Contents Electric field measurement holds immense significance in various domains, including power transmission, aerospace engineering, the petrochemical industry, and meteorological detection. In recent years, with the depletion of fossil fuels, there has been an urgent need for clean and low-carbon energy trans-formation!” Large-scale distributed energy will become the main body of new power sources in the power grid and occupy a domi-nant position in the power structure[2]. With a plethora of clean energy and power electronic equipment connected to the grid, the fundamental characteristics of the future grid are undergoing pro-found transformations’” Real- time measurement feedback and dynamic adjustment of power grid state quantities are required[4] Electric field information is one of the basic physical quantities of the power system. It contains a large amount of information on the operating status of power grid equipment. Through edge computing, deep learning, and artificial intelligence methods, the intelligent perception of equipment status information and intelli-gent self-healing of faults can be quickly realized. This provides crucial foundational support for intelligent equipment status per-ception, deep information fusion, and optimal resource allocation in new power systems[5]–[7]. Therefore, the accurate measurement of electric field information has become an urgent need for the digital development of new power systems. Figure 1 describes the network of sensors in a smart grid for information perception.
The application of an electric field sensor requires not only a sensor with a wide frequency range and high dynamic range, but also insulation, miniaturization, and the capability for device inte-gration“-” When measuring the electric field, the charge generated by the dielectric on the surface of the electric field sensor usually leads to a certain degree of distortion of the electric field[10], If a part of the sensor is grounded, it will cause interference from the ground wire into the measurement loop, resulting in a change to the electric field distribution. This can result in significant distortion of the electric field, greatly reducing the accuracy of sensor measurements and posing challenges for large-scale applications.
At present, the miniature electric field sensors commonly used are divided into optical sensors[11], [12], mechanical sensors[13], [14], D-dot sensors[15], and so on, according to different working principles. The optical sensor converts the electric field signal into an optical signal using energy coupling and the electro-optic effect. It has the characteristics of lossless transmission, a wide measurement frequency range, and a fast dynamic response[16], [17]. The optical sensors for high electric field measurements can achieve wide bandwidths of up to 100 MHz and high resolutions of up to 50 V/m. For low-field measurements, the optical sensors can even reach GHz bandwidths and mV/ m resolutions'”, With the rapid development of micro- nano technology, the micro-electric field sensors based on microelectromechanical systems (MEMS) technology have received the attention of researchers. The primary sensing principles utilized by MEMS electric field sensors encompass charge induction, electrostatic force actuation, piezoresistive effect, and other related mechanlsms[19], [20]. The miniature MEMS electric field sensors boast a resolution of approximately 250 V/m and can measure electric fields up to 2500 V/m, offering exceptional integration, miniaturization, and sensitivity. The D-dot sensor detects electric fields by measuring the rate of change in the electric displacement vector, exhibiting wide frequency bandwidth and minimal dispersion, making it a popular choice for ultra - wideband electromagnetic pulse measurements. Due to its compact size, the sensor is well-suited for measuring confined spaces[21], [22].
For the optical sensor, the sensing and measuring modules are connected via optical fiber. The change in refractive index or light intensity reflects the electric field intensity, isolating the electrical signal of the signal acquisition unit and avoiding ground wire coupling interference. This ensures high accuracy in measuring electric fields, which is why most commercial electric field sensors are optical sensors. However, the integration is challenging due to the requirement for a complete set of optical systems, and its mea-surement accuracy heavily relies on the performance of optical devices while being susceptible to signal offset caused by temperature[23]. As of yet, the optimal solution is currently unavailable. Andreas Kainz et al. [8] developed a MEMS electric field sensor with a movable silicon spring, which operated on the principle of elec-trostatic coupling. The change in luminous flux caused by the movable silicon block blocking the LED was measured using a photodiode. Since the optical signal isolates the interference of the ground wire, the electric field is undistorted. However, the prepa-ration process is complicated due to the requirement for a complex optical measurement system and the output of the sensor demands high stability of LED. This hinders large-scale development and application, and researchers have not conducted in-depth research on this basis.
For non -optical electric field sensors, such as MEMS and D-dot, the back-end signal conditioning is integrated into the printed circuit board (PCB). The sensing module and measurement module directly convert electrical signals, while electrostatically induced charges are transformed into voltage signals[24] As the acquisition system solely relies on electrical signals, it is susceptible to ground wire coupling which can interfere with the signal and lead to a reduction in measurement accuracy of the electric field sensor. Currently, a satisfactory solution has not yet been found. There-fore, the majority of current electric field sensors are optical. However, there is a pressing need to develop non-optical alternatives that offer low cost, minimal distortion, and high stability.
Therefore, this paper will concentrate on analyzing the impact of ground wire coupling signals on non -optical electric field sensor measurement accuracy and designing a signal acquisition system for the sensor to achieve distortion-free electric field measure-ments. The article is organized as follows. Section 1 introduces the sources of error in electric field measurement under coupled interference from ground wires. In Section 2, we establish a stan-dardized calibration platform for electric fields without any intrusion from ground wires and propose a vertical movement calibration method for electric field sensors. In Section 3, we assess the impact of ground coupling signals on the measurement accuracy of electric field sensors under two typical operating conditions: uniform electric fields generated by parallel plates and non-uniform electric fields produced by transmission lines.
Analysis of Error Sources in Electric Field Measurements from Coupled Ground Wires Interference
Since the optical sensor can reflect the electric field signal through the refractive index or light intensity information of the optical signal, it can realize the isolation of ground wire interference, and measure the electric field without distortion. However, the difficulty of integrating optical devices and temperature stability is not being resolved[12], Non -optical electric field sensors may introduce ground wire interference, leading to the reduced measurement accuracy of the electric field. Taking MEMS electric field sensors as an example, we analyzed the primary source of ground inter-ference.
The MEMS electric field sensor system is shown in Figure 2, which mainly includes sensing electrodes, drive modules, signal acquisition and processing modules, and power supply modules. The main sources of ground interference include two parts: power supply and signal acquisition modules. For instance, due to the tiny mechanical deformation of MEMS electric field sensors, the electrical signal derived from displacement signals is typically at microvolt or microampere levels, necessitating a backend operational amplifier device for signal amplification[25], [26]. The utilization of other types of MESM sensors, such as piezoresistive-based MEMS electric field sensors, necessitates the incorporation of supplementary drive modules and consequently requires corre-sponding drive power[27], [28]. Hence, the power supply of these drive modules and op-amp devices may introduce ground wire inter-ference. To mitigate this issue, it is recommended to utilize a floating potential power source such as a battery or an isolation transformer to obtain a stable non -grounded power supply.
The signal acquisition module is another significant source of ground interference, and it is arguably the most critical one. Oscilloscopes are commonly utilized as acquisition instruments for voltage and current signals. However, grounding the acquisition resistance of the oscilloscope may introduce ground wire interfer-ence into the electric field measurement circuit, leading to a sig-nificant discrepancy between the measured electric field signal and its actual value.
The schematic diagram of the signal acquisition circuit of the electric field sensor is shown in Figure 3, while Figure 3(a) displays an ideal circuit diagram when measuring space electric fields in a non-contact manner. When the output signal of the sensor passes through the signal acquisition system, the circuit can be equivalent to that shown in Figure 3(b). The signal acquisition device can be conceptualized as a parallel circuit model comprising resistors and capacitors. Assuming a uniform electric field, the HV voltage is
However, the connection of the signal acquisition device to the measurement circuit results in
To further investigate the impact of ground wire interference on the output accuracy of electric field sensors, a standardized electric field-testing platform was established in this study, and an in -depth analysis was conducted on the effects of ground wire interference on various types of electric field sensors. Moreover, the sensor signal acquisition system is optimized to ensure accurate measurement results without distortion, and a comparative analysis of the performance of different sensors is conducted.
Experimental Equipment and Test System Without Coupled Ground Wires Interference
2.1 Electric Field Sensors
The MEMS and D-dot electric field sensors used in the research were examined for the influence of ground wire coupling on mea-surement accuracy, and a solution was proposed to achieve undistorted measurements of electric fields. An electric field sensor with a data wireless transmission system was used. To compare the distortion-free electric field measurement effect, an optical sensor was selected for comparison. The physical map of the electric field sensors is depicted in Figure 4, wherein the optical sensor measures
The optical sensor, as shown in Figure 4(a), utilizes the Pockels effect to introduce linearly polarized light, generated by the laser source, into the sensor via a polarization-maintaining fiber. Under the influence of the electric field, it is conveyed through a single-mode fiber to an optical detector where it is transformed into an electrical signal that reflects the magnitude of the electric field being measured[29]. The transfer function of the measurement sys-tem can be expressed as
\begin{equation*} U_{\text{out}}=A\{1+b\cos[\varphi_{0}+\varphi(E)]\}\tag{1}\end{equation*}
The MEMS sensor, as shown in Figure 4(b), is based on the single-layer sidewall sensing principle of Schwarz-Christopher mapping[30], The single-layer sidewall edge sensing structure undergoes periodic motion due to the shielding electrode, resulting in a periodic exchange of charge between the sensing electrode and sensor substrate. By detecting this periodically exchanged charge, the electric field to be measured is detected:
\begin{equation*} I=2\omega\varepsilon_{0}n_{\mathrm{s}}EA_{\mathrm{s}}\tag{2}\end{equation*}
The D-dot sensor, as shown in Figure 4(c), is obtained by using a differential parallel capacitor plate. When the electric field \begin{equation*} I=\displaystyle \frac{\text{dQ}}{\mathrm{d}t}=\omega\varepsilon_{0}E_{0}\cos\omega t\tag{3}\end{equation*}
The wireless sensor, as illustrated in Figure 4(d), employs the principle of electrostatic induction for electric field sensing and is applied with a differential structure to mitigate common mode interference. To eliminate interference from ground wires, the previous coaxial cable method has been replaced with wireless data transmission mode.
2.2 Electric Field Sensor Calibration Test Platform Without Coupled Ground Wires Interference
The calibration of the electric field sensor has a significant impact on the accuracy of electric field measurements. However, the con-ventional electric field calibration platform conducts calibration at a fixed position on the planar electrode, disregarding the impact of vertical displacement of the electric field sensor. Therefore, it is crucial to establish a calibration platform that meets the require-ments of electric field testing to ensure precise analysis of ground wire intrusion to the electric field sensor. The electric field calibration test platform is shown in Figure 5.
Applying a voltage \begin{equation*} E_{0}=\displaystyle \frac{U}{D}\tag{4}\end{equation*}
Due to the limited size of the plate electrode, edge effects are inevitable, resulting in a relative deviation \begin{equation*} \delta=\frac{E_{\text{mid}}-E_{0}}{E_{0}}\times 100\%\tag{5}\end{equation*}
The relative deviation
The electric field sensor is positioned within the gap between the parallel plate electrodes. Due to the presence of the sensor vol-ume, there is a disturbance in the distribution of electric fields, leading to distortion. The impact of this sensor volume (V) on electric field intensity can be expressed by Eq. (6):
\begin{equation*} \delta=\frac{V}{D^{3}}\times 100\%\tag{6}\end{equation*}
Since the miniature sensor is small in size and the size does not exceed
Since the sensor is placed in a uniform electric field, the electric force lines will be distorted, resulting in a certain deviation from the true value of the electric field. When moving the sensor along the center line of the plate gap, the electric field distortion near the upper and lower plates is most severe, and the electric field distortion is minimal at the midpoint of the gap. Therefore, we analyzed the distortion of the electric field when the sensor moved an offset distance from the midpoint of the gap. A model was built in COMSOL Multiphysics for simulation analysis, and the simulation results are shown in Figure 8. It can be observed that when the sensor deviates from the center of the gap, symmetrical distortion arises in the electric field with a greater degree of distortion occur-ring at a larger offset distance. The relative error remains below 0.1% when the electric field deviates by up to 2 cm from its central position, it can be regarded as a constant electric field. Thus, the electric field sensor can be calibrated within this range of positions.
In summary, to conduct a thorough and precise analysis of the measurement error of an electric field sensor, it is necessary to operate under harsh experimental conditions and perform accuracy testing and error analysis only after meeting the aforementioned requirements.
Influence of Ground Coupling Signal on Measurement Accuracy of Electric Field Sensor
3.1 Uniform Electric Field Under Parallel Plate Electrodes
The first step involved conducting calibration
The optical field sensor's signal was converted from optical fiber to electrical signal by the photoelectric detector and ultimately gathered by an oscilloscope. The signals from both D-dot and MEMS sensors were acquired through coaxial cables and analyzed using oscilloscopes, while the wireless sensor transmitted its signals via Bluetooth.
The measurements of the four electric field sensors are compared and analyzed in Figure 9. It is apparent that there exists a significant dispersion in the electric field measurement obtained by both the D-dot electric field sensor and the MEMS sensor. When the test point (
The electric field measurement errors of the four electric field sensors located at different positions were further analyzed, and the results are depicted in Figure 10. Figure 10(a) illustrates that the D-dot electric field sensor exhibits an error of approximately 6.8% in electric field measurement when the midpoint is offset 1 cm in a uniform electric field with a gap of 30 cm. The electric field measurement error increases to about 14.2% when the offset is increased to 2 cm. As the offset distance increases, a larger mea-surement error will appear, which significantly impacts the accuracy of electric field measurements obtained using this sensor. MEMS electric field sensors, as shown in Figure 10(b), also exhibit a similar pattern. When the gap center is shifted by 1 cm, the electric field measurement error is about 6.4%, and when the gap center is shifted upward by 2 cm, the electric field measurement error is 13.2%. When the center of the gap is shifted downward by 2cm, the electric field measurement error is 11.4%, which shows that the measurement error increases at larger offset distances. This indicates that the presence of a ground wire signal in the mea-surement unit causes interference when the sensor position is changed, leading to significant measurement inaccuracies. The optical sensor, as shown in 0(c), exhibits negligible electric field measurement error, the measurement error is within 3% and does not increase with offset distance. This indicates that the optical electric field sensor's measurement error is not caused by ground wire interference. The error in the measurement of the optical sensor may be attributed to laser fluctuations or an excessively large half-wave electric field value of the electro-optic crystal. For the wireless sensor, Figure 10(d) demonstrates that the majority of electric field measurement errors are within a 2% range and remain consistent regardless of sensor offset distance. This effectively achieves ground wire interference isolation and results in high -accuracy electric field measurements.
Through the aforementioned analysis, it is evident that the intrusion of the ground wire in MEMS and D-dot sensors leads to a reduction in measurement accuracy. Furthermore, measurements obtained at different positions exhibit varying results; however, they maintain excellent linearity. The results indicate that the cali-bration coefficient of the electric field is affected by ground wire interference, and the error increases significantly with the distance from the center of the uniform electric field. Even if the sensor has high linearity in calibration, a large error may occur in the actual electric field measurement due to off-center calibration, rendering the calibration result incapable of reflecting the true electric field value. Moreover, when measuring complex non-uniform electric fields with calibrated sensors, larger measurement errors may arise. Therefore, by optimizing the signal acquisition system, this paper achieved distortion-free measurement of electric fields.
3.2 Non-Uniform Electric Field Under Transmission Line
The interference law of ground for the four sensors under a uniform electric field was analyzed in the front. To further investigate the impact of ground interference on the measurement accuracy of four electric field sensors under complex conditions, this paper employed non-uniform electric field measurements of transmission line conductors to analyze the measurement performance of these sensors in an inhomogeneous electric field environment.
In this paper, a transmission line experimental test platform was constructed, as depicted in Figure 11. The conductors consist of aluminum rods with a radius of 3 cm, which are supported by insulating rods to a height
Firstly, an analysis of the electric field distribution beneath the transmission line was conducted. By applying the Gaussian theorem and mirror image method, it can be inferred that the electric field distribution underneath the transmission line conforms to,
\begin{equation*} E(r)=\displaystyle \frac{U}{r\ln\frac{2H-a}{a}}\cdot\frac{2H}{2H-a}\tag{7}\end{equation*}
Based on the previous analysis, the four sensors have been calibrated on a calibration platform and subjected to an electric field distribution test under transmission lines. The results are presented in Figure 12. Figure 12(a) demonstrates that the electric field mea-surement results of the wireless field sensor are in complete agree-ment with the theoretical simulation electric field measurement results, indicating excellent measurement accuracy of the sensor. Simultaneously, the measurement outcomes of the optical electric field sensor are in agreement with the values obtained from theo-retical simulations. The optical sensor can isolate the interference of ground wire signals and achieve distortion-free measurement of electric fields. Although the wireless sensor optimized in this paper is not composed of all-dielectric materials, it still achieves distortion-free electric field measurements. However, D-dot and MEMS electric field sensors exhibit significant measurement errors. Specifically, the measured value of the D-dot electric field sensor is lower than the theoretical simulation value, while that of the MEMS electric field sensor is higher.
2(b) depicts a diagram for analyzing measurement errors between the measured values of four sensors and their cor-responding theoretical simulation values. It can be observed that the discrepancy between the measured wireless sensor electric field value and theoretical simulation electric field is within 5%, while the optical electric field measurement error is approximately 8%. Possible causes of measurement errors may include the rapid decay of the electric field near the transmission line, which has decreased to less than 1 kV/m at a distance of 40 cm from the center of the wire. This can result in low sensor output and potential inaccuracies in measurements within this range. For the D-dot sensor, the electric field measurement error caused by ground wire coupling interference under transmission lines exceeds 50%, while for MEMS sensors, it can be as high as 150%. This indicates that ground interference in anon-uniform electric field can result in significant inaccuracies of the sensor, thereby compromising the ability of an electric field sensor to provide accurate measurements and adversely impacting its overall utility. However, the use of wireless sensors is an effective solution.
Conclusions
This paper examined the impact of ground wire coupling interference on electric field sensor measurement accuracy, identified sources of such interference, and analyzed its effects on electric field measurement precision. A miniature electric field sensor of wireless transmission was compared with existing D-dot, MEMS, and optical sensors in terms of performance. The four sensors' performances were analyzed under both uniform electric fields generated by parallel plates and non-uniform electric fields of transmission lines.
In a uniform electric field, the accuracy of electric field measurement by MEMS and D-dot is reduced due to ground wire intrusion, with maximum errors reaching 13.4% and 14.2%, respectively, when the offset center distance is 2 cm. The optical sensor exhibits a measurement error within 5%, whereas the wire-less sensor's error is less than 3%. This indicates that ground wire coupling significantly impacts electric field measurement accuracy, and both the optical and wireless sensors can effectively isolate such interference.
Fig. 12Electric field distribution test of transmission line. (a) electric field distribution and (b) measurement errors In the case of transmission lines, the discrepancy between wireless sensor electric field measurements and theoretical simulation electric field is within 5%, while optical electric field measurement error is approximately 10%. For the D-dot sensor, the measurement error of the electric field under the transmission line exceeds 50%, while that of the MEMS sensor is as high as 150%, indicating that the ground coupling interference signal seriously undermines the measurement accuracy of sensors.
This paper provides a thorough analysis of the impact of ground coupling interference on electric field sensor measurements and demonstrates that our wireless sensor enables accurate measurement without distortion. The measurement accuracy of the wireless sensor surpasses that of optical sensors, and it boasts a small size, low cost, high precision, and distortion-free measurement. It holds great potential in applications such as intelligent equipment status perception and fault warning in new power systems.
Declaration of Competing Interest
The authors have no competing interests to declare that are relevant to the content of this article.
ACKNOWLEDGEMENTS
This work was supported in part by the National Key Research and Development Program of China under Grant 2022YFB3206800 and in part by the National Natural Science Foundation of China under Grant 52125703.