# An Experimental Strategy for Characterizing Inductive Electromagnetic Energy Harvesters

^{*}

## Abstract

**:**

^{3}.

## 1. Introduction

## 2. CT-based Energy Harvesting System Model

#### 2.1. Equivalent Electrical Circuit of the Energy Harvester

_{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.

_{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.

#### 2.2. Linear and Nonlinear Behavior of the Energy Harvester Model.

_{S}is the number of turns in the secondary winding and N

_{P}= 1 for the CT in Figure 2. Hence, the maximum total secondary current, I

_{st}, can be expressed as:

_{lm}is the magnetizing current, whose instantaneous value can be written as:

_{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 Figure 2 is represented by L

_{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,${A}_{eff}$, the magnetic core path length, ${l}_{eff},$and N

_{s}. These parameters are used in the Simscape model of the non-linear inductor, which can be specified with varying levels of nonlinearity [45]. Figure 3 shows the magnetization curve, also called B-H curve, of the nonlinear inductor in Figure 2. H and B correspond with the magnetic field strength and the magnetic flux density, respectively. The nonlinear behaviour of the CT is represented by the B-H curve, which in turn constitutes the magnetization curve of the core. In the linear region of the magnetization curve when the relative permeability is constant, L

_{m}can be express by using Equation (4):

^{−7}H/m, and ${\mu}_{r}$ is the relative permeability, which depends on the core material and can be estimated from the magnetization curve (see Figure 3). The specific values for the rest of parameters are given in Section 4 for the proposed harvester in this paper.

_{eff}of the coil, the voltage induced in a Ns-turn winding can be expressed by:

_{p}(t) = I

_{p}cos(ωt + φ) is the sinusoidal AC current through the primary conductor and 2πr is the circumference of the circle in which the magnetic field is calculated. This value can be considered the magnetic path length, l

_{eff}, for a toroidal core. Then, Equation (5) can be expressed as:

_{m}in Figure 2. The benefits of letting the core go into soft saturation should outweigh the negative impact of saturation. Hence, the operating range of the core should not be beyond the onset of the knee region in Figure 3. This value is calculated by limiting the level of THD for the secondary current to a particular value, critical THD, which will depend on the harvester configuration.

#### 2.3. Saturation Characterization

_{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 Figure 4c. Consequently, the THD value of I

_{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.

## 3. Simulation-Based Characterization of the Inductive Electromagnetic Energy Harvester

_{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 Figure 2. To gain a clear insight about the influence of the compensating capacitor, two models are used: Model 1, which includes the resistive load and rectifier; and Model 2 with a resistive load, rectifier and compensating capacitor. Figure 3 represents the B-H curve of the non-linear inductor used in both models and the cross-sectional area A

_{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.

#### 3.1. Model 1. Simulation with an Energy Harvester with Rectifier and Resistive Load Without Reactive Power Compensation.

#### 3.2. Model 2. Simulation with an Energy Harvester with Rectifier and Reactive Power Compensation

_{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.

_{L}and R

_{L}to some extent could be regarded as the matching impedance for the harvester for a certain level of core saturation.

## 4. Verification of the Model Accuracy. Experimental Results and Energy Harvester Prototype

_{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 Figure 2 and by simulating them for power comparison purposes. The grain oriented Si-steel was the best option due to the reduction in the size and weight of the magnetic core for the same harvested power. This comparative study has not been included because it is beyond the scope of this paper.

_{L}, C

_{L}for N

_{S}= 200 and I

_{p}= 5 A.

_{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 Figure 6, which showed that for values of C

_{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.

^{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 [32,33]. In [37] the power density for a primary current of 60A is equal to 45.96 mW/cm

^{3}. Finally, in [29] considering a primary current of5 A and for a nanocrystalline core, the power density reaches 7.82 mW/cm

^{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.

## 5. Conclusions

^{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.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 5.**(

**a**) Output power; (

**b**) THD; (

**c**) V

_{load}; and (

**d**) I

_{load}as a function of I

_{p}, R

_{L}and Ns.

**Figure 6.**Power, THD, V

_{load}and I

_{load}as a function of R

_{L}and CL for Ip = 5 A and Ns = 200.

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 |

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 |

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 |

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**MDPI and ACS Style**

Martín Sánchez, P.; Rodríguez Sánchez, F.J.; Santiso Gómez, E.
An Experimental Strategy for Characterizing Inductive Electromagnetic Energy Harvesters. *Sensors* **2020**, *20*, 647.
https://doi.org/10.3390/s20030647

**AMA Style**

Martín Sánchez P, Rodríguez Sánchez FJ, Santiso Gómez E.
An Experimental Strategy for Characterizing Inductive Electromagnetic Energy Harvesters. *Sensors*. 2020; 20(3):647.
https://doi.org/10.3390/s20030647

**Chicago/Turabian Style**

Martín Sánchez, Pedro, Fco. Javier Rodríguez Sánchez, and Enrique Santiso Gómez.
2020. "An Experimental Strategy for Characterizing Inductive Electromagnetic Energy Harvesters" *Sensors* 20, no. 3: 647.
https://doi.org/10.3390/s20030647