Sun dog stcu...(circ)

20th European Photovoltaic Solar Energy Conference and Exhibition, Barcelona, Spain, 2005

SunDogTM STCU: A GENERIC SUN TRACKING CONTROL UNIT
FOR CONCENTRATION TECHNOLOGIES

I.Luque-Heredia, J.M.Moreno, G.Quéméré, R. Cervantes, P.H.Magalhães
Inspira, SL, C/Chile, 10, Las Matas, 28290 Madrid.
email: iluque@inspira.es

ABSTRACT: The present development status of the SunDogTM sun tracking control unit is here described.
SunDogTM is an electronic controller devised to deliver the stringent accuracies and reliabilities required by high
concentration technologies, a present offshoot of the world’s most dynamic PV markets, offering Solar a route to the
conquest of wholesale electricity prices. Profiting from the high processing power and the low costs attained by
today’s ubiquitous embedded systems, SunDogTM STCU is based in a sun ephemeris computation core implemented
in a low-end microcontroller. The effect of the characteristic error sources which cut down the tracking accuracy of
this “open-loop” approach is greatly suppressed by the inclusion of a generic error model, valid for any configuration
of tracking axes, on which SunDogTM performs automated calibration at onset. The advantages of this computerized
controller are further exploited providing efficient handling of management and emergency situations, versatile man-
machine interface, and extended connectivity resources enabling Internet monitoring.
Keywords: Concentrators, Tracking, Strategy

1. INTRODUCTION fitting of the parameters of the model at onset with some
set of performance errors, automatically collected,
Field experience gathered up to know with characterizes the error sources intervening and can be
photovoltaic concentrators consistently points out closed- used from then on to correct the output of the preliminary
loop, sensor based, tracking controllers, as not being up ephemeris outputs, restoring in such a way the open-loop
to the severe reliability standards required by the low tracking scheme.
maintenance plants, which sustain the economic
feasibility plans of these technologies [1]. 2. THE TRACKING ERROR MODEL
Open-loop controllers, based in the computation of
sun ephemeris, implemented as digital embedded Leaving aside the JPL style of numerical
systems, appear as a reliable and almost maintenance- ephemeredes based on interpolation of tabulated
free alternative, able to attain the increasingly high numerically integrated solutions of the equations of
accuracies demanded by the rising trends in celestial motion, which is the most accurate approach
concentration ratio, and offering the possibility of available to date but requiring significant data storage
including added value content, such as remote control and updating, relatively simple approximate analytic
and monitoring capabilities, at reasonable costs when solutions can be also be obtained of these equations,
getting into industrial volumes. which in the case of the sun, attain accuracies in the 0.1
However an open-loop controller even if operating arc minutes range, which is a firm enough basis for CPV
on the very precise sun ephemeris equations available to tracking control. Sun ephemeredes for sun tracking
date, is affected, once connected in the field to its purposes are usually adjusted to output topocentric
appointed concentrator, by many error sources which can horizontal coordinates (azimuth & elevation), which are
highly degrade its final tracking accuracy well below its then to be converted into rotation angles measured from
ephemeris’ nominal value, and to the point of even a certain reference orientation in the one or two axes of
missing concentrator’s specifications. the tracker under control. However when converting to
Among these error sources the most significant have these coordinates into axes turns, default assumptions are
a deterministic nature and mainly result from to be made regarding the in-field arrangement of the
characterization inaccuracies, i.e. tolerance deviations tracking axes and their reference orientations. These
appearing in the controller’s default assumptions assumptions even if specified to the tracker and
regarding the tracker’s installation or manufacturing. concentrator manufacturer and to the installation crews
Drifts in the internal timing required for the computation will be met within tolerance margins, and these
of the sun ephemeris, is the other critical error source deviations will imply a significant decrease in the final
which is to be restrained. Second order error sources, and accuracy of the ephemeris guided aiming. Process
also to some extent predictable, such as gravitational tolerance shrinking is always a costly effort which may
bending in wide aperture trackers, the effect of mismatch quickly override the tight cost constraints usually
in multi-secondary axis trackers, or even ephemeris imposed on CPV technologies. So in order to relax
inaccuracies, due to the effect of local atmospheric manufacturing and installation requirements, while
refraction, might have to be considered as well. limiting the tracking accuracy losses, a set up calibration
Feedback of the tracking errors caused by the approach can be developed, in which a mathematical
referred sources is to be somehow integrated, in the model characterizing the sources of departure from the
control strategy in order to suppress them. This open loop conversion assumptions can be used, and its parameters
core strategy blended with the fed back closed-loop, is fitted to a set of tracking errors collected at onset. Once
sometimes referred as the hybrid approach, which in past the parameters quantifying the share of the different error
implementations have been mainly connected to control sources in the resulting tracking errors, are obtained, the
theory [2]. Instead the method here proposed relies in the model tuned to those values will be used to correct the
principles of automated instrumentation calibration, ephemeris output from the on.
based in the modeling of systematic error sources. The The calibration model developed here assumes the



tracker’s axes and their reference orientations have the or again the improper assembly of aperture frame or
same reference system as the horizontal Az./El. optics.
coordinate system used by the ephemeris, i.e. the These six parameters appear in a 2 → 2 function,
grounded, or primary axis pointing to the local zenith consisting in the composition of five partial transforms,
with its reference orientation pointing south, and the and converting horizontal coordinates provided by the
secondary axis, the one which is fixed to the primary ephemeris to pairs of angular rotations for both axes.
always remains at right angles with it, and has its Behavior of this calibration function can be visualized
reference orientation pointing the horizon, in other through the usual grid transform representation in
words, the ideal pedestal tracker. complex variable analysis (Fig.1).
Six are the parameters characterizing the departure of
the real tracker under control form the ideally assumed:
• Primary axis azimuth ( φ ) and zenith angle ( θ ):
These two parameters are the azimuth and zenith angle
coordinates determining the real orientation of the
primary axis, which no matter the axis configuration is
always defined as the axis which is fixed to the ground.
This is mainly an installation error due to the imprecise
foundation of the tracker Figure 1. A simple calibration transform applied to a
• Primary axis offset ( β ): rectangular grid in the azimuth-elevation plane (rad) into
This parameter determines the location of the reference the plane of axes angle rotations in a two axis tracker,
orientation of the primary. Reference orientation is when θ = 15º and the remaining parameters are zero
usually determined by a specific sensor, or the index
mark when working with optical encoders. Misplacement The fact that the assumed reference system for the
of this sensor during manufacturing or its incorrect tracker under control is that of an ideal pedestal tracker is
alignment at installation may cause this error. When just a convention and the model is able to correct
φ = θ = 0 , β simply becomes the angular offset to the horizontal ephemeris coordinates to any two axes
south. configuration, including others frequently used such as
These first three parameters are in the referred order the tilt-roll assembly (ideally φ = θ = π 2 ). In order to
the nutation, precession, and spin Euler angles which maintain this generality of the model no simplifying
relate any two reference systems with a common origin, assumption have been made regarding the transform
and only these will be required if our tracker has only parameters.
one axis, the primary axis, such as in present polar,
azimuthal, or horizontal axis trackers. In case a 3. MODEL FITTING
secondary axis is attached to the primary, three more
parameters are required and the pointing vector is Discarding simplifying linearization which would
introduced as that one which is oriented by the joint decrease the generality of the model, the parameters
action of the two tracking axis, and if aligned with the characterizing a specific tracker and its in-field
sun vector produces the maximum power output of the installation will have to be fitted to a set of tracking error
concentrator array. observations by means of iterative non-linear
• Non-orthogonality of axes ( λ ): optimization techniques. Provided the target has been to
This parameter takes the value of the difference to the integrate this numerical procedure in a low cost
right angle between the primary and secondary axis. This embedded system based in an 8 bit microcontroller,
mainly being a manufacturing error source, a non zero programming efficiency was a must, and good
value for this angle implies the two axis tracker is no conditioning of the maximum likelihood estimation
longer ideal and a cone of orientations around the (MLE) function is required. Least squares, was the MLE
primary axis will remain out of reach. chosen which even if there are other more robust
• Pointing vector axial tilt ( δ ): estimators, is by far the one presenting the most effective
The pointing vector is assumed normal to the secondary non-linear minimization techniques. The existence of
axis and contained in the horizontal plane when this axis local minima obliged to resort to the global optimization
rotation is zero. The axial tilt of the pointing vector is toolbox, and finally a clustered multi-start with
the difference angle to a plane normal to the secondary Levenberg-Marquardt [3],[4] based local searching was
axis. This error can have its origin in the defective implemented. Robustness is further conferred by means
assembly of the tracker’s aperture frame, but also in the of a pre-fit outlier filter discarding clearly defective error
misalignment of the concentrator optics. observations. In order both to test the reliability of the
• Secondary axis offset ( η ): local search stage, once running in the microcontroller, it
The secondary axis offset accounts not only for the was tested on the Moré set of test functions [5]. This was
difference angle between the plane normal to the primary also useful to choose among the three compilers available
axis and the reference orientation of the secondary axis, depending on the accuracies in the fits obtained when
but also for the difference angle between this reference compared to this same fits in a Intel Pentium 4 processor.
orientation and the plane containing the pointing vector First attempts on fitting the calibration transform with
and the secondary axis, i.e. a radial tilt which is the error sets produced by the calibration transform tuned at
second value characterizing pointing vector departure a prefixed solution, during the solstices and equinox, had
from assumptions. This error therefore derives from both a very lengthy convergence in the microcontroller due to
the misplacement of the secondary axis reference sensor the existence of multiple local minima. Careful analyses
showed most of the local minima were so in a wide sense



and appeared in the frontier of discontinuities. Lacking to 1º accurate) could be made of each solution (Table I).
physical meaning these discontinuities were isolated,
with the help of the graphical representation of all the (Case) Module Best fit estimate of mount
combinations of two dimensional search subspaces (Fig. (1) “all glass” Fresnel 500X θ = 2 º , λ = −1º , δ = 2º , η = 45º
2), and progressively smoothed by convenient fixes in (2) TIR-R 1000X θ = 2 º , λ = −1º , δ = 32º , η = 45º
the definition of the constituent transforms. This was a (3) Fresnel 500X θ = 2 º , λ = −1º , δ = 2 º , η = 5º
painstaking process which however finally achieved the
Table I: Three test mounts, modules employed, and a
acceleration of the convergence required to make the
priori estimates of the best fit parameter solution.
process feasible.
After this revision of the calibration transform
A dawn to dusk session collecting tracking errors for
definition the simulated tests, which where performed for
the three mounts was carried out, were the measurements
several sets of solution parameters, representing different
time stamp was obtained from a GPS and precise
types of tracker concepts or tolerance degrees in their
pointing was assumed at maximum short circuit current
production and installation, and with tracking error sets
output. Ephemeris used for the LS [6] fit had a mean
of a maximum of 100 points, mean error and error
accuracy of 0.06º when running in the microcontroller.
standard deviation in the fits obtained by the
microcontroller where in the 0.5 prad range and
convergence times in the 1 to 5 minutes range, and only a
tough case which required almost 2 hours.

Figure 2. Levenberg-Marquardt sample local searches
meeting a global (0.17,1.35) and a local minima (3.31,-
1.35) at two dimensional subspace of the search space
(φ, θ ) for LS best fit.
Figure 3. Trell Tracker at IES-UPM, showing the three
test mounts with their corresponding modules (Table I).
3. PHYSICAL VALIDATION OF THE MODEL
Case φ θ β λ δ η σmin
The calibration transform was now properly defined,
however physical validation of the model was still 1 24.19 1.84 13.58 -0.69 2.04 43.92 0.19
2 39.33 1.70 -2.95 -1.07 33.90 43.71 0.37
required. For this purpose a laboratory two axis pedestal 3 22.38 2.13 14.65 -1.09 1.03 4.44 0.17
tracker was designed. Able to withstand up to 100kg of
Table II: Best fit solutions for the three cases, and their
payload in its 4m2 aperture, the positioning resolution of
corresponding Min Std Deviation for model fitness (deg)
its proprietary drives, the high accuracy of its encoder set
up, and its internal sun ephemeris allow for overall
As seen in Table II in all three cases the best fit
tracking accuracies in the 0.1º (max. error) range, if
parameters obtained were within the referred 1º range
ideally installed. The structure of this lab tracker,
from its initial estimates, which is a first successful
commercially named Trell Tracker, integrates the
indication of the physical compliancy of the model. In
tracking control in its structure, and presents a user
addition resorting to LS theory we could estimate the
interface front panel which includes LCD display of the
minimum standard deviation of supposedly normally
axis turn angles in encoder counts.
Three different mounts where provided in the distributed measurement errors σmin in order to further
aperture of this tracker for three different prototype ensure the model is physically grounded. The three
concentration modules, all of them housing a micro- σmin estimates shown in Table II agree with the observed
concentrator parquet and with concentration factors limitations of the measuring process which are
500X and 1000X (Fig. 3). These mountings where significantly affected by some outliers introduced by the
prepared so that their best fit parameter solution in the manual procedure employed. The TIR-R module due to
calibration transform, highlights a certain parameter, and its highest acceptance angle is the one introducing the
with the aid of a digital inclinometer some estimates (up
highest σmin estimate errors in the error observations.



4. MODEL EXTENSIONS acceptance angle distance, can resort to some wide angle
sensor such as an aperture plane irradiance sensor, but
After model validation further work was produced in beyond some point the search is to proceed blindly and
order to introduce in our model other second order produce extensive plane searching routines, i.e. spiral
tracking error sources. A tracker specific module is search [7]. Thereafter maximization of the power
included which is to host a model of the variation of the function with tracker’s coordinates is required.
pointing vector with orientation due to gravitational It is worth noting here that the tracking error set is
bending. Also the effect of manufacturing tolerances in not necessarily to be obtained from the Sun, in principle
the drive chain gearings when it is not possible to mount any other light source with precise analytic kinematics,
axis turn sensors directly in the primary axis can be and with enough emitting power to extract a measurable
introduced in the case of the most common linear drives. output from the concentrator, would suffice. In this
Multi-secondary axis trackers, i.e. those integrating respect the full moon proves to be a good candidate, as
several secondary axes mechanically linked in order to far as it will enable night calibrations not interfering with
decrease aperture wind profile, are also considered in concentrator’s daily production. Its 0.49º apparent
order to take into account the effect of the electrical diameter is very similar to the suns’, while its irradiance
mismatch of the CPV arrays in each secondary axis as is six orders of magnitude smaller than the sun, so its
well as their overall connection scheme, in order to photo-generated current is still within reach of cheap
locate the pointing vector. current sensing devices. In the other hand the full moon
Even if Internet connectivity or GPS might provide irradiance is three orders of magnitude above that of the
atomic time synchronicity to the tracking control unit most brilliant planets and stars so it will be easily
internal clock, availability of high accuracy ephemeredes distinguishable by the concentrator when searching the
provides an immediate and autonomous alternative to night sky. Moon ephemeris and phase equations have
precise time-keeping. A time drift parameter has been been analyzed and encoded for the development of a
included in the model in such a way that it can be fitted Moon error collection procedure on which to fit the error
with a tracking error set either, jointly with the rest of the model.
parameters or individually within periodic time Along with these performance enhancements, long
adjustment procedures. term accuracy tests are being conducted on several
The complexity of the calibration transform when SunDog based systems.
introducing these new parameters, obliged to switch in
the Levenberg-Marquardt module from working on
analytic derivatives to its finite-difference counterpart,
which anyhow does not significantly decrease either
accuracy or convergence time.

7. PHYSICAL IMPLEMENTATION

The above described capacities have been
implemented in an electronic embedded system, based on
an 8 bit microcontroller, along with the required chipset
and sensors to carry out the described algorithms and
perform the analog measurements, and also motor
driving units and an encoder decoding and interpolation
subsystem. Named SunDogTM for commercial purposes,
it is supplied with SunDog Monitor a Windows Figure 4. SunDogTM STCU (left) along with its SunDog
application to run in a locally or remotely connected PC Monitor virtual interface software (above right), and
as a virtual user interface. It also integrates an WWW remote control panel hosted by its internal web
interchangeable modem for PSTN, RF, Ethernet or server (below right)
GSM/GPRS Internet connectivity, which enables e-mail
reporting and web based control and monitoring. This work has been supported by the European
Prepared for operation in harsh environments its rugged Commission through the funding of the project
enclosure integrates a simple control front panel (Fig. 4). FULLSPECTRUM (Ref. N: SES6-CT-2003-502620)

5. ONGOING WORK REFERENCES
[1] A. Maish, Proc. of the 20thIEEE PVSC, (1988) 1309
Manual collection of tracking errors is a tiresome and [2] I. Luque-Heredia et al. Proc. of the 3rd Int. Conf. on
error prone task, which demands automation, in order Solar Concentrators, (2005)
prevent outliers creeping in and increase the accuracy of [3] A.A, Törn, 2nd IFAC Symposium on Stochastic
the corrected ephemeris. Control, 19, (1986)
Automatic error collection has already been [4] D.W. Marquardt, Journal of the Society of Industrial
extensively simulated proving efficient performance. In it and Applied Mathematics, 11, 2 (1963), 431
direct search of the alignment of pointing and sun vector [5] J. Moré et al. ACM Transactions on Mathematical
to obtain each tracking error measurement, imposes, to Software, 7, 1, (1981), 17
some extent, the use of the concentrators power output or [6] T.C. Van Flandern, et al The Astrophysical Journal
some approximately equivalent variable, such as short Supplement Series,41,(1979), 391
circuit current, as feedback signal. Preliminary search [7] R. Baeza-Yates et al, Information and Computation,
until sun and pointing vectors get into the concentrator’s 106, (1993), 234


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