*Article* **A Simplified Method to Avoid Shadows at Parabolic-Trough Solar Collectors Facilities**

### **Nuria Novas 1, Aránzazu Fernández-García 2 and Francisco Manzano-Agugliaro 1,\***


Received: 10 January 2020; Accepted: 6 February 2020; Published: 13 February 2020

**Abstract:** Renewable energy today is no longer just an affordable alternative, but a requirement for mitigating global environmental problems such as climate change. Among renewable energies, the use of solar energy is one of the most widespread. Concentrating Solar Power (CSP) systems, however, is not ye<sup>t</sup> fully widespread despite having demonstrated grea<sup>t</sup> efficiency, mainly thanks to parabolic-trough collector (PTC) technology, both on a large scale and on a small scale for heating water in industry. One of the main drawbacks to this energy solution is the large size of the facilities. For this purpose, several models have been developed to avoid shadowing between the PTC lines as much as possible. In this study, the classic shadowing models between the PTC rows are reviewed. One of the major challenges is that they are studied geometrically as a fixed installation, while they are moving facilities, as they have a tracking movement of the sun. In this work, a new model is proposed to avoid shadowing by taking into account the movement of the facilities depending on their latitude. Secondly, the model is tested to an existing facility as a real case study located in southern Spain. The model is applied to the main existing installations in the northern hemisphere, thus showing the usefulness of the model for any PTC installation in the world. The shadow projected by a standard, the PTC (S) has been obtained by means of a polynomial approximation as a function of the latitude (Lat) given by S = 0.001 − Lat<sup>2</sup> + 0.0121 − Lat + 10.9 with R<sup>2</sup> of 99.8%. Finally, the model has been simplified to obtain in the standard case the shadows in the running time of a PTC facility.

**Keywords:** CSP; PTC rows; solar; shadowing; energy; renewable energy
