# A Shear-Mode Piezoelectric Heterostructure for Electric Current Sensing in Electric Power Grids

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## Abstract

**:**

## 1. Introduction

## 2. Structure and Analysis

_{3}(PZT5H) is chosen as the material of the piezoelectric plates. The dimension of each PZT5H plate is 1 mm (d

_{p}) × 6 mm (w

_{p}) × 3 mm (l

_{p}). The material of the permanent magnet is NdFeB (N35), and the size of the magnet is 5 mm (d

_{m}) × 6 mm (w

_{m}) × 22 mm (l

_{m}). The magnet also acts as a retaining plate for the cymbal structure. Under the action of the AC magnetic field produced by the two-wire power cord, the magnet is acted upon by an AC magnetic force due to the nonuniform AC magnetic field acting on the magnet. The magnetic force results in amplified shear stress on the piezoelectric plates. Then, a voltage is produced, due to the piezoelectric effect of the piezoelectric material.

_{m}can be expressed as

_{m}is the magnetic charge density, σ

_{m}= B

_{r}[25], B

_{r}is the remnant flux density, S

_{m}is the surface area of one pole of the magnet, and H

_{1a}and H

_{1b}are the magnetic fields on the bottom and top surfaces of the magnet, respectively. F

_{m}can be expressed as a power series of the electric current I, and the coefficients of the power series can be determined by fitting curve. Assuming that the vertical force (in 1-direction) acting on one piezoelectric plate by the magnet is F

_{m}/2, the vertical force acting on the magnet by one piezoelectric plate is the same in amplitude and opposite in direction (−F

_{m}/2).

_{t}exerted by the brass cap on one piezoelectric plate. Based on the decomposition of the force F

_{t}, the following equation is obtained

_{s}(in 3-direction) can be expressed as

_{p}and l

_{p}are respectively the thickness (in 1-direction) and length (in 3-direction) of one piezoelectric plate, l

_{m}is the length of the magnet (w

_{m}and d

_{m}are respectively the width and the thickness of the magnet), and l

_{t}is the length of the top part of the brass cap. Then, the shear stress acting on one piezoelectric plate is

_{p}is the width of one piezoelectric plate. Based on piezoelectric constitutive equations in shear-mode [26], the electric field in 1-direction of the piezoelectric material is given by

_{15}is the shear stiffness constant, and ${c}_{55}^{D}$ is the elastic stiffness coefficient (at constant D

_{1}) in shear-mode. In open-circuit condition, the electric displacement D

_{1}= 0. Thus, the output voltage of one piezoelectric plate is obtained as

_{m}for determined material and geometric parameters of the device, which depends on the magnetic field magnetic field gradient ΔH on the NdFeB magnet. For current-to-voltage conversion application, the conversion factor can be defined as

## 3. Results and Discussions

_{max}is maximal deviation between the experimental results and the fitting results, and V

_{max}represents the full-scale output of the device. The corresponding results are 0.9% and 0.67% for d = 0 mm and d = 3 mm, respectively. Compared with the resonant structures, the high linearity makes the presented device very suitable for current sensing in electric power systems.

_{15}.

_{in}) was applied in the coil for current-to-voltage conversion. The experimental output peak voltage increases from 33.18 mV to 270.85 mV with approximately linear response to the current at the low-frequency of 1 kHz, as shown in Figure 7. It also can be seen from the inset of Figure 7 that the factor λ exhibits an approximate flat response. It varies in the range of 0.68 V/A to 0.83 V/A, with an average value of 0.77 V/A. The results show that the heterostructure has the potential to produce large magnetoelectric effect without using magnetostrictive materials and bias magnetic field [27,28].

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 5.**(

**a**) Induced voltage versus time at 50 Hz for d = 0 mm and (

**b**) Histogram for the voltage at 1.5 A.

**Figure 7.**Output open-circuit voltage as a function of the input electric current in the coil at 1 kHz. The inset indicates the conversion factor in the current range of 40 mA to 400 mA.

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**MDPI and ACS Style**

He, W.; Yang, A.
A Shear-Mode Piezoelectric Heterostructure for Electric Current Sensing in Electric Power Grids. *Micromachines* **2019**, *10*, 421.
https://doi.org/10.3390/mi10060421

**AMA Style**

He W, Yang A.
A Shear-Mode Piezoelectric Heterostructure for Electric Current Sensing in Electric Power Grids. *Micromachines*. 2019; 10(6):421.
https://doi.org/10.3390/mi10060421

**Chicago/Turabian Style**

He, Wei, and Aichao Yang.
2019. "A Shear-Mode Piezoelectric Heterostructure for Electric Current Sensing in Electric Power Grids" *Micromachines* 10, no. 6: 421.
https://doi.org/10.3390/mi10060421