Transformer iron core residual magnetism calculation method and system based on voltage integration and JA inverse model

Abstract

The invention provides a transformer iron core residual magnetism calculation method and system based on voltage integration and a JA inverse model. The method comprises the steps that voltage and current data of a primary winding of a transformer are collected; integrating the voltage data through a voltage integration method to calculate integral residual magnetic flux; and on the basis of the fitting excitation inrush current waveform obtained through simulation and the actual excitation inrush current waveform, an integral residual magnetism error is calculated until the integral residual magnetism error is within a threshold value range, and then the final integral residual magnetic flux serves as a calculation result of the residual magnetism of the transformer iron core. According to the method, the residual magnetism of the transformer iron core can be determined more quickly in actual engineering, and the accuracy is considered.

Description

Technical Field

[0001] This invention relates to the field of transformer core residual magnetism calculation technology, and particularly to a method and system for calculating transformer core residual magnetism based on voltage integral and JA inverse model, computer storage medium, and electronic equipment. Background Technology

[0002] With the nation's increasing emphasis on the smart grid strategy, ensuring the reliable operation of the power grid has become the cornerstone of power system progress. Modern power grids not only need to handle large-scale power transmission but also cope with increasingly complex operating environments and demands. Against this backdrop, transformers, as core equipment in the power grid architecture, directly impact the overall stability of the grid through their performance and efficiency. Rapid switching on and off is an essential part of power grid operation; however, this process inevitably generates a large amount of inrush current, which not only poses a potential threat to equipment but may also cause frequency fluctuations and voltage instability in the power grid. Therefore, research on inrush current suppression strategies has become extremely critical. This is not only related to the durability of equipment but also to the economic operation and environmental goals of the power grid.

[0003] Currently, the most effective strategy for suppressing inrush current is phase-selective closing technology. This is primarily applied at the moment a transformer connects to the grid. By accurately determining and selecting the appropriate closing phase through residual magnetism, the peak inrush current at the instant of closing is reduced. Specifically, sensors installed on the switchgear or transformer monitor the grid voltage and current in real time. By calculating the relevant phase difference information, the optimal closing point is determined, thereby reducing the generation of inrush current.

[0004] Calculating remanence using the voltage integration method is a simple and readily available approach; the remanence is obtained by integrating the voltage across the transformer after the switch is turned off. However, determining the upper and lower limits of integration using this method remains a research challenge. Furthermore, the magnitude of the error generated by voltage integration is difficult to calculate. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention discloses a method for calculating remanence based on voltage integral and the JA inverse model, comprising the following steps:

[0006] A method for calculating the residual magnetism of transformer cores based on voltage integral and JA inverse model includes the following steps:

[0007] Collect primary winding voltage data and primary winding current data of the transformer;

[0008] Within the integration time constrained by the lower and upper limits of integration, the primary winding voltage data is integrated using the voltage integration method to calculate the integrated residual magnetic flux of the transformer core.

[0009] Based on the primary winding voltage data and primary winding current data, an inverse JA model is established. Furthermore, the fitted excitation inrush current waveform is obtained by integrating the residual magnetic flux and JA inverse model simulation. Based on the fitted excitation inrush current waveform and the actual excitation inrush current waveform, the integrated residual magnetization error is calculated.

[0010] The integral residual magnetism error is compared with a preset threshold range. When the integral residual magnetism error is not within the threshold range, the integration time of the voltage integral method is adjusted, and then the integral residual flux is recalculated and the fitted excitation inrush current waveform is obtained again until the integral residual magnetism error is within the threshold range. Then the final integral residual flux is used as the calculation result of the transformer core residual magnetism.

[0011] Preferred,

[0012] Within the integration time constrained by the lower and upper limits of integration, the primary winding voltage data is integrated using the voltage integration method to calculate the integrated residual flux of the transformer core, including:

[0013] Under power frequency voltage, observe the voltage-time waveform of the primary winding. If |t1-t2|≤0.001s and |U1-U2|≥U / 2, then it is considered that there is a tripping action between t1 and t2. Where U is the voltage amplitude, U1 is the instantaneous voltage value at time t1, and U2 is the instantaneous voltage value at time t2.

[0014] The time point before the first sine wave peak before the tripping action is taken as the lower limit of integration t; the time constant is determined by the circuit parameters or the tripping waveform, and it is assumed that the tripping voltage decays to zero after five times the time constant τ. The time point when the tripping voltage decays to zero is t+5*τ as the upper limit of integration.

[0015] By integrating the voltage between the lower and upper limits of integration, the integrated residual magnetic flux of the transformer core is obtained according to the following formula:

[0016] (1)

[0017] In the formula, Φ r1 e1 represents the integral residual flux; e1 is the primary winding voltage data; N1 is the number of turns in the primary winding coil.

[0018] Preferred,

[0019] Further simulations using the integrated residual flux and the JA inverse model were conducted to obtain the fitted inrush current waveform. Based on the fitted inrush current waveform and the actual inrush current waveform, the integrated residual flux error was calculated, including:

[0020] Using the magnetic induction intensity B of the primary winding as the input of the JA inverse model, the output magnetic field intensity H is used to obtain the fitted excitation inrush current waveform.

[0021] The actual inrush current waveform generated at the instant of switching on the primary winding of the transformer was obtained by using a closing experiment;

[0022] The percentage error of the fitted excitation inrush current waveform is obtained by dividing the absolute value of the difference between the maximum value of the fitted excitation inrush current waveform and the maximum value of the actual inrush current waveform by the maximum value of the actual inrush current waveform. This percentage error is then used as the integral residual magnetism error.

[0023] Preferred,

[0024] The preset threshold range is within 30%, based on the following: according to actual engineering experience, the inrush current after phase selection and closing needs to be suppressed to within 30% error.

[0025] Preferred,

[0026] Using the magnetic flux density B of the primary winding as the input to the JA inverse model, and outputting the magnetic field strength H, the fitted excitation inrush current waveform is obtained, including:

[0027] When a power frequency voltage is applied to the unloaded primary winding of a transformer on the secondary side, the following equation is obtained according to the law of magnetic flux conservation:

[0028] (2)

[0029] In the formula, U1, R1, and N1 represent the primary winding voltage, coil resistance, and number of coil turns, respectively; Φ1 represents the total magnetic flux of the iron core after the switch is closed.

[0030] From equation (2), we obtain the following equation:

[0031] (3)

[0032] Among them, U m The rated voltage of the transformer is α, which represents the voltage closing angle at t=0, i.e., the instant the switch is closed, and ω is the angular frequency.

[0033] Solving the differential equation of formula (3), we obtain the function of the total magnetic flux Φ1 of the iron core changing with time:

[0034] (4)

[0035] In the formula,

[0036] θ = arctan(ωL1 / R1). Since the resistive component accounts for a very small proportion of the equivalent impedance seen from the primary side of the transformer when it is running under no-load, R1≈0, so θ≈90°.

[0037] L1 represents the self-inductance coefficient of the primary winding.

[0038] A is a constant representing the amplitude of the transient magnetic flux, which is calculated using the initial conditions when the transformer is switched on, i.e., t=0.

[0039] because It is a constant term, so it is called steady-state magnetic flux and denoted as Φ. m The following formula exists:

[0040] (5)

[0041] According to the law of conservation of magnetic flux, the magnetic flux inside the iron core is equal before and after closing the circuit and should also be equal to the integral residual magnetic flux Φ. r1 , put t=0 and Φ r1 Substituting equation (5) into equation (4), we get the following equation:

[0042] (6)

[0043] Furthermore, we can obtain:

[0044] (7)

[0045] In the formula, Φ r1 Φ is the integrated residual magnetic flux; Φ1 is the total magnetic flux of the transformer core after closing; Φ m For steady-state magnetic flux;

[0046] This leads to the relationship between the magnetic induction intensity B of the primary winding and time, B(t).

[0047] Then, input B(t) into the JA inverse model to obtain the function H(t) of the primary winding magnetic field strength H changing with time, and obtain the fitted excitation inrush current waveform.

[0048] Preferred,

[0049] The percentage error of the fitted excitation inrush current waveform is obtained by dividing the absolute value of the difference between the maximum value of the fitted excitation inrush current waveform and the maximum value of the actual inrush current waveform by the maximum value of the actual inrush current waveform. This percentage error is then used as the integral residual magnetism error, including:

[0050] Using the actual excitation inrush current waveform and the inherent structural parameters of the transformer, the magnetic field strength H corresponding to the instant after closing is calculated, and the magnetic induction intensity B is obtained by B = μH, where μ is the permeability of the transformer core material.

[0051] The total magnetic flux Φ2 of the transformer core at the instant after closing is obtained by using Φ2=B*S, where S is the cross-sectional area of ​​the transformer core.

[0052] Substituting the total magnetic flux Φ2 of the transformer core and the closing angle at the instant after closing into the following formula, we can obtain the inverse residual magnetic flux Φ. r2 :

[0053]

[0054] Based on the reverse calculation of the residual magnetic flux Φ r2 With the integral residual flux Φ r1 Calculate the integral remanence error:

[0055] Find Φ r2 With Φ r1 The absolute value of the difference, and further divided by Φ. r2 To calculate the integral residual magnetism error.

[0056] Preferred,

[0057] The integral residual magnetization error is compared with a preset threshold range. When the integral residual magnetization error is not within the threshold range, the integration time of the voltage integration method is adjusted, and then the integral residual flux is recalculated and the fitted excitation inrush current waveform is obtained again until the integral residual magnetization error is within the threshold range. Then, the final integral residual flux is used as the calculation result of the transformer core residual magnetism, including:

[0058] The first threshold Φ is calculated using the following formula. rmax :

[0059]

[0060] Among them, the maximum value of the total magnetic flux of the iron core Φ max For steady-state magnetic flux Φ m 1.3 times;

[0061] Further based on the first threshold Φ rmax With Φ r2 The error calculation is based on a preset threshold range:

[0062] Φ rmax With Φ r2 The absolute value of the difference, divided by Φ r2 As a preset threshold range;

[0063] If the integral residual magnetism error is compared with a preset threshold range, and the integral residual magnetism error is not within the threshold range, the integration time of the voltage integration method is adjusted until the error is within the preset threshold range. The final integral residual magnetic flux Φ is then calculated. r1 The result is used as the calculation result of the residual magnetism of the transformer core.

[0064] Furthermore, this invention also provides a remanence calculation system based on voltage integral and JA inverse model, which includes:

[0065] The data acquisition module is used to acquire primary winding voltage data and primary winding current data of the transformer.

[0066] The integration module is used to integrate the primary winding voltage data using the voltage integration method within the integration time constrained by the lower and upper limits of integration, in order to calculate the integrated residual magnetic flux of the transformer core.

[0067] The integral residual magnetism error calculation module is used to establish the JA inverse model based on the primary winding voltage data and primary winding current data, and further obtain the fitted excitation inrush current waveform through the simulation of integral residual magnetic flux and JA inverse model, and calculate the integral residual magnetism error based on the fitted excitation inrush current waveform and the actual excitation inrush current waveform.

[0068] The comparison module is used to compare the integral residual magnetism error with a preset threshold range. When the integral residual magnetism error is not within the threshold range, the integration time of the voltage integration method is adjusted, and then the integral residual flux is recalculated and the fitted excitation inrush current waveform is obtained again until the integral residual magnetism error is within the threshold range. Then the final integral residual flux is used as the calculation result of the transformer core residual magnetism.

[0069] Furthermore, the present invention discloses a computer storage medium comprising computer instructions that, when executed on a computer, cause the computer to perform any of the methods described above.

[0070] Furthermore, the present invention discloses an electronic device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described in any of the preceding descriptions.

[0071] Compared with the prior art, the beneficial effects of this invention are as follows:

[0072] This invention solves the problem of difficulty in selecting the upper limit of voltage integration, and provides a method for calculating the voltage integration result by using inrush current after closing the circuit based on fitting the hysteresis loop using the JA model. This invention analyzes the residual magnetism error by integrating the residual magnetic flux and simulating the inrush current waveform during closing, and then calculates the residual magnetism using the closing inrush current to iteratively calculate the integrated residual magnetic flux when necessary until it meets the preset threshold range and satisfies the accuracy of the calculation result. Attached Figure Description

[0073] Figure 1 This is a flowchart illustrating a method for calculating the residual magnetism of a transformer core based on voltage integral and JA inverse model, as described in one embodiment of the present invention.

[0074] Figure 2 This is a schematic diagram of a transformer single-phase excitation test circuit in one embodiment of the present invention;

[0075] Figure 3This is a transformer tripping voltage waveform in one embodiment of the present invention;

[0076] Figure 4 This is a fitted excitation inrush current waveform diagram in one embodiment of the present invention;

[0077] Figure 5 This is an actual excitation inrush current waveform diagram in one embodiment of the present invention;

[0078] Figure 6 This is a measurement and fitting diagram of hysteresis loop in one embodiment of the present invention;

[0079] Figure 7 This is a schematic diagram of a wideband voltage sensor measurement system in one embodiment of the present invention. Detailed Implementation

[0080] The following will refer to the appendix. Figures 1 to 7 Specific embodiments of the invention are described in more detail below. While specific embodiments of the invention are shown in the accompanying drawings, it should be understood that the invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the invention and to fully convey its scope to those skilled in the art.

[0081] It should be noted that certain terms are used in the specification and claims to refer to predetermined components. Those skilled in the art will understand that different terms may be used to refer to the same component. This specification and claims do not distinguish components based on differences in terminology, but rather on differences in function. The terms "comprising" or "including" used throughout the specification and claims are open-ended and should be interpreted as "comprising but not limited to." The following descriptions are preferred embodiments for carrying out the invention; however, these descriptions are for the purpose of understanding the general principles of the specification and are not intended to limit the scope of the invention. The scope of protection of this invention is determined by the appended claims.

[0082] To facilitate understanding of the embodiments of the present invention, the following will provide further explanation and description with reference to the accompanying drawings and several specific embodiments, and the accompanying drawings do not constitute a limitation on the embodiments of the present invention.

[0083] In one embodiment, the present invention discloses a method for calculating the residual magnetism of a transformer core based on voltage integral and JA inverse model, comprising the following steps:

[0084] Collect primary winding voltage data and primary winding current data of the transformer;

[0085] Within the integration time constrained by the lower and upper limits of integration, the primary winding voltage data is integrated using the voltage integration method to calculate the integrated residual magnetic flux of the transformer core.

[0086] Based on the primary winding voltage data and primary winding current data, an inverse JA model is established. Furthermore, the fitted excitation inrush current waveform is obtained by integrating the residual magnetic flux and JA inverse model simulation. Based on the fitted excitation inrush current waveform and the actual excitation inrush current waveform, the integrated residual magnetization error is calculated.

[0087] The integral residual magnetism error is compared with a preset threshold range. When the integral residual magnetism error is not within the threshold range, the integration time of the voltage integral method is adjusted, and then the integral residual flux is recalculated and the fitted excitation inrush current waveform is obtained again until the integral residual magnetism error is within the threshold range. Then the final integral residual flux is used as the calculation result of the transformer core residual magnetism.

[0088] It can be seen that the present invention solves the problem of the difficulty in selecting the upper limit of voltage integration, and provides a method for calculating the voltage integration result by using the inrush current after closing the circuit based on fitting the hysteresis loop using the JA model. The present invention analyzes the residual magnetism error by integrating the residual magnetic flux and simulating the inrush current waveform during closing, and then uses the closing inrush current to calculate the residual magnetism to iteratively calculate the integrated residual magnetic flux when necessary until it meets the preset threshold range and satisfies the accuracy of the calculation result.

[0089] In another embodiment,

[0090] Within the integration time constrained by the lower and upper limits of integration, the primary winding voltage data is integrated using the voltage integration method to calculate the integrated residual flux of the transformer core, including:

[0091] Under power frequency voltage, observe the voltage-time waveform of the primary winding. If |t1-t2|≤0.001s and |U1-U2|≥U / 2, then it is considered that there is a tripping action between t1 and t2. Where U is the voltage amplitude, U1 is the instantaneous voltage value at time t1, and U2 is the instantaneous voltage value at time t2.

[0092] The time point before the first sine wave peak before the tripping action is taken as the lower limit of integration t; the time constant is determined by the circuit parameters or the tripping waveform, and it is assumed that the tripping voltage decays to zero after five times the time constant τ. The time point when the tripping voltage decays to zero is t+5*τ as the upper limit of integration.

[0093] By integrating the voltage between the lower and upper limits of integration, the integrated residual magnetic flux of the transformer core is obtained according to the following formula:

[0094] (1)

[0095] In the formula, Φ r1 e1 represents the integral residual flux; e1 is the primary winding voltage data; N1 is the number of turns in the primary winding coil.

[0096] In another embodiment,

[0097] Further simulations using the integrated residual flux and the JA inverse model were conducted to obtain the fitted inrush current waveform. Based on the fitted inrush current waveform and the actual inrush current waveform, the integrated residual flux error was calculated, including:

[0098] Using the magnetic induction intensity B of the primary winding as the input of the JA inverse model, the output magnetic field intensity H is used to obtain the fitted excitation inrush current waveform.

[0099] The actual inrush current waveform generated at the instant of switching on the primary winding of the transformer was obtained by using a closing experiment;

[0100] The percentage error of the fitted excitation inrush current waveform is obtained by dividing the absolute value of the difference between the maximum value of the fitted excitation inrush current waveform and the maximum value of the actual inrush current waveform by the maximum value of the actual inrush current waveform. This percentage error is then used as the integral residual magnetism error.

[0101] In another embodiment,

[0102] The preset threshold range is within 30%, based on the following: according to actual engineering experience, the inrush current after phase selection and closing needs to be suppressed to within 30% error.

[0103] In another embodiment,

[0104] Using the magnetic flux density B of the primary winding as the input to the JA inverse model, and outputting the magnetic field strength H, the fitted excitation inrush current waveform is obtained, including:

[0105] When a power frequency voltage is applied to the unloaded primary winding of a transformer on the secondary side, the following equation is obtained according to the law of magnetic flux conservation:

[0106] (2)

[0107] In the formula, U1, R1, and N1 represent the primary winding voltage, coil resistance, and number of coil turns, respectively; Φ1 represents the total magnetic flux of the iron core after the switch is closed.

[0108] From equation (2), we obtain the following equation:

[0109] (3)

[0110] Among them, U m The rated voltage of the transformer is α, which represents the voltage closing angle at t=0, i.e., the instant the switch is closed, and ω is the angular frequency.

[0111] Solving the differential equation of formula (3), we obtain the function of the total magnetic flux Φ1 of the iron core changing with time:

[0112] (4)

[0113] In the formula,

[0114] θ = arctan(ωL1 / R1). Since the resistive component accounts for a very small proportion of the equivalent impedance seen from the primary side of the transformer when it is running under no-load, R1≈0, so θ≈90°.

[0115] L1 represents the self-inductance coefficient of the primary winding.

[0116] A is a constant representing the amplitude of the transient magnetic flux, which is calculated using the initial conditions when the transformer is switched on, i.e., t=0.

[0117] because It is a constant term, so it is called steady-state magnetic flux and denoted as Φ. m The following formula exists:

[0118] (5);

[0119] According to the law of conservation of magnetic flux, the magnetic flux inside the iron core is equal before and after closing the circuit and should also be equal to the integral residual magnetic flux Φ. r1 , put t=0 and Φ r1 Substituting equation (5) into equation (4), we get the following equation:

[0120] (6)

[0121] Furthermore, we can obtain:

[0122] (7)

[0123] In the formula, Φ r1 Φ is the integrated residual magnetic flux; Φ1 is the total magnetic flux of the transformer core after closing; Φ m For steady-state magnetic flux;

[0124] This leads to the relationship between the magnetic induction intensity B of the primary winding and time, B(t).

[0125] Then, input B(t) into the JA inverse model to obtain the function H(t) of the primary winding magnetic field strength H changing with time, and obtain the fitted excitation inrush current waveform.

[0126] In another embodiment,

[0127] The percentage error of the fitted excitation inrush current waveform is obtained by dividing the absolute value of the difference between the maximum value of the fitted excitation inrush current waveform and the maximum value of the actual inrush current waveform by the maximum value of the actual inrush current waveform. This percentage error is then used as the integral residual magnetism error, including:

[0128] Using the actual excitation inrush current waveform and the inherent structural parameters of the transformer, the magnetic field strength H corresponding to the instant after closing is calculated, and the magnetic induction intensity B is obtained by B = μH, where μ is the permeability of the transformer core material.

[0129] The total magnetic flux Φ2 of the transformer core at the instant after closing is obtained by using Φ2=B*S, where S is the cross-sectional area of ​​the transformer core.

[0130] Substituting the total magnetic flux Φ2 of the transformer core and the closing angle at the instant after closing into the following formula, we can obtain the inverse residual magnetic flux Φ. r2 :

[0131]

[0132] Based on the reverse calculation of the residual magnetic flux Φ r2 With the integral residual flux Φ r1 Calculate the integral remanence error:

[0133] Find Φ r2 With Φ r1 The absolute value of the difference, and further divided by Φ. r2 To calculate the integral residual magnetism error.

[0134] In another embodiment,

[0135] The integral residual magnetization error is compared with a preset threshold range. When the integral residual magnetization error is not within the threshold range, the integration time of the voltage integration method is adjusted, and then the integral residual flux is recalculated and the fitted excitation inrush current waveform is obtained again until the integral residual magnetization error is within the threshold range. Then, the final integral residual flux is used as the calculation result of the transformer core residual magnetism, including:

[0136] The first threshold Φ is calculated using the following formula. rmax :

[0137]

[0138] Among them, the maximum value of the total magnetic flux of the iron core Φ max For steady-state magnetic flux Φ m 1.3 times;

[0139] Further based on the first threshold Φ rmax With Φ r2 The error calculation is based on a preset threshold range:

[0140] Φ rmax With Φ r2 The absolute value of the difference, divided by Φ r2 As a preset threshold range;

[0141] If the integral residual magnetism error is compared with a preset threshold range, and the integral residual magnetism error is not within the threshold range, the integration time of the voltage integration method is adjusted until the error is within the preset threshold range. The final integral residual magnetic flux Φ is then calculated. r1 The result is used as the calculation result of the residual magnetism of the transformer core.

[0142] Since the actual secondary protection setting value is generally 1.3 times the rated value, the error of the inrush current after phase selection and closing cannot exceed 30%. This invention calculates the maximum error range of voltage integral residual magnetism by reverse calculation based on the maximum permissible error range of the inrush current. Since the error of voltage integration mainly comes from the uncertainty of the integration time, the voltage integration time is adjusted, for example, by adjusting the upper limit of integration, by adjusting the time constant τ, or by adjusting a multiple of the time constant τ, or by fine-tuning the lower limit of integration, until the error of voltage integral residual magnetism is within the maximum permissible error range. The integral residual flux at this point is the final calculated residual flux of the transformer core.

[0143] It should be noted that after quickly calculating the accurate residual magnetism of the transformer core using the method of this invention, the optimal voltage closing angle can be further calculated using the following formula by employing a synchronous switch to select and close the unloaded transformer. This solves the problem of closing failure caused by inrush current of the converter transformer during high-voltage power transmission.

[0144] { α = − a r c c o s ( Φ r Φ m ) , Φ r < 0 α = [ π − a r c c o s ( Φ r Φ m ) ] , Φ r > 0 ,

[0145] Where, Φ r The result of the calculation of the residual magnetism of the transformer core is given by the above formula, and α is taken as the optimal voltage closing angle.

[0146] To better understand, such as Figures 1 to 5 As shown, this invention discloses a method for calculating the residual magnetism of a transformer core based on voltage integral and the JA inverse model, including:

[0147] Step 1: Based on the key parameters of the UHV converter transformer and fast circuit breaker, construct the experimental platform, including a power frequency power supply, a single-phase transformer, a fast switch, a high-voltage probe and Rogowski coil, and an oscilloscope. The connection method is as follows: Figure 2 As shown, the power frequency power supply, fast switch, and Rogowski coil are connected in series in the primary winding of a single-phase transformer. The high-voltage probe is connected in parallel across the two ends of the primary winding coil of the transformer to measure the voltage of the primary winding. The Rogowski coil measures the primary circuit current. The secondary side of the transformer is unloaded.

[0148] Step 2: Apply voltage to the power supply, and display the voltage and current waveforms on the oscilloscope. At a certain moment, disconnect the fast switch and record the voltage-time change data of the primary winding when the transformer is tripped under single-phase excitation test. Subsequently, close the fast switch and record the current-time waveform data at the moment of closing.

[0149] Step 3, determine the integral residual flux of the transformer using the voltage integration method, including:

[0150] Step 3.1: Process the collected voltage-time data, as shown in the following figure. Figure 3 As shown. According to the judgment condition: under the power frequency voltage, observe the voltage-time waveform. If |t1-t2|≤0.001s and |U1-U2|≥U / 2, then it is considered that there is a tripping action between t1 and t2; where U is the voltage amplitude, U1 is the instantaneous voltage value at time t1, and U2 is the instantaneous voltage value at time t2.

[0151] Step 3.2, according to Figure 3 The time point of the first sine wave peak before the tripping action is taken as the lower limit of integration. Since there is a 90° phase angle between the winding voltage and the core flux, the core flux of the transformer is zero at this time. Taking t=-0.01, the time constant τ is determined by the circuit parameters or the time required for the amplitude of the tripping waveform to decay to 1 / e times. Let "the voltage decays to zero after five times the time constant" be used as the criterion for the end of voltage decay. The time point t+5τ is taken as the upper limit of integration.

[0152] Step 3.3: Integrate the trip voltage waveform between the lower and upper limits of integration. The integral result, calculated using the following formula, is the integrated residual flux of the transformer:

[0153]

[0154] Step 4: Build the JA inverse model using MATLAB to simulate the magnetic properties of the transformer core. The JA inverse model is obtained by measuring the core hysteresis loop and fitting the parameters. Specifically, this includes:

[0155] Step 4.1: Since the traditional JA model takes magnetic field strength H as input and outputs magnetic induction intensity B, the inverse JA model is established to take B as input and output H.

[0156] For example, the hysteresis parameters of the material are first determined by measuring the hysteresis loop of the iron core and fitting the parameters, including: reversible magnetic susceptibility a; irreversible magnetic susceptibility k; domain wall migration coefficient α; saturation magnetization Ms; and coercivity coefficient c.

[0157] The traditional differential form of magnetization M with respect to magnetic field strength H, as shown below, can be rewritten as the differential form of magnetic induction B:

[0158]

[0159] d M d B = [ ( 1 − c ) d M i r r d B e + c μ 0 d M a n d H e 1 + μ 0 ( 1 − α ) ( 1 − c ) d M i r r d B e + c ( 1 − α ) d M a n d H e ]

[0160] In the formula, M an The magnetization is hysteresis-free, expressed in A / m; M irr The irreversible magnetization is represented by δ; δ is the direction coefficient characterizing the change in magnetic field strength, taking 1 when the direction of change is positive and -1 when it is negative; μ0 is the free permeability; B e H e These are the effective magnetic flux density and the effective magnetic field strength, respectively.

[0161] By describing the mathematical language of the above formula in MATLAB as m-language program code, we can obtain the JA inverse model with magnetic induction intensity B as input and magnetic field intensity H as output.

[0162] Step 4.2: If a power frequency voltage is applied to the primary winding of a U-shaped transformer with no secondary load, the following relationship is established for the primary winding based on the principle of magnetic flux conservation:

[0163] .

[0164] Since the current at this time satisfies i1=N1Φ / L1, the formula can be transformed to obtain a function of the magnetic flux of the iron core changing with time:

[0165]

[0166] Φ m Steady-state magnetic flux can be calculated using the following formula:

[0167]

[0168] Step 4.3: Based on the total magnetic flux Φ(t), the relationship between the magnetic induction intensity B of the primary winding coil and time is calculated using Φ=B*S (where S is the area of ​​the primary winding coil). Inputting B(t) into the JA inverse model outputs the function H(t) representing the change of the primary winding magnetic field intensity H over time.

[0169] For example, the current-time waveform can be calculated using the following formula, and the inrush current waveform can be fitted as follows: Figure 4 As shown.

[0170]

[0171] In the formula, I i It is the current passing through the closed magnetic circuit in the primary winding.

[0172] See Figure 4The current-time waveform at the closing moment is shown. The current is very large at the closing moment and then decays. It can be seen that an inrush current will be generated when closing.

[0173] Step 4.4: Subsequently, close the fast switch, and use an oscilloscope to record the actual inrush current waveform generated at the instant of the transformer primary winding combination switch, such as... Figure 5 As shown. By comparing the maximum value of the fitted excitation inrush current waveform with the maximum value of the actual excitation inrush current waveform, the influence of the integral residual magnetization error on the closing inrush current can be analyzed. Furthermore, in the subsequent process, the concept of error and preset threshold range can be used to determine the integration time of the voltage integration method.

[0174] Step 5: Select the data of the first peak of the actual inrush current after closing the circuit breaker, and perform the following sub-steps:

[0175] Step 5.1: Calculate the primary winding magnetic field strength at the instant of closing based on the actual inrush current waveform. Substitute the calculated magnetic field strength H value into the JA inverse model, as follows: Figure 6 As shown, the magnetic induction intensity B of the primary winding is obtained, and the total magnetic flux of the transformer core at the instant of closing is obtained by Φ=B*S.

[0176] Step 5.2: Based on the total magnetic flux of the iron core and the closing angle at the instant of closing, the residual magnetism value is further obtained by reverse calculation. The calculation process is shown in the following formula:

[0177]

[0178] Step 5.3, calculate the inverse remanence value Φ. r2 Integral remanence Φ obtained by integrating with voltage r1 By comparing and verifying the error caused by the voltage integration method, we continuously optimize the integration time until the error meets the standard.

[0179] In another embodiment, an excitation voltage of 1479V is applied to a single-phase transformer, followed by a tripping operation, as follows: Figure 3 As shown, the first winding trip voltage is obtained. It is known that a tripping operation occurs at t=0. The obtained voltage is integrated from the peak voltage before tripping, with an integration time of 5τ, where τ is the time required for the tripping waveform amplitude to decay to 1 / e times, τ=0.003s. Finally, the integrated residual flux Φ is calculated. r1 =0.0022Wb.

[0180] The fast switch closes at a closing angle α = 60°, and the transformer primary winding closing current is recorded, as shown in Figure 5. The peak value of the first peak of the inrush current is I. m =0.1095A, the calculated magnetic field strength H = 57.53 A / m. See here. Figure 6By fitting the hysteresis loop using the JA inverse model, the magnetic flux density B corresponding to the magnetic field strength H is found. Since B = 1.68 T, the actual total magnetic flux Φ = 0.01848 Wb can be further calculated. Furthermore, the residual magnetism Φ derived from the inrush current is obtained. r2 =0.0017Wb.

[0181] It can be seen that the present invention can use the inrush current after closing to reverse the integral residual magnetism before closing, and the hysteresis loop fitted by the JA inverse model is applied in the steps, which increases the accuracy of reversing the residual magnetism from the inrush current.

[0182] At the same time, the integral residual magnetism Φ after the circuit breaker is opened is selected. r1 Substituting 0.0022Wb and the closing angle α=60° into the aforementioned formula, we obtain the flux transformation function Φ(t) after closing. Further utilizing the JA inverse model, we obtain the magnetic field strength function H(t) output by the JA inverse model, and then obtain the current I(t). For example... Figure 4 As shown, this current is the fitted inrush current calculated based on the JA inverse model, with the first peak value I... m0 =0.1005 and the first peak value of the actual inrush current caused by actual closing I m By comparing with 0.1095A, we can observe the integral remanence Φ. r1 The error has a negligible impact on the inrush current. This demonstrates the accuracy and practicality of the method disclosed in this invention.

[0183] It is understood that, before closing the circuit, if there is a certain error in the integral residual magnetism and the error is in line with engineering practice, the present invention can further obtain the peak value of the closing excitation inrush current through the JA inverse model.

[0184] In another embodiment, the present invention employs a wideband voltage sensor, using a GIS hand-window type wideband voltage sensor based on distributed capacitance sensing and integrated impedance transformation as the measurement unit, with a frequency range of 10Hz~100MHz. The wideband voltage sensor is used to acquire the internal voltage of the transformer coil when the circuit breaker is tripped.

[0185] The principle of the capacitance sensor measurement system is as follows: Figure 7 As shown. The high-voltage arm capacitor C1 of the sensor consists of the GIS busbar, the sensing electrode, and the SF6 gas gap between them. SF6 gas capacitors have high stability, and once the structure is fixed, it basically does not change. The low-voltage arm capacitor C2 can be made of polyimide film as the capacitor dielectric. Polyimide film has a relative dielectric constant of 3.4 and a dielectric strength of 100 ~ 300 kV / mm. Its dielectric constant remains basically unchanged with changes in operating frequency and temperature, and it still has good stability over a wide temperature and frequency range.

[0186] During operation, a wideband voltage sensor is installed on the circuit breaker side to obtain the voltage inside the transformer coil when the circuit breaker is tripped. The wideband voltage sensor monitors the transformer's port voltage, calculates the integral value of the voltage waveform at the moment of power failure, and evaluates the residual magnetism of the iron core.

[0187] Furthermore, in another embodiment, the present invention also provides a remanence calculation system based on voltage integral and JA inverse model, comprising:

[0188] The data acquisition module is used to acquire primary winding voltage data and primary winding current data of the transformer.

[0189] The integration module is used to integrate the primary winding voltage data using the voltage integration method within the integration time constrained by the lower and upper limits of integration, in order to calculate the integrated residual magnetic flux of the transformer core.

[0190] The integral residual magnetism error calculation module is used to establish the JA inverse model based on the primary winding voltage data and primary winding current data, and further obtain the fitted excitation inrush current waveform through the simulation of integral residual magnetic flux and JA inverse model, and calculate the integral residual magnetism error based on the fitted excitation inrush current waveform and the actual excitation inrush current waveform.

[0191] The comparison module is used to compare the integral residual magnetism error with a preset threshold range. When the integral residual magnetism error is not within the threshold range, the integration time of the voltage integration method is adjusted, and then the integral residual flux is recalculated and the fitted excitation inrush current waveform is obtained again until the integral residual magnetism error is within the threshold range. Then the final integral residual flux is used as the calculation result of the transformer core residual magnetism.

[0192] Furthermore, in another embodiment, the present invention also discloses a computer storage medium, wherein the storage medium includes computer instructions that, when executed on a computer, cause the computer to perform any of the methods described above.

[0193] Furthermore, in another embodiment, the present invention discloses an electronic device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described in any of the preceding descriptions.

[0194] The basic principles of this application have been described above with reference to specific embodiments. However, it should be noted that the advantages, benefits, and effects mentioned in this application are merely examples and not limitations, and should not be considered as essential features of each embodiment of this application. Furthermore, the specific details disclosed above are for illustrative and facilitative purposes only, and are not limitations. These details do not limit the application to the necessity of employing the aforementioned specific details for implementation.

[0195] The above description has been given for purposes of illustration and description. Furthermore, this description is not intended to limit the embodiments of this application to the forms disclosed herein. Although numerous exemplary aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations thereof.

Claims

1. A method for calculating the residual magnetism of a transformer core based on voltage integral and JA inverse model, characterized in that, It includes the following steps: Collect primary winding voltage data and primary winding current data of the transformer; Within the integration time constrained by the lower and upper limits of integration, the primary winding voltage data is integrated using the voltage integration method to calculate the integrated residual magnetic flux of the transformer core. Based on the primary winding voltage data and primary winding current data, an inverse JA model is established. Furthermore, the fitted excitation inrush current waveform is obtained by integrating the residual magnetic flux and JA inverse model simulation. Based on the fitted excitation inrush current waveform and the actual excitation inrush current waveform, the integrated residual magnetization error is calculated. The integral residual magnetism error is compared with a preset threshold range. When the integral residual magnetism error is not within the threshold range, the integration time of the voltage integral method is adjusted, and then the integral residual flux is recalculated and the fitted excitation inrush current waveform is obtained again until the integral residual magnetism error is within the threshold range. Then the final integral residual flux is used as the calculation result of the transformer core residual magnetism.

2. The method according to claim 1, characterized in that, Preferably, within the integration time constrained by the lower and upper limits of integration, the primary winding voltage data is integrated using the voltage integration method to calculate the integrated residual flux of the transformer core, including: Under power frequency voltage, observe the voltage-time waveform of the primary winding. If |t1-t2|≤0.001s and |U1-U2|≥U / 2, then it is considered that there is a tripping action between t1 and t2. Where U is the voltage amplitude, U1 is the instantaneous voltage value at time t1, and U2 is the instantaneous voltage value at time t2. The time point before the first sine wave peak before the tripping action is taken as the lower limit of integration t; the time constant is determined by the circuit parameters or the tripping waveform, and it is assumed that the tripping voltage decays to zero after five times the time constant τ. The time point when the tripping voltage decays to zero is t+5*τ as the upper limit of integration. By integrating the voltage between the lower and upper limits of integration, the integrated residual magnetic flux of the transformer core is obtained according to the following formula: （1） In the formula, Φ r1 e1 represents the integral residual flux; e1 is the primary winding voltage data; N1 is the number of turns in the primary winding coil.

3. The method according to claim 2, characterized in that, Further simulations using the integrated residual flux and the JA inverse model were conducted to obtain the fitted inrush current waveform. Based on the fitted inrush current waveform and the actual inrush current waveform, the integrated residual flux error was calculated, including: Using the magnetic induction intensity B of the primary winding as the input of the JA inverse model, the output magnetic field intensity H is used to obtain the fitted excitation inrush current waveform. The actual inrush current waveform generated at the instant of switching on the primary winding of the transformer was obtained by using a closing experiment; The percentage error of the fitted excitation inrush current waveform is obtained by dividing the absolute value of the difference between the maximum value of the fitted excitation inrush current waveform and the maximum value of the actual inrush current waveform by the maximum value of the actual inrush current waveform. This percentage error is then used as the integral residual magnetism error.

4. The method according to claim 1, characterized in that, The preset threshold range is within 30%, based on the following: according to actual engineering experience, the inrush current after phase selection and closing needs to be suppressed to within 30% error.

5. The method according to claim 3, characterized in that, Using the magnetic flux density B of the primary winding as the input to the JA inverse model, and outputting the magnetic field strength H, the fitted excitation inrush current waveform is obtained, including: When a power frequency voltage is applied to the unloaded primary winding of a transformer on the secondary side, the following equation is obtained according to the law of magnetic flux conservation: （2） In the formula, U1, R1, and N1 represent the primary winding voltage, coil resistance, and number of coil turns, respectively; Φ1 represents the total magnetic flux of the iron core after the switch is closed. From equation (2), we obtain the following equation: （3） Among them, U m The rated voltage of the transformer is α, which represents the voltage closing angle at t=0, i.e., the instant the switch is closed, and ω is the angular frequency. Solving the differential equation of formula (3), we obtain the function of the total magnetic flux Φ1 of the iron core changing with time: （4） In the formula, θ = arctan(ωL1 / R1). Since the resistive component accounts for a very small proportion of the equivalent impedance seen from the primary side of the transformer when it is running under no-load, R1≈0, so θ≈90°. L1 represents the self-inductance coefficient of the primary winding. A is a constant representing the amplitude of the transient magnetic flux, which is calculated using the initial conditions when the transformer is switched on, i.e., t=0. because It is a constant term, so it is called steady-state magnetic flux and denoted as Φ. m The following formula exists: （5） According to the law of conservation of magnetic flux, the magnetic flux inside the iron core is equal before and after closing the circuit and should also be equal to the integral residual magnetic flux Φ. r1 , put t=0 and Φ r1 Substituting equation (5) into equation (4), we get the following equation: （6） Furthermore, we can obtain: （7） In the formula, Φ r1 Φ is the integrated residual magnetic flux; Φ1 is the total magnetic flux of the transformer core after closing; Φ m For steady-state magnetic flux; This leads to the relationship between the magnetic induction intensity B of the primary winding and time, B(t). Then, input B(t) into the JA inverse model to obtain the function H(t) of the primary winding magnetic field strength H changing with time, and obtain the fitted excitation inrush current waveform.

6. The method according to claim 5, characterized in that, The percentage error of the fitted excitation inrush current waveform is obtained by dividing the absolute value of the difference between the maximum value of the fitted excitation inrush current waveform and the maximum value of the actual inrush current waveform by the maximum value of the actual inrush current waveform. This percentage error is then used as the integral residual magnetism error, including: Using the actual excitation inrush current waveform and the inherent structural parameters of the transformer, the magnetic field strength H corresponding to the instant after closing is calculated, and the magnetic induction intensity B is obtained by B = μH, where μ is the permeability of the transformer core material. The total magnetic flux Φ2 of the transformer core at the instant after closing is obtained by using Φ2=B*S, where S is the cross-sectional area of ​​the transformer core. Substituting the total magnetic flux Φ2 of the transformer core and the closing angle at the instant after closing into the following formula, we can obtain the inverse residual magnetic flux Φ. r2 : ， Based on the reverse calculation of the residual magnetic flux Φ r2 With the integral residual flux Φ r1 Calculate the integral remanence error: Find Φ r2 With Φ r1 The absolute value of the difference, and further divided by Φ. r2 To calculate the integral residual magnetism error.

7. The method according to claim 6, characterized in that, The integral residual magnetization error is compared with a preset threshold range. When the integral residual magnetization error is not within the threshold range, the integration time of the voltage integration method is adjusted, and then the integral residual flux is recalculated and the fitted excitation inrush current waveform is obtained again until the integral residual magnetization error is within the threshold range. Then, the final integral residual flux is used as the calculation result of the transformer core residual magnetism, including: The first threshold Φ is calculated using the following formula. rmax : ， Among them, the maximum value of the total magnetic flux of the iron core Φ max For steady-state magnetic flux Φ m 1.3 times; Further based on the first threshold Φ rmax With Φ r2 The error calculation is based on a preset threshold range: Φ rmax With Φ r2 The absolute value of the difference, divided by Φ r2 As a preset threshold range; If the integral residual magnetism error is compared with a preset threshold range, and the integral residual magnetism error is not within the threshold range, the integration time of the voltage integration method is adjusted until the error is within the preset threshold range. The final integral residual magnetic flux Φ is then calculated. r1 This is the result of the calculation of the residual magnetism of the transformer core.

8. A remanence calculation system based on voltage integral and JA inverse model, characterized in that, It includes: The data acquisition module is used to acquire primary winding voltage data and primary winding current data of the transformer. The integration module is used to integrate the primary winding voltage data using the voltage integration method within the integration time constrained by the lower and upper limits of integration, in order to calculate the integrated residual magnetic flux of the transformer core. The integral residual magnetism error calculation module is used to establish the JA inverse model based on the primary winding voltage data and primary winding current data, and further obtain the fitted excitation inrush current waveform through the simulation of integral residual magnetic flux and JA inverse model, and calculate the integral residual magnetism error based on the fitted excitation inrush current waveform and the actual excitation inrush current waveform. The comparison module is used to compare the integral residual magnetism error with a preset threshold range. When the integral residual magnetism error is not within the threshold range, the integration time of the voltage integration method is adjusted, and then the integral residual flux is recalculated and the fitted excitation inrush current waveform is obtained again until the integral residual magnetism error is within the threshold range. Then the final integral residual flux is used as the calculation result of the transformer core residual magnetism.

9. A computer storage medium, characterized in that, The storage medium includes computer instructions that, when executed on a computer, cause the computer to perform the method according to any one of claims 1 to 7.

10. An electronic device, characterized in that, The electronic device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the method according to any one of claims 1 to 7.

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