8.flyback inverter controlled by sensorless current

7/29/2019 8.Flyback Inverter Controlled by Sensorless Current

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 4, AUGUST 2005 1145

Flyback Inverter Controlled by Sensorless CurrentMPPT for Photovoltaic Power System

Nobuyuki Kasa, Member, IEEE, Takahiko Iida, and Liang Chen

AbstractThis paper presents a flyback inverter controlled bysensorless current maximum power point tracking (MPPT) fora small photovoltaic (PV) power system. Although the proposedsystem has small output power such as 300 W, a few sets of smallPV power systems can be easily connected in parallel to yieldhigher output power. When a PV power system is constructed witha number of small power systems, the total system cost will in-crease and will be a matter of concern. To overcome this difficulty,this paper proposes a PV system that uses no expensive dc currentsensor but utilizes the method of estimating the PV current fromthe PV voltage. The paper shows that the application of this novelsensorless current flyback inverter to an MPPT-operated PV

system exhibits satisfactory MPPT performance similar to theone exhibited by the system with a dc current sensor as well. Thispaper also deals with the design method and the operation of theunique flyback inverter with center-tapped secondary winding.

Index TermsDigital signal processors, photovoltaic (PV) powersystems, pulsewidth-modulated (PWM) inverters.

I. INTRODUCTION

PHOTOVOLTAIC (PV) systems have been developed to

overcome an energy crisis in terms of ecology. The PV

system consists of the PV array and the PV power conditioner,

and the PV power conditioner usually can be subdivided

into both a dcdc converter to control the dc voltage and avoltage-source inverter to connect to the ac utility grid line.

Since a PV or a solar cell module can generate rather small

electric power of approximately 100 W per unit square meter

under fine weather conditions, the PV power conditioner adopts

the maximum power point tracking (MPPT) technique to utilize

the PV array efficiently. The PV voltage and PV current are

required to calculate the PV output power for the MPPT oper-

ation. Therefore, an expensive dc current sensor is absolutely

required, thereby introducing the problem of high expense for

the PV small power system. As listed in the literature [1][10],

there are a number of main circuit configurations for the PV

power conditioners suitable for a rating less than 1 kW, and we

also had proposed a kind of buckboost-type inverter that had

two sets of ac semiconductor switches to convert dc power to

ac power [4]. However, this proposed inverter required two sets

of the dc sources of PV arrays, which, respectively, supplied

the positive and negative half-cycle current to the ac utility grid

line. This proposed inverter circuit has been improved to one

dc-source-type inverter as reported in the literature [11][13].

Manuscript received May 19, 2004; revised October 11, 2004. Abstract pub-lished on the Internet April 28, 2005.

The authors are with the Department of Electronic Engineering, OkayamaUniversity of Science, Okayama 700-0005, Japan (e-mail: [email protected]).

Digital Object Identifier 10.1109/TIE.2005.851602

One of the improved main circuit configurations is named the

flyback inverter with center-tapped secondary winding [13].

In this paper, the flyback inverter with center-tapped sec-

ondary winding is used to improve the operating performance

of the newly proposed sensorless current flyback inverter.

The flyback inverter with center-tapped secondary winding is

already presented in the literature [12][14]; however, since the

method still does not have widespread familiarity, the features

are summarized here as follows. No dcdc converter is required,

as the flyback inverter can directly convert the specified dc

power to ac power, where the dc voltage is not related to theoperation. The main circuit configuration becomes very simple

and the number of power semiconductor switches used is less

than that of a conventional one; these features contribute to

the cost reduction of the total system. As the electric potential

of the PV array can be fixed at the ground potential, there is

no possibility of any static capacity between the PV array and

the ground to generate any troublesome discharge current. On

the other hand, this discharge current becomes an inevitable

one when the conventional bridge inverter circuit configuration

is applied. The control algorithm is very simple and of open

loop and is found to be equipped enough to run the PV power

conditioner.

The detailed design method of the flyback inverter is dis-

cussed in Section II of this paper. For the MPPT operation, the

PV voltage and the PV current are required to calculate the PV

output power. Using a digital signal processor (DSP), the PV

current is calculated from the voltage across the capacitor con-

nected to the PV array. Section III treats in detail the algorithm

for the calculation including the flowchart. The experimental re-

sults show that the sensorless current system has a performance

similar to that of a system with the current sensors. The details

are provided in Section IV.

II. FLYBACK INVERTER WITH CENTER-TAPPED

SECONDARY WINDING

A. Operation of Flyback Inverter With Center-Tapped

Secondary Winding

Fig. 1 shows the main circuit configuration of a prototyped

PV power conditioner. The flyback inverter consists of three in-

sulated gate bipolar transistors (IGBTs), two diodes, and a fly-

back transformer with center-tapped secondary winding. The

flyback transformer has the functions to not only generate the

ac power but also to isolate between the PV array and the ac

utility grid line to protect against any electric accident. The pri-

mary winding is connected to the PV array and IGBT1, where

the DSP-driven IGBT1 has width-modulated gate pulses. Two

0278-0046/$20.00 2005 IEEE


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1146 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 4, AUGUST 2005

Fig. 1. Circuit configuration and operation modes of flyback inverter withcenter-tapped secondary winding.

sets of ac semiconductor switches, one composed of IGBT2

and Diode in series and another, IGBT3 and Diode in

series, are, respectively, connected to each terminal of the sec-

ondary winding of the flyback transformer. They can switch re-

ciprocally and synchronously with the polarity of the ac utility

grid line. The switching sequences and waveforms are shown

in Fig. 2. Fig. 1 shows the operating modes of the flyback in-

verter with center-tapped secondary winding. Mode I is defined

for the situation where IGBT1 is at on-state with all other IGBTsin off and the stored energy in is discharged to the ac utility

grid line with the polarity of synchronized with that of the

ac utility grid line. Mode II is defined for the duration where

IGBT2 is at on-state with all the rest in off, implying the stored

energies in and being released to the ac utility grid line and

giving the positive polarity. Modes I and II are switched alter-

nately at high switching frequency during the positive half cycle.

The envelope of the peak current through the primary winding

of the flyback transformer is modulated by the pulsewidth mod-

ulated (PWM) gate pulse of IGBT1 to a sinusoidal form and

is in phase with the ac utility grid line voltage. Mode III is for

the negative half-cycle polarity. Mode I and III are switched al-

ternately at high switching frequency during the negative halfcycle. The current flowing through IGBT1 is controlled in the

Fig. 2. Switching sequences.

Fig. 3. Circuit configuration applying transformer model.

same manner in the negative half cycles as it is controlled in thepositive half cycles.

B. Design of Inductance

The strong effect of the winding inductances of the flyback

transformer on the performance of the inverter calls for a very

careful design. In the following analysis, it is assumed that the

transformer is an ideal one and has the equivalent magnetizing

inductance of in the primary side as shown in Fig. 3. As

the turns ratio between the primary and secondary winding of

the flyback transformer is only two, the mutual inductances be-

tween primary and secondary and also between primary

and secondary become . Fig. 4(a) shows how the cur-rent in the magnetizing inductance of flows in the discon-

tinuous current mode (DCM). is defined as the crest value

of the enveloped peak current in when the inverter operates

at the rated full power of and the summation of and

is just equal to the duration at the crest point

of the current. Here, is the ac utility grid line frequency and

is the total number of the switching periods during the half

cycle . Using these symbols as defined above, the

and of IGBT1 can be expressed as

(1)

(2)


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KASA et al.: FLYBACK INVERTER CONTROLLED BY SENSORLESS CURRENT MPPT FOR PV POWER SYSTEM 1147

Fig. 4. Inductor current mode in DCM. (a) Waveforms of inductor current in

L

during half cycle of ac utility grid line. (b) Waveforms of switch current,inductor current in

L

, and capacitor voltage during thek

th switching period.

where is the root-mean-square value of ac utility grid line

voltage and is the capacitor voltage of . Using (1) and (2),

the is expressed as

(3)

On the other hand, the rated maximum output power

is expressed as

(4)

where is given by . Substituting (4) into (3), the in-

ductance is finally given by

(5)

C. Calculation of Switch-On Period

As shown in Fig. 4(b), the enveloped peak current in the mag-

netizing inductance during the arbitrary th switching pe-

riod is expressed as

(6)

where is the time from the starting point of the th switching

period in seconds.

Equation (6) can be written using the sine angle addition for-

mula. Therefore, as is a small value, is approx-

imated as

(7)

As the flyback inverter is operated in DCM, the IGBT

switch current is started from zero initial current at everyswitching as shown in Fig. 4(b); the switch current during the

th switching period is expressed as

(8)

where is the threshold voltage of IGBT1, and is the

on-resistance of IGBT1.

As is a small value, can be approximated as

(9)

When the intersection of and is set to the

switch-on period, we obtain the pulsewidth of the th

switching pulse by solving from (7) and (9) as

(10)

III. MAXIMUM POWER POINT TRACKING WITHOUT

CURRENT SENSOR

As the PV array has the nonlinear characteristics on thepower versus voltage chart as shown in Fig. 5, the linear control

theory cannot be applied to extract the maximum electric power

from the PV array. The perturbation-and-observation method is

often used for the MPPT in many PV systems [15], [16]. In this

method, the periodically controlled increase or decrease of the

PV voltage moves the operating points toward the maximum

power point. Usually, the maximum point is tracked by varying

the duty ratio of the switching device switched to its on-state.

In the conventional system, it is required to calculate the PV

output power, which is given by the product of the PV voltage

and PV current. The PV current is usually detected by using

an expensive dc current sensor and, therefore, demands an

alternative means to achieve cost reduction in measuring the dccurrent. In this paper, it is proposed to calculate the PV current


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Fig. 5. PV characteristics.

Fig. 6. Equivalent circuit offlyback inverter (primary side only).

from the PV voltage as described below by the aid of a digital

signal processor (DSP) in real time. It is considered that the PV

current consists of the summation of the capacitor currentand the switch current as shown in Fig. 6

(11)

When (11) is integrated in the interval of the switching

period shown in Fig. 4(b), we get

(12)

is defined as the averaged current of in the

interval , and the total amount of the electric charge which

flows out from the PV array during the th switching period is

defined as and expressed as

(13)

In the same way

(14)

(15)

where and are defined as the total amount of

electric charges stored in the capacitor and flowing through

the switch of IGBT1 during interval , respectively. Fig. 4(b)

shows the capacitor voltage and the switch current waveforms

during the th switching period. When and

are defined as the capacitor voltages at the ends of the th

and the th switching periods, respectively, the relation betweenthese capacitor voltages and the electric charge is ex-

pressed as

(16)

The averaged capacitor current during the th switching pe-

riod is given by

(17)

where . The average capacitor current

is expressed as

(18)

A it can be assumed that the switch current is composed of the

magnetizing current in the flyback transformer and the capacitor

is so large that the fluctuation of the capacitor voltage during the

switching period can be neglected, then the switch current can

be expressed as

(19)

(20)

The relation between the electric charge and the switch cur-

rent is expressed as

(21)

From (15), the averaged switch current during the th

switching period is expressed as

(22)

The average switch current is obtained as

(23)

Finally, the average PV current can be estimated as

(24)


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Fig. 7. Flowchart of interrupt routine fort ( k )

includingI

calculation and MPPT.

Fig. 7 shows an outline of the flowchart of the interrupt rou-

tine for including the PV current estimation and MPPT.The main program is not shown in Fig. 7. The examples of the

parameters and their values listed below can be set in the main

program as their respective initial conditions: ,

, , , , and

, . Moreover, all pulsewidth data for

the rated full-load condition are stored in the ROM table of the

main program in the entries from to .

The is reset to zero by the interrupt routine program which

is started by the external interrupt signal at every zero-crossing

electrical angle of the ac utility grid line voltage in order to

synchronize the generated inverter voltage with the ac utility

grid line voltage. This interrupt routine is repeated continuouslyat the repetition rate of 9.6 kHz after which is reset to

zero again. When is less than , is calculated by

(24). When coincides with , is renamed to .

The repetitive frequency controller is used for smoothing of

the output power. We make the repetitive frequency controller

switch to the MPPT routine every six times of the interrupt

routine, and so the repetitive frequency is Hz in

our experimental system. The MPPT routine or the process of

so-called perturbation-and-observation method is started and

is calculated as

(25)

Then, the PV power is given as the product of

and . is compared to the last PV powerand the sign of is given by the process as shown in Fig. 7.

Then, the new duty ratio is decided by the summation of

the last duty ratio and the newly decided differentiation

as expressed by

(26)

where (27)

Each is given by the product of and

as

(28)

The data of is derived from the parallel I/O port of the

DSP board. As mentioned in Section I, it will be found that the

control algorithm is open loop and a very simple one.

IV. EXPERIMENTAL RESULTS

Fig. 8 shows the experimental system configuration. Three

PV modules with the electrical output rating of 109 W per

module are used in our system. The DSP, type TMS320C31,

is used to control the PV power conditioner and the MPPT

including the PV current and pulsewidth calculation. The

pulsewidth data are derived from the parallel I/O port

of the DSP board and the data are delivered to the complexprogrammable logic device (CPLD) in order to generate the


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Fig. 8. System configuration.

TABLE ICIRCUIT PARAMETERS

PWM pulses. In the experimental system, the PV current is

monitored by the dc current sensor and, thus, detected for the

measurement. IGBT1 is driven by the switching frequency of9.6 kHz. IGBT2 and IGBT3 are switched alternatively with

some dead times, and these switches are synchronized to the

ac utility grid line frequency of 60 Hz. The flyback inverter is

operated in DCM. The main circuit parameters are listed in

Table I.

Fig. 9 shows the waveforms of the output voltage ,

the output current , and the switch current , when the

flyback inverter generates the output power of 300 W. The

P-SPICE simulation yields the waveforms given in Fig. 9(a).

On the other hand, the experiment mentioned above exhibits

the waveforms given in Fig. 9(b). It is found that these wave-

forms are in good agreement with each other and also that theprototyped flyback inverter can operate at a power factor of

almost unity.

Fig. 10 shows how the efficiency and input power depend

on the duty ratio , where the input power corresponds to the

PV output power. The inductance and maximum pulsewidth of

IGBT1 are designed for the prototyped flyback inverter so as

to generate a maximum power of 300 W. It is found that the

inverter has the efficiency of approximately 89% at the rated

output power, and the transformer and IGBT1 are responsible

for most of the power loss.

In order to verify the calculated current from (24), the dc cur-

rent sensor is tentatively connected between the capacitor

and PV array shown in Fig. 8. The measured and calculated cur-rents are compared with each other as shown in Fig. 11. The

Fig. 9. Output voltage and current and switch current waveforms.(a) Simulation results. (b) Experimental results.

Fig. 10. Efficiency and input power of flyback inverter with center-tappedsecondary windings.

upper waveform in Fig. 11(a) is the current of measured

by the dc current sensor, while the lower one is the one calcu-

lated by (24). It is observed that transient phenomena occurs in

the switch-on interval caused by the inrush current in capacitor

, since capacitor is not pre-charged in the switch-off in-

terval. Comparing these curves reveals the fact that both curves

are similar to each other. However, it is also observed that thereare some delays on the lower waveform caused by the sampling


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Fig. 11. Comparison of estimated PV current and measured one.(a) Waveforms of PV current. (b) Proportional relations of PV currents.

period of the processor program. The rated PV current is 3 A

and it is scaled in 8 bit, when the current is measured through

the dc current sensor and the A/D converter in our system. Then,

the resolution of the current is 0.012 A. Fig. 11(b) shows the ex-

perimental results which compare the estimated PV current cal-

culated by (24) with the measured PV current. Since an estimate

error of the PV current is within 0.012 A, proportional relations

between the estimated current and the measured one are kept as

shown in this figure.

Fig. 12 shows the experimental results of the MPPT perfor-

mance. At the time of experiment, it is a fine weather day and

the solar intensity is 807 W/m . We can estimate roughly that

the maximum power is 242 W, because the rated power is 300W when the solar intensity is 1000 W/m as shown in Fig. 5.

Fig. 12. Comparison of MPPT performance. (a) With current sensor.(b) Without current sensor.

To obtain the maximum power, the duty ratio must be approxi-

mately 0.9 which is obtained from Fig. 10. The PV generates the

power of 40 W at the initial conditions of , when the

MPPT route in Fig. 7 is not operated. The MPPT operation of

the PV power conditioner is started at time 0. Since the repetitive

frequency of MPPT is 10 Hz and is 0.01, we can estimatethat the time interval until arriving at the maximum power is ap-

proximately 6 s. It is observed from Fig. 12 that the PV power

conditioner can track the maximum power of 242 W after 6.3 s

from the start of MPPT operation. Fig. 12(a) shows the MPPT

performance with the dc current sensor, which means that the

measured isused inthe interrupt routine program shown

in Fig. 7. On the other hand, Fig. 12(b) shows the MPPT per-

formance without the dc current sensor, which means that the

calculated by (24) is used in the interrupt routine pro-

gram. Similar performance in the two cases proves the fact that

the proposed current-sensorless method can track the maximum

power point with the same efficiency as the conventional MPPTmethod can with the current sensor.

V. CONCLUSION

A sensorless current flyback inverter has been proposed,

which can be applied to a PV system guided by MPPT opera-

tion. To verify the operation of the sensorless current flyback

inverter, a prototype flyback inverter with center-tapped sec-

ondary winding is used. However, the novel sensorless method

can be applied to any type of flyback inverter with fixed

switching frequency and DCM operation. The comparison of

the tests by the flyback inverters with the dc current sensor and

without it prove that there is no operational difference betweenthem, including the MPPT performance. The novel sensorless


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method can contribute to the space saving and cost reduction

of the PV power conditioner from both the theoretical and

experimental points of views. The experimental data show that

the sensorless current flyback inverter can be applied to MPPT

for the PV small power system with successful performance.

ACKNOWLEDGMENTThe authors would like to thank R. Yamada of Shindengen

Electric Manufacturing Company, Ltd., Japan, for his help in

this study.

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ICPE98, Seoul, Korea, Oct. 1998, pp. 978981.[6] N. Kasa, T. Iida, and H. Iwamoto, An inverter using buck-boost type

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[8] T. Shimizu, N. Nakamura, and K. Wada, A novel flyback-type utilityinteractive inverter for AC module systems, in Proc. ICPE01, Seoul,Korea, Oct. 2001, pp. 518522.

[9] N. Kasa, T. Iida, and G. Majumdar, Maximum power point tracking

without current sensor for small scale photovoltaic power system, inProc. ICPE01, Seoul, Korea, Oct. 2001, pp. 631634.

[10] Y. Konishi, S. Chandhaket, K. Ogura, and M. Nakaoka, Utility-in-teractive modulated sinewave inverter with a high frequency flybacktransformer link for small-scale solar photovoltaic generator, in Proc.

ICPE01, Seoul, Korea, Oct. 2001, pp. 683686.[11] R. Yamada, N. Kasa, and T. Iida, Photovoltaic systems with flyback

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Nobuyuki Kasa (S96M98) was born in Japan in1969. He received the B.E., M.E., and Ph.D. degreesin electronic engineering from Tokyo MetropolitanInstitute of Technology, Tokyo, Japan, in 1993, 1995,

and 1998, respectively.In 1998, he joined the Department of Electronic

Engineering, Okayama University of Science,

Okayama, Japan, where he is currently an AssistantProfessor. He was a Visiting Research Scholar in theDepartment of Electrical and Computer Engineering,University of Victoria, Canada, in 2003. His research

interests include ac motor drive systems and photovoltaic power systems.Dr. Kasa received the Excellent Paper Presentation Award from the Institute

of Electrical Engineers of Japan in 1999.

Takahiko Iida was born in Japan in 1939. He

received the Bachelor of Engineering degree fromKobe University, Kobe, Japan, in 1961, and the

Doctoral degree from Osaka University, Osaka,Japan, in 1982.

He was with Mitsubishi Electric Corporation(MELCO), Japan, from 1961 to 1989. In 1989, he

joined Okayama University of Science, Okayama,Japan, where he is currently a Professor in theDepartment of Electronic Engineering, Faculty ofEngineering.

Prof. Iida has been an International Member of IEC/SC47D since 1996. He isalso Chairman of the Domestic Semiconductor Package Technical Committee.He received the Technical Prize from the Japan Electric Industry in 1975, the

Invention Encouragement Prize from the Japan Invention Association in 1975,and the Committee Prize Paper Award from the IEEE Industry ApplicationsSociety in 1995.

Liang Chen was born in Xin Jiang, China, in 1968.He received the B.S degree from XiAn Mining Col-lege, XiAn, China. He is currently working towardthe Ph.D. degree at Okayama University of Science,Okayama, Japan.

He is also with the Department of ElectricalEngineering, Xin Jiang University, Xin Jiang, China,where his research interests include photovoltaic

power systems.

8.flyback inverter controlled by sensorless current

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