1. Introduction
As the construction scale of modern smart grids continues to expand, a large number of distributed energy sources and power electronics will be introduced into the transmission network, making complex changes in the transmission line environment and greatly increasing the frequency of voltage fluctuations in the distribution network, and the quality of power supply will be affected [
1,
2,
3,
4]. Therefore, in order to maintain the safety and stable operation of the power network and detect fluctuations and faults of power parameters in the distribution network in a timely manner, a safe and reliable voltage parameter monitoring device is urgently needed which can accurately monitor the key nodes of the power system [
5,
6]. Currently, the mainstream voltage measurement method is contact measurement, which requires the metal part of the line to be pulled out and connected to the equipment for voltage measurement. When the actual line voltage measurement is carried out, the insulation layer needs to be stripped, which will cause damage to the line. Sometimes, contact measurement requires that the power supply of the distribution network also produces a greater interference to the normal operation of the power network [
7]. Therefore, with the improvement of the requirements for the use of various types of power equipment, researchers have begun to explore the application of noncontact voltage measurement methods in power transmission networks on-line monitoring [
8,
9].
The principle of noncontact voltage sensors is to convert the large primary-side voltage into a smaller value of the secondary-side voltage suitable for meter measurement through electromagnetic field coupling to achieve electrical isolation of high voltage and avoid workers directly measuring high-voltage contacts, which has high safety and practicality [
10,
11,
12]. However, noncontact measurement based on the principle of capacitance voltage division introduces many uncertainties, such as different heights of overhead lines to ground, changes in environmental factors such as temperature and humidity in different climates, and foreign objects near the sensor such as towers and trees, which can cause changes in the primary capacitance of the line and sensor, leading to changes in the voltage division ratio and affecting the measurement accuracy [
13]. Researchers have conducted a series of studies on this issue.
Reference [
14] presents a noncontact measurement scheme for the AC voltage of insulated conductors, which forms a capacitive network between conductors and ground by using appropriate probes. This method can reduce the influence of some parasitic parameters through FFT data processing with an error of less than 0.75%. However, this method can only measure valid values and cannot obtain complete waveforms, and the position relationship between sensors and cables is not easy to determine during measurement and can easily affect measurement results [
14]. Reference [
15] presents a two-probe contactless measurement scheme based on electric field coupling, which can effectively reduce errors caused by interference sources in other directions, but the problem of parasitic capacitance changes caused by environmental changes has not been solved. Reference [
16] presents a noncontact voltage measurement method, but this method requires external large-scale equipment, and the measurement requires the power to be off, so it cannot be applied in engineering practices. Reference [
17] presents a sensor with a three-electrode structure, in which the sensor electrodes are placed in a ring during measurement. This method can improve the sensor insulation performance and improve the electric field distribution, but because the exact spatial location of overhead transmission lines is usually unknown and dynamic in practice, this leads to undetermined errors being introduced into the measurement [
17].
In this paper, the AC voltage measurement model of a transmission line is equivalent to the three-capacitance coupled voltage dividing model, and the relationship between the first and second capacitance and the voltage dividing ratio of the sensor is analyzed. A noncontact self-calibration method for AC voltage measurement of transmission lines is proposed, and an integrated small measurement system is formed. This method can reduce the impact of the change in partial pressure ratio on the measurement results, improve the measurement accuracy, and verify the feasibility of the method through simulation and experiment.
2. Principle of Noncontact Measuring Three-Capacitor Voltage Divider
Noncontact measurement of transmission lines uses the principle of three-capacitor coupled voltage divider, and the equivalent circuit is shown in
Figure 1:
Assume that the sensor is a coaxial cylindrical structure with the transmission line as the axis. In the figure
C1 is the primary capacitance produced by the coupling of the inner pole plate of the sensor with the transmission line,
C is the sensor capacitance, and
C2 is the secondary capacitance between the outer pole plate and the ground of the sensor. Based on the equivalent circuit model, the voltage
Vx to be measured on the transmission line can be calculated by the following formula:
If the charge on the capacitor plate is
q, the above formula can be written:
The values of
V1,
V, and
V2 can be calculated by the following formula:
Therefore, the capacitance voltage division
k calculation can be described as follows:
To sum up, if the values of capacitance C, C1, and C2 are known, and the possible changes between capacitance C, C1, and C2 in the measurement environment are known, then only the value of V can be measured to obtain Vx.
Take a single-core transmission line as an example, we use a cylindrical sensor, assuming the radius of the transmission line to be measured is
r, and the radii of the inner and outer electrodes of the sensor capacitor
C are
r1 and
r2, respectively, as shown in
Figure 2.
Capacitance values can be calculated by:
In the equation,
L is the column length of the sensor, and the
C2 value can be calculated by electro-image method with the following formula:
where λ is the charge per unit length of the transmission line,
h is the height of the transmission line from the ground, and
V2 is the potential difference from the outer electrode of the sensor to the ground. The derivation of the formula shows that if the primary and secondary capacitances are accurately known, the voltage on the transmission line can be calculated from the voltage on the sensor capacitance. Until the voltage on the transmission line is accurately known, there is no way to be able to determine the secondary capacitance, so even if the primary capacitance is determined, the measurement of the transmission line voltage cannot be completed, and the stability of the sensor voltage division ratio is disturbed by multiple environmental variables such as height to ground and climate, so that the influence of such stray parameters on the capacitance must be reduced or excluded if noncontact accurate measurements are to be achieved [
18,
19].
3. Self-Calibration Measurement Principle and System Design
This paper designs a noncontact AC voltage measurement system, as shown in
Figure 3, which can be used as the basis for self-calibration of the measurement to exclude the influence of capacitance changes on the measurement accuracy.
As shown in the figure, the system consists of a coupled capacitance probe, a conditioning circuit module, a data collector, and a host computer. This method first precalibrates the reference signal applied to the housing of the no-load probe to obtain the signal containing the stray parameters. Then, the cable to be measured is placed for formal measurement. Through frequency analysis of the output signal and extracting the information of the target frequency band, the stray parameters are eliminated. By modeling the dynamic system, the differential equation describing the system is established, and the valid values of the voltage signal are calculated and restored.
3.1. Design of Coupled Capacitive Probe
The probe design is based on the three-capacitor voltage dividing principle described above, and the schematic diagram is shown in
Figure 4. The probe connects the inner pole template with the analog front-end circuit through a coaxial cable. One end of the coaxial cable’s inner core is connected to the inductive plate on the inner surface of the probe to obtain the measured voltage signal, and the other end is connected to the analog circuit as output. The outer conductive mesh of the coaxial cable is connected to the signal generator at one end and to the probe outer surface at the other end to inject a reference signal into the probe. Therefore, a coupling capacitance
C1 is formed between the inner plate of the capacitance probe and the line to be measured. A capacitance value
C exists between the inner and outer plates of the sensor, and a capacitance
C2 exists between the outer plate of the sensor and the ground, which constitutes a three-capacitance voltage dividing structure.
The value of
C1 can be approximately expressed as the capacitance between two coaxial cylinders with air dielectric:
The dielectric constant
ε0 = 8.85 pF/m,
L is the length of the electrodes,
dE is the diameter of the inner surface of the electrodes, and
dC is the diameter of the conductor of the measured cable. In order to verify the relationship between capacitance and probe size, the probe structure was simulated by finite element method.
Figure 5 shows the distribution of electric field in the inner space after the sensor probe package clips the cable to be measured.
From
Figure 5, it can be seen that the spatial electric field inside the sensor is evenly distributed around the traverse to be measured and can be steadily perceived by the inner pole of the sensor. Based on the previous derivation, it is known that the sensor capacity
C1 is one of the key factors to achieve accurate measurement. To determine its relationship with the sensor size, since most cables are less than 10 mm in diameter, the bayonet diameter of the probe used to fix the cable is designed to be 10 mm. The key values that affect the
C1 size of the probe are the length of the electrode
L and the diameter of the inner surface of the electrode
dE. The capacitance distribution of the probe is calculated, and the results are shown in
Figure 6 and
Figure 7:
According to the previous discussion, the coupling capacitance
C1 between the inner pole plate of the probe and the cable to be measured is not only an important parameter to determine the value of the signal to be measured, but it also affects the measurement accuracy in conjunction with the stray parameters, so the value is not too large or too small. Therefore, the sensor size is determined as the electrode length
L = 10 cm, the inner surface diameter
dE = 3.6 cm, and the C1 value is less than 4.92 pF. The probe prototype shown in
Figure 8 was fabricated using photosensitive resin as raw material by 3D printing.
3.2. Realization of Self-Calibration Principle
In order to achieve the system measurement function, a circuit module with operational amplifier as the core component is planned to overlay the
Vx sensed by the coupling capacitance with the
Vin excitation signal through the operational amplifier. The circuit diagram is shown in
Figure 9.
According to the circuit between the sensor probe and the circuit module, it can be found that the grounding of the end to be measured is not in common with the grounding of the end to be measured, thus achieving electrical isolation. The secondary capacitance C2 in the three-capacitance model proposed above is replaced by the parasitic capacitance Cin, the potential at the measured point is raised, and subsequent measurements only need to consider the effect of the line stray parameter Cin on the measurements. By precalibrating the probe, a calibration signal containing Cin can be obtained and excluded from subsequent frequency analysis.
The core function of the circuit is implemented using the Texas Instruments (TI) OPA320AIDBVT chip, which has a 20 MHz high gain bandwidth product and can avoid system measurement errors to some extent [
16].
R1 = 200Ω and R2 = 2 kΩ. The magnification is 10 times, compensated by the feedback capacitance Cf in parallel with R2, which avoids the instability caused by the equivalent input capacitance CE = C1 + Cin + C, with a value of 2.2 nF.
Based on the probe structure and the circuit module, the following relationships can be obtained. When the system access frequency is only
ωin and when the reference signal of
Vin in is
Vx = 0, the amplitude of the output signal
Vout0 can be calculated as follows:
ωin values need to be distinguished from the voltage frequency to be measured, otherwise the voltage data to be measured will be lost. When the system is connected to both the cable
Vx to be measured and the reference signal
Vin, the following voltage–current relationship exists between the input and output of the operational amplifier:
I is the displacement current flowing through the probe, which is obtained by Laplace transformation:
Then, the above expression can be converted into
Vout calculation relation of output differential signal by operational amplifier:
The coupling signal expressed above can be regarded as a coupling signal formed by the superimposition of the reference signal component and the signal component to be measured.
Then, the
Vout can be calculated as:
A set of system input and output reference values was obtained during precalibration.
Fin values can be calculated from Formula (12) and precalibration measurement parameters:
Vout can be analyzed by FFT to obtain two components: the component
VX whose frequency is ω
x and the component
Vin whose frequency is
ωin. The two components both produce a sinusoidal curve; the amplitude
VOx and
VOin are given by the following formula:
The valid value of the voltage to be measured can be calculated from the
Fin value obtained by analyzing the input–output relationship during precalibration and the
Vin component amplitude–frequency parameter obtained by FFT frequency analysis.
In summary, the measurement and self-calibration system for noncontact AC voltage is designed.
4. Setting up Measurement System and Experimental Results
To verify the feasibility of the self-calibration mechanism described above and verify the results of the theoretical analysis section, an experimental platform is set up as shown in
Figure 10:
In this experiment, VK702WH from the Shenzhen vking company, China, is used as the data acquisition device. This device is a customized model, has a wireless transmission function, and can be used as a reference signal for a signal generator to generate custom frequency. The functions of each port are shown in
Figure 11:
(1) is a digital signal input that enables eight channels of differential input, but in the context of this application, only a single channel input is used. (2) is the analog signal output, and the +5 V port is used as the analog voltage output port when the optional analog output module is used. The 12 V battery is used to power the data collector, and there is no need to connect more large-scale devices to the measurement site. Therefore, the proposed measurement system achieves small volume, integrated measurement, and can meet the measurement requirements under different working conditions.
In addition, the Agilent digital multimeter is added as an auxiliary acquisition channel in the experiment, and the valid value of the output of the voltage source is measured directly as a reference. The experimental site is shown in
Figure 12:
Because this method measures power frequency lines, the voltage signal to be measured at 220 V, 50 Hz is given by the voltage source. During the measurement, 100 mV and 1 kHz reference AC signals are overlaid and experimented. The waveform is shown in
Figure 13:
It can be seen that the waveform in the figure is the superimposed waveform of a sinusoidal signal, which contains the reference signal component and the signal component to be measured; the measured signal is separated by FFT using MATLAB, and the data waveform is calculated and reduced to compare with the measured waveform of the Tektronix probe, as shown in
Figure 14.
Similarly, the linearity of the system was tested using a sinusoidal input signal
VX. Ten voltage signals in the range of 80–120% of the rated voltage were selected for measurement according to the voltage calibration standard, and the input raw voltage was measured directly with an Agilent digital multimeter at the same time. The result is shown in
Figure 15:
It can be seen that this measurement method can realize the self-calibration of spurious parameters, restore the voltage waveform to be measured, and have better measurement performance and linearity.
5. Conclusions
In this paper, a noncontact measurement and self-calibration method of the AC voltage of industrial frequency is proposed in order to be able to explore different measurement methods of the AC voltage of the distribution network, with the main work described as follows:
- (1)
The line and the earth as a large capacitance to its voltage division, according to the structural relationship between the wire and the sensor, which is the abstraction of the three−capacitance equivalent model of voltage sensing.
- (2)
The environmental factors that may affect the partial pressure ratio of the sensor are analyzed according to the equivalent model, and the principle of self-calibration of the sensor is proposed on this basis.
- (3)
A noncontact measurement system for AC voltage was constructed, a prototype sensor probe and a back-end conditioning circuit were designed and fabricated, and an experimental platform was built to systematically validate the proposed method and prove the feasibility of the method.
At present, the probe made in this article can be further optimized. A hinged structure can be designed to make the probe form an integrated structure, and a fixture design can be added inside the probe to keep the cable to be measured in alignment. These problems need further study. In addition, this paper only experimentally verifies the feasibility of a power frequency single-phase line method under 220 V. Future research will expand the application of this self-calibrated noncontact voltage measurement method under wide-band and high-voltage conditions and explore how to apply this measurement system to three-phase transmission lines. The noncontact AC measurement system proposed in this paper can meet the requirements of miniaturization, high accuracy, live installation, and stable performance. It has a positive significance for the research and application of new distributed devices and on-line voltage monitoring systems of distribution networks.
Author Contributions
Conceptualization, R.W. and C.S.; methodology, R.W. and W.Z.; software, W.Z. and K.C.; validation, R.W. and W.Z.; formal analysis, R.W.; investigation, A.J. and W.Z.; resources, C.S. and W.Z.; data curation, Y.Y. and K.C.; writing—original draft preparation, R.W. and Y.Y.; writing—review and editing, R.W., C.S. and W.Z.; supervision, A.J.; project administration, W.Z. and K.C. All authors have read and agreed to the published version of the manuscript.
Funding
This research was supported by the funding of Yunnan Academy of Science and Technology “Research and development of new smart sensor technology to promote green energy development” (202104BN050011).
Data Availability Statement
The data used to support the findings of this study are included within the article.
Conflicts of Interest
The authors declare no conflict of interest.
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