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OPTICAL RADIATION
MEASURMENTS FORPHOTOVOLTAIC APPLICATIONS:
INSTRUMENTATION
UNCERTAINITY ANDPERFORMANCE
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OVERVIEW
The basic calibration and measurement
uncertainty associated with this instrumentation
are based on guidelines described in ISO and
BIPM guide.
ThereThere areare twotwo typestypes ofof radiometricradiometric instrumentationinstrumentation usedused forforcharacterizingcharacterizing broadbandbroadband andand spectralspectral irradianceirradiance forfor PVPVapplicationsapplications
1.1. Spectral radiometric measurementSpectral radiometric measurementsystems(systems( spectroradiometersspectroradiometers))
2.2. Broadband radiometers (Broadband radiometers ( pyranometerspyranometers andandpyrheliometerspyrheliometers).).
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1.1. Spectro radiometers: Used toSpectro radiometers: Used to
measure spectral distributionmeasure spectral distribution
of solar simulators and naturalof solar simulators and natural
sunlight.sunlight.
Spectroradiometers & Broadband Radiometers
2.2. Broadband radiometers: Used toBroadband radiometers: Used to
access solar recourses foraccess solar recourses for
renewable applications andrenewable applications and
develop and validate broadbanddevelop and validate broadband
solar radiation models forsolar radiation models for
estimating system performanceestimating system performance
outdoorsoutdoors
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SpectroradiometerSpectroradiometer includeinclude classicclassic scanningscanning gratinggrating monchromatormonchromator andand diodediode arrayarrayspectroradiometerspectroradiometer.. NISTNIST opticaloptical techtech.. divisondivison providesprovides aa calibratedcalibrated 10001000WW incandescentincandescent
tungstentungsten halogenhalogen lamplamp withwith tabulatedtabulated spectralspectral irradianceirradiance data(data( 3030 wavelength)wavelength) forfor thesethese
radiometersradiometers..
Spectroradiometer Calibration & Measurement
Fig. shows calibration geometry for diode array spectrometer.Fig. shows calibration geometry for diode array spectrometer.
500 mm
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Graph: Response curve
Wavelength
(nm)
Typical
Value
(W/cm*-3)
Relative expanded
uncertainty in %,k=2
250 0.2 1.8
350 7 1.1
655 170 0.9
900 215 1.1
1600 115 1.4
2400 40 4.4
Table: Statement of uncertainty withTable: Statement of uncertainty withspectral calibration (NIST)spectral calibration (NIST)
Spectroradiometer Calibration & Measurement
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Historically total uncertainty) was computed asHistorically total uncertainty) was computed as
U*2=U*2= (bias)*2 +(bias)*2 + (2 x random)*2(2 x random)*2
Random values were related to variance of measured data sets.Random values were related to variance of measured data sets.
Biases were estimates of deviations from a true value.Biases were estimates of deviations from a true value.
For uncertainty measurement GUM defines two types of values:For uncertainty measurement GUM defines two types of values:
Type A values derived from statistical methodType A values derived from statistical method
Type B values derived by other means such as scientific judgment, experience,Type B values derived by other means such as scientific judgment, experience,
specs. ,comparisons.specs. ,comparisons.
GUM replaces historical factor of 2 with coverage factorGUM replaces historical factor of 2 with coverage factorkk andand
U*2=U*2= (Type B)*2+(Type B)*2+ (kx Type A)*2(kx Type A)*2
U is expanded uncertainty and kis in the range 2 to 3 for confidence intervals ofU is expanded uncertainty and kis in the range 2 to 3 for confidence intervals of
95% and 99% respectively.95% and 99% respectively.
Uncertainty Analysis
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For each parameter Type A and Type B estimates are based on specs. OfFor each parameter Type A and Type B estimates are based on specs. Of spectroradiometerspectroradiometer,,
previous measurements or educated estimates.previous measurements or educated estimates.
Lab Spectral Calibration Uncertainly
Table: Uncertainties for 95% confidence interval, Spectroradiometer calibration 250 nm to 1600 nm
Type A (Statistical) UNC(%) STDUNC(%)
distance(2/500mm) 0.8 0.4
wavelength precision 0.01 0.005
power current (Irr dl/di%)* 0.2 0.2
NIST lamp precision 1.13 0.565
detector sig/noise 1.00E-04 5.00E-04
sig detection system 1 0.5
temp sensitivity 1 0.5
observed noise 3 1.5
Type B UNC(%) STDUNC(%)
NIST transfer 1.82 0.91
distance 0.8 0.4
Stray Light 1.00E-04 0.00005
Lamp
Alignment 0.1 0.05
Power Current* 0.2 0.2
shunt bias(-
.000002) 0.04 0.02
wavelength 0.01 0.005
Effective Degree of freedom >100
Coverage Factor (k) 2
Confidence Interval 95%
Expanded Uncertainty 4.15%
TOTAL UNCERT(%) STD UNCERT(%)
TYPE A 3.6 1.808
TYPE B 2.001 1.015
Combined 4.154 2.077
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An analysis similar to that in previous table can be conducted on wavelength by wavelengthAn analysis similar to that in previous table can be conducted on wavelength by wavelengthbasis.basis.
For exFor ex : Fig. compares the measurement of 7 NIST spectral irradiance standards as unknown: Fig. compares the measurement of 7 NIST spectral irradiance standards as unknownsources, using a system calibrated using 8sources, using a system calibrated using 8thth lamp.lamp.
Envelope of estimated standard uncertainties is shown by thickhatched lines.
Lab Spectral Calibration Uncertainty
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Experience has showed that 1% error produces a 9% irradiance error at 300nmExperience has showed that 1% error produces a 9% irradiance error at 300nm
and a 4% irradiance error at 1000nmand a 4% irradiance error at 1000nm
Combined uncertainties are the root sum square (RSS) of type A and type BCombined uncertainties are the root sum square (RSS) of type A and type B
standard uncertainties.standard uncertainties.
Expanded uncertainties is the RSS of type A and type B standard uncertaintiesExpanded uncertainties is the RSS of type A and type B standard uncertaintieswith the coverage factorkapplied to achieve the desired confidence intervals.with the coverage factorkapplied to achieve the desired confidence intervals.
Lab Spectral Calibration Uncertainty
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BROADBAND RADIOMETER
CALIBRATION AND MEASURMENTS
Broadband solar radiation measurements are important inBroadband solar radiation measurements are important in pvpv module and arraymodule and arrayperformance monitoring and evaluation.performance monitoring and evaluation.
The basis for the calibration of these instruments is the group of 7 absoluteThe basis for the calibration of these instruments is the group of 7 absolute
cavity radiometers (ACR) denoted as World Standard Group the mean ofcavity radiometers (ACR) denoted as World Standard Group the mean ofwhich establish the world radiometric ref. (WRR)which establish the world radiometric ref. (WRR)
World radiometric ref. and calibration techniques:World radiometric ref. and calibration techniques:
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ResponsivityResponsivity of a diffusedof a diffused pyranometerpyranometer
Rsd=(U-S) /[B * cos (Z)]
UU unshadedunshaded o/p voltage from sensorso/p voltage from sensors
SS shaded o/p voltage from sensorsshaded o/p voltage from sensors
ZZ Zenith angle (45 deg.)Zenith angle (45 deg.)
BB is measured by ACRis measured by ACR
PyrheliometerPyrheliometer reponsivitiesreponsivities ((Rs,ORs,O/P/P signalsignal perper stimulusstimulus unit)unit) areare derivedderived byby directdirectcomparisonscomparisons withwith refref.. ACRsACRs traceabletraceable toto WRRWRR..
PryanometrerPryanometrer responsivitiesresponsivities are derived from the component summation technique by usingare derived from the component summation technique by using
G=B cos (Z)+D
GG ref. global irradianceref. global irradianceBB BeamBeam measurmentmeasurment of cavity radiometerof cavity radiometer
DD shadedshaded pyranometerpyranometer ( diffuse) measurement( diffuse) measurement
Broadband Radiometer Calibration And
Measurements
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Several types of detectors such as silicon cells and thermal detectors such asSeveral types of detectors such as silicon cells and thermal detectors such as
resistance thermometers, thermopiles are used forresistance thermometers, thermopiles are used for pyrheliometerspyrheliometers andand
pyranometerspyranometers..
Radiometer Uncertainty SourcesRadiometer Uncertainty Sources
Thermal OffsetsThermal Offsets
BSRN have characterized thermal zeroBSRN have characterized thermal zerooffsets in thermopileoffsets in thermopile pyranometrespyranometres with allwith all--
blacksensors measuring diffuse radiation.blacksensors measuring diffuse radiation.
The offsets in the shaded andThe offsets in the shaded and unshadedunshaded
states are different and are a source ofstates are different and are a source of
uncertainty in the shadeuncertainty in the shade unshadeunshade
calibrations.calibrations.
MODTRAN atmospheric spectralMODTRAN atmospheric spectral radiativeradiative
transfer code is used to compute short wavetransfer code is used to compute short wave
and long wave direct beam and skyand long wave direct beam and sky
radiationradiation
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As shown in previous graph, direct beam has significant energy in short waveregion from 1000nm to 2800nm,therefore for several different water vapour
conc. and direct normal irradiances same shaded signal is possible from the
pyranometer. by varying total precipitable water vapour from 0.5 atm-cm to 3.5
atm-cm,MODTRAN modeling result in differences of about 0.5% in Rs.
Geometric, Enviormental And Equipment Uncertainty
Additional well known contributors to radiometer calibration and measurment
uncertanity includes: accuracy of zenith angle calculation,non-Lambertian
cosine response of detector surface, temp. coffecients, linearity andelectromagnetis interfearence
Other Spectral Effects
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UshadeUshade computed from the propagation of error formula for shadecomputed from the propagation of error formula for shade--unshadeunshade calibration eq. is:calibration eq. is:
U*2(shade)=[U*2(shade)=[(U)(U)Rs.eRs.e(U)]*2 + [(U)]*2 + [(S)(S)Rs.eRs.e(S)]*2 + [(S)]*2 + [(B)(B)Rs.eRs.e(B)]*2 + [(B)]*2 + [(Z)(Z)Rs.eRs.e(Z)]*2(Z)]*2
For component summation, propagation of error formula becomes:For component summation, propagation of error formula becomes:
U*2(SUM)=[U*2(SUM)=[(U)(U)Rs.eRs.e(U)]*2 + [(U)]*2 + [(D)(D)Rs.eRs.e(D)]*2 + [(D)]*2 + [(B)(B)Rs.eRs.e(B)]*2 + [(B)]*2 + [(Z)(Z)Rs.eRs.e(Z)]*2(Z)]*2
Sensitivity Functions
Shade unshadesensitivityfunctions
Summationsensitivityfunctions
Shade -unshade totaluncertainty
Summationtotaluncertainty
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ResponsivityResponsivity functionsfunctions derivedderived fromfrom calibrationcalibration datadata withwith thethe offsetsoffsets embeddedembedded inin
thethe resultresult shouldshould bebe usedused toto retrieveretrieve thethe mostmost accurateaccurate irradianceirradiance fromfrom aa
pyranometerpyranometer..GraphGraph showsshows pyranometerpyranometer responsivityresponsivity VsVs ZenithZenith angleangle.. UncertanityUncertanity
inin eacheach pyranometerpyranometer calibrationcalibration isis summarizedsummarized inin tabletable..
Responsivity Functions
Type A(Statistical) UNC(%) STD UNC(%)
WRR Transfer 0.2 0.2
Cos(z)(2Z bin) 0.01 0.005
Dif(2.5%d=>0.25%ref.) 0.125 0.063
Temp(2Z bin) 0.1 0.05
Data Logger Precision 5.00E-03 2.50E-03
ACR(wind,T) 0.025 0.013
Temp Chg(10C) 0.25 0.125
Diff Offset B&W 0.125 0.063
UUT IR OFFSET 0.25 0.125
EMI/Thermal EMF 0.01 0.005
Type B UNC(%) STD UNC(%)
Logger Bias 0.09 0.09
WRR Std U95 0.3 0.3
Cos(z);Z100
Coverage Factor(k) 2
Expanded Uncertainty 1.84%
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TheThe responsivityresponsivity for a given zenithfor a given zenithangle at the time of measurement,angle at the time of measurement,Rs(m),can be obtained from a fit of theRs(m),can be obtained from a fit of theform:form:
Rs(z)am/pm=Rs(z)am/pm= ai.cos*ai.cos*ii(z)(z)
{{ii=0 to 46 and=0 to 46 and aiai are 46 coefficients forare 46 coefficients foreach morning and afternoon set of Z}each morning and afternoon set of Z}
With this approach, uncertainty of aboutWith this approach, uncertainty of about++-- 1.8% in measured1.8% in measured pyranometerpyranometer datadatacan be achieved.can be achieved.
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When ACR andWhen ACR and pyrheliometerspyrheliometers are pointed at the sun, tracking errors may arise.are pointed at the sun, tracking errors may arise.The final tally of theThe final tally of the pyrheliometerpyrheliometer uncertainty components is shown in table. Withuncertainty components is shown in table. Withdeployment to the fielddeployment to the field pyrheliometerpyrheliometer data becomes subject to additional trackingdata becomes subject to additional trackingand window issues deferring data logger specifications, etc. These requires anand window issues deferring data logger specifications, etc. These requires anadditional analysis specific to the deployment for estimating total uncertainty in theadditional analysis specific to the deployment for estimating total uncertainty in thefield measurement.field measurement.
Pyrheliometer Uncertainities
Type A(Statistical) UNC(%) STD UNC(%)
WRR Transfer 0.2 0.2
Temp Response UUT 0.500 0.050
Data Logger Precision 0.005 0.0025
Linearity(empirical) 0.200 0.100
ACR(wind,T) .025 .013
Tracking Variations 0.125 0.250
Spectral(window) 0.500 0.500
EMI/Thermal EMF 0.010 0.005
Type B UNC(%) STD UNC(%)
Logger Bias 0.09 0.09WRR Std U95 0.3 0.3
Temp Response UUT 5.00E-01 0.25
ACR Bias(M,wind,T) 0.025 0.013
Temp B(event to
event)10C 0.25 0.125
Spectral Error 0.5 0.5
Tracking Bias 0.25 0.0125EMI/Thermal EMF 0.5 0.005
TOTAL UNCERT(%) STD UNCERT(%)
Type A 0.802 0.615
Type B 0.851 0.504
Combined 1.169 0.918
Effective Degree of freedom >100
Coverage Factor(k) 2
CONFIDENCE INTERVAL 95.00%
EXPANDED UNCERTAINTY 1.59%
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Sensitivity functions derived from the functional form of the shade unshadeand components summation pyranometer calibaration techniques show thatuncertanities in ignal voltages including thermal offset voltages,affectcalibration result the most.
Finally empirical comparisions of several solar radiometer instrumentation setsillustrate that the best measurment accuracy for broadband radiation is of the
order of 3%,and spectrally dependent ncertanity for spectro radiometersystems range from 4% in the visible to 8% to 10% in the ultra violet andinfrared regions.
CONCLUSIONS
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