.

B. Relationship Between the Panel Power and Grid Power

The power input from the panel is constant under a con-stant insolation and the power output to the grid is time-

varying at twice of the grid frequency. Mathematically

(1)

(2)

(3)

where , , and are the peak voltage, peak current, and

angular frequency of the grid, respectively, and

is the peak instantaneous grid power.

Fig. 3 illustrates the relationships between and . Atthe steady state, the average value of is equal to . That is

(4)

The capacitor acts as a buffer for absorbing the difference

between and . Fig.3 depicts the low-frequency profileof

the capacitor voltage varying between and

at a dc value of . Thus

(5)

(6)

where .

If , will increase, and vice versa. As shown in

Fig. 3

(7)

and

(8)

Consider the time interval , in-

creases from to . Thus, for

(9)

By substituting and into (9), it

can be shown that

(10)

Moreover

(11)

C. Operation of the Buck-Boost-Derived Converter

Fig. 4(a) shows the equivalent circuit of the front stage

buck-boost-derived converter operating in discontinuous con-duction modethe inductor current begins with zero in

every switching cycle. The converter input is represented by a

voltage source , while its output is represented by a rectified

sinusoidal voltage source . The components , , ,

and form a classical buck-boost converter with its output

connecting in series with for supplying to . Fig. 4(b)(e)

show the topological sequence of operations. Fig. 5 shows the

theoretical waveforms of the gate signal to , , , and

, and the states of , , , and . The switching period

is . The operations are described as follows.

1) Topology 1 [Fig. 4(b)]: The switch

is on and is off. The inductor is charged up. Thediodes and are off. Hence

(12)

Hence, the peak current of , , is given by

(13)

Also, the average current from , , is

(14)

It is noted that is relatively fixed under a constant

insolation, implying that a constant solar energy willbe converted into the grid.


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Fig. 4. Equivalent circuit of the front stage converter. (a) Equivalent circuit.(b) Topology 1. (c) Topology 2. (d) Topology 3. (e) Topology 4.

Fig. 5. Theoretical waveforms. (a) ! t 6= ( = 2 ) or 3 = 2 . (b) ! t = = 2 and

3 = 2

.

2) Topology 2 [Fig. 4(c)]:

The switch is off and is on. The diode starts

conducting and blocks. The stored energy in is

released to , together with . Thus

(15)

The output current , which is equal to , asshown in Fig. 2, is sensed and integrated. If the inte-


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grated value is equal to or larger than the integrated

value ofthe referencecurrent , will be turned

off. Mathematically

(16)

The current reference is derived by multiplying

the rectified ac voltage and the controller output

.

3) Topology 3

[Fig. 4(d)]: The energy remaining in the coupled in-

ductors after Topology 2 will transfer to in this

topology. Both and are off. blocks and

starts conducting. Mathematically

(17)

However, when the instantaneous power to the grid is

at maximum (i.e., and ), the converter

will go to Topology 4 directly. The term

equals zero at those moments and is the critical

condition for determining the value of , which will

be shown in Section II-D. The waveforms are shown

in Fig. 5(b).

4) Topology 4 [Fig. 4(e)]:

All switches are off, until is switched on again in

Topology 1.

D. Determination of

As shown in Fig. 2, is used to adjust the magnitude of

in (16) for determining . Thus, considering the wave-

forms in Topology 2 shown in Fig. 5 and (16)

(18)

where , and is the instantaneous

output grid current before the voltage transformation by .

By solving (18), it can be shown that

(19)

Referring to Fig. 3, at , and

. Thus, and , where

and represent the peak values of the sinusoidal voltage

and current output respectively. The value of is at maximum,

which is denoted by . Thus, consider the area under the

waveform of in Fig. 5(b)

and so

(20)

By comparing (19) and (20), it can be seen that at ,

for equality, the determinant must be

zero. That is

(21)

Hence, from (4), (13) and (14)

Therefore

(22)

Thus, the average value of (i.e., ) is load independent.

Thus an error amplifier EA1 is used to compare the

and and regulate the magnitude of the output current.

As shown in Fig. 2, if is larger than , will be

increased, and vice versa.

E. Turns-Ratio of the Coupled InductorsThe primary-to-secondary turns-ratio of the coupled induc-

tors is determined by ensuring that still blocks in Topology

2. Thus, by referring Fig. 4(c)

(23)

Thus, the R.H.S. of (23) is maximum when is maximum

(i.e., ). By using (22), if

(24)

But, the voltage stresses on the switches increases with the value

of . It can be shown that

(25a)

(25b)

(25c)

(25d)

where , , , are the voltagestresses of , , , and , respectively.


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F. Maximum Power Point Tracking of the Panel

Tracking the maximum power point (MPP) of the solar panel

is based on the frequency modulation technique in [11] that the

PWM signal to is modulated with a low-frequency signal.

The panel is modeled by a Thevenins equivalent circuit, which

consists of a voltage source connected in series with an output

resistance around the MPP. Both and are subject tothe level of insolation and temperature. The input voltage and

equivalent input resistance of the converter are and , re-

spectively. Assuming 100% conversion efficiency

(26)

The rate of change of with respect to and can be

shown to be

(27)

At the MPP, and . Hence

(28)

where is the average input voltage. This equation gives the

required dynamic input characteristics of the converter, in which

has small-signal variation of subject to a small-signal

change of .

Iftheswitchingfrequency of ismodulatedwith a small-

signal sinusoidal variation

(29)

where is the nominal switching frequency, is the modu-

lating frequency and is much lower than , and is the max-

imum frequency deviation.

consists of two components, including an average resis-

tance and a small variation . That is

(30)

As shown in [14], for the buck-boost converter

(31)

By differentiating (31), it can be shown that

(32)

has an average value of and a small variation , which

can be expressed as

(33)

Fig. 6. Setup of the laboratory prototype.

and

(34)

At the MPP, . and

. The tracking method is based on com-

paring the magnitudes of and , an error term is

defined as

(35)

where and are, respectively, the peak value of

and the scaling factor for . At the MPP, the converter

will match with the panel. The sign of gives the required ad-

justment direction of the duty cycle of

(36a)

(36b)

(36c)

The tracking method in Fig. 2 is explained as follows. is mod-

ulated with a small-signal sinusoidal variation. and are

sensed. is then scaled down by the factor of and is com-

pared with . isobtained byusinga peak detector to extract

the value of the ac component in . The switching frequency

component in is removed by using a low-pass (LP) filter.

The error amplifier EA2 controls the PWM modulator to ad-

just by moving to the required value. The technique willkeep track of the output characteristics of solar panels without

approximating the voltage-current relationships [11].

III. EXPERIMENTAL VERIFICATION

A laboratory prototype has been built and investigated. The

input side consists of three 10-W panels (Siemens SM-10)

connecting in series. A stainless steel cover is put on the panels

to ensure uniform illumination on the panels. The setup is

shown in Fig. 6. The surface temperature is kept at about 40 C

throughout the test. The output power to the output resistance

characteristics of the panel at different insolation

levels is shown in Fig. 7. varies from 38 to 122 whenthe insolation level is changed from 1500 W/m to 350 W/m .


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Fig. 7.p 0 r

characteristics of the panel.

TABLE ICOMPONENT VALUES OF THE LABORATORY PROTOTYPE

The output power is also decreased from 34 W to 12 W. The

component values and parameters of the prototype inverter are

tabulated in Table I. The switching frequency of is 20 kHz,

with a maximum frequency deviation of 2 kHz (10%) using a

1 kHz modulating signal.

The system is simulated with PSIM 4.1 [15]. Fig. 8(a) shows

the simulated voltage and current waveforms of and at

the insolation level of 1500 W/m . Fig. 8(b) and (c) show the

waveforms of , , and at and , re-

spectively. Fig. 9 shows the corresponding experimental wave-

forms at the insolation levels of 1500 W/m . Figs. 10 and 11

show the waveforms of , , and under the insolations

of 750 W/m and 350 W/m , respectively. It can be seen that

the results under the insolation level of 1500 W/m are in close

agreement with the simulated results and the ones in Fig. 5. The

average value of the capacitor voltage is around 30 V, which

is equal to , under the three insolation levels. This con-

firms the expression in (22). Fig. 12 shows the harmonic con-

tents of the output current at the insolation level of 1500 W/mwith different values of , including 1000 F, 470 F, and

Fig. 8. Simulated voltage and current waveforms. (a) v , i . (b) v , iand

i

at! t = = 4

. (c)v

,i

andi

at! t = = 2

.

220 F and compared with the IEEE Std. 929-2000 (IEEE Rec-

ommended Practice for Utility Interface of Photovoltaic (PV)

Systems) [16]. They are all within the harmonic limits. Table II

shows the tracking and conversion efficiencies of the system at

different insolation levels. The tracking efficiency, which is the

ratio of the tracked power to the maximum extractable power,

can be maintained at over 96% over the insolation range. The

overall conversion efficiency from the panel to the grid is over83%.


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Fig. 9. Experimental voltage and current waveforms at the insolation level of1500 W/m . (a)

v

(Ch 3: 100 V/div),i

(Ch 4: 0.1 A/div) andv

(Ch 2:

10 V/div) (Timebase: 2 ms/div). (b) ! t = = 4 . v (Ch 1: 10 V/div), i (Ch2: 5 A/div) and

i

(Ch 3: 5 A/div) (Timebase: 20 s = d i v

). (c)! t = = 2

.

v (Ch 1: 10 V/div), i (Ch 2: 5 A/div) and i (Ch 3: 5 A/div) (Timebase:20 s = d i v ).

The transient response of the inverter system is investigatedby suddenly changing the insolation level from 350 W/m to

Fig. 10. Experimental voltage and current waveforms at the insolation levelof 750 W/m . v (Ch 3: 100 V/div), i (Ch 4: 0.1 A/div) and v (Ch 2:10 V/div) (Timebase: 2 ms/div).

Fig. 11. Experimental voltage and current waveforms at the insolation levelof 350 W/m .

v

(Ch 3: 100 V/div),i

(Ch 4: 0.1 A/div) andv

(Ch 2:10 V/div) (Timebase: 2 ms/div).

Fig. 12. Harmonic contents ofi

at the insolation level of 1500 W/m withdifferent values of

C

, including 1000

F, 470

F, and 220

F.

1500 W/m . Fig. 13(a) shows the waveforms of , and .Fig. 13(b) shows the response when the insolation is changed


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TABLE IITRACKING AND INVERSION EFFICIENCIES OF THE PROTOTYPE

Fig. 13. Transient responses of the inverter system. (Ch 2: v , 10 V/div; Ch4:

i

, 0.1 A/div), (Timebase: 100 ms/div). (a) From 350 W/m to 1500 W/m .(b) From 1500 W/m to 350 W/m .

from 1500 W/m to 350 W/m . With the insolation level in-

creased, the output current cannot be increased instantaneously.

Thus, the capacitor voltage increases during the transient pe-

riod. Conversely, with the insolation level decreased, the output

current cannot be decreased instantaneously. Thus, the capacitorvoltage decreases during the transient period. Nevertheless, the

capacitor will revert back to 30 V in both cases after the tran-

sient period, confirming the control mechanism. The transient

period takes about 0.6 s.

IV. CONCLUSION

This paper has discussed the implementation and perfor-mance of an integrated inverter for photovoltaic systems. The

inverter provides the function of tracking the MPP of the panels

and shaping the output current over wide insolation level.

A 30-W laboratory prototype has been built. The tracking

capability, inversion efficiency, and large-signal responses at

different insolations have been investigated. Theoretical pre-

dictions have been confirmed with the experimental results of

the prototype.

REFERENCES

[1] G. Foley, Photovoltaic applications in rural area of the developing

world, Tech. Rep., World Bank, New York, 1995.[2] C. J. Hatiziadoniu, F. Chalkiadakis, and V. Feiste, A power conditioner

for a grid-connected photovoltaic generator based on the 3-level in-

verter, IEEE Trans. Energy Conv., vol. 14, no. 4, pp. 16051610, Dec.1999.

[3] K. Y. Khouzam, Technical and economic assessment of utility inter-active PV systems for domestic applications in South East Queens-

land, IEEE Trans. Energy Conv., vol. 14, no. 4, pp. 15441550,Dec. 1999.

[4] T. Markvart, Solar Electricity. New York: Wiley, 1994.

[5] H. Becker, K. Kiefer, V. Hoffmann, U. Rindelhard, and G. Heilscher,

Five years of operational experience in the German 1000-Roofs-PVprogrammeresults of monitoring and system inspection, in Proc. 14th

Eur. Photovoltaic Solar Energy Conf., Barcelona, Spain, Jul. 1997, pp.

16771680.[6] H. Oldenkamp, I. De Jong, C. Baltus, S. Verhoeven, and S. Elstgeest,

Reliability and accelerated life tests of the ac module mounted OKE4inverter, in Proc. 25th IEEE Photovoltaic System Conf., May 1996, pp.13391342.

[7] A. Lohner, T. Meyer, and A. Nagel, A new panel-integratable inverterconcept for grid-connected photovoltaic systems, in Proc. IEEE Int.Symp. Industrial Electronics, Jun. 1996, pp. 827831.

[8] M. Meinhardt et al., Miniaturized low profile module integrated con-verter for photovoltaic applications with integrated magnetic compo-

nents, in Proc. IEEE Applications Power Electron. Conf. Expo., Mar.1999, pp. 305311.

[9] M. Calais, J. Myrzik, T. Spooner, and V. Agelidis, Inverters forsingle-phase grid connected photovoltaic systemsan overview,in Proc. IEEE Power Electronic Specialists Conf., Jun. 2002, pp.

19952000.[10] S. B. Kjaer, J. K. Pedersen, and F. Blaabjerg, Power inverter topologies

for photovoltaic modulesa review, in Proc. IEEE Industry Applica-tions Conf., vol. 2, 2002, pp. 782788.

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Billy M. T. Ho (S02) was born in Hong Kong in1979. He received the B.Eng. (first class honors) de-gree in electronic engineering from the City Univer-sity of Hong Kong in 2001 where he is currently pur-suing the Ph.D. degree in power electronics.

His research interests include computer-aidedsimulation techniques, photovoltaic panels powerconversion, control methodologies, and inverter

applications.Mr. Ho received the Simatelex Charitable Foun-dation Scholarships for two consecutive years during

his undergraduate studies.

Henry Shu-Hung Chung (M95SM03) receivedthe B.Eng. and Ph.D. degrees in electrical engi-neering from The Hong Kong Polytechnic Universityin 1991 and 1994, respectivelty.

Since 1995, he has been with the City Universityof Hong Kong (CityU). He is currently a Professorin the Department of Electronic Engineering andChief Technical Officer of e.Energy Technology

Limited (an associated company of CityU). Hehas authored five research book chapters, and over200 technical papers including 90 refereed journal

papers in his research areas, and holds four US patents. His research interestsinclude time- and frequency-domain analysis of power electronic circuits,switched-capacitor-based converters, random-switching techniques, controlmethods, digital audio amplifiers, soft-switching converters, photovoltaicsystems, and electronic ballast design.

Dr. Chung received the Grand Applied Research Excellence Award fromthe City University of Hong Kong in 2001. He was IEEE Student BranchCounselor and Track Chair of the Technical Committee on Power ElectronicsCircuits and Power Systems of the IEEE Circuits and Systems Society,from 1997 to 1998. He was Associate Editor and Guest Editor of the IEEETRANSACTIONS ON CIRCUITS AND SYSTEMS, PART I: FUNDAMENTAL THEORYAND APPLICATIONS, from 1999 to 2003. He is currently an Associate Editor ofthe IEEE TRANSACTIONS ON POWER ELECTRONICS.

an integrated inverter with maximum power

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