###### Abstract  
Recently, there has been a significant focus on developing various energy harvesting technologies to power remote electronic sensors, data loggers, and communication devices for smart grid systems. Among these technologies, magnetic energy harvesting stands out as one straightforward method to extract substantial power from current-carrying overhead lines. Due to the relatively small size of the harvester, the high currents in the distribution system quickly saturate its magnetic core. Consequently, the magnetic harvester operates in a highly nonlinear manner. The nonlinear nature of the downstream AC to DC converters further complicates the process, making precise analytical modeling a challenging task. In this paper, a clamped type overhead line magnetic energy harvester with a controlled active rectifier generating significant DC output power is investigated. A piecewise nonlinear analytical model of the magnetic harvester is derived and reported. The modeling approach is based on the application of the Froelich equation. The chosen approximation method allowed for a complete piecewise nonlinear analytical treatise of the harvester's behavior. The main findings of this study include a closed-form solution that accounts for both the core and rectifiers' nonlinearities and provides an accurate quantitative prediction of the harvester's key parameters such as the transfer window width, optimal pulse location, average DC output current, and average output power. To facilitate the study, a nonlinear model of the core was developed in simulation software, based on parameters extracted from core experimental data. Furthermore, theoretical predictions were verified through comparison with a computer simulation and experimental results of a laboratory prototype harvester. Good agreement between the theoretical, simulation, and experimental results was found. magnetic cores; analytical models; saturation magnetization; magnetic flux; magnetic energy harvesting +
Footnote †: journal: applied sciences  
whereas the OLMEH operates with a constant voltage load. To exploit the full range of B-H characteristics, OLMEH's core is usually allowed to run into the saturation regions. The inherent nonlinearity of the magnetic core makes the OLMEH's analysis and design a challenging problem [6; 7; 8; 9]. Furthermore, extracting the full available power that the OLMEH can provide requires properly matching the OLMEH parameters to attain the maximum power point conditions [10]. An additional advantage of an OLMEH is that it can harvest the energy from a multi-kV level AC transmission line to power electronic devices operating at a low DC voltage of only a few volts [11; 12; 13; 14] while avoiding the application of bulky high-voltage step-down transformers, thus saving hardware and installation costs. To derive the DC voltage, an OLMEH requires a suitable power electronics interface, which can be either passive or active. Passive OLMEHs utilize uncontrolled diode bridge rectifiers to implement the AC-DC conversion, offering simplicity and higher reliability [10; 15]. To maximize the power density, the OLMEH should be matched to the load (typically of a constant voltage type) by appropriate selection of cross-sectional area of the core and number of secondary winding turns. Therefore, such an approach is referred to as \"maximum power point matching\" (MPPM) and allows for maximizing the harvested OLMEH power for a wide range of primary current magnitudes [16]. Yet, in cases where the CVL is a battery, its voltage is expected to vary depending on its charging state. Thus, only near-optimal matching can be attained. Active rectification is another viable approach to attain DC power at OLMEH's output.