Flat plate non-contact voltage measurement method based on variable capacitance and parameter desensitization

Abstract

The invention discloses a panel non-contact voltage measurement method based on variable capacitance and parameter desensitization, and belongs to the technical field of distribution network voltage measurement. The objective of the invention is to solve the problem of unstable high-voltage non-contact voltage measurement precision caused by ground capacitance change and coupling capacitance uncertainty. The method comprises the following steps: step 1, designing a bipolar plate variable capacitance coupling mechanism, establishing an equivalent circuit model of the bipolar plate variable capacitance coupling mechanism, changing a capacitance voltage dividing loop through a switching switch and an adjusting capacitor, and measuring trans-impedance voltages between inner and outer copper electrodes in different states; 2, on the basis of an equivalent circuit, voltage equations in different states are combined, and a line voltage inversion formula capable of eliminating influences of coupling capacitance and ground capacitance at the same time is deduced; and 3, calibrating system parameters in the inversion formula by using a least square method, analyzing the sensitivity of each parameter, and reducing the sensitivity of key parameters through optimization design so as to realize high-precision non-contact voltage measurement.

Description

Technical Field

[0001] This invention pertains to distribution network voltage measurement technology, specifically relating to a non-contact voltage measurement method for a flat plate based on variable capacitance and parameter desensitization. Background Technology

[0002] Since the power system has entered the stage of intelligent development, voltage, as a core parameter reflecting equipment operating status, power quality, and fault early warning, has always been a key area for breakthroughs in the industry, particularly in terms of the safety, accuracy, and scenario adaptability of its measurement technology. Traditional contact-based voltage measurement requires breaking the equipment's insulation layer and directly connecting to a live circuit, which not only poses safety risks such as high-voltage electric shock and equipment short circuits but also requires interrupting system operation for installation and maintenance, making it difficult to meet the core requirement of "uninterrupted operation and maintenance" in modern power systems. Against this backdrop, non-contact voltage measurement technology has developed rapidly due to its unique advantages of "no physical contact and no power outage." It indirectly infers voltage values ​​by sensing the electric and magnetic fields around a live conductor or by utilizing capacitive coupling effects. It has formed diversified technical solutions in high-voltage transmission lines, power electronic equipment, and industrial monitoring, becoming an important research branch in the field of power measurement. Addressing the technical pain point of ground capacitance interference in distribution network scenarios and combining the development trend of non-contact voltage measurement technology, this paper proposes a non-contact voltage measurement planar structure. This structure uses bipolar plates and adjustable capacitors for capacitive voltage division to eliminate the influence of ground capacitance on the measurement. Summary of the Invention

[0003] The purpose of this invention is to solve the problem of unstable accuracy in high-voltage non-contact voltage measurement caused by variations in ground capacitance and uncertainties in coupling capacitance. Accurate high-voltage non-contact voltage measurement is achieved through a non-contact coupling mechanism.

[0004] The technical solution adopted in this invention is as follows:

[0005] A non-contact voltage measurement method for a flat plate based on variable capacitance and parameter desensitization includes the following steps:

[0006] Step 1: Design a bipolar plate variable capacitor coupling mechanism and propose a capacitor-coupled non-contact voltage measurement method based on topology transformation; change the capacitor voltage divider circuit by switching the switch and adjusting the capacitor, and measure the transresistance voltage between the inner and outer copper electrodes under different conditions.

[0007] Step 2: Based on the equivalent circuit in Step 1, combine the voltage equations under different states to derive the line voltage inversion formula that can simultaneously eliminate the influence of coupling capacitance and ground capacitance.

[0008] Step 3: Use the least squares method to calibrate the system parameters in the inversion formula and analyze the sensitivity of each parameter. Reduce the sensitivity of key parameters through optimized design, thereby achieving high-precision non-contact voltage measurement.

[0009] Furthermore, step 1 specifically includes the following steps:

[0010] Step 1.1: Design a bipolar plate variable capacitor coupling mechanism through topology transformation;

[0011] To solve the coupling capacitance Due to environmental factors and other interferences, measurement becomes difficult, and the influence of ground capacitance must also be considered. Based on topology transformation, a capacitively coupled non-contact voltage measurement method is proposed. The coupling capacitor... and the voltage to be measured All are treated as unknowns to be solved. By using topological transformation and capacitor voltage division to change the output voltage, the voltage to be measured is calculated using differential calculation, thereby realizing the solution of the unknowns. and The solution. The topological transformation structure is as follows. Figure 2 As shown.

[0012] Step 1.2: Draw the equivalent circuit diagram of the probe;

[0013] Based on the electric field coupling relationship between the circuit and the probe, the equivalent measurement principle of the displacement current method is plotted. Figure 3 , Figure 4 The equivalent circuit includes at least the coupling capacitance between the wire and the inner copper electrode. Adjustable capacitance between inner and outer copper electrodes (Adjustable to) The capacitance between the wire and the outer copper electrode (Adjustable to) External copper electrode to ground capacitance and the additional capacitor switched by switch S. .

[0014] Step 1.3: Measure the transresistance voltage between the inner and outer copper electrodes under different conditions by switching the switch and adjusting the capacitor;

[0015] By controlling the opening and closing of switch S, and adjusting the adjustable capacitor... Equivalent capacitance of external copper electrode This allows the probe to form at least four different capacitive network topologies; corresponding to each of these states, the response voltage between the inner and outer copper electrodes is measured, obtaining at least four sets of voltage measurements. , , , .

[0016] Furthermore, step 2 specifically includes the following steps:

[0017] Step 2.1: Based on the principle of equivalence Figure 3, Figure 4 Drive the circuit voltage With sensor measuring voltage , , , From the expression for the coupling capacitance between the two sides, the line voltage inversion formula can be obtained;

[0018] When switch S is open, the measured voltage is as follows:

[0019] (1)

[0020] When adjusting the adjustable capacitor (After setting the capacitor to two levels) Adjust the outer copper electrode Make the capacitance from the wire to the external copper electrode be The measured voltage is as follows:

[0021] The coupling capacitance between the wire and the inner copper electrode is The adjustable capacitance between the inner and outer copper electrodes is (Adjustable to) The capacitance between the wire and the outer copper electrode is (Adjustable to) External copper electrode to ground capacitance and the additional capacitor switched by switch S. The voltage to be measured is The instrument measures the voltage as follows: (Transformed by a switch) )

[0022] (2)

[0023] When switch S is closed, the capacitor is connected. Adjustable capacitor Return to its original position; the capacitance between the inner and outer copper electrodes is... ,Right now , measuring voltage for:

[0024] (3)

[0025] When adjusting the adjustable capacitor (After setting the capacitor to two levels) Adjust the outer copper electrode Make the capacitance from the wire to the external copper electrode be When switch S is closed, the capacitor is connected. The capacitance between the inner and outer copper electrodes is ,Right now Voltage between the inner and outer copper electrodes of the left probe for:

[0026] (4)

[0027] The combined equations (1), (2), (3), and (4) can eliminate ground capacitance. and coupling capacitor The effect on the measured voltage is used to determine the line voltage. The inversion formula:

[0028] (5)

[0029] in, , , , This refers to the switching capacitor and the capacitance between the inner and outer copper electrodes. , , , The voltage between the inner and outer copper electrodes measured by the sensor before and after switch S is opened and closed. This represents the capacitance of the external copper electrode to ground. The height of a 10kV overhead transmission line is 12-15m, and the rate of change of the capacitance of the external copper electrode to ground is negligible. When the dimensions of the sensor's dual probes are determined and installed on the distribution network line, the equivalent circuit diagram... , , , Both can be considered as constants, so equation (5) can be expressed as:

[0030] (6)

[0031]

[0032] Step 2.2: By analyzing the error propagation and amplification mechanism, perform parameter sensitivity analysis on the inversion formula;

[0033] This represents the actual value of the output voltage. Indicates the measured voltage. ∆ represents the relative error between the true value of the output voltage and the measured voltage. Indicates the absolute error of the measured voltage:

[0034] (7)

[0035] Taking the partial derivative of the voltage parameter in equation (3), we quantify the impact of measurement error on the result. (This represents the relative error between the actual input voltage and the calculated voltage).

[0036] (8)

[0037] use It can quantify the deviation of voltage from the true value ∆ At that time, for the measurement line Inversion error:

[0038] (9)

[0039] After solving the expression and performing error analysis, the sensitivity analysis and measurement error are obtained. ( , The effects of the measured voltage error on the retrieved line voltage error are characterized respectively. The curve of change with coupling capacitance is as follows Figure 5 As shown, when the capacitance parameter changes within a certain range, the overall sensitivity shows a gradual trend from the high value region to the low value region, and the surface is relatively smooth with no obvious peak.

[0040] Furthermore, step 3 specifically includes the following steps:

[0041] Step 3.1: Use the least squares method to calibrate the system parameters in the inversion formula;

[0042] To solve equation (6) using the least squares method, the equation needs to be transformed first to construct a voltage vector (containing voltage measurement terms) and a calibration parameter vector (containing constants to be determined), and then derived through least squares matrix operations. The transformed result of equation (6) can be expressed as a linear combination equation:

[0043] (10)

[0044] Expand and organize the linear combination of "constant term × voltage product term": extract all "voltage product terms" (as "input features" for least squares) and construct a vector. , :

[0045] (11)

[0046] (12)

[0047] Using the constants A, B, C, D, E, F, G, H to be determined as "calibration parameters", construct a vector:

[0048] (13)

[0049] If there are multiple sets of measurement data (different i corresponds to different voltage measurement values), then all sets... Stacked row-wise into matrix M. According to the least squares method, when M columns are full rank, the optimal... The solution is the one that minimizes the sum of squared residuals. Since the right-hand side is the zero vector, if... Reversible, solution:

[0050] (14)

[0051] Step 3.2: Based on the parameter sensitivity analysis results, reduce the sensitivity of key parameters through design optimization;

[0052] Analysis results indicate that the slope of the scaling factor in the inversion formula is the main reason for the high parameter sensitivity. By adjusting the probe structure parameters, the... and The ratio of the two values ​​is used to make it work in the flat region of the sensitivity curve, thereby reducing the impact of measurement voltage fluctuations on the inversion results and achieving high-precision measurement with an error of less than 3%.

[0053] Because the present invention adopts the above-described technical solution, it has the following beneficial effects:

[0054] This invention solves the coupling capacitor problem by designing a bipolar plate variable capacitor coupling mechanism and applying topology transformation techniques (step 1). The technical problems of inaccurate measurement due to changes in environmental factors and interference from ground capacitance in line voltage measurement have been solved. The coupling capacitance and the voltage to be measured are simultaneously treated as unknowns for solution, which fundamentally avoids the impact of changes in environmental factors on measurement accuracy and significantly improves the stability and reliability of non-contact voltage measurement.

[0055] This invention changes the capacitor voltage divider circuit by switching the switch and adjusting the capacitor to obtain the trans-resistance voltage between the inner and outer copper electrodes under at least four different topological states (step 1.3). This solves the technical problem that a single measurement cannot distinguish the influence of multiple unknown parameters, and achieves the effect of providing multi-dimensional measurement data. This lays the data foundation for the subsequent elimination of the combined influence of coupling capacitor and ground capacitance, and enables the system to handle complex electromagnetic environments.

[0056] This invention derives a line voltage inversion formula (step 2.1) by simultaneously solving voltage equations under different topological states, which can eliminate the influence of coupling capacitance and ground capacitance. This solves the technical problem of unstable measurement accuracy caused by changes in ground capacitance in traditional non-contact voltage measurement methods, achieves accurate line voltage inversion, overcomes measurement drift caused by changes in installation location, humidity, temperature and other factors in the power system operating environment, and greatly improves the accuracy and environmental adaptability of non-contact measurement.

[0057] This invention utilizes the least squares method to calibrate system parameters and perform sensitivity analysis, optimizing probe structural parameters to operate in the flat region of the sensitivity curve (step 3.2). This solves the technical problem that high parameter sensitivity in the inversion formula leads to the amplification of small measurement errors, achieving the effect of reducing the system's sensitivity to measurement fluctuations. It significantly improves the robustness and long-term stability of the entire measurement system, enabling non-contact measurement technology to meet the stringent requirements of power systems for measurement accuracy.

[0058] This invention organically combines a bipolar plate variable capacitor coupling mechanism, multi-topology state measurement, voltage inversion formula derivation, and parameter sensitivity optimization design, resulting in a significant synergistic effect. It not only completely avoids the safety hazards of traditional contact-based voltage measurement but also overcomes the inherent defect of conventional non-contact measurement technologies where accuracy drops sharply under different installation distances and environmental conditions. This synergistic effect enables the system to maintain high-precision voltage measurement capabilities without damaging equipment insulation or requiring system power outages, achieving a balance between safety and accuracy. It provides reliable technical support for distribution network condition monitoring, fault early warning, and power quality management, filling the technological gap in the application of existing non-contact voltage measurement technologies in complex real-world environments. Attached Figure Description

[0059] Figure 1 This is a simplified flowchart of the invention process;

[0060] Figure 2 This is a schematic diagram of a topology model;

[0061] Figure 3 It is the equivalent circuit diagram of the measurement system;

[0062] Figure 4 This is the equivalent circuit diagram of the switch closure measurement system;

[0063] Figure 5 It is a parameter sensitivity curve. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described embodiments are merely some embodiments of the invention, and not all embodiments. The components of the embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0065] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0066] It should be noted that relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0067] Technical issue: Eliminate the impact of changes in ground capacitance on measurement accuracy based on a non-contact voltage measurement method.

[0068] Technical means: A non-contact voltage measurement method for a flat plate based on variable capacitance and parameter desensitization, comprising the following steps:

[0069] Step 1: Design a bipolar plate variable capacitor coupling mechanism and propose a capacitor-coupled non-contact voltage measurement method based on topology transformation; change the capacitor voltage divider circuit by switching the switch and adjusting the capacitor, and measure the transresistance voltage between the inner and outer copper electrodes under different conditions.

[0070] Step 2: Based on the equivalent circuit in Step 1, combine the voltage equations under different states to derive the line voltage inversion formula that can simultaneously eliminate the influence of coupling capacitance and ground capacitance.

[0071] Step 3: Use the least squares method to calibrate the system parameters in the inversion formula and analyze the sensitivity of each parameter. Reduce the sensitivity of key parameters through optimized design, thereby achieving high-precision non-contact voltage measurement.

[0072] In the above scheme, step 1 specifically includes the following steps:

[0073] Step 1.1: Design a bipolar plate variable capacitor coupling mechanism through topology transformation;

[0074] To solve the coupling capacitance Due to environmental factors and other interferences, measurement becomes difficult, and the influence of ground capacitance must also be considered. Based on topology transformation, a capacitively coupled non-contact voltage measurement method is proposed. The coupling capacitor... and the voltage to be measured All are treated as unknowns to be solved. By using topological transformation and capacitor voltage division to change the output voltage, the voltage to be measured is calculated using differential calculation, thereby realizing the solution of the unknowns. and The solution. The topological transformation structure is as follows. Figure 2 As shown.

[0075] Step 1.2: Draw the equivalent circuit diagram of the probe;

[0076] Based on the electric field coupling relationship between the circuit and the probe, the equivalent measurement principle of the displacement current method is plotted. Figure 3 , Figure 4 The equivalent circuit includes at least the coupling capacitance between the wire and the inner copper electrode. Adjustable capacitance between inner and outer copper electrodes (Adjustable to) The capacitance between the wire and the outer copper electrode (Adjustable to) External copper electrode to ground capacitance and the additional capacitor switched by switch S. .

[0077] Step 1.3: Measure the transresistance voltage between the inner and outer copper electrodes under different conditions by switching the switch and adjusting the capacitor;

[0078] By controlling the opening and closing of switch S, and adjusting the adjustable capacitor... Equivalent capacitance of external copper electrode This allows the probe to form at least four different capacitive network topologies; corresponding to each of these states, the response voltage between the inner and outer copper electrodes is measured, obtaining at least four sets of voltage measurements. , , , .

[0079] In the above scheme, step 2 specifically includes the following steps:

[0080] Step 2.1: Based on the principle of equivalence Figure 3 , Figure 4 Drive the circuit voltage With sensor measuring voltage , , , From the expression for the coupling capacitance between the two sides, the line voltage inversion formula can be obtained;

[0081] When switch S is open, the measured voltage is as follows:

[0082] (1)

[0083] When adjusting the adjustable capacitor (After setting the capacitor to two levels) Adjust the outer copper electrode Make the capacitance from the wire to the external copper electrode be The measured voltage is as follows:

[0084] The coupling capacitance between the wire and the inner copper electrode is The adjustable capacitance between the inner and outer copper electrodes is (Adjustable to) The capacitance between the wire and the outer copper electrode is (Adjustable to) External copper electrode to ground capacitance and the additional capacitor switched by switch S. The voltage to be measured is The instrument measures the voltage as follows: (Transformed by a switch) )

[0085] (2)

[0086] When switch S is closed, the capacitor is connected. Adjustable capacitor Return to its original position; the capacitance between the inner and outer copper electrodes is... ,Right now , measuring voltage for:

[0087] (3)

[0088] When adjusting the adjustable capacitor (After setting the capacitor to two levels) Adjust the outer copper electrode Make the capacitance from the wire to the external copper electrode be When switch S is closed, the capacitor is connected. The capacitance between the inner and outer copper electrodes is ,Right now Voltage between the inner and outer copper electrodes of the left probe for:

[0089] (4)

[0090] The combined equations (1), (2), (3), and (4) can eliminate ground capacitance. and coupling capacitor The effect on the measured voltage is used to determine the line voltage. The inversion formula:

[0091] (5)

[0092] in, , , , This refers to the switching capacitor and the capacitance between the inner and outer copper electrodes. , , , The voltage between the inner and outer copper electrodes measured by the sensor before and after switch S is opened and closed. This represents the capacitance of the external copper electrode to ground. The height of a 10kV overhead transmission line is 12-15m, and the rate of change of the capacitance of the external copper electrode to ground is negligible (after determining the height, the change in capacitance to ground is negligible, and finally, interference from capacitance to ground is eliminated). When the dimensions of the sensor's dual probes are determined and installed on the distribution network line, the equivalent circuit diagram shows... , , , Both can be considered as constants, so equation (5) can be expressed as:

[0093] (6)

[0094]

[0095] Step 2.2: By analyzing the error propagation and amplification mechanism, perform parameter sensitivity analysis on the inversion formula;

[0096] This represents the actual value of the output voltage. Indicates the measured voltage. ∆ represents the relative error between the true value of the output voltage and the measured voltage. Indicates the absolute error of the measured voltage:

[0097] (7)

[0098] Taking the partial derivative of the voltage parameter in equation (3), we quantify the impact of measurement error on the result. (This represents the relative error between the actual input voltage and the calculated voltage).

[0099] (8)

[0100] use It can quantify the deviation of voltage from the true value ∆ At that time, for the measurement line Inversion error:

[0101] (9)

[0102] After solving the expression and performing error analysis, the sensitivity analysis and measurement error are obtained. ( , The effects of the measured voltage error on the retrieved line voltage error are characterized respectively. The curve of change with coupling capacitance is as follows Figure 5 As shown, when the capacitance parameter changes within a certain range, the overall sensitivity shows a gradual trend from the high value region to the low value region, and the surface is relatively smooth with no obvious peak.

[0103] Furthermore, step 3 specifically includes the following steps:

[0104] Step 3.1: Use the least squares method to calibrate the system parameters in the inversion formula;

[0105] To solve equation (6) using the least squares method, the equation needs to be transformed first to construct a voltage vector (containing voltage measurement terms) and a calibration parameter vector (containing constants to be determined), and then derived through least squares matrix operations. The transformed result of equation (6) can be expressed as a linear combination equation:

[0106] (10)

[0107] Expand and organize the linear combination of "constant term × voltage product term": extract all "voltage product terms" (as "input features" for least squares) and construct a vector. , :

[0108] (11)

[0109] (12)

[0110] Using the constants A, B, C, D, E, F, G, H to be determined as "calibration parameters", construct a vector:

[0111] (13)

[0112] If there are multiple sets of measurement data (different i corresponds to different voltage measurement values), then all sets... Stacked row-wise into matrix M. According to the least squares method, when M columns are full rank, the optimal... The solution is the one that minimizes the sum of squared residuals. Since the right-hand side is the zero vector, if... Reversible, solution:

[0113] (14)

[0114] Step 3.2: Based on the parameter sensitivity analysis results, reduce the sensitivity of key parameters through design optimization;

[0115] Analysis results indicate that the slope of the scaling factor in the inversion formula is the main reason for the high parameter sensitivity. By adjusting the probe structure parameters, the... and The ratio of the two values ​​is used to make it work in the flat region of the sensitivity curve, thereby reducing the impact of measurement voltage fluctuations on the inversion results and achieving high-precision measurement with an error of less than 3%.

Claims

1. A non-contact voltage measurement method for a flat plate based on variable capacitance and parameter desensitization, characterized in that, Includes the following steps: Step 1: Design a bipolar plate variable capacitor coupling mechanism, establish its equivalent circuit model, change the capacitor voltage divider circuit by switching the switch and adjusting the capacitor, and measure the transresistance voltage between the inner and outer copper electrodes under different topological states. Step 2: Based on the equivalent circuit model in Step 1, the voltage equations under different topological states are combined to derive the line voltage inversion formula that can simultaneously eliminate the influence of coupling capacitance and ground capacitance. Step 3: Use the least squares method to calibrate the system parameters in the inversion formula and analyze the sensitivity of each parameter. Reduce the sensitivity of key parameters through optimized design, thereby achieving high-precision non-contact voltage measurement.

2. The method according to claim 1, characterized in that, Step 1 specifically includes the following steps: Step 1.1: Through topological transformation, design a bipolar plate variable capacitor coupling mechanism to couple the capacitors... and the voltage to be measured All are treated as unknowns to be solved. By using topological transformation and capacitor voltage division to change the output voltage, the voltage to be measured is calculated using differential calculation, thereby realizing the solution of the unknowns. and Solving for; Step 1.2: Based on the electric field coupling relationship between the circuit and the probe, draw the equivalent circuit diagram of the probe; The equivalent circuit includes at least: the coupling capacitance between the wire and the inner copper electrode. Adjustable capacitance between inner and outer copper electrodes Adjustable to Capacitance between the wire and the outer copper electrode Adjustable to External copper electrode to ground capacitor and the additional capacitor switched by switch S. . Step 1.3: By controlling the opening and closing of switch S, and adjusting the adjustable capacitor... Equivalent capacitance of external copper electrode This allows the probe to form at least four different capacitive network topologies; corresponding to each of these states, the response voltage between the inner and outer copper electrodes is measured, obtaining at least four sets of voltage measurements. , , , .

3. The method according to claim 2, characterized in that, Step 2 specifically includes the following steps: Step 2.1: Derive the circuit voltages based on the equivalent circuit diagram. With sensor measuring voltage , , , From the expression for the coupling capacitance between the two sides, the line voltage inversion formula can be obtained; When switch S is open, the measured voltage is as follows: (1) When adjusting the adjustable capacitor for Adjust the outer copper electrode Make the capacitance from the wire to the external copper electrode be The measured voltage is as follows: (2) When switch S is closed, the capacitance between the inner and outer copper electrodes is ,Right now , measuring voltage for: (3) When switch S is closed, and the adjustable capacitor is The external copper capacitor is The capacitance between the inner and outer copper electrodes is Measure the voltage between the inner and outer copper electrodes of the left probe. (4) Combined equations (1), (2), (3), and (4) to eliminate ground capacitance and coupling capacitor The effect on the measured voltage is used to determine the line voltage. The inversion formula: (5) When the dimensions of the dual-probe sensor are determined and it is installed in the power distribution network, the equivalent circuit diagram... , , , Since both are considered constants, equation (5) can be expressed as: (6) Step 2.2: By analyzing the error propagation and amplification mechanism, perform parameter sensitivity analysis on the inversion formula; This represents the actual value of the output voltage. Indicates the measured voltage. ∆ represents the relative error between the true value of the output voltage and the measured voltage. Indicates the absolute error of the measured voltage: (7) Taking the partial derivative of the voltage parameter in equation (3), the expression for quantifying the impact of measurement error on the result is: (8) use It can quantify the deviation of voltage from the true value ∆ At that time, for the measurement line Inversion error: (9)。 4. The non-contact voltage measurement method based on the displacement current method of a variable capacitor coupling mechanism according to claim 3, characterized in that... Step 3 specifically includes the following steps: Step 3.1: Use the least squares method to calibrate the system parameters in the inversion formula; To solve equation (6) using the least squares method, the equation needs to be transformed first to construct the voltage vector and calibration parameter vector. Then, through matrix operations of least squares, the transformed result of equation (6) can be expressed as a linear combination equation: (10) Expand and organize the linear combination of "constant term × voltage product term": extract all "voltage product terms" as "input features" for least squares, and construct a vector. , : (11) (12) Using the constants A, B, C, D, E, F, G, H to be determined as "calibration parameters", construct a vector: (13) If there are multiple sets of measurement data, and different values ​​of voltage i correspond to different voltage measurements, then all sets... Stacked row-wise into matrix M, according to the least squares method, when M columns are full rank, the optimal... The solution is the one that minimizes the sum of squared residuals. Since the right-hand side is the zero vector, if... Reversible, solution: (14) Step 3.2: Based on the parameter sensitivity analysis results, reduce the sensitivity of key parameters through design optimization; Adjust the probe structure parameters and change and The ratio of to make the system operate in the flat region of the sensitivity curve; find the region on the parameter sensitivity curve where the sensitivity is less than a threshold, which is 3%.

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