understanding solar tracker...

Understanding Tracker Accuracy and its Effects on CPV

M. Davis, T. Williams (GreenMountain Engineering)M. Martínez, D. Sanchéz (ISFOC)

Presented at the 5th International Conference on Solar ConcentratorsPalm Desert, CA, Nov. 16-19, 2008

Understanding CPV Tracking Accuracy ICSC5, 2008-11-19 (2/29)

Presentation Outline

• Background• Accuracy Measurement• Accuracy Specs & Reporting• Real-world Data


About GreenMountain Engineering• Engineers dedicated to the advancement of cleantech• Engineering design services and problem-solving, from

R&D labs to commercial-scale manufacturing• Since 2003, over 60 client projects in PV, 30 in CPV

Modules & Receivers Manufacturing ToolsTrackers & Controllers


(Most) CPV Requires Tracking

There is no single solution that has been proven best for all applications– there is still room for innovation in tracking.


Why “Understand Tracker Accuracy”?There are two different reasons to have good methods of

characterizing tracker accuracy:

• Technically relevant tracker accuracy metrics help predict system energy production andLevelized Cost of Energy (LCOE)*.

• Standardized, repeatable, generalized methods of characterization allow side-by-side comparison between different tracker designs.

Trackers are a significant component of system cost–avoiding overdesign and allowing more assembly/installation variation can reduce cost.

* See, for example, M. Campbell et al., “The Drivers of the Levelized Cost of Electricity for Utility-Scale Photovoltaics”, SunPower Corp 2008



• Background• Accuracy Measurement• Accuracy Specs & Reporting• Data


Tracking Accuracy Measurement

For further discussion, see for example:• I. Luque-Heredia, et al. “A Sun Tracking Error Monitor […]”, EUPVSEC 2005• C. Cancro, et al. “Field Testing the PhoCUS Solar Tracker […]”, ICSC 2007• M. Davis, et al. “Machine Vision […] for Characterizing Tracker Performance”,

IEEE PVSC 2008

A variety of methods have been used to measure pointing accuracy. Many are essentially optical methods.

Calibration plays an important role in the accuracy of these methods.

Optics (pinhole, lenses, filters)

image sensor, algorithms

Sun


Measuring Tracker Accuracy Today• Trac-Stat SL1• A diagnostic instrument for

measuring the performance of solar trackers

• 0.02° accuracy• Datalogging capability6”


A Note on Reference FramesPointing errors reported in a sensor’s reference frame are not the same

as errors in the tracker’s axes of motion or earth reference frame.Vector transformations can be performed based on current tracker

angle or even just time of day and location (via sun position calculations)

))ˆˆ(ˆ()ˆˆ(ˆ)1(ˆˆˆˆ akacakcacacab zyxGND ××+×+−=−=−

Transforming from sensor reference frame:

(for certain assumptions about system rotation, otherwise there are multiple possible solutions)



• Background• Accuracy Measurement• Accuracy Specs & Reporting• Real-world Data


Accuracy Spec -- MetricsDesirable in an accuracy spec:• Correlates with system energy production• Assesses full tracker performance (mechanical,

controller, algorithms, calibration) • Measureable, on-site, in real installationsUndesirable:• Too conservative (promotes tracker overdesign)• Too optimistic (based on a “perfect day”, etc)• Arbitrarily penalizes certain tracker architectures

in ways not related to real-world performance


Accuracy – not a single number?Having a single number for a spec

(inverter efficiency, module watts, and so on) is simplest.

However, the goal of much of the PV and CPV industry is large-scale deployments.

At this scale, it is reasonable to expect the purchaser to look at and interpret a more detailed set of specs. Inverter Efficiency

DC-DC Regulator Efficiency


A Side Note on ConvolutionVarious data sets with matching or nested dependent

variables can be convolved or combined. For example, in the context of spectral performance:

solar spectrum optics’ transmissivity cell spectral responsivity

cell output,by wavelength

B 18.2

G 18.6

R 21.8

cell output

nm nm nm

nm


Accuracy Specs Not to Use

• Ephemeris calculation accuracy (<<0.01°, but this doesn’t matter if there are other uncompensated errors)

• Motor encoder resolution – not really accuracy• Worst-case accuracy (too conservative as an only spec)• Simulated accuracy• Mean pointing accuracy (skewed unfairly by horizon-

pointing performance)


Accuracy Specs – Mixed Usefulness• Mean pointing accuracy over the subset of a day for

which the sun elevation is above (10°)– While this avoids penalizing a tracker for not being able to point directly

at the horizon, this choice of 10 degrees is arbitrary and will penalize certain trackers disproportionately.

• Median pointing accuracy– While a median could be used to remove outliers, this is a roundabout

way of doing it.

• 95th percentile accuracy (the pointing accuracy the tracker exceeds over 95% of sunrise-to-sunset hours)– This is another way to remove outliers from a data set, and has the

advantage of being fairly simple to compute and explain, and fairly relevant, but is also somewhat arbitrary and not necessarily best-coupled to energy production.


Accuracy Specs – Potentially Useful?• Graphs of tracking error as functions of

– Sun elevation and azimuth (can be determined by time of day and location, without other sensors)

– Tracker position (on local tracker axes)– Ambient temperature– Wind speed and direction– DNI, GNI

• These provide data sets that can potentially be combined with site assessment data collected at different sites (or from existing databases), where trackers have not yet been installed.


Sample High-Level WorkflowTracker Testing Data

Raw

Data from Site AssessmentAnalyzed

Annual Energy Projections

Module Data

t

t

t

DN

IE

rror

Tem

p

Temp

Elevation

Wind

Err

orE

rror

Err

or

Wind

Elevation

Temp

Cum

ulat

ive

DN

I %C

umul

ativ

e D

NI %

DN

I %

t

Ene

rgy

Pow

er

Angle

(this slide is just a conceptual example– the process itself is not easy and there are many difficult-to-measure variables to include)


Wind Speed (m/s) Vs. Deflection (deg)

0

0.1

0.2

0.3

0.4

0.5

0.6

0 5 10 15 20 25 30 35

Wind Speed [m/s]

Def

lect

ion

[deg

]

45 degrees elevation60 degrees elevation

Other Accuracy Concerns – Weight* & Wind**

* For more information, see for example: A. Hakenjos, et al. “Field Performance FLATCON High Concentration PV Systems”, EUPVSEC 2007** For more information, see for example I Luque-Heredia, et al. “CPV Tracking Systems: Performance Issues, Specifications & Design”, ICSC 2007

Image: GreenMountain Engineering

Image: SOLARGENIX

Error bars show backlash



• Background• Accuracy Measurement• Accuracy Specs & Reporting• Data


Data Sources & Notes• ISFOC testing• Several HCPV manufacturers who are SL1 customers

provided data anonymously.• GreenMountain testing

• Data taken between March ‘08 and November ‘08 (primarily Oct ‘08 and later)

• Not “champion data”– data from a range of conditions.– A few manufacturers included disclaimers such as: data was

before optimal tracker alignment and calibration had been performed, or without the newest control algorithms.

• Very preliminary data/results– additional statistical analysis and interpretation will be performed in the future.


0%

20%

40%

60%

80%

100%

120%

0.00 0.05 0.10 0.15 0.20 0.25

Tracking Error (degrees)(Relative to Tracking Error @ moment of Max Array Power)

CPV

Arr

ay P

ower

(nor

mal

ized

)System Acceptance Angles

Correlation, though not necessarily causation.

Could indicate that the effective acceptance angle of the system (influenced by panel-to-panel misalignment and tracker deflection) is much tighter than an individual module’s acceptance angle.


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 100 200 300 400 500 600 700 800 900 1000

Direct Normal Irradiance (W/m^2)

Trac

king

Err

or (D

egre

es)

[Var

iatio

n fr

om M

edia

n]Tracking Error vs Irradiance

• One

• Two

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 100 200 300 400 500 600 700 800 900

Global Irradiance (W/m^2)

Trac

king

Err

or (D

egre

es)

[Var

iatio

n fr

om th

e M

edia

n]

Slight correlation shown between irradiance and tracking accuracy.

Not a CPV-optimized tracker, global irradiance

CPV tracker, DNI


0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 10 20 30 40 50 60 70

Sun Elevation (Degrees)

Trac

king

Err

or (D

egre

es)

ABCDEFGH

Tracking Errors, Various TrackersA wide range of accuracies (some could be partially sensor or tracker misalignment)

Increased error at low sun elevations

Significant scatter for brief periods of time


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 10 20 30 40 50 60 70

Sun Elevation (Degrees)

Trac

king

Err

or (D

egre

es)

[Var

iatio

n fr

om M

edia

n] ABCDEFGH

Tracking Errors, Various TrackersThis graph subtracts median tracking error components (optimistic, assumes perfect initial alignment/calibration of the tracker).

Tracking variation of 0.1-0.2° from median is common, more is present on some trackers (but does it occur during unimportant low-DNI times?).


0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.01 0.1 1 10

Tracking Error (Ratio of Daily Median)

Cum

ulat

ive

DN

I

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

9:36 10:48 12:00 13:12 14:24 15:36 16:48

Time of Day

Trac

king

Err

or (R

atio

of D

aily

Med

ian)

The P Plot Concept

0

100

200

300

400

500

600

700

800

900

0

100

200

300

400

500

600

700

800

900

DN

I [W

/m̂2]

0

100

200

300

400

500

600

700

800

900

7:00 8:06 9:13 10:20 11:26 12:33 13:40 14:46

Time of Day

[ just demonstration data, from non-CPV system ]


Cumulative DNI

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.01 0.1 1 10

Maximum Tracking Error (degrees, log scale)[ normalized to be variation from Median Tracking Error ]

Cum

ulat

ive

DN

I ene

rgy

Times when the tracking error was less than 0.2 ° correspond to approximately 90% of this day’s total direct irradiance (DNI-seconds).

Note that the somewhat optimistic calculation of tracking error is being used here and in the following graph.

This is an normalization process that assumes that the median error in each axis is caused by issues which can be calibrated out (for example, installation alignment of the tracker or sensor).


DNI vs Time as weighting

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.01 0.1 1

Maximum Tracking Error (degrees, log scale)[ normalized to be variation from Median Tracking Error ]

Cumulative DNI energy

Cumulative Time About 5% of the time, tracking error was above 0.3°

However, this >0.3° error corresponded to only about 1% of the day’s total DNI energyTracking error was < 0.1°

nearly 45% of the day, but only 13% of the day’s DNI energy occurred during these times.


Conclusions• It is possible to measure tracking

accuracy in the field.

• Examining and analyzing detailed data sets can provide more insight than a single numerical value.

• Without optimal alignment, tuning, and calibration, CPV tracking errors of 0.1°to 2.0° have been observed.– Tracking is not as trivial as “just

calculate the sun ephemeris position”.

• The need for future tracker cost reduction can be assisted by a careful understanding of performance and design trade-offs.

Image: GreenMountain Engineering


Acknowledgments• ISFOC, and especially María Martínez, for supporting us in this

work.

• CPV manufacturers and Trac-Stat customers who were willing to anonymously share real field data.

• The ICSC-5 Conference Committee.

• All of the previous contributors to the shared body of CPV technical knowledge whose work we’ve drawn on.

[ This document was originally presented with additional verbal commentary to explain particular slides. For further information or details, contact Max Davis at [email protected] ]

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