Inductive Power Line Harvester With Flux Guidance for Self-Powered Sensors

Self-powered sensors are expected to enable new large-scale deployment and location access capabilities for sensor systems. Energy-harvesting devices have been shown to provide adequate power densities, but their dependence on very specific environmental conditions restricts their applicability. Energy harvesting from power line infrastructure offers an architecture for addressing this challenge because such infrastructure is widely available. In this article, an inductive power line harvester concept is presented based on a flux concentration approach adapted to a closed-loop core geometry. Flux concentration is studied by simulation, showing a 26% flux increase using a 1:3 geometrical concentration ratio in a closed-loop core. A $20\times 20\times25$ mm prototype with a U-shaped soft-core sheet and a 200-turn Cu coil around a 5-mm-diameter, 20-mm-long soft-core rod is introduced. The total device volume is 9.1 cm3. Characterization results on a power line evaluation setup for currents up to 35-A rms and a 50-Hz–1-kHz range are presented. Power between 2.2 mW (50 Hz) and 233 mW (1 kHz) is demonstrated on an ohmic load, from a 10-A rms power line current, employing impedance matching with reactance cancellation. The corresponding power densities are 0.24 and 25 mW/cm3 per total device volume. This performance is adequate for enabling self-powered wireless sensor networks installed along power distribution lines.


I. INTRODUCTION
T HE energy autonomy of sensors is currently a major lim- iting factor in their development and deployment.This is especially true for applications that intend to enable advanced information services in remote and inaccessible environments.Self-powered sensors are expected to enhance the reliability and functionality of monitoring technologies and expand them to scale and environments that are not accessible by traditional power supply methods.Harvesting ambient energy, including motion, thermal, and solar sources, has been shown to provide adequate power density for supporting duty-cycled microsensor use cases [1], [2], [3].A key challenge in these technologies is their reliance on very specific environmental conditions and installation methods, requiring bespoke design and development for each type of location.To overcome this, the expansion of applicability to multiple orientations [4], multiple power sources [5], and broadband motion [6] has been proposed.
On the other hand, inductive harvesting from power lines is applicable to several environments of key interest, such as industrial plant and warehouses, utility and transportation networks, commercial and residential buildings, as well as vehicle environments, including cars, trucks, trains, and aircraft.The omnipresence of power lines in these environments offers an opportunity for overcoming the challenge of narrow applicability and provides self-powered sensors suitable for a wider application range.
While various other power line harvesting methods, including capacitive [7], [8] and magnetic force motion [9], [10], [11] coupling, have been proposed, inductive coupling is particularly attractive due to the advanced know-how that is available from other very common applications, including large-scale generators and electrical appliance transformers.In harvesting, the requirements for noninvasive installation, miniaturization, as well as operation at the maximum power delivery point create a new device engineering environment for inductive transducers.
To enhance the available magnetic flux density B, soft magnetic layers in flux-concentrating geometries have been considered.In microsystems, these magnetic flux concentrators have been shown to enhance the local magnetic field for microelectromechanical systems (MEMS), including resonator magnetometers [12], magnetoresistive sensors [13], [14], and current sensors [15].The proposed structures include thin deposited layers [16], trapezoidal [15], tapered [17], and filleted and chamfered shapes [14].Three-dimensional structures have also been implemented [15].With such methods, sensors with increased sensitivity, signal level, and signal-to-noise ratio can be achieved.
In inductive energy transduction, geometrical flux funneling can reduce the required soft core and coil mass.In addition, it allows a significant reduction of coil resistance for a given amount of flux.Overall, the higher B can lead to a considerable increase of power density for inductive energy collectors [17].The employment of bow-tie and H-shaped structures for flux funneling has been investigated in [18] and [19], respectively.Another nonfunneling flux guiding method using a U-shape core has been reported in [20].Hshaped flux-funneling structures for energy harvesting from the magnetic field around structures that carry a spatially distributed current (e.g., the body return current path of vehicles including aircraft) have been studied in [17], [19], and [21].A power supply, including power management and supercapacitor intermediate storage based on this method and developed for an industry-defined aircraft use case, was demonstrated in [22] and a further study of magnetic funneling on a similar device was reported in [23].A prototype of around 100 cm 3 developed for railway applications was demonstrated to provide 40 mW at a 250-mm distance from a 200-A, 50-Hz emulated railway structural current in [24].
Most of these flux-funneling devices, implementations, and studies focus on open-loop structures, which have the benefit of simpler installation and allow the exploitation of a wider range of alternating environmental fields.In this article, the flux concentration study in magnetic fields around conductors is extended to include closed-loop cores around single current direction cables.The magnetic field in indicative symmetric as well as flux-funneling core geometries is studied by numerical simulation in Section II, using the COMSOL Multiphysics finite-element modeling software suit.A prototype flux-funneling energy harvester is presented in Section III.In Section IV, the device performance is characterized using a custom evaluation setup and the power delivery to an ohmic load for various source current frequency and intensity is studied.The maximum power point is analyzed, the benefit of reactance cancellation is experimentally quantified, and conclusions are discussed in Section V.

II. SIMULATION STUDY A. Flux Concentration
The effect of introducing a ferromagnetic material in a homogeneous environmental magnetic field has been studied in [23].In a simple rod geometry, magnetic pole alignment in the material leads to its magnetization field, which increases the magnetic flux density B in the material at the Fig. 1.Simulated magnetic flux by a μ r = 200 core cylinder in a 1-μT uniform field, from [23], illustrating the concentration effect.Fig. 2. Flux concentration ratio versus core aspect ratio, calculated from simulations as indicatively shown in Fig. 1.The flux improvement lies in the order-of-magnitude of the core length/diameter ratio [23].
expense of a weaker flux density around it.Three-dimensional simulation results, visualizing the flux concentration effect for a rod with relative magnetic permeability μ r = 200, diameter D, and height L in a 1-μT field, are shown in Fig. 1 (from [23]).The total flux concentration is determined by μ r , but it also depends on geometry.Simulated flux increase ratio results as a function of the core L/D ratio have been presented in [23] and are also shown in Fig. 2. Increasing μ r results in moderate concentration increase.In contrast, the flux concentration increase follows, in an order-of-magnitude approximation, the geometric aspect ratio of the core, for L/D ≥ 1.
These results are for the case of introducing a soft core in a large space with a uniform magnetic field.The core dimensions are much smaller than the overall length of the flux trajectory around the field source (e.g., a current line) and the flux concentration occurs only in the vicinity of the core.This is why the flux-funneling ratio is defined by the geometry rather than by μ r , as shown in Fig. 2.
In contrast, if the core can form a complete loop around the current line that causes the field, the reluctance of a full-loop trajectory through the core is reduced by a factor equal to μ r because [25] where μ 0 is the permeability of space, l is the average loop length, and S is the core cross section.In such cases, the increase of B in the core is indeed equal to μ r of the material.Simulations of the magnetic field vector norm and the axial current skin effect of a 10-mm-diameter Cu wire carrying a 1-A amplitude current of various frequencies are presented in Fig. 3. Plotting both fields together is possible because the current and flux densities are studied in separate, complementary areas, i.e., inside and outside the conductor, respectively.The 300-, 500-, and 800-Hz values were selected in correspondence to aircraft sensing use cases, in which the operating frequency of power lines lies in the 360-800-Hz range [26], [27].The skin effect is visible in the grayscale current density field at 500 Hz and, more pronounced, at 800 Hz.
The field increase due to the presence of a full-loop core that is observed in Fig. 3 is indeed by a factor of μ r = 200.In practice, the harvester needs to be installed onto existing wire infrastructure, and therefore, even in applications where wrap-around installations are permissible, a clip-on mechanism must be used, resulting in a small core loop gap with length l g , which is usually very small compared to l.The reluctance will then be [25] The second term in (2) dominates R tot for μ r values greater than l/l g , which is usually in the range between 10 and 100.Therefore, the flux concentration achievable in clip-on energy harvesters is limited by the loop gap rather than by μ r .

B. Flux Guidance
As mentioned, further flux density increase can be achieved by employing structures that guide flux such as to concentrate it into a smaller area, obtaining a higher B that is beneficial for inductive energy transduction.Experimental and simulation studies have demonstrated that in open-core transducers, and in addition to the flux concentration achieved by single rod shapes studied in Section II-A, additional concentration can be obtained by using H-shaped structures [17], [19].If L is the flange length and D is the central rod diameter of the H-shaped structure, an additional concentration by a factor of L/D can be achieved, assuming a flange width W equal to D. Experimental results from an energy-harvesting device employing such a flux concentrator, including a study of the effect of the flange thickness τ on device performance, have been presented in [23].
Flux funneling in the case of a core loop around the current carrying conductor can be studied using a structure with two semicylindrical parts of different lengths, as shown in Fig. 4(a).This geometry is selected for a clear visualization of the flux-funneling effect in a closed-loop geometry and  From these results, it is possible to obtain the open-circuit voltage and power output for certain coil geometries, either by including electromagnetic induction to the finite-element simulation or, analytically, through Faraday's law.An analytical model for this purpose has been presented in [17].In Section III, this flux guidance method is employed for the design and fabrication of a clip-on power line energy harvester.

III. DEVICE FABRICATION AND CHARACTERIZATION METHOD
Based on the study presented in Section II as well as on analysis, simulation, and experimental results of [17], [19], [22], [23], and [28], a clip-on, wrap around inductive energy-harvesting transducer was fabricated.The longer semicylindrical core was implemented using a 0.5-mm-thick Ni-Fe alloy sheet, with 80% Ni composition and nominal  A 20-mm-long, 5-mm-diameter ferrite rod with μ r = 250 and a mass of 1.8 g was used as flux bridge between the two U-shape legs.The geometrical funneling ratio of this structure is therefore L/D = 4.In this way, a fluxfunneling structure similar in principle with that studied in Section II is implemented, with the rod corresponding to the short semicylindrical core part.This geometry was designed to allow a simple practical assembly and installation on existing power lines, without the need of fabricating complex magnetic soft-core structures.
A 200-turn, 0.2-mm-diameter enameled Cu wire coil was hand-wound around the rod.The series resistance and inductance of the coil-core structure were measured to be 2.6 and 1 mH, respectively.When installed within the U-shaped core, the resistance and inductance were increased to 3.2 and 7 mH, respectively.The total coil-core mass (excluding

TABLE I MEASURED MASS AND FEATURES OF THE HARVESTER COMPONENTS
the U-shape core) was measured to be 5.0 g.A photograph of the prototype energy harvester is shown in Fig. 7.In the picture, the coil and rod have been slid out of their normal position, which lies at the axial center of the U-shaped core, to allow their view.A schematic description of the overall device design architecture is shown in Fig. 8.Only one of the two U-shaped cores shown in Fig. 8 was included in the prototype.A summary of the masses and features of the energy harvester components are presented in Table I.
The device was characterized on a custom power line setup capable of providing up to 20-A rms current through cables with Cu cross-sectional area of 2.5 mm 2 or greater, in the audio frequency range.The conductor current was monitored using a Keysight U1583 clamp probe connected to a Fluke 787B

IV. RESULTS AND DISCUSSION
The energy harvester was tested with direct connection to a resistive load for a power line current range between 1 and 35 A rms, in the 50-Hz-1-kHz frequency range.These conditions correspond to electrical power line characteristics anticipated for aircraft.The rms voltage output V R measured on the load as a function of load resistance R L is plotted in Fig. 10, for a power line rms current of 10 A. The corresponding average power delivered to the load is presented in Fig. 11.The maximum power delivery occurs at a loadmatching condition, which in the general case of a coil is expressed as R L,m = |Z L |, where R L,m is the maximum power delivery load resistance value and Z L is the complex output impedance of the coil.This condition occurs at a load voltage V L,m near but not exactly at the half open-circuit voltage (V OC ) point because the load voltage is This is in line with the data of Figs. 10 and 11, in which the maximum power is obtained at a V R value slightly higher than V OC /2 for all frequencies.The V OC and maximum power point (V L,m , R L,m and maximum power P L,m ) are extracted from Figs. 10 and 11 and presented in Table II.A power output of 2.2, 18, 26, 70, and 187 mW is demonstrated for 50 Hz, 360 Hz, 500 Hz, 800 Hz, and 1 kHz, respectively.
The dependence of open-circuit voltage on frequency is plotted in the inset of Fig. 10.The voltage scales with frequency in accordance with Faraday's law of induction, from which a linear increase is expected.Above 360 Hz, a deviation from Faraday's law zero-crossing linear fit is observed.This indicates an increase of flux concentration, which is attributed to less reluctance at core interface gaps and better core performance at higher frequencies.Furthermore, the observed power-frequency dependence deviates significantly from the theoretical power scaling with f 2 .This is attributed in part to the nonlinear V OC scaling observed in the inset of Fig.   but also to the increase of coil impedance with frequency.The imaginary part of Z L can be compensated by connecting a capacitor C S in series with the coil, selected to present a reactance opposite to the inductive reactance of the coil.This complex matching is frequency dependent, which means that a different C S value is optimal for each frequency.C S required for each frequency was experimentally determined by connecting the optimum load R L,m through different C S capacitors and monitoring the load voltage.The C S value that maximizes the load voltage was selected, as this is the value that provides the best possible reactance cancellation.The C S values for each frequency are included in Table II.Subsequently, the load resistance value for maximum power delivery must be redetermined, to match the magnitude of the remaining output impedance of the coil-capacitor system.The corresponding R L -sweep results are shown as dashed lines in Fig. 11.From these data, the new maximum power points, including the optimal load voltage V L,m , optimal load resistance R L,m , and maximum power P L,m , were determined.The results are also included in Table II.The optimal load values and the corresponding average power are also plotted in Fig. 12 for comparison.For 50 Hz, no voltage increase was achieved even with C S values over 100 μF.This is because the output impedance magnitude before reactance cancellation was 5 , which is close to the independently measured coil ohmic resistance of 3.2 .The cancellation of reactance in the range of a few ohms is difficult to achieve with discrete components, as the capacitor series resistance and ohmic effects at the additional contacts become significant.Therefore, the 50-Hz frequency is not included in the reactance cancellation study of this work.A significant reduction of output impedance is observed in the case of 360 Hz (from 26 to 13 ), 500 Hz (from 31 to 20 ), 800 Hz (from 39 to 27 ), and 1 kHz (from 41 to 29 ).Due to imperfect cancellation, the remaining impedance is still complex.This results in a smaller but still observable shift of the optimal power delivery point from the half-V OC condition, apparent in Table II for 800 Hz and 1 kHz.Given that a large part of the coil inductance is compensated for, the increase of output impedance with frequency is attributed to core losses.The skin effect for Cu for frequencies below 1 kHz is larger than 2 mm and therefore negligible in the 0.2-mm-diameter wire used in this energy harvester implementation.A significant power increase is demonstrated, delivering 24, 36, 94, and 233 mW at 360 Hz, 500 Hz, 800 Hz, and 1 kHz, respectively, from a 10-A rms current.
The scaling of the transducer performance with power line current was studied in a separate experiment.The measured open-circuit rms voltage output for power line currents in the range 1-20 A rms is plotted in Fig. 13 for different frequencies.
From these measurements, the total magnetic flux through the coil can be calculated from Faraday's law.The corresponding spatial average magnetic flux density is plotted in Fig. 14.The nonlinear B increase with power line current beyond 5-A rms, corresponding to a spatial average of 0.1-T rms as shown in Fig. 14, is attributed to local core saturation near the flux-turning core interfaces.This was also apparent as voltage waveform distortion for power line currents beyond 20-A rms (corresponding to 0.25 T rms).A higher magnetic field density and more apparent distortion was observed for 50 Hz in comparison with other frequencies at the same power line current.Due to this high distortion, results up to only 17-A rms are recorded to avoid a possibly erroneous indication at this frequency.

V. CONCLUSION
Power line harvesting can be used for implementing selfpowered sensors in a broad range of industrial, infrastructure, civil, and vehicle environments.Simulations show that flux-funneling soft-core structures can offer a geometrical amplification of magnetic flux density for both open-and closed-loop cores, substantially increasing the output power density of inductive energy harvesters.This increase is not only due to core mass reduction but also mainly due to the reduction of coil area and thereby the coil resistance, which increases the power output at load-matching conditions as discussed in detail in [17].
A 20 × 20 × 25 mm energy-harvesting prototype with total volume 9.1 cm 3 was introduced, designed for unidirectional ac power lines of diameter up to 10 mm.It employs a closed-loop soft core with a flux-funneling geometry.Power delivery improvement between 25% and 35% was demonstrated by adding reactive compensation capacitors for a frequency range between 360 Hz and 1 kHz.The power supply was shown to deliver 2.2, 24, 36, 94, and 233 mW at 50 Hz, 360 Hz, 500 Hz, 800 Hz, and 1 kHz, respectively, into an optimal ohmic load, from a 10-A rms power line current.The corresponding power densities are 0.24, 2.6, 3.9, 10.2, and 25 mW/cm 3 .A comparison with other power line harvesters in various environments, intended for implementing self-powered sensors, is presented in Table III.
The power output scales with the square of current amplitude and frequency.Hence, a comparative figure of merit in mW/(cm 3 • A 2 • Hz 2 ) units could be defined and calculated from the data in Table III.On the other hand, the suitability of each method for different applications depends on the environmental conditions and installation limitations involved.Therefore, an analysis of applicability would be required for a comparative study of performance.Such a study would be technically useful, but it lies beyond the scope of the present work.
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TABLE III OVERVIEW OF ENERGY-HARVESTING DEVICES FOR ENVIRONMENTAL ELECTROMAGNETIC FIELDS
The results presented in this article show that the power density of power line energy harvesters can surpass the power demand of typical wireless sensors even in demanding sensing scenarios.For example, the wireless strain sensor node architecture of [33] has a maximum power consumption of around 100 mW and can operate with less than 1-mW continuous power in duty-cycled acquisition and transmission mode.Flux funneling, advanced core-coil design, and reactive impedance matching are expected to allow the adoption of power line harvesting technology for self-powered wireless sensors in aircraft and railway in the near future.The employment of flux concentration in the radial direction, by reducing the core sheet thickness at the coil area, is expected to further increase magnetic flux and power density and hence the scalability and practicality of inductive energy collectors.In this direction, magnetic saturation is expected to impose an upper power density limit [34] but may also be considered as a method to protect power management electronics from undesirable high-voltage spikes.
The power density demonstrated in this article may allow the implementation of self-powered sensors deployable along power lines in industrial, vehicle, and transportation environments.Due to the wide availability of power lines in such environments, the proposed method offers a self-powering architecture that addresses the challenge of narrow applicability of energy-harvesting device designs, opening up the way for commercial and industrial deployment of self-powered sensors.

Fig. 3 .
Fig. 3. Simulated axial current and vector norm magnetic flux density of a 10-mm-diameter Cu wire carrying a 1-A current of various frequencies, at a cross section perpendicular to the wire at the center of the core length.(a) Finite-element modeling mesh.(b) No ferrite core.(c) Ring ferrite core with 10 mm inner diameter, 20 mm outer diameter, and μ r = 200.(d) Ring ferrite core with 20 mm inner diameter, 30 mm outer diameter, and μ r = 200.The skin effect is visible in the current density distribution at 500 and 800 Hz.

Fig. 4 .
Fig. 4. Simulated axial current and magnetic flux density norm of a 10-mm-diameter Cu wire carrying a 1-A current at 500 Hz with a flux-funneling core loop with 20 mm inner diameter, 30 mm outer diameter, and μ r = 200.(a) Mesh and dimensions.(b) Case of equal lengths, L/D = 1 (no funneling).(c) Indicative case of L/D = 2 resulting in flux funneling.

Fig.
Fig. Simulated total flux through the central D × τ cross section of the short core part of Fig. 4 as a function of L/D ratio.The corresponding average B is indicated on the right axis.

Fig. 6 .
Fig. 6.Simulated B vector field showing the flux concentration effect.

Fig. 8 .
Fig. 8. Schematic of the overall device design concept.

Fig. 10 .
Fig. 10.Measured harvester rms voltage output on a resistive load as a function of load resistance for 10-A rms power line current of various frequencies.

Fig. 11 .Fig. 12 .
Fig.11.Average power on load as a function of load resistance, corresponding to the measurements of Fig.10for 10-A rms power line current of various frequencies.The corresponding measurements using a series capacitor for reactance compensation are also shown in dashed lines.

Fig. 13 .
Fig. 13.Measured open-circuit voltage of the energy harvester as a function of power line current for different frequencies.

Fig. 14 .
Fig. 14.Average magnetic flux density through the coil as a function of power line current for different frequencies, calculated from the open-circuit voltage measurements of Fig. 13.Measured data from an extended current range, up to 35-A rms, not shown in Fig. 13 are included here.

TABLE II MAXIMUM
POWER DELIVERY POINTS EXTRACTED FROM THE DATA IN FIGS. 10 AND 11.VOLTAGE VALUES ARE RMS