Condition monitoring of high voltage power lines through self-powered sensor systems has become a priority for utilities with the aim of detecting potential problems, enhancing reliability of the power transmission and distribution networks and mitigating the adverse impact of faults. Energy harvesting from the magnetic field generated by the alternating current flowing through high voltage lines can supply the monitoring systems with the required power to operate without relying on hard-wiring or battery-based approaches. However, developing an energy harvester, which scavenges the power from such a limited source of energy, requires detailed design considerations, which may not result in a technically and economically optimal solution. This paper presents an innovative simulation-based strategy to characterize an inductive electromagnetic energy harvester and the power conditioning system. Performance requirements in terms of the harvested power and output voltage range, or level of magnetic core saturation can be imposed. Different harvester configurations, which satisfy the requirements, have been produced by the simulation models. The accuracy and efficiency of this approach is verified with an experimental setup based on an energy harvester, which consists of a Si-steel magnetic core and a power conditioning unit. For the worst-case scenario with a primary current of 5 A, the maximum power extracted by the harvester can be as close as 165 mW, resulting in a power density of 2.79 mW/cm^{3}.

Condition monitoring of high-voltage power lines plays an important role in the design and operation of electrical power networks, providing a comprehensive view of the state of the transmission power systems or the electric grid infrastructure. The purpose of condition monitoring is twofold: Firstly, it boosts revenue by reducing installation, maintenance and operating costs. This is especially true when self-powered and autonomous sensors are used, which allow the utility shutdown to be reduced, since battery-powered sensors have a fixed and limited lifespan. Secondly, condition monitoring improves supply reliability since periodic inspections are required, although these are usually carried out by less reliable, traditional, on-ground visual means. The significant advantages condition monitoring brings to the grid operators, can however be outweighed by the operating costs and maintenance requirements of monitoring sensors. Needless to say, this runs counter to the reduction of the reinforcement and maintenance costs grid operators are seeking to achieve these days. Finally, condition monitoring allows predictive rather than corrective maintenance to be done, prolonging the useful life of the assets in the grid at the expense of increased risk of failure. This risk can be mitigated by collecting accurate and real-time information about the performance and operating condition of the grid.

Energy harvesting as power source for condition monitoring is increasingly being investigated as an attractive alternative to batteries, particularly in low power sensing applications. Likewise, the advances in wireless network technologies and the reduction in power requirements of electronic devices have paved the way to independent remote sensing nodes. These features have made condition monitoring a viable reality.

In the literature, there is a broad range of different architectures for energy harvesting systems. However, all of them have some blocks in common as depicted in

Regarding the energy sources and harvester, there are several alternatives that have been reported in the literature. Wind power [

As far as the power and storage management circuit are concerned, power electronics are required for several reasons. Firstly, high power extraction involves impedance matching between the energy harvester, and the load, i.e., when the load impedance equals the complex conjugate of the source impedance [

This paper presents a simulation-based strategy for characterizing a CT-based inductive electromagnetic energy harvesting system, in terms of the core material through its magnetization curve, number of turns in the secondary winding, magnetic path length and cross-sectional area of the core, copper cross section of the winding, primary current, length of the copper wire, load resistance and compensating capacitor, inter alia. This work introduces a new energy harvester design strategy aiming at extracting the maximum power from a high voltage line. An experimental setup with different configurations validates this strategy. The MATLAB/Simulink tool is used for modeling the energy harvesting system and for data visualization. The system is able to accurately estimate the matching impedance, the optimal dimensions of the coil and the power harvested for different primary current conditions and different loads. As a result, a rapid prototype design is developed.

The remainder of this paper is organized as follows. In

In this section, an electrical circuit model of the inductive electromagnetic harvester based on the electromagnetic theory and the equivalent circuit of a current transformer is presented. As stated in the introductory section, CTs are generally used to measure line currents in electric power systems. This is done by sensing the magnetic field generated by the current. In that context, the main purpose of CT is to translate the primary current in a high voltage power line into the secondary current whose value is directly proportional to the primary current and inversely proportional to the number of turns in the secondary winding. However, current transformers can also be used as energy harvesters to power electronics attached to the power line for condition monitoring purposes. In fact, a CT is a preferred device to harvest power in the grid nowadays. There are several reasons for this assumption. Firstly, the current-transformer-based inductive harvester encloses the conductor to obtain maximum magnetic coupling. As a result, the power density of this type of energy harvester is relatively high and maximum amount of power can be extracted from the magnetic field. Secondly, the installation of this type of CT-based harvesters does not require a major power shutdown, provided a split magnetic core is used. Thirdly, the CT is galvanically isolated from the high voltage power line. Therefore, in principle a malfunction of the CT does not degrade the reliability of the monitored system. Finally, the CT tolerates harsh operating conditions without degradation in performance.

_{p}, which generates the magnetic field, H, and the flux density B inside the core. This induces a voltage in the secondary winding and, when a resistive load is connected to the harvester, the current flowing through it is proportional to the primary current, provided the core is not in hard saturation.

In _{S}, the secondary leakage resistance, represents the power loss of the secondary winding. The magnetic flux losses of secondary windings are represented by the leakage inductance Ls. If the magnetic core has high permeability, most of the mutual linkage flux is confined to the core. The leakage flux can be assumed proportional to the current producing it and it depends on the geometry of the winding and core. Therefore, it can be assumed that the leakage inductance, Ls, is constant accounting for the voltage drop induced by the leakage flux. Finally, C_{L} is used to compensate the inductive behaviour of the harvester aiming to harvest the maximum power available at low primary current, the startup primary current, at which the available power is limited.

Considering that the harvester is based on an ideal CT, the current flowing through the secondary winding can be evaluated by using the amp turn equation:_{S} is the number of turns in the secondary winding and N_{P} = 1 for the CT in _{st}, can be expressed as:_{lm} is the magnetizing current, whose instantaneous value can be written as:

While the magnetic core is not saturated, i.e., I_{lm} ≈ 0, the harvested current going to the load, I_{s}, is only determined by the primary current divided by N_{S}. The magnetic core, however, exhibits nonlinear behavior, which in _{m}, a nonlinear inductor that plays the role of the CT magnetization inductance. L_{m} can be modelled by using the magnetization curve of the core, i.e., the magnetic flux density versus magnetic field strength characteristic, the core cross sectional area,_{s}. These parameters are used in the Simscape model of the non-linear inductor, which can be specified with varying levels of nonlinearity [_{m} can be express by using Equation (4):^{−7} H/m, and

For a core material with high permeability, the magnetizing inductance takes a high value and the harvester works as an ideal CT. This is the ideal CT operation that takes place in the linear region of the B-H curve where the core is not saturated, and the entire transformer current is delivered to the load. This is also the working region for a CT-based primary current measurement device, where the primary current can be estimated by measuring the secondary current, since they are proportional to each other. When the core is operating in the knee or in the flat tail regions in the B-H curve, the core is said to be saturated. Uncontrolled core saturation can bring about detrimental effects as stated below.

According to Faraday’s law, the voltage developed by the core is proportional to the time derivative of B. A sinusoidal AC current flowing through the primary conductor generates a time-varying magnetic field around the wire, and through the magnetic core the magnetic field is turned into a time-varying magnetic flux density (B(t)). Voltage is induced across the terminals of the secondary winding when the magnetic flux (Φ(t)) crosses the loops in the secondary winding. If B(t) is uniform over and perpendicular to the area A_{eff} of the coil, the voltage induced in a Ns-turn winding can be expressed by:_{p}(t) = I_{p}cos(ωt + φ)_{eff}, for a toroidal core. Then, Equation (5) can be expressed as:

From Equation (5), B(t) can be derived as follows:

One of the negative effects of core saturation occurs when the operating point in the B-H curve of the core is in the flat tail regions where B takes a constant value regardless of the variation in H and time (see

In this paper a MATLAB/Simulink-based simulation model is implemented to characterize the energy harvester in terms of several parameters: (i) the minimum power required by the monitoring system; (ii) the load resistance to keep the core operating within the transfer window for the designed voltage range; (iii) the compensating capacitor to extract maximum power when the startup primary current flows through the primary conductor; (iv) the number of turns in the secondary; and (v) the maximum level of core saturation. This latter parameter cannot be obtained directly from the model. Two related parameters can be considered and measured to estimate the level of saturation, namely: (i) the Total Harmonic Distortion (THD) of the induced voltage in the secondary winding or the secondary current; and (ii) the deviation of the current in the secondary winding from the ideal value based on the current source behavior, i.e., value I_{m} in

When the magnetic core is not saturated or in soft saturation (_{lm} lags 90º the total secondary current, I_{st}, on account of the resistive load connected for the harvester. In soft saturation, the time-varying value of the magnetizing inductance makes I_{lm} different from zero, which causes the distortion of the load current. By calculating the THD of the load current, the level of core saturation can be estimated. When the core goes through the knee region in the magnetizing curve towards deeper saturation, still without reaching hard saturation where B(t) = Bsat and the inductive voltage equals zero, I_{load} is virtually zero during a period of time within the line cycle. This leads to more distortion of I_{load}, as can be seen in _{load}, can be taken as an indicator of core saturation. This value will be used as an additional requirement to determine the load resistance and the compensating capacitor values for maximum power extraction purposes.

As stated above, the process of characterization of an inductive electromagnetic energy harvester is not straightforward, on account of the number of variables involved. In _{p}), number of turns in the secondary winding (N_{S}), load resistance (R_{L}), compensating capacitor (C_{L}), core cross-sectional area, core magnetic path length and the core magnetization curve, inter alia. The key aim consists in defining the relationship between the output power and the aforementioned variables. In literature, the relationship among some of them has been determined through analytical models. However, these analytical models have to be combined with the power management circuits required for power conforming and voltage regulation. In this section, this relationship is defined by implementing a simulation approach based on the circuit depicted in _{eff} and the magnetic path length l_{eff} correspond to the values of the core used in the prototype of the harvester shown in Table 3. It is important to remember that the energy harvester is modeled by an ideal transformer, the nonlinear inductor, and the secondary leakage resistance and inductance.

This model is used to evaluate the amount of power that can be extracted by a harvester with rectifier and resistive load (see

From the

Although

To prove the effectiveness of the strategy presented in this paper, a set of requirements is established and the harvester configurations which satisfy the requirements are depicted in more easily readable form.

From

Model 2 allows the compensating capacitor to be evaluated for maximum power transfer. When there is reactive power compensation, the energy harvester will provide more power to the load. This produces an undesirable side-effect on the harvester: higher power will increase voltage in the magnetizing inductance thereby increasing the magnetizing current and leading the core into saturation with smaller primary current. This fact can be observed in _{L,} with values ranging from 5 to 25 μF. For the simulation, Ns equals 200 turns, with the primary current being 5 A, since it is the worst case scenario.

To harvest more than 150 mW, for the startup primary current, the compensating capacitor should take values between 12 and 14 µF with the corresponding load resistance. The pairs of C_{L} and R_{L} to some extent could be regarded as the matching impedance for the harvester for a certain level of core saturation.

The accuracy of the models proposed is verified by developing a prototype of the harvester. The simulation results are compared with the measurements obtained by different configurations of the prototype.

The energy harvester consists of a CT with a Si-steel magnetic core characterized by the B-H curve shown in

The choice of the material and size of the core relies on several variables. Firstly, the power capability of the core in terms of the amount of power harvested as a function of the primary current i.e., mW per A in I_{p}. Secondly, the core window area should provide sufficient space for the primary wire and the secondary winding. Thirdly, the core should have a high saturation flux density, Bsat. The higher Bsat the greater the amount of power that can be extracted since more magnetic energy can be collected by the core. Finally, transmission line operating requirements have to be complied with. A bulky core, for instance, may increase the sag of the transmission line. Two core materials have been considered: ferrite and grain oriented Si-steel material. The final choice of the core material and size was made by using the magnetization curves in the nonlinear inductor in

The secondary of the CT has been designed to provide several winding configurations with 91, 154 and 200 turns. Furthermore, a capacitor bank and a potentiometer have been included for resistive load and compensating capacitor definition aiming at simulating different loading conditions. The wire size for the secondary winding is chosen taking into consideration the power losses, which depends on how much current is being drawn from the winding, the length of the wire and the wire resistivity.

Several harvester configurations have been tested and verified. Regarding the energy harvester based on Model 1, the estimated and measured power along with the relative error for different values of Ns, RL and Ip are evaluated and represented in

As far as Model 2 is concerned, _{L}, C_{L} for N_{S} = 200 and I_{p} = 5 A.

The power is calculated in the same way as that used in Model 1 and the same conclusions can be reached regarding the influence of the core saturation upon the output power. However, for a startup current of 5 A when reactive power compensation is achieved, the output power obtained is larger than that of Model 1. This power critically depends on the value of the compensating capacitor. For example, for C_{L} = 30 μF, the output power is lower than in the cases when C_{L} = 10 μF and C_{L} = 16.9 μF. This fact was seen in _{L} greater than 20 μF the output power sharply decreases. Hence, the output power is very sensitive to the value of C_{L}, which depends on the value of the magnetizing inductance, L_{m}. The latter exhibits great variability under core saturation in both the knee region and in deeper saturation, which hinders the ability of the model to better estimate the compensating capacitor under such conditions. This is the reason behind the increase in the relative error for C_{L} = 30 μF. According to the relative error range, Model 2 is reasonably precise, allowing the range of potential capacitor values to be estimated for maximum power extraction.

In order to assess the performance of the proposed inductive electromagnetic energy harvester for high voltage power lines, the common standards of power per unit of magnetic core volume, i.e., power density, and power per unit of the primary current can be used. However, for comparison purposes the power density in mW/cm^{3} is more suitable, since most works in the literature utilize this parameter. For the worst case scenario, at the startup current of 5 A, the harvested power density can reach 2.79 mW/cm^{3}. Therefore, the harvester proposed in this paper outperforms other approaches to electromagnetic inductive energy harvesters [^{3}. Finally, in [^{3} and for a ferrite core 1.97 mW/cm^{3}. High permeability of nanocrystalline cores account for their best power density, although at the expense of cost and, most importantly, nanocrystalline cores cannot be easily split because of poor mechanical integrity.

In this paper, simulation-based characterization of inductive electromagnetic energy harvesters has been analyzed for two different harvester models. Conflicting design goals, such as maximizing the output power while limiting the output voltage levels and keeping the magnetic core at the onset of saturation, have been simultaneously addressed. Furthermore, an additional insight into the relationship among the different parameters involved in the harvester design process, has been provided. With an eye to potential applications, an experimental estimation technique has been developed, such that the variables influencing the performance of any electromagnetic energy harvester can be evaluated from arbitrary values of output power, primary current, output voltage range and level of core saturation, to name but a few. Two significant contributions have been made in the work presented in this paper: (i) by using a simple MATLAB/Simulink electrical circuit based on a current transformer, an inductive electromagnetic energy harvester can be rapidly deployed; (ii) the level of magnetic core saturation has been estimated and controlled through the evaluation of the total harmonic distortion of the secondary current. The performance of the estimation technique has been experimentally validated by creating a prototype for the harvester, which consists of a Si-steel magnetic core and a power conditioning unit. For the worst case scenario with a startup current of 5A, and for a secondary winding of 200 turns, achieving reactive power compensation, the maximum power extracted by the harvester can be as close as 165 mW, which represents a power density of 2.79 mW/cm^{3}. The results obtained confirm that the proposed simulation strategy is accurate in predicting the behavior of the harvester for different operating points and under several loading conditions.

All the authors conceived the idea, and designed and performed the experiments. P.M.S. carried out the simulations and wrote the paper. F.J.R.S. and E.S.G. were involved in the process of correction. All authors have read and agreed to the published version of the manuscript.

This work has been supported by the Autonomous Community of Madrid under the project P2018/EMT-4366 and by the Spanish Ministry of Science and Technology under the project RTI2018-098865-B-C33.

The authors declare no conflict of interest.

Block diagram of an energy harvesting system.

Equivalent electrical circuit of a CT-based electromagnetic energy harvester.

Magnetization curve of the non–linear inductor.

(

(_{load}; and (_{load} as a function of I_{p}, R_{L} and Ns.

Power, THD, V_{load} and I_{load} as a function of R_{L} and CL for Ip = 5 A and Ns = 200.

Circuit schematic diagram of the prototype of the harvester.

Verification of Model 1 accuracy.

Verification of Model 2 accuracy.

Harvester configurations for a particular/specific set of requirements.

I_{p}(A) |
R_{L}(Ω) |
V_{load}(V) |
I_{load}(mA) |
THD (%) | Power (mW) |
---|---|---|---|---|---|

12 | 65 | 3.21 | 49.42 | 6.3 | 158 |

12 | 70 | 3.44 | 49.15 | 5.6 | 169 |

13 | 60 | 3.24 | 54.08 | 6.8 | 175 |

13 | 65 | 3.49 | 53.81 | 5.8 | 188 |

14 | 50 | 2.95 | 59.04 | 6.5 | 174 |

14 | 55 | 3.23 | 58.76 | 5.8 | 189 |

15 | 40 | 2.56 | 64.05 | 6.3 | 164 |

15 | 45 | 2.86 | 63.74 | 6.6 | 182 |

15 | 50 | 3.17 | 63.45 | 6.9 | 201 |

15 | 55 | 3.47 | 63.16 | 5 | 219 |

Harvester configurations for specific requirements.

C_{L}(μF) |
R_{L}(Ω) |
V_{load}(V) |
I_{load}(mA) |
THD (%) | Power (mW) |
---|---|---|---|---|---|

12 | 47 | 2.66 | 56.72 | 7.9 | 151.25 |

12 | 37 | 2.35 | 63.76 | 7.2 | 150.43 |

13 | 39 | 2.48 | 63.61 | 7.5 | 157.80 |

13 | 41 | 2.60 | 63.48 | 7.8 | 165.22 |

14 | 31 | 2.16 | 69.76 | 8.7 | 150.89 |

Harvester parameters.

Parameter | Value | Unit |
---|---|---|

Core material | Silicon steel | |

Magnetic path length (leff) | 19.70 | cm |

Cross-sectional area (Aeff) | 312 | mm^{2} |

Core window area | 1000 | mm^{2} |

Weight | 0.420 | Kg |

Ns | 200, 154, 91 | turns |

Winding wire diameter | 1 | mm |

Average length per turn | 80 | mm |

Maximum height | 25 | mm |

Saturation magnetic flux density, B_{sat} |
1.7 | T |