A reverse power flow-oriented oil-immersed transformer field-circuit-magnetic-thermal-flow coupling simulation modeling and hotspot deviation evaluation method

Abstract

The present application relates to a kind of oil-immersed transformer field-circuit-magnetic-thermal-flow coupling simulation modeling and hotspot deviation evaluation method for reverse power flow, belong to the field of power transformer digital modeling and operating state simulation evaluation.This method obtains transformer parameters and distribution network bidirectional power flow operating parameters, calculates reverse power flow degree coefficient, converts reverse sending power, reactive power, power factor, line impedance, tap position and harmonic state into low-voltage side complex voltage excitation;Synchronously switch the source-load connection relationship and current reference direction of high-low voltage port;Establish the multi-physical field model of core, winding and insulating oil, complete the loss density conservation mapping and thermal-flow iteration solution;Output hotspot temperature, hotspot high temperature area barycenter deviation, magnetic density limit ratio, winding eddy current loss increment, insulation thermal aging acceleration factor and reverse power flow allowable interval.The present application can be used for transformer reverse power flow operating risk evaluation under the condition of distributed new energy access.

Description

Technical Field

[0001] This invention belongs to the field of digital modeling and operational status simulation evaluation of power transformers, and involves the technical fields of finite element simulation of power transformers, reverse power flow analysis of distribution networks, thermal safety assessment of oil-immersed transformers and insulation thermal aging status assessment. Specifically, it relates to a field-circuit-magnetic-thermal-current coupled simulation modeling and hot spot offset assessment method for oil-immersed transformers oriented towards reverse power flow. Background Technology

[0002] With the large-scale integration of distributed photovoltaic (PV) power, energy storage, electric vehicles, and adjustable loads into the distribution network, the traditional unidirectional power supply mode from the high-voltage side to the low-voltage side is gradually transforming into a bidirectional power flow mode. In scenarios such as high PV power generation, low load, or reverse power transmission from energy storage, the low-voltage side may send power back to the high-voltage side. The distribution transformer or the main transformer of the user substation may switch from step-down operation to step-up operation, forming a reverse power flow reverse transmission condition.

[0003] The internal temperature rise and insulation life of an oil-immersed transformer are typically determined by core losses, winding DC losses, winding eddy current losses, stray losses of structural components, and heat dissipation through the circulating insulating oil. Existing multiphysics simulation methods mostly use positive rated load or short-circuit conditions as the default scenario, usually taking the high-voltage side as the input excitation terminal and the low-voltage side as the load terminal, focusing on solving the magnetic field, temperature field, and flow field distribution under rated positive operation.

[0004] It should be noted that for an ideally linear and perfectly symmetrical transformer, a simple reversal of the active power direction does not necessarily lead to a significant change in the internal physical field. The main reasons for the difference under reverse power flow conditions are: the rise in low-voltage side voltage increases the core flux density; changes in tap position alter the equivalent turns ratio and excitation voltage; changes in power factor and reactive power flow direction alter the phase relationship between the leakage magnetic field and winding current; the injection of harmonic voltage or current from the distributed generation side increases additional losses; the boundary conditions of the winding ports change when the low-voltage side is used as the excitation end; and the magnetic flux density and iron loss increase nonlinearly after the core enters the nonlinear BH region.

[0005] In existing technologies, some methods simply change the direction of the load current or apply low-voltage side voltage in the finite element model. They lack the conversion process from the reverse power state of the distribution network to the finite element port boundary conditions, and also lack switchable modeling rules for forward and reverse power flows in the same field-circuit coupling model. Therefore, it is difficult to accurately identify the loss redistribution, hot spot location shift and temperature rise risk boundary caused by reverse power flow. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide a simulation modeling and hot spot offset assessment method for oil-immersed transformers with field-circuit-magnetic-thermal-current coupling for reverse power flow. The reverse power flow state of the distribution network side is converted into the finite element field-circuit port boundary. The port source-load connection relationship and current reference direction are switched synchronously according to the power flow mode. The forward and reverse operating conditions are calculated in a unified model, and the centroid offset and temperature rise safety boundary of the hot spot high temperature region are output.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A method for simulation modeling and hotspot shift evaluation of field-magnetic-thermal-fluid coupling in oil-immersed transformers oriented towards reverse power flow includes the following steps: S1. Obtain bidirectional power flow operation status parameters, including obtaining the target oil-immersed transformer parameters and the bidirectional power flow operation parameters of the distribution network; S2. Establish a reverse power flow complex voltage excitation model for the low-voltage side: Under the unified port power and current reference direction, calculate the reverse power flow complex voltage excitation for the low-voltage side based on the reverse power flow degree coefficient, high-voltage side voltage stability constraint, transformer equivalent impedance, line impedance, power factor and tap position. S3. Construct a forward and reverse power flow port-external circuit switching matrix: Establish an external circuit model including high-voltage port, low-voltage port, equivalent branch of external power source or distributed power source, equivalent impedance of grid and load branch, and synchronously switch the connection relationship and current reference direction between high and low voltage ports and equivalent branch of external power source or distributed power source, load branch and equivalent impedance of grid through port switching matrix. S4. Establish a three-dimensional equivalent finite element model of an oil-immersed transformer: Establish a three-dimensional finite element model including the core, windings (low-voltage windings and high-voltage windings), main insulation, insulating oil, oil channels, oil tank, and heat dissipation boundary. S5. Perform field-magnetic coupling solution: Under reverse power flow complex voltage excitation, perform field-magnetic coupling solution to obtain the non-uniform loss density of the core, winding and structural components; S6. Establish a non-uniform loss density conservation mapping method: map the non-uniform loss density conservation into a distributed volume heat source in the thermal-fluid coupling model; S7. Perform a two-way coupled thermal-fluid iterative solution to obtain the temperature field and flow field distribution under different reverse current conditions; S8. Extract the center of gravity shift and temperature rise risk indicators of hot spot high temperature area: Calculate the temperature-weighted center of gravity coordinates of hot spot high temperature area from the set of winding units whose temperature is not lower than the maximum winding temperature minus the preset temperature difference, and extract the hot spot temperature, hot spot position offset vector and reverse power flow temperature rise safety boundary.

[0008] S9: Model calibration and result output.

[0009] Furthermore, in step S1, the parameters of the target oil-immersed transformer include rated capacity, rated voltage, connection group, short-circuit impedance, no-load loss, load loss, tap position, cooling method, material parameters (core material parameters, winding material parameters), heat dissipation parameters (insulating oil thermal properties parameters), and structural parameters (oil channel structural parameters, oil tank and radiator structural parameters).

[0010] The bidirectional power flow operating parameters of the distribution network include the stable voltage on the high-voltage side, the actual voltage on the low-voltage side, the active power fed back from the low-voltage side, the reactive power fed back from the low-voltage side, the power factor, the line impedance, the output of distributed generation sources, the load level, and the harmonic content. The direction of active power injection from the low-voltage side to the high-voltage side is defined as the positive direction, and all port power, current, and reactive power are uniformly referenced according to this direction definition.

[0011] The reverse power flow intensity coefficient α is used to characterize the intensity of the reverse power flow from the low-voltage side to the high-voltage side relative to the rated capacity of the transformer. The reverse power flow intensity coefficient α is defined as the ratio between the reverse active power flow with the active power injection direction from the low-voltage side to the high-voltage side as positive and the rated capacity of the transformer, and is used to set at least two reverse power flow simulation conditions.

[0012] (1) in, To transmit active power from the low-voltage side to the high-voltage side according to the unified reference direction defined above, This refers to the rated capacity of the transformer. max (·) indicates a function that takes the larger value. When When the value is less than or equal to zero, it is determined to be a forward power flow or a non-reverse power flow condition; reverse power flow and Use the same port reference direction marking.

[0013] Furthermore, in step S2, the calculation of the reverse power flow complex voltage excitation on the low-voltage side specifically includes: based on the transformer's T-type or π-type equivalent circuit, combined with the high-voltage side voltage stability constraints, transformer leakage impedance, line impedance, tap position, and power factor, calculating the coefficients for different reverse power flow degrees. α Low-voltage side reverse power flow complex voltage excitation.

[0014] The low-voltage side current is determined according to the complex power relationship: (2) in, This refers to the low-voltage side phase current or equivalent line current phasor. To send back active power, To reverse reactive power, U LV * It is the conjugate of the low-voltage side complex voltage.j The imaginary unit; Given a high-voltage side reference voltage Transformer equivalent impedance Low-voltage side line impedance and tap ratio At that time, among them, k t Defined as the voltage transformation coefficient from the high-voltage side to the low-voltage side under the current tap position; the fundamental complex voltage excitation on the low-voltage side can be expressed as: (3) in, The degree of reverse current is α Low-voltage side fundamental voltage excitation; This is the reference voltage for the high-voltage side; Z T The equivalent impedance of the transformer; Z line This refers to the low-voltage side line impedance. I LV This is the low-voltage side current phasor.

[0015] When harmonic voltage injection exists on the low-voltage side, the amplitude and phase of each harmonic are incorporated into the reverse power flow complex voltage excitation vector; when harmonic current data is obtained, it is first converted into the complex voltage of the corresponding harmonic based on the equivalent impedance of the external network on the low-voltage side, and then incorporated into the reverse power flow complex voltage excitation vector. (4) in, This is the complex voltage excitation vector for the reverse power flow on the low-voltage side; For the low-pressure side h The amplitude of the second harmonic complex voltage; For the first h Subharmonic phase; H The highest harmonic order included; superscript. T This represents the transpose of a vector.

[0016] Equations (2) to (4) are used to convert the reverse power, reactive power, power factor, tap position, line impedance and harmonic state of the distribution network side into complex voltage boundary conditions of the low-voltage port of the finite element field-circuit coupling model. When considering the nonlinearity of the iron core, the excitation vector containing harmonic components is solved by time-domain field-circuit coupling to obtain the time-averaged loss density in the corresponding period.

[0017] Furthermore, in step S3, a forward and reverse power flow port-external circuit switching matrix is ​​constructed. Specifically, this includes establishing an external circuit model that includes a high-voltage port, a low-voltage port, an external power source, the grid equivalent impedance, load branches, and distributed generation equivalent branches. In forward power flow mode, the high-voltage port is connected to the distributed generation equivalent branch or an external voltage source, and the low-voltage port is connected to the load branch. In reverse power flow mode, the low-voltage port is connected to the distributed generation equivalent branch or an external voltage source, and the high-voltage port is connected to the grid Thevenin equivalent absorption branch, making the same three-dimensional finite element model applicable to both forward and reverse power flow calculations.

[0018] (5) Where σ is the trend pattern identifier, σ=+ indicates a positive trend, σ= Indicates reverse current; M σ For trend mode σ The corresponding port switching matrix; M + and M - These are the port switching matrices for forward and reverse power flow, respectively; U src The source voltage vector; U sink The receiving-end voltage vector; U HV This refers to the voltage at the high-voltage side port. U LV This is the low-voltage side port voltage.

[0019] The port switching matrix not only changes the port order of the source and receiver, but also synchronously selects the equivalent branch of the distributed power supply or external voltage source, load branch, and grid equivalent impedance branch connected to the corresponding port, and updates the positive current direction in a unified manner, so that the port power conservation relationship and the finite element winding excitation direction are consistent under different power flow modes.

[0020] Further, in step S4, a three-dimensional equivalent finite element model of the oil-immersed transformer is established. Specifically, this includes: establishing a three-dimensional model based on the target transformer's structural parameters, encompassing the core, low-voltage winding, high-voltage winding, main insulation, oil channels, insulating oil, tank, and heat dissipation boundaries. (See [link to relevant documentation]). Figure 4 For laminated iron cores, an equivalent anisotropic parameter model of the laminates that satisfies error constraints is adopted, rather than simply treating the iron core as a homogeneous conductor; equivalent permeability, equivalent electrical conductivity, and equivalent thermal conductivity are set in the lamination plane direction and the lamination thickness direction, respectively.

[0021] The equivalent rule for laminated iron cores is corrected using no-load loss, iron loss curves, and a Bertotti-type loss model, and the error between the equivalent model and the calibration data obtainable from the set nonlinear BH magnetization curve meets a preset threshold. (6) in, P 0 represents no-load loss. P k For load loss, The top oil temperature, This refers to the hot spot temperature of the winding. Set the model calibration error threshold; This is the deviation in no-load loss. For load loss deviation, For top oil temperature deviation, For hot spot temperature deviation; when the calibration data only contains a portion of the quantities, calculate the relative error for the obtained calibration quantities and take the maximum value.

[0022] Further, in step S5, the field-magnetic coupling solution is performed, specifically including: inputting the reverse power flow complex voltage excitation vector obtained in step S2 into the port switching matrix in step S3, and solving for the core magnetic flux density distribution, leakage magnetic field distribution, winding current density distribution, core loss density, winding losses (winding DC loss, winding eddy current loss), and stray losses of structural components under different reverse power flow levels. The magnetic field control equation is expressed as: (7) in, For magnetic vector position, The reluctance is related to magnetic flux density and temperature. Equivalent conductivity The external circuit excitation current density, For induced current density, B , where is the magnetic flux density T For temperature, t For time.

[0023] Core losses are calculated using a decomposition model of hysteresis loss, classical eddy current loss, and additional losses. (8) in, The unit volume loss density of the iron core; , , These are the hysteresis loss coefficient, the classical eddy current loss coefficient, and the additional loss coefficient, respectively. f For frequency; B m This represents the peak value of the magnetic flux density. β This is the hysteresis loss index.

[0024] Winding losses include temperature-related DC resistance losses, skin effect losses, proximity effect losses, and eddy current losses induced by leakage magnetic field: (9) in, This refers to the loss density per unit volume of the winding. ρ 20 The winding resistivity at 20℃ (reference temperature); κ It is the temperature coefficient of resistance; T For winding temperature; Current density; For skin effect loss density; The density is the proximity effect loss density; The density of eddy current loss induced by leakage magnetic field.

[0025] Furthermore, in step S6, a non-uniform loss density conservation mapping method is established, specifically including: mapping the core loss density, winding loss density, and structural component loss density obtained from the field-circuit coupled simulation to the thermal-fluid coupled model according to the mesh nodes or element volumes. The non-uniform loss density conservation mapping satisfies the total loss conservation of each component before and after mapping, and transfers the loss density in the electromagnetic field mesh to the thermal-fluid coupled mesh through volume superposition weights, interpolation functions, or element integration methods, and the relative total loss error of each component before and after mapping does not exceed a preset mapping error threshold.

[0026] During the mapping process, the total loss of each component is kept constant: (10) in, The loss density is calculated for the electromagnetic field. For distributed volume heat sources in the heat-fluid model, For the corresponding component area; It is a spatial position vector. It is a volume infinitesimal element. The components are numbered: core represents the iron core, winding represents the winding, and tank represents the oil tank. The consistency of the heat source between the electromagnetic mesh and the thermal flux mesh is ensured by interpolation functions, element integration, or volume cross-weighting. The total loss error before and after mapping is calculated for each component. When the relative error exceeds the preset mapping error threshold, the mesh is refined again or the interpolation order is adjusted.

[0027] Furthermore, in step S7, a two-way thermal-fluid coupling solution is performed, specifically including: Based on the heat transfer control equation, fluid continuity equation, momentum equation, and energy equation, a heat-fluid model for insulating oil under natural or forced circulation is established: (11) in, To find the gradient, u For oil flow velocity, p For pressure, ρ o The density of the insulating oil, μ o For dynamic viscosity, β o The coefficient of volume expansion. c p For specific heat capacity, k o is the thermal conductivity. g It is the acceleration due to gravity. T For temperature, T 0 is the reference temperature. q T As a heat source for the body, Let T be the winding resistivity at temperature T. During the calculation, the insulating oil density, dynamic viscosity, thermal conductivity, specific heat capacity, and winding resistivity are updated according to temperature. The thermal-fluid coupling calculation is considered converged when the maximum temperature difference, average oil velocity difference, and the change in the weighted center coordinates of the hot spot temperature region between two consecutive iterations are all less than a preset threshold. (12) in, n This is the thermal-fluid coupling iteration step; , and The first n The temperature field, oil flow velocity field, and centroid coordinates of the hot spot high-temperature region in the next iteration; , and These are the convergence thresholds for temperature, velocity, and hotspot location, respectively.

[0028] Furthermore, in step S8, the hot spot location offset vector is determined by the difference between the temperature-weighted center coordinates of the hot spot high-temperature region under reverse power flow conditions and the temperature-weighted center coordinates of the hot spot high-temperature region under forward rated reference conditions; the reverse power flow temperature rise safety boundary is determined based on the hot spot temperature limit, the top layer oil temperature limit, the maximum magnetic flux density limit, and the insulation thermal aging acceleration factor limit.

[0029] Extract the center of gravity shift and temperature rise risk indicators of the hot spot high temperature area, specifically including: extracting the maximum winding hot spot temperature, top oil temperature, temperature-weighted center of gravity coordinates of the hot spot high temperature area, hot spot position shift vector, maximum magnetic flux density limit ratio, winding eddy current loss increment coefficient, top oil temperature increment, insulation thermal aging acceleration factor, and reverse power flow temperature rise safety boundary based on the thermal-fluid coupling solution results.

[0030] (13) In the formula, The coefficient for the degree of reverse current is α The temperature-weighted center coordinates of the hot spot high-temperature region The weighted center coordinates of the temperature in the corresponding hot-spot high-temperature region under the positive rated reference operating condition. The coefficient for the degree of reverse current is α The hot spot location offset vector at that time. The hot spot high-temperature region is defined as the winding temperature not lower than the maximum winding temperature under this operating condition minus the preset temperature difference Δ. T hs The set of elements. The temperature-weighted center is calculated using the portion of each element whose temperature exceeds the threshold and the element volume as weights.

[0031] (14) in, K B This is the maximum magnetic flux density limit ratio. B max For maximum magnetic flux density, B lim Preset magnetic flux density limit; η we This is the winding eddy current loss increment coefficient. This refers to the winding eddy current loss under reverse power flow conditions. This refers to the winding eddy current loss under the positive rated reference operating condition.

[0032] (15) in, It is an accelerating factor for thermal aging of insulation. Here, exp(·) represents the hotspot temperature; 383K is the absolute temperature of the reference hotspot. θ hs +273 represents the absolute temperature converted from the hotspot Celsius temperature. Based on the hotspot temperature limit, top oil temperature limit, maximum magnetic flux density limit, and insulation thermal aging acceleration factor limit, the reverse power flow temperature rise safety boundary is determined: (16) In the formula, α allow The maximum permissible reverse current coefficient; sup represents the supremum; θ hs ( α The degree of reverse current is α Hotspot temperature at that time; θ lim For hotspot temperature limits; θ top ( α ( ) represents the top oil temperature; θ top,lim This refers to the top oil temperature limit. F lim This is the limit for the thermal aging acceleration factor of insulation.

[0033] Furthermore, in step S9, model calibration and result output specifically include: calibrating the model using at least one of the following: factory no-load loss, load loss, short-circuit temperature rise test, top layer oil temperature monitoring data, fiber optic temperature measurement data, bench reverse power flow test data, or on-site reverse power flow operation data; when the error between the simulation result and the obtained calibration data exceeds a preset threshold, the heat dissipation boundary, material parameters, loss coefficient, or mesh density are corrected and recalculated.

[0034] The final output includes low-voltage side complex voltage excitation, port switching status, magnetic flux density distribution, loss distribution, oil flow velocity distribution, temperature field distribution, hot spot high-temperature region center of gravity offset path, maximum magnetic flux density limit ratio, winding eddy current loss increment, top oil temperature increment, insulation thermal aging acceleration factor, and reverse power flow allowable range under different reverse power flow levels.

[0035] The beneficial effects of this invention are as follows: 1) The reverse power state of the distribution network is converted into a low-voltage side complex voltage excitation vector, and when the harmonic current is known, it is equivalently converted into the corresponding harmonic complex voltage through an external network, which solves the problem that the finite element port boundary is difficult to determine under the reverse power flow condition.

[0036] 2) By synchronously switching the voltage source branch, load branch, grid equivalent impedance branch and current reference direction through the port switching matrix, forward and reverse power flow calculations can be realized in the same field-circuit coupling model, which improves the consistency of comparative analysis between different operating conditions.

[0037] 3) By mapping the non-uniform loss density conservation, the electromagnetic loss redistribution can be accurately transferred to the thermal-fluid model.

[0038] 4) By using the temperature-weighted center offset vector of hot spot high-temperature regions and the output of the reverse power flow allowable interval, the sensitivity of single grid hot spot nodes to the results is reduced, and the simulation results are transformed into quantitative indicators that can be used for operational risk assessment.

[0039] 5) Calibrate the closed loop through experimental or operational data to avoid the model remaining only at the level of qualitative simulation.

[0040] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0041] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1The overall flowchart of the simulation modeling and hot spot offset evaluation method for oil-immersed transformers with reverse power flow provided by the present invention is shown below. Figure 2 This diagram illustrates the connection relationship between the transformer port and the external circuit, as well as the switching of the current reference direction, under both forward and reverse power flow conditions. Figure 3 A schematic diagram of the calculation model for the voltage rise excitation on the low-voltage side of the reverse power flow; Figure 4 A schematic diagram of a three-dimensional equivalent finite element model of an oil-immersed transformer; Figure 5 A schematic diagram of the nonlinear BH curve and loss decomposition model of the iron core; Figure 6 A schematic diagram of the electromagnetic field loss density being conserved in the heat-fluid model; Figure 7 A schematic diagram of the weighted center shift path of temperature in hotspot high-temperature regions under different degrees of reverse current. Figure 8 This is a schematic diagram illustrating the division of the safety boundary and warning interval for temperature rise in the reverse current flow. Detailed Implementation

[0042] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0043] Please see Figures 1 to 8 This embodiment provides a method for simulation modeling and hotspot offset assessment of field-magnetic-thermal-current coupling in oil-immersed transformers oriented towards reverse power flow. The method uses an oil-immersed power transformer with a rated capacity of 50 MVA, a rated voltage of 110 / 10.5 kV, and a short-circuit impedance of 8% as the implementation object. Its no-load loss, load loss, connection group, tap range, tank size, oil passage size, and radiator parameters are obtained from design drawings, nameplates, or factory test reports. If the implementation object is a distribution transformer or a new energy step-up transformer, the corresponding rated capacity, voltage level, and cooling method parameters can be replaced using the same process.

[0044] In this embodiment, the transformer design, materials, oil passages, and radiator parameters shown in Table 1 are used as engineering inputs for the field-circuit-magnetic-thermal-fluid coupling simulation, and the forward rated reference operating condition and reverse power flow operating condition data shown in Table 2 are used to calibrate and verify the model.

[0045] Table 1. Main Design, Material and Heat Dissipation Input Parameters of Transformer

[0046] Table 2 Calibration and verification data for forward rated reference condition and reverse power flow condition

[0047] As shown in Table 2, under the positive rated reference condition, the simulated load loss is 180.0 kW, which is 2.6% different from the short-circuit test value of 175.4 kW at 75℃. The deviations of the winding hot spot temperature and the top oil temperature are 1.8 K and 1.3 K, respectively, indicating that the winding resistance temperature correction, oil channel equivalent modeling and radiator heat transfer boundary can well reproduce the measured temperature rise level.

[0048] When the reverse power flow coefficient α=1.00, the low-voltage side line voltage rises from 10.50kV to 11.05kV, and the equivalent active power absorbed by the high-voltage side is 49.0MW. Since the excitation end switches from the high-voltage side to the low-voltage side under reverse operating conditions, and the tap position, power factor, and low-voltage side voltage rise collectively change the core magnetic flux density and end leakage flux distribution, the model calculations show that the no-load loss increases from 34.0kW under the forward rated operating condition to 39.5kW, the load loss increases from 180.0kW to 188.6kW, the winding loss increases from 165.6kW to 173.8kW, the winding hot spot temperature rises from 93.0℃ to 98.4℃, and the top oil temperature rises from 63.8℃ to 66.7℃. The center of gravity of the hot spot high-temperature region shifted from rhs=(0.18m,0.00m,1.42m) to rhs=(0.24m,0.00m,1.20m). This result indicates that under near-rated reverse power supply conditions, reverse power flow not only increases the total loss and temperature rise level, but also alters the end leakage magnetic field, local winding losses, and hot spot location distribution.

[0049] In both operating conditions, the errors in no-load loss, load loss, and winding loss are all less than 5%, the top oil temperature error is less than 3K, and the hot spot temperature error is less than 5K, meeting the calibration targets set in this embodiment. Compared with the forward rated reference operating condition, under the reverse power flow condition of α=1.00, the increase in low-voltage side voltage, the increase in no-load loss, and the enhancement of end winding loss jointly push up the hot spot temperature, and the center of gravity of the hot spot moves towards the end of the low-voltage winding and the region with lower oil velocity. After the above calibration, the hot spot temperature, top oil temperature, magnetic flux density limit ratio, and thermal aging acceleration factor under different reverse power flow degrees can be used as the basis for dividing the safe zone, warning zone, and over-limit zone.

[0050] First, collect power distribution network operation data. For a given time... t Obtain the output of distributed power sources on the low-voltage side. P DG (t Low-voltage load P L ( t reactive power Q ( t ), measured voltage on the low-voltage side U LV ( t ), target voltage of high-voltage side bus U HV,ref ( t ), line impedance Z line Power factor cosφ Divider gear k t and harmonic voltage or harmonic current content. Active power injection from the low-voltage side to the high-voltage side is defined as positive, and reverse active power can be determined by... P rev ( t )=max( P DG ( t )- P L ( t The reverse current degree coefficient is calculated by equation (1), and further obtained by equation (1). α .

[0051] For the positive rated reference condition with α=0, the specified positive rated load and power factor are set, and the high-voltage side port is set as the input excitation terminal and the low-voltage side port is set as the load terminal; for α For the reverse power flow condition with a voltage > 0, the low-voltage side complex voltage excitation vector is calculated according to equations (2) to (4), and the voltage source or distributed power source equivalent branch at the low-voltage side port, the grid Thevenin equivalent absorption branch at the high-voltage side port, and the current reference direction are synchronously switched using equation (5). Thus, the forward rated operating condition and multiple reverse power flow conditions are all calculated in the same three-dimensional finite element model. See [reference needed]. Figure 2 .

[0052] During modeling, the core adopts an equivalent anisotropic parameter model of grained silicon steel sheets. Taking 30Q130 grained silicon steel sheets as an example, the thickness of the silicon steel sheets is set to the order of 0.30mm, and a nonlinear BH magnetization curve is input. (See [reference needed]). Figure 5 The core loss can be corrected by decomposing hysteresis loss, classical eddy current loss and additional loss according to the iron loss curve provided by the material manufacturer or by Equation (8). This setting is used to reflect the difference in lamination direction and local saturation effect, rather than simply replacing the laminated core with a low conductivity monolithic block.

[0053] The winding adopts a layered conductor model or an equivalent conductor model. For winding regions that need to be analyzed for local hot spots, the winding is divided into several pie segments or wire pie units along the axial and radial directions, and the mesh is refined for the end regions with strong leakage magnetic fields. For regular winding regions far from hot spots, equivalent conductors can be used to reduce the amount of computation. The winding resistivity is updated according to the temperature function, and the winding loss is decomposed into DC resistance loss, skin effect loss, proximity effect loss and leakage magnetic field induced eddy current loss according to equation (9).

[0054] Insulating oil, as an insulating and heat transfer medium, has thermophysical properties including density, specific heat capacity, thermal conductivity, dynamic viscosity, and coefficient of volumetric expansion, which update with temperature. For electromagnetic field solutions, insulating oil is not treated as a conductive path; if conductivity needs to be set, it is calculated based on measured volume resistivity or dielectric loss, taking the insulating oil as an example of an extremely low conductivity level, such as 10. -12 S / m to 10 -10 The S / m range is used instead of the values ​​used for conductive media.

[0055] The oil tank and radiator can be modeled using an equivalent heat transfer boundary model. For finned radiators, the equivalent heat transfer coefficient is calculated based on the fin geometry, material thermal conductivity, fin efficiency, and natural or forced convection conditions, and then applied to the outer wall of the oil tank or the equivalent surface of the radiator. If the application includes an oil pump or fan, the corresponding flow boundary or convection enhancement coefficient is added to the thermal-fluid model.

[0056] During mesh generation, locally refined meshes are used for core joints, winding ends, main leakage flux channels, narrow oil ducts, and expected hot spot areas; boundary layer meshes or adaptive meshes that can reflect the buoyancy-driven cycle are used for the oil region. To avoid model simplification leading to result distortion, the error constraint described in equation (6) is used for equivalent verification, and mesh independence checks are performed again after each parameter correction.

[0057] When solving for field-circuit coupling, the external circuit module outputs the voltage, current, and phase of the high-voltage and low-voltage ports according to the port switching matrix, and transmits the connection relationships of the source end, receiver end, and grid equivalent impedance branches to the magnetic field module; the magnetic field module outputs the core magnetic flux density, leakage magnetic field, and winding current density. For the forward rated operating condition, the focus is on verifying the no-load loss, load loss, and maximum magnetic flux density; for the reverse power flow operating condition, the focus is on extracting the local magnetic flux density changes caused by the low-voltage side complex voltage excitation, the changes in eddy current losses at the low-voltage winding ends, and the changes in the peak loss position.

[0058] During loss mapping, the core loss, winding loss, and stray loss of structural components in the electromagnetic field grid are mapped to distributed volume heat sources in the heat-fluid model according to equation (10). See [reference needed]. Figure 6If the electromagnetic grid and the thermal flow grid are inconsistent, data transfer is performed using volume overlap integral, nearest neighbor weighting, or shape function interpolation, and the total loss error before and after mapping is calculated for each component. If the error exceeds the preset mapping error threshold, the grid is refined again or the interpolation order is adjusted.

[0059] When solving the thermal-fluid coupling problem, Equation (11) is used to calculate the flow rate, pressure, and temperature distribution of the insulating oil under natural or forced circulation, and Equation (12) is used to determine convergence. After each thermal iteration, the winding resistivity, insulating oil viscosity, oil density, and thermal conductivity are updated, and the calculation of loss or heat source is returned until the temperature, oil velocity, and hot spot location all meet the convergence requirements.

[0060] In each group α Next, extract the winding hot spot temperature. θ hs ( α Top oil temperature θ top ( α Maximum magnetic flux density B max ( α ), winding eddy current loss P we ( α ) and the weighted coordinates of temperature in hotspot high-temperature areas r hs ( α The winding temperature should not be lower than the maximum winding temperature under this operating condition, minus the preset temperature difference Δ. T hs The set of elements is defined as the hot spot high-temperature region, and its centroid coordinates are calculated using the portion of each element whose temperature exceeds the threshold and the element volume as weights; the positive rated reference condition is used as the reference condition. r hs Using (0) as a reference, calculate the hotspot location offset vector according to equation (13), and obtain the hotspot offset direction, offset distance, and offset path. See [reference needed]. Figure 7 .

[0061] During risk assessment, the maximum magnetic flux density limit ratio and winding eddy current loss increment coefficient are calculated according to formula (14), the insulation thermal aging acceleration factor is calculated according to formula (15), and the reverse power flow allowable range is determined according to formula (16). θ hs , θ top , K B or F AA If any of the indicators exceeds the corresponding limit, then the corresponding α If the indicator is close to the limit but does not exceed the limit, it is determined to be in the warning zone; other operating conditions are determined to be in the safe zone. See [link to relevant documentation]. Figure 8 .

[0062] To establish a closed-loop verification process, the model is first calibrated under positive rated operating conditions using factory no-load loss, load loss, short-circuit temperature rise test data, and top oil temperature or fiber optic temperature measurement data. For example, the loss error can be set to be no greater than 5%, the top oil temperature error no greater than 3K, and the hot spot temperature error no greater than 5K. If the errors do not meet the requirements, the iron loss coefficient, winding resistivity, heat dissipation boundary, or oil flow parameters are then corrected.

[0063] For reverse power flow conditions, secondary calibration can be performed using reverse power flow operation data from low-voltage side distributed power sources, bench test data, or field monitoring data. Calibration includes low-voltage side voltage rise, high-voltage side absorbed power, winding hot spot temperature, top oil temperature, and oil flow velocity. This calibration closed loop enables the model not only to perform trend analysis but also to output a usable reverse power flow operating margin for engineering applications.

[0064] After the calculation is completed, the system outputs tables and curves, including α The corresponding relationships between the low-voltage side excitation voltage, maximum magnetic flux density, core loss, winding eddy current loss, hot spot temperature, top oil temperature, and insulation thermal aging acceleration factor; output such as Figure 7 The path of the center of gravity shift in the hot, high-temperature region is shown, and the output is as follows: Figure 8 The boundaries of the safe zone, warning zone, and over-limit zone are shown.

[0065] In this embodiment, if an increase in the reverse current flow leads to an increase in the amplitude of the fundamental complex voltage on the low-voltage side, coupled with harmonic injection and changes in the lag or lead power factor, the leakage magnetic field at the low-voltage winding ends and the winding eddy current losses may locally increase. The center of gravity of the temperature increase in the hot spot high-temperature area may shift from the upper-middle region under the forward rated operating condition to the end or a region with lower oil flow velocity. This shift result is used to alert maintenance personnel to pay attention to the accelerated local thermal aging of insulation, rather than judging the operational risk solely based on the global average temperature rise.

[0066] The above embodiments are described using oil-immersed transformers as an example, but the present invention is not limited to a specific capacity or voltage level. The method of the present invention can be used for distribution transformers, new energy step-up transformers, industrial user main transformers, or transformers with on-load tap-changing functions, as long as there is reverse power transmission from the low-voltage side to the high-voltage side and the risk of internal electromagnetic-thermal-current coupling needs to be assessed.

[0067] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for simulation modeling and hotspot shift evaluation of field-magnetic-thermal-current coupling in oil-immersed transformers oriented towards reverse power flow, characterized in that, The method includes: Obtain the parameters of the target oil-immersed transformer and the bidirectional power flow operation parameters of the distribution network; Under the unified port power and current reference direction, the reverse power flow complex voltage excitation on the low-voltage side is calculated based on the reverse power flow degree coefficient, high-voltage side voltage stability constraint, transformer equivalent impedance, line impedance, power factor and tap position. Construct a forward and reverse power flow port-external circuit switching matrix: Establish an external circuit model including high-voltage port, low-voltage port, equivalent branch of external power source or distributed power source, equivalent impedance of grid and load branch, and synchronously switch the connection relationship and current reference direction between high and low voltage ports and equivalent branch of external power source or distributed power source, load branch and equivalent impedance of grid through port switching matrix. A three-dimensional finite element model was established, including the iron core, windings, main insulation, insulating oil, oil channels, oil tank, and heat dissipation boundary. The non-uniform loss density of the core, windings and structural components is obtained by solving the field-circuit coupling under reverse power flow complex voltage excitation. The non-uniform loss density conservation is mapped to a distributed volume heat source in the thermal-fluid coupling model; A two-way coupled thermal-fluid iterative solution was performed to obtain the temperature field and flow field distribution under different degrees of reverse current flow. Calculate the temperature-weighted center coordinates of the hot spot high-temperature region from the set of winding units whose temperature is not lower than the maximum winding temperature minus the preset temperature difference, and extract the hot spot temperature, hot spot position offset vector, and reverse power flow temperature rise safety boundary.

2. The method for simulation modeling and hotspot offset evaluation of field-magnetic-thermal-fluid coupling of oil-immersed transformers oriented towards reverse power flow as described in claim 1, is characterized in that, The parameters of the target oil-immersed transformer include rated capacity, rated voltage, connection group, short-circuit impedance, no-load loss, load loss, tap position, cooling method, material parameters, heat dissipation parameters, and structural parameters; the material parameters include core material parameters and winding material parameters; the heat dissipation parameters include thermal properties of insulating oil; and the structural parameters include oil duct structure parameters, oil tank and radiator structure parameters. The bidirectional power flow operation parameters of the distribution network include the stable voltage on the high-voltage side, the actual voltage on the low-voltage side, the active power fed back from the low-voltage side, the reactive power fed back from the low-voltage side, the power factor, the line impedance, the output of distributed generation, the load level, and the harmonic content; the direction of active power injection from the low-voltage side to the high-voltage side is defined as the positive direction, and all port power, current, and reactive power are uniformly referenced according to this direction definition. The reverse power flow degree coefficient is defined as the ratio between the reverse active power (with the active power injection direction from the low-voltage side to the high-voltage side as positive) and the rated capacity of the transformer, and is used to set at least two reverse power flow simulation conditions.

3. The method for simulation modeling and hotspot offset evaluation of field-magnetic-thermal-fluid coupling of oil-immersed transformers oriented towards reverse power flow as described in claim 1, is characterized in that... The calculation of the reverse power flow complex voltage excitation on the low-voltage side specifically includes: based on the transformer's T-type or π-type equivalent circuit, combined with the high-voltage side voltage stability constraints, transformer leakage impedance, line impedance, tap position, and power factor, calculating the coefficients for different reverse power flow degrees. α Low-voltage side reverse power flow complex voltage excitation; The low-voltage side current is determined according to the complex power relationship: in, This refers to the low-voltage side phase current or equivalent line current phasor. To send back active power, To reverse reactive power, U LV * It is the conjugate of the low-voltage side complex voltage. j The imaginary unit; Given a high-voltage side reference voltage Transformer equivalent impedance Low-voltage side line impedance and tap ratio At that time, among them, k t Defined as the voltage transformation coefficient from the high-voltage side to the low-voltage side under the current tap position; the fundamental complex voltage excitation on the low-voltage side is expressed as: in, The degree of reverse current is α Low-voltage side fundamental voltage excitation; When harmonic voltage injection exists on the low-voltage side, the amplitude and phase of each harmonic are incorporated into the reverse power flow complex voltage excitation vector; when harmonic current data is obtained, it is first converted into the complex voltage of the corresponding harmonic based on the equivalent impedance of the external network on the low-voltage side, and then incorporated into the reverse power flow complex voltage excitation vector. in, This is the complex voltage excitation vector for the reverse power flow on the low-voltage side; For the low-pressure side h The amplitude of the second harmonic complex voltage; For the first h Subharmonic phase; H The highest harmonic order included; superscript. T This represents the transpose of a vector.

4. The method for simulation modeling and hotspot offset evaluation of field-magnetic-thermal-fluid coupling of oil-immersed transformers oriented towards reverse power flow as described in claim 1, is characterized in that... The port switching matrix is ​​used to synchronously switch the distributed power equivalent branch or external voltage source, load branch, grid equivalent impedance branch, and current reference direction of the high and low voltage ports according to the power flow mode. In the forward power flow mode, the high voltage side port is connected to the distributed power equivalent branch or external voltage source, and the low voltage side port is connected to the load branch. In the reverse power flow mode, the low voltage side port is connected to the distributed power equivalent branch or external voltage source, and the high voltage side port is connected to the grid Thevenin equivalent absorption branch.

5. The method for simulation modeling and hotspot offset evaluation of field-magnetic-thermal-fluid coupling of oil-immersed transformers oriented towards reverse power flow as described in claim 1, characterized in that, The core in the three-dimensional finite element model adopts a lamination equivalent anisotropic parameter model that satisfies error constraints, and equivalent magnetic permeability, equivalent electrical conductivity and equivalent thermal conductivity are set in the lamination plane direction and thickness direction, respectively. The equivalent rule for laminated iron cores is corrected using no-load loss, iron loss curves, and a Bertotti-type loss model, and the error between the equivalent model and the calibration data obtained from the set nonlinear BH magnetization curve meets a preset threshold. in, P 0 represents no-load loss. P k For load loss, The top oil temperature, This refers to the hot spot temperature of the winding. Set the model calibration error threshold; This is the deviation in no-load loss. For load loss deviation, For top oil temperature deviation, For hot spot temperature deviation; when the calibration data only contains a portion of the quantities, calculate the relative error for the obtained calibration quantities and take the maximum value.

6. The method for simulation modeling and hotspot offset evaluation of field-magnetic-thermal-fluid coupling of oil-immersed transformers oriented towards reverse power flow as described in claim 1, is characterized in that... The above-mentioned field-magnetic coupling solution under reverse power flow complex voltage excitation specifically includes: inputting the reverse power flow complex voltage excitation vector into the port switching matrix, and solving the core magnetic flux density distribution, leakage magnetic field distribution, winding current density distribution, core loss density, winding loss and structural component stray loss under different reverse power flow degrees. Core losses are calculated using a decomposition model of hysteresis loss, classical eddy current loss, and additional losses. in, The unit volume loss density of the iron core; , , These are the hysteresis loss coefficient, the classical eddy current loss coefficient, and the additional loss coefficient, respectively. f For frequency; B m This represents the peak value of the magnetic flux density. β The hysteresis loss index; Winding losses include temperature-related DC resistance losses, skin effect losses, proximity effect losses, and eddy current losses induced by leakage magnetic field: in, This refers to the loss density per unit volume of the winding. ρ 20 The resistivity of the winding at 20℃; κ It is the temperature coefficient of resistance; T For winding temperature; Current density; For skin effect loss density; The density is the proximity effect loss density; The density of eddy current loss induced by leakage magnetic field.

7. The method for simulation modeling and hotspot offset evaluation of field-magnetic-thermal-fluid coupling of oil-immersed transformers oriented towards reverse power flow as described in claim 1, is characterized in that... The non-uniform loss density conservation mapping satisfies the total loss conservation of each component before and after mapping, and transfers the loss density in the electromagnetic field grid to the thermal-fluid coupling grid through volume superposition weighting, interpolation function or unit integration method, and the relative total loss error of each component before and after mapping is not higher than the preset mapping error threshold.

8. The method for simulation modeling and hotspot offset evaluation of field-magnetic-thermal-fluid coupling of oil-immersed transformers oriented towards reverse power flow as described in claim 1, characterized in that, The heat-flow bidirectional coupling iterative solution specifically includes updating the insulating oil density, dynamic viscosity, thermal conductivity, specific heat capacity, and winding resistivity according to temperature, and using the changes in the weighted center coordinates of the maximum temperature difference, average oil velocity difference, and hot spot high-temperature region temperature as convergence criteria.

9. The method for simulation modeling and hotspot offset evaluation of field-magnetic-thermal-fluid coupling of oil-immersed transformers oriented towards reverse power flow as described in claim 1, characterized in that, The hot spot location offset vector is determined by the difference between the temperature-weighted center coordinates of the hot spot high-temperature region under reverse power flow conditions and the temperature-weighted center coordinates of the hot spot high-temperature region under forward rated reference conditions; the reverse power flow temperature rise safety boundary is determined based on the hot spot temperature limit, the top oil temperature limit, the maximum magnetic flux density limit, and the insulation thermal aging acceleration factor limit.

10. The method for simulation modeling and hotspot offset evaluation of field-magnetic-thermal-fluid coupling of oil-immersed transformers oriented towards reverse power flow as described in claim 1, characterized in that, The method also includes model calibration, specifically including: calibrating the model using at least one of the following: factory no-load loss, load loss, short-circuit temperature rise test, top oil temperature monitoring data, fiber optic temperature measurement data, bench reverse power flow test data, or field reverse power flow operation data; when the error between the simulation results and the obtained calibration data exceeds a preset threshold, the heat dissipation boundary, material parameters, loss coefficient, or mesh density are corrected and recalculated.

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