The increasing demand of green energy brought to a request to improve the efficiency of solar panels and of their capability to generate electricity. Among the various solutions studied and developed, the most diffused one is, for sure, the solar tracker. Such device permits the orientation of the panels towards the sun during its daily movement from east to west. The less the misalignment angle is, the more the effective collection area is and, consequently, the more the energy production is.

Despite the various models on the market, solar tracker structural layouts are all very similar. Solar panels are connected to a long horizontal tube hinged by bearings to a certain number of vertical poles inserted into the ground. An electrical actuator, generally located in the middle of the tracker, rotates the main tube by a leverage and works as constraint, once the wanted position is reached.

Although the geometrical and technological simplicity can be misleading, solar trackers require an extensive and careful design, in order to be able to withstand, not only the static, but even the dynamic loads induced by the wind. Due to their shape, very similar to a thin flat plate, solar panels work in an air flow that generates lift and drag, according to the relative angle between them and the stream velocity. Therefore, they are subjected to both a forced response generated by the wind and aeroelastic instabilities. The estimation of the maximum dynamic pressure encountered by the structure during its life and the calculation of the induced static stresses become, in this way, only the first step in the development of a reliable device.

The most probable dynamic effect encountered by solar trackers in their life is generated by air turbulence inducing time variant loads, able to excite structural resonances. Due to their layout, solar trackers generally have torsional modes at very low frequencies: the horizontal tube used to support the panels acts as the only torsional spring in the structure. It is constrained on ground by the actuator and its stiffness decreases when the total span increases. A good design aims at raising the frequency of the first mode to a value higher than the maximum harmonic contribution of the wind. Theoretical Kaimal and von Karman wind power spectrum densities show that such threshold depends on the height from the ground and on the mean speed. According to the several standards such as the ASCE 7, a threshold of 1 Hz can be fixed without loss of generality.

Vicoter (www.vicoter.it) is an Italian consulting society dealing with the structural dynamics mainly in the aerospace and energy sectors. Its competences integrate the numerical and experimental methods to provide its clients the most suitable solution in the vibration field. Due to their approach, Vicoter’s engineers were entrusted by RCM (www.rcm-italia.com) to develop a validated analytical model of its new prototype of solar tracker, so to verify its compatibility with resonance requests and to study the possibility to build wider versions.

Three parameters must be experimentally identified to obtain a correlated model:

- The stiffness of the actuator, influencing the first symmetric torsional mode.
- The real torsional stiffness of the main tube accounting for the joints among the various parts, influencing the second antisymmetric torsional mode.
- The equivalent stiffness of the soil, influencing third lateral mode, induced by flexibility of the vertical pylons.

Moreover, an estimation of the modal damping is required if also analyses of dynamic response are planned.

An on-field experimental test campaign was carried out, to recover the needed information on the real dynamic behaviour of the solar tracker installed as in operative conditions. Two configurations were studied, with and without balancing masses. Studies were performed with two SIMO (Single Input Multi Output) tests, by installing fifteen accelerometers in two layouts, appropriately located to obtain an excellent spatial reconstruction of the modes. The solar tracker was excited in two locations by a long stroke shaker, a special purpose device able to load adequately flexible structures which present high displacements.

The first three vibration modes have been identified in terms of frequency, shape and damping starting from FRFs (Frequency Response Functions) between all the outputs and the load cell.

The finite element model was then updated according to the experimentally obtained information, resulting in an optimal match of the data.

Solar trackers are also affected by other wind induced dynamic effects:

- Vortex shedding. It is the alternating detachment of the vortices at the ends of the panels. This phenomenon creates forces that generate an alternating torsion of the panel plane. If the shedding frequency of these vortices, and, therefore, the resulting torsional loads, assumes the same value of a torsional natural frequency of the structure, the response is amplified and potentially disruptive. Vortex shedding frequency can be estimated quite simply assuming an adequate Strouhal number: it grows linearly with the average wind speed and diminish as the orientation angle increases. Also in this case, a possible solution would be to raise the torsional natural frequency of the system above the maximum achievable by such loads. Anyway, the satisfaction of such requirement even at angles below 15°, would require a torsional stiffness which is not reasonable for the single-axis tracker case.
- Divergence. Unlike the previous phenomena, divergence and torsional flutter are instabilities related to aeroelastic problems. Simplifying, it can be said that the torsional dynamic behaviour of the solar tracker is forced by a twisting moment due to the wind and it can be decomposed / linearized into two contributions: one proportional to the rotation angle and one proportional to the rotation speed. Being the former proportional to the rotation, it can be interpreted as an equivalent aerodynamic torsional stiffness, while the latter, being proportional to the rotation speed, can be interpreted as an equivalent aerodynamic torsional damping. In a flat plate at low angles of incidence, the aerodynamic stiffness term works as a negative torsional stiffness. It is proportional to the square of the speed and therefore, at a certain speed, it equals the structural torsional stiffness, cancelling the overall one. In this situation, the torsional equilibrium is not reacted with any stiffness and the shaft twists until it breaks. This disruptive phenomenon is a static instability occurring in a not-oscillatory way. The divergence speed can be estimated starting from the correlated finite element model, introducing the aerodynamic part which, in this situation, is well approximated by the VLM (Vortex Lattice Method).
- Torsional flutter (Torsional galloping, SDOF flutter). This instability is very similar to the divergence one, but here, the aerodynamic damping term deletes the structural damping. Solar tracker acquires energy from the air flow and vibrates in torsion, until it breaks. This aeroelastic problem is much more complicated than divergence: the flutter derivative of the torsional velocity (a term that multiplies the angular velocity to give the torque) is, indeed, non-linear and depending both on the angle of the follower and on the velocity itself. The trend of these derivatives can be known through wind tunnel tests or through CFD studies and they can be found in literature.

Based on the obtained correlated finite element model, Vicoter continues its collaboration with RCM to study the impact of the various wind-induced effects on the of solar tracker prototype, so to design a safety strategy based on structural strength and adequate stow position.

Vicoter thanks RCM for the trust received in the development of this project and the opportunity to publish this article, Dr. Umberto Bellotti of Bellum Laboratories for sharing of his wide on-field experience on the behaviour of solar trackers subjected to wind and Prof. Marco Morandini of Politecnico di Milano for the long and vibrant discussions about the best method to obtain reliable and cost-effective solutions to aeroelastic problems.