Research Article Performance of Series Connected GaAs ...downloads.hindawi.com/journals/aoe/2014/824181.pdf · Research Article Performance of Series Connected GaAs Photovoltaic Converters

Research ArticlePerformance of Series Connected GaAs Photovoltaic Convertersunder Multimode Optical Fiber Illumination

Tiqiang Shan and Xinglin Qi

TheThird Department, Mechanical Engineering College, Shijiazhuang 050000, China

Correspondence should be addressed to Tiqiang Shan; [email protected]

Received 26 September 2014; Accepted 6 December 2014; Published 21 December 2014

Academic Editor: Armin Gerhard Aberle

Copyright © 2014 T. Shan and X. Qi. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In many military and industrial applications, GaAs photovoltaic (PV) converters are connected in series in order to generate therequired voltage compatible with most common electronics. Multimode optical fibers are usually used to carry high-intensity laserand illuminate the series connected GaAs PV converters in real time. However, multimode optical fiber illumination has a speckledintensity pattern. The series connected PV array is extremely sensitive to nonuniform illumination; its performance is limitedseverely by the converter that is illuminated the least.This paper quantifies the effects ofmultimode optical fiber illumination on theperformance of series connected GaAs PV converters, analyzes the loss mechanisms due to speckles, and discusses the maximumillumination efficiency. In order to describe the illumination dependent behavior detailedly, modeling of the series connected PVarray is accomplished based on the equivalent circuit for PV cells. Finally, a series of experiments are carried out to demonstratethe theory analysis.

1. Introduction

An increasing application of GaAs PV converters is theconversion of monochromatic light into electrical power [1–5]. A typical application of this technology is the opticaltransmission of energy or power-by-light. Electrical energydelivery in power-by-light systems represents a promisingalternative for copper wires [6]. In such systems, the laserlight is mostly transmitted through an optical fiber anda PV receiver converts the optical energy into electricalenergy. These systems are used in places where the use ofelectrical energy is not recommendable, taking advantage ofthe properties of optical fiber such as electrical insulation,immunity from EMI, RF, and lightning. Examples of theseapplications are found in fields such as the oil industry,remote sensing, aerospace, explosions, high voltage powerlines, and nuclear plants [7, 8]. In these applications, therequired voltage of the electronic circuit is generally higherthan that supplied by a single GaAs PV converter; this valueis about 1 V.Therefore, GaAs converters are always connectedin series to match the required voltage. One of the principaladvantages to pursuing this technology is that electric power

can be generated in a far smaller volume than required bya DC-DC converter. This option is more compact and hasthe possibility of integrating the GaAs PV converters with anelectronic circuit.

Fiber illumination is important because some of today’soptical power transfer applications do not have line ofsight between the optical source and series connected PVconverters.The optical power is delivered via optical fiber to aregionwith insufficient volume to afford beam-shaping opticswith which to uniformly illuminate the series connectedPV converters. It has been shown that the least illuminatedconverter dominates the system performance [9]. It is thisdilemma that leads to the need for research into the perfor-mance of series connected GaAs PV converters under fibercoupled laser diode illumination.

Large core, step-index multimode optical fibers are usu-ally used to carry high power levels over short distances.Multimode optical fiber illumination has a speckled intensitypattern and the illumination efficiency is a function of theratio of the individual converter area within the series con-nected PV arrays to the speckle correlation area. Nonuniform

Hindawi Publishing CorporationAdvances in OptoElectronicsVolume 2014, Article ID 824181, 6 pageshttp://dx.doi.org/10.1155/2014/824181

2 Advances in OptoElectronics

Figure 1: The illumination profile of step-index multimode fiber.

illumination could reduce the efficiency of electric conversionand decrease the lifetime of PV converters [10]. This paperquantifies the effects of step-index multimode optical fibernonuniform illumination on the performance of series con-nected GaAs PV converters, analyzes the loss mechanismsdue to speckles, and discusses the maximum illuminationefficiency undermultimode illumination. In order to describethe illumination dependent behavior detailedly, an analyticalmodel of the series connected PV converters is accomplishedbased on the equivalent circuit for PV cells. To demonstratethe theory analysis above, finally, a series of experiments arecarried out.

2. Multimode Optical Fiber Illumination

The operating voltage of the series connected PV convertersin the string is the sum of the operating voltages of the sub-converters, whereas the current through each subconverter isthe same and equal to the current of the external circuit. Theconverter generating the lowest short circuit current, referredto as the individual mismatched converter, determines thesystem current and the device performance [11].Therefore, inthe case of series connectedGaAs PV converters, nonuniformillumination can cause a significant efficiency drop. Thismakes the spatial profile of the illumination source a criticalparameter.

2.1. Mean Speckle Correlation Area. The illumination profileproduced under step-index multimode optical fiber illu-mination contains speckles due to the interference of thedifferent modes. Speckles are random regions of fluctuationin the intensity profile [12]. If the speckle is large enoughit can create a situation where converters within a seriesconnected GaAs PV array are weakly illuminated, therebylimiting the current. The illumination profile from a step-index multimode fiber shown in Figure 1 is speckled; theillumination efficiency is a function of the ratio of theindividual converter area to the speckle correlation area.

This section is based on a detailed discussion of thestatistical properties of speckle [13]. The mean speckle corre-lation area is calculated by evaluating the normalized mutualintensity of the speckled intensity pattern incident uponthe series connected PV array [13, 14]. The mean specklecorrelation area of an intensity pattern propagating from astep-index multimode optical fiber is given by

𝑆𝐶 =𝜆2𝑧2

𝜋𝑎2, (1)

where 𝑎 is the core diameter of the fiber, 𝜆 is the wavelength,and 𝑧 is the propagation distance from the fiber.

The speckle correlation area is directly related to both thepropagation distance and wavelength and inversely related tothe fiber core diameter. Keeping the fiber core diameter to amaximumwhileminimizing thewavelength and propagationdistance is critical in reducing the size of the speckle andtherefore increasing the illumination efficiency.

2.2. Illumination Efficiency. The amplitude of the generatedphotocurrent, 𝐼

𝑃, is determined by

𝐼𝑃= 𝐼𝐿𝑆𝐷𝑅, (2)

where 𝐼𝐿is the irradiance (W/cm2), 𝑆

𝐷is the area of a

single converter (cm2), and 𝑅 is the wavelength dependentresponsivity (A/W) [15].

Speckle is a random phenomenon and as such mustbe treated statistically. The illumination efficiency, 𝐸

𝐼, is

determined by the converter that is illuminated the least. Tobegin this discussion, we define 𝐸

𝐼for multimode optical

fiber illumination as

𝐸𝐼=𝐼𝑆min𝑆𝐷𝑅

⟨𝐼𝑆⟩ 𝑆𝐷𝑅=𝐼𝑆min⟨𝐼𝑆⟩

=⟨𝐼𝑆⟩ − 𝜎𝐼

⟨𝐼𝑆⟩

= 1 −𝜎𝐼

⟨𝐼𝑆⟩= 1 −

1

√𝜇,

(3)

where ⟨𝐼𝑆⟩ is the mean integrated speckled intensity across

any individual converter within the array, 𝐼𝑆min is the

minimum integrated speckled intensity across an individualconverter within the array, and 𝜎

𝐼is the standard deviation of

the integrated speckle pattern [14].The variable 𝜇 is a function of the ratio of the converter

area, 𝑆𝐷, to the speckle correlation area, 𝑆

𝐶, and is defined as

⟨𝐼𝑆⟩

𝜎𝐼

= √𝜇. (4)

An exact expression for𝜇 is found for a square aperturewhichis analogous to an individual square PV cell [14],

𝜇 = [√𝑆𝐶

𝑆𝐷

erf (𝜋𝑆𝐷𝑆𝐶

) − (𝑆𝐶

𝜋𝑆𝐷

)(1 − exp(−𝜋𝑆𝐷𝑆𝐶

))]

−2

.

(5)

Advances in OptoElectronics 3

I

V

+

−

Isc Is

Rs

Rsh

(a)

I

V

+

−

Isc Is1 Is2

Rs

Rsh

(b)

I

V

+

−

Isc Is

Rs

(c)

Figure 2: PV cells equivalent circuit models, (a) single-diode model, (b) double-diode model, and (c) simplified model.

This equation is then modified for a rectangular PV cell andis now in the form of

𝜇 = {[√𝑆𝐶

𝐿2

1

erf (𝜋𝐿2

1

𝑆𝐶

) − (𝑆𝐶

𝜋𝐿2

1

)

× (1 − exp(−𝜋𝐿2

1

𝑆𝐶

))]

× [√𝑆𝐶

𝐿2

2

erf (𝜋𝐿2

2

𝑆𝐶

) − (𝑆𝐶

𝜋𝐿2

2

)

× (1 − exp(−𝜋𝐿2

2

𝑆𝐶

))]}

−1

,

(6)

where 𝐿1and 𝐿

2are the dimensions of the rectangular cell.

The minimum integrated speckled intensity is definedas being one standard deviation below the mean in (3). Assuch, it is an upper limit for the illumination efficiency. Theactual value may be lower due to the probability of havinga value of 𝐼𝑆min that is lower than one standard deviationbelow the mean. In addition, nonuniform intensity envelopeacross the series connected PV converters will also lower theillumination efficiency.

3. Mathematical Model

Modeling of the series connected PV converters is accom-plished based on the equivalent circuit for PV cells. Thetraditionalmodels of PV cells represented by a current sourcein parallel with one or two diodes are shown in Figure 2. Thesingle-diode model shown in Figure 2(a) includes four com-ponents: photocurrent source, diode parallel to the source,series resistor 𝑅𝑠, and shunt resistor 𝑅sh. In double-diodemodel shown in Figure 2(b), an extra diode is added forbetter curve fitting in low irradiance level conditions [16]. Inmost cases, due to the exponential equation of a p-n diodejunction, it is difficult to determine these five parameters insingle-diode model or six parameters in double-diode modelmathematically. Since the shunt resistance 𝑅sh is large, it canusually be neglected [17].The single-diodemodel anddouble-diode model can, thus, be simplified into Figure 2(c), anequivalent circuit model of this study.

The light-generated current of the PV cell dependslinearly on the illumination. At a certain optical power 𝑃inwith thewavelength 𝜆, the short circuit current 𝐼sc for an idealPV cell is given by

𝐼sc =𝑞𝜆

ℎ𝑐𝑃in𝑄ext (𝜆) , (7)

where ℎ is the Planck constant, 𝑐 is the velocity of light invacuum, 𝑞 is the electronic charge, and𝑄ext(𝜆) is the externalquantum efficiency (QE).

According to the simplified model of PV cells, theilluminated current 𝐼 and voltage 𝑉 are represented as

𝐼 = 𝐼sc − 𝐼𝑠0 (exp(𝑉 + 𝐼𝑅

𝑠

𝑉𝑡

) − 1) , (8)

where𝑉𝑡= 𝑛𝑘𝑇/𝑞, on the assumption that𝑇 = 300K and 𝑛 =

1, 𝑉𝑡≈ 25mV, and 𝐼

𝑠0, 𝑅𝑠, and 𝑛 are the saturation current,

series resistance, and ideality factor, respectively.In respect that exp((𝑉+𝐼𝑅𝑠)/𝑉𝑡) ≫ 1 [18], the illuminated

current 𝐼 and voltage 𝑉 can be represented as

𝐼 = 𝐼sc − 𝐼𝑠0 exp(𝑉 + 𝐼𝑅𝑠

𝑉𝑡

) . (9)

At the open circuit state, the saturation current 𝐼𝑠0is obtained

as

𝐼𝑠0= 𝐼sc exp(−

𝑉oc𝑉𝑡

) . (10)

The output electrical power 𝑃out of PV cells is given by𝑃 = 𝐼𝑉. In principle, the current 𝐼

𝑚and the voltage 𝑉

𝑚

at the maximum output power can be obtained from thecondition of 𝑑𝑃/𝑑𝑉 = 0, but the educed expressions are ofgreat complexity. According to Antonio and Steven [18], oneempirical expression can be used to represent this relation:

𝐹𝐹 =𝐼𝑚𝑉𝑚

𝐼sc𝑉oc= 𝐹𝐹0(1 − 𝑟

𝑠) , (11)

where 𝐹𝐹0= (Voc − ln(Voc + 0.72))/(Voc + 1), Voc = 𝑉oc/𝑉𝑡, and

𝑟𝑠= 𝑅𝑠𝐼sc/𝑉oc.

Using (11), the series resistance is given by

𝑅𝑠= (1 −

𝐹𝐹

𝐹𝐹0

)𝑉oc𝐼sc. (12)


All expressions mentioned above would be effectual, oncondition that Voc > 15 and 𝑟𝑠 < 0.4. In general, the precisionis higher than 1% [18]. For GaAs PV cells, it is reasonable toassume that 𝑉oc = 1.0 V; thus, Voc = 40 > 15, 𝐹𝐹0 = 0.89.Another condition is that 𝑟

𝑠< 0.4; namely, require 𝐹𝐹 >

0.6𝐹𝐹0= 0.53; in fact, this condition can be reached easily

for GaAs PV cells.When 𝑁 identical PV converters are connected in series

and placed under nonuniform illumination, the 𝐼-𝑉 curve ofseries connected PV converters is best expressed in the formof a summation of logarithmic terms,

𝑉 (𝐼) =

𝑁

∑

𝑖=1

[𝑉𝑡ln(

𝐼sci − 𝐼

𝐼𝑠0

) − 𝐼𝑅𝑠𝑖] ,

𝑉 (𝐼) =

𝑁

∑

𝑖=1

[𝑉𝑡ln(

𝐼sci − 𝐼

𝐼𝑠0

) − 𝐼(1 −𝐹𝐹

𝐹𝐹0

)𝑉oc𝐼sci] ,

(13)

where 𝐼 is limited by the illumination current generated fromthe least illuminated converter (𝐼sci).

4. Experiments and Analysis

The current limiting effect of the least illuminated converteris illustrated with an experiment where an illuminated seriesconnected GaAs PV array was partially shadowed.The seriesconnected GaAs PV array consists of 6 converters. In thisexperiment, a 105𝜇m core diameter, 0.22NA step-indexmultimode optical fiber is adopted. PV converters based onGaAs are mostly used for the conversion of red or near-infrared laser light. In our experiments, the illuminationsource is an 808 nmmultimode laser with amaximumoutputpower of 94WCW, and the spectral width of the lasersource is about 4 nm. An entire row consisting of three seriesconnected cells was shadowed incrementally and the shortcircuit current was recorded. As shown in Figure 3, there is alinear relationship between the percent shadow and percentdecrease in output current. The current is greatly reducedwhen the entire row is shadowed. Diffraction and reflectionaccount for the less than 100% decrease in output currentwhen the entire row is completely shadowed.

Illumination efficiency when using multimode illumina-tion is dependent on the ratio of the PV converter area to themean speckle correlation area. This theory is demonstratedby measuring the output current relative to the optical powerincident upon the series connected PV converters at thedistances of which the speckle correlation area and powerwere determined. To achieve a wider ratio of PV converterarea to mean speckle correlation area, the mean specklecorrelation area is increased by increasing the distancebetween the series connected PV converters and the fiber.The decreased illumination intensity at the greater distanceswas compensated for in the experimental calculations. Theillumination efficiency is calculated by

𝐸𝐼 =𝐼out𝑃𝑢𝑅, (14)

100

80

60

40

20

0

Curr

ent d

ecre

ase (

%)

0 20 40 60 80 100 120 140

Shadow (%)

Figure 3:The current limiting effect of the least illuminated convert-er.

1.0

0.8

0.6

0.4

0.2

0.0

Illum

inat

ion

effici

ency

(%)

0 10 20 30 40 50 60 70 80

w

Calculated resultsMeasured results

Figure 4: The illumination efficiency as a function of PV converterarea to mean speckle correlation area.

where 𝐸𝐼is the ratio of the measured output current, 𝐼out, to

the current that would be produced given a uniform beam,𝑃𝑢.Figure 4 shows the experimental results with the illu-

mination efficiency plotted as a function of the ratio ofPV converter area to mean speckle correlation area, 𝑤. Themeasured results are found to be in close agreement with thetheoretical prediction in trend, but the measured efficienciesare lower than predicted. This can be explained by the waythat the illumination efficiency is defined. As mentionedearlier, the illumination efficiency is defined as the minimallyilluminated converter in the series connected PV array beingilluminated at a level that is a standard deviation belowthe mean. Probabilities exist that the minimally illuminatedconverter will be illuminated at a level lower than a standarddeviation below the mean. In addition, the intensity envelope

Advances in OptoElectronics 5

35

30

25

20

15

10

5

0

Curr

ent (

mA

)

0 1 2 3 4 5 6 7

Voltage (V)

w = 10

w = 20

w = 30

w = 40

w = 50

Figure 5: 𝐼-𝑉 characteristics for different ratios of PV converter tomean speckle correlation area.

was nonuniform which also contributes to a decrease inillumination efficiency.

Experimental determination of the 𝐼-𝑉 characteristics ofseries connected GaAs PV converters is required for its appli-cation. The efficiency can be calculated from the maximumpower point of the measured 𝐼-𝑉 curve and the determinedillumination efficiency. The optical loss that results fromshadowing by the metal lines and from sacrifice of activelight receiving area for formation of the isolation channelswas compensated for in the experimental calculations. Inprevious experiments, the conversion efficiency of 51.9% at1W/cm2 has been achieved for a single GaAs PV converterwith 𝐼sc = 36.38mA, 𝑉oc = 1.07V, and 𝑃max = 31.14mW.Figure 5 shows the 𝐼-𝑉 characteristics of series connectedPV converters measured at 1W/cm2, for different values of𝑤 (10, 20, 30, 40, and 50).The measured data can serve to theinfluence of nonuniform illumination that worsen the deviceperformance.

Also presented in experiment results are properties of theshort circuit current, open circuit voltage, maximum outputpower, and conversion efficiency of the series connectedGaAs PV converters. As seen in Table 1, the open circuitvoltage increases slightly with 𝑤 increasing; an importantfactor penalizing the efficiency is the decrease in the shortcircuit current that results from the speckle undermultimodeoptical fiber illumination.

5. Conclusions

Multimode optical fiber illumination has a speckled intensitypattern.Therefore, themain subject of this paper is to evaluatethe effects of step-index multimode optical fiber nonuni-form illumination on the performance of series connectedGaAs PV converters. The current limiting effect of the leastilluminated converter is illustrated with an experiment. As

Table 1: Measured results of the performance parameters.

𝑤 𝐼sc (mA) 𝑉oc (V) 𝑃max (mW) 𝜂 (%)10 23.08 5.93 109.5 30.420 26.24 6.04 126.8 35.230 27.61 6.18 136.5 37.940 28.44 6.23 142.0 39.450 29.01 6.30 146.4 40.7

shown in experiment results, there is a linear relationshipbetween the percent shadow and percent decrease in outputcurrent of the series connected PV converters under mul-timode illumination. Illumination efficiency is determinedby the ratio of the converter area to the speckle correlationarea. Theoretical study demonstrates that keeping the fiberdiameter to a maximum while minimizing the wavelengthand propagation distance is critical in reducing the size ofthe speckle and thus increasing the illumination efficiency.Although the measured data of the illumination efficiencyis lower than predicted due to the probabilities that theminimally illuminated converter will be illuminated at alevel lower than a standard deviation below the mean, themeasured results are found to be in close agreement withthe theoretical prediction in trend. The data in both casesshows that illumination efficiency decreases rapidly for ratiosless than 10. In addition, the 𝐼-𝑉 characteristics of seriesconnected PV converters measured at 1W/cm2, for differentconverter/speckle ratios, serve to the influence of the specklesthat worsen the device performance.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

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Research Article Performance of Series Connected GaAs ...downloads.hindawi.com/journals/aoe/2014/824181.pdf · Research Article Performance of Series Connected GaAs Photovoltaic Converters