# Modeling a Wave Energy Harvester for Supplying Data Buoys
## 1 Introduction  
Wireless sensor networks are becoming increasingly widespread in a variety of applications. An emerging field of application is represented by the monitoring of the marine environment aimed at weather forecasting, climate monitoring and protection of coastal area through networks of sensors positioned on floating buoys [1]. To power the electronic devices placed in these floating buoys in a reliable and maintenance-free way, the most efficient approach is represented by the use of energy harvesting systems that exploit the energy available in the surrounding environment [2; 3; 4; 5]. The most abundant and easily exploitable source of energy is certainly solar energy. However, this source has limitations. In fact, it is not available at night, depends on atmospheric conditions and is not available for long periods of time at high geographical latitudes. Furthermore, some types of floating buoys, called lagrangian drifters, are almost totally submerged in order to easily follow sea currents and are therefore not suitable for mounting solar panels because they would often be below sea level [6]. To overcome the issue of energy insufficiency in a single energy harvesting device, hybrid harvesting devices that exploit multiple sources have been proposed in recent years. The most obvious energy source besides solar energy in a floating buoy is undoubtedly the marine energy, i.e., the energy associated with the movement of sea waves [7]. For this reason, many research efforts are underway to develop wave energy harvesters using small, lightweight and inexpensive devices that can be easily integrated into small floating data buoys. Although the research and design of high-power large-scale wave energy converters date back to 1940 and, to date, more than 1000 designs of wave energy converters have been proposed worldwide [6], wave energy harvesters for small data buoys are much more recent [1]. The research in this field has shown that TENG and piezoelectric technologies are very promising in terms of their potential [8; 9; 10; 11; 12], but at the moment they have limitationsrelated to the conversion efficiency and output power levels, which are lower than other technologies such as those that are electromagnetic [13]. The most widespread electromagnetic transducers for high-power wave energy converters are based on rotating or linear generators. Differently, in the case of small low-power systems for data buoys, ad hoc electromagnetic generators with different structures have been developed in order to reduce the weight and dimensions. It is worth mentioning the wave energy harvester based on a swinging structure [14], which includes the two-body self-reacting point absorber [15], the harvester exploiting a moving mass with ropes [16], the counterweight pendulum structures [17; 18], the biaxial and double pendulum systems [19; 20], the chaotic pendulum-based harvester [21] and the tumbler-inspired electromagnetic generator [22]. To overcome the relative complexity of the above structures due to the connection of a plurality of mechanical structures, an interesting annular electromagnetic generator was presented in [23]. It is based on a magnetic ball moving inside an annular shell, due to the pitching effect of the waves. Coils wrapped around the outside of the shell interact with the magnetic field of the moving magnetic ball, and an electromotive force is generated to supply an electric load. The simplicity and the effectiveness of this wave energy harvester are remarkable. However, to maximize the generation of the electromotive force, the plane of the coils must be perpendicular to the changing magnetic field, while in the annular harvester, the direction of the magnetic field of the rotating sphere changes continuously due to rolling. Moreover, the ball moves due to the component of the weight force tangent to the annular shell, and this force is reduced to zero in the upper and lower areas of the ring.