Electromagnetic voltage transformer frequency characteristic modeling and performance improving method

Abstract

The invention relates to a frequency characteristic modeling and performance improving method for an electromagnetic voltage transformer, which comprises the following steps of: firstly, establishing an equivalent circuit model of a standard voltage transformer, and acquiring an excitation impedance value on the basis of the existing iron core parameters by adopting a complex permeability method; secondly, through an equivalent circuit model, analyzing to obtain a no-load error function of the standard voltage transformer, and through simulation calculation, obtaining a no-load error response curve of the standard voltage transformer under 20Hz-3000Hz; simulation results show that the standard voltage transformer has a large error value under high frequency and does not meet the accuracy level requirement. According to the establishment of an error transmission model, the correlation between a no-load error value and the number of turns and the cross sectional area of the standard voltage transformer is indicated, and it can be known through simulation analysis that when the number of turns of a primary side winding is reduced or the cross sectional area of an iron core is increased, the error value of the standard voltage transformer is reduced. Therefore, by adopting the method provided by the invention, the performance of the standard voltage transformer can be effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of voltage transformers, and in particular relates to a method for modeling the frequency characteristics of an electromagnetic voltage transformer and improving its performance. Background Art

[0002] The voltage transformer is a transformer in principle, used to transmit the corresponding voltage signal to the measuring instrument. In the power market, it is mainly used for electric energy measurement. Its accuracy directly affects the fairness and justice of electric energy transactions. The standard voltage transformer is used to calibrate and analyze the measured voltage transformer to ensure that the error level is controlled within the corresponding accuracy range.

[0003] Under the current "double-high" power system, the frequency amplitude range is huge. The traditional standard voltage transformer can only measure the industrial frequency signal and cannot meet the measurement requirements under wide frequency. Therefore, it is necessary to analyze its error frequency characteristics under wide frequency and propose corresponding performance improvement methods.

[0004] In the technical solution recorded in the Chinese patent: "A method for measuring wide-band error of voltage transformer" (application number: 201811386628.4), the primary side of the standard voltage transformer and the primary side of the voltage transformer to be tested are first connected in parallel, and the secondary side of the standard voltage transformer and the secondary side of the voltage transformer to be tested are both connected to the error measurement device; then the power supply device is used to input a voltage signal to the primary side of the standard voltage transformer; the error measurement device then calculates the secondary differential pressure and the voltage angle; the ratio difference and the angle difference of the voltage transformer to be tested are calculated based on the secondary differential pressure signal and the voltage angle, and the wide-band error of the voltage transformer to be tested is calculated based on the ratio difference and the angle difference; this method does not take into account the error value of the standard voltage transformer under wide frequency, thereby affecting the accuracy of voltage transformer measurement. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a method for modeling and improving the frequency characteristics of an electromagnetic voltage transformer, which can effectively improve the error accuracy of a standard voltage transformer.

[0006] The technical solution adopted by the present invention is:

[0007] A method for modeling and improving the frequency characteristics of an electromagnetic voltage transformer comprises the following steps:

[0008] Step 1: Frequency modeling steps:

[0009] An equivalent circuit model of a standard voltage transformer is established, and the excitation impedance value of the standard voltage transformer is obtained based on the existing core parameters by using the complex permeability method. Secondly, the error function formula of the standard voltage transformer is analyzed and obtained through the equivalent circuit model. After simulation calculation, the error frequency response curve of the standard voltage transformer at 20Hz to 3000Hz is obtained.

[0010] Step 2: Performance improvement steps:

[0011] An error transmission model of a standard voltage transformer is established, and the correlation between the error value and the number of turns and cross-sectional area of ​​the standard voltage transformer is analyzed. By increasing or decreasing the number of primary winding turns or the cross-sectional area of ​​the core by 10%, the influence of the number of turns and cross-sectional area on the error is characterized in detail, so as to facilitate the improvement of the error accuracy of the standard voltage transformer at 20Hz~3000Hz.

[0012] The step 1 comprises the following steps:

[0013] Step 1.1: Take a 10kV standard voltage transformer as the test product, with a rated voltage of 10 / 0.1kV, a core material of silicon steel sheet B30P105, and a cross-sectional area of ​​S = 50cm 2 The average magnetic circuit length is 78cm, and the turns ratio is 9000 / 90. First, the corresponding excitation impedance value is obtained according to its equivalent circuit model. The equivalent circuit model is shown in Figure 1 shown.

[0014] When analyzing the harmonic characteristics of electromagnetic transformers, the influence of distributed capacitance is often considered, while the change of excitation impedance with frequency is ignored. For high-precision standard voltage transformers that take into account wide frequency, the frequency characteristics of excitation impedance need to be considered.

[0015] The nonlinearity of excitation impedance is mainly affected by the excitation characteristics of ferromagnetic materials, which include two parameters: one is magnetic permeability, which represents the ability of ferromagnetic materials to conduct magnetic flux, and is usually represented by real permeability μ, which is defined as the ratio of magnetic flux density B to magnetic field intensity H, and is usually extracted from the DC magnetization curve; the other is the core loss angle, which represents the phase angle of magnetic induction intensity B lagging behind the magnetic field intensity H under AC excitation due to the influence of ferromagnetic loss, represented by θ;

[0016] The real and imaginary parts of the complex permeability are:

[0017]

[0018] In formula (1), μ' is the real part of the complex permeability, B m is the real part of magnetic flux density, H m is the real part of magnetic field intensity, θ is the core loss angle;

[0019]

[0020] In formula (2), μ” is the imaginary part of the complex magnetic permeability;

[0021] The core loss tangent is:

[0022]

[0023] When a DC current flows through the coil, the loss generated can be considered as DC loss. The corresponding DC resistance is determined by the material and geometric structure of the coil. The calculation formula is as follows:

[0024]

[0025] In formula (4), R1 is the DC resistance of the coil, ρ is the wire resistivity, l1 is the length of the primary winding wire, and S is the cross-sectional area of ​​the wire.

[0026] In actual design, the leakage inductance of the transformer primary winding can be estimated by analytical method, and the calculation formula is as follows:

[0027]

[0028] In formula (5), N1 represents the number of turns of the primary winding, p represents the average turn length of the winding, h represents the height of the winding, Δ, d1 and d2 represent the thickness of the insulation layer between the primary and secondary windings, the thickness of the primary winding and the thickness of the secondary winding respectively; μ0 represents the vacuum permeability.

[0029] In the calculation of transformer parameters, the excitation impedance value is related to the real and imaginary parts of the complex permeability. The corresponding relationship is as follows:

[0030]

[0031] In formula (6), L m is the excitation inductance; l is the length of the iron core magnetic path;

[0032]

[0033] In formula (7), R m is the excitation resistance, and ω is the angular frequency of the applied signal.

[0034] Step 1.2: The errors of standard voltage transformers include ratio difference and phase difference. Ratio difference refers to the error caused by the actual transformation ratio of the voltage transformer being unequal to the rated transformation ratio during measurement; phase difference refers to the phase difference between the primary voltage phasor and the secondary voltage phasor.

[0035] according to Figure 1 The standard voltage transformer equivalent circuit diagram shown in the figure shows that the difference between the secondary voltage and the primary voltage of the standard voltage transformer is:

[0036] ΔU(ω)=U2(ω)-U1(ω)=-I2(ω)(Z1(ω)+Z2(ω))-I m (ω)Z m (ω)(8);

[0037] In formula (8), ΔU(ω) is the difference between the primary winding voltage and the secondary winding voltage, U1(ω) is the primary winding voltage value, U2(ω) is the secondary winding voltage value, I2(ω) is the current value flowing through the secondary winding, Z1(ω) is the primary winding impedance value, Z2(ω) is the secondary winding impedance value, and I m (ω) is the current value flowing through the excitation impedance, Z m (ω) is the excitation impedance value.

[0038] Then the error of the standard voltage transformer is:

[0039]

[0040] In formula (9), U1(ω) is the primary winding voltage value, Z L (ω) is the load value.

[0041] According to the definition of mutual inductor error, the calculation formulas for the no-load ratio difference and phase difference are:

[0042]

[0043] In formula (10), ε0(ω) is the no-load ratio difference.

[0044] δ0(ω)=∠(Z1(ω)+Z m (ω))-∠Z m (ω) (11);

[0045] In formula (11), δ0(ω) is the no-load phase difference, ∠(Z1(ω)+Z m (ω)) is the phase sum of the primary impedance and the excitation impedance, ∠Z m (ω) is the excitation impedance phase value.

[0046] The standard voltage transformer is an electromagnetic voltage ratio standard, and its secondary has no load or is close to zero load. Therefore, the present invention focuses on the no-load error characteristics of the standard voltage transformer.

[0047] According to R1, L1, R m , L m The corresponding calculation formula is substituted into the no-load error formula, and the no-load error calculation formula related to the complex permeability and some core parameters can be derived as follows:

[0048]

[0049] Substituting the corresponding core parameters into the above formula, we can get the wide-frequency response curve of the standard voltage transformer at 20Hz~3000Hz, as shown in Figure 2 , Figure 3 shown.

[0050] In step 2, the construction flow chart of the standard voltage transformer error transmission model is as follows: Figure 6 As shown, it includes equations (4) to (7) and equations (10) to (13).

[0051] The step 2 comprises the following steps:

[0052] Step 2.1: Under actual working conditions, due to the different manufacturing methods, winding processes, and materials used for standard voltage transformers, some parameters will change. By analyzing the derived error calculation formula, it can be seen that the number of turns and cross-sectional area of ​​the standard voltage transformer will affect the no-load error. The influence of changing the number of turns and cross-sectional area on the no-load ratio difference and angle difference is now analyzed through simulation calculation.

[0053] Step 2.2: By increasing or decreasing the number of primary winding turns or the cross-sectional area of ​​the core by 10%, the corresponding no-load error value is obtained. The simulation results are as follows: Figure 4(a) to Figure 5(b) As shown in the figure, analysis shows that when the number of turns of the primary winding is reduced, the no-load ratio difference and angle difference of the standard voltage transformer at 20Hz-3000Hz are reduced; when the cross-sectional area of ​​the core is increased, the ratio difference decreases, and the angle difference changes slightly, but the reduction of the angle difference can still be reflected at high frequencies. Therefore, reducing the number of turns of the primary winding or increasing the cross-sectional area of ​​the core can reduce the error value of the standard voltage transformer, which also provides a reference for the structural design of the standard voltage transformer under wide frequency.

[0054] The present invention provides a method for modeling the frequency characteristics of an electromagnetic voltage transformer and improving its performance, and the technical effects are as follows:

[0055] 1) Step 1.1 of the present invention adopts the complex permeability method to obtain the excitation impedance value based on the existing core parameters. The relationship between the excitation impedance and the complex permeability is shown in formulas (6) and (7). The excitation impedance value obtained by the complex permeability is more accurate than other formulas.

[0056] 2) In step 1.2 of the present invention, the no-load error function of the standard voltage transformer is analyzed by using the equivalent circuit model as shown in equations (10) and (11), and then R1, L1, R m , L m Substituting the corresponding calculation formula into equation (12) and equation (13), we can get the formula. By comparing with the actual measured value, the error of this formula is small.

[0057] 3) In order to meet the measurement requirements, the error of the transformer cannot be too large. Step 2.1 of the present invention finds through equations (12) and (13) that the number of turns and cross-sectional area of ​​the standard voltage transformer will affect the no-load error. Therefore, the influence of the number of turns and cross-sectional area on the transformer error is analyzed through simulation.

[0058] 4) Through simulation analysis, step 2.2 of the present invention shows that reducing the number of turns of the primary winding or increasing the cross-sectional area of ​​the core can reduce the no-load error value of the standard voltage transformer, which provides good theoretical and parameter support for the design of the standard voltage transformer under wide frequency. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 This is the equivalent circuit model diagram of the standard voltage transformer.

[0060] Figure 2 This is the frequency response curve of the standard voltage transformer ratio difference.

[0061] Figure 3 This is the standard voltage transformer angle difference frequency response curve.

[0062] FIG4( a ) is a graph showing the effect of changing the standard voltage transformer N1 on the contrast difference;

[0063] FIG4( b ) is a graph showing the effect of changing the diagonal difference of the standard voltage transformer N1.

[0064] FIG5( a ) is a graph showing the effect of changing the standard voltage transformer S on the contrast difference;

[0065] Figure 5(b) is a graph showing the effect of changing the standard voltage transformer S on the contrast difference.

[0066] Figure 6 Schematic diagram of the process flow for building a voltage transformer error propagation model. DETAILED DESCRIPTION

[0067] A method for modeling and improving the frequency characteristics of an electromagnetic voltage transformer is proposed. The method mainly analyzes the frequency characteristics of the transformer at 20Hz-3000Hz, and obtains a frequency response model under a wide frequency band through simulation modeling. The corresponding error function formula is derived according to the equivalent circuit diagram, and then the error formula related to the core parameters is obtained according to the transfer model. The specific method for improving the transformer performance is obtained through simulation analysis.

[0068] Figure 1 This is the equivalent circuit model diagram of the standard voltage transformer. When the core magnetic circuit saturation is not considered, the main magnetic flux Φ and leakage magnetic flux Φ of the standard voltage transformer are σ1The frequency f of the power supply voltage u1 changes sinusoidally with time t. According to the law of electromagnetic induction, the instantaneous value of the induced electromotive force generated by the main magnetic flux on the winding is:

[0069]

[0070] Then the effective value of the induced electromotive force E and the main magnetic flux amplitude Φ m The relationship is:

[0071]

[0072] In formula (15): Φ m is the main magnetic flux amplitude; B m is the amplitude of magnetic induction intensity; N is the number of winding turns; S is the cross-sectional area of ​​the core.

[0073] Without considering the leakage flux and winding direct resistance voltage drop, it is assumed that u1≈e1, U1≈E, and U1 is the effective value of the power supply voltage. Under the premise that the transformer structure parameters (S, N) remain unchanged, when U1 is the same, B m It is inversely proportional to its frequency f, so when the frequency f of U1 decreases, the magnetic induction intensity of the iron core will increase. The rated working magnetic induction intensity of the standard voltage transformer iron core is often greater than 1.0T, and it is likely to saturate as the frequency f decreases. Therefore, in order to keep the magnetic induction intensity of the iron core unchanged, when the frequency f decreases, it is necessary to increase the cross-sectional area S of the iron core or increase the number of winding turns N.

[0074] Figure 1 In the figure, L1 and R1 are the leakage inductance and DC resistance of the primary winding, L m , R m are the magnetizing inductance and magnetizing resistance, L2 and R2 are the secondary winding leakage inductance and DC resistance (converted to the primary side), Z L It is a standard voltage transformer load (converted to the primary side), U1 is the primary voltage, and U2 is the secondary voltage (converted to the primary side).

[0075] According to the relevant parameters in Table 1, the value of μ can be derived. By comparing the simulation and measured models, the reliability and accuracy of the μ value calculated by the formula are proved, which provides corresponding parameter support for the next step of simulation of standard voltage transformer at 20Hz-3000Hz.

[0076] Table 1 Core parameters

[0077]

[0078] Figure 2 The frequency response curve of the standard voltage transformer ratio difference is shown in Figure 1. The corresponding error function formula is derived through the equivalent circuit model. Substituting the parameter values ​​in Table 1, the frequency response curve of the standard voltage transformer at 20Hz-3000Hz is obtained. Figure 2 It can be seen that when the frequency is between 20 Hz and 700 Hz, the ratio difference meets ±0.05%, and the ratio difference at 700 Hz is -0.048%. However, when the frequency exceeds 700 Hz or even greater, the ratio difference does not meet the accuracy requirement.

[0079] Figure 3 This is the frequency response curve of the standard voltage transformer angle difference. Through simulation analysis, it is found that when the frequency is between 20Hz and 700Hz, the angle difference is within 2', and the angle difference at 700Hz is -1.95'. However, when the frequency exceeds 700Hz or even greater, the angle difference does not meet the accuracy requirements.

[0080] Figures 4(a), 4(b), 5(a), and 5(b) are the influence curves of changing the number of turns and cross-sectional area of ​​the standard voltage transformer on the contrast difference and the angle difference, respectively. The error function formula related to the core parameters is derived through the transfer model and substituted into the data in Table 1.

[0081] From the analysis of Figure 4(a), it can be seen that when the number of primary winding turns increases by 10%, the ratio difference of the standard voltage transformer at 20Hz-3000Hz increases, and when the number of primary winding turns decreases by 10%, the ratio difference decreases; from the analysis of Figure 4(b), it can be seen that when the number of primary winding turns increases by 10%, the angle difference of the standard voltage transformer at 20Hz-3000Hz increases, and when the number of primary winding turns decreases by 10%, the angle difference decreases.

[0082] From the analysis of Figure 5(a), it can be seen that when the cross-sectional area of ​​the iron core is increased by 10%, the ratio difference of the standard voltage transformer at 20Hz-3000Hz decreases, and when the cross-sectional area of ​​the iron core is reduced by 10%, the ratio difference increases; from the analysis of Figure 5(b), it can be seen that when the cross-sectional area of ​​the iron core is increased by 10%, the angular difference of the standard voltage transformer at 20Hz-3000Hz decreases, and when the cross-sectional area of ​​the iron core is reduced by 10%, the angular difference increases.

[0083] Therefore, reducing the number of turns of the primary winding or increasing the cross-sectional area of ​​the core will reduce the error value of the standard voltage transformer. This method can effectively improve the performance of the transformer.

Claims

1. A method for modeling and improving the frequency characteristics of an electromagnetic voltage transformer, characterized in that The following steps are involved: Step 1: Frequency modeling steps: An equivalent circuit model of a standard voltage transformer is established, and the excitation impedance value of the standard voltage transformer is obtained based on the existing core parameters by using the complex permeability method. Secondly, the error function formula of the standard voltage transformer is analyzed and obtained through the equivalent circuit model, and the error frequency response curve of the standard voltage transformer is obtained through simulation calculation. Step 2: Performance improvement steps: The correlation between the error value and the number of turns and cross-sectional area of ​​the standard voltage transformer is analyzed. By increasing or decreasing the number of turns of the primary winding or the cross-sectional area of ​​the core, the influence of the number of turns and cross-sectional area on the error is characterized to improve the error accuracy of the standard voltage transformer.

2. According to claim 1, a method for frequency characteristic modeling and performance improvement of an electromagnetic voltage transformer is characterized in that: The step 1 comprises the following steps: Step 1.1: First, obtain the corresponding excitation impedance value according to its equivalent circuit model. For the standard voltage transformer taking into account the wide frequency, consider the frequency characteristics of the excitation impedance; The nonlinearity of excitation impedance is affected by the excitation characteristics of ferromagnetic materials and includes two parameters: one is magnetic permeability, which represents the ability of ferromagnetic materials to conduct magnetic flux, expressed by real magnetic permeability μ, which is defined as the ratio of magnetic flux density B to magnetic field intensity H, extracted from the DC magnetization curve; the other is the core loss angle, which represents the phase angle of magnetic induction intensity B lagging behind the magnetic field intensity H under AC excitation due to the influence of ferromagnetic loss, expressed by θ; The real and imaginary parts of the complex permeability are: In formula (1), μ' is the real part of the complex permeability, B m is the real part of magnetic flux density, H m is the real part of magnetic field intensity, θ is the core loss angle; In formula (2), μ” is the imaginary part of the complex magnetic permeability; The core loss tangent is: When a DC current flows through the coil, the loss generated is considered to be a DC loss. The corresponding DC resistance is determined by the material and geometric structure of the coil. The calculation formula is as follows: In formula (4), R1 is the DC resistance of the coil, ρ is the wire resistivity, l1 is the length of the primary winding wire, and S is the cross-sectional area of ​​the wire; The leakage inductance of the transformer primary winding is estimated by analytical method, and the calculation formula is as follows: In formula (5), N1 represents the number of turns of the primary winding, p is the average turn length of the winding, h is the height of the winding, Δ, d1 and d2 are the thickness of the insulation layer between the primary and secondary windings, the thickness of the primary winding, and the thickness of the secondary winding respectively; μ0 is the vacuum permeability; In the calculation of transformer parameters, the excitation impedance value is related to the real and imaginary parts of the complex permeability. The corresponding relationship is as follows: In formula (6), L m is the excitation inductance; l is the length of the iron core magnetic path; In formula (7), R m is the excitation resistance, ω is the angular frequency of the applied signal; Step 1.2: The errors of standard voltage transformers include ratio error and phase error. Ratio error refers to the error caused by the difference between the actual transformation ratio and the rated transformation ratio during the measurement of the voltage transformer; phase error refers to the phase difference between the primary voltage phasor and the secondary voltage phasor; The difference between the secondary voltage and the primary voltage of the standard voltage transformer is: ΔU(ω)=U2(ω)-U1(ω)=-I2(ω)(Z1(ω)+Z2(ω))-I m (ω)Z m (ω)(8); In formula (8), ΔU(ω) is the difference between the primary winding voltage and the secondary winding voltage, U1(ω) is the primary winding voltage value, U2(ω) is the secondary winding voltage value, I2(ω) is the current value flowing through the secondary winding, Z1(ω) is the primary winding impedance value, Z2(ω) is the secondary winding impedance value, and I m (ω) is the current value flowing through the excitation impedance, Z m (ω) is the excitation impedance value; Then the error of the standard voltage transformer is: In formula (9), U1(ω) is the primary winding voltage value, Z L (ω) is the load value; According to the definition of mutual inductor error, the calculation formulas for the no-load ratio difference and phase difference are: In formula (10), ε0(ω) is the no-load ratio difference; δ0(ω)=∠(Z1(ω)+Z m (ω))-∠Z m (oh) (11); In formula (11), δ0(ω) is the no-load phase difference, ∠(Z1(ω)+Z m (ω)) is the phase sum of the primary impedance and the excitation impedance, ∠Z m (ω) is the phase value of the excitation impedance; Analysis of the no-load error characteristics of standard voltage transformers: According to R1, L1, R m , L m The corresponding calculation formula is substituted into the no-load error formula, and the no-load error calculation formula related to the complex permeability and core parameters is derived as follows: By substituting the corresponding core parameters into the above formula, the wide-frequency response curve of the standard voltage transformer at 20Hz~3000Hz is obtained.

3. The method for frequency characteristic modeling and performance improvement of an electromagnetic voltage transformer according to claim 1, characterized in that: The step 2 comprises the following steps: Step 2.1: The number of turns and cross-sectional area of ​​the standard voltage transformer will affect the no-load error. The influence of changing the number of turns and cross-sectional area on the no-load ratio difference and angle difference is analyzed through simulation calculation; Step 2.2: By increasing or decreasing the number of primary winding turns or the cross-sectional area of ​​the core by 10%, the corresponding no-load error value is obtained. When the number of primary winding turns is reduced, the no-load ratio difference and angle difference of the standard voltage transformer at 20Hz-3000Hz are reduced; when the cross-sectional area of ​​the core is increased, the ratio difference decreases, and the angle difference does not change much, but the reduction in the angle difference can still be reflected at high frequencies; therefore, reducing the number of primary winding turns or increasing the cross-sectional area of ​​the core can reduce the error value of the standard voltage transformer.

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