Maximum power point tracking with capacitor identifier for photovoltaic power system

Maximum power point tracking with capacitor identifier for photovoltaic power system

N.Kasa, T.lida and H.lwamoto

Abstract: A perturbation and observation method with a capacitor identifier is prcscnted for maximum power point tracking (MPPT) in a photovoltaic power system. Usually, by increasing or decreasing the duty ratio of on-state of switching device, the maximum powcr point is tracked. The variation of duty ratio is determined by considering its circuit parameters. However, it is known that actual capacitance of an electrolytic capacitor in parallel with the photovoltaic array has 50% tolerance of its iioniinal value. If the variation of duty ratio is determined based on its nominal value, the performancc of the MPPT is degraded. T~LIS, we must change tlic variation of the duty ratio accordingly, based on its actual value. In the systcm presented, the model reference adaptive system is adapted to identify thc capacitor, so the capacitance can be accurately cstimated and the variation of the duty ratio can be corrccted by the estimated value. As a result, the high performancc of the MPPT may be obtained. Experimental rcsults are presented using a proposed power inverter using buck-boost choppcr circuits.

1 Introduction

It is necessary to produce pollution-free natural energy and to obtain, that photovoltaic power systcms have bcen developed for home use. The voltage-power characteristic of photovoltaic array is not linear because of the variation which is caused by solar intensity and temperature, and wc cannot adopt the linear control theory easily to obtain the maximum power of the photovoltaic array. The pcrturba- Lion and ObServdtioll method is often used for the maxi- tnuin power point tracking (MPPT) in many photovoltaic power systems [l]. The method moves the operating point toward the maximum powcr point by periodically increasing or decreasing the voltage of the photovoltaic array. Usually, by increasing or decreasing the duty ratio of on- state of switching device, the inaximuin power point is tracked.

The variation of duty ratio is determined by considering its circuit parameters. Several papers treat the characteristic variation of photovoltaic array by temperature. and the variation of duty ratio is determined by considering the temperature. However, there is no discussion about a fluctuation of the electrolytic capacitor in parallel with the photovoltaic array. It is known that its actual capacitance has 50% tolerance of its nomiiial value. If the capacitance is changed on the condition where the variation of duty ratio is determined based on the nominal value, the performance of MPPT is degraded because the variation of duty ratio is not optimum for the system. Thus, we must know tlic

0 IEE, 2000 IEE Prowditgv onlinc 110. 2oooO641 DOL 10.1049/ipcpa:20000641 f a p a received 19th Apiil 2000 N. Kasa a i d T. lida arc with tlic Dcpartiiiciit of Elcclroiiic Engineering, Okayama Univcidy of Scicncc, 1-1 Ridriicho, Okdyaima 7000005, Japan H. Iwanioto i s with tlic Power Dcvicc Division, Milsuhislii Elccltic Corp”i- tion, 1-1 -I IinrJuIa-higilslii, Nishi-ku, Fakuoka X19-0192, .lapin

/E l ; l ’ ~ o c . - E l ~ ~ ~ l ~ . / ’ o w A[,[)/., l’d 147, No. 6, iVosoiiher 2fiIlfi

information of capacitance and change the variation of duty ratio.

This paper presents a perturbation and observation method with an idcntificator of capacitor for MPPT in a photovoltaic system. We adapt the model reference adaptive system to estimate the capacitance. This allows us to get tlie accurate capacit“ and correct the variation of duty ratio by the capacitance. As a result, a high performance of MPPT may be obtained. In convcntioaal systems, the method is used in the DC-DC converter. In our system, we adopt the method to a proposed inverter using BucI- Boost type chopper circuits. Simulated and experimental results are shown using the prototype photovoltaic power systems.

2

Usually, the interface circuits between the photovoltaic arrays and the utility grid lines consist of a voltage source invertcr. However, the current source inverter and the power inverter were adopted in photovoltaic power systems PI.

I n our system, thc power inverter consists of two sets of Buck-Boost type chopper circuit. Thc inerit of the system lies in the fact that the main circuit is rather simple and the number of switching devices which arc used in tlie system is less than that in the conventional system. A transformer is not necessary for the system and an inductor which links to ii utility grid line is smaller than the conventional system. In the system, there is no earth-leakage current at all in the theoretical base because the grand level between the photovoltaic array and utility line is the same.

Inverter using Buck-Boost type chopper circuits

2. I Operation ofproposed inverter Figs. I n , I h , 2tr and 2h show the main circuit diagram of the proposed photovoltaic power system. In this circuit, two sets of photovoltaic array (PV array) and Buck-Boost type chopper circuit arc connected in antiparallel construc- tion with the output capacitor C, which generatcs the AC

4‘17

voltage, Both choppers arc operated at the fixed frequency in the discoiitinuous conduction mode (DCM), because thc whole power of the photovoltaic arrays is transferred to utility line in the term of one switching.

pv arrav IGBTl lGBT2 D1

c 2 & utility grid line L2

c1 U C

c3 mz L1 -- -- r

c2 ZT utility L2 grid line

J L

PV array IGBT3 IGBT4 D2

b Fig. 1 Siqm qf opemtioii U Stage 1 6 Stage I I

lGBT2 D1

utility grid line

a

PV array IGBTI lGBT2 01

. . PV array lGBT3 IGBT4 02

b Fig. 2 Strrga of’operuiion U Stage 111 b Slagc IV

Figs. la, lb, 2u and 2b show the operation stages of proposed inverter. Stage I is defined for the situation where IGBTl is in on-state and all the other IGBTs are at off- state condition. In other words, the PV array energy is transferred to the inductor L, and the stored energy in C is discharged to the utility grid line giving a positive polarity. The stage 11 is defined for the duration when IGBT2 is in on-state and the rest are at off-state condition, implying that both the stored energies in Cis released to the AC utility grid line giving a positive polarity. The stages 111 and IV are the negative polarity conditions against the stages I and 11, respectively.

498

2.2 Analysis of circuit When the equivalent rcsistances of stages I and I1 arc assumed to be RI and K2, respectively, thc state equations arc exprcssed as

whcre, L is reactancc of L, and L,, /c is a number of the switching, VDc is the voltage of a PV array, and VAC is the voltage of utility grid line. With i , (k) = i2(k ~ 1) in eqn. 1 and i 2 ( / ) = il(/c) in eqn. 2 at the time t = 0, thc above equations arc solved as follows:

In the iuverter, the inductor current is operatcd in DCM. Then the abovc equations arc exprcssed as follows:

whcre, f is the kequency of utility grid line and N is the number of the switching times in thc term of 16

inductor current iP

n\

0 $ 6 ntk

1 p - l p k N

switching no.

Fig. 3 Ciwent wive,firi?i qfiiidmior oid . ~ i ~ ’ ; t ~ h i i i g ~ ~ ~ ~ ~ ~ . ~

2.3 Design of inductor In the pth term, when the inductor current i, includes the highest peak point, the highest pcak currcnt 4, is given by

Fig. 3 shows the waveform of inductor current in the 11th tcrm. The widths of switching for the 11th teim are expressed as follows:

IEE Pvo~. -ElwIr . POWW A p p . , I‘d 147, No. 6. Mownher 2000

When above equations are substituted to the following equation

(11) 1.

Ton. + T o 1 . J = __ 2N.f

I/, is expressed by

The output power PL,,/ which is supplied to lhc utility grid line is given by

P,,+L = VAC;, sin ~ 1 ~ 1 6 ' sin 0,' (13) IVf

The power f'(,., which is consuincd by capacitor C, is the difference between thc power in the (p - 1)tli aind /it11 ternis, and it is expressed as

K l C I A C ' ]Ic: 1 ___ (sin' - sill' (14)

Then the power which mist be stored in tlic inductor is cxpressed as follows:

,up

p = Pc + P?,il (15)

We design the rccactancc L, with the actual power stored in the inductor equal to the power that must be stored in it.

When tlic relation of power givcn in eqn. 16 is substituted in the abovc equation, we obtain

Solving for L, wc get

V/lC V2C L = 41V f I~~:(l/ijc + f i v ~ ~ ; , ) ~ ( 2 sin' 8,-siii' 8,- 1)

The inductance L as given in the above equation is utilised in the following equation to calculate the width of switching for tlic kth term.

(19)

aiid the energy which is stored in the inductor is expressed as follows:

Then the width of switching for the kth lcrni is expressed as the next equation.

3 identification of capacitance

Figs. 4a and h shows current-voltagc aiid power-voltage characteristics of the photovoltaic array. The characteristics are mcasured on 1 pm and 3 pin. The maximum power point, which is located at knce of the P-V curve (Fig. 40), is moved by a solar intensity and a temperature. To track the maximum power point, the perturbation and observation method is adapted. It moves the operating point toward the inaximtim power point by periodically increasing or decreasing the photovoltaic array voltage. To incrcase or decrease its voltage, the duly ratio of on-state of switching device is changed in thc pulsewidth modulation (PWM) converter or inverter.

Maximum power point tracking and

300 -

50 voitage,V '00 b

Usually, the variation or duty ratio for MPPT is dctcr- mined by considering the circuit parameters. However, the circuit consists of the electrolytic capacitor in parallel with the photovoltaic array. The actual capacitance has SO% tolerance of its nominal value and it deteriorates year by ycar [3]. We think that the fluctuation of its capacitance affects the characteristics of the system and therefore study the effect caused by the variation. Thcn wc must determine the variation of duly-ratio in accordance with the fluctuation of the circuit parameters in ordcr to realise the high performmm of MPPT.

3. I Transfer function for maximum power point tracking To study the charactcristics of the maximum power point tracking when thc capacitance changes, we consider the transrer function of the Buck-Boost chopper.

Fig. S shows the Buck-Boost chopper for the photovoltaic power system. When the IGBT is on-stale, the voltage and current equations arc as follows:

(24)

499

Fig. 5 i?uclc-Boo.st type chopper

When the IGBT is at off-state and the diode is in on-state, the voltage and current equations are given by

The duty ratio of on-state is D and the one of off-state is D'. By a statc average method [4], the abovc equations are expressed as the next equation.

wherc A = (Zoq/KT) exp(v,q/KT). K is Boltzman constant and T is the array temperature in K [5]. From the abovc equation, the transfer function is obtained as

The bode diagrams are shown in Figs. 60 and b. On the condition where the feedback gains are same values, the capacitance of the transfer function is 1mF for Fig. 60 and

. .: -20 ol -30 -40'

3 5 10 10 I 0' 10

frequency, radis b

Fig. 6 , de d & r m ci Capacitance I mF h Capacitance IOmF

500

lOmF for Fig. 611, respectively. If the capacitance is changed on the condition where the variation of duty ratio is determined based on the nominal value, the p e r f o r m " of MPPT is degraded as follows. When the capacitance is larger than its nominal value, the systcm tends to be unsta- ble because the phase margin is poor. When the capaci- Vancc is smaller, the response of the system is bad because thc feedback gain becomes small.

3.2 Identification of capacitor We know that the fluctuation of the capacitance affects the perfoimance of MPPT. Thus, to avoid degrading the performance, we must obtain the information of the variation of capacitance, In this paper, we adapt thc model refcrence adaptive system to estimate the capacitance then we can get the accurate capacitance.

The voltage and current equation of capacitor is given by

where, v,, is the voltage of capacitor, V0 is the initial voltage of capacitor, i, is the current into the capacitor and C, is the capacitance or capacitor in parallel with the photovoltaic array. The above equation is expressed as follows:

A t . c s

71,(k) = vC(k - 1) + - ~ , ( k - 1) (30)

where, At is a sampling period. The adjustable model is expresscd as follows:

i,(k - 1) (31) At & ( k ) = V C ( k - 1) +

& ( k - 1)

where, Pc is the estimated voltage and er is the estimated capacitance.

The identification equation is given by

based on the model rcference adaptive system. Herc, y is a gain for the identification. We adopt the least mean square algorithm for the identification, because the calculation time is shorter [6].

3.3 Maximum power point tracking We adopt the pcrturbation and observation method to the inverter using Buck-Boost type chopper circuits, In our system, we can estimate thc capacitance based on the model reference adaptive system, then we get the accurate capacitance in any time. To correct the variation of duty ratio for MPPT by the estimated capacitancc, we can obtain the high performance of MPPT.

Fig. 7 shows the flowchart of proposed maximum power point tracking. First, the voltage and current of PV army and the capacitor current are detected through A D con- verters. The capacitance C, is estimated and the estimated capacitance is used to corrcct the variation of duty ratio for MPPT as shown in the following equation.

AD = A D , * Csn,/Cs(k) ( 3 3 ) where, AD, is the variation of duty ratio which is determined based on the nominal capacitance and CYn is the nominal capacitance, The input power P,,(/c) is calculated by thc detected values and compared to that calculated at the previous sampling P,s(/c ~ 1). Here, a is the increased or decreased value of duty ratio and n(k - 1) is the same at the previous sampling. The relationship between a( / ) and U(/< - 1) decides increase or decrease of the duty ratio. In this

[mi P M - u e m P,,~wI. A/, / , / , vC~/. 147, N ~ . 6, ,vove,,z/,r.i. 200n

/ interrupt start \ 7 - l

L

ic(k), V,(k), iJk) detection

7- -- --

I l /ES(k) calculation 1

L-.

I P,(k) calculation I

I 1 D(k)=D(k-l)+a(k)

L

1

L Fig.7 llowdturi rfMPPT

w q , the inaxiinum power point is tracking based on the perturbation and observation method.

4 Experimental results

Fig. 8 shows our experimental system in which six photovoltaic arrays are used. The DSP type TMS320C3 1 oTT1 is used to control the whole power system and calculate each switching pattern of IGBT. The switching frequency of the IGBTs (9.6kHz) is synchronised to the frequency ol‘ the utility grid line. The circuit parameters are listed in Table 1.

PV arrav

utility line

DSP system I L_~~~~~~~.~._.._......-....._I

Fig. 8 ,!~vpoiinmtri/ . sy tw~7

Table 1: Circuit parameters

L1 261iti Cl I O O O ~ F

L2 26bH C, 1OOOpF

C 12pF vac IOOV f 60Hz f,,., 9.6kHr

Fig. 9 shows the experimental output current aid vollage waveforms of the prototype photovoltaic power system. Here the waverorm or the voltage of the intermediate capacitor C’ and the output current of the utility grid h c are shown, with the output power of the invcrtcr being SOOW. It is found that the proposed inverter. supplies the AC power to the utility grid line with the power factor of nearly unity.

Fig. 10 shows the experimental result of capacitance estimation. In this Figure, the x-axis indicates the time and the y-axis indicates capacitance. In this experinlent, we use two

IEE Pm.-Elcwl,. POIIW A/$, Vu/, 147. No. 6, N o v w d r r ?OOO

store data

interrupt end --)

electrolytic capacitors whose nominal capacitaiices are 4700 and 2200pF. These capacitors are not degraded aid the error between the actual and nomiiial capacitance is within 5‘%,. On the condition, the gain for estimation y is 0.1, and the output powers in cstiinatiiig 4700 and 2200~F are 300W and 100W, respectively. At tiinc f = 1.5, the capacitance estimation starts. The results show that the estimated capacitor caii be estimatcd at the actual capacitance 4700 and 2200pF. When thc output power is large, the time of estimation Leiids to be short because the capacitor current becomes large.

As we confilmed that the accuratc capacitancc was obtained by the proposed method, the prototype system works when the maxiniiim power point is 400W. Fig. I 1 shows the experiniental result of MPP7 oil thc condition where the capacitor is changed from 2200pF7 lo 1000~iF. At time t = 5, the maximum power point tracking starts. After 25s, the system can be stable at the maxiniurn power poiiil instead of the fluctuation of the capacitance.

5 Conclusions

A perturbation and observation method with a capacitor identifier for the maximum power point tracking in a photovoltaic power system is proposed. The power inverter

using Ruck-.Roost chopper circuits is proposed for the system, and the capacitor in parallcl with the photovoltaic array is identified based on the motlcl refcrcnce adaptive system. From tlic simulated and experiinental results which were obtained from thc proposcd photovoltaic power sys- kin, the powcr or photovoltaic array can be transfcrred to the utility grid linc with nearly unity power factor at the maximum power point instead of the fluctuation of the capacitmce. All the observation and cxpcrimental results lead to the fact that our proposed irivcrtcr is suitable for the photovollaic power system utilised in the honie.

6 References

1 IIUA. C., LJN, J., and CI-[EN. C.: ‘~mplemcntation or con- trolled photovoltaic syslciir with pclk power lracking’, ‘ m s . b7d I&ctron., 1908, 45, (I), pp. 99 IO/ NAGAO, M., HOKIKAWA, [ I . , and IIARADA, I<.; ‘Pliotovollaic system using buck-boost I’WM invcrlcr’. 7iwnr. h.w Elcctr. Eng. Jpn., I994,114-D, pp. 885W92 TAKESFIITA. T., TOYODA, Y . . KIM, Y.J., and M4TSU1, N.: ‘DC voltage control and harmonic suppression of PIT coiivertcr’. SI’C-09-65, pp. 85-90 €IARADA, K., NINOMIYA, T., u rd GU, R.: ‘The fundamcnVals of switched-modc convertcrs’ (Corona Publishing Co., Tokyo, 1992) SUGIMOTO, H., and DONG, HUIAN: ‘A new schemc for maximum photovollaic p o \ w cl-iicking control’. PCC-Nagaokii’97, 1997, pp. 691 696 SHINNAKA, S.: ‘Adaplive algorithnis’ (Sangyo Toslro Co., Tokyo) KASA, N., W A , ‘T,, iurd IWAMOTO, 11.: ‘An inverter using buck- boost type chopper ciicu system’. Proceedings of 1

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Maximum power point tracking with capacitor identifier for photovoltaic power system