## 1 Introduction  
High voltage transmission lines (HVTL) are the structures within power supply systems devoted to the transportation of electric energy [1]. These systems are long-lasting assets requiring huge investments on the long-term period [2]. HVTL are nowadays considered even more strategic infrastructure due to the rising trend in electricity demand observed worldwide [3]. While in developing countries, the easiest way to strengthen the power delivery is the construction of new transmission lines, in countries where the network is already established, the solution is to update the capacity of already existing lines [4]. In the context of uprating, special conductors have been under development to work at higher operative temperatures, allowing a higher flow of current. They are called high temperature low sag conductors (HTLS) since their stranding is studied to limit the increase in sag with the increase in temperature [5]. Sag is an important parameter in the field of HVTL. It represents the distance measured from the conductor to the straight line linking two suspension points of a span. If sag increases excessively, the distance of conductors from the ground (specified by standards) may be insufficient from a safety point of view. Another tool for optimizing the current flow in a grid is using dynamic line rating (DLR) models, which are employed to dynamically vary the capacity of transmission lines according to environmental conditions [6]. In this case, too, sag is a parameter that can significantly influence DLR and, therefore, its monitoring is becoming significant. Moreover, on standard transmission lines, the seasonal change can cause the tensile load to vary a significant amount, and hence can cause a variation in sag too. If the sag value is too low, stresses in the conductors increase and this can lead to failures if stressful environmental condition occur. In addition, a decrease in sag can result in vertical span changes, which can lead to issues on the towers. On the other hand, an excessive sag can lead to more frequent phase to phase short circuits in the case of large spans and, in general, old lines present a permanent deformation which leads to a sag increase [7]. Therefore, it is clear that a continuous monitoring of the sag parameter would represent a significant improvement in the maintenance activities of transmission lines. Moreover, monitoring sag with accuracy and in real-time is very important to guarantee reliable and safe operations in smart grid networks [8]. For these reasons, different examples of sag measurement techniques are present in literature. In [9], a method relying on GPS measurements to estimate sag is described. This method allows to perform real time sag measurement. The accuracy of this measurement system is increased through enhancement techniques which generally rely on complex algorithms. Moreover, errors in GPS data can decrease the accuracy in the sag estimation. Another approach is represented by the use of robots running on the line for inspections, as presented in [10]. The limitations of this solution are represented by high cost of the machines and the fact that they may require manual controlling to work properly. The use of a simple optomechanical system with chirped fiber Bragg gratings for sag estimation is proposed and tested in [11]. The main advantage of this solution is the fact that optical sensors are insensitive to high electromagnetic fields and that this technique allows to detect wire elongation with a non-invasive measurement. However, its real feasibility for a permanent installation on a real HVTL is not clear, since the sensor is composed of fragile components. A patented device for sag estimation through vibration measurements is presented in [12]. The developed method is interesting and proposes a local tension measurement obtained by imposing a deflection of the cable inside the sensor. However, this feature does not allow the sensor to be a compact and light device.