Research on Non-Contact Low-Voltage Transmission Line Voltage Measurement Method Based on Switched Capacitor Calibration

Abstract

Capacitive-coupling non-contact voltage sensors face a key challenge: their probe-conductor coupling capacitance varies, making it hard to accurately determine the division ratio. This capacitance is influenced by factors like the conductor’s insulation material, radius, and relative position. To address this challenge, this paper proposes a sensor gain self-calibration method based on switching capacitors. This method obtains multiple sets of real-time measurement outputs by connecting and switching different standard capacitors in parallel with the sensor’s structural capacitance, and then simultaneously solves for the coupling capacitance and the voltage under test, thereby achieving on-site autonomous calibration of the sensor gain. To effectively suppress interference from stray electric fields in the surrounding space, a shielded coaxial probe structure and corresponding back-end processing circuitry were designed, significantly enhancing the system’s anti-interference capability. Finally, an experimental platform incorporating insulated conductors of various diameters was built to validate the method’s effectiveness. Within the 100–300 V power-frequency range, the reconstructed voltage amplitude shows a maximum relative error of 1.06% and a maximum phase error of 0.76°, and harmonics are measurable up to the 50th order. Under inter-phase electric field interference, the maximum relative error of the reconstructed voltage amplitude is 1.34%, demonstrating significant shielding effectiveness. For conductors with diameters ranging from 6 mm² to 35 mm², the measurement error is controlled within 1.57%. These results confirm the method’s strong environmental adaptability and broad applicability across different conductor diameters.

1. Introduction

Currently, electromagnetic and capacitive voltage transformers are widely used in line voltage detection. However, these devices have an inherent limitation of ferromagnetic resonance, so they are generally only suitable for measuring power frequency voltage signals. In addition, voltage transformers are difficult to achieve wide deployment in distribution networks due to their relatively large size and the requirement for contact-based installation [1]. Nowadays, with the development of smart grid technology, the traditional contact measurement is gradually difficult to meet the requirements of intelligence, miniaturization, and convenience of power equipment [2,3,4,5]. Non-contact voltage sensors can measure voltage without compromising the insulation layer of the wire, ensuring no impact on the safe and stable operation of the power grid. This feature aligns seamlessly with the requirements of distributed sensing networks in smart grids [6].

At present, the non-contact current measurement technology based on the principle of magnetic field induction is relatively mature and has been commercialized. The integrated sensor chips launched by Texas Instruments (TI), Analog Devices Inc (ADI), and other companies enable High-precision current non-contact measurement can be realized directly [7,8]. The non-contact voltage measurement technology based on capacitive coupling is still in the development stage. In the practical application of engineering, the more advanced Fluke T6-1000 technology electrical tester has a measurement accuracy of only ±3% under the environment of 18–28 °C [9]. The reason for affecting the measurement accuracy is that the coupling voltage is easily affected by the diameter of the measuring wire, the distance between the wire and the sensor, and the thickness of the insulating layer, which leads to the inaccurate reconstruction of the voltage of the wire to be measured. At the same time, the interference in the environment will also have a great impact on the measurement results.

In order to solve the above problems, domestic and foreign scholars have conducted a lot of research. In [10], a non-contact voltage sensor integrating two capacitive plates is proposed. By placing the two induction plates in a four-layer printed circuit board, the differential capacitance between the two plates is estimated by calculation under the condition of knowing the thickness and material of the conductor insulation layer, and then the wire voltage to be measured is solved by the transfer function. However, the transfer function of the sensor needs to be recalculated when the type of wire changes, so the applicability of the sensor is poor in different scenarios. In [11], based on the principle of electric field coupling, a new type of cylindrical voltage sensor is proposed by Ansoft Maxwell. Through the electric field simulation of different shapes of electrodes, it is concluded that the circular plate electrode has the lowest requirements for installation position. At the same time, this paper simulated the internal and external diameter, length, material properties and other parameters of the cylindrical plate electrode to explore their influence on the induced electric field, but did not propose a solution to the change in coupling capacitance in sensor measurement. A non-contact voltage measurement method based on electrical field radiation is proposed in [12], and the corresponding voltage reconstruction algorithm is proposed based on theoretical analysis, which can ignore the influence of the eccentricity of the wire. The AC voltage error is within 1.63%, and the DC voltage error is within 1.54% in the three-point detection, but the solution process is complex. However, the solution process is complex, and different algorithms need to be rebuilt for different wires to be measured.

Reference [13] eliminated the influence of the input capacitance of the Transimpedance amplifier and the equivalent capacitance of the probe on the ground using harmonic injection. References [14,15] by injecting a reference signal to eliminate the influence of unknown capacitance between the probe and the wire, greatly improve the accuracy of the measurement. However, due to the lack of a shielding layer, this method is easy to be interfered with by the surrounding coupling electric field, whether in the overhead transmission line or in the complex low-voltage distribution network line. Reference [16] addresses the issue that in non-contact voltage measurements using single-capacitor probes, the sensor’s transfer function is easily affected by the measurement environment and the distance between the sensor’s sensing electrode and the target conductor. To mitigate or eliminate these influences, a method involving the addition of a second sensing probe is proposed. However, this approach requires the mutual capacitance between the two probes to exceed the coupling capacitance, which is challenging to achieve in practical measurements.

Reference [17] proposed a self-calibration method based on impedance transformation to address the issue of sensor gain variation caused by unknown coupling capacitance. This method obtains two sets of voltage outputs by switching in parallel different capacitors and resistors, and eliminates the unknown coupling capacitance through simultaneous equations of the transfer functions. However, the structural capacitance is measured by instruments, and the backend circuit is exposed to electromagnetic fields, inevitably introducing measurement errors. References [18,19] presented a voltage monitoring method combining capacitive coupling measurement with magnetic field sensing. A magnetic sensor array is used to determine the spatial position of the transmission line, thereby constructing a coupling capacitance matrix related to the sensing probe, and the voltage measurement matrix coefficients are determined based on the relative spatial positions obtained from the magnetic sensors. Nevertheless, the coupling capacitance in this method is susceptible to environmental variations, requiring frequent recalibration; moreover, the decoupling coefficient matrix is complex, which may lead to error amplification and processing delays.

Variations in conductor diameter, insulation thickness, and the distance between the sensor probe and the measured conductor can alter the primary coupling capacitance. This leads to changes in voltage division ratios and inaccurate measurements. Additionally, surrounding stray electric fields can interfere with measurement accuracy. To address these issues, this paper proposes a self-calibration method based on switched capacitance. Firstly, the fundamental principles of capacitive coupling voltage measurement are analyzed, along with the key factors influencing the primary coupling capacitance. A calibration method based on switched capacitance is then proposed, and its feasibility is analyzed. Subsequently, the sensor probe and the backend conditioning circuit are designed. Finally, an experimental platform is established to validate the proposed method.

2. Sensor Principle and Calibration Method

2.1. Fundamental Principles of Capacitive Coupling Measurement

In Figure 1, C_p represents the coupling capacitance between the wire under test and the sensing electrode plate, C_s denotes the structural capacitance formed between the two metal plates of the sensor, V_i is the input voltage of the wire under test, R_m is the sampling resistor, and V_o is the output voltage. Under these conditions, the transfer function of the sensing system can be expressed as:

$${\displaystyle \frac{V_o(s)}{V_{\mathrm{i}}(s)}}={\displaystyle \frac{s{R}_m{C}_p}{1+s{R}_m(C_p+C_s)}}.$$

(1)

When the sensor operates in self-integration mode, where $s{R}_m(C_p+C_s)>>1$, the transfer function in (1) can be simplified as:

$${\displaystyle \frac{V_o(s)}{V_{\mathrm{i}}(s)}}={\displaystyle \frac{C_p}{C_p+C_{\mathrm{s}}}}.$$

(2)

The Equation (2) indicates that when the sensor operates in self-integration mode, its gain depends solely on C_p and C_s. The structural capacitance C_s within the sensor probe is fixed, whereas C_p is influenced by the diameter of the wire under test, its insulation material, and the distance between the probe and the wire.

A simulation analysis of the variation in coupling capacitance for several common low-voltage distribution conductors specified in the national standard, as well as for different distances between the conductors and the sensing probe, was conducted using COMSOL 6.0. The effective area of the sensing electrode plate is 225 mm², and the distance between the probe and the conductor ranges from 0.5 mm to 4 mm with a step size of 0.1 mm. The simulation results of the coupling capacitance for multiple conductors are shown in Figure 2.

The simulation results indicate that when the distance between the probe and the conductor (h_p) is 0.5 mm, the coupling capacitance values between conductors of 6 mm² and 35 mm² differ by 18.9%, while the difference between 35 mm² and 25 mm² conductors is 3.66%. If the distance varies, the relative error increases further. Under the same conductor size of 35 mm², changing h_p from 0.5 mm to 0.6 mm results in a 6.1% difference in the line-to-probe coupling capacitance, and increasing hp from 0.5 mm to 1 mm causes the difference to rise to 26.9%. In these simulations, the sensing electrode plate is positioned directly beneath the tested conductor; actual measurements with positional deviations will lead to even greater capacitance errors. Overall, C_p is highly sensitive to both the conductor diameter and the relative distance between the probe and the conductor. To address the issue of uncertain coupling capacitance leading to difficulty in determining sensor gain, this paper proposes a voltage measurement method based on switched capacitor calibration.

2.2. Principle of Calibration

The fundamental principle of the calibration method is illustrated in Figure 3. Capacitors C_b1, C_b2, and C_b3 are connected in parallel across C_s, along with switches S₁, S₂, and S₃. V_in represents the input voltage of the conductor under test.

Assuming that C_b1, C_b2, and C_b3 in Figure 3 are all equal to C_b, when control switch S₁ is closed while S₂ and S₃ are open, capacitor C_b1 is individually connected to the measurement circuit. The resulting first output voltage V_o1 is:

$$V_{o1}(s)={\displaystyle \frac{s{C}_p{R}_m{V}_{in}(s)}{1+s(C_s+C_p+C_b)R_m}}.$$

(3)

When the sensor operates in self-integration mode, the transfer function shown in (3) can be simplified as:

$$V_{o1}=V_{in}{\displaystyle \frac{C_p}{C_s+C_p+C_b}}.$$

(4)

Subsequently, when switches S₁ and S₂ are closed while S₃ is open, and when all switches are closed, the sensor output voltages are, respectively:

$$V_{o2}=V_{in}{\displaystyle \frac{C_p}{C_p+C_s+2C_b}}$$

(5)

$$V_{o3}=V_{in}{\displaystyle \frac{C_p}{C_p+C_s+3C_b}}$$

(6)

By rearranging (4), (5), and (6), we obtain:

$$\left\{\begin{array}{l}{V}_{o1}{C}_p-V_{in}{C}_p+V_{o1}{C}_s+C_b=0\\ V_{o2}{C}_p-V_{in}{C}_p+V_{o2}{C}_s+2C_b=0\\ V_{o3}{C}_p-V_{in}{C}_p+V_{o3}{C}_s+3C_b=0\end{array}\right.$$

(7)

In (7), the measured values V_o1, V_o2, V_o3, and the externally connected capacitance C_b are known, while the three unknowns are C_p, C_s, and V_in. Since the system of equations is nonlinear, these unknowns cannot be solved analytically directly. However, under experimental conditions, Vin is a known parameter with a specific measurable value. Based on this, we can uniquely determine C_p and C_s by combining root-finding algorithms with a Mean Squared Error (MSE) objective function. Specifically, C_s is first calibrated under experimental conditions. Subsequently, during actual voltage measurement and calibration, with C_s fixed and known, the same method is used to solve for V_in in real time.

2.3. Feasibility Analysis of the Calibration Method

To verify the accuracy of the decoupling method, we constructed a pure capacitive circuit model using the Multisim v14.0, as illustrated in Figure 4.

In the simulation, C_p is set to 6.7 pF, C_s to 20.5 pF, and the backend capacitors are all set as C_b1 = C_b2 = C_b3 = 1 nF. First, switch S₁ is closed while switches S₂ and S₃ remain open, yielding the output voltage V_o1. Next, switches S₁ and S₂ are closed with S₃ still open to obtain output voltage V_o2. Finally, all three switches S₁, S₂, and S₃ are closed to acquire the output voltage V_o3. The input voltage is varied from 100 V to 300 V. The resulting output voltages, along with C_p and C_s, are recorded in

Table 1. Simulation verifies the coupling capacitance and structural capacitance obtained by decoupling.

Vin (V)	Vo1 (mV)	Vo2 (mV)	Vo3 (mV)	Cp (pF)	Cs (pF)
100	652	330	221	6.69	20.68
120	783	397	266	6.71	20.18
140	913	463	310	6.71	20.64
160	1040	529	354	6.71	20.77
180	1170	595	398	6.71	20.21
200	1300	661	443	6.72	20.15
220	1430	727	487	6.72	20.84
240	1570	793	531	6.68	20.10
260	1700	859	575	6.68	20.35
280	1830	925	620	6.69	20.49
300	1960	991	664	6.69	20.55

.

As shown in the data of Table 1, the arithmetic mean values of C_p and C_s are 6.70 pF and 20.45 pF, respectively. These results indicate that the employed algorithm achieves high decoupling accuracy and that the calculated capacitance values are independent of the applied line voltage. As previously analyzed, C_p is highly sensitive to changes in the measured conductor’s diameter and the relative position between the conductor and the probe, whereas C_s remains essentially unaffected.

3. Sensor Circuit and Structural Design

3.1. Design of the Probe Structure

The sensor probe adopts a coaxial design, which effectively shields against interference from surrounding stray electric fields. The sensing probe consists of a sensing electrode, a grounding electrode, and an insulating dielectric. To further minimize the impact of electromagnetic interference on the backend processing circuitry, an integrated sensor probe with a shielding enclosure has been designed. Its structure is illustrated in Figure 5, where the yellow areas represent sections covered with copper foil.

An electric field of 10 kV/m was applied in the surrounding space to evaluate the electromagnetic shielding effectiveness of the enclosure. Figure 6 shows a snapshot of the electric field distribution at the center of the probe. It can be observed that, under electrostatic equilibrium, the electric field intensity inside the enclosure cavity is effectively reduced to zero.

The probe’s length and radius also affect its shielding performance. To determine the optimal probe parameters, a parametric simulation was conducted to study the impact of varying the ratios l₁/l₂ and r₁/r₂ on the shielding effectiveness. Two comparative models were established: one with an interference source and one without. The induced voltage deviation under different structural parameters was quantitatively evaluated, and the resulting percentage deviations are plotted in Figure 7.

As shown in Figure 7, the shielding effectiveness of the coaxial probe is positively correlated with the ratio l₁/l₂. When l₁ is fixed, the shielding performance improves gradually as l₂ decreases; however, once the ratio l₁/l₂ exceeds 1.5, further enhancements in shielding capability become negligible. Additionally, the shielding ability is also positively correlated with the ratio r₁/r₂. The poorest shielding performance occurs when r₁/r₂ approaches 1. With r₁ held constant, reducing r₂ enhances the coaxial probe’s shielding, though this effect is less pronounced compared to changes in length l.

Moreover, a larger sensing electrode can capture electric field signals over a wider area, thereby improving the sensor’s measurement accuracy. To simultaneously achieve a larger coupling capacitance and smaller structural capacitance within the allowable radius for the conductor under test, we investigated how coupling capacitance and structural capacitance vary with changes in the sensor radius r and length l. The probe length l₁ was fixed at 8 cm, and l₂ was increased from 2 cm to 8 cm in increments of 0.4 cm. The probe radius r₁ was fixed at 2.5 cm, and r₂ was increased from 0.8 cm to 2.3 cm in 0.1 cm increments. The resulting data were plotted as curves in Figure 8 and Figure 9.

As shown in Figure 8a, with the increase in the inner radius, C_s gradually increases while C_p decreases, intersecting at r₂ = 1.4 cm. Figure 8b illustrates that as the inner radius grows, the ratio $C_p/(C_p+C_s)$ decreases nonlinearly. This is because the rate of change in C_s is greater than that of C_p. From Figure 9a, it can be observed that both the structural capacitance and coupling capacitance increase progressively with the probe length, with C_s rising more rapidly after 6 cm.

Taking into account both the need for a larger sensing area to capture more electric field signals and the requirement to accommodate test conductors of varying radii around a larger circumference, the coaxial sensor probe parameters selected in this study are presented in

Table 2. Probe-circuit integrated probe parameter design.

Parameter	Value (cm)	Parameter	Value (cm)
l1	8	l2	6
r1	2.5	r2	1.2
a	8	b	5
c	6	/	/

. The length and width of the shielding enclosure are determined based on the probe’s length and diameter, while the enclosure’s height is designed to accommodate the size of the circuit board.

3.2. Circuit Design

The designed sensor is primarily intended for measuring 220 V power frequency line voltages. Therefore, the prerequisite for achieving the aforementioned calibration is that the sensor, both before and after incorporating the capacitor, maintains the self-integration operating mode at the 50 Hz working frequency, meaning the output voltage amplitude is linearly independent of the signal frequency. To this end, the sensor’s three critical corner frequencies ω_h1, ω_h2, and ω_h2 must remain much lower than 100π before and after each switching action. Given that ω_h1 > ω_h2 > ω_h3, it is sufficient for the sensor to satisfy the condition (8) to ensure it consistently operates in self-integration mode during actual measurements.

$${\displaystyle \frac{1}{R_m\left(C_p+C_s+C_b\right)}}<<2\pi \times 50$$

(8)

According to the Equation (8) and the previous analysis of the sensor’s coupling capacitor and structural capacitance, the effects of the sampling resistor and capacitor on the sensor’s cutoff frequency are illustrated in Figure 10. The figure shows that only when both R_m and C_b take relatively large values can the sensor maintain self-integration operation at the 50 Hz frequency.

The topology of the designed circuit in this paper is shown in Figure 11. To prevent interference from the oscilloscope’s input impedance affecting the incorporated capacitor during measurements, a voltage follower is connected at the output of the voltage conversion stage. The operational amplifier used is the OPA192, which is powered by a TPS65133 dual power converter that converts the 3.7 V from a lithium battery into ±5 V. The relay is controlled by a microcontroller in conjunction with a transistor. The switching component is a TQ2SA-L2 relay, with an open-state impedance greater than 1 GΩ and a closed-state impedance less than 75 mΩ. The sensor probe is connected to the signal conditioning circuit via a coaxial cable, and the signal conditioning circuit is also connected to the oscilloscope through a coaxial cable.

Table 3. Measure the capacitance and resistance of the system.

Parameter	Value	Parameter	Value
Cb1	0.94 (nF)	Cb2	1.05 (nF)
Cb3	0.97 (nF)	Rm	10 MΩ

lists the parameters of the circuit components. To reduce calibration errors and improve measurement accuracy, the component parameters were all obtained using the TH2840B precision LCR meter.

4. Experimental Testing and Result Analysis

4.1. Experimental Platform Setup

Under experimental conditions, the test platform shown in Figure 12 was established. The input voltage of the wire under test was provided by an ANB13-1KA (Wuxi Anes New Energy Equipment Co., Ltd., Wuxi, China) AC voltage source. The output signal from the sensor’s backend circuit was acquired using a SIGLENT SDS2502X (SIGLENT, Shenzhen, China) oscilloscope connected through a Tektronix P6051A (Tektronix Inc., Beaverton, OR, USA) high-voltage probe. Simultaneously, a Tektronix P5202A (Tektronix Inc., USA) probe was used for comparative measurements of the amplitude and phase of the AC output voltage. During the experiment, the wire under test passed through the inductive probe, whose sensing electrode and ground electrode were connected to the positive and negative input terminals of the signal processing circuit, respectively.

4.2. Capacitor Calibration

After completing the assembly of the experimental platform shown in Figure 12, testing commenced. Initially, under experimental conditions, the sensor’s structural capacitance was calibrated by controlling the three-phase voltage source to output only the B-phase voltage. The specific procedure involved closing switch S₁ via a relay and measuring the RMS value of the output voltage displayed on the oscilloscope after processing by the backend circuit, recorded as V_o1. Then, with switch S₁ kept closed, switch S₂ was also closed to record the output voltage V_o2. Finally, switches S₁, S₂, and S₃ were all closed to record the output voltage V_o3. The AC power supply output voltage was set in the range of 100 to 300 V with 20 V increments, and the above measurement steps were repeated accordingly. Using the decoupling method described earlier, the structural capacitance Cs of the sensor was calculated from the measured output voltages V_o1, V_o2, and V_o3, with the results shown in Figure 13. The results indicate that the average structural capacitance of the sensor designed in this study is 22.76 pF, which will be used as a known parameter in the subsequent voltage reconstruction experiments.

4.3. Amplitude Accuracy Test

After completing the calibration of C_s, testing was conducted following the same measurement procedures, maintaining the output voltage range but reducing the step size to 10 V. Based on the solution method described above, the input voltage V_in was reconstructed, and the reconstructed voltage V_r was obtained. Figure 14 presents the fitting curve between the actual output voltage measured by the Tektronix P5202A high-voltage probe and V_r, along with the corresponding relative error, which is calculated according to (9). It can be observed from the figure that within the voltage test range of 100 to 300 V, the maximum relative error of V_r is 1.06%, and the linear fitting degree is close to 1, demonstrating high reconstruction accuracy.

$$\epsilon ={\displaystyle \frac{V_{in}-V_r}{V_{in}}}\times 100\%$$

(9)

4.4. Phase Accuracy Test and Bandwidth Measurement

At an output voltage of 200 V from the voltage source, the reconstructed voltage waveform was compared with the output waveform measured by the Tektronix P5202A probe, as shown in Figure 15. The red curve represents the reconstructed voltage waveform, while the black dashed curve indicates the real-time output waveform of the voltage source. The relative phase error between them is 0.76°, demonstrating that the sensor prototype exhibits minimal phase shift at 50 Hz AC measurement and possesses excellent dynamic response characteristics.

Figure 16 shows the amplitude-frequency response curve of the designed sensor. As can be seen from the curve, the bandwidth of the sensor reaches 3 kHz. This bandwidth supports the accurate measurement of the 50th harmonic, which means the sensor can capture high-order harmonic components in voltage signals. This characteristic fully meets the bandwidth requirements for voltage harmonic measurement specified in the IEC 61000-4-30 standard [20].

4.5. Anti-Interference and Shielding Performance Test

The anti-interference capability of the sensor probe was tested. Following the procedure of the previous capacitance calibration experiment, voltages of the same magnitude as those on the B-phase test conductor were applied to the A-phase and C-phase test conductors to simulate inter-phase interference in a three-phase transmission line scenario. As shown in Figure 17, the reconstructed voltage error data under conditions with and without interference sources are plotted as line graphs. The results indicate that the relative error of the reconstructed voltage is 1.34% in the presence of interference sources, which is 0.28% higher than that without interference sources. This demonstrates that the coaxial probe effectively shields against inter-phase interference and surrounding electric field coupling interference, and also confirms the feasibility of using the electric-field coupled voltage sensor for measurements in complex real-world environments.

To verify the shielding effectiveness of the sensor probe’s shielding enclosure against surrounding stray electric fields, experiments were conducted based on the previous amplitude accuracy tests by placing the backend circuitry module both inside and outside the shielding box. The error characteristic curves are shown in Figure 18. As shown in the figure, compared to the scenario where the back-end measurement circuit is placed inside a shielding enclosure, the relative error of the reconstructed voltage reaches as high as 1.31% when the back-end measurement circuit is not shielded. This indicates that the shielding box can effectively reduce interference from external power-frequency electric fields to a certain extent, thereby improving the accuracy of voltage measurements.

4.6. Wire Diameter Adaptability Test

To validate the universality of the proposed self-calibration method across transmission lines of various specifications, five representative PVC-insulated cables were selected for testing by the International Standard [21]. The cross-sectional areas of these cables are 6 mm², 10 mm², 16 mm², 25 mm², and 35 mm², respectively. During the experiments, the AC voltage source provided output voltages of 100 V, 200 V, and 300 V. Voltage measurements were conducted sequentially on these different cables. To simulate the randomness of practical measurements, no special fixation was applied to the cables; instead, they were directly placed inside the sensor probe. The reconstructed voltages and their relative errors are presented in Figure 19.

As shown in Figure 19, the maximum errors between the actual output voltages and reconstructed voltages for cables with cross-sectional areas of 6 mm², 10 mm², 16 mm², 25 mm², and 35 mm² were 0.88%, -0.71%, -1.12%, 0.6%, and -1.57%, respectively. Under varying measurement conditions, the absolute value of errors remained within 2%. These results demonstrate that the proposed method maintains high accuracy in voltage reconstruction across different wire diameters, confirming its strong adaptability to various scenarios.

5. Conclusions

This paper addresses the challenge in non-contact voltage measurement where variations in coupling capacitance lead to difficulty in accurately determining the sensor’s division ratio. A self-calibration voltage measurement method based on switched capacitance is proposed. By introducing a decoupling algorithm, the method achieves automatic calibration of sensor gain across various measurement scenarios, effectively eliminating measurement errors caused by fluctuations in coupling capacitance. The designed coaxial sensor probe is equipped with a shielding box that significantly suppresses interference from stray external electric fields on the backend circuitry, thereby enhancing measurement stability and accuracy.

Experimental results show that within the power frequency voltage range of 100 V to 300 V, the maximum amplitude reconstruction error of this method is 1.06%, the phase error is only 0.76°, and it supports the measurement of the 50th harmonic, which fully verifies its effectiveness. Under conditions with and without interference sources, the measurement error shift is only 0.28%, confirming the shielding box’s outstanding capability in reducing environmental interference. Scenario adaptation tests conducted with wires of different cross-sectional areas show that the maximum error remains controlled within 1.57%, meeting measurement requirements for various wire gauges and verifying the method’s good adaptability to different wire diameters.

At present, the proposed method has been experimentally validated only for low-voltage distribution systems. Future work will extend the method to high-voltage measurement fields, focusing on optimizing probe designs to meet stringent insulation requirements. Additionally, further improvements to the sensor self-calibration algorithm are planned to realize truly fully non-contact voltage measurement under diverse field environments.