**Authors: **Eng.Potito Cordisco PhD, Senior Project Manager, Vicoter

Eng. Mauro Terraneo, Chief Technical Officer, Vicoter

The increase in demand of solar energy dictated by the ecological transition, the augment of the price of fossil fuels and the desire for internal production, will plausibly lead to an ever-greater diffusion of photovoltaic systems and the use of increasingly efficient solutions.

From a structural point of view, the way currently most pursued to optimize the production process is to orient the solar panels in a manner that during the day (and seasons) they could always show the largest possible exposed area. These solutions, whether single-axis or dual-axis, have an important effect on the increment of produced energy, but require more careful design than the more classic fixed or seasonal installations, given their intrinsic lower stiffness. The need to reduce as much as possible the material used in the construction of the structure further amplifies this criticality.

The wind, and in a minor part the snow, represents for the solar panels supporting structures practically the only source of loads and consequently the main cause of catastrophic failure. Dynamic pressure, squared function of the wind velocity, pushes on the panels generating forces and moments that stress the structure and the actuation system.

Leaving apart dynamic phenomena, playing in any case an important role in the development of reliable solar trackers, the first sizing must be carried out to ensure that the structure is able to withstand, without damage that affects its functionality, all the static wind conditions to which it will be subjected during its years of operational life.

Wishing to guarantee to its customers a cost-effective product, able to bear even the loads of the windiest zones of Italy, RCM (www.rcm-italia.com) asked to Vicoter (www.vicoter.it) to support it in the development of a numerical methodology that was at the same time simple, scalable, efficient but able to appropriately estimate the stresses and the safety margins of its SunRacker™.

Solar trackers, in the simplest way can be sketched as a series of poles stuck in the ground, connected by a horizontal tube. The latter is hinged to such vertical beams, permitting the rotation around its axis. Solar panels are mounted on such horizontal beam and moving an actuator, generally single and located in the middle of structure, a leverage is rotated and their plane put at the desired angular position.

Cinematically a solar tracker is a mechanism with a single degree of freedom: the rotation around the axis passing through the aligned bearings installed at the ends of the vertical pillars. When the actuation system is put in position, structure becomes statically determined and can be studied using linear static analyses.

The use of a detailed finite element model is in these cases the most obvious choice for stress estimation. For SunRacker™ prototype it is specifically valid having at disposal to correlate the model experimental information regarding its real stiffness, the actuator equivalent one and the corresponding height of the support poles. Such data was obtained from a previous test campaign, wanted by RCM and performed by Vicoter (see our previous article ‘Design of a solar tracker for wind loads’), aimed at determining the first natural frequencies.

Once validated the structural behaviour, key point in the procedure to obtain reliable results is the assessment of the aerodynamic loads. When the wind hit a solar tracker, a lift force, normal to the stream, and a drag force, parallel to the stream, are generated. Such forces are function of the angle between the air velocity and the panel. Even their application point depends by the angle of attack and, in general, it doesn’t lay on the cinematic rotational axis. In such way born even an aerodynamic torsional moment which contributes strongly to the stress field.

Has been
demonstrated by numerous wind tunnel tests that a solar panel in a fluid stream
behaves as a flat plate of same area and the approximation to use lift, drag
and moment data of the latter, instead of the specific panel ones, is
completely valid. The effects of the slight differences are far lesser than the
uncertainties on the wind conditions, i.e. real direction, and can be
neglected. C_{L}, C_{D} and C_{m} of a flat plate are
well known from the literature, even for high angles of attack, and multiplying
them by the dynamic pressure and the panel surface (and chord for the C_{m})
the required aerodynamic loads are found. Due to the objectives of the present
work and its need of simplicity and generality such method has been preferred
to the most onerous, costly and case dependent CFD analyses.

As said, the generated forces and moments are dependent by the orientation of each panel. To assess reliable loads basing on the nominal configuration, implicitly is assumed that the stiffness of the solar tracker, the torsional one in this case, is high enough to ensure that the deformed condition does not substantially differ from the undeformed one. Under this hypothesis, the wind load is independent of the structural elasticity and can be calculated without considering the latter. Due to their layout solar tracker are prone to high rotations at the extremities that are more and more important the longer it is. Such angular differences pose severe uncertainties on the applicability of the simplification.

It is therefore important, to obtain a better estimate of the loads acting in the structure, to evaluate the real aeroelastic behaviour, modifying the aerodynamic loads according to the real angle present between the solar panel and the wind, when the latter is acting.

For this purpose, it is necessary to use a calculation code that integrates both the structural and aerodynamic analysis at the same time. Initially the aerodynamic loads evaluated in the undeformed condition are applied to the structure and its deformation calculated. The aerodynamic incidence is then modified according to what emerged from the first iteration and the aerodynamic loads re-evaluated, this time based on the changed geometry. A second iteration deformation is then estimated using the new forces/moments. The procedure continues until convergence is reached; a situation in which the aerodynamic loads, given in input to the undeformed model are those obtained by evaluating them on the deformed model.

To have a lean and fast calculation method available but at the same time sufficiently accurate, Vicoter has developed a numerical procedure to analyse the present problem. This procedure can calculate the aerodynamic forces and moments acting on the deformed configuration, to be subsequently applied to the finite element model to evaluate the stresses in the various parts.

For the calculation of the aerodynamic coefficients the tabular values of the flat plate at the different angles were used

For the structural calculation a lumped parameter model of the torsional stiffness of the solar tracker was created. Each panel was assigned a single degree of freedom, corresponding to its rotation around the torsional axis. The 26 dofs (the configuration studied has 26 solar panels) were then connected to each other by suitable torsional springs whose stiffness was calibrated starting from the finite element model. An additional degree of freedom, placed in the middle of the structure, was introduced to simulate the compliance of the torsion constraint given by the non-ideal behaviour of the actuator.

Applying the iterative method described above for the aeroelastic estimation, the values of the rotation angles of each panel and the corresponding loads that are generated/generate them are obtained. The latter are strongly higher than the ones obtained with the rigid hypothesis, especially at low angles of attack.

The aerodynamic loads calculated with the aeroelastic procedure were then applied to the previously realized finite element model to assess the reduction of the safety margins in the various parts of the structure. Other than this effect an important amplification of the constraint force that the actuator must apply is observed.