Non-Invasive Voltage Measurement Device Based on MEMS Electric Field Sensor and Applications

Abstract

In the context of new power systems, the safe and accurate sensing of voltage data is crucial for the secure and stable operation of power grids. Given that existing voltage measurement devices cannot meet the development requirements for wide-area deployment and distributed monitoring, this paper designs a non-intrusive voltage measurement device based on MEMS (micro-electromechanical system) electric field sensors, which are characterized by their small size, low power consumption, ease of installation and strong anti-interference ability. Firstly, the paper introduces the voltage measurement principle and analyzes the equivalent circuit based on this analysis; secondly, the key structural design of the measurement device is completed and the prototype of the device is developed; finally, the accuracy and anti-jamming tests of the measurement device are conducted by establishing an experimental platform, followed by field applications. Experimental results demonstrate that the voltage measurement device has high measurement accuracy, and the maximum error is only 1.215%. Additionally, the device has a good shielding capability against the coupled electric field of surrounding interference conductors, with a maximum error increase of 1.313%. In a 10 kV overhead line voltage test, the device can accurately obtain the actual voltage. The voltage measuring device developed in this paper can provide data support for the condition assessment of overhead lines and effective monitoring means for the safe and stable operation of the power system.

1. Introduction

In the context of achieving “double carbon” goals, sensor technology is pivotal for the future development of power grids towards green environmental protection. Voltage parameters directly reflect the operation state and fault characteristics of electrical equipment and transmission lines, making them the most critical electrical parameter within a power system. Existing voltage measurement technologies can be categorized into invasive and non-invasive methods [1]. Invasive measurement techniques, such as traditional pressure dividers, require direct connection to live components, which alters the topology of the measurement system and poses safety risks [2]. Furthermore, invasive methods can damage equipment and line insulation, complicating installation and maintenance tasks [3,4,5,6]. In practical voltage measurements, particularly in complex environments, it is often impractical to remove the insulation layer, or it is inconvenient to destroy the insulation.

With the increase in voltage level, the complexity of processes and the risks associated with contact measurement operations on towers are also gradually increasing. Additionally, the equipment size and performance limitations cannot meet the requirements of safe and reliable measurement. In contrast, non-invasive measurement technology does not require penetration of wire insulation or power equipment and does not involve direct electrical connection to lines and equipment [7,8,9,10,11,12,13]. The D-dot electric field sensor mainly measures transient voltages based on the rate of change of the electric field. It has a wide frequency band and rapid response. However, the electric field is prone to distortion and is susceptible to environmental interference, necessitating the optimization of shielding technology [9]. An electro-optic effect sensor modulates the refractive index of light by using an electric field. The integrated type is small in size and highly sensitive, although temperature compensation is difficult [10]. Electrostatic force MEMS sensors are based on electrostatic force displacement measurement. They are small in size and low in cost; however, the mechanical structure limits their high-frequency response, and vibrations can affect their service life [11]. Coupled capacitive voltage sensors mainly utilize the principle of stray capacitance voltage division, featuring a wide dynamic range and high insulation strength. However, stray electricity is susceptible to environmental interference, which results in low measurement accuracy and necessitates complex anti-interference processing [12,13]. Compared to invasive measurement methods, non-invasive measurement not only facilitates the safe and stable operation of the power grid but is also highly compatible with the requirements of plug-and-play distributed sensing networks. Nevertheless, it also has its own shortcomings and lacks mature measurement devices [14,15].

Micro-electromechanical-system-based [16] electric field microsensors have a small volume and low power consumption, which meets the requirements of the current distributed measurement of new power systems [17]. This study presents a piezoelectric cantilever-beam-type miniature electric field sensor, which comprises two sets of piezoelectric cantilever beams to prepare PZT (Lead Zirconate Titanate) films by the sol–gel method. On this basis [18], a piezoelectric-driven MEMS electric field sensor that utilizes the fixed electrode and the driving electrode as the induction electrode and the shielding electrode is proposed. When measuring the electric field, the driving electrode generates an induced current signal that forms an interactive shielding with the fixed electrode. Additionally, researchers have developed an MEMS electric field sensor based on electrostatic force coupling [14,15]. The principle behind the metal film is that it is displaced by electrostatic force in the electric field to be measured and measures the displacement through the laser displacement sensor so as to determine the intensity of the electric field to be measured. However, MEMS electric field sensors have low resolution and sensitivity due to the necessity for complex optical systems for measurement assistance. Hu Jun, Han Zhifei, et al. proposed an MEMS electric field sensor that utilizes the static power and piezoresistance coupling [19]. This sensor converts the external electric field into strain via the electrostatic force of the metal film and transforms this strain into a measurable electrical signal using piezoresistive materials. However, current sensing technology research mainly focuses on the MEMS electric field sensor itself, with limited reports on non-invasive voltage measurement devices based on MEMS electric field sensors. In addition, the existing measuring devices lack anti-electromagnetic interference measures, which can easily lead to measurement errors.

In this paper, a non-invasive 10 kV AC (Alternating Current) line voltage measuring device based on an MEMS electric field sensor is designed and developed. Firstly, the principle of voltage measurement based on the MEMS electric field sensor was introduced, and the equivalent circuit was analyzed. Secondly, the key structure of the measuring device was designed, and the prototype of the non-invasive voltage measuring device was developed. Finally, accuracy and anti-interference tests of the device were completed by constructing an experimental platform, and the application was verified on a 10 kV overhead line. Compared to other MEMS electric field sensors, the torsional electric field sensor based on piezoelectric-driven periodic shielding designed in this paper has stable measurement performance, high space utilization, low power consumption and minimal effects, making it suitable for overhead wire application.

2. Theoretical Approach

2.1. Voltage Measurement Principle

The principle of voltage measurement is shown in Figure 1. The coupled capacitor formed by the tested wire and the metal electrode and the fixed value capacitor are designed in series to form a voltage sensing unit that converts the high voltage of the overhead line into a measurable low voltage [20,21,22]. The fixed value capacitor utilizes a metal film capacitor, which is less affected by temperature, voltage and frequency, making it suitable for complex on-site environments. It can be directly integrated into the chip. The design of the MEMS sensor adopts a torsion sensor based on a piezoelectric-driven comb tooth structure for periodic shielding. This design achieves periodic shielding of the comb tooth structure through the inverse piezoelectric effect of the PZT electrode, thereby modulating to facilitate electric field induction measurement. The MEMS sensor converts the low-voltage signal obtained from the voltage sensing unit into an output signal that is proportional to it. Consequently, the measuring device consists of a voltage sensing unit and an MEMS sensor. The external packaging of the MEMS sensor includes the MEMS electric field chip, the metal top plate and the ceramic bottom plate to protect the MEMS chip.

When an AC drive voltage is applied to the MEMS sensor, the drive structure causes the shield electrode to vibrate back and forth [17]. The electric field strength on the shielding electrode is strong when it is far from the induction electrode, but weak when it is close to it. According to the Gaussian theorem, the electric field strength on a metal electrode is proportional to its surface area.

$$Q=\epsilon E_n$$

(1)

where ε is the permittivity around the sensitive structure and E_n is the electric field strength on the induced electrode. Due to the periodic shielding provided by the shielding electrode, an alternating charge will manifest on the induction electrode under the action of the charge induction principle. The magnitude of the induced charge Q(t) on the shielding electrode is

$$Q(t)=k_q{X}_r{E}_n\sin ({\omega }_{s}t+\theta )+Q_0$$

(2)

In this formula, k_q is the charge variable of the induction electrode in unit amplitude, which is related to the dielectric constant and the vibration mode of the shielding electrode; X_r is the vibration amplitude of the shielding electrode; ω_s is the voltage drive frequency; θ is the phase angle of drive voltage; Q₀ is the initial induced charge amount of the induction electrode.

Then the output current of the MEMS electric field sensor, i_out, is

$$i_{\mathrm{out}}={\displaystyle \frac{dQ\left(t\right)}{dt}}=k_q{X}_r{\omega }_s{E}_n\cos \left({\omega }_{s}t+\theta \right)$$

(3)

The output signal of the MEMS electric field sensor is a voltage signal formed by the lock-in amplification of the output current, and the output voltage U_out of the MEMS sensor is

$$U_{\mathrm{out}}=k{i}_{\mathrm{out}}$$

(4)

where k is the phase-in magnification of the sensor; thus, k_E = kk_qX_rω_s. The output voltage is U_out, the valid value of which can be expressed as

$$U_{\mathrm{out}}=k_E{E}_n$$

(5)

When the output voltage of the voltage sensing unit is measured with the MEMS sensor, the electric field between the metal roof of the MEMS sensor and the ceramic bottom plate generates a uniform electric field E, and the relationship between the MEMS electric field sensor output voltage U_out and the conductor voltage to be tested U_s can be expressed as

$$U_{\mathrm{out}}=k_{E}E=k_E{\displaystyle \frac{U_m}{d}}={\displaystyle \frac{k_E{U}_s}{kd}}$$

(6)

where k_E stands for the sensitivity coefficient of the internal MEMS electric field sensor chip; d is the equivalent distance between the metal roof and the ground bottom plate in the external package of the electric field sensor. Therefore, the voltage measurement of the overhead line to be measured can be realized by obtaining the output data of the MEMS electric field sensor.

2.2. Circuit-Equivalent Model Analysis

The equivalent circuit analysis model established based on the principle of voltage measurement is shown in Figure 2 [23]. In the picture, U_s is the voltage of the conductor to be measured, U_m is the output voltage of the voltage induction unit, the capacitor C₁ is the coupling capacitance between the wire and the metal electrode, resistance R_b is the equivalent resistance with shield wire, capacitor C_b is the coupling capacitance of the inner wire and the grounding shield, and capacitor C₂ is a standard low-voltage arm capacitor.

Ignoring the edge effect, the coupled capacitor C₁ can be estimated as [20]

$$C_1={\displaystyle \frac{1}{{\displaystyle {\int }_0^h\frac{dz}{{\epsilon }_1(2r+\frac{(h-z)(b_1-2r)}{h})(a+\frac{z(L_1-a_1)}{h})}}}}$$

(7)

In the Equation (7), ԑ₁ is the spatial dielectric permittivity; L₁ and 2r are the equivalent length and width of the transmission wire, respectively; a₁ and b₁ are the lengths of the induced metal plate along the wire direction and perpendicular to the wire direction, respectively; h is the distance between the wire and the metal plate; and the integral interval of the variable z is [0, h].

Because the shield cable of length L₂ is coaxial, resistance R_b and capacitance C_b are calculated by the following formulas:

$$R_{\mathrm{b}}={\displaystyle \frac{L_2}{2}}\sqrt{{\displaystyle \frac{f\mu }{\pi \sigma }}}({\displaystyle \frac{1}{a_2}}+{\displaystyle \frac{1}{b_2}})$$

(8)

$$C_{\mathrm{b}}={\displaystyle \frac{2\pi {\epsilon }_0{\epsilon }_2{L}_2}{\ln (b_2/a_2)}}$$

(9)

where μ is the magnetic permeability, σ is the electrical conductivity, f is the frequency of the pending lead at 50 Hz, ԑ₂ is the relative dielectric constant of the shielded cable medium, a₂ is the inner wire radius, and b₂ is the outer shield radius.

Based on the above equivalent circuit model and the principle of capacitive coupling, the relationship between the voltage on the sensor metal roof and the conductor voltage to be measured can be expressed as

$$U_m={\displaystyle \frac{C_1}{C_1+(1+s{C}_1{R}_b)(C_b+C_2)}}·U_s$$

(10)

C₁ and C_b are the pF level-size capacitance, and R_b represents tens of µ Ω resistance, so it can be calculated that sC₁R_b << 1. Formula (10) can be simplified to

$$U_m={\displaystyle \frac{C_1}{C_1+C_b+C_2}}·U_s$$

(11)

So the voltage to be tested and the voltage on the sensor metal roof can be expressed as

$$U_s={\displaystyle \frac{C_1+C_b+C_2}{C_1}}·U_m=k_1{U}_m$$

(12)

In this formula, k₁ is the voltage calibration coefficient between the voltage to be measured and the voltage of the induction electrode, where C₁ depends on the shape of the transmission wire and the metal electrode and their relative positions, C_b depends on the material and shape of the shielded cable, and C₂ depends on the sensor’s own ground parameters, so the value of k₁ can be determined by checking the equipment installation. Finally, the line voltage can be measured by Equation (12).

3. Measurement Device Design

3.1. Design of Induction Structure

Based on the principle of voltage measurement, the structure of the sensing device has been designed, and its parameters have been optimized. The shape of the induction electrode is crucial in influencing the measurement output result. When the actual measured output voltage of the sensor deviates significantly from the true measured value, calibration using Equation (12) may exacerbate the error. To evaluate the impact of various external metal induction electrodes on the measured output, according to the GB/T 35086-2018 general specification for MEMS electric field sensors, different metal electrode shapes were designed and customized as shown in Figure 3.

By fixing the metal induction electrode of the MEMS electric field sensor at a distance directly below the wire, the metal induction electrodes with different shapes and area sizes were tested, and the output signals of the MEMS sensor are shown in

Table 1. Output of the sensor under the electrodes of different shapes and sizes.

Electrode Slice	Square 1	Square 2	Square 3	Square 4	Square 5	Round 1	Round 2	Round 3	Round 4	Round 5	Arc 1	Arc 2	Arc 3	Arc 4	Arc 5
Area/cm2	6	12	18	24	30	π	2.25π	4π	6.25π	9π	3π	3π	6π	6π	12π
Sensor output/V	1.86	2.14	2.30	2.54	2.80	1.70	1.94	2.14	2.40	2.70	2.02	2.06	2.60	2.60	3.32
Output per unit area/V·cm−2	0.31	0.178	0.128	0.106	0.093	0.541	0.274	0.17	0.122	0.095	0.214	0.219	0.138	0.138	0.088

and Figure 4.

As shown in Table 1, for the same type of metal induction electrode, the output of the sensor increases with the area of the induction electrode. As the area of the metal induction electrode increases, the coupling capacitance between it and the wire increases, and the equivalent capacitance is almost unchanged. According to Formula (11), it can be analyzed that the coupling capacitor of the wire increases, so the output of the sensor increases. However, with the increase in the area of the induced structure, the impact of the external coupling interference also increases [20]. Therefore, the area of the induction structure should not be increased indefinitely during the design of the induction electrode.

As demonstrated in Table 1, for the same type of metal induction electrode, the output of the sensor increases with the area of the induction electrode. This increase occurs because the area of the metal induction electrode expands, the coupling capacitance between it and the wire also increases, while the equivalent capacitance remains relatively constant. According to Formula (11), it can be analyzed that the coupling capacitor of the wire increases, so the output of the sensor increases. However, with the increase in the area of the induced structure, the influence of the external coupling interference increases [20]. Therefore, in the design of the induction electrode, the area of the induction structure should not be increased indefinitely.

Combining the findings presented in Figure 4, it can be concluded that as the area of the inductive structure increases, the sensor output per unit area decreases, indicating a reduction in the utilization rate of the inductive structure. For the square, round and arc sensor output response values, it was found that the arc structure exhibits a small utilization rate change with the increase of area, compared to the square and round structures. This is due to the arc shape of the induction structure and wire shape matching. In the design of the sensor with same area, the more compact the internal space is, the larger the sensor output is. However, when using the square and circular induction structures, when obtaining the same output result, the area of the induction structure should be increased, resulting in a decrease in the utilization rate of the induction structure, and eventually leading to a larger volume of the measurement device. Considering the output performance, utilization rate and practical situation, it is reasonable to adopt the arc-shaped electrode as the inductive structure.

3.2. Design of Voltage Measurement Device

The key structure of the MEMS electric field sensor is designed based on the principle of voltage measurement. The structure of the non-invasive line voltage measurement device is shown in Figure 5. Its structure includes a metal induction electrode, a cable with a shield layer, a shielding structure, a shielding metal cap and a rear end circuit module. To shield the sensitive structure from interference by other conductors, the metal electrode is designed as part of the shielding structure. The induction electrode and the shielding electrode are arranged in concentric circles, with the radius and arc angle of the shielding electrode being greater than those of the induction electrode. Additionally, the side position of the shielding electrode is aligned with the center of the induction electrode. The gap between the induction electrode and the outer cylinder is filled with epoxy resin for fixation and insulation. During measurement, the open circular metal induction electrode is fixed near the transmission line. The metal induction electrode generates an induction voltage due to the charge induction principle, which is connected to the electric field sensor measurement area in the shielded metal cap through the cable with a shielded layer. The internal electric field measurement of the cap is composed of upper and lower plate and an MEMS electric field sensor chip, and the internal can constitute an approximately uniform strong electric field. Since the upper and lower gaps are fixed, the internal field strength can be accurately measured using the MEMS electric field sensor. By applying the principle of capacitor partial voltage, the electric potential of the transmission line can be calculated accurately.

To facilitate measurement, the device is designed with controllable opening and closing mechanisms for practical application. The device is installed and opened and closed by the remote control motor of the upper machine, which effectively simplifies the installation operation of the device. Additionally, the device also includes a high-speed data acquisition unit and a wireless communication unit. The wireless communication unit utilizes ultra-low-power-consumption NB-IoT (Narrowband Internet of Things) to enable data communication. The power supply for the device adopts a ±3 V DC power supply, and the sensor shell structure is made of the thermoplastic polymer material with a breakdown strength of 35 MV/m, which meets the insulation performance measurement requirements of the transmission lines or cables with or without an insulation layer. The final model and prototype of the non-invasive voltage measuring device based on an MEMS electric field sensor are shown in Figure 6. The device length is 9.6 cm, and the height is 6.8 cm. Compared to traditional power system measuring equipment, the volume of the device has been significantly reduced, and the power consumption is maintained within 0.5 W.

4. Experimental Test and Result Analysis

4.1. Construction of the Experimental Platform

Due to the 6 to 7 m height of 10 kV lines, which is not suitable for laboratory testing, this paper simulates the test at a height of 2 meters, constructing the experimental platform as shown in Figure 7. During the experiment, the measuring device was fixed on the wire, which had a diameter of 22 mm and a length of 3 m. The power frequency AC voltage of the wire was generated by the 20kVA test transformer (customized, China). The reference voltage was measured by the oscilloscope (Tektronix DPO 7104C, USA) after passing through the 370:1 voltage divider (customized, China).

4.2. Accuracy Test

According to the standard evaluation of electric fields in a flat electrode, the sensing device has an effective measurement range of 0–50 kV for field strength. To assess the accuracy of the device in measuring 10 kV line voltage, the calibrated measuring device refers to the transformer accuracy test method. The measurement points were selected as 80%, 90%, 100%, 110% and 120% of the rated voltage. At the five test points, the voltage measurement device and oscilloscope display values were read, with each measurement point representing multiple measurement data, and the average value was taken as the measurement result. The measurement relative error of δ was calculated. If the schematic value of the oscilloscope is U_N (i.e., actual value), the output display value of the measurement device is U_X, and the relative error calculation formula is

$$\delta =(U_X-U_N)\times 100\%/U_N$$

(13)

The corresponding output and relative deviation δ experimental data results are shown in

Table 2. Voltage accuracy test results.

Test Potential	Standard Value		Output Value UX/Kv	Error Δ/%
	Oscilloscope Reading/V	Theoretical Truth Value UN/V
4.61 kV gear	12.456	4.609	4.592	−0.369
	12.459	4.610	4.592	−0.390
5.19 kV gear	14.026	5.190	5.244	1.040
	14.024	5.189	5.137	−1.002
5.77 kV gear	15.589	5.769	5.796	0.468
	15.589	5.768	5.820	0.870
6.35 kV gear	17.158	6.348	6.396	0.803
	17.160	6.349	6.420	1.118
6.92 kV gear	18.674	6.909	6.975	0.955
	18.680	6.912	6.996	1.215

.

As can be seen from Table 2, the maximum measurement error of the voltage measuring device is only 1.215% in the power frequency voltage range of 4.61–6.92 kV, and the visible device can realize the accurate measurement of steady state voltage.

4.3. Anti-Interference Test

In order to verify the anti-interference capability of the device, through the anti-interference study of the control variable deployment device, one parallel wire of the same size as the measured wire was used as the source of interference, as shown in Figure 8.

The wire for the first set of suspension measuring device experiments was grounded. The voltage of the jamming wire was gradually increased from 1 kV to 10 kV. We recorded ten sets of measurement data and observed the zero output of the measurement device; the second set of experiments takes a 1 kV voltage to 10 kV, with a voltage of the suspension measurement device. In the control group, the two wires were measured with 1 kV voltage, gradually increased to 10 kV, resulting in a set of interference traverse measurement data. When the first set of experiments was performed, the device output remained consistently at 0, demonstrating that the sensor’s zero output is stable and cannot be disturbed by the surrounding coupling electric field. For the experimental testing in the second and third groups, the measured data are shown in

Table 3. Anti-interference measurement results.

Test Potential	Standard Value		Output Value UX with No Interference Wire/kV	Output Value UX with an Interference Wire/kV	Error δ/%
	Oscilloscope Reading/V	Theoretical True Value UN/V
1 kV	2.705	1000.85	1.012	1.024	1.186
2 kV	5.408	2000.96	1.980	2.006	1.313
3 kV	8.112	3001.44	3.058	3.089	1.014
4 kV	10.812	4000.44	4.073	4.125	1.277
5 kV	13.515	5000.55	5.069	5.086	0.335
6 kV	16.220	6001.4	6.120	6.107	−0.212
7 kV	18.924	7001.88	7.066	7.075	0.127
8 kV	21.625	8001.25	8.120	8.121	0.012
9 kV	24.326	9000.62	9.175	9.195	0.218
10 kV	27.031	10,001.47	10.196	10.220	0.235

.

It can be seen from Table 3 that the device can accurately measure the voltage of 1–10 kV. The output voltage value is slightly increased compared with the non-interference wire device, but the increase range is small, and the maximum error increase is 1.313%. Compared with the existing voltage sensors [24], the maximum measurement error of this study has been reduced by more than 1%. Actual measurements confirm that the device exhibits strong resistance to interference.

4.4. Field Application Test

We conducted the field measurement of the device on a 10 kV multi-loop overhead line, with the developed measurement device installed on the three-phase wire, as shown in Figure 9.

The wire was arranged horizontally, where the BC phase spacing was 50 cm, the spacing of the other two phases was 120 cm, and the wire cross-section area was 150 mm², with a height of 14 m. There was a triangular 35 kV transmission line 2.5 m above the wire and another horizontal 10 kV transmission line 2.5 m below the wire.

The field test time lasted for one hour; the current measured line voltage data were recorded every 10 min, and seven sets of data were recorded per phase. According to the actual situation, the theoretical output of the device should be an effective value of 5.774 kV. The actual measurements are shown in

Table 4. Voltage detection data of 10 kV transmission line.

To Test Phase	Voltage/kV
	1	2	3	4	5	6	7
A-phase	5.320	5.375	5.421	5.420	5.604	5.358	5.441
B-phase	5.731	5.901	5.882	5.631	5.667	5.881	5.502
C-phase	6.127	5.895	5.921	6.031	5.830	5.911	6.122

and Figure 10.

The line phase voltage measured by the terminal receiving device is not exactly 5.774 kV, which may be attributed to two primary factors. First, the installation position of the device is close to the tower of the transmission line. In addition to the influence of the transmission lines, there are other equipment influences; on the other hand, the line voltage may float, so there is a certain deviation between the final measurement result and the theoretical result. According to Formula (13), it is calculated that the maximum output error is only 7.86%, and the maximum floating voltage is only about 400 V, which is within the acceptable range of power detection operation for the detection voltage of the kV level.

5. Conclusions

This paper studies the principle of voltage measurement based on a MEMS electric field sensor and analyzes the equivalent circuit. Additionally, the key structure is designed, and the prototype of non-invasive voltage measuring device is developed. Finally, accuracy and anti-interference tests of the device were completed through the experimental platform, and the application was verified on the 10 kV overhead line. The following conclusions were drawn:

• The maximum relative deviation of the developed measuring device is 1.215% in the voltage range from 4.61 kV to 6.92 kV, which can accurately measure the steady-state voltage.
• The output of the measuring device is stable at the zero position. In the case of alternating electric field coupling, the device can suppress the interference of the spatial electromagnetic field, with the maximum error increase of 1.313%, showing good shielding and anti-interference ability.
• In the practical application of the measuring device on a 10 kV line, the measurement floating error is much less than the voltage to be measured, being within the acceptable range of power detection operation, which verifies the effectiveness of the design architecture in this paper and lays a foundation for subsequent promotion and reference.

The voltage measuring device based on the MEMS electric field sensor designed in this paper has the potential for application in the field, which can effectively realize the on-line monitoring of the transmission line voltage, and can provide reliable data support for the safe and stable operation of the power system.