Multi-frequency piezoelectric vibration energy harvesters powered sensing in power grid transformer

Multi-frequency piezoelectric vibration energy harvesters powered sensing in power grid transformer | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Multi-frequency piezoelectric vibration energy harvesters powered sensing in power grid transformer Lu Wang, Congsheng Duan, Chunlong Li, Qian Wang, Hui Huang, Dengfeng Ju, and 5 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3736998/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract With the development of smart grid, many wireless sensor nodes (WSN) used in monitoring grid equipment need continuous power supply. This work propose a multi-frequency array piezoelectric vibration energy harvester (PVEH) powering WSN based on the grid transformers vibration of 100, 200 and 300 Hz. The PZT bimorph with U shaped mass sturcture is design and opitimized by finite element simulation. The bonding method of epoxy conductivity and insulation is studied for PZT bimorph and aluminum packaged PVEHs. The equivalent circuit modeling and interface circuit of PVEHs are studied in LTspice simulation. Through the whole system design of the array PVEHs powered WSN circuit with LTC3331 chip, the WSN can run continuously in simultation and experimental verification. The feasibility of multi-frequency PVEH powered WSN is verified on the 500 kV transformer in filed operation. This research has important application value to the design of WSN self-power supply for smart grid. Physical sciences/Engineering/Electrical and electronic engineering Physical sciences/Nanoscience and technology/Other nanotechnology/Environmental, health and safety issues smart grid vibration energy harvesting power management circuit self-powered WSN Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction Wireless sensor is critical for information acquisition in smart power grid. The online wireless monitoring of voltage, current, temperature, vibration, partial discharge and other sensors is the general trend of intelligent power grid. To ensure the sensor can maintain long-term stable operation, it is very important to solve the problem of sustainable power supply. Energy harvesting technology is the mainstream solution of self power supply [ 1 ], such as harvesting electric [ 2 ] and magnetic field energy [ 3 ] from power lines, and harvesting solar energy [ 4 ] and wind energy [ 5 ] from outdoor environment. However, the transformer oil tank is filled with oil and equipped with electromagnetic shielding. These energy sources are not easily available for the power transformer shell. Fortunately, the vibration energy generated by the transformer during operation can be harvested. Referring to the vibration sensor to monitor the operating state of transformer winding and iron core online. Meanwhile, the vibration energy harvester (VEH) is perfect for placement with the vibration sensors. The vibration frequency spectrum generated by the shell in the operation of the power grid transformer presents the peak value of 100 Hz and its multiple frequency points such as 200 and 300 Hz. The amplitude is positively correlated with the transformer capacity. The vibration acceleration of small capacity such as 100 kVA transformer is around 0.1 g, and the vibration acceleration of large capacity like 500 kVA transformer is around 0.5 g. The power sensor can operate intermittently, with the average power consumption at the mW level. The existing MEMS PVEH small volume has low output power, only microwatts level [ 6 ]. The target vibration source such as the transformer has several fixed vibration energy peak frequency points, and the combination of multi-frequency point resonant PVEH can obtain more output power. Therefore, it is urgent to design accurate multi-frequency point resonance in PVEH. Shahruz[ 7 ] Designed a mechanical bandpass filtering device, multiple cantilever beams constitute an array, design the length and quality of each beam, can achieve resonance in a wide frequency range. Tang [ 8 ] processed the PZT piezoelectric cantilever array using epoxy resin bonding and MEMS etching processes, with an output power of 11.56 µW under 1 g, and 514.1 Hz acceleration excitation. Zhao [ 9 ] designed an LZO film array PVEH with three resonance frequencies of 999 Hz, 1210 Hz and 1277 Hz, with a maximum load power of 2.3 µW. It can be seen that the PVEH piezoelectric layer using MEMS process has thin thickness and light mass, resulting in high resonance frequency and low output power. PVEH additional mass has low resonance frequency and high output power. Toyabur [ 10 ] proposed a four secondary beams connected to the main beam which is a flexible clamp beam. The four secondary cantilever beam each acts as a single degree of freedom PVEH. Experimental tests show that the four secondary beams resonant frequencies are 10,14,16 and 20 Hz, respectively. One of the secondary beams produced a maximum peak power of 249.78 µW at a base acceleration of 0.4 g at 16 Hz. Xiao [ 11 ] designed and produced a broad band VEH based on piezoelectric disks with four output peaks between 120–250 Hz, and has generated power of 5.14, 6.65, 9.7 and 10 mW with external load resistance of 15 kΩ, respectively. Zhang [ 12 ] designed a piezoelectric cantilever of longitudinal 3-layered array with 28.9, 33.6 and 38.6 Hz, and nonlinear extension can be realized through overlapping collision. The design of the resonant frequency points of these multi-beam array structures is more convenient, but the relatively complex electrical connections should be considered. Wu [ 13 ] makes a comparative study on the electrical connection of piezoelectric array hybrid output, and proposes a method of changing the matching resistance in series and parallel to realize wide-band energy harvesting and power enhancement. However, before the rectifier filter circuit, the piezoelectric plate is directly in phase difference, resulting in charge loss. Most studies only considered the PVEH response output under sweep modulation, resulting in one beam in the piezoelectric array. In practice, the energy of each frequency point in the power spectrum is superimposed, and each beam in the piezoelectric array is resonant working. For multi-PZT voltage processing any phase input, Xia [ 14 ] introduces a self-powered dual inductive voltage rectifier interface circuit. The multimodal structure can also achieve multi-frequency PVEH effect through a single piezoelectric element. Ashraf [ 15 ] designed a low frequency and high frequency combination structure to realize the 6th order multimode electromagnetic energy harvesting. Li [ 16 ] designs a multi-branch sandwich PVEH that generates 1.55 V, 6.21 V and 2.48 V at low harmonic excitation of 0.02 g, with three resonant frequencies of 28.12 Hz, 24.74 Hz and 18.18 Hz, respectively. The T-shaped double-branch beam designed by Deng [ 17 ] can realize the 4-order resonance frequency and multidirectional energy harvesting. Although its single electrical output configuration is simple, it is difficult to adjust the required resonance frequency point and voltage response amplitude, and it is difficult to work at the same time. Multimodal and complex vibration modes still require more segmented electrode units for array electrical connection. Therefore, it is a better method of multi-frequency point vibration energy extraction to design PVEH with several different single resonance frequencies through electrical connection. The resonant frequency of PVEH designed and manufactured should match the peak frequency of environmental vibration power, and PVEH with wide bandwidth is easier to cover the target frequency point. Many nonlinear frequency extension methods have been studied [ 18 ] to obtain large amplitudes under small excitations through magnetic coupling multi-steady states to broaden the operating frequency band [ 19 ]. But this brings about an increase in complex volume and a loss of power density. Strongly coupled piezoelectric materials have the characteristic of improving stiffness, and can obtain peak power frequency response range in open circuit and short circuit states [ 20 ]. The resonant frequency can be adjusted within this range only through load impedance. Roundy [ 21 ] given the theoretical maximum power of the PVEH, as long as the transducer is strongly coupled, when the damping is equal to the mechanical damping, the theoretical maximum power can be reached. Methods to improve the single PVEH power density [ 22 ] include large mass, low damping, and high electromechanical coupling coefficient. Experimental prototypes are often fixed with screws, but the product needs to be encapsulated to prevent loosening and frequency drift. Wang [ 23 ] designed a PVEH which used two L-shaped tungsten block on the copper-based PZT, and improved the packaging process by obtaining lower damping by inserting the aluminum alloy frame and high power density of 5 mW/g 2 /cm 3 . The simple evaluation standard for the use of piezoelectric materials for PVEH can refer to [ 20 ]. Because the maximum power of the system is saturated in the strong coupling state, it is meaningless to blindly improve the electromechanical coupling coefficient of piezoelectric materials. The PZT is relatively easy to reach the strong coupling state, while the piezoelectric materials such as PVDF and AlN are often weakly coupled, which needs to improve the electromechanical coupling of the system through the nonlinear interface circuit. There are many studies on the interface circuit of PVEH [ 24 ], whose purpose is to enhance the electromechanical coupling of weak coupling system through switching topology, or realize the impedance matching of wide load range, but the automatic control of switch has efficiency loss. For the strong coupling system, the standard full bridge rectifier filter interface circuit can reach the saturation power [ 25 ]. To supply WSN, PVEH at multi-frequency point requires multi-source power management design, so the equivalent circuit model of PVEH is required. Wang [ 26 ] proposed a wireless sensor nodes system which powered by vibration energy. Based on experiment and finite element simulation build a complete system-level coupled circuit model to predict the PVEH performance characteristics. The undervoltage lockout (UVLO) interval based on LTC3588 chip is only about 4-5V and cannot be adjusted, which cannot be set at the maximum power transmission voltage point to start the discharge. For small capacity capacitance, the single discharge energy is small, so WSN cannot be started. Therefore, it is necessary to do system design and simulation for PVEH power management to achieve high efficiency and large capacity charge and discharge. This study gives the multifrequency array PVEHs design and manufacturing test method. According to the vibration characteristics of power transformer and needed self supply power, the finite element model are design and optimized and lump system parameters are identified for PVEHs array covering 100, 200 and 300 Hz. The bonding method of epoxy conductivity and insulation is studied. The packaged PVEH prototype is prepared, and the vibration response under multi-frequency sine signal superposition is tested. The model of self-supply equivalent circuit of PVEH is established. Three electrical connection modes of multiple source input are discussed, and the optimal interface circuit scheme is verified experimentally. The power management circuit is systematic modeling and designed with a large UVLO interval. The feasibility of temperature WSN for multi-frequency point vibration power supply is verified in the laboratory and transformer field. This study has important application value for transformer multi-frequency point PVEH and WSN self-supply design. 2. PVEHs design and fabrication 2.1 Modeling and simulation A 2-dimensional model of PVEH build in COMSOL multiphysics to analysis stress, electromechanical coupling frequency and eigenfrequency response in 0.1 g acceleration. Reference [ 23 ] provides a design method for U-shaped mass. As shown in Fig. 1 (a), a PZT bimorph is sandwished by fixed aluminium base to from a cantilever. Two rectangular big mass and two rectangular small mass form a U-shaped proof mass at the tip of the cantilever. The big mass ensures the enough kinetic energy, and the small mass ensure the enough length of piezoelectric cantilever. Simulation of big mass length depended open circuit voltage frequency response curves is shown in Fig. 1 (b). This indicates that increasing the length to 22 mm can increase the voltage frequency response and reduce the resonant frequency. Simulation of big mass thickness depended open circuit voltage frequency response curves is shown in Fig. 1 (c). This indicates that increasing the thickness can reduce the resonant frequency and increase the voltage frequency response. In order to match the power grid transformer vibration of 100Hz, the big mass thickness is designed to be 5mm. In the assembly process, the bonding layer thickness is related to the thickness of the groove. Simulation of bonding layer thickness depended open circuit voltage frequency response curves is shown in Fig. 1 (d) and PZT stress along the bimorph length is shown in Fig. 1 (e). Those indicate that increasing the bonding layer thickness can little reduce the resonant frequency, but sharply reduce the PZT clamping root stress concentration. Having enough thickness greatly improves reliability. However, the viscoelastic bonding materials will increase more anchor damping and decrease the voltage frequency response. The trade off bonding layer thickness of 0.15 mm is good. PVEH has different resonant frequency in short circuit (1 kΩ) and open circuit (10 MΩ) state. The root mean square (RMS) power with frequency and different load resistance is plotted in Fig. 1 (f). At 96.8 Hz at 600 kΩ and 103.4 Hz at 50 kΩ, two peak power points are found near 0.3 mW. Between the two peak power points, the flat saddle area demonstrates a certain broadband energy harvesting capability. A half peak power of 0.15mW can be reached between 95Hz and 110Hz, which covers 100Hz of grid transformer vibration. 2.2 Fabrication and package In the assembly, the first key processe is Epoxy conductive bonding of two PZT and a copper substrate to form a series bimorph. Therefore, the regulation method of the Epoxy bonding thickness and the effect on the resistance were investigated. Epoxy was applied evenly and two 0.2 mm copper pieces were bonded at room temperature. The bonding temperature was 70 ℃, bonding pressure was 0.1 MPa and bonding time was 2 h. The bonding layer thickness using the optical microscope, the relationship among the mesh number, thickness and resistance of the measured bonding layer are shown in Fig. 2 (a). When 150 mesh, 300 mesh and 420 mesh plates are printed, the bonding layer thickness is 63 µ m, 35 µ m and 15 µ m, respectively, and the resistance between the upper and lower copper plates is 16.55 MΩ, 65 mΩ and 15 mΩ, respectively. Therefore, the upper and lower copper sheets can be regarded as electrical insulation when using 150 mesh screens, and the good electrical conductivity of the double copper sheet adhesive layer prepared by 300 mesh and 420 mesh screen may be due to the surface roughness of the copper sheet and the contact between parts of the upper and lower copper sheets during the bonding process. Integrated aluminum alloy frame is fabricated by 3D printing. AB glue is used for the insulation adhesive of bimorph and mass block and frame. The insulating adhesive of tungsten block and copper substrate to form additional mass block. The cantilever formed by the bimorph inserted into the aluminum alloy frame. The wire leads to the electrode through welding double wafer as shown in Fig. 2 (b). Doping metal particles in the Epoxy can enhance conductivity, but it will reduce bonding strength, leading to interface slip during vibration, reducing the stress and voltage of the piezoelectric layer. Figure (c) shows the piezoelectric output time-domain curve under the same forced vibration. The Epoxy in this study is not mixed with metal particles, and has a higher piezoelectric output. Due to the use of a thinner bonding layer to ensure conductivity and bonding strength. The three PVEH prototypes prepared and the dimensions are shown in Fig. 2 (d). The copper sheet is insert in the frame as the stopper to adjust the stopper distance of the mass block and the frame, which can limit deflection and protect the piezoelectric cantilever in case of overload. 2.1 Test of multi-frequency PVEHs By using the vibration platform (Econ VT9008) and exciter (JZK-50), PVEH prototype performance shown in Fig. 2 (e). The PVEHs are excitated at 0.1g acceleration and sweep the frequency around 100 Hz, 200 Hz and 300 Hz. In Fig. 3 , experimental results shown the resonant frequency in short circuit (1 kΩ) and open circuit (10 MΩ) state are 95.8 and 102.8 Hz for PVEH1, 188.5 and 203.9 Hz for PVEH2, 288.7 and 305.3 Hz for PVEH3, respectively. Experimental RMS power and peak voltage in different load resistance at 0.1g acceleration are shown in Fig. 3 . The maximum RMS powers are 0.316 mW for PVEH1 in 100 Hz, 0.128 mW for PVEH2 in 200 Hz, and 0.085 mW for PVEH3 in 300 Hz, respectively. PVEH system parameter identification can be used for accurate lumped parameter modeling. The load resistance R and the capacitor C p were measured using the industrial multimeter EX 503. The stiffness is measured by static deflection method. The static displacement and stiffness of the PVEH are measured by SJ-10N dynamometer. PVEH system and structure parameters are shown in Table 2. By using bulk PZT and glue filling bimorph into aluminum alloy frame process let the PVEH have high effective electromechanical coupling coefficient and high mechanical quality factor, as will the high figure of merit FoM = k e 2 Q . The system is strongly coupling if the FoM is bigger than 2 [ 27 ] and by changing the load impedance will behave broadband peak power. Table 1 PVEH system and structure parameters PVEH 100 Hz 200 Hz 300 Hz Piezoelectric layer size (mm) 20×14×0.4 14×20×0.4 14×20×0.6 Substrate size (mm) 30×14×0.2 22×20×0.2 22×20×0.3 Small mass size (mm) 10×14×2 8×20×2 8×20×2 Big mass size (mm) 22×14×5 18×20×5 18×20×5 Package frame size (mm) 38×16×18 28×22×18 28×22×18 Clamp capacitance (nF) 7.64 7.02 6.65 System stiffness (N/m) 10489 55248 128205 Equivalent mass (g) 28.9 39.4 39.0 Short circuit resonant frequency (Hz) 95.8 188.5 288.7 Open resonant frequency (Hz) 102.8 203.9 305.3 Power-electric coupling factor (N/V) 0.0036 0.0082 0.0103 Quality factor 31.546 34.843 31.646 Electromechanical coupling coefficient k e 0.389 0.414 0.343 FoM 4.7817 5.9708 3.7429 Maximum RMS power (mW) 0.316 0.128 0.085 3. Multi-frequency PVEHs powered WSN design 3.1 Multi-PVEHs circuit modeling To match the PVEH generated power and load power, it is necessary to study the power management circuit. A PVEH circuit model can economically and conveniently compare the output power of various circuit schemes. The voltage capacitance (VC) model is equivalent to a voltage source model based on its open circuit voltage. The current capacitance (IC) model is equivalent to a current source model based on its short circuit current. These ignore the electromechanical coupling, which reduces the reference value of the circuit model. According to the lumped parameter model of the PVEH established earlier in this paper, the electrical model can be established by converting the corresponding parameters into the corresponding electrical domain parameters. For the power supply model of resistance inductance capacitor voltage capacitor (RLCVC) model, The mechanical quantities in the PVEH aggregate parameter model are converted into electrical quantities for circuit simulation by electromechanical analogy. Parameters of equivalent circuit model of the PVEHs are shown in Table 2 as follows: Table 5 Parameters of equivalent circuit model Mechanical quantity Electrical quantity 100 Hz PVEH 200 Hz PVEH 300 Hz PVEH Exciting force (N) \(F=MA{\beta }_{F}\) Inductance (H) \({L}_{m}=F/\theta\) 2187.5 592.5 366.29 Mass (kg) \(M=K/(2\pi {f}_{sc}\) ) 2 Resistance (kΩ) \({R}_{m}=D/{\theta }^{2}\) 51.5 20.1 20.99 Compliance (m/N) 1/K Capacitance (nF) \({C}_{m}={\theta }^{2}/\) K 1.24 1.204 0.8305 Damping (N*s/m) \(D=2\pi {f}_{sc}{\eta }_{S}M\) Voltage source (V) \({V}_{m}=F/\theta\) 10.68 4.84 3.708 Velocity (m/s) \(\dot{Z}={C}_{p}\dot{V}+V/R\) Current source (mA) \({I}_{m}=\theta \dot{Z}\) 0.191 0.225 0.166 Where M represents the equivalent mass, A is the acceleration, the \({f}_{sc}\) is short-circuit resonance frequency, the \({\eta }_{S}\) is structural loss factor, and \({\beta }_{F}\) is the force correction factor. Taking the 200 Hz PVEH as an example, the IC model, VC model, and IC model, RLCVC model are established as shown in Fig. 4 (a). The circuit models are scanned from 170 Hz to 230 Hz in the open circuit state of 10 MΩ. The simulation results and test data are compared in Fig. 4 (b). The resonance frequency of the RLCVC model is 204.02 Hz and the open circuit voltage is 25.2 V, which is very close to the actual tested prototype frequency 203.87 Hz and open circuit voltage 24.98 V, which verifies the correctness of the model frequency domain state. The load power comparison in Fig. 4 (c) also verifies the correctness of the RLCVC model in the load state. 3.2 Multi-PVEHs interface circuit To explore the optimal power management circuit scheme of multiple prototypes, the equivalent model and charging simulation of 330 µF capacitor are done in LTspice. After full bridge rectification, the 3 PVEHs prototypes equivalent models are connected in parallel as Fig. 4 (e) and series as Fig. 4 (f). The capacitor charging curves are shown in Fig. 4 (g). Although the steady-state voltage in series is higher than that in parallel, parallel connection has a faster charging speed below 25.8 V. Considering that the power management chip operates within 20 V, it is recommended to choose parallel connection for greater charging power. According to the work \({W}_{c}=C\varDelta {U}^{2}/2={P}_{c}{t}_{c}\) , the charging power \({P}_{c}\) from 0 to 10 V is 0.485 mW with 68 s in parallel connection, and 0.275 mW with 120 s in series connection. 3.3 WSN power analysis and modeling To monitor the environment information around the transformer, the commercial temperature and humidity sensor with Bluetooth (MBS-6003z) is selected as the WSN. The working voltage of the WSN is DC2.5V-3.3V, the sampling frequency is 1Hz, and it can intuitively display the temperature and humidity information with local has low power screen and remote mobile applications. By using the low-power load analyzer EMK850 + with the DC power supply, the power consumption of the WSN is tested shown in Fig. 5 (a). In Fig. 5 (b), the tested power consumption of wireless temperature and humidity sensor is mainly consisted of four parts, the energy consumption is 6.9 mJ when start WSN with 1.5 s. The energy consumption is 0.0475 mJ when sensing the temperature and humidity information with 25 ms every 1 s. The energy consumption is 0.533 mJ when sending the RF information with 130 ms every 10 s. The sleep current is 10 µA. Thus, the total energy consumption is 7.893 mJ to make the WSN start normally and send first information, and the total working time is more than 11.5s. The appropriate energy storage element will be selected according to this energy. The measured power consumption is shown in Table 6 . An equivalent time-varying load model was built in LTspice to describe the WSN power consumption, as shown in Fig, the equivalent load model of WSN consists of four parts, namely sleep resistance Rs, sensing current I3, startup current I2, and RF current I1. The simulation curve of current and voltage consumption of the equivalent load model after applying 3.3V voltage is shown in Fig. 5 (c). The superposition of the four parts of power consumption is basically consistent with the test curve in Fig. 5 (d). Table 6 Power consumption parameters of WSN experiment measurement Symbol Parameter Value \({V}_{cc}\) Supply voltage 3.3 V \({T}_{s}\) Sensing cycle time 1 s \({T}_{RF}\) Radio-frequency cycle time 10 s \({t}_{p}\) Start-up current time 1 s \({t}_{s}\) Single sensing current time 25 ms \({t}_{RF}\) Single RF current time 130 ms \({I}_{p}\) Average start-up current 1.42 mA \({I}_{S}\) Sensing average current 0.59 mA \({I}_{RF}\) Radio-frequency average current 1.24 mA \({I}_{sl}\) Sleep current 10 µA 3.4 Power management circuit Among the typical commercial power management chips with micropower energy harvesting, the BQ25504, LTC3105, and et al, Where BQ25504 and LTC3105 have the maximum power point tracking (MPPT) function, However, external low dropout voltage linear regulator (LDO) increases the loss of the circuit. The LTC3588 and LTC3331 has a full-bridge rectifier and larger input voltage range from 2.7–20 V for LTC3588 and 3–19 V for LTC3331. The undervoltage lockout (UVLO) interval of LTC3588 is about only from 4V to 5V, lead to less discharge energy. To give enough WSN starting energy, a larger capacitor should be chosen but with larger leakage current and volume. The LTC3331 has a wide range of 3–18 V can be set as UVLO interval, which match the PVEH varied input voltage change. The backup battery interface of LTC3331 further improve the long-term stability of power supply. Due to the maximum output power corresponding voltage is 8 V for our 100 Hz PVEH, the UVLO interval of LTC3331 is set from 5–10 V in our design. As the energy storage element, the electrolytic capacitor has large optional capacitor value, high limited voltage, long cycle life and low price, which can realize fast charging and discharging. A capacitor of 330 µF with the limited voltage of 25V is choosen as the energy storage element connected to Vin. Due to it has discharge energy of 12.375 mJ from 10 to 5 V. The circuit model of 100 Hz PVEH powering WSN with LTC3331 was built using LTspice as Fig. 5 (a), and simulated as Fig. 5 (b). The WSN equivalent power load at the output end can be periodically connected and disconnected from the power supply. When the PVEH charges the energy storage capacitors from 0 to 10 V with 136 s, the chip UVLO function is turned on and provide a stable 3.3V voltage for the WSN load continuously for 14 s. When the energy storage capacitor is discharged to the undervoltage lock lower limit threshold of 5 V, the chip will disconnect from the load. Energy storage capacitor stop the discharge and the voltage rise again to the set upper limit threshold of 10 V after 72 s for discharge. So repeatedly, the PVEH power management periodically provides a stable power supply to the WSN load, which ensures the normal startup and sustainable cyclical operation of the load system. To compare the powering WSN ability by single frequency PVEH and multi-frequency PVEHs, the circuit model of 100 Hz, 200 Hz, 300 Hz PVEHs paralleling powering WSN with LTC3331 was also built and simulated as Fig. 5 (c) and (d). Three PVEHs charges the energy storage capacitors from 0 to 10 V with shorter time of 84 s, and powering the WSN for longer time of 30 s, which proves stronger power generation than only one PVEH. 4. Experiment and application 4.1 Experimental verification Vibration and electrical experiments verify the performance of one and three PVEHs powered WSN as Fig. 6 (a). The three PVEH prototypes array of 100 Hz, 200 Hz, 300 Hz is covered by power management circuit broad and arranged on the vibrator platform and connected to the and WSN as Fig. 6 (b). The JDS6600 signal generator gives a sinusoidal 100 Hz and a mixed signal of 100 Hz, 200 Hz, 300 Hz in 0.1 g acceleration respectively as Fig. 6 (c). The test voltage curves of the energy storage capacitor and the load WSN was observed by the oscilloscope as shown in Fig. 6 (d). The 100 Hz PVEH takes 137 s to charge capacitor from 0 V to 10 V with charging power of 0.143 mW, and powers WSN for 18.8 s with discharge interval of 86 s. The three PVEHs take shorter times of 89 s to charge capacitor from 0 V to 10 V with charging power of 0.22 mW, and powers WSN for longer time of 27.2 s with shorter discharge interval of 65.5 s. The experimental results are relatively consistent with the simulation results, which shows the correctness of the whole system circuit modeling of the multi-frequency PVEHs powered WSN. When the voltage reaches 10V, the WSN starts to work, the energy storage capacitor first experienced a rapid power loss process from 10 V to 6.6V, releasing the energy of 9.3 mJ, while the WSN requires energy of 6.9 mJ, and the LTC3331 power circuit efficiency is calculated to be about 74%. The charging voltage curves of tri-frequency PVEHs at different accelerations of 0.1 g, 0.2 g, 0.3 g are shown in Fig. 6 (e). The greater the acceleration, the greater the vibration energy, and the shorter the charging start time. The WSN will not power down after startup at more than 0.2 g accelerations excitation. It is adequate to meet the demand for continuous monitoring of temperature and humidity sensing. 4.2 Application in power grid transformer To verify the practical application of WSN self-power supply by tri-frequency PVEHs in grid transformer tank vibration, the actual outdoor application test was verified on the 500 kV Yongzhou substation of Nanning Power Supply Bureau. This work tests and analyzes the vibration characteristics of the 500 kV grid transformer shell by three axis wireless accelerometer. The vibration test spectrum data of transformer at several points is shown in Fig. 8 (a). The vibration frequency of the transformer presents the distribution characteristics of 50 Hz, 100 Hz and multiple frequency. For different measurement points, such as fans, side shell, front shell, column, flange plate, their peak acceleration and frequency vary. It is recommended to select PVEH array with corresponding resonant frequency points for specific vibration points. The field application of tri-frequency PVEHs powered WSN in grid transformer column is shown in Fig. 8 (b). The vibration test spectrum of transformer column indicates the peak accelerations are 0.055 g at 100 Hz, 0.234g at 200 Hz, 0.113 g at 300 Hz; Under this excitation, the tri-frequency PVEHs charge the storage capacity from 0 V to 10 V with 33.6 s and charging power of 0.49 mW, then starts power on the WSN and stabilizes around 8 V. The tri-frequency PVEHs powered WSN works continuously to send temperature and humidity information to the Bluetooth receiver at 10 s interval. The mobile phone of the inspection personnel can get the wireless data without cross the safe distance of 5 m of the large transformer, which guarantees the personal safety of the inspection personnel to a certain extent. Relying on the array PVEHs and power management circuit can help the intelligent development of the power grid. 5. Conclusion This article focuses on the design of vibration energy harvesters for multiple vibration frequency points of transformers. Through theoretical calculation and simulation, the resonant frequencies of PVEH under different parameters are obtained. By controlling the parameters, the short-circuit and open-circuit resonant frequencies of PVEH include the characteristic frequency points of 100 Hz, 200 Hz, and 300 Hz of the transformer to maintain the output power at a high value. Explored the effect of epoxy resin layer thickness on the output of piezoelectric bimorphs, and selected 420 mesh screen printing process to obtain piezoelectric bimorphs with good output performance. After assembly, the output power of the three prototypes were 0.316 mW, 0.128 mW, and 0.085 mW, respectively, which can meet the power requirements of low-power sensors. The equivalent electrical model of the prototype was calculated using the coupling relationship between the mechanical and electrical domains. The parallel output scheme of the three prototypes was determined through LTspice simulation, and the obtained sensor power consumption model was simulated at the system level with the equivalent model of the prototype through testing, providing guidance for the actual testing scheme. Tested in the laboratory, it takes 137 s for a 100Hz PVEH to charge capacitors from 0 V to 10 V, with a charging power of 0.143 mW. It can operate wireless sensors for 18.8 s and a discharge interval of 86 s. Three frequency point PVEHs have a shorter charging time of 89 s for 0–10 V capacitors, a charging power of 0.22 mW, and can operate wireless sensors for 27.2 s with a shorter interval of 65.5 s, which is close to the simulation results. Finally, on-site experiments were conducted on a 500 kV transformer. The three frequency PVEHs charged the energy storage capacitor from 0 V to 10 V in 33.6 s, with a charging power of 0.49 mW. Then, the wireless sensor was continuously powered and the capacitor stabilized at around 8V. The multi frequency vibration energy collection prototype proposed in this article is of great significance in promoting the development of smart grids and ensuring the safety of grid workers. Declarations Acknowledgements This work is supported by the R&D project of State Grid Corporation of China (Development of vibration energy harvesting device and Research on self power supply technology of sensor based on micro kinetic energy, No. 5500-202158417A-0-0-00). Data Availability Statement: The data that support the findings of this study are available from the corresponding author upon reasonable request. Conflicts of Interest: The authors declare no conflict of interest. References C. Li, H. Huang, Y. Liang, Q. Chai, R. Zhao, and C. Hu, "Power Sensor-oriented Development and Challenges of Environmental Energy Harvesting Technologies," Electric Power, vol. 54, no. 2, pp. 27–35, 2021. F. Yang, L. Du, H. Yu, and P. Huang, "Magnetic and Electric Energy Harvesting Technologies in Power Grids: A Review," Sensors , vol. 20, no. 5, Mar 9 2020, doi: 10.3390/s20051496 . Y. Xu et al. , "Recent Progress of Electrode Materials for Flexible Perovskite Solar Cells," Nanomicro Lett , vol. 14, no. 1, p. 117, Apr 30 2022, doi: 10.1007/s40820-022-00859-9 . S. Gao et al. , "Triboelectric–electromagnetic hybridized module for energy harvesting of power transmission lines galloping and self-powered galloping state monitoring," Nano Energy, vol. 101, 2022, doi: 10.1016/j.nanoen.2022.107530 . P. Jiang, Z. Zhang, J. Zhang, B. Deng, J. Deng, and Z. Pan, "Research on vibration characteristics and Multi-parameter state recognition of ± 500 kV converter transformer under fluctuating conditions," International Journal of Electrical Power & Energy Systems, vol. 136, 2022, doi: 10.1016/j.ijepes.2021.107748 . M. Sawane and M. Prasad, "MEMS piezoelectric sensor for self-powered devices: A review," Materials Science in Semiconductor Processing, vol. 158, 2023, doi: 10.1016/j.mssp.2023.107324 . S. M. Shahruz, "Design of mechanical band-pass filters for energy scavenging," Journal of Sound and Vibration , vol. 292, no. 3–5, pp. 987–998, 2006, doi: 10.1016/j.jsv.2005.08.018 . G. Tang et al. , "Fabrication and analysis of high-performance piezoelectric MEMS generators," Journal of Micromechanics and Microengineering, vol. 22, no. 6, 2012, doi: 10.1088/0960-1317/22/6/065017 . X. Zhao, S. Li, C. Ai, H. Liu, and D. Wen, "Fabrication and Characterization of the Li-Doped ZnO Thin Films Piezoelectric Energy Harvester with Multi-Resonant Frequencies," Micromachines (Basel), vol. 10, no. 3, Mar 26 2019, doi: 10.3390/mi10030212 . R. M. Toyabur, M. Salauddin, and J. Y. Park, "Design and experiment of piezoelectric multimodal energy harvester for low frequency vibration," Ceramics International , vol. 43, pp. S675-S681, 2017, doi: 10.1016/j.ceramint.2017.05.257 . Z. Xiao, T. q. Yang, Y. Dong, and X. c. Wang, "Energy harvester array using piezoelectric circular diaphragm for broadband vibration," Applied Physics Letters, vol. 104, no. 22, 2014, doi: 10.1063/1.4878537 . B. Zhang, H. Li, S. Zhou, J. Liang, J. Gao, and D. Yurchenko, "Modeling and analysis of a three-degree-of-freedom piezoelectric vibration energy harvester for broadening bandwidth," Mechanical Systems and Signal Processing, vol. 176, 2022, doi: 10.1016/j.ymssp.2022.109169 . P. H. Wu, Y. J. Chen, B. Y. Li, and Y. C. Shu, "Wideband energy harvesting based on mixed connection of piezoelectric oscillators," Smart Materials and Structures, vol. 26, no. 9, 2017, doi: 10.1088/1361-665X/aa7981 . H. Xia et al. , "Self-Powered Dual-Inductor MI-PSSHI-VDR Interface Circuit for Multi-PZTs Energy Harvesting," IEEE Transactions on Power Electronics, vol. 37, no. 4, pp. 3753–3762, 2022, doi: 10.1109/tpel.2021.3124828 . K. Ashraf, M. H. Md Khir, J. O. Dennis, and Z. Baharudin, "Improved energy harvesting from low frequency vibrations by resonance amplification at multiple frequencies," Sensors and Actuators A: Physical, vol. 195, pp. 123–132, 2013, doi: 10.1016/j.sna.2013.03.026 . X. Li, K. Yu, D. Upadrashta, and Y. Yang, "Multi-branch sandwich piezoelectric energy harvester: mathematical modeling and validation," Smart Materials and Structures, vol. 28, no. 3, 2019, doi: 10.1088/1361-665X/aaf8bf . H. Deng, Y. Du, Z. Wang, J. Zhang, M. Ma, and X. Zhong, "A multimodal and multidirectional vibrational energy harvester using a double-branched beam," Applied Physics Letters, vol. 112, no. 21, 2018, doi: 10.1063/1.5024567 . X. Ma, H. Li, S. Zhou, Z. Yang, and G. Litak, "Characterizing nonlinear characteristics of asymmetric tristable energy harvesters," Mechanical Systems and Signal Processing, vol. 168, 2022, doi: 10.1016/j.ymssp.2021.108612 . S. W. Zhiyuan Li, Shengxi Zhou, "Multi-solution phenomena and nonlinear characteristics of tristable galloping energy harvesters with magnetic coupling nonlinearity," Communications in Nonlinear Science and Numerical Simulation, 2023, doi: 10.1016/j.cnsns.2022.107076 . D. Gibus, P. Gasnier, A. Morel, A. Ameye, and A. Badel, "A strong electromechanically coupled and low-damped harvester for resonant frequency tuning," presented at the 2021 IEEE 20th International Conference on Micro and Nanotechnology for Power Generation and Energy Conversion Applications (PowerMEMS), 2021. S. Roundy, "A study of low level vibrations as a power source for wireless sensor nodes," Computer Communications 2003. W. Q. Liu, A. Badel, F. Formosa, and Y. P. Wu, "A new figure of merit for wideband vibration energy harvesters," Smart Materials and Structures, vol. 24, no. 12, 2015, doi: 10.1088/0964-1726/24/12/125012 . L. Wang et al. , "A packaged piezoelectric vibration energy harvester with high power and broadband characteristics," Sensors and Actuators A: Physical, vol. 295, pp. 629–636, 2019, doi: 10.1016/j.sna.2019.06.034 . B. Zhang, H. Liu, S. Zhou, and J. Gao, "A review of nonlinear piezoelectric energy harvesting interface circuits in discrete components," Applied Mathematics and Mechanics, vol. 43, no. 7, pp. 1001–1026, 2022, doi: 10.1007/s10483-022-2863-6 . Y. Liao and J. Liang, "Unified modeling, analysis and comparison of piezoelectric vibration energy harvesters," Mechanical Systems and Signal Processing, vol. 123, pp. 403–425, 2019, doi: 10.1016/j.ymssp.2019.01.025 . L. Wang et al. , "System level design of wireless sensor node powered by piezoelectric vibration energy harvesting," Sensors and Actuators A: Physical, vol. 310, 2020, doi: 10.1016/j.sna.2020.112039 . Y. Liao and H. Sodano, "Optimal power, power limit and damping of vibration based piezoelectric power harvesters," Smart Materials and Structures, vol. 27, no. 7, 2018, doi: 10.1088/1361-665X/aabf4a . Additional Declarations (Not answered) Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3736998","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":263936293,"identity":"4f35e41d-3b08-4d7b-bcac-38102f224a02","order_by":0,"name":"Lu Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1ElEQVRIie3PsQ6CMBCA4TMksJCw1kF9hZomhITBVymLXZA4Mjh0YmX2LXyEkia4QFgZdXNg4AmMBfdaNxP7L3fDfcMB2Gw/2xHWAGLaHFOCgQDIL0nC39cGBF9b+QAs2aXqagR5nHCvFXrSZPtIkcOZSxdBwxLuZ1RLQpGGeCIlKLIoZMKRj/WkG2bC3Jk8TUifkpsiNJgJNyC7fgiBYrZVv5CI1owUfqonyzIl45jHG9xX9348xavSa/RE5SI6DSQApsX9dK9yxnkE3ODWZrPZ/rIXsrVDhS33xssAAAAASUVORK5CYII=","orcid":"","institution":"Xi'an Jiaotong University","correspondingAuthor":true,"prefix":"","firstName":"Lu","middleName":"","lastName":"Wang","suffix":""},{"id":263936294,"identity":"b0f31b0c-263f-4610-9f89-bcc647101213","order_by":1,"name":"Congsheng Duan","email":"","orcid":"","institution":"Xi'an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Congsheng","middleName":"","lastName":"Duan","suffix":""},{"id":263936295,"identity":"1ff41c9f-7706-4d1a-826d-a42f61932458","order_by":2,"name":"Chunlong Li","email":"","orcid":"","institution":"State Grid Smart Grid Research Institute Co., Ltd","correspondingAuthor":false,"prefix":"","firstName":"Chunlong","middleName":"","lastName":"Li","suffix":""},{"id":263936296,"identity":"dc04eb4b-460d-471b-a6dc-da139ddfc213","order_by":3,"name":"Qian Wang","email":"","orcid":"","institution":"Xi'an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Qian","middleName":"","lastName":"Wang","suffix":""},{"id":263936297,"identity":"33f58407-79c8-4349-8c93-c79e2c22bca9","order_by":4,"name":"Hui Huang","email":"","orcid":"","institution":"State Grid Smart Grid Research Institute Co., Ltd","correspondingAuthor":false,"prefix":"","firstName":"Hui","middleName":"","lastName":"Huang","suffix":""},{"id":263936298,"identity":"6e44f9eb-7589-4b9c-b776-bba7ece07868","order_by":5,"name":"Dengfeng Ju","email":"","orcid":"","institution":"State Grid Smart Grid Research Institute Co., Ltd.","correspondingAuthor":false,"prefix":"","firstName":"Dengfeng","middleName":"","lastName":"Ju","suffix":""},{"id":263936299,"identity":"e5be34e8-ba7e-4c47-a7a3-c706a5a1ddc0","order_by":6,"name":"Hongjing Liu","email":"","orcid":"","institution":"State Grid Beijing Electric Power Research Institute","correspondingAuthor":false,"prefix":"","firstName":"Hongjing","middleName":"","lastName":"Liu","suffix":""},{"id":263936300,"identity":"04b10cfc-b706-4246-8e2e-c540375958de","order_by":7,"name":"Xiangguang Han","email":"","orcid":"","institution":"Xi'an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Xiangguang","middleName":"","lastName":"Han","suffix":""},{"id":263936301,"identity":"7e2816f6-d760-47af-b9f4-7d7154c6bc9f","order_by":8,"name":"Libo Zhao","email":"","orcid":"https://orcid.org/0000-0001-6101-8173","institution":"Xi'an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Libo","middleName":"","lastName":"Zhao","suffix":""},{"id":263936302,"identity":"3d94f6a6-2170-476d-ad0e-f1079287c28c","order_by":9,"name":"Zhuangde Jiang","email":"","orcid":"","institution":"Xi'an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Zhuangde","middleName":"","lastName":"Jiang","suffix":""},{"id":263936303,"identity":"414ff64b-98d8-45b5-b548-c9800cdd4223","order_by":10,"name":"Ryutaro MAEDA","email":"","orcid":"","institution":"Xi'an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Ryutaro","middleName":"","lastName":"MAEDA","suffix":""}],"badges":[],"createdAt":"2023-12-11 05:25:34","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3736998/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3736998/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":49019941,"identity":"9bdecd0b-6900-4238-ab4c-4ea34c24482d","added_by":"auto","created_at":"2024-01-01 08:17:29","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":338383,"visible":true,"origin":"","legend":"\u003cp\u003ePVEH modeling and simulation: (a) COMSOL model; (b) Big mass length depended open circuit voltage frequency response curves; (c) Big mass thickness depended open circuit voltage frequency response curves; (d) Bonding layer thickness depended open circuit voltage frequency response curves.(e) PZT stress along the bimorph length;(f) RMS power with frequency and load resistance.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-3736998/v1/2aa414c8ffef23cd5f9ab506.png"},{"id":49019768,"identity":"6ae493df-46ca-46b4-8844-1281a66c8376","added_by":"auto","created_at":"2024-01-01 08:09:29","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":766824,"visible":true,"origin":"","legend":"\u003cp\u003e(a) The relationship among conductivity, epoxy thickness, and screen mesh; (b) PVEH assembled with conductive and insulating epoxy structure diagram; (c) Voltage response curve of PVEH with different epoxy; (d) Packaged multi-frequency PVEHs prototypes of 100 Hz, 200 Hz, and 300 Hz; (e) PVEH test platform.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-3736998/v1/d86cae62bad4fcac1e8869a4.png"},{"id":49019767,"identity":"6812af31-0e01-4a08-89d2-ecb954c0fb99","added_by":"auto","created_at":"2024-01-01 08:09:29","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":239220,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental peak voltage frequency response curves at short-circuit and open-circuit of (a) PVEH1, (b) PVEH2, (c) PVEH3, respectively. Experimental peak voltage and RMS power in different load resistance of (d) PVEH1 in 100 Hz, (e) PVEH2 in 200 Hz, (f) PVEH3 in 300 Hz, respectively.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-3736998/v1/21ba629629db654f5ba2796c.png"},{"id":49019943,"identity":"e2128d17-3827-414c-8823-f6ba0a1fba34","added_by":"auto","created_at":"2024-01-01 08:17:29","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":191104,"visible":true,"origin":"","legend":"\u003cp\u003e(a) 200Hz prototype equivalent circuit model. (b) Sweep frequency curve; (c) Load voltage comparison; (d) Load power comparison. (e) Three prototype series connection schemes; (f) Parallel connection scheme; (g) Charging comparison.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-3736998/v1/cf904240782b6d3ba4c18b35.png"},{"id":49020086,"identity":"c077aa7b-5f1b-4a48-ab79-ad87e60acc6f","added_by":"auto","created_at":"2024-01-01 08:25:29","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":594870,"visible":true,"origin":"","legend":"\u003cp\u003eWSN power test: (a) power test platform; (b) WSN power consumption curves; (c) LTspice equivalent load model (d) LTspice load power curves.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-3736998/v1/0fdb6976be4da5ae072c78c5.png"},{"id":49019764,"identity":"25ce4dff-1f1d-438e-9adf-0dd9b5e21f3a","added_by":"auto","created_at":"2024-01-01 08:09:29","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":415709,"visible":true,"origin":"","legend":"\u003cp\u003e(a) The circuit model and (b) simulation results of 100Hz PVEH powering WSN with LTC3331. (c) The circuit model and (d) simulation results of 100 Hz, 200 Hz, 300 Hz PVEHs powering WSN with LTC3331.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-3736998/v1/2afbccef85cf1906a23dafed.png"},{"id":49019765,"identity":"5e1200d0-4fcf-4de8-a543-f76f228ce0f2","added_by":"auto","created_at":"2024-01-01 08:09:29","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":268184,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Test platform of PVEH powered WSN; (b) Tri-frequency PVEH prototype covered by power management circuit board (c)100 Hz and mixing signal of 100 Hz, 200 Hz, 300 Hz; (d) Charging voltage curves comparison between 100 Hz PVEH and tri-frequency PVEHs at 0.1g and (e) different accelerations of 0.1 g, 0.2 g, 0.3 g.\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-3736998/v1/eb22747e1e95c699cedc6ef9.png"},{"id":49019770,"identity":"42c48ed7-8fa2-40b4-9380-c6475e278bfb","added_by":"auto","created_at":"2024-01-01 08:09:29","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":1890219,"visible":true,"origin":"","legend":"\u003cp\u003e(a) The vibration test data of 500 kV grid transformer at several points. (b) The field application of tri-frequency PVEHs powered WSN in grid transformer\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-3736998/v1/dc59279ef3c41570322745d2.png"},{"id":53210318,"identity":"f4e1dd18-0e57-4819-afc7-6587ec7bddb1","added_by":"auto","created_at":"2024-03-22 01:28:34","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5330412,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3736998/v1/2409ffc4-6548-45eb-9da7-eb097342619a.pdf"}],"financialInterests":"(Not answered)","formattedTitle":"Multi-frequency piezoelectric vibration energy harvesters powered sensing in power grid transformer","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eWireless sensor is critical for information acquisition in smart power grid. The online wireless monitoring of voltage, current, temperature, vibration, partial discharge and other sensors is the general trend of intelligent power grid. To ensure the sensor can maintain long-term stable operation, it is very important to solve the problem of sustainable power supply. Energy harvesting technology is the mainstream solution of self power supply [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e], such as harvesting electric [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] and magnetic field energy [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] from power lines, and harvesting solar energy [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] and wind energy [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] from outdoor environment. However, the transformer oil tank is filled with oil and equipped with electromagnetic shielding. These energy sources are not easily available for the power transformer shell.\u003c/p\u003e \u003cp\u003eFortunately, the vibration energy generated by the transformer during operation can be harvested. Referring to the vibration sensor to monitor the operating state of transformer winding and iron core online. Meanwhile, the vibration energy harvester (VEH) is perfect for placement with the vibration sensors. The vibration frequency spectrum generated by the shell in the operation of the power grid transformer presents the peak value of 100 Hz and its multiple frequency points such as 200 and 300 Hz. The amplitude is positively correlated with the transformer capacity. The vibration acceleration of small capacity such as 100 kVA transformer is around 0.1 g, and the vibration acceleration of large capacity like 500 kVA transformer is around 0.5 g. The power sensor can operate intermittently, with the average power consumption at the mW level. The existing MEMS PVEH small volume has low output power, only microwatts level [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. The target vibration source such as the transformer has several fixed vibration energy peak frequency points, and the combination of multi-frequency point resonant PVEH can obtain more output power. Therefore, it is urgent to design accurate multi-frequency point resonance in PVEH.\u003c/p\u003e \u003cp\u003eShahruz[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] Designed a mechanical bandpass filtering device, multiple cantilever beams constitute an array, design the length and quality of each beam, can achieve resonance in a wide frequency range. Tang [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] processed the PZT piezoelectric cantilever array using epoxy resin bonding and MEMS etching processes, with an output power of 11.56 \u0026micro;W under 1 g, and 514.1 Hz acceleration excitation. Zhao [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] designed an LZO film array PVEH with three resonance frequencies of 999 Hz, 1210 Hz and 1277 Hz, with a maximum load power of 2.3 \u0026micro;W. It can be seen that the PVEH piezoelectric layer using MEMS process has thin thickness and light mass, resulting in high resonance frequency and low output power.\u003c/p\u003e \u003cp\u003ePVEH additional mass has low resonance frequency and high output power. Toyabur [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] proposed a four secondary beams connected to the main beam which is a flexible clamp beam. The four secondary cantilever beam each acts as a single degree of freedom PVEH. Experimental tests show that the four secondary beams resonant frequencies are 10,14,16 and 20 Hz, respectively. One of the secondary beams produced a maximum peak power of 249.78 \u0026micro;W at a base acceleration of 0.4 g at 16 Hz. Xiao [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] designed and produced a broad band VEH based on piezoelectric disks with four output peaks between 120\u0026ndash;250 Hz, and has generated power of 5.14, 6.65, 9.7 and 10 mW with external load resistance of 15 kΩ, respectively. Zhang [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] designed a piezoelectric cantilever of longitudinal 3-layered array with 28.9, 33.6 and 38.6 Hz, and nonlinear extension can be realized through overlapping collision. The design of the resonant frequency points of these multi-beam array structures is more convenient, but the relatively complex electrical connections should be considered.\u003c/p\u003e \u003cp\u003eWu [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] makes a comparative study on the electrical connection of piezoelectric array hybrid output, and proposes a method of changing the matching resistance in series and parallel to realize wide-band energy harvesting and power enhancement. However, before the rectifier filter circuit, the piezoelectric plate is directly in phase difference, resulting in charge loss. Most studies only considered the PVEH response output under sweep modulation, resulting in one beam in the piezoelectric array. In practice, the energy of each frequency point in the power spectrum is superimposed, and each beam in the piezoelectric array is resonant working. For multi-PZT voltage processing any phase input, Xia [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] introduces a self-powered dual inductive voltage rectifier interface circuit.\u003c/p\u003e \u003cp\u003eThe multimodal structure can also achieve multi-frequency PVEH effect through a single piezoelectric element. Ashraf [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] designed a low frequency and high frequency combination structure to realize the 6th order multimode electromagnetic energy harvesting. Li [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] designs a multi-branch sandwich PVEH that generates 1.55 V, 6.21 V and 2.48 V at low harmonic excitation of 0.02 g, with three resonant frequencies of 28.12 Hz, 24.74 Hz and 18.18 Hz, respectively. The T-shaped double-branch beam designed by Deng [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] can realize the 4-order resonance frequency and multidirectional energy harvesting. Although its single electrical output configuration is simple, it is difficult to adjust the required resonance frequency point and voltage response amplitude, and it is difficult to work at the same time. Multimodal and complex vibration modes still require more segmented electrode units for array electrical connection.\u003c/p\u003e \u003cp\u003eTherefore, it is a better method of multi-frequency point vibration energy extraction to design PVEH with several different single resonance frequencies through electrical connection. The resonant frequency of PVEH designed and manufactured should match the peak frequency of environmental vibration power, and PVEH with wide bandwidth is easier to cover the target frequency point. Many nonlinear frequency extension methods have been studied [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] to obtain large amplitudes under small excitations through magnetic coupling multi-steady states to broaden the operating frequency band [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. But this brings about an increase in complex volume and a loss of power density. Strongly coupled piezoelectric materials have the characteristic of improving stiffness, and can obtain peak power frequency response range in open circuit and short circuit states [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. The resonant frequency can be adjusted within this range only through load impedance.\u003c/p\u003e \u003cp\u003eRoundy [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] given the theoretical maximum power of the PVEH, as long as the transducer is strongly coupled, when the damping is equal to the mechanical damping, the theoretical maximum power can be reached. Methods to improve the single PVEH power density [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] include large mass, low damping, and high electromechanical coupling coefficient. Experimental prototypes are often fixed with screws, but the product needs to be encapsulated to prevent loosening and frequency drift. Wang [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] designed a PVEH which used two L-shaped tungsten block on the copper-based PZT, and improved the packaging process by obtaining lower damping by inserting the aluminum alloy frame and high power density of 5 mW/g\u003csup\u003e2\u003c/sup\u003e/cm\u003csup\u003e3\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe simple evaluation standard for the use of piezoelectric materials for PVEH can refer to [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Because the maximum power of the system is saturated in the strong coupling state, it is meaningless to blindly improve the electromechanical coupling coefficient of piezoelectric materials. The PZT is relatively easy to reach the strong coupling state, while the piezoelectric materials such as PVDF and AlN are often weakly coupled, which needs to improve the electromechanical coupling of the system through the nonlinear interface circuit. There are many studies on the interface circuit of PVEH [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e], whose purpose is to enhance the electromechanical coupling of weak coupling system through switching topology, or realize the impedance matching of wide load range, but the automatic control of switch has efficiency loss. For the strong coupling system, the standard full bridge rectifier filter interface circuit can reach the saturation power [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTo supply WSN, PVEH at multi-frequency point requires multi-source power management design, so the equivalent circuit model of PVEH is required. Wang [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] proposed a wireless sensor nodes system which powered by vibration energy. Based on experiment and finite element simulation build a complete system-level coupled circuit model to predict the PVEH performance characteristics. The undervoltage lockout (UVLO) interval based on LTC3588 chip is only about 4-5V and cannot be adjusted, which cannot be set at the maximum power transmission voltage point to start the discharge. For small capacity capacitance, the single discharge energy is small, so WSN cannot be started. Therefore, it is necessary to do system design and simulation for PVEH power management to achieve high efficiency and large capacity charge and discharge.\u003c/p\u003e \u003cp\u003eThis study gives the multifrequency array PVEHs design and manufacturing test method. According to the vibration characteristics of power transformer and needed self supply power, the finite element model are design and optimized and lump system parameters are identified for PVEHs array covering 100, 200 and 300 Hz. The bonding method of epoxy conductivity and insulation is studied. The packaged PVEH prototype is prepared, and the vibration response under multi-frequency sine signal superposition is tested. The model of self-supply equivalent circuit of PVEH is established. Three electrical connection modes of multiple source input are discussed, and the optimal interface circuit scheme is verified experimentally. The power management circuit is systematic modeling and designed with a large UVLO interval. The feasibility of temperature WSN for multi-frequency point vibration power supply is verified in the laboratory and transformer field. This study has important application value for transformer multi-frequency point PVEH and WSN self-supply design.\u003c/p\u003e"},{"header":"2. PVEHs design and fabrication","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Modeling and simulation\u003c/h2\u003e \u003cp\u003eA 2-dimensional model of PVEH build in COMSOL multiphysics to analysis stress, electromechanical coupling frequency and eigenfrequency response in 0.1 g acceleration. Reference [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] provides a design method for U-shaped mass. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a), a PZT bimorph is sandwished by fixed aluminium base to from a cantilever. Two rectangular big mass and two rectangular small mass form a U-shaped proof mass at the tip of the cantilever. The big mass ensures the enough kinetic energy, and the small mass ensure the enough length of piezoelectric cantilever.\u003c/p\u003e \u003cp\u003eSimulation of big mass length depended open circuit voltage frequency response curves is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b). This indicates that increasing the length to 22 mm can increase the voltage frequency response and reduce the resonant frequency. Simulation of big mass thickness depended open circuit voltage frequency response curves is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(c). This indicates that increasing the thickness can reduce the resonant frequency and increase the voltage frequency response. In order to match the power grid transformer vibration of 100Hz, the big mass thickness is designed to be 5mm.\u003c/p\u003e \u003cp\u003eIn the assembly process, the bonding layer thickness is related to the thickness of the groove. Simulation of bonding layer thickness depended open circuit voltage frequency response curves is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(d) and PZT stress along the bimorph length is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(e). Those indicate that increasing the bonding layer thickness can little reduce the resonant frequency, but sharply reduce the PZT clamping root stress concentration. Having enough thickness greatly improves reliability. However, the viscoelastic bonding materials will increase more anchor damping and decrease the voltage frequency response. The trade off bonding layer thickness of 0.15 mm is good.\u003c/p\u003e \u003cp\u003ePVEH has different resonant frequency in short circuit (1 kΩ) and open circuit (10 MΩ) state. The root mean square (RMS) power with frequency and different load resistance is plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(f). At 96.8 Hz at 600 kΩ and 103.4 Hz at 50 kΩ, two peak power points are found near 0.3 mW. Between the two peak power points, the flat saddle area demonstrates a certain broadband energy harvesting capability. A half peak power of 0.15mW can be reached between 95Hz and 110Hz, which covers 100Hz of grid transformer vibration.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Fabrication and package\u003c/h2\u003e \u003cp\u003eIn the assembly, the first key processe is Epoxy conductive bonding of two PZT and a copper substrate to form a series bimorph. Therefore, the regulation method of the Epoxy bonding thickness and the effect on the resistance were investigated. Epoxy was applied evenly and two 0.2 mm copper pieces were bonded at room temperature. The bonding temperature was 70 ℃, bonding pressure was 0.1 MPa and bonding time was 2 h.\u003c/p\u003e \u003cp\u003eThe bonding layer thickness using the optical microscope, the relationship among the mesh number, thickness and resistance of the measured bonding layer are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (a). When 150 mesh, 300 mesh and 420 mesh plates are printed, the bonding layer thickness is 63 \u0026micro; m, 35 \u0026micro; m and 15 \u0026micro; m, respectively, and the resistance between the upper and lower copper plates is 16.55 MΩ, 65 mΩ and 15 mΩ, respectively. Therefore, the upper and lower copper sheets can be regarded as electrical insulation when using 150 mesh screens, and the good electrical conductivity of the double copper sheet adhesive layer prepared by 300 mesh and 420 mesh screen may be due to the surface roughness of the copper sheet and the contact between parts of the upper and lower copper sheets during the bonding process.\u003c/p\u003e \u003cp\u003eIntegrated aluminum alloy frame is fabricated by 3D printing. AB glue is used for the insulation adhesive of bimorph and mass block and frame. The insulating adhesive of tungsten block and copper substrate to form additional mass block. The cantilever formed by the bimorph inserted into the aluminum alloy frame. The wire leads to the electrode through welding double wafer as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (b).\u003c/p\u003e \u003cp\u003eDoping metal particles in the Epoxy can enhance conductivity, but it will reduce bonding strength, leading to interface slip during vibration, reducing the stress and voltage of the piezoelectric layer. Figure (c) shows the piezoelectric output time-domain curve under the same forced vibration. The Epoxy in this study is not mixed with metal particles, and has a higher piezoelectric output. Due to the use of a thinner bonding layer to ensure conductivity and bonding strength.\u003c/p\u003e \u003cp\u003eThe three PVEH prototypes prepared and the dimensions are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (d). The copper sheet is insert in the frame as the stopper to adjust the stopper distance of the mass block and the frame, which can limit deflection and protect the piezoelectric cantilever in case of overload.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Test of multi-frequency PVEHs\u003c/h2\u003e \u003cp\u003eBy using the vibration platform (Econ VT9008) and exciter (JZK-50), PVEH prototype performance shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (e). The PVEHs are excitated at 0.1g acceleration and sweep the frequency around 100 Hz, 200 Hz and 300 Hz. In Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, experimental results shown the resonant frequency in short circuit (1 kΩ) and open circuit (10 MΩ) state are 95.8 and 102.8 Hz for PVEH1, 188.5 and 203.9 Hz for PVEH2, 288.7 and 305.3 Hz for PVEH3, respectively.\u003c/p\u003e \u003cp\u003eExperimental RMS power and peak voltage in different load resistance at 0.1g acceleration are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The maximum RMS powers are 0.316 mW for PVEH1 in 100 Hz, 0.128 mW for PVEH2 in 200 Hz, and 0.085 mW for PVEH3 in 300 Hz, respectively.\u003c/p\u003e \u003cp\u003ePVEH system parameter identification can be used for accurate lumped parameter modeling. The load resistance \u003cem\u003eR\u003c/em\u003e and the capacitor \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e were measured using the industrial multimeter EX 503. The stiffness is measured by static deflection method. The static displacement and stiffness of the PVEH are measured by SJ-10N dynamometer.\u003c/p\u003e \u003cp\u003ePVEH system and structure parameters are shown in Table\u0026nbsp;2. By using bulk PZT and glue filling bimorph into aluminum alloy frame process let the PVEH have high effective electromechanical coupling coefficient and high mechanical quality factor, as will the high figure of merit \u003cem\u003eFoM\u0026thinsp;=\u0026thinsp;k\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eQ\u003c/em\u003e. The system is strongly coupling if the \u003cem\u003eFoM\u003c/em\u003e is bigger than 2 [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] and by changing the load impedance will behave broadband peak power.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePVEH system and structure parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePVEH\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e100 Hz\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e200 Hz\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e300 Hz\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePiezoelectric layer size (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20\u0026times;14\u0026times;0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e14\u0026times;20\u0026times;0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e14\u0026times;20\u0026times;0.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSubstrate size (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30\u0026times;14\u0026times;0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e22\u0026times;20\u0026times;0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e22\u0026times;20\u0026times;0.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSmall mass size (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10\u0026times;14\u0026times;2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8\u0026times;20\u0026times;2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8\u0026times;20\u0026times;2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBig mass size (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e22\u0026times;14\u0026times;5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e18\u0026times;20\u0026times;5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e18\u0026times;20\u0026times;5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePackage frame size (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e38\u0026times;16\u0026times;18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e28\u0026times;22\u0026times;18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e28\u0026times;22\u0026times;18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eClamp capacitance (nF)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.65\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSystem stiffness (N/m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10489\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e55248\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e128205\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEquivalent mass (g)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e28.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e39.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e39.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eShort circuit resonant frequency (Hz)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e95.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e188.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e288.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOpen resonant frequency (Hz)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e102.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e203.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e305.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePower-electric coupling factor (N/V)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0036\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0082\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0103\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eQuality factor\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e31.546\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e34.843\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e31.646\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eElectromechanical coupling coefficient \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.389\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.414\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.343\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eFoM\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.7817\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5.9708\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.7429\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaximum RMS power (mW)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.316\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.085\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3. Multi-frequency PVEHs powered WSN design","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Multi-PVEHs circuit modeling\u003c/h2\u003e \u003cp\u003eTo match the PVEH generated power and load power, it is necessary to study the power management circuit. A PVEH circuit model can economically and conveniently compare the output power of various circuit schemes. The voltage capacitance (VC) model is equivalent to a voltage source model based on its open circuit voltage. The current capacitance (IC) model is equivalent to a current source model based on its short circuit current. These ignore the electromechanical coupling, which reduces the reference value of the circuit model. According to the lumped parameter model of the PVEH established earlier in this paper, the electrical model can be established by converting the corresponding parameters into the corresponding electrical domain parameters. For the power supply model of resistance inductance capacitor voltage capacitor (RLCVC) model, The mechanical quantities in the PVEH aggregate parameter model are converted into electrical quantities for circuit simulation by electromechanical analogy. Parameters of equivalent circuit model of the PVEHs are shown in Table\u0026nbsp;2 as follows:\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eParameters of equivalent circuit model\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMechanical quantity\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eElectrical quantity\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e100 Hz PVEH\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e200 Hz PVEH\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e300 Hz PVEH\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExciting force (N)\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(F=MA{\\beta }_{F}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInductance (H)\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({L}_{m}=F/\\theta\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2187.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e592.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e366.29\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMass (kg)\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(M=K/(2\\pi {f}_{sc}\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003e)\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eResistance (kΩ)\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{m}=D/{\\theta }^{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e51.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e20.99\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCompliance (m/N)\u003c/p\u003e \u003cp\u003e1/K\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCapacitance (nF)\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({C}_{m}={\\theta }^{2}/\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003eK\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.204\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.8305\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDamping (N*s/m)\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(D=2\\pi {f}_{sc}{\\eta }_{S}M\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVoltage source (V)\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({V}_{m}=F/\\theta\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.708\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVelocity (m/s)\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\dot{Z}={C}_{p}\\dot{V}+V/R\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCurrent source (mA)\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I}_{m}=\\theta \\dot{Z}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.191\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.225\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.166\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eWhere \u003cem\u003eM\u003c/em\u003e represents the equivalent mass, \u003cem\u003eA\u003c/em\u003e is the acceleration, the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{sc}\\)\u003c/span\u003e\u003c/span\u003e is short-circuit resonance frequency, the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\eta }_{S}\\)\u003c/span\u003e\u003c/span\u003e is structural loss factor, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\beta }_{F}\\)\u003c/span\u003e\u003c/span\u003e is the force correction factor.\u003c/p\u003e \u003cp\u003eTaking the 200 Hz PVEH as an example, the IC model, VC model, and IC model, RLCVC model are established as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (a). The circuit models are scanned from 170 Hz to 230 Hz in the open circuit state of 10 MΩ. The simulation results and test data are compared in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (b). The resonance frequency of the RLCVC model is 204.02 Hz and the open circuit voltage is 25.2 V, which is very close to the actual tested prototype frequency 203.87 Hz and open circuit voltage 24.98 V, which verifies the correctness of the model frequency domain state. The load power comparison in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (c) also verifies the correctness of the RLCVC model in the load state.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Multi-PVEHs interface circuit\u003c/h2\u003e \u003cp\u003eTo explore the optimal power management circuit scheme of multiple prototypes, the equivalent model and charging simulation of 330 \u0026micro;F capacitor are done in LTspice. After full bridge rectification, the 3 PVEHs prototypes equivalent models are connected in parallel as Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (e) and series as Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (f).\u003c/p\u003e \u003cp\u003eThe capacitor charging curves are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (g). Although the steady-state voltage in series is higher than that in parallel, parallel connection has a faster charging speed below 25.8 V. Considering that the power management chip operates within 20 V, it is recommended to choose parallel connection for greater charging power. According to the work \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({W}_{c}=C\\varDelta {U}^{2}/2={P}_{c}{t}_{c}\\)\u003c/span\u003e\u003c/span\u003e, the charging power \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P}_{c}\\)\u003c/span\u003e\u003c/span\u003e from 0 to 10 V is 0.485 mW with 68 s in parallel connection, and 0.275 mW with 120 s in series connection.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.3 WSN power analysis and modeling\u003c/h2\u003e \u003cp\u003eTo monitor the environment information around the transformer, the commercial temperature and humidity sensor with Bluetooth (MBS-6003z) is selected as the WSN. The working voltage of the WSN is DC2.5V-3.3V, the sampling frequency is 1Hz, and it can intuitively display the temperature and humidity information with local has low power screen and remote mobile applications. By using the low-power load analyzer EMK850\u0026thinsp;+\u0026thinsp;with the DC power supply, the power consumption of the WSN is tested shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e (a).\u003c/p\u003e \u003cp\u003eIn Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e (b), the tested power consumption of wireless temperature and humidity sensor is mainly consisted of four parts, the energy consumption is 6.9 mJ when start WSN with 1.5 s. The energy consumption is 0.0475 mJ when sensing the temperature and humidity information with 25 ms every 1 s. The energy consumption is 0.533 mJ when sending the RF information with 130 ms every 10 s. The sleep current is 10 \u0026micro;A. Thus, the total energy consumption is 7.893 mJ to make the WSN start normally and send first information, and the total working time is more than 11.5s. The appropriate energy storage element will be selected according to this energy.\u003c/p\u003e \u003cp\u003eThe measured power consumption is shown in Table \u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e6\u003c/span\u003e. An equivalent time-varying load model was built in LTspice to describe the WSN power consumption, as shown in Fig, the equivalent load model of WSN consists of four parts, namely sleep resistance Rs, sensing current I3, startup current I2, and RF current I1. The simulation curve of current and voltage consumption of the equivalent load model after applying 3.3V voltage is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e (c). The superposition of the four parts of power consumption is basically consistent with the test curve in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e (d).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePower consumption parameters of WSN experiment measurement\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSymbol\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({V}_{cc}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSupply voltage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.3 V\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({T}_{s}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSensing cycle time\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1 s\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({T}_{RF}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRadio-frequency cycle time\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10 s\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({t}_{p}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStart-up current time\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1 s\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({t}_{s}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSingle sensing current time\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e25 ms\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({t}_{RF}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSingle RF current time\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e130 ms\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I}_{p}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAverage start-up current\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.42 mA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I}_{S}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSensing average current\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.59 mA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I}_{RF}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRadio-frequency average current\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.24 mA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I}_{sl}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSleep current\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10 \u0026micro;A\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Power management circuit\u003c/h2\u003e \u003cp\u003eAmong the typical commercial power management chips with micropower energy harvesting, the BQ25504, LTC3105, and et al, Where BQ25504 and LTC3105 have the maximum power point tracking (MPPT) function, However, external low dropout voltage linear regulator (LDO) increases the loss of the circuit. The LTC3588 and LTC3331 has a full-bridge rectifier and larger input voltage range from 2.7\u0026ndash;20 V for LTC3588 and 3\u0026ndash;19 V for LTC3331. The undervoltage lockout (UVLO) interval of LTC3588 is about only from 4V to 5V, lead to less discharge energy. To give enough WSN starting energy, a larger capacitor should be chosen but with larger leakage current and volume. The LTC3331 has a wide range of 3\u0026ndash;18 V can be set as UVLO interval, which match the PVEH varied input voltage change. The backup battery interface of LTC3331 further improve the long-term stability of power supply.\u003c/p\u003e \u003cp\u003eDue to the maximum output power corresponding voltage is 8 V for our 100 Hz PVEH, the UVLO interval of LTC3331 is set from 5\u0026ndash;10 V in our design. As the energy storage element, the electrolytic capacitor has large optional capacitor value, high limited voltage, long cycle life and low price, which can realize fast charging and discharging. A capacitor of 330 \u0026micro;F with the limited voltage of 25V is choosen as the energy storage element connected to Vin. Due to it has discharge energy of 12.375 mJ from 10 to 5 V.\u003c/p\u003e \u003cp\u003eThe circuit model of 100 Hz PVEH powering WSN with LTC3331 was built using LTspice as Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e (a), and simulated as Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e (b). The WSN equivalent power load at the output end can be periodically connected and disconnected from the power supply. When the PVEH charges the energy storage capacitors from 0 to 10 V with 136 s, the chip UVLO function is turned on and provide a stable 3.3V voltage for the WSN load continuously for 14 s. When the energy storage capacitor is discharged to the undervoltage lock lower limit threshold of 5 V, the chip will disconnect from the load. Energy storage capacitor stop the discharge and the voltage rise again to the set upper limit threshold of 10 V after 72 s for discharge. So repeatedly, the PVEH power management periodically provides a stable power supply to the WSN load, which ensures the normal startup and sustainable cyclical operation of the load system.\u003c/p\u003e \u003cp\u003eTo compare the powering WSN ability by single frequency PVEH and multi-frequency PVEHs, the circuit model of 100 Hz, 200 Hz, 300 Hz PVEHs paralleling powering WSN with LTC3331 was also built and simulated as Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e (c) and (d). Three PVEHs charges the energy storage capacitors from 0 to 10 V with shorter time of 84 s, and powering the WSN for longer time of 30 s, which proves stronger power generation than only one PVEH.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Experiment and application","content":"\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Experimental verification\u003c/h2\u003e \u003cp\u003eVibration and electrical experiments verify the performance of one and three PVEHs powered WSN as Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (a). The three PVEH prototypes array of 100 Hz, 200 Hz, 300 Hz is covered by power management circuit broad and arranged on the vibrator platform and connected to the and WSN as Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (b). The JDS6600 signal generator gives a sinusoidal 100 Hz and a mixed signal of 100 Hz, 200 Hz, 300 Hz in 0.1 g acceleration respectively as Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (c). The test voltage curves of the energy storage capacitor and the load WSN was observed by the oscilloscope as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (d). The 100 Hz PVEH takes 137 s to charge capacitor from 0 V to 10 V with charging power of 0.143 mW, and powers WSN for 18.8 s with discharge interval of 86 s. The three PVEHs take shorter times of 89 s to charge capacitor from 0 V to 10 V with charging power of 0.22 mW, and powers WSN for longer time of 27.2 s with shorter discharge interval of 65.5 s.\u003c/p\u003e \u003cp\u003eThe experimental results are relatively consistent with the simulation results, which shows the correctness of the whole system circuit modeling of the multi-frequency PVEHs powered WSN. When the voltage reaches 10V, the WSN starts to work, the energy storage capacitor first experienced a rapid power loss process from 10 V to 6.6V, releasing the energy of 9.3 mJ, while the WSN requires energy of 6.9 mJ, and the LTC3331 power circuit efficiency is calculated to be about 74%.\u003c/p\u003e \u003cp\u003eThe charging voltage curves of tri-frequency PVEHs at different accelerations of 0.1 g, 0.2 g, 0.3 g are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (e). The greater the acceleration, the greater the vibration energy, and the shorter the charging start time. The WSN will not power down after startup at more than 0.2 g accelerations excitation. It is adequate to meet the demand for continuous monitoring of temperature and humidity sensing.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Application in power grid transformer\u003c/h2\u003e \u003cp\u003eTo verify the practical application of WSN self-power supply by tri-frequency PVEHs in grid transformer tank vibration, the actual outdoor application test was verified on the 500 kV Yongzhou substation of Nanning Power Supply Bureau. This work tests and analyzes the vibration characteristics of the 500 kV grid transformer shell by three axis wireless accelerometer. The vibration test spectrum data of transformer at several points is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e (a). The vibration frequency of the transformer presents the distribution characteristics of 50 Hz, 100 Hz and multiple frequency. For different measurement points, such as fans, side shell, front shell, column, flange plate, their peak acceleration and frequency vary. It is recommended to select PVEH array with corresponding resonant frequency points for specific vibration points.\u003c/p\u003e \u003cp\u003eThe field application of tri-frequency PVEHs powered WSN in grid transformer column is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e (b). The vibration test spectrum of transformer column indicates the peak accelerations are 0.055 g at 100 Hz, 0.234g at 200 Hz, 0.113 g at 300 Hz; Under this excitation, the tri-frequency PVEHs charge the storage capacity from 0 V to 10 V with 33.6 s and charging power of 0.49 mW, then starts power on the WSN and stabilizes around 8 V. The tri-frequency PVEHs powered WSN works continuously to send temperature and humidity information to the Bluetooth receiver at 10 s interval. The mobile phone of the inspection personnel can get the wireless data without cross the safe distance of 5 m of the large transformer, which guarantees the personal safety of the inspection personnel to a certain extent. Relying on the array PVEHs and power management circuit can help the intelligent development of the power grid.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eThis article focuses on the design of vibration energy harvesters for multiple vibration frequency points of transformers. Through theoretical calculation and simulation, the resonant frequencies of PVEH under different parameters are obtained. By controlling the parameters, the short-circuit and open-circuit resonant frequencies of PVEH include the characteristic frequency points of 100 Hz, 200 Hz, and 300 Hz of the transformer to maintain the output power at a high value. Explored the effect of epoxy resin layer thickness on the output of piezoelectric bimorphs, and selected 420 mesh screen printing process to obtain piezoelectric bimorphs with good output performance. After assembly, the output power of the three prototypes were 0.316 mW, 0.128 mW, and 0.085 mW, respectively, which can meet the power requirements of low-power sensors. The equivalent electrical model of the prototype was calculated using the coupling relationship between the mechanical and electrical domains. The parallel output scheme of the three prototypes was determined through LTspice simulation, and the obtained sensor power consumption model was simulated at the system level with the equivalent model of the prototype through testing, providing guidance for the actual testing scheme. Tested in the laboratory, it takes 137 s for a 100Hz PVEH to charge capacitors from 0 V to 10 V, with a charging power of 0.143 mW. It can operate wireless sensors for 18.8 s and a discharge interval of 86 s. Three frequency point PVEHs have a shorter charging time of 89 s for 0\u0026ndash;10 V capacitors, a charging power of 0.22 mW, and can operate wireless sensors for 27.2 s with a shorter interval of 65.5 s, which is close to the simulation results. Finally, on-site experiments were conducted on a 500 kV transformer. The three frequency PVEHs charged the energy storage capacitor from 0 V to 10 V in 33.6 s, with a charging power of 0.49 mW. Then, the wireless sensor was continuously powered and the capacitor stabilized at around 8V. The multi frequency vibration energy collection prototype proposed in this article is of great significance in promoting the development of smart grids and ensuring the safety of grid workers.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work is supported by the R\u0026amp;D project of State Grid Corporation of China (Development of vibration energy harvesting device and Research on self power supply technology of sensor based on micro kinetic energy,\u0026nbsp;No. 5500-202158417A-0-0-00).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability Statement:\u0026nbsp;\u003c/strong\u003eThe data that support the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of Interest:\u0026nbsp;\u003c/strong\u003eThe authors declare no conflict of interest.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eC. Li, H. Huang, Y. Liang, Q. Chai, R. Zhao, and C. Hu, \"Power Sensor-oriented Development and Challenges of Environmental Energy Harvesting Technologies,\" Electric Power, vol.\u0026nbsp;54, no. 2, pp.\u0026nbsp;27\u0026ndash;35, 2021.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eF. Yang, L. Du, H. Yu, and P. Huang, \"Magnetic and Electric Energy Harvesting Technologies in Power Grids: A Review,\" \u003cem\u003eSensors\u003c/em\u003e, vol.\u0026nbsp;20, no. 5, Mar 9 2020, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.3390/s20051496\u003c/span\u003e\u003cspan address=\"10.3390/s20051496\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eY. Xu \u003cem\u003eet al.\u003c/em\u003e, \"Recent Progress of Electrode Materials for Flexible Perovskite Solar Cells,\" \u003cem\u003eNanomicro Lett\u003c/em\u003e, vol.\u0026nbsp;14, no. 1, p.\u0026nbsp;117, Apr 30 2022, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1007/s40820-022-00859-9\u003c/span\u003e\u003cspan address=\"10.1007/s40820-022-00859-9\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eS. Gao \u003cem\u003eet al.\u003c/em\u003e, \"Triboelectric\u0026ndash;electromagnetic hybridized module for energy harvesting of power transmission lines galloping and self-powered galloping state monitoring,\" Nano Energy, vol.\u0026nbsp;101, 2022, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.nanoen.2022.107530\u003c/span\u003e\u003cspan address=\"10.1016/j.nanoen.2022.107530\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eP. Jiang, Z. Zhang, J. Zhang, B. Deng, J. Deng, and Z. Pan, \"Research on vibration characteristics and Multi-parameter state recognition of \u0026plusmn;\u0026thinsp;500 kV converter transformer under fluctuating conditions,\" International Journal of Electrical Power \u0026amp; Energy Systems, vol.\u0026nbsp;136, 2022, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.ijepes.2021.107748\u003c/span\u003e\u003cspan address=\"10.1016/j.ijepes.2021.107748\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eM. Sawane and M. Prasad, \"MEMS piezoelectric sensor for self-powered devices: A review,\" Materials Science in Semiconductor Processing, vol.\u0026nbsp;158, 2023, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.mssp.2023.107324\u003c/span\u003e\u003cspan address=\"10.1016/j.mssp.2023.107324\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eS. M. Shahruz, \"Design of mechanical band-pass filters for energy scavenging,\" \u003cem\u003eJournal of Sound and Vibration\u003c/em\u003e, vol.\u0026nbsp;292, no. 3\u0026ndash;5, pp.\u0026nbsp;987\u0026ndash;998, 2006, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.jsv.2005.08.018\u003c/span\u003e\u003cspan address=\"10.1016/j.jsv.2005.08.018\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eG. Tang \u003cem\u003eet al.\u003c/em\u003e, \"Fabrication and analysis of high-performance piezoelectric MEMS generators,\" Journal of Micromechanics and Microengineering, vol.\u0026nbsp;22, no. 6, 2012, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1088/0960-1317/22/6/065017\u003c/span\u003e\u003cspan address=\"10.1088/0960-1317/22/6/065017\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eX. Zhao, S. Li, C. Ai, H. Liu, and D. Wen, \"Fabrication and Characterization of the Li-Doped ZnO Thin Films Piezoelectric Energy Harvester with Multi-Resonant Frequencies,\" Micromachines (Basel), vol.\u0026nbsp;10, no. 3, Mar 26 2019, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.3390/mi10030212\u003c/span\u003e\u003cspan address=\"10.3390/mi10030212\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eR. M. Toyabur, M. Salauddin, and J. Y. Park, \"Design and experiment of piezoelectric multimodal energy harvester for low frequency vibration,\" \u003cem\u003eCeramics International\u003c/em\u003e, vol.\u0026nbsp;43, pp.\u0026nbsp;S675-S681, 2017, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.ceramint.2017.05.257\u003c/span\u003e\u003cspan address=\"10.1016/j.ceramint.2017.05.257\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZ. Xiao, T. q. Yang, Y. Dong, and X. c. Wang, \"Energy harvester array using piezoelectric circular diaphragm for broadband vibration,\" Applied Physics Letters, vol.\u0026nbsp;104, no. 22, 2014, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1063/1.4878537\u003c/span\u003e\u003cspan address=\"10.1063/1.4878537\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eB. Zhang, H. Li, S. Zhou, J. Liang, J. Gao, and D. Yurchenko, \"Modeling and analysis of a three-degree-of-freedom piezoelectric vibration energy harvester for broadening bandwidth,\" Mechanical Systems and Signal Processing, vol.\u0026nbsp;176, 2022, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.ymssp.2022.109169\u003c/span\u003e\u003cspan address=\"10.1016/j.ymssp.2022.109169\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eP. H. Wu, Y. J. Chen, B. Y. Li, and Y. C. Shu, \"Wideband energy harvesting based on mixed connection of piezoelectric oscillators,\" Smart Materials and Structures, vol.\u0026nbsp;26, no. 9, 2017, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1088/1361-665X/aa7981\u003c/span\u003e\u003cspan address=\"10.1088/1361-665X/aa7981\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eH. Xia \u003cem\u003eet al.\u003c/em\u003e, \"Self-Powered Dual-Inductor MI-PSSHI-VDR Interface Circuit for Multi-PZTs Energy Harvesting,\" IEEE Transactions on Power Electronics, vol.\u0026nbsp;37, no. 4, pp.\u0026nbsp;3753\u0026ndash;3762, 2022, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1109/tpel.2021.3124828\u003c/span\u003e\u003cspan address=\"10.1109/tpel.2021.3124828\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eK. Ashraf, M. H. Md Khir, J. O. Dennis, and Z. Baharudin, \"Improved energy harvesting from low frequency vibrations by resonance amplification at multiple frequencies,\" Sensors and Actuators A: Physical, vol.\u0026nbsp;195, pp.\u0026nbsp;123\u0026ndash;132, 2013, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.sna.2013.03.026\u003c/span\u003e\u003cspan address=\"10.1016/j.sna.2013.03.026\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eX. Li, K. Yu, D. Upadrashta, and Y. Yang, \"Multi-branch sandwich piezoelectric energy harvester: mathematical modeling and validation,\" Smart Materials and Structures, vol.\u0026nbsp;28, no. 3, 2019, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1088/1361-665X/aaf8bf\u003c/span\u003e\u003cspan address=\"10.1088/1361-665X/aaf8bf\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eH. Deng, Y. Du, Z. Wang, J. Zhang, M. Ma, and X. Zhong, \"A multimodal and multidirectional vibrational energy harvester using a double-branched beam,\" Applied Physics Letters, vol.\u0026nbsp;112, no. 21, 2018, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1063/1.5024567\u003c/span\u003e\u003cspan address=\"10.1063/1.5024567\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eX. Ma, H. Li, S. Zhou, Z. Yang, and G. Litak, \"Characterizing nonlinear characteristics of asymmetric tristable energy harvesters,\" Mechanical Systems and Signal Processing, vol.\u0026nbsp;168, 2022, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.ymssp.2021.108612\u003c/span\u003e\u003cspan address=\"10.1016/j.ymssp.2021.108612\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eS. W. Zhiyuan Li, Shengxi Zhou, \"Multi-solution phenomena and nonlinear characteristics of tristable galloping energy harvesters with magnetic coupling nonlinearity,\" Communications in Nonlinear Science and Numerical Simulation, 2023, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.cnsns.2022.107076\u003c/span\u003e\u003cspan address=\"10.1016/j.cnsns.2022.107076\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eD. Gibus, P. Gasnier, A. Morel, A. Ameye, and A. Badel, \"A strong electromechanically coupled and low-damped harvester for resonant frequency tuning,\" presented at the 2021 IEEE 20th International Conference on Micro and Nanotechnology for Power Generation and Energy Conversion Applications (PowerMEMS), 2021.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eS. Roundy, \"A study of low level vibrations as a power source for wireless sensor nodes,\" Computer Communications 2003.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eW. Q. Liu, A. Badel, F. Formosa, and Y. P. Wu, \"A new figure of merit for wideband vibration energy harvesters,\" Smart Materials and Structures, vol.\u0026nbsp;24, no. 12, 2015, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1088/0964-1726/24/12/125012\u003c/span\u003e\u003cspan address=\"10.1088/0964-1726/24/12/125012\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eL. Wang \u003cem\u003eet al.\u003c/em\u003e, \"A packaged piezoelectric vibration energy harvester with high power and broadband characteristics,\" Sensors and Actuators A: Physical, vol.\u0026nbsp;295, pp.\u0026nbsp;629\u0026ndash;636, 2019, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.sna.2019.06.034\u003c/span\u003e\u003cspan address=\"10.1016/j.sna.2019.06.034\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eB. Zhang, H. Liu, S. Zhou, and J. Gao, \"A review of nonlinear piezoelectric energy harvesting interface circuits in discrete components,\" Applied Mathematics and Mechanics, vol.\u0026nbsp;43, no. 7, pp.\u0026nbsp;1001\u0026ndash;1026, 2022, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1007/s10483-022-2863-6\u003c/span\u003e\u003cspan address=\"10.1007/s10483-022-2863-6\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eY. Liao and J. Liang, \"Unified modeling, analysis and comparison of piezoelectric vibration energy harvesters,\" Mechanical Systems and Signal Processing, vol.\u0026nbsp;123, pp.\u0026nbsp;403\u0026ndash;425, 2019, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.ymssp.2019.01.025\u003c/span\u003e\u003cspan address=\"10.1016/j.ymssp.2019.01.025\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eL. Wang \u003cem\u003eet al.\u003c/em\u003e, \"System level design of wireless sensor node powered by piezoelectric vibration energy harvesting,\" Sensors and Actuators A: Physical, vol.\u0026nbsp;310, 2020, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.sna.2020.112039\u003c/span\u003e\u003cspan address=\"10.1016/j.sna.2020.112039\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eY. Liao and H. Sodano, \"Optimal power, power limit and damping of vibration based piezoelectric power harvesters,\" Smart Materials and Structures, vol.\u0026nbsp;27, no. 7, 2018, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1088/1361-665X/aabf4a\u003c/span\u003e\u003cspan address=\"10.1088/1361-665X/aabf4a\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"smart grid, vibration energy harvesting, power management circuit, self-powered WSN","lastPublishedDoi":"10.21203/rs.3.rs-3736998/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3736998/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWith the development of smart grid, many wireless sensor nodes (WSN) used in monitoring grid equipment need continuous power supply. This work propose a multi-frequency array piezoelectric vibration energy harvester (PVEH) powering WSN based on the grid transformers vibration of 100, 200 and 300 Hz. The PZT bimorph with U shaped mass sturcture is design and opitimized by finite element simulation. The bonding method of epoxy conductivity and insulation is studied for PZT bimorph and aluminum packaged PVEHs. The equivalent circuit modeling and interface circuit of PVEHs are studied in LTspice simulation. Through the whole system design of the array PVEHs powered WSN circuit with LTC3331 chip, the WSN can run continuously in simultation and experimental verification. The feasibility of multi-frequency PVEH powered WSN is verified on the 500 kV transformer in filed operation. This research has important application value to the design of WSN self-power supply for smart grid.\u003c/p\u003e","manuscriptTitle":"Multi-frequency piezoelectric vibration energy harvesters powered sensing in power grid transformer","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-01-01 08:09:24","doi":"10.21203/rs.3.rs-3736998/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"efec39b1-3ac3-4170-9fcf-dcca05714a66","owner":[],"postedDate":"January 1st, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":27830582,"name":"Physical sciences/Engineering/Electrical and electronic engineering"},{"id":27830583,"name":"Physical sciences/Nanoscience and technology/Other nanotechnology/Environmental, health and safety issues"}],"tags":[],"updatedAt":"2024-03-22T01:20:24+00:00","versionOfRecord":[],"versionCreatedAt":"2024-01-01 08:09:24","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3736998","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3736998","identity":"rs-3736998","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}