A method for balancing and optimizing excitation inductance and leakage inductance of a multi-core fractional-turn transformer
Patent Information
- Application Number
- CN202611528184.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-09-30
- Publication Date
- 2026-11-03
AI Technical Summary
Existing technologies struggle to characterize the main flux coupling and leakage flux characteristics of each sub-unit in a split-core fractional-turn transformer, and lack unified unbalance quantification indicators and directional optimization methods, leading to uneven current distribution and inconsistent pulse output.
By measuring the incremental self-inductance of the primary side and the mutual inductance parameters of the primary winding and the common secondary winding of each sub-unit, the equivalent excitation inductance and leakage inductance vectors are constructed, decomposed into common-mode and differential-mode components, an imbalance index is constructed, and the structural parameters are directionally corrected based on the sensitivity matrix.
Independent characterization and balanced optimization of the electromagnetic properties of each sub-unit were achieved, improving the consistency of current distribution and the stability of pulse output, while reducing computational costs and the number of prototype iterations.
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Abstract
Description
Technical Field
[0001] This invention relates to the fields of parameter testing and electromagnetic design technology for pulse power transformers, special transformers, and magnetic components, and particularly to a method for optimizing the balance of excitation inductance and leakage inductance in a multi-core fractional-turn transformer. This method can extract the main magnetic flux coupling parameters and leakage flux parameters of each sub-unit at a specified magnetization operating point, establish an imbalance characterization between sub-units, and accordingly make directional corrections to the core structure, winding layout, and related design parameters. Background Technology
[0002] In high-voltage, high-current, and fast pulse energy conversion applications, transformers typically need to simultaneously meet the requirements of high turns ratio, low leakage inductance, small excitation current, and good pulse consistency. Among these, the widely used design scheme is the split-core fractional-turn transformer.
[0003] The split-core fractional-turn transformer divides the overall magnetic circuit into multiple independent sub-cores with separate main magnetic circuits. Each sub-core has a one-turn primary winding, and a common secondary winding connects all the sub-cores simultaneously. When each sub-unit has the same flux change rate under balanced excitation, the induced voltages formed by the coupling between the common secondary winding and each sub-core are superimposed at the secondary port with the same polarity. This allows for a system-level primary equivalent number of turns of less than one turn, thus achieving a high turns ratio with fewer turns.
[0004] However, a split-core fractional-turn transformer consists of multiple sub-units with different geometric positions, assembly paths, and each responsible for the magnetization process. Factors such as the effective cross-sectional area of the sub-core, magnetic circuit length, air gap, material state, assembly position, primary-secondary spacing, conductor loop area, and local coupling relationship of the common secondary side can all lead to deviations in the magnetizing inductance and leakage inductance of each sub-unit. These deviations will cause uneven current distribution in each primary branch, inconsistent local magnetic flux density, and further affect the rise process and flat-top stability of the output pulse on the common secondary side.
[0005] Existing transformer testing methods typically focus on overall port parameters, such as no-load inductance, short-circuit inductance, or overall leakage inductance. For split-core structures with multiple independent primary sides and a common secondary side, a single overall parameter is insufficient to distinguish between main flux coupling deviation and leakage flux deviation, and it is also difficult to map port measurement results to specific sub-units. On the other hand, relying solely on finite element field distribution or trial-and-error adjustments usually requires high computational costs and multiple rounds of prototype iterations, and lacks a unified unbalance quantification index and calculable parameter correction directions. Improvements are often only achieved by changing the overall number of winding turns or uniformly adjusting the air gap of all cores, but this simultaneously alters the parameters of other balanced sub-units, offering only a temporary solution.
[0006] Therefore, there is an urgent need to design a method for identifying, evaluating, locating and optimizing the electromagnetic characteristic parameters of each sub-unit in a split-core fractional-turn transformer, so as to establish a traceable relationship between measurement data and structural design parameters. Summary of the Invention
[0007] The purpose of this invention is to provide an optimization method for balancing the excitation inductance and leakage inductance of a multi-core fractional-turn transformer, in order to solve the problems of existing overall port testing, which makes it difficult to characterize the main magnetic flux coupling characteristics and leakage magnetic flux characteristics of each sub-unit, difficult to locate the source of imbalance, and lack of directional optimization closed loop for structural parameters.
[0008] The multi-core fractional-turn transformer includes at least the following: magnetic core, There are one primary winding and one common secondary winding, among which The value is an integer not less than 3. Each sub-core is arranged according to a predetermined geometric rule, forming an independent closed main magnetic circuit. No two sub-cores share a complete closed main magnetic flux path. Each sub-core has a corresponding one-turn solid primary winding, and each primary winding has an independent electrical port. The common secondary winding is an integer-turn winding and is coupled to each sub-core using a consistent magnetic flux linkage. The first primary winding, the first The individual magnetic cores and the common secondary winding are related to the first The secondary side sections of the coupled sub-cores together constitute the first... Subunits, of which .
[0009] The method includes the following steps:
[0010] S1. Obtain the structural parameters, material parameters, and winding parameters of the multi-core fractional-turn transformer. Determine the physical turns ratio of each sub-unit based on the primary and secondary magnetic flux connection relationship, and determine the corresponding inductance measurement conditions. Under the condition that the common secondary winding and other non-tested primary windings are open-circuited, perform self-inductance measurement on each primary winding in sequence to obtain the incremental self-inductance of the primary winding of each sub-unit. Under the condition that other non-tested primary windings are open-circuited, connect the primary winding of each sub-unit to the common secondary winding in sequence with two opposite series polarities and measure the corresponding combined inductance respectively, and then calculate the mutual inductance parameters between each primary winding and the common secondary winding.
[0011] S2. Based on the physical turns ratio, primary-side incremental self-inductance, and mutual inductance parameters of each sub-unit, the equivalent excitation inductance and equivalent leakage inductance of each sub-unit are calculated using the primary-side reverse Γ-type equivalent circuit model.
[0012] S3. Construct the equivalent magnetizing inductance and equivalent leakage inductance into magnetizing inductance vector and leakage inductance vector, and decompose them into magnetizing inductance common-mode component, magnetizing inductance differential-mode component, leakage inductance common-mode component and leakage inductance differential-mode component.
[0013] S4. Based on the common-mode component of the excitation inductor, the differential-mode component of the excitation inductor, the common-mode component of the leakage inductor, and the differential-mode component of the leakage inductor, respectively, construct the excitation imbalance index and the leakage inductance imbalance index, and compare them with preset thresholds to determine the electromagnetic characteristic balance state. If neither index exceeds the preset threshold, it indicates that the excitation inductance and leakage inductance of each sub-unit meet the balance requirements. If the electromagnetic characteristic balance requirements are not met, determine the deviation sub-unit and deviation type based on the amplitude and polarity of the differential-mode component.
[0014] S5. Determine candidate main adjustment correction variables based on the type of deviation: excitation deviation corresponds to the air gap parameter of the sub-core, and leakage inductance deviation corresponds to the spacing parameter between the local section of the common secondary winding and the sub-core; by applying perturbation to each candidate main adjustment correction variable, obtain the residual change, and construct a sensitivity matrix for solving the optimal correction amount;
[0015] S6. Based on the sensitivity matrix, establish an optimization model for candidate master tone correction variables. Under the constraints of air gap range, spacing parameters, magnetic flux density, temperature rise, and manufacturing tolerance, solve for the optimal correction direction and correction amount of the candidate master tone correction variables. Accordingly, update the structural or manufacturing parameters of the deviation sub-unit and re-execute the sub-unit electromagnetic characteristic evaluation. When the imbalance index still does not meet the threshold, iteratively update the candidate master tone correction variables until both the excitation imbalance index and the leakage inductance imbalance index meet the preset threshold.
[0016] Furthermore, step S1 is as follows:
[0017] S11. Obtain the effective cross-sectional area, equivalent magnetic circuit length, air gap size, spatial position and magnetic material parameters of each sub-core, and obtain the number of turns, conductor size, conductor path, winding position, winding spacing and winding polarity parameters of each primary winding and common secondary winding.
[0018] Based on the magnetic flux linkage between a single primary winding and a common secondary winding, determine the physical turns ratio between the primary winding and the common secondary winding in each sub-unit.
[0019]
[0020] in, The number of turns in the primary winding for each sub-unit. This refers to the number of turns in the common secondary winding. This physical number of turns ratio... This differs from the system-level fractional turns equivalent turns ratio formed when n sub-units operate together.
[0021] Based on the excitation amplitude, bias magnetic field, and preset magnetic flux density variation range of the split-core fractional-turn transformer, the magnetization operating point to be evaluated is set.
[0022] S12, for the first The primary winding, the common secondary winding, and the winding excluding the first... All primary windings except the first primary winding remain open, and the first primary winding... Each primary winding is connected to the LCR bridge as the winding under test, and the corresponding sub-unit is measured. primary side incremental self-inductance Traverse all sub-units and obtain the primary edge incremental self-inductance of all sub-units. .
[0023] S13, Select the first The nth sub-unit is used as the currently tested sub-unit, so that except for the nth sub-unit... All primary windings except the first primary winding remain open. The primary winding and common secondary winding of each sub-unit are connected in series with the first polarity, that is, the non-corresponding leads of the primary winding are connected to the corresponding leads of the common secondary winding, and the corresponding first combined inductance is measured.
[0024] The first The primary winding and common secondary winding of each sub-unit are connected in the second series polarity, that is, the non-corresponding leads of the primary winding are connected to the non-corresponding leads of the common secondary winding, and the corresponding second combined inductance is measured.
[0025] Calculate the first Mutual inductance parameters between the primary winding and the common secondary winding Its expression is
[0026]
[0027] By traversing each sub-unit, the mutual inductance parameters between each primary winding and the common secondary winding are obtained. And the signs of each mutual inductance parameter are unified according to the preset winding reference direction.
[0028] Furthermore, step S2 is as follows:
[0029] Based on the common physical turns ratio of each sub-unit , No. The primary incremental self-inductance of the primary winding and the Mutual inductance parameters between the primary winding and the common secondary winding Calculate the first The equivalent magnetizing inductance of each sub-unit converted to the original side and equivalent leakage inductance ,in
[0030]
[0031]
[0032] This step is performed sequentially on each sub-unit to obtain the equivalent magnetizing inductance and equivalent leakage inductance of each sub-unit.
[0033] Furthermore, step S3 is as follows:
[0034] S31. Based on the equivalent magnetizing inductance and equivalent leakage inductance of each sub-unit, construct the magnetizing inductance vector according to the preset numbering order of each sub-unit.
[0035]
[0036] and leakage vector
[0037]
[0038] S32. Construct a unit common-mode basis vector with all elements equal.
[0039]
[0040] And construct a differential mode projection matrix orthogonal to the unit common mode basis vectors.
[0041]
[0042] in, It is an n-order identity matrix.
[0043] S33. Project the excitation inductance vector onto the common-mode subspace and the differential-mode subspace respectively to obtain the common-mode component of the excitation inductance.
[0044]
[0045] Differential mode component of magnetizing inductance
[0046]
[0047] The leakage inductance vector is projected onto the common-mode subspace and the differential-mode subspace, respectively, to obtain the leakage inductance common-mode component.
[0048]
[0049] and leakage inductance differential mode component
[0050]
[0051] Furthermore, the excitation imbalance index and leakage inductance imbalance index are constructed as follows:
[0052] According to the common-mode component of the excitation inductor Differential mode component of magnetizing inductance Calculate the excitation imbalance index
[0053]
[0054] According to the common-mode component of the leakage inductance and leakage inductance differential mode component Calculate the leakage inductance imbalance index
[0055]
[0056] In the formula, and These are the preset lower limits of positive inductance, which have the dimension of inductance.
[0057] Furthermore, the specific details of the deviation sub-unit and deviation type determined based on the amplitude and polarity of the differential mode component are as follows:
[0058] The excitation imbalance index With preset excitation balance threshold Compare and use the leakage inductance imbalance index Balance with preset leakage inductance threshold Comparison. When and If the conditions are not met, each sub-unit is determined to meet the preset electromagnetic characteristic balance requirements; otherwise, each sub-unit is determined not to meet the preset electromagnetic characteristic balance requirements.
[0059] When a sub-unit does not meet the preset electromagnetic characteristic balance requirement, for the sub-unit that does not meet the preset electromagnetic characteristic balance requirement, its differential mode component of the excitation inductance is queried sequentially. The corresponding elements in the table are used to calculate the normalized values.
[0060]
[0061] and leakage inductance differential mode component The corresponding elements in the table are used to calculate the normalized values.
[0062]
[0063] in, and These are the first components of the differential mode of the magnetizing inductance and the differential mode of the leakage inductance, respectively. One element, and These are the arithmetic mean values of the equivalent magnetizing inductance and equivalent leakage inductance of each sub-unit, respectively. and These are the preset lower limits of positive inductance, which have the dimension of inductance.
[0064] When the Each subunit satisfies and When at least one condition is met, the first The following sub-units are identified as deviation sub-units, among which... and These are the preset excitation positioning threshold and the preset leakage inductance positioning threshold, respectively.
[0065] The deviation types include magnetizing inductance deviation and leakage inductance deviation, when When, it is determined that the deviation subunit has an excitation inductance deviation; when When the above conditions are met, it is determined that the deviation subunit has a leakage inductance deviation; when the conditions are met simultaneously... and When this occurs, it is determined that the deviation subunit has a mixed deviation.
[0066] According to the elements in the differential mode component of the excitation inductance Elements in the differential mode component of leakage inductance The sign of the variable determines the direction of the deviation: when the element in the corresponding differential mode component is greater than zero, it is determined that the magnetizing inductance or leakage inductance of the corresponding deviation sub-unit is larger than the average inductance level of each sub-unit; when the element in the corresponding differential mode component is less than zero, it is determined that the magnetizing inductance or leakage inductance of the corresponding deviation sub-unit is smaller than the average inductance level of each sub-unit.
[0067] Furthermore, the candidate principal modulator variable is determined according to the following principles:
[0068] When the deviation subunit has an excitation inductance deviation, the air gap parameter of the corresponding sub-core is determined as a candidate main adjustment correction variable for the excitation inductance deviation; when the deviation subunit has a leakage inductance deviation, the spacing parameter between the secondary side section of the common secondary winding corresponding to the deviation subunit and the sub-core is determined as a candidate main adjustment correction variable for the leakage inductance deviation; when the deviation subunit has a mixed deviation, both the air gap parameter and the spacing parameter are determined as candidate main adjustment correction variables.
[0069] Furthermore, obtaining the residual changes and constructing the sensitivity matrix for solving the optimal correction specifically includes:
[0070] 1) Assemble the candidate principal modifier variables into a modifier variable vector. ,in Adjust variables for candidate keynote speakers. The number of candidate master tone correction variables is given, and the elements in the correction variable vector include at least one of the sub-core air gap parameter and spacing parameter corresponding to the deviation sub-unit.
[0071] 2) Construct an electromagnetic characteristic imbalance residual vector based on the differential mode components of the excitation inductance and leakage inductance.
[0072]
[0073] The electromagnetic characteristic unbalanced residual vector is used to characterize the excitation inductance deviation and leakage inductance deviation of each sub-unit.
[0074] The first variable in the modified variable vector is then processed sequentially. Each candidate modulator variable is subject to a preset perturbation. While keeping other candidate principal correction variables unchanged, the unbalanced electromagnetic characteristic vector after disturbance is obtained through at least one of the following methods: magnetic circuit analytical calculation, electromagnetic field simulation, or sample disturbance test. .
[0075] 3) According to the first Given the preset disturbances of each candidate master correction variable and their corresponding changes in the electromagnetic characteristic imbalance residual vector, calculate the corresponding sensitivity vector.
[0076]
[0077] Further construct the sensitivity matrix
[0078]
[0079] Furthermore, the optimization model for the candidate principal modulator variable is constructed as follows:
[0080] Based on the sensitivity matrix An optimization model for candidate principal correction variables is established with the goal of minimizing the weighted L2 norm of the unbalanced electromagnetic characteristic residual vector after perturbation.
[0081]
[0082] in, This is the vector of correction values for the candidate principal modifier variables. The weight matrix is determined based on the preset balance thresholds of the excitation inductance imbalance index and the leakage inductance imbalance index.
[0083] Furthermore, in step S6, when solving for the correction amount of the candidate master correction variable, at least one of the following constraints is applied to the correction amount of the candidate master correction variable: sub-core air gap adjustment range constraint, spacing parameter adjustment range constraint between the secondary side section of the common secondary winding and the corresponding sub-core, sub-core magnetic flux density constraint, temperature rise constraint, and manufacturing tolerance constraint. Under the constraints, the optimization model is solved to obtain the correction direction and correction amount of the candidate master correction variable.
[0084] Subsequently, according to the correction direction and correction amount, at least one of the following is updated: the air gap parameter of the sub-core within the deviation sub-unit and the spacing parameter between the secondary side section of the common secondary winding and the sub-core.
[0085] Compared to traditional solutions, this invention has the following core advantages:
[0086] 1. This invention improves the electromagnetic parameter measurement and modeling methods for multi-core fractional-turn transformers, enabling independent characterization of the main magnetic flux coupling characteristics and leakage flux characteristics of each sub-unit. By sequentially measuring the open-circuit incremental self-inductance of each primary winding and the combined inductance of each primary winding and the common secondary winding under two opposite series polarities, the mutual inductance parameters of each sub-unit are obtained. Based on the equivalent circuit, the equivalent magnetizing inductance and equivalent leakage inductance are extracted separately, avoiding the problem of being unable to distinguish between main magnetic flux coupling deviation and leakage flux deviation solely based on the overall transformer port parameters.
[0087] 2. Construct a unified and quantitative evaluation method for the electromagnetic characteristic balance of multi-core fractional-turn transformers. This invention constructs parameter vectors based on the equivalent magnetizing inductance and equivalent leakage inductance of each sub-unit, and decomposes them into common-mode and differential-mode components, thereby obtaining quantitative excitation imbalance and leakage inductance imbalance indices.
[0088] 3. This invention enables targeted corrections with clear physical orientations based on different deviation mechanisms. It uses the air gap parameter of the sub-core of the deviation sub-unit as a candidate principal adjustment variable for excitation inductance deviation, and the spacing parameter between the secondary side section of the common secondary winding and the corresponding sub-core as a candidate principal adjustment variable for leakage inductance deviation. It is generally believed that the air gap and spacing have cross-coupling effects on excitation / leakage inductance, making independent control difficult. This invention uses a sensitivity matrix to simultaneously characterize the direct and cross-influences of each correction variable on excitation and leakage inductance deviations, thereby improving the targeting and effectiveness of structural parameter correction. It also reveals for the first time the physical mapping relationship between the differential mode component of electromagnetic parameters and structural correction variables, and constructs a complete closed-loop optimization system based on this. Attached Figure Description
[0089] Figure 1 This is a schematic flowchart of the method of the present invention;
[0090] Figure 2(a) in the figure refers to the four-core fractional-turn transformer described in the embodiment of the present invention; Figure 2 (b) in the figure is a sub-unit of the four-core fractional-turn transformer described in the embodiment of the present invention;
[0091] Figure 3 This is a schematic diagram of the air gap parameters and winding spacing of the deviation sub-unit;
[0092] Figure 4 Wiring method for identifying self-inductance parameters of sub-units;
[0093] Figure 5 (a) in the diagram represents the wiring method for extracting mutual inductance parameters: first series polarity; Figure 5 (b) in the diagram represents the wiring method for extracting mutual inductance parameters: second series polarity;
[0094] Figure 6 A comparison diagram of the effects before and after optimization using the optimization method provided in this embodiment of the invention for a four-core fractional-turn transformer; Figure 6 (a) shows the optimized waveforms of the primary winding currents in the first four paths; Figure 6 (b) shows the optimized waveform of the four primary winding currents; Figure 6 (c) in the figure represents the optimized voltage waveform of the front and secondary windings; Figure 6 In the figure, (d) represents the optimized secondary winding voltage waveform. Detailed Implementation
[0095] To make the objectives, technical solutions, and advantages of this invention clearer, the following detailed description, in conjunction with the accompanying drawings and embodiments, provides a method for evaluating and optimizing the electromagnetic characteristics of sub-units of a split-core fractional-turn transformer provided by this invention. It should be noted that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.
[0096] This embodiment uses a four-core fractional-turn transformer as the evaluation and correction object. The equivalent magnetizing inductance and equivalent leakage inductance of each sub-unit are measured, extracted and balanced, and the corresponding structural parameters are corrected according to the evaluation results.
[0097] like Figure 2As shown in (a), the four-core fractional-turn transformer includes a first sub-core, a second sub-core, a third sub-core, and a fourth sub-core arranged circumferentially along a common axis, and a first primary winding P1, a second primary winding P2, a third primary winding P3, and a fourth primary winding P4 respectively wound on each sub-core, as well as a common secondary winding S. The main magnetic circuits of each sub-core are independent of each other, and there is no common closed main magnetic flux path between any two sub-cores; each primary winding is a single-turn solid winding and is electrically independent of each other; the common secondary winding S is an integer-turn winding and is coupled to each sub-core with the same magnetic flux linkage structure and electrically connected to the same common secondary winding port.
[0098] In this embodiment, the basic design parameters of the four-core fractional-turn transformer are as follows:
[0099] The core material of the fractional-turn transformer is 0.18mm oriented thin silicon steel, with a stacking factor of 0.95, and the actual cross-sectional area of the sub-core is 50cm². 2 The effective magnetic circuit length is 70cm, and the preset air gap is... The corresponding total air gap spacing is 4mm. Actual transformer assembly parameters do not require measurement.
[0100] Each primary winding is composed of a single layer of thin copper foil, wherein the effective conductor cross-sectional area of the thin copper foil is... The common secondary winding has 20 turns and is formed by winding a single strand of enameled copper wire. The effective conductor cross-sectional area of the single strand of enameled copper wire is... .
[0101] like Figure 2 As shown in (b) of the diagram, the first The first magnetic core, Among the primary windings and the common secondary winding, the first... The secondary side sections of the coupled sub-cores together constitute the first... Subunits, of which The physical turns ratio of the primary winding to the common secondary winding in each of the sub-units for
[0102]
[0103] in, The number of turns in the primary winding for each sub-unit. This represents the number of turns in the common secondary winding.
[0104] The pulse repetition frequency corresponding to the magnetization operating point to be evaluated is 10Hz, the effective excitation time of a single pulse is 5μs, the primary side excitation amplitude is 1kV, the rated operating temperature is 25℃, the bias magnetic field is unbiased, and the preset maximum magnetic flux density is 1T.
[0105] like Figure 3 As shown, each sub-core includes a main core, an auxiliary core, and upper and lower yokes bridging the upper and lower ends of the main and auxiliary cores. The primary winding is wound on the main core. Air gaps are provided between the upper and lower yokes and their corresponding main and auxiliary cores. The air gap dimensions at each connection point are denoted as [insert dimensions here]. The distance between the common secondary winding and the surface of the corresponding sub-core main core is denoted as . .
[0106] The flowchart of the optimization method for balancing the excitation inductance and leakage inductance of a multi-core fractional-turn transformer provided in this embodiment is as follows: Figure 1 As shown, it includes the following steps:
[0107] S1. Obtain the primary incremental self-inductance of each sub-unit and the mutual inductance parameters between the primary winding and the common secondary winding.
[0108] S11. Before measurement, first calibrate the test probe and connection fixture of the LCR bridge. Connect the test probe to the connecting wires and fixtures used in the actual measurement, and perform open-circuit calibration and short-circuit calibration in sequence to compensate for the parasitic capacitance, parasitic inductance, and contact impedance introduced by the test probe, connecting wires, and fixtures themselves. After calibration, keep the position and connection method of the test probe, connecting wires, and fixtures unchanged to reduce the impact of changes in the measurement connection state on the consistency of measurement results of each subunit.
[0109] S12. Demagnetize the first to fourth sub-cores. Specifically, with the primary windings of the first to fourth sub-cores remaining open, an alternating demagnetizing excitation is applied to each sub-core through the common secondary winding. The initial amplitude of the alternating demagnetizing excitation is set to an amplitude that enables each sub-core to form alternating positive and negative magnetization, and gradually decreases according to a preset decay law until the amplitude of the alternating demagnetizing excitation decays to zero, at which point demagnetization is considered complete. If the magnetization operating point to be evaluated contains a non-zero bias magnetic field, the bias magnetic field needs to be established and maintained through an independent biasing device.
[0110] S13, such as Figure 4 As shown, in the measurement of the first When the primary winding of the first primary winding increases its self-inductance, connect the test terminals of the LCR bridge to the first... The two external terminals of the primary winding simultaneously enable the common secondary winding and the winding excluding the first... All primary windings except for the one primary winding remain open. Read the inductance parameters measured by the LCR bridge and use them as the first... The primary winding's incremental self-inductance near the magnetization operating point .
[0111] The above measurement process was performed sequentially on the first to fourth primary windings to obtain...
[0112]
[0113] S14. After completing the measurement of the self-inductance parameters of the first to fourth primary windings, the mutual inductance parameters between each primary winding and the common secondary winding are identified in sequence. Figure 5 The wiring method for identifying mutual inductance parameters of sub-units, wherein, Figure 5 (a) in the diagram represents the connection method where the primary winding and the common secondary winding are connected according to the first series polarity, that is, the non-same-name terminal lead of the primary winding is connected to the same-name terminal lead of the common secondary winding. Figure 5 (b) in the diagram represents the wiring method where the primary winding and the common secondary winding are connected according to the second series polarity, i.e., the non-corresponding leads of the primary winding are connected to the non-corresponding leads of the common secondary winding. Identify the... When selecting the mutual inductance parameters of the first subunit, choose the... One primary winding is used as the current primary winding under test, while the other three non-tested primary windings are kept open.
[0114] First, the first The primary winding and the common secondary winding are connected in series with the first series polarity. The test terminals of the LCR bridge are connected to the new port formed by the series connection, and the inductance of the first combination is measured. First combination of inductors Its physical composition is as follows:
[0115]
[0116] In the formula, For the self-inductance of the common secondary winding, For the first The mutual inductance parameters between the primary winding and the common secondary winding.
[0117] Next, the first The primary winding and the common secondary winding are connected in series with the second polarity. The test terminals of the LCR bridge are connected to the new port formed by the series connection, and the second combined inductance is measured. The second combination of inductors Its physical composition is as follows:
[0118]
[0119] The above combined inductance measurement process is performed sequentially on the first to fourth sub-units to obtain the combined inductance measurement results under two series polarities.
[0120]
[0121] and
[0122]
[0123] Based on the difference between the first and second combined inductances, the first... Mutual inductance parameters between the primary winding and the common secondary winding
[0124]
[0125] And thus obtain
[0126]
[0127] The mutual inductance parameters characterize the primary-secondary coupling relationship.
[0128] S2. Calculate the equivalent magnetizing inductance and equivalent leakage inductance of each sub-unit referred to the original side.
[0129] After identifying the incremental self-inductance and mutual inductance parameters of the primary side of the first to fourth sub-units, the equivalent excitation inductance and equivalent leakage inductance of each sub-unit converted to the primary side are extracted using the inverse Γ-type equivalent circuit model on the primary side.
[0130] For the Each sub-unit, based on its physical turns ratio Incremental self-inductance of the original side and the mutual inductance parameters between the primary winding and the common secondary winding Calculate the corresponding equivalent magnetizing inductance. Equivalent leakage inductance of the original side
[0131]
[0132]
[0133] S3. Construct the excitation inductance vector and leakage inductance vector.
[0134] S31. Based on the equivalent magnetizing inductance and equivalent leakage inductance of each sub-unit, sort them according to the preset numbering order of each sub-unit, and substitute the measured parameters to obtain the magnetizing inductance vector.
[0135]
[0136] and leakage vector
[0137]
[0138] S32. Furthermore, to characterize the average level of each sub-unit parameter and its deviation from the average level, a unit common mode basis vector of the four-sub-unit system is constructed.
[0139]
[0140] Sum and difference mode projection matrix
[0141]
[0142] S33. Based on the aforementioned unit common-mode basis vector, calculate the common-mode component of the excitation inductance vector as follows:
[0143]
[0144] The differential-mode component of the excitation inductance vector is calculated based on the differential-mode projection matrix.
[0145]
[0146] Similarly, the common-mode component of the leakage inductance vector is calculated as follows:
[0147]
[0148] Calculate the differential mode component of the leakage inductance vector
[0149]
[0150] S4. Construct excitation imbalance index and leakage inductance imbalance index, and determine the deviation sub-unit and deviation type based on the amplitude and polarity of the differential mode component.
[0151] S41. After obtaining the common-mode component, differential-mode component, common-mode component, and differential-mode component of the excitation inductance of the first to fourth sub-units, construct the excitation imbalance index and leakage inductance imbalance index respectively to evaluate the balance state (electromagnetic characteristic balance / consistency state) of the excitation inductance and leakage inductance among the four sub-units.
[0152] According to the common-mode component of the excitation inductor Differential mode component of magnetizing inductance Calculate the excitation imbalance index for
[0153]
[0154] According to the common-mode component of the leakage inductance and leakage inductance differential mode component Calculate the leakage inductance imbalance index for
[0155]
[0156] In the formula, and These are the preset lower limits of positive inductance with inductance dimensions, preferably... , .
[0157] S42. Compare the excitation imbalance index with a preset excitation balance threshold, and compare the leakage inductance imbalance index with a preset leakage inductance balance threshold. If one or both exceed the preset threshold, it is determined that the electromagnetic characteristic balance requirement is not met. In this embodiment, the preset excitation balance threshold and the preset leakage inductance balance threshold are respectively set to... , The excitation imbalance index and leakage inductance imbalance index are compared with their respective preset balance thresholds. and Therefore, it is determined that the first to fourth sub-units as a whole do not meet the preset electromagnetic characteristic balance requirements. Specifically, the excitation inductance parameter does not meet the preset balance requirements, while the leakage inductance parameter does. Thus, the electromagnetic characteristic imbalance in this embodiment is mainly manifested as an imbalance in the excitation inductance between the sub-units, and no correction is needed for the leakage inductance parameter.
[0158] S43. Further, the deviation sub-unit causing the imbalance of the excitation inductor is determined based on the amplitude of each element in the differential mode component of the excitation inductor. The absolute values of the elements in the differential mode component of the excitation inductor corresponding to each sub-unit are as follows:
[0159]
[0160] The average value of the elements in the differential mode component of the excitation inductance of each sub-unit is used as the reference. The reference element in the differential mode component of the excitation inductance is...
[0161]
[0162] Furthermore, by normalizing the elements in the differential mode component of the excitation inductance, we can obtain...
[0163]
[0164] The excitation positioning threshold is preset according to the excitation inductance balance requirement. In this embodiment, the excitation positioning threshold is... Therefore, the second sub-unit was determined to be the deviation sub-unit for subsequent structural parameter correction.
[0165] S5. Determine candidate principal correction variables based on the deviation type, and construct a sensitivity matrix for solving the optimal correction amount.
[0166] S51. Since the leakage inductance imbalance index does not exceed the preset leakage inductance balance threshold, the spacing parameter between the common secondary winding and the corresponding sub-core will not be adjusted in this round of correction. Listed as variables to be adjusted, while the air gap parameter corresponding to the second sub-core is... It was determined to be a candidate principal correction variable for excitation inductance deviation.
[0167] S52. Construct a residual vector based on the differential-mode components of the excitation inductance and leakage inductance. Since the average values of the excitation inductance and leakage inductance are both greater than the corresponding positive lower limit, the differential mode component obtained in step S3 is substituted into the electromagnetic characteristic unbalanced residual vector to obtain...
[0168]
[0169] in, , These are the average values of the magnetizing inductance and leakage inductance of the four sub-units, respectively.
[0170] Substituting specific values yields
[0171]
[0172]
[0173] Because the equivalent magnetizing inductance of the second sub-unit is relatively large, a preset disturbance is applied to the second sub-core along the direction of increasing the air gap. The perturbed air gap size is obtained. , The air gap size of the second sub-core before the first round of correction. The disturbance amount is determined based on the manufacturing tolerance of the air gap of the second sub-core, the allowable adjustment range, and the identifiability of changes in the air gap by electromagnetic parameters, and should be significantly greater than the air gap machining and assembly errors, while remaining within a range of local linear approximation effectiveness.
[0174] S53. After completing the air gap parameter perturbation, repeat steps S1 to S4 using at least one of the following methods: magnetic circuit analytical calculation, electromagnetic field simulation, or sample perturbation test, to obtain the perturbed primary-side self-inductance and mutual inductance.
[0175]
[0176]
[0177] and equivalent magnetizing inductance, equivalent leakage inductance
[0178]
[0179]
[0180] And construct the electromagnetic property imbalance residual vector after perturbation.
[0181]
[0182] in,
[0183]
[0184]
[0185] In contrast, the normalized excitation inductance deviation of the second sub-unit decreased from 0.877 to 0.781, indicating that adjusting the air gap parameters of the second sub-core along the direction of increasing air gap can reduce the positive excitation inductance deviation of the second sub-unit.
[0186] S54. Based on the relationship between the electromagnetic characteristic imbalance residual vector changes before and after the disturbance, calculate the sensitivity vector corresponding to the air gap parameters of the second sub-core.
[0187]
[0188] Among them, the element in the sensitivity vector corresponding to the deviation of the excitation inductance of the second sub-unit is: This indicates that increasing the air gap of the second sub-core can reduce the positive excitation inductance deviation of the second sub-unit, and the disturbance direction of the air gap parameters is consistent with the expected correction direction. Furthermore, the excitation imbalance index after disturbance is... The leakage inductance imbalance index is
[0189] Therefore, it can be concluded that the air gap of the second sub-core increases. Subsequently, the excitation imbalance index decreased from approximately 50.82% to approximately 45.32%, but remained above the preset excitation balance threshold; the leakage inductance imbalance index decreased from approximately 2.53% to approximately 0.78%, continuing to meet the preset leakage inductance balance requirement. Therefore, the aforementioned The air gap adjustment amount is used as a sensitivity identification disturbance amount to further correct the direction and amount of the second sub-core air gap parameter in subsequent calculations, rather than being directly used as the final correction amount.
[0190] S6. Establish an optimization model for the candidate dominant correction variables and solve for the optimal correction amount.
[0191] S61. Establish a local linear correction model for the air gap parameters of the second sub-core.
[0192]
[0193] In the formula, This is a weight matrix determined based on preset thresholds for the magnetizing inductance imbalance index and the leakage inductance imbalance index.
[0194] Since both the excitation inductance residual and the leakage inductance residual have been normalized, this embodiment... Take a unit weight matrix and use the minimum L2 square of the corrected electromagnetic property imbalance residual vector as the optimization objective.
[0195]
[0196] Considering that the sensitivity matrix is based on The air gap perturbation is obtained. To ensure the effectiveness of the local linear approximation, the air gap correction amount for this round is limited to the corresponding trust region.
[0197]
[0198] Without considering the trust region constraint, the unconstrained correction amount corresponding to the local linear optimization model is:
[0199]
[0200] Since this correction amount exceeds the effective range of the local linear model in this round, the unconstrained solution is not directly adopted. Within the trust region, the objective function decreases with increasing air gap correction; therefore, the optimal correction for this round is taken as 0.1 mm. Accordingly, the air gap size of the second sub-core is adjusted from the initial value... Updated to .
[0201] The actual structural design parameters are updated according to the aforementioned correction amounts. If the disturbance is completed through prototype adjustment tests, the disturbed prototype structure is directly used as the structure after the first round of corrections. Otherwise, the updated parameters are used instead. Repeat steps S1 to S4 until both the excitation imbalance index and the leakage inductance imbalance index do not exceed 5% and determine the correction structure.
[0202] To verify the superiority of the method provided in this embodiment in improving the electromagnetic performance balance of a four-core fractional-turn transformer, a comparison was made between the effects before and after optimization, and the results are as follows: Figure 6 As shown in the figure, before optimization, there was a significant uneven current distribution among the four windings, especially in the second primary winding P2 (winding 2 in the figure), where the current was significantly lower than the other windings. After adopting the improved method, the peak current range of the four windings decreased from 22.63 kA to 6.75 kA, and the coefficient of variation decreased from 16.53% to 4.25%; the steady-state current range decreased from 26.34 kA to 7.77 kA, and the coefficient of variation decreased from 28.16% to 6.78%. Throughout the entire effective conduction phase, the normalized mean square deviation of the four currents decreased by 74.80%. The results indicate that the optimization method effectively improves the consistency of current distribution among the windings.
[0203] In summary, this invention, by sequentially measuring the primary-side self-inductance parameters of each sub-unit and the mutual inductance parameters between the primary winding and the common secondary winding, employs a primary-side reverse... The equivalent circuit model extracts the equivalent magnetizing inductance and equivalent leakage inductance of each sub-unit converted to the original side, realizing independent characterization of the main magnetic flux coupling characteristics and leakage flux characteristics. By constructing residual vectors and imbalance indices through common-mode / differential-mode decomposition, quantitative evaluation of consistency among sub-units and precise location of deviation sub-units are achieved. Based on the amplitude and polarity of the differential-mode component, the deviation type is mapped to candidate correction variables such as air gap or winding spacing. Combined with sensitivity matrix and trust region constraints, iterative optimization is performed, realizing closed-loop control from electromagnetic parameter deviation to structural parameter correction. This method does not rely on finite element simulation scanning or repeated prototype manufacturing; it only requires conventional LCR bridge measurements and a small number of physical disturbance tests, offering advantages such as low testing cost, fast convergence speed, and clear physical orientation. This invention can be widely applied in the design and manufacturing of electromagnetic devices with strict branch consistency requirements, such as core-split fractional-turn transformers, multi-phase parallel magnetic components, and high-power pulse transformers.
[0204] The accompanying drawings illustrating the embodiments of the present invention will make the objectives, technical solutions, and advantages of the present invention clearer. It should be noted that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention. All equivalent substitutions and improvements made within the framework of the methods and principles provided by the present invention should be included within the protection scope of the present invention.
Claims
1. A method for optimizing the balance of excitation inductance and leakage inductance in a multi-core fractional-turn transformer, characterized in that: The multi-core fractional-turn transformer includes multiple magnetically independent sub-cores, multiple electrically independent primary windings, and a common secondary winding. A sub-unit is defined as a sub-core, its primary winding, and the secondary section of the common secondary winding coupled to it. The method includes: S1. Obtain the primary side incremental self-inductance of each sub-unit and the mutual inductance parameters between the primary winding and the common secondary winding; S2. Calculate the equivalent magnetizing inductance and equivalent leakage inductance of each sub-unit when referred to the original side using the equivalent circuit model; S3. Construct the excitation inductance vector and leakage inductance vector, and decompose them into the common-mode component of the excitation inductance, the differential-mode component of the excitation inductance, the common-mode component of the leakage inductance, and the differential-mode component of the leakage inductance. S4. Construct excitation imbalance index and leakage inductance imbalance index, and determine the deviation sub-unit and deviation type based on the amplitude and polarity of the differential mode component; when both indices do not exceed the preset threshold, it indicates that the excitation inductance and leakage inductance of each sub-unit meet the balance requirements. S5. Determine candidate principal correction variables based on the type of deviation, apply perturbation to each candidate principal correction variable, obtain the residual change, and construct a sensitivity matrix for solving the optimal correction amount. S6. Establish an optimization model for candidate master correction variables, solve for the optimal correction amount, and update the structural parameters of the deviation sub-unit until both the excitation imbalance index and the leakage inductance imbalance index meet the preset threshold.
2. The optimization method according to claim 1, characterized in that, S1 specifically includes: S11. Connect each primary winding to the LCR bridge in sequence as the winding under test, and keep the common secondary winding and other primary windings open, and read the primary incremental self-inductance of each primary winding. S12. With the primary winding not under test open, connect each primary winding to the common secondary winding in sequence according to the first series polarity, that is, connect the non-same-name terminal lead of the primary winding to the same-name terminal lead of the common secondary winding, and measure the first combined inductance; connect each primary winding to the common secondary winding in sequence according to the second series polarity, that is, connect the non-same-name terminal lead of the primary winding to the non-same-name terminal lead of the common secondary winding, and measure the second combined inductance. The mutual inductance parameters of each subunit are calculated based on the difference between the first combined inductance and the second combined inductance.
3. The optimization method according to claim 1, characterized in that, S2 specifically includes: Based on the primary-side incremental self-inductance and mutual inductance parameters of each sub-unit, calculate the equivalent magnetizing inductance and equivalent leakage inductance of each sub-unit referred to the primary side. The equivalent magnetizing inductance of each sub-unit is the product of the mutual inductance parameter and the physical turns ratio of that sub-unit; the equivalent leakage inductance of each sub-unit is the primary-side incremental self-inductance of that sub-unit minus the product of the mutual inductance parameter and the physical turns ratio of that sub-unit. The physical turns ratio is the common turns ratio of all sub-units, which is equal to the ratio of the number of turns in the primary winding of a single sub-unit to the number of turns in the common secondary winding.
4. The optimization method according to claim 1, characterized in that, S3 specifically includes: S31. Based on the equivalent magnetizing inductance and equivalent leakage inductance of each sub-unit, construct the magnetizing inductance vector and leakage inductance vector respectively according to the preset numbering order of each sub-unit. S32. Construct a unit common mode basis vector with equal elements and a differential mode projection matrix orthogonal to the unit common mode basis vector; S33. Project the excitation inductance vector and leakage inductance vector to the common-mode subspace and the differential-mode subspace respectively to obtain the common-mode component of the excitation inductance, the differential-mode component of the excitation inductance, the common-mode component of the leakage inductance, and the differential-mode component of the leakage inductance.
5. The optimization method according to claim 1, characterized in that, The excitation imbalance index and leakage inductance imbalance index are constructed as follows: Based on the common-mode component of the excitation inductance Differential mode component of magnetizing inductance Constructing excitation imbalance index ； In the formula, This is a preset lower limit for positive inductance with inductance dimensions; Based on the common-mode component of leakage inductance and leakage inductance differential mode component To match the excitation imbalance index The same form is used to construct the leakage inductance imbalance index. .
6. The optimization method according to claim 1, characterized in that, The specific details of the deviation sub-unit and deviation type based on the amplitude and polarity determination of the differential mode component are as follows: When the excitation imbalance index or leakage inductance imbalance index exceeds the preset threshold, the corresponding element in the differential mode component of the excitation inductance of each sub-unit is queried in turn and the normalized value is calculated. And the corresponding elements of each sub-unit in the leakage inductance differential mode component and calculate the normalized values. , Indicates the first Subunits; When the Each subunit satisfies and When at least one of the values is greater than a preset positioning threshold, the first... Each sub-unit is identified as a deviation sub-unit; The deviation types include magnetizing inductance deviation and leakage inductance deviation, when When the deviation exceeds a preset positioning threshold, it is determined that the deviation subunit has an excitation inductance deviation; when When the deviation exceeds a preset positioning threshold, it is determined that the deviation subunit has a leakage sensing deviation; when and When all values are greater than the preset positioning threshold, it is determined that the deviation subunit has a mixed deviation; When the corresponding element value of the deviation sub-unit in the differential mode component of the excitation inductance or the differential mode component of the leakage inductance is greater than zero, it is determined that the excitation inductance or leakage inductance of the deviation sub-unit is larger than the average level of each sub-unit; otherwise, it is determined that the excitation inductance or leakage inductance of the deviation sub-unit is smaller than the average level of each sub-unit.
7. The optimization method according to claim 6, characterized in that, The candidate main adjustment correction variables are determined according to the following principles: when there is an excitation inductance deviation in the deviation sub-unit, the air gap parameter of the sub-core in the deviation sub-unit is determined as a candidate main adjustment correction variable for the excitation inductance deviation; when there is a leakage inductance deviation in the deviation sub-unit, the spacing parameter between the secondary side section of the common secondary winding and the sub-core in the deviation sub-unit is determined as a candidate main adjustment correction variable for the leakage inductance deviation; when there is a mixed deviation in the deviation sub-unit, both the air gap parameter and the spacing parameter are determined as candidate main adjustment correction variables.
8. The optimization method according to claim 7, characterized in that, The specific steps of applying perturbations to each candidate principal correction variable, obtaining residual changes, and constructing a sensitivity matrix for solving the optimal correction amount include: 1) The candidate master correction variables are combined into a correction variable vector, and the elements in the correction variable vector include at least one of the sub-core air gap parameter and the spacing parameter corresponding to the deviation sub-unit; 2) Construct a residual vector based on the differential mode components of the excitation inductance and leakage inductance, and then sequentially apply the first... Apply a preset perturbation to each candidate principal modulation correction variable, while keeping the other candidate principal modulation correction variables unchanged, and obtain the perturbed residual vector; 3) According to the first The preset disturbances of each candidate principal correction variable and their corresponding changes in the residual vector are used to calculate the corresponding sensitivity vector, which represents the degree of influence of the candidate principal correction variable on the residual vector. A sensitivity matrix is further constructed by arranging the aforementioned sensitivity vectors in a preset order.
9. The optimization method according to claim 1, characterized in that, The optimization model for the candidate principal correction variables is constructed as follows: Based on the sensitivity matrix An optimization model for candidate principal correction variables is established with the goal of minimizing the weighted L2 norm of the perturbated residual vector: ； in, This is the vector of correction values for the candidate principal modifier variables. The weight matrix is determined based on preset thresholds for the magnetizing inductance imbalance index and the leakage inductance imbalance index. This is the residual vector constructed based on the differential mode components of the excitation inductance and leakage inductance.
10. The optimization method according to claim 1, characterized in that, In step S6, when solving for the correction amount of the candidate master correction variable, at least one of the following constraints is applied: the adjustment range constraint of the sub-core air gap parameter, the adjustment range constraint of the spacing parameter between the secondary side section of the common secondary winding and the corresponding sub-core, the sub-core magnetic flux density constraint, the temperature rise constraint, and the manufacturing tolerance constraint. Under the constraints, the optimization model is solved to obtain the correction direction and correction amount of the candidate master correction variable. According to the correction direction and correction amount, at least one of the following is updated: the air gap parameter of the sub-core in the deviation sub-unit and the spacing parameter between the secondary side section of the common secondary winding and the sub-core.