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# Modelling Photovoltaic Systems Using PSpice - 45271 09

(Parte **1** de 4)

9 Small Photovoltaics

Summary

This chapter addresses common PV practical applications composed of small numbers of PV cells or modules operating under natural or artificial light. An effective irradiance value is calculated to take into account different spectra of artificial light. Correspondence between radiometric and photometric quantities is used. The random generation of I(V) characteristics of small PV modules is performed and Monte Carlo randomly generated numbers are used to generate PSpice time series of radiation, which can be used to see the PV system operation in detail. This method is used to show how a solar pocket calculator works, as well as a flash light and a street light system.

9. I Introduction

Photovoltaic systems are known by the average person, not only by the media coverage of large PV plants or autonomous standalone systems, but also, by the PV power supply of small systems in a wrist watch, a pocket calculator, a car sunroof and many other applications where small PV arrays are a cheap solution for consumer applications or professional systems. This chapter covers the specific issues raised by these small PV systems.

9.2 Small Photovoltaic System Constraints

In general, small photovoltaic systems are used either as an entirely autonomous system or as an auxiliary power supply to extend the life of the system beyond the lifetime of a battery pack. This means that in general these systems include a battery and hence most of the concepts developed in Chapter 7 for standalone systems are still valid. There are, however, some differences. Because the solar (or more generally light) energy availability is often unpredictable (think for instance in a wrist watch), the nature and spectrum of the ‘light’

246 SMALL PHOTOVOLTAICS energy is very different from the spectrum and radiation data used in conventional standalone or grid connected systems (think for instance in a desk light). Moreover the load can also be of a different nature than that of standard home appliances, for example

LEDs can be a common load used in lighting applications. And finally the overall system requirements may be of a different nature because the application may only require to enforce the battery supply but not fully balanced autonomy from solar energy. These specific and different matters are the subject of this chapter.

9.3 Radiometric and Photometric Quunfitr’es

Some small photovoltaic systems operate under artificial light in offices or homes and this raises the question of how to design such systems, when the electrical properties of solar cells or modules are generally known under standard illumination conditions (either

AM1.5 G or AMO). Artificial light has a different spectral irradiance than the sunlight and, moreover, the measure of artificial light magnitudes is given in photometric units rather than in radiometric units. The main difference is that photometric quantities are a measure of visible light and are weighted by the responsivity of the human eye by means of the function V(X), which is the CIE sensitivity curve. In fact there are two CIE sensitivity curves, one for the photopic response of the eye and one for the scotopic (eye adapted to the dark) response.

For the purpose of this book we will refer to photopic response. Figure 9.1 shows the CIE photopic responsivity curve, which is given in relative values normalized to unity at a wavelength of 550 nm. The numerical data are available in the file ‘cie.st1’ in Annex 9.

l.E-05 I I 360 460 560 660 760

Wavelength (nm)

Figure 9.1 Photopic CE responsivity curve V(X)

Table 9.1 summarizes some important magnitudes and units for comparison. In general a small PV system will be receiving light measured in units of illuminance, which is what really will tell us how much energy is available to the solar cells. On the other hand, artificial light sources are rated by two magnitudes:

0 electrical power consumed (given in watts); and 0 luminous radiant flux produced (given in lumen).

LUMINOUS FLUX AND /LfUM/NAlyQ ZW

Table 9.1 Radiometric and photometric magnitudes

Radiometric Photometric Conversion factor 555m magnitude Units magnitude Units of wavelength (ptdqxc flh)

Radiant flux W Luminous flux lm (lumen) 1 lumen = I.MA x 1~~ w

Irradiance Radiant Wlsr Luminous Im/sr 1 Im/sr = 1 cadel 1w=683bm

W/m2 G Illuminance Lux 1 lux = 1 Id2 1 W/m2 = 683 lux Gt intensity intensity

9.4 luminous Flux and Illuminance

The transformation from the luminous radiant flux produced by a light sour@e to the illuminance received by the PV system depends on the relative geometry of the source- receiver path. The following concepts are of interest.

9.4.1 Distance square law

The steradian (sr) is the unit of a solid angle. The solid angle subtended by the surface of Its sphere at its centre is equal to 47r steradians. Consistent with this definition, if we are interested in the relative value of the illen- at two distances of the radiant source, dl and d2, a given luminous flux of one lumen ~21 produce illuminance values related by:

which is the distance square law.

9.4.2 Relationship between luminous flux and illuminance

The illuminance G, in lux at a given distance of a light source relates to the luminous Rux Q, in lumen, considering the geometry in Figure 9.2, as

Figure 9.2 Geometry used to define photometric magnitudes

248 SMALL PHOTOVOLTAICS where d is the distance between source and target and $2 is the solid angle of the lamp. If the lamp can be considered as a point isotropic source, then the solid angle is 47r. If the radiation is restricted to a smaller solid angle due to shadowing, then the solid angle in equation (9.2) is given by,

R=47r- where Q is the shadowed angle. 27r(l- a cos -) 2 (9-3)

Example 9.1

Consider that we measure 20 lux at a distance of 5 m from a street light. Calculate the value of the luminous flux of the lamp which has a shadow angle of 60".

0 = 47~ - 274 1 - cos 30") = 1.619 sr (9-4) Then the luminous flux is calculated:

at, = 20(5)211.619 = 5809.5 lm (9-5)

9.5 Solar Cell Short Circuit Current Density Produced by an Artificial Light

The short circuit current produced by an illuminated solar cell was calculated in Chapter 2. Remember that the short circuit current density is given by,

0 J,, = lo O.SOSQE(X)XIx dX (9-6) which is the integral over all wavelengths of the spectral short circuit current density when the solar cell is illuminated by a standard spectrum such as AM1.5; the irradiance is given by the integral of the spectral irradiance Zx.

G=J ZxdX 0 (9.71

When an artificial light is concerned, the information we generally have is the value of the illuminance G, provided by the artificial light at a given distance from the source. The illuminance of a light spectrum is defined by:

SOLAR CELL SHORT CIRCUIT CURRENT DENSITY PRODUCED BYAN ARTIFICJAL UGM’ 249 where K,,, is the luminous efficacy and equals 683 lux/W/m2 for a photopic CEE curve, dxkml is the spectral irradiance of the artificial light, and V(A) is the photopic CIE eye ~~sivi~y (for daylight conditions).

The spectrum of artificial light sources is normally available in normalized fam to a maximum value of unity, Z,+rt),Iom, and an example is shown in Figure 9.3 [9.%].

300 400 500 600 700 800 Wavelength (nm)

Figure 9.3 Typical spectrum of a fluorescent light (after normalization, from Alex Ryer, in hap:// w.int1-1ight.codhandbook Light Measurement Handbook, 1988)

It is convenient to select a value for a scale factor, K, such that the value of the illuminance of the normalized artificial light spectrum is 1 lux as follows:

Now, the integral in equation (9.9) can be calculated using a PSpice file as follows:

I *normalization.cir .include fluorescent-rel.stl .includecie.stl .param k=0.0292 vfluor 90Ostimulusvfluorescent-re1 vcie 91 0 stimulus vcie elux92Ovalue={sdt~v~90~*v~91~*k*683*le6~};computestheilluminance . tran 0. Olu 0.770~ 0.38~ 0. Olu .probe . end where the fluorescent light normalized spectrum and the CIE curve are both included by .stl files as sources in nodes (90) and (91), respectively. The computation of the integral of equation (9.9) is performed by the e-device ‘elux2’ for given values of the normalization

250 SMALL PHOlOVOLlAlCS 1 .ov

0.5V ov 350ns 400ns 450ns 500ns 5501-1s 600ns 650ns 700ns 75011s 800ns

Time V(90) 0 V(91) v V(92)

Figure 9.4 Spectral irradiance of a fluorescent light and CIE responsivity of the human eye, both normalized to a maximum value of 1. Integral in equation (9.9) using K = 0.0292 gives a value of 1 lux after integration in the visible spectrum. Wuming: the x-axis shows the wavelength in units of nm constant K and of the illuminance value G, as illustrated in Figure 9.4, where the wavelength integral of the product of the spectral irradiance and the CIE curve is shown using a value for K = 0.0292 W/m2pm. With this value the integral in equation (9.9) is unity.

Once the value of K is known, the spectral irradiance corresponding to an illuminance of 1 lux is given by:

The value of the short circuit current produced by a solar cell when illuminated by this artificial light of I lux illuminance can be calculated provided the quantum efficiency of the solar cell is known:

(9.1 1)

Therefore, in the general case of an illuminance G, which is different from unity, the short circuit current collected will be:

Jsc(urt) = Gu0.0292 O.~O~QE(X)~IA- 1- (urt) dX (9.12) 0 s:

Figure 9.5 shows the spectral current density calculated for the silicon solar cell described and simulated in Chapter 2, but in this case comparing the effect of the light

SOLAR CELL SHORT CIRCUIT CURRENT DENSITY PRODUCED BYAN ARTIFICIAL DGM 25p source spectrum, namely AM1.5 G at 100 W/m2, with a fluorescent light producing ipn illuminance of 5000 lux. For the artificial light computation the ‘jsc-silicon-artcir’ hs&ed in Annex 9 has been used, calling a new ‘jsc-art.lib’ subcircuit, which is also Me& b Ihe Annex. The result of the simulation is shown in Figure 9.5.

8.0rnV

6.0rnV 4.0rnV

2.0rnV ov 0.3~s 0.4~~ 0.5~s 0.6~s 0.7~~ 0.8~ 0.91s 1.0p l.lps 1aS

X V(10) + V(1) A V(1010) + V(101) Tirne

Figure 9.5 Comparison between the spectral current density under AM1.5 G and 100Wh2 (upper graph) and under 5000 lux artificial fluorescent light. Warning: x-axis is the wavelength in micram and

the y-axis is the spectral current density in mA/cm2pm

As can be seen the longer wavelengths of the spectrum present in the AM15 light spectrum produce higher density current than in the fluorescent light, which has pr long wavelength content.

9.5.1 Effect of the illuminance

As shown above, neglecting temperature effects on the short circuit current, the effect of the value of the illuminance on the short circuit current is linear:

where Jsc~. (art) is the value of the short circuit current density for a value of the illuminance of 1 lux.

9.5.2 Effect of the quantum efficiency

As described in Chapter 2, the value of the quantum efficiency at a given wavelength depends on the values of the reflection coefficient, absorption coefficient, geometrical

252 SMALL PHOTOVOLTAICS parameters such as the thickness of the cell and emitter depth, semiconductor parameters such as lifetimes and mobilities, and on technology parameters such as the surface recombination velocities.

If we run the simulation of a solar cell with several values of these parameters, the results can be compared as shown in Table 9.2.

Table 9.2 Comparison of the short circuit currents of several solar cells and light sources

Cell#2 Baseline with Cell#3 is equal to surface recombination Cell#2 with enhanced Baseline cell#l velocities 1 cds diffusion lengths

J,, (AM1.5 @1 kW/m2) 31.811 32.672 36.67

Jsc( 1 lux) 121 123 128.9 Ratio 3.8 x lop6 3.79 x 3.51 x low6

(mA/cm2) (nA/cm2) (1 ludAM1.5)

As can be seen the ratio of the generated short circuit current density between artificial light and sunlight, depends little on the solar cell parameter values. Then for a silicon solar cell it can be estimated that approximately,

(9.14)

Of course, different solar cells and different light sources will require a new and specific

If the solar cell is illuminated by an arbitrary combination of natural and artificial light, computation of this ratio.

then the resulting short circuit current considering equation (9.14) is given by:

(9.15) where G,f is the effective irradiance, which is given (taking into account that G, = IOOO), by :

Gefs = G + 3.8 x 10-3G, (9.16)

Exumple 9.2

Consider a light source of 8000 lumen in a room and we have a pocket calculator with a small solar array of four devices in series with a total surface of 2cm2. The light has a

ILLUMINANCE EQUIVALENT OFAM1.5 G JPFC7WM 241 reflector which aproximately produces a hemispherical radiation of the light. The dimnce from the light source to the top of the table where the pocket calculator is located is 1.6 m. The solar array has been rated at standard AM1.5 conditions to produce 20mA/cm2 sbrt circuit current density. Calculate the short circuit current produced under the artikiaf bgbk assuming that the operating temperature is 25 "C. The first thing to calculate is the illuminance received by the solar array.

Qv 8000 G --=-- - 497.6 lux '' - d2R 1.622~ (9.17) where a solid angle of 2n has been used to account for the hemispherical radiation. Next the short circuit current density is calculated,

JsCcarl~ z 3.8 x 10-6Js,(A~l,s~G, = 3.8 x x 20 x x 497.6 = 37.8p4/em2 (9.18)

As the array is made of four cells in series and the area of one solar cell is 0.5 an2, the total short circuit current is 37.8 x x 0.5 = 18.9pA (9.19)

9.6 l(V) Characteristics Under ArtXkial light

As has been shown in Section 9.5 the short circuit current under artificial light can be calculated provided the quantum efficiency of the solar cell, light spectrum and illuminmce are known. The open circuit voltage and the full Z(V) characterisitics can also be known because the dark saturation density current is independent of the light spectrum as described in Chapter 2, and hence the value calculated from the rated values of short circuit current and open circuit voltage under AM1.5 standard conditions is valid for artificial light calculations as well.

9.7 Illuminance Equivalent of AM 1.5 G Spectrum

Indoor photovoltaic devices receive a random mixture of natural and artificial light. The mixture is random in time for the same user and in location or activity for different users. Natural light in office spaces or homes will have a different spectral distribution than the standard AM1.5 we are using in this book, and depends on the environment. Again, as the data available from solar cell manufacturers have been measured under AM1.5 G standard

254 SMALL PHOTOVOLTAICS spectra a conversion factor or equivalence between the irradiance and illuminance of the AM1.5 spectrum will be useful. The illuminance of the AM1.5 G spectrum (1000 W/rn2) is given by:

760 nm G -=.I ZxK,,,V(X)dX '' - 962.5 3mnm (9.20) where again I, is the spectral AM1.5 irradiance. The reference irradiance of AM1.5G (1000 W/m2) is given by

G -- 'ow mIxdX - 962.5 (9.21)

(Parte **1** de 4)