Method, system and equipment for predicting temperature rise of voltage transformer caused by ferromagnetic resonance

Abstract

The invention relates to the technical field of voltage transformers, in particular to a method, a system and equipment for predicting temperature rise of a voltage transformer caused by ferromagnetic resonance. According to the method, in a ferromagnetic resonance time period, based on a to-be-predicted ferromagnetic resonance initial equivalent circuit of the voltage transformer, the primary side of a primary and secondary equivalent inductor of the voltage transformer is equivalent to a controlled current source, the secondary side of the primary and secondary equivalent inductor of the voltage transformer is equivalent to a controlled voltage source, and primary equivalent excitation resistors of the voltage transformer are connected to the two ends of the controlled current source in parallel; connecting a voltage transformer equivalent ground capacitor at two ends of the controlled voltage source in parallel, and constructing a target equivalent circuit; and calculating the excitation current of the voltage transformer in the current time step through a numerical calculation method, establishing a three-dimensional model of the to-be-predicted voltage transformer, inputting the excitation current of the voltage transformer in the current time step into finite element simulation software, and obtaining predicted temperature distribution of each computational domain of the voltage transformer in the current time step. According to the invention, the prediction precision of the temperature rise of the voltage transformer caused by ferromagnetic resonance is obviously improved.

Description

Technical Field

[0001] The present invention relates to the technical field of voltage transformers, and in particular to a method, system and device for predicting temperature rise of a voltage transformer caused by ferromagnetic resonance. Background Art

[0002] With the rapid development of my country's power grid, higher requirements have emerged for the safe and stable operation of distribution networks. Electromagnetic potential transformers (PTs) occupy a crucial position in distribution networks, primarily responsible for measuring busbar voltage on the high-voltage side and user electricity consumption. However, in actual operation, external disturbances can cause three-phase system voltage imbalance, leading to saturation of the PT core and a decrease in the magnetizing inductance. This incompatibility with the system's equivalent ground capacitance causes frequent ferromagnetic resonance in the PT, accompanied by numerous harmonics, which is particularly pronounced in low-voltage distribution networks. In this resonant state, the current flowing through the PT windings can jump to tens or even hundreds of times the rated operating current. Because the internal heat of the PT cannot be promptly dissipated to the surrounding air through conduction and convection, the internal temperature of the PT rises rapidly, resulting in a loss of insulation performance and even explosion.

[0003] Voltage transformers in distribution networks are usually installed in distribution cabinets and are small in size, which makes direct measurement extremely difficult. Therefore, there is currently a lack of research on temperature prediction of electromagnetic voltage transformers in distribution networks during ferromagnetic resonance. One study took into account the ferromagnetic resonance of electromagnetic voltage transformers and established a simulation model of a 10kV neutral point ungrounded system based on ATP-EMTP. The effects of leakage reactance and iron loss were taken into account, and the instantaneous disappearance of single-phase grounding fault was used as the excitation mode of ferromagnetic resonance. The effects of factors such as busbar length, PT excitation characteristics, PT DC resistance and single-phase grounding transition resistance on the PT resonant voltage and current waveforms were simulated. Although a large number of ferromagnetic resonance voltage and current waveforms were obtained, the influence of overcurrent on PT temperature was not further considered. Another study combined the actual parameters of a certain type of EMU voltage transformer to establish a 1:1 three-dimensional model of the voltage transformer, measured the excitation characteristic curve of the PT core, calculated the equivalent heat transfer coefficient and equivalent specific heat capacity of the material, set the ambient temperature to 40°C, the primary winding heating power to 0.03W, the secondary winding heating power to 0.04W and 0.03W, and the core power to 3W, and obtained the temperature field of the PT during resonance. However, the heat source in this model is a constant equivalent heat source, which is inconsistent with the real-time change of the heat source power during the resonance of the actual electromagnetic voltage transformer, and the simulation results lack accuracy.

[0004] Existing methods for predicting the temperature rise of distribution network voltage transformers caused by ferromagnetic resonance generally treat the winding and core as a single heat source and set the excitation current to a fixed value. However, during the actual resonance of an electromagnetic voltage transformer, the excitation current varies with the resonance time, resulting in unstable heat source power. Therefore, existing methods have difficulty accurately predicting the temperature of the electromagnetic voltage transformer during resonance, which also makes the electromagnetic voltage transformer's insulation susceptible to burnout due to overheating. To calculate the real-time excitation current, an equivalent circuit is constructed using the DC resistance of the primary winding and the excitation inductance. Under normal operating conditions, the primary excitation resistance and excitation inductance of the voltage transformer are connected in parallel. The primary excitation resistance of the voltage transformer is relatively large, so the excitation resistance has a relatively small impact on the excitation current. Therefore, existing methods often ignore the primary excitation resistance to simplify the excitation current calculation. Furthermore, due to the large load impedance on the PT secondary side, it is usually ignored in the excitation current calculation. This simplification can save excitation current calculation time. However, during the ferroresonance process, the circuit's operating state undergoes significant changes. The primary-side excitation resistance plays a significant role in limiting current, consuming energy, and influencing the resonance's starting conditions, resonant frequency, and amplitude. Ignoring this factor will prevent an accurate description of the actual changes in current and voltage during ferroresonance, leading to deviations in the analysis and calculation of the ferroresonance phenomenon and inaccurate temperature calculations in certain PT calculation domains. Furthermore, the saturation effect of the excitation inductance, a nonlinear characteristic closely related to the excitation current, is also affected by the secondary-side parameters. Ignoring the interaction between this nonlinear characteristic and the secondary-side parameters in the analysis will prevent an accurate understanding of the circuit's true operating state during ferroresonance, reducing the accuracy of voltage transformer temperature predictions under ferroresonance. This makes it difficult for operators to detect equipment overheating risks in advance, hindering the timely implementation of effective preventive measures and impacting the stable operation of the entire distribution network. Summary of the Invention

[0005] To this end, the technical problem to be solved by the present invention is to overcome the existing method for predicting the temperature rise of the distribution network voltage transformer caused by ferromagnetic resonance. The excitation current is set to a fixed value, which is inconsistent with the actual dynamic changes. The method for calculating the excitation current in real time ignores the primary excitation resistance and simplifies the secondary winding into an ideal transformer model or a simple load impedance, resulting in poor temperature prediction accuracy during resonance of the electromagnetic voltage transformer, which makes the insulation of the electromagnetic voltage transformer easily burn out due to overheating.

[0006] To solve the above technical problems, the present invention provides a method for predicting the temperature rise of a voltage transformer caused by ferromagnetic resonance, comprising:

[0007] During the ferromagnetic resonance period, based on the initial equivalent circuit of the voltage transformer ferromagnetic resonance to be predicted, the primary side of the equivalent inductance of the primary and secondary sides of the voltage transformer is equivalent to a controlled current source, and the secondary side is equivalent to a controlled voltage source. The primary equivalent excitation resistance of the voltage transformer is connected in parallel at both ends of the controlled current source, and the equivalent capacitance of the voltage transformer to ground is connected in parallel at both ends of the controlled voltage source to construct the target equivalent circuit of the ferromagnetic resonance of the voltage transformer to be detected;

[0008] Based on the excitation current of the voltage transformer at the previous time step and the core excitation characteristic curve of the voltage transformer with respect to magnetic flux and excitation current, the inductance value of the primary equivalent excitation inductance of the voltage transformer at the previous time step is obtained;

[0009] Based on the target equivalent circuit of the voltage transformer to be tested, the circuit structure parameters and the inductance value of the primary equivalent excitation inductance of the voltage transformer in the previous time step, the excitation current of the voltage transformer in the current time step is calculated by numerical calculation method;

[0010] Using finite element simulation software, a three-dimensional model of the voltage transformer to be predicted is established, and the excitation current of the voltage transformer at the current time step is input into the finite element simulation software to obtain the predicted temperature distribution of each calculation domain in the three-dimensional model of the voltage transformer at the current time step.

[0011] Preferably, the ferromagnetic resonance target equivalent circuit of the voltage transformer to be detected includes:

[0012] The equivalent resistance of the center point to ground, one end of which is connected to the positive pole of the power supply and the other end is grounded;

[0013] The line equivalent resistor has one end connected to the negative pole of the power supply and the other end connected to the high potential end of the line equivalent capacitance to ground;

[0014] The equivalent capacitance of the line to ground, with its low potential end grounded;

[0015] A controlled current source is connected in parallel with the primary equivalent excitation resistance of the voltage transformer and the primary equivalent excitation inductance of the voltage transformer to form a parallel circuit;

[0016] A primary equivalent DC resistance of the voltage transformer, one end of which is connected to the line equivalent resistance, and the other end of which is connected to the parallel circuit consisting of the controlled current source, the primary equivalent excitation resistance of the voltage transformer, and the primary equivalent excitation inductance of the voltage transformer;

[0017] a controlled voltage source connected in parallel with the equivalent capacitance of the voltage transformer to ground;

[0018] The voltage transformer is equivalent to the ground capacitance, and its low potential end is grounded.

[0019] Preferably, the circuit structure parameters include: the effective value of the power supply voltage, the resistance of the line equivalent resistance, the capacitance of the line-to-ground equivalent capacitance, the resistance of the primary equivalent DC resistance of the voltage transformer, the inductance of the primary equivalent excitation inductance, and the core excitation characteristic curve of the voltage transformer regarding the resonant voltage and excitation current.

[0020] Preferably, the step of calculating the excitation current of the voltage transformer at the current time step by a numerical calculation method based on the target equivalent circuit of the voltage transformer to be detected, the circuit structure parameters, and the inductance value of the primary equivalent excitation inductance of the voltage transformer at the previous time step includes:

[0021] Using the node voltage method, a node voltage equation is established for each node in the target equivalent circuit of the voltage transformer to be tested for ferromagnetic resonance. The circuit structure parameters and the inductance value of the primary equivalent excitation inductance of the voltage transformer at the previous time step are substituted into the node voltage equation to obtain a set of equations for all node voltages at the current time step.

[0022] The core excitation characteristic curve of the voltage transformer with respect to the resonant voltage and the excitation current is divided into multiple linear segments by a piecewise linear method, and a linear equation of the excitation current and the resonant voltage in each linear segment is obtained;

[0023] Based on the equations for all node voltages at the current time step and the linear equations for the excitation current and resonant voltage in each linear segment, a differential equation for the target equivalent circuit of the ferromagnetic resonance of the voltage transformer to be detected at the current time step is constructed;

[0024] By using the trapezoidal integration method, the differential equation of the target equivalent circuit of the ferromagnetic resonance of the voltage transformer to be tested at the current time step is approximately integrated to obtain the approximate value of the excitation current of the voltage transformer at the current time step;

[0025] The excitation current approximation of the voltage transformer at the current time step is corrected by the Newton-Raphson method to obtain the excitation current of the voltage transformer at the current time step.

[0026] Preferably, the step of dividing the core excitation characteristic curve of the voltage transformer with respect to the resonant voltage and the excitation current into a plurality of linear segments by a piecewise linear method and obtaining a linear equation of the excitation current and the resonant voltage in each linear segment comprises:

[0027] Determine the number of intervals that need to be divided into the core excitation characteristic curve of the voltage transformer with respect to the resonant voltage and the excitation current and the boundaries of each interval. For the interval [a, b], based on the function values f(a) and f(b) of the core excitation characteristic curve of the voltage transformer with respect to the resonant voltage and the excitation current corresponding to the interval endpoints a and b, construct the equivalent linear function f1(x) of the core excitation characteristic curve of the voltage transformer with respect to the resonant voltage and the excitation current in the interval [a, b]. The construction formula is:

[0028]

[0029] The linear equations of the excitation current and resonant voltage in the linear segment corresponding to the interval [a, b] are:

[0030] I ′ =∫ a b f1(U X )dx

[0031] Among them, f1(U X ) is the equivalent linear function obtained by linearly approximating the core excitation characteristic curve of the voltage transformer with respect to the resonant voltage and the excitation current on the interval [a, b], a is the left endpoint of the interval [a, b], b is the right endpoint of the interval [a, b], f(a) is f(U X ) in U X = the function value at a, f(b) is f(U X ) in U X = the function value at b, f(U X ) is the core excitation characteristic curve of the voltage transformer regarding the resonant voltage and excitation current, U X is the resonant voltage, I ′ To represent the equivalent linear function f1(U X ) is the excitation current obtained by integrating .

[0032] Preferably, the step of inputting the excitation current of the voltage transformer at the current time step into finite element simulation software to obtain the predicted temperature distribution of each calculation domain in the three-dimensional model of the voltage transformer at the current time step includes:

[0033] Set the voltage transformer material parameters in the finite element simulation software;

[0034] Set the bottom surface temperature of the voltage transformer to a constant temperature, and set the voltage transformer heat transfer coefficient, external air temperature, and initial temperature of the voltage transformer material. Set the voltage transformer material to solid, and set the physical field boundary condition on the outer surface of the voltage transformer to "convective heat flux."

[0035] Set the primary and secondary terminals of the voltage transformer group. Set the physics interface for the voltage transformer core to "Ampere's Law in Solids," the loss calculation to "Steinmetz" loss model, and the physics settings for the voltage transformer primary winding, core, and secondary winding to "A-field specification fixed."

[0036] Set the maximum and minimum cell sizes, and the meshing method to "Free Tetrahedron Mesh" to divide the 3D voltage transformer model into multiple computational domains.

[0037] Based on the primary winding current of the voltage transformer, the secondary winding current of the voltage transformer and the excitation current of the voltage transformer at the current time step, the vector magnetic potential of each computational domain at the current time step is calculated;

[0038] Based on the vector magnetic potential of each computational domain at the current time step, the predicted temperature distribution of each computational domain in the three-dimensional model of the voltage transformer at the current time step is obtained through the set temperature rise solution algorithm.

[0039] Preferably, the material parameters of the voltage transformer include: constant-pressure heat capacity, thermal conductivity, and material density of the voltage transformer insulation; constant-pressure heat capacity, thermal conductivity, material density, relative dielectric constant, conductivity, and effective magnetic field modulus of the voltage transformer core; the number of turns of the primary winding and the secondary winding of the voltage transformer, conductor conductivity, conductor cross-sectional area, constant-pressure heat capacity, thermal conductivity, material density, relative dielectric constant, and relative magnetic permeability of the voltage transformer.

[0040] Preferably, the temperature rise solution algorithm includes: heat conduction control equation, heat convection control equation, and heat radiation control equation.

[0041] The present invention also provides a system for predicting temperature rise of a voltage transformer caused by ferromagnetic resonance, comprising:

[0042] An equivalent circuit construction module is used to, within a ferromagnetic resonance period, based on an initial equivalent circuit of the voltage transformer ferromagnetic resonance to be predicted, treat the primary side of the voltage transformer's primary and secondary equivalent inductance as equivalent to a controlled current source, and the secondary side as equivalent to a controlled voltage source, connect the primary equivalent excitation resistance of the voltage transformer in parallel across the controlled current source, and connect the equivalent ground capacitance of the voltage transformer in parallel across the controlled voltage source, to construct a target equivalent circuit of the ferromagnetic resonance of the voltage transformer to be detected;

[0043] An inductance value acquisition module is used to obtain the inductance value of the primary equivalent excitation inductance of the voltage transformer at the previous time step based on the excitation current of the voltage transformer at the previous time step and the iron core excitation characteristic curve of the voltage transformer with respect to magnetic flux and excitation current;

[0044] An excitation current calculation module is used to calculate the excitation current of the voltage transformer at the current time step by a numerical calculation method based on the target equivalent circuit of the voltage transformer to be detected, the circuit structure parameters, and the inductance value of the primary equivalent excitation inductance of the voltage transformer at the previous time step;

[0045] The prediction module is used to use finite element simulation software to establish a three-dimensional model of the voltage transformer to be predicted, input the excitation current of the voltage transformer at the current time step into the finite element simulation software, and obtain the predicted temperature distribution of each calculation domain in the three-dimensional model of the voltage transformer at the current time step.

[0046] The present invention also provides a device for predicting temperature rise of a voltage transformer under ferromagnetic resonance, comprising:

[0047] The memory is used to store a computer program; the processor is used to implement the steps of the above-mentioned method for predicting the temperature rise of a voltage transformer under ferromagnetic resonance when executing the computer program.

[0048] The above technical solution of the present invention has the following beneficial effects compared with the prior art:

[0049] The method, system, and device for predicting the temperature rise of a voltage transformer caused by ferromagnetic resonance described in the present invention take into account the real-time measurement of the excitation current of the electromagnetic voltage transformer to improve the temperature prediction accuracy of the electromagnetic voltage transformer during resonance. However, if the secondary side parameters are directly measured and then included in the calculation using a simple proportional relationship or empirical formula, the complex influence of the secondary side parameters on the primary side excitation current cannot be accurately reflected. Therefore, the present invention couples the influence of the secondary side parameters into the primary side calculation by equating the primary side of the voltage transformer's primary and secondary side equivalent inductance to a controlled current source and the secondary side to a controlled voltage source, and converts the secondary side impedance to the primary side through a transformation ratio. In addition, the primary side excitation resistance is taken into consideration. Based on the controlled current source, the controlled voltage source, the primary side equivalent DC resistance of the voltage transformer, the primary side equivalent excitation resistance of the voltage transformer, the primary side equivalent excitation inductance of the voltage transformer, and the equivalent ground capacitance of the voltage transformer, an equivalent circuit of the ferromagnetic resonance target of the voltage transformer to be detected is constructed, which overcomes the problem of ignoring the secondary side load and the primary side of the voltage transformer when calculating the excitation current in the prior art. The defects of the effective excitation resistance can be more accurately simulated, and the interaction between the primary and secondary sides can be avoided. The calculation deviation caused by the traditional method ignoring the equivalent excitation resistance and secondary side effect of the voltage transformer primary side is avoided. By accurately and real-time calculating the excitation current under ferromagnetic resonance, the calculated excitation current is input into the three-dimensional model of the voltage transformer. Based on physical principles such as thermal magnetic coupling, through numerical calculation, a more accurate temperature distribution prediction result of each calculation domain of the voltage transformer under ferromagnetic resonance can be obtained. The temperature rise prediction accuracy of the voltage transformer under ferromagnetic resonance is greatly improved, and the safety and stability of the electromagnetic voltage transformer are effectively guaranteed. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below based on specific embodiments of the present invention in conjunction with the accompanying drawings, wherein:

[0051] Figure 1 It is a flow chart of a method for predicting temperature rise of a voltage transformer caused by ferromagnetic resonance according to the present invention;

[0052] Figure 2 This is the equivalent circuit diagram of the ferromagnetic resonance target after the three voltage transformers are connected in three phases;

[0053] Figure 3 is the target equivalent circuit of the ferromagnetic resonance of the voltage transformer to be tested of the A-phase line voltage transformer;

[0054] Figure 4 is the excitation current waveform of the voltage transformer under different resonance types, Figure 4 (a) is the excitation current waveform of the voltage transformer under the frequency division resonance I1 type. Figure 4 (b) is the excitation current waveform of the voltage transformer under the fundamental frequency resonance I2 type. Figure 4 (c) is the excitation current waveform of the voltage transformer under high-frequency resonance I3 type;

[0055] Figure 5 This is the flow chart for calculating the excitation current of the voltage transformer under ferromagnetic resonance;

[0056] Figure 6 It is a three-dimensional model diagram of voltage transformer;

[0057] Figure 7 is the temperature distribution diagram of the voltage transformer during ferromagnetic resonance. Figure 7 (a) is the three-dimensional temperature distribution diagram of the voltage transformer during ferromagnetic resonance. Figure 7 (b) is the temperature distribution diagram of the voltage transformer cross section during ferromagnetic resonance;

[0058] Explanation of the markings in the specification: 1. Power supply of phase A line; 2. Line equivalent resistance of phase A line; 3. Single-phase grounding switch of phase A line; 4. Line equivalent capacitance to ground of phase A line; 5. Equivalent DC resistance of primary side of voltage transformer of phase A line; 6. Equivalent excitation resistance of primary side of voltage transformer of phase A line; 7. Equivalent excitation inductance of primary side of voltage transformer of phase A line; 8. Equivalent inductance of primary and secondary side of voltage transformer of phase A line; 9. Equivalent capacitance to ground of voltage transformer of phase A line; 10. Equivalent capacitance to ground of center point of phase A line; 11. Equivalent capacitance to ground of voltage transformer of phase B line; 12. Equivalent capacitance to ground of voltage transformer of phase C line; 13. Voltage transformer model consists of voltage transformer insulation; 14. Primary winding of voltage transformer; 15. Iron core of voltage transformer; 16. Secondary winding of voltage transformer. DETAILED DESCRIPTION

[0059] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0060] Reference Figure 1 As shown, this embodiment 1 provides a method for predicting the temperature rise of a voltage transformer caused by ferromagnetic resonance, comprising the following steps:

[0061] Step S1: During the ferromagnetic resonance period, based on the initial equivalent circuit of the voltage transformer ferromagnetic resonance to be predicted, the primary side of the equivalent inductance of the primary and secondary sides of the voltage transformer is equivalent to a controlled current source, and the secondary side is equivalent to a controlled voltage source. The primary side equivalent excitation resistance of the voltage transformer is connected in parallel across the controlled current source, and the equivalent ground capacitance of the voltage transformer is connected in parallel across the controlled voltage source to construct a target equivalent circuit of the ferromagnetic resonance of the voltage transformer to be detected.

[0062] like Figure 2 As shown, Figure 2 This is the equivalent circuit diagram of the ferromagnetic resonance target after the three voltage transformers are connected in three phases.

[0063] The target ferromagnetic resonance equivalent circuit of the three voltage transformers connected in three phases includes: Phase A, Phase B, Phase C, and a center-point-to-ground equivalent resistor 10. One end of the voltage transformers for Phase A, Phase B, and Phase C is connected to one another and to one end of the center-point-to-ground equivalent resistor 10. The other end of the center-point-to-ground equivalent resistor 10 is grounded. The voltage transformer equivalent circuits for Phase A, Phase B, and Phase C are identical.

[0064] Taking phase A as an example, the phase A line includes: power supply 1, line equivalent resistance 2, single-phase grounding switch 3, line-to-ground equivalent capacitance 4, voltage transformer primary equivalent DC resistance 5, voltage transformer primary equivalent excitation resistance 6, voltage transformer primary equivalent excitation inductance 7, voltage transformer primary-secondary equivalent inductance 8, and voltage transformer equivalent-to-ground capacitance 9.

[0065] The voltage transformer equivalent capacitance to ground 9 is connected in parallel with the secondary side of the voltage transformer primary and secondary equivalent inductance 8, and one end is grounded, serving as the output voltage U s The other end of the voltage transformer equivalent to ground capacitance is connected to one end of the voltage transformer equivalent to ground capacitance 11 of the B phase line. The other end of the voltage transformer equivalent to ground capacitance 11 of the B phase line is connected to one end of the voltage transformer equivalent to ground capacitance 12 of the C phase line, and the other end of the voltage transformer equivalent to ground capacitance 12 of the C phase line is used as the output voltage U s the other end.

[0066] Starting from the A phase line, the voltage transformer equivalent to ground capacitance 9 is connected in parallel with the secondary side of the voltage transformer primary and secondary equivalent inductance 8, and one end is grounded, as the output voltage U s The other end is connected to the voltage transformer equivalent to ground capacitance 11 of the B phase line, the other end of the voltage transformer equivalent to ground capacitance 11 of the B phase line is connected to one end of the voltage transformer equivalent to ground capacitance 12 of the C phase line, and finally the other end of the voltage transformer equivalent to ground capacitance 12 of the C phase line is used as the output voltage U s The other end of the circuit is connected to form a complete closed loop.

[0067] The effective value of the voltage transformer power supply voltage of phase A, B, and C is recorded as U A 、U B and U C , the phase difference is 120°, and the resistance of the circuit equivalent resistance 2 is recorded as R L , the capacitance of the line to ground equivalent capacitance 4 is recorded as C L μF; the resistance of the primary equivalent DC resistance 5 of the voltage transformer is recorded as R0, and the inductance of the primary equivalent excitation inductance 7 is recorded as L e The excitation characteristic is B(I), where B(·) is the magnetic induction intensity, I is the current, and the capacitance of the voltage transformer equivalent to the ground capacitance 9 is C1.

[0068] When ferromagnetic resonance occurs in the voltage transformer, the voltage transformer core is saturated and the primary side excitation current increases sharply, causing the internal temperature of the voltage transformer to rise in a short period of time, which endangers the normal operation of the voltage transformer.

[0069] In this embodiment, specifically, the initial equivalent circuit of the voltage transformer ferromagnetic resonance to be predicted includes: the primary equivalent DC resistance 5 of the voltage transformer and the primary equivalent excitation inductance 7 of the voltage transformer;

[0070] In this embodiment, specifically, the ferromagnetic resonance target equivalent circuit of the voltage transformer to be detected includes:

[0071] The center point to ground equivalent resistance 10 has one end connected to the positive electrode of the power supply 1 and the other end grounded;

[0072] A line equivalent resistor 2, one end of which is connected to the negative electrode of the power supply 1, and the other end of which is connected to the high potential end of the line-to-ground equivalent capacitor 4;

[0073] The line-to-ground equivalent capacitance 4 has its low potential end grounded;

[0074] A controlled current source is connected in parallel with the primary equivalent excitation resistance 6 of the voltage transformer and the primary equivalent excitation inductance 7 of the voltage transformer to form a parallel circuit;

[0075] The voltage transformer primary equivalent DC resistance 5 has one end connected to the line equivalent resistance 2 and the other end connected to the parallel circuit consisting of the controlled current source, the voltage transformer primary equivalent excitation resistance 6 and the voltage transformer primary equivalent excitation inductance 7;

[0076] a controlled voltage source connected in parallel with the voltage transformer equivalent capacitance to ground 9;

[0077] The voltage transformer has an equivalent capacitance to ground 9, and its low potential end is grounded.

[0078] The ferromagnetic resonance phenomenon of a voltage transformer is closely related to the nonlinear magnetic properties of the iron core. By treating the primary side as a controlled current source and the secondary side as a controlled voltage source, the present invention can better reflect the nonlinear changes in the electromagnetic relationship of the voltage transformer under different operating conditions, particularly during ferromagnetic resonance. The controlled source can dynamically adjust its output based on the voltage and current changes in the circuit, accurately simulating the changes in inductance parameters when the iron core is saturated, making the equivalent circuit more consistent with the actual ferromagnetic resonance process.

[0079] Considering the equivalent DC resistance of the voltage transformer primary is crucial for calculating the excitation current under the ferromagnetic resonance phenomenon. In accurately describing current characteristics, the equivalent DC resistance of the voltage transformer primary can limit the current amplitude, making the calculated excitation current amplitude more realistic and avoiding large deviations between the calculated and true values caused by ignoring the resistance. It can also reflect the current trend and truly present its complex changes over time, facilitating in-depth analysis of the resonance development process and providing a basis for accurately grasping the ferromagnetic resonance state. This overcomes the drawback of existing excitation current calculations that ignore the secondary load and the effects of the equivalent excitation resistance of the voltage transformer primary. It can more accurately simulate the interaction between the primary and secondary sides, avoiding the calculation errors caused by traditional methods that ignore the equivalent excitation resistance of the voltage transformer primary and the effects of the secondary side.

[0080] Step S2: based on the excitation current of the voltage transformer at the previous time step and the core excitation characteristic curve of the voltage transformer with respect to magnetic flux and excitation current, obtaining the inductance value of the primary equivalent excitation inductance of the voltage transformer at the previous time step;

[0081] Step S3: Calculating the excitation current of the voltage transformer at the current time step by a numerical calculation method based on the target ferromagnetic resonance equivalent circuit of the voltage transformer to be detected, the circuit structure parameters, and the inductance value of the primary equivalent excitation inductance of the voltage transformer at the previous time step;

[0082] When a single-phase ground fault occurs, if the line-to-ground equivalent capacitance 4 and the voltage transformer primary equivalent excitation inductance 7 mismatch, ferroresonance will occur. The capacitance of the voltage transformer's line-to-ground equivalent capacitance 4 affects the type of ferroresonance, resulting in various types of resonance, including high-frequency resonance, fractional frequency resonance, and fundamental frequency resonance.

[0083] like Figure 3 As shown, Figure 3 The target equivalent circuit of the voltage transformer ferromagnetic resonance to be detected for the voltage transformer of phase A is shown in Figure 1. Taking phase A as an example, the present invention treats the primary side of the voltage transformer's primary-secondary equivalent inductance 8 as a controlled current source and the secondary side as a controlled voltage source. Taking into account the influence of the voltage transformer's primary equivalent excitation resistance, the relationship between the resonant voltage and excitation current can be determined.

[0084] The electrical parameter relationship of phase A line is:

[0085]

[0086] By simplifying the electrical parameter relationship of phase A, the expression representing the relationship between the excitation current and the resonant voltage is:

[0087]

[0088] Among them, I X is the excitation current of the voltage transformer, U X is the resonant voltage, U 11 is the voltage across the controlled current source, U 12 is the voltage across the controlled voltage source, R0 is the equivalent DC resistance of the primary side of the voltage transformer, I 11 is the current of the controlled current source, I 12 is the current of the controlled voltage source, R e is the primary equivalent excitation resistance of the voltage transformer, L e is the equivalent excitation inductance of the primary side of the voltage transformer, and C1 is the equivalent capacitance to ground of the voltage transformer.

[0089] It can be seen from the expression that characterizes the relationship between the excitation current and the resonant voltage that, in addition to the traditional equivalent circuit for calculating the excitation current, the present invention also takes into account the equivalent excitation resistance of the primary side of the voltage transformer and the equivalent capacitance to ground of the voltage transformer. By equating the primary side of the equivalent inductance of the primary and secondary sides of the voltage transformer to a controlled current source and the secondary side to a controlled voltage source, the influence of the secondary side parameters is coupled into the primary side calculation, and the secondary side impedance is converted to the primary side through the transformation ratio, thereby avoiding the calculation deviation caused by the traditional method of ignoring the equivalent excitation resistance of the primary side of the voltage transformer and the secondary side effect.

[0090] In this embodiment, the ferromagnetic resonance period is preset to T op -T cl , set ground fault, set T cl At the time step, the single-phase grounding switch 3 is closed, T opThe single-phase grounding switch 3 is disconnected at the time step. The capacitance of the equivalent capacitor 4 to ground when the line undergoes high-frequency resonance, frequency division resonance, and fundamental frequency resonance is set to c1μF, c2μF, and c3μF respectively.

[0091] like Figure 4 As shown, Figure 4 is the excitation current waveform of the voltage transformer under different resonance types, Figure 4 (a) is the excitation current waveform of the voltage transformer under the frequency division resonance I1 type. Figure 4 (b) is the excitation current waveform of the voltage transformer under the fundamental frequency resonance I2 type. Figure 4 (c) in the figure shows the excitation current waveform of the voltage transformer under the high-frequency resonance type I3. During the solution process, the voltage of each node and the current of each branch are continuously updated, and the changes in the electrical quantities of the electromagnetic voltage transformer during the ferromagnetic resonance process are obtained, such as the amplitude and phase of the primary-side overvoltage, excitation current, and zero-sequence voltage.

[0092] During the ferromagnetic resonance process, the excitation characteristics of the voltage transformer will change, and the excitation current will also change accordingly. Due to the nonlinear characteristics of ferromagnetic resonance, the changes in electromagnetic quantities present complex transient characteristics, including different resonance modes such as high frequency, frequency division and fundamental frequency resonance, involving the mutual conversion and dynamic balance of electric field energy and magnetic field energy. Therefore, after setting the parameters of each module of the target equivalent circuit of the ferromagnetic resonance of the voltage transformer to be detected and the single-phase grounding fault, this embodiment uses a numerical calculation method to solve and calculate the electromagnetic transient process of the system. The calculation process is as follows: Figure 5 As shown, Figure 5 This is the flow chart for calculating the excitation current of the voltage transformer under ferromagnetic resonance.

[0093] In this embodiment, preferably, the excitation current of the voltage transformer at the current time step is calculated by a numerical calculation method based on the target equivalent circuit of the voltage transformer to be detected, the circuit structure parameters, and the inductance value of the primary equivalent excitation inductance of the voltage transformer at the previous time step, including:

[0094] Using the node voltage method, a node voltage equation is established for each node in the target equivalent circuit of the voltage transformer to be tested for ferromagnetic resonance. The circuit structure parameters and the inductance value of the primary equivalent excitation inductance of the voltage transformer at the previous time step are substituted into the node voltage equation to obtain a set of equations for all node voltages at the current time step.

[0095] In this embodiment, specifically, the circuit structure parameters include: the effective value of the power supply voltage, the resistance of the line equivalent resistance, the capacitance of the line-to-ground equivalent capacitance, the resistance of the primary equivalent DC resistance of the voltage transformer, the inductance of the primary equivalent excitation inductance, and the core excitation characteristic curve of the voltage transformer with respect to the resonant voltage and excitation current.

[0096] Based on the node voltage method, the equation for solving the ferromagnetic resonance excitation current of the voltage transformer is:

[0097] G1U1+G2U2+…G n U n =I n ,

[0098] Among them, G1 is the conductance sum of the branches connected to the first node, G2 is the conductance sum of the branches connected to the second node, G n is the conductance and the inductance of the branch connected to the nth node, including the resistance, capacitance and inductance of each branch. According to the saturation characteristics of the excitation inductance, the excitation characteristic curve is approximated by the piecewise linear method using linear segments. U1 is the voltage of the first node, U2 is the voltage of the second node, and U n is the voltage of the nth node, I n is the current flowing into each node, including the excitation current.

[0099] The core excitation characteristic curve of the voltage transformer with respect to the resonant voltage and the excitation current is divided into multiple linear segments by a piecewise linear method, and a linear equation of the excitation current and the resonant voltage in each linear segment is obtained;

[0100] In this embodiment, preferably, the step of dividing the core excitation characteristic curve of the voltage transformer with respect to the resonant voltage and the excitation current into a plurality of linear segments by a piecewise linear method, and obtaining a linear equation of the excitation current and the resonant voltage in each linear segment comprises:

[0101] Determine the number of intervals that need to be divided into the core excitation characteristic curve of the voltage transformer with respect to the resonant voltage and the excitation current and the boundaries of each interval. For the interval [a, b], based on the function values f(a) and f(b) of the core excitation characteristic curve of the voltage transformer with respect to the resonant voltage and the excitation current corresponding to the interval endpoints a and b, construct the equivalent linear function f1(x) of the core excitation characteristic curve of the voltage transformer with respect to the resonant voltage and the excitation current in the interval [a, b]. The construction formula is:

[0102]

[0103] The linear equations of the excitation current and resonant voltage in the linear segment corresponding to the interval [a, b] are:

[0104] I ′ =∫ a b f1(U X )dx

[0105] Among them, f1(U X) is the equivalent linear function obtained by linearly approximating the core excitation characteristic curve of the voltage transformer with respect to the resonant voltage and the excitation current on the interval [a, b], a is the left endpoint of the interval [a, b], b is the right endpoint of the interval [a, b], f(a) is f(U X ) in U X = the function value at a, f(b) is f(U X ) in U X = the function value at b, f(U X ) is the core excitation characteristic curve of the voltage transformer regarding the resonant voltage and excitation current, U X is the resonant voltage, I ′ To represent the equivalent linear function f1(U X ) is the excitation current obtained by integrating .

[0106] If piecewise linear analysis is not performed, I represents the interval [a, b]. The excitation current is obtained by integrating the function f(x) of the voltage transformer's core excitation characteristic curve with respect to resonant voltage and excitation current. f(x) is the voltage transformer's core excitation characteristic curve with respect to resonant voltage and excitation current. Because the excitation characteristic curve often exhibits complex nonlinearity, integral calculations are difficult and may require the use of complex algorithms such as numerical integration, which is a time-consuming process. The piecewise linear method directly applies basic integral formulas, greatly reducing the number of calculation steps and computational complexity, thereby significantly improving computational efficiency and obtaining the excitation current result in a shorter time. Furthermore, due to the nonlinearity of the voltage transformer's core excitation characteristic curve with respect to resonant voltage and excitation current, directly integrating the entire curve to calculate the excitation current is prone to deviation from the actual value. The piecewise linear method uses linear functions to approximate the original curve in each subinterval, aligning with local variation trends. Particularly, by subdividing the intervals at steep points in the curve, the integral result is closer to the actual value, improving the accuracy of the excitation current.

[0107] Based on the equations for all node voltages at the current time step and the linear equations for the excitation current and resonant voltage in each linear segment, a differential equation for the target equivalent circuit of the ferromagnetic resonance of the voltage transformer to be detected at the current time step is constructed;

[0108] By using the trapezoidal integration method, the differential equation of the target equivalent circuit of the ferromagnetic resonance of the voltage transformer to be tested at the current time step is approximately integrated to obtain the approximate value of the excitation current of the voltage transformer at the current time step;

[0109] The trapezoidal integration method is used to approximate the integration of the differential equation of the ferromagnetic resonance target equivalent circuit of the voltage transformer to be detected at the current time step during the ferromagnetic resonance period. For the inductor element, the integration approximation is performed within a time step Δt. According to the trapezoidal integration formula, it can be obtained: Among them, i n+1 is the current at the n+1th time step, i n is the current of the nth time step, Δt is the time step, L is the inductance value, u n is the voltage at the nth time step, u n+1 is the voltage at the n+1th time step. The treatment of the capacitor is similar. Set the ferromagnetic resonance period to t seconds and the time step to 0.0001s.

[0110] Through the above-mentioned integral approximate processing of components such as inductance and capacitance in the current time step, the node voltage equation at the current time step in the ferromagnetic resonance period is solved, and the solutions include but are not limited to the approximate value of the excitation current at the current time step in the ferromagnetic resonance period, the voltage and current values of each component, etc., so as to comprehensively analyze the electrical characteristics of the voltage transformer during the ferromagnetic resonance process.

[0111] The excitation current approximation of the voltage transformer at the current time step is corrected by the Newton-Raphson method to obtain the excitation current of the voltage transformer at the current time step.

[0112] The core of the Newton-Raphson method is to approximate the exact solution of a system of equations through continuous iteration. In each iteration, the Jacobian matrix of the system of equations is calculated based on the current approximate solution. The Jacobian matrix is then used to correct the approximate solution, gradually bringing it closer to the true solution. The Newton-Raphson method solves the problem as follows:

[0113] According to the differential equation of the target ferromagnetic resonance equivalent circuit of the voltage transformer to be detected, the objective function F(y) of the differential equation of the target ferromagnetic resonance equivalent circuit of the voltage transformer to be detected is Taylor expanded at y=y0, and then y-y0=Δy is set, and the remainder is ignored to obtain:

[0114] F(y)=F(y0)+F ′ (y0)Δy,

[0115] To find the value of y when F(y)=0, let F(y)=0, that is:

[0116] F(y0)+F ′ (y0)Δy=0,

[0117] Further calculation yields:

[0118]

[0119] Compare the errors after each calculation:

[0120]

[0121] Where y is the variable to be solved, which can be an electrical quantity such as node voltage or current. In this embodiment, y is the excitation current of the voltage transformer, y0 is the approximate value of y, Δy is the increment of y in each iteration, and F ′ (y0) is the first-order derivative of the objective function F(y) of the differential equation of the ferromagnetic resonance target equivalent circuit of the voltage transformer to be detected at y=y0, m is the approximate value of y calculated at the m+1th iteration, y m+1 is the approximate value of y+1 calculated at the m+1th iteration, where m is the number of iterations.

[0122] The absolute similarity iterative approximation error ξ a Relative error threshold ξ b For comparison, if |ξ a |>ξ b , the iterative calculation continues, otherwise it stops. Through such continuous iterative correction, the approximate value of the excitation current obtained based on the trapezoidal integration method is gradually optimized, and finally a more accurate excitation current of the voltage transformer during ferromagnetic resonance is obtained, thereby more accurately analyzing the electrical characteristics of the voltage transformer during ferromagnetic resonance.

[0123] Typically, the equivalent circuit model of an electromagnetic voltage transformer includes the primary DC resistance and magnetizing inductance, ignoring the primary magnetizing resistance. The secondary side may be simplified to an ideal transformer model or a simple load impedance. Traditional methods for calculating the excitation current focus primarily on the parameters of the primary DC resistance and magnetizing inductance. Because the excitation current is primarily determined by the primary excitation branch, combining these two parameters based on traditional circuit theory allows for a relatively fast and accurate estimation of the excitation current under normal operation, meeting general engineering analysis requirements.

[0124] However, during ferroresonance, the core's saturation state fluctuates frequently. The primary-side excitation resistance plays a significant role in limiting current and influencing resonant characteristics. Traditional methods, if employed, will fail to accurately simulate the true variations in excitation current during ferroresonance, impacting the accuracy of temperature rise predictions for voltage transformers in ferroresonance. Furthermore, the system's nonlinear characteristics (such as the saturation effect of the excitation inductance) and distributed parameters (such as capacitance to ground) are crucial. To simplify calculations, traditional methods ignore secondary-side parameters and address their effects solely using the transformation ratio. This simplification can lead to errors when dealing with high-frequency or nonlinear phenomena, as the capacitance and inductance of the secondary affect the primary's equivalent impedance through the transformer's transformation ratio.

[0125] Therefore, the present invention uses the primary side of the primary-secondary equivalent inductance 8 of the voltage transformer as a controlled current source and the secondary side as a controlled voltage source, and couples the influence of the secondary side parameters into the calculation of the primary side through these controlled sources, and converts the impedance of the secondary side to the primary side through the transformation ratio, so that the excitation current can be calculated more accurately.

[0126] According to the actual structure of the electromagnetic voltage transformer in the distribution network, a 1:1 three-dimensional model of the voltage transformer is established using finite element simulation software, such as Figure 6 As shown, Figure 6 This is a three-dimensional model diagram of the voltage transformer.

[0127] The three-dimensional model diagram of the voltage transformer includes: voltage transformer insulation 13, voltage transformer primary winding 14, voltage transformer core 15, and voltage transformer secondary winding 16; among them, the voltage transformer secondary winding 16 is wound on the voltage transformer core 15, and the voltage transformer primary winding 14 is wound on the outside of the voltage transformer secondary winding 16 in the form of a concentric cylindrical structure. The voltage transformer primary winding 14, the voltage transformer core 15, and the voltage transformer secondary winding 16 are cast into a fixed shape using the voltage transformer insulation 13 to form the outer shell of the voltage transformer.

[0128] Step S4: Using finite element simulation software, a three-dimensional model of the voltage transformer to be predicted is established, and the excitation current of the voltage transformer at the current time step is input into the finite element simulation software to obtain the predicted temperature distribution of each calculation domain in the three-dimensional model of the voltage transformer at the current time step.

[0129] In this embodiment, the magnetic field and solid heat transfer modules in the finite element simulation software are used to calculate the PT temperature.

[0130] In this embodiment, specifically, inputting the excitation current of the voltage transformer at the current time step into the finite element simulation software to obtain the predicted temperature distribution of each calculation domain in the three-dimensional model of the voltage transformer at the current time step includes:

[0131] Set the voltage transformer material parameters in the finite element simulation software;

[0132] In this embodiment, specifically, the voltage transformer material parameters include:

[0133] ① The constant pressure heat capacity of the voltage transformer insulation 13 is c1J / (kg·K), the thermal conductivity is K1W / (m·K), and the material density is ρ1kg / m 3 .

[0134] ②The number of turns of the primary winding 14 of the voltage transformer is N1, and the conductivity of the wire is σ wire-1 S / m, the cross-sectional area of the conductor is j wire-1 m 2 .

[0135] ③ The constant pressure heat capacity of the voltage transformer core 15 is c2J / (kg·K), the thermal conductivity is K2W / (m·K), and the material density is ρ2kg / m 3 , the relative dielectric constant is ε2, and the conductivity is σ iron S / m, and the effective magnetic field norm is B1A / m.

[0136] ④ The number of turns of the secondary winding 16 of the voltage transformer is N2, and the conductivity of the wire is σ wire-2 S / m, the cross-sectional area of the conductor is j wire- 2m 2 .

[0137] ⑤ The constant pressure heat capacity of the voltage transformer primary winding 14 and the voltage transformer secondary winding 16 is c3J / (kg·K), the thermal conductivity is k3W / (m·K), and the material density is ρ3kg / m 3 , the relative dielectric constant is ε3, and the relative magnetic permeability is μ3.

[0138] Through the "Material" node in the finite element simulation software, select a suitable material from the material library, or customize the material parameters, and then set the above-mentioned voltage transformer material parameters.

[0139] Set the bottom surface temperature of the voltage transformer to a constant temperature T1K and set the voltage transformer heat transfer coefficient hW / (m 2 ·K), external air temperature T ext K, initial temperature of voltage transformer material T0K; set the voltage transformer material to solid, and set the physical field boundary condition of the voltage transformer outer surface to "convective heat flux";

[0140] In the finite element simulation software's "Heat Transfer in Solids" physics field, select the bottom surface of the voltage transformer, add a "Temperature" boundary condition, and set the temperature to a constant value. In the "Heat Transfer in Solids" physics field, select the outer surface of the voltage transformer and add a "Convective Heat Flux" boundary condition, setting the heat transfer coefficient and the external air temperature. In the "Initial Conditions" of the "Heat Transfer in Solids" physics field, set the initial temperature of the voltage transformer material. In the material properties, ensure that all voltage transformer materials are of the solid type.

[0141] Set the primary and secondary terminals of the voltage transformer group. Set the physics interface for the voltage transformer core 15 to "Ampere's Law in Solids," the loss calculation to "Steinmetz" loss model, and the physics setting for the voltage transformer primary winding 14, core 15, and secondary winding 16 to "A Field Specification Fixed."

[0142] In the geometric model of the finite element simulation software, select the primary and secondary side incoming terminals of the voltage transformer, add the "current" boundary condition, enter the corresponding current value, select the voltage transformer core in the "magnetic field" physics field, select the "Ampere's Law in Solids" physics field interface, select the "Steinmetz" loss model in the physics field settings of the core, and set the relevant parameters, select the primary winding, core and secondary winding of the voltage transformer in the "magnetic field" physics field, and set the physics field to "A field specification fixed".

[0143] Set the maximum cell size to D1mm, the minimum cell size to D2mm, and the meshing method to "free tetrahedron mesh" to divide the 3D voltage transformer model into multiple computational domains.

[0144] In the finite element simulation software, in the "Mesh" node, in the "Mesh Sequence", set the maximum element size and the minimum element size, select "Free Tetrahedron Mesh" as the meshing method, and click "Build All" to mesh the three-dimensional model of the voltage transformer and divide it into multiple calculation domains.

[0145] Based on the current I of the primary winding 14 of the voltage transformer at the current time step wire-1 (t)A, voltage transformer secondary winding 16 current I wire-2 (t)A, excitation current I of voltage transformer X (t), calculate the vector magnetic potential of each computational domain at the current time step;

[0146] To do this, add a Stationary or Transient study to the Study node in the FEM simulation software. In the Study Settings, enter the primary and secondary currents of the voltage transformer at the current time step. Run the study, and the FEM simulation software will calculate the vector magnetic potential for each computational domain based on the input currents.

[0147] Based on the vector magnetic potential of each computational domain at the current time step, the predicted temperature distribution of each computational domain in the three-dimensional model of the voltage transformer at the current time step is obtained through the set temperature rise solution algorithm.

[0148] In the finite element simulation software's "Results" node, add a "Derived Values" or "Plot" to view the calculation results. Based on the calculated vector magnetic potential, the temperature distribution is solved using the finite element simulation software's built-in solid heat transfer equation and the specified boundary conditions.

[0149] Among them, the temperature rise solution algorithm includes: the vector magnetic potential control equation of the voltage transformer in the current region with an external excitation source; the vector magnetic potential control equation of the voltage transformer in the non-current region without an external excitation source, the heat conduction control equation, the heat convection control equation, and the heat radiation control equation.

[0150] Combining magnetic field and heat transfer theory, the transient temperature distribution of the voltage transformer when ferromagnetic resonance occurs is calculated. Assuming that there is an external excitation source in the current region, the vector magnetic potential control equation of the voltage transformer can be expressed as:

[0151]

[0152] Where A is the vector magnetic potential, is a vector differential operator, μ is the material magnetic permeability, unit is H / m, I X is the excitation current of the voltage transformer, in V, and S is the winding cross-sectional area, in m 2 , ω is the angular frequency, the unit is rad / s, σ is the material conductivity, the unit is S / m.

[0153] In the non-current region without an external excitation source, the vector magnetic potential control equation of the voltage transformer can be expressed as:

[0154]

[0155] When the voltage transformer is in operation, heat is transferred through heat conduction, heat convection and heat radiation, causing the temperature of the voltage transformer's main insulation, windings and core to rise. The governing equations for heat conduction, heat convection and heat radiation are:

[0156]

[0157] q0=hA0ΔT

[0158]

[0159] Where T is the solid temperature, k is the thermal conductivity, Q v is the volume heat generation rate, ρ is the material density, c is the material specific heat capacity, q0 is the transferred heat, h is the heat transfer coefficient, A0 is the effective contact area between the solid and the liquid, ΔT is the temperature difference between the solid and the fluid, σ is the Boltzmann constant, T ext is the ambient temperature.

[0160] Based on the first embodiment, the second embodiment uses the JDZ-10Q electromagnetic voltage transformer to specifically illustrate a method for predicting the temperature rise of a voltage transformer under ferromagnetic resonance. The second embodiment sets the effective value of the three-phase power supply 1 to be 10 kV, the resistance of the line equivalent resistor 2 to be 0.625 Ω, the capacitance of the line-to-ground equivalent capacitor 4 to be 0.1 μF, the resistance of the primary equivalent DC resistor 5 of the voltage transformer to be 5340 Ω, and the resistance of the primary equivalent excitation resistor 6 of the voltage transformer to be 1×10 10Ω and the excitation characteristic parameters of the voltage transformer are added to obtain the inductance value of the primary equivalent excitation inductance 7 of the voltage transformer at the current time step. According to the excitation current calculation method at resonance, the excitation current I1 of the phase A line voltage transformer at the current time step is obtained.

[0161] The interpolation function is set according to the excitation current I1 of the voltage transformer of phase A at the current time step. The number of turns of the primary winding is 14956, the conductivity of the wire is 57142857S / m, and the cross-sectional area of the wire is 2.5×10-7m 2 The number of turns of the secondary winding is 150, the conductivity of the wire is 57142857S / m, and the cross-sectional area of the wire is 1×10-6m 2 The bottom surface of the voltage transformer is set to a constant temperature of 20℃ and a heat transfer coefficient of 5W / (m 2 ·K) and the external temperature is 20℃, the temperature distribution of each calculation domain of the voltage transformer at the current time step is obtained according to Equations 9 to 13.

[0162] like Figure 7 As shown, Figure 7 is the temperature distribution diagram of the voltage transformer during ferromagnetic resonance. Figure 7 (a) is the three-dimensional temperature distribution diagram of the voltage transformer during ferromagnetic resonance. Figure 7 Figure (b) shows the temperature distribution across the voltage transformer during ferromagnetic resonance. This allows for the prediction of the voltage transformer's temperature rise due to ferromagnetic resonance. The primary winding temperature during the frequency-division ferromagnetic resonance event is the highest, approximately 176°C. This temperature reaches the melting point of the epoxy resin used for the voltage transformer insulation, which inevitably leads to insulation damage. Furthermore, the secondary winding temperature is approximately 116°C, while the core temperature is the lowest, approximately 98°C.

[0163] The third embodiment provides a system for predicting temperature rise of a voltage transformer caused by ferromagnetic resonance, including:

[0164] An equivalent circuit construction module is used to obtain the initial equivalent circuit of the voltage transformer ferromagnetic resonance to be predicted within the ferromagnetic resonance period, and to equate the primary side of the voltage transformer's primary and secondary equivalent inductance to a controlled current source and the secondary side to a controlled voltage source. Based on the controlled current source, the controlled voltage source, the voltage transformer's primary equivalent DC resistance, the voltage transformer's primary equivalent excitation resistance, the voltage transformer's primary equivalent excitation inductance, and the voltage transformer's equivalent capacitance to ground, a target equivalent circuit of the voltage transformer ferromagnetic resonance to be detected is constructed.

[0165] An inductance value acquisition module is used to obtain the inductance value of the primary equivalent excitation inductance of the voltage transformer at the previous time step based on the excitation current of the voltage transformer at the previous time step and the iron core excitation characteristic curve of the voltage transformer with respect to magnetic flux and excitation current;

[0166] An excitation current calculation module is used to calculate the excitation current of the voltage transformer at the current time step by a numerical calculation method based on the target equivalent circuit of the voltage transformer to be detected, the circuit structure parameters, and the inductance value of the primary equivalent excitation inductance of the voltage transformer at the previous time step;

[0167] The prediction module is used to use finite element simulation software to establish a three-dimensional model of the voltage transformer to be predicted, input the excitation current of the voltage transformer at the current time step into the finite element simulation software, and obtain the predicted temperature distribution of each calculation domain in the three-dimensional model of the voltage transformer at the current time step.

[0168] The fourth embodiment provides a device for predicting temperature rise of a voltage transformer under ferromagnetic resonance, including:

[0169] The memory is used to store a computer program; the processor is used to implement the steps of the above-mentioned method for predicting the temperature rise of a voltage transformer under ferromagnetic resonance when executing the computer program.

[0170] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0171] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0172] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0173] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0174] Obviously, the above embodiments are merely examples for clarity of explanation and are not intended to limit the implementation methods. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all implementation methods here. Obvious variations or modifications arising therefrom remain within the scope of protection of the present invention.

Claims

1. A method for predicting temperature rise of a voltage transformer caused by ferromagnetic resonance, characterized in that: include: During the ferromagnetic resonance period, based on the initial equivalent circuit of the voltage transformer ferromagnetic resonance to be predicted, the primary side of the equivalent inductance of the primary and secondary sides of the voltage transformer is equivalent to a controlled current source, and the secondary side is equivalent to a controlled voltage source. The primary equivalent excitation resistance of the voltage transformer is connected in parallel at both ends of the controlled current source, and the equivalent capacitance of the voltage transformer to ground is connected in parallel at both ends of the controlled voltage source to construct the target equivalent circuit of the ferromagnetic resonance of the voltage transformer to be detected; Based on the excitation current of the voltage transformer at the previous time step and the core excitation characteristic curve of the voltage transformer with respect to magnetic flux and excitation current, the inductance value of the primary equivalent excitation inductance of the voltage transformer at the previous time step is obtained; Based on the target equivalent circuit of the voltage transformer to be tested, the circuit structure parameters and the inductance value of the primary equivalent excitation inductance of the voltage transformer in the previous time step, the excitation current of the voltage transformer in the current time step is calculated by numerical calculation method; Using finite element simulation software, a three-dimensional model of the voltage transformer to be predicted is established, and the excitation current of the voltage transformer at the current time step is input into the finite element simulation software to obtain the predicted temperature distribution of each calculation domain in the three-dimensional model of the voltage transformer at the current time step.

2. The method for predicting temperature rise of a voltage transformer caused by ferromagnetic resonance according to claim 1, characterized in that: The ferromagnetic resonance target equivalent circuit of the voltage transformer to be tested includes: The equivalent resistance of the center point to ground, one end of which is connected to the positive pole of the power supply and the other end is grounded; The line equivalent resistor has one end connected to the negative pole of the power supply and the other end connected to the high potential end of the line equivalent capacitance to ground; The equivalent capacitance of the line to ground, with its low potential end grounded; A controlled current source is connected in parallel with the primary equivalent excitation resistance of the voltage transformer and the primary equivalent excitation inductance of the voltage transformer to form a parallel circuit; A primary equivalent DC resistance of the voltage transformer, one end of which is connected to the line equivalent resistance, and the other end of which is connected to the parallel circuit consisting of the controlled current source, the primary equivalent excitation resistance of the voltage transformer, and the primary equivalent excitation inductance of the voltage transformer; a controlled voltage source connected in parallel with the equivalent capacitance of the voltage transformer to ground; The voltage transformer is equivalent to the ground capacitance, and its low potential end is grounded.

3. The method for predicting temperature rise of a voltage transformer caused by ferromagnetic resonance according to claim 1, characterized in that: The circuit structure parameters include: the effective value of the power supply voltage, the resistance of the line equivalent resistance, the capacitance of the line-to-ground equivalent capacitance, the resistance of the primary equivalent DC resistance of the voltage transformer, the inductance of the primary equivalent excitation inductance, and the iron core excitation characteristic curve of the voltage transformer regarding the resonant voltage and excitation current.

4. The method for predicting temperature rise of a voltage transformer caused by ferromagnetic resonance according to claim 3, characterized in that: The method of calculating the excitation current of the voltage transformer at the current time step by a numerical calculation method based on the target equivalent circuit of the voltage transformer to be detected, the circuit structure parameters, and the inductance value of the primary equivalent excitation inductance of the voltage transformer at the previous time step includes: Using the node voltage method, a node voltage equation is established for each node in the target equivalent circuit of the voltage transformer to be tested for ferromagnetic resonance. The circuit structure parameters and the inductance value of the primary equivalent excitation inductance of the voltage transformer at the previous time step are substituted into the node voltage equation to obtain a set of equations for all node voltages at the current time step. The core excitation characteristic curve of the voltage transformer with respect to the resonant voltage and the excitation current is divided into multiple linear segments by a piecewise linear method, and a linear equation of the excitation current and the resonant voltage in each linear segment is obtained; Based on the equations for all node voltages at the current time step and the linear equations for the excitation current and resonant voltage in each linear segment, a differential equation for the target equivalent circuit of the ferromagnetic resonance of the voltage transformer to be detected at the current time step is constructed; By using the trapezoidal integration method, the differential equation of the target equivalent circuit of the ferromagnetic resonance of the voltage transformer to be tested at the current time step is approximately integrated to obtain the approximate value of the excitation current of the voltage transformer at the current time step; The excitation current approximation of the voltage transformer at the current time step is corrected by the Newton-Raphson method to obtain the excitation current of the voltage transformer at the current time step.

5. The method for predicting temperature rise of a voltage transformer caused by ferromagnetic resonance according to claim 4, characterized in that: The method divides the core excitation characteristic curve of the voltage transformer with respect to the resonant voltage and the excitation current into a plurality of linear segments by a piecewise linear method, and obtains a linear equation of the excitation current and the resonant voltage in each linear segment, including: Determine the number of intervals that need to be divided into the core excitation characteristic curve of the voltage transformer with respect to the resonant voltage and the excitation current and the boundaries of each interval. For the interval [a, b], based on the function values f(a) and f(b) of the core excitation characteristic curve of the voltage transformer with respect to the resonant voltage and the excitation current corresponding to the interval endpoints a and b, construct the equivalent linear function f1(x) of the core excitation characteristic curve of the voltage transformer with respect to the resonant voltage and the excitation current in the interval [a, b]. The construction formula is: The linear equations of the excitation current and resonant voltage in the linear segment corresponding to the interval [a, b] are: Among them, f1(U X ) is the equivalent linear function obtained by linearly approximating the core excitation characteristic curve of the voltage transformer with respect to the resonant voltage and the excitation current on the interval [a, b], a is the left endpoint of the interval [a, b], b is the right endpoint of the interval [a, b], f(a) is f(U X ) in U X = the function value at a, f(b) is f(U X ) in U X = the function value at b, f(U X ) is the core excitation characteristic curve of the voltage transformer regarding the resonant voltage and excitation current, U X is the resonant voltage, I′ is the equivalent linear function f1(U X ) is the excitation current obtained by integrating .

6. The method for predicting temperature rise of a voltage transformer caused by ferromagnetic resonance according to claim 1, characterized in that: The step of inputting the excitation current of the voltage transformer at the current time step into the finite element simulation software to obtain the predicted temperature distribution of each calculation domain in the three-dimensional model of the voltage transformer at the current time step includes: Set the voltage transformer material parameters in the finite element simulation software; Set the voltage transformer bottom surface temperature to a constant temperature, and set the voltage transformer heat transfer coefficient, external air temperature, and initial temperature of the voltage transformer material. Set the voltage transformer material to solid, and set the physical field boundary condition on the voltage transformer outer surface to "Convective Heat Flux." Set the primary and secondary terminals of the voltage transformer group. Set the physics interface for the voltage transformer core to "Ampere's Law in Solids," the loss calculation to "Steinmetz" loss model, and the physics settings for the voltage transformer primary winding, core, and secondary winding to "A-field specification fixed." Set the maximum and minimum cell sizes and the meshing method to "Free Tetrahedron" to divide the 3D voltage transformer model into multiple computational domains. Based on the primary winding current of the voltage transformer, the secondary winding current of the voltage transformer and the excitation current of the voltage transformer at the current time step, the vector magnetic potential of each computational domain at the current time step is calculated; Based on the vector magnetic potential of each computational domain at the current time step, the predicted temperature distribution of each computational domain in the three-dimensional model of the voltage transformer at the current time step is obtained through the set temperature rise solution algorithm.

7. The method for predicting temperature rise of a voltage transformer caused by ferromagnetic resonance according to claim 6, characterized in that: The material parameters of the voltage transformer include: constant-pressure heat capacity, thermal conductivity, and material density of the voltage transformer insulation; constant-pressure heat capacity, thermal conductivity, material density, relative dielectric constant, conductivity, and effective magnetic field modulus of the voltage transformer core; the number of turns of the voltage transformer primary winding and the voltage transformer secondary winding, conductor conductivity, conductor cross-sectional area, constant-pressure heat capacity, thermal conductivity, material density, relative dielectric constant, and relative magnetic permeability.

8. The method for predicting temperature rise of a voltage transformer caused by ferromagnetic resonance according to claim 6, characterized in that: The temperature rise solution algorithm includes: heat conduction control equation, heat convection control equation, and heat radiation control equation.

9. A voltage transformer temperature rise prediction system caused by ferromagnetic resonance, characterized in that: include: An equivalent circuit construction module is used to, within a ferromagnetic resonance period, based on an initial equivalent circuit of the voltage transformer ferromagnetic resonance to be predicted, treat the primary side of the voltage transformer's primary and secondary equivalent inductance as equivalent to a controlled current source, and the secondary side as equivalent to a controlled voltage source, connect the primary equivalent excitation resistance of the voltage transformer in parallel across the controlled current source, and connect the equivalent ground capacitance of the voltage transformer in parallel across the controlled voltage source, to construct a target equivalent circuit of the ferromagnetic resonance of the voltage transformer to be detected; An inductance value acquisition module is used to obtain the inductance value of the primary equivalent excitation inductance of the voltage transformer at the previous time step based on the excitation current of the voltage transformer at the previous time step and the iron core excitation characteristic curve of the voltage transformer with respect to magnetic flux and excitation current; An excitation current calculation module is used to calculate the excitation current of the voltage transformer at the current time step by a numerical calculation method based on the target equivalent circuit of the voltage transformer to be detected, the circuit structure parameters, and the inductance value of the primary equivalent excitation inductance of the voltage transformer at the previous time step; The prediction module is used to use finite element simulation software to establish a three-dimensional model of the voltage transformer to be predicted, input the excitation current of the voltage transformer at the current time step into the finite element simulation software, and obtain the predicted temperature distribution of each calculation domain in the three-dimensional model of the voltage transformer at the current time step.

10. A device for predicting temperature rise of a voltage transformer under ferromagnetic resonance, characterized in that: include: memory for storing computer programs; A processor is configured to implement the steps of the method for predicting the temperature rise of a voltage transformer under ferromagnetic resonance as described in any one of claims 1 to 8 when executing the computer program.

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