Technical Digest of the International PVSEC-14, Bangkok, Thailand, 2004 LO20-033

553

Time Responses of a Crystalline Silicon Solar Cell to Varying Light Inputs : Equivalent Components Determination

Nutthapon Wongyao, Krissanapong Kirtikara, Chaya Jivacate and Dhirayut ChenvidhyaClean Energy Systems Group (CES),

King Mongkut’s University of Technology Thonburi, Bangkok, Thailand.Corresponding Author: N. Wongyao <w.nutthapon@lycos.com>

ABSTRACT

Equivalent electrical components of a dynamic model ofsolar cells and modules have been determined from inputtingcells and modules with sinusoidal or periodic voltage signals.This paper describes methods that use light inputs so thatequivalent components of solar cells can be determined fromvoltage and current time responses.

1. IntroductionThe dynamic or AC equivalent circuit of a solar cell,

shown in Fig. 1 with its various electrical components,consists of resistance components that are voltage andfrequency independent, i.e. Rs and Rsh, and voltage dependentrd(V). The two capacitance components are voltagedependent transition capacitance CT(V) and voltage andfrequency dependent diffusion capacitance CD(V,ω) [1].For static or DC characteristics, only Rs and Rsh are adequatefor cell description. Few methods have illustrated howvarious dynamic components can be determined. They areusually based on frequency domain analysis, which is basedon electrical sinusoidal signals and periodic signals underdark or biased conditions[2][3].

Figure 1. AC equivalent circuit of a solar cell.

2. Theory

If we input a light square wave signal of intensity Io at afrequency ω to a cell connecting to a load Rl, its voltage andcurrent time responses can be observed. Rl can vary fromopen circuit condition to short circuit condition and thisdetermines operating points (V and I) of the cell. Therefore,we can expect that different Rl results in different rd, CT andCD. Considering that a square wave signal consists of infinitenumbers of frequencies, the cell electrical components,voltage and frequency dependent and independent ones, canbe determined. For square inputs, time responses would havedifferent characteristics owing to the voltage and frequencydependent nature of components.

We can show that for a square wave input the currenttime response i(t) and voltage response would usually take arising exponential form for the increasing intensity part and adecaying exponential for the falling intensity part. We note

that the time response depends on voltage and frequency, aswell as the time of observation. The time constant (τ) of acurrent response at any time t, voltage V and frequencyω canbe written as the equation

( )

( )

+

++

+

+

+=

shd

shdLs

Lsshd

shdTD

RRRR

RR

RRRRRR

CCVt

)(),,( ωτ

(1)

In principle, measurements at a few square wave inputs,or a few periodic waveform inputs, at different voltages,would allow one to determine various components of the cell.

3. Experment

We use a 10 cm-square x-Si solar cell with zero bias andinput it with pulsating light. Light intensity was varied twoways, i.e. as square wave of frequencies 0.1, 0.25 and 0.5 Hzand impulses at 10kHz. We report in this paper only theresults from the square wave light inputs. Rl is varied fromshort circuit condition, 0.1, 0.7 and 1.4 Ω and open circuitcondition.

We measure the voltage drop v(t) across the resistance Rland then calculate the current i(t). The rise time and fall timeat every 10% interval from zero to the maximum response ofi(t) are then determined.

4. Results and Discussion

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Time (s)

Vol

tage

(V)

light intensity

shot circuit

0.1 Ohm

0.7 Ohm

0.14 Ohm

open circuit

Figure 2. Voltage drop across Rl at the light frequency of 0.25 Hz.

We show as an example voltage time response of the cellilluminated with the square wave light at 0.25 Hz underdifferent load conditions. It can be clearly seen thatunder the same intensity and frequency, the voltage drops aredifferent. This is due to the fact that rd, CT and CD aredissimilar at different Rl.

554

Figure 3 shows the same results, however, voltagevalues have been normalized. The different time responsescan also be clearly observed.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Time (s)

V/V

max

light intensity

short circuit

0.1 Ohm

0.7 Ohm

0.14 Ohm

open circuit

Figure 3. Normalized voltage drop across Rl at the lightfrequency of 0.25 Hz.

We next illustrate the time response at different times ofthe rising and falling intensity parts of v(t). We calculatedv/dt at every time interval of 10%, from zero to themaximum response. This is also a measure of the rate ofchange of the time constantτ , from the equation (1) above.We plot these in Figures 4 and 5. It is evident that τ varieswith time t due to the voltage dependent rd, CT and CD. Inordinary circuits containing a number of voltage independentresistance and capacitance, time constant would remainunchanged at all times, t.

0.0

2.0

4.0

6.0

8.0

10.0

0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100

Time Interval (%)

dV/d

t in

1/m

s

short circuit

0.1 Ohm0.7 Ohm

1.4 Ohm

open circuit

Figure 4. Rate of change of normalized voltage drop acrossRl at the light frequency of 0.25 Hz, on the rising lightintensity part.

0.0

2.0

4.0

6.0

8.0

10.0

0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100

Time Interval (%)

dV/d

t in

1/m

s

short circuit

0.1 Ohm0.7 Ohm

1.4 Ohmopen circuit

Figure 5. Rate of change of normalized voltage drop acrossRl at the light frequency of 0.25 Hz, on the falling lightintensity part.

The effects of varying frequencies of light intensity onthe time response are shown in Figure 6. We calculate thechanges in time responses between 10% and 90% of the

maximum voltage values. It is clear that the time response isfrequency dependent due to frequency dependent CD.

We have not attempted to calculate the actual values ofrd, Rs, Rsh, CT and CD. However, methods lend themselves tosuch calculation.

0

200

400

600

800

1000

1200

short circuit 0.1 0.7 1.4 open circuit

Resistance (Ohm)

Tim

e (m

s)

0.5Hz (increasing intensity)

0.25Hz (increasing intensity)

0.1Hz (increasing intensity)

0.5Hz (decreasing intensity)

0.25Hz (decreasing intensity)

0.1Hz (decreasing intensity)

Figure 6. Rise times (from 10-90% of maximum) and falltimes (from 90-10% of maximum) of voltage response at various frequencies of light intensity.

5. Conclusion

We illustrate that voltage and current time responses of asolar cell can be used to determine its equivalent electricalcomponents. The concept can be extended for solar cellmodules.

ACKNOWLEDGEMENTS

The authors are grateful to the assistances given by theresearchers and graduate students of the Clean EnergySystems Group, the School of Energy and Materials, theFaculty of Engineering and the Pilot Plant Development andTraining Institute of KMUTT.

REFERENCES

[1] H.S. Rauschenbach, Solar cell array design handbook,Van Nostrand Reinhold, pp.52-63 (1980).

[2] D. Chenvidhya, “PV grid-connected systems forresidential distribution system: dynamic impedancecharacterization of solar cells and PV modules”, Doctorof Engineering Thesis, King Mongkut’s University ofTechnology Thonburi, (2002).

[3] D. Chenvidhya, K. Kirtikara and C. Jivacate, “A newcharacterization method for solar cell dynamicimpedance,” Solar Energy Materials and Solar Cells,Vol.80, Issue 4 pp.459-464 (2003).

[4] N. Wongyao, “Study of the effect of clouds onphotovoltaic grid connected systems”, Master ofEngineering Thesis, King Mongkut’s University ofTechnology Thonburi, (2003).