A four-winding transformer equivalent modeling method for CHB-QAB topology

Abstract

The application discloses a CHB-QAB topology four-winding transformer equivalent modeling method, and relates to the technical field of circuit equivalent models. The method comprises the following steps: based on the structural parameters of the four-winding transformer, a primary side winding, a secondary side winding and an insulation layer leakage magnetic field strength distribution model are respectively constructed; based on all the leakage magnetic field strength distribution models, first leakage magnetic energy, second leakage magnetic energy and third leakage magnetic energy are determined according to the Ampere loop law and linear magnetic field assumption; the second leakage magnetic energy is converted to the primary side, the equivalent leakage magnetic energy and the first and third leakage magnetic energy are added, and are converted into the equivalent leakage inductance of the primary side; based on the equivalent leakage inductance of the primary side and the equivalent leakage magnetic energy, the excitation inductance of the four-winding transformer is modeled as the equivalent self-inductance of the secondary side winding, and an equivalent circuit model of the four-winding transformer is obtained. The application fundamentally simplifies the model structure of the equivalent circuit model, and greatly improves the establishment rate of the four-winding transformer equivalent model.

Description

Technical Field

[0001] This invention relates to the field of circuit equivalent model technology, and in particular to an equivalent modeling method for a four-winding transformer with CHB-QAB topology. Background Technology

[0002] With the increasing penetration of renewable energy and the gradual increase in the proportion of DC load, AC / DC systems are being used more and more widely in power transmission and smart grids. High-power topologies connecting medium- and high-voltage hybrid AC / DC systems are also gradually becoming a research hotspot. The key device in this topology, providing power transmission, voltage transformation, and electrical isolation, is the high-power transformer. Due to limitations in insulation and manufacturing processes, the leakage inductance of medium- and high-voltage high-power transformers is often difficult to ignore. Therefore, constructing an equivalent inductance model to analyze its impact on the overall energy transmission of the topology is crucial.

[0003] In recent years, the medium- and high-voltage AC / DC conversion topology composed of cascaded H-bridge-Quad active bridge (CHB-QAB) converters has become a commonly used topology in medium- and high-voltage hybrid AC / DC network systems. The key unit responsible for safe power conversion is the medium- and high-voltage high-power four-winding transformer.

[0004] Existing schemes for establishing equivalent models of multi-winding transformers mostly involve converting the actual magnetic circuit of the transformer, including the reluctance and leakage magnetic paths of each segment, into circuit elements one by one. The implementation process includes: firstly, based on the transformer's core geometry, winding distribution, and ampere-turn relationship, decomposing the main magnetic flux path, the leakage magnetic paths between windings, and the windings themselves into a series of series or parallel reluctances ( R m ) units, forming a magnetic circuit network diagram. Next, the magnetic reluctance ( R m The dual is the inductor in the circuit. L ), will magnetomotive force source ( N i The dual is a current source. i ), will magnetic flux ( Φ The dual is voltage () u Finally, the integrated circuit model is constructed by connecting the inductors of each pair (representing the main magnetic flux and the magnetic reluctance of each leakage path) to an ideal transformer (reflecting the ampere-turn balance and voltage transformation relationship) to form a complete equivalent circuit containing multi-port leakage inductance and excitation branches.

[0005] In existing methods for establishing equivalent models of multi-winding transformers, the number of reluctance units in the core column and leakage flux channel increases nonlinearly with each additional winding in the magnetic circuit of the multi-winding transformer. After dualization, the equivalent circuit nodes and inductor elements expand rapidly, causing the leakage flux paths between windings to overlap. The inductance matrix has numerous off-diagonal elements and complex coupling relationships, which seriously affects the establishment rate of the equivalent model of the multi-winding transformer. Summary of the Invention

[0006] Therefore, it is necessary to provide an equivalent modeling method for a four-winding transformer with CHB-QAB topology to address the above-mentioned technical problems.

[0007] This invention provides an equivalent modeling method for a four-winding transformer with a CHB-QAB topology. The four-winding transformer includes: multiple primary windings, multiple secondary windings, and an insulation layer surrounding the primary and secondary windings. The equivalent modeling method includes: Obtain the structural parameters of the four-winding transformer in the CHB-QAB topology; Based on structural parameters, and according to Ampere's circuital law and the assumption of linear distribution of the magnetic field inside the winding under low-frequency operating conditions, leakage magnetic field intensity distribution models of the primary winding, secondary winding and their corresponding insulation layer regions are constructed respectively. Based on the leakage magnetic field intensity distribution model, the first leakage magnetic energy of the insulation layer between adjacent primary windings, the second leakage magnetic energy of the insulation layer between adjacent secondary windings, and the third leakage magnetic energy of the insulation layer between the primary winding and the secondary winding are determined by the magnetic energy density integral. Based on the transformer turns ratio of the primary and secondary windings, the second leakage flux energy is converted to the primary winding to obtain the equivalent leakage flux energy; the equivalent leakage flux energy is added to the first and third leakage flux energy to obtain the total equivalent leakage flux energy of the primary winding, and the total equivalent leakage flux energy of the primary winding is converted into equivalent leakage inductance according to the conversion relationship between electromagnetic energy and inductance parameters. Based on the equivalent leakage flux energy and equivalent leakage inductance, the magnetizing inductance of the four-winding transformer is modeled as the equivalent self-inductance located on the secondary winding, resulting in an equivalent circuit model that describes the leakage inductance and magnetizing characteristics of the four-winding transformer in power transmission.

[0008] Optionally, the structural parameters of the four-winding transformer in the CHB-QAB topology include: the actual number of turns in the equivalent windings of the primary and secondary windings, the number of layers in the primary and secondary windings, the height of the equivalent windings of the primary and secondary windings, the insulation layer thickness and average magnetic circuit length of the primary and secondary windings, the equivalent thickness of the single-layer windings of the primary and secondary windings, and the average magnetic circuit length of the insulation layer between the primary and secondary windings.

[0009] Optionally, the leakage magnetic field intensity distribution model includes: A model of leakage magnetic field intensity distribution in the leakage magnetic field region inside the primary winding and the insulation layer; Model of leakage magnetic field intensity distribution in the leakage magnetic field region inside the secondary winding and the insulation layer; A model of the leakage magnetic field intensity distribution in the leakage magnetic field region inside the insulation layer between the primary and secondary windings.

[0010] Optionally, based on the following formula and the assumption of linear distribution of the magnetic field inside the winding under low-frequency operating conditions, leakage magnetic field intensity distribution models of the primary winding, secondary winding, and their corresponding insulation layer regions are constructed respectively: ; in, l px The height of the equivalent winding on the primary side. l sx The height of the equivalent winding on the secondary side. d ins1 The thickness of the insulation layer around the primary winding. d ins2 The thickness of the insulation layer around the secondary winding. d px The equivalent thickness of a single-layer winding on the primary side. d sx The equivalent thickness of the secondary side single-layer winding. l 1 represents the average magnetic path length of the primary winding. l 2 represents the average magnetic path length of the secondary winding. l i The average magnetic path length of the insulation layer between the primary and secondary windings. H wind The magnetic field strength in the winding. H ins1 The magnetic field strength within the insulation layer surrounding the primary winding. H ins2 This refers to the magnetic field strength within the insulation layer surrounding the secondary winding. N px This refers to the actual number of turns in the equivalent winding of the primary winding. I p For primary side current, n For the first n Layer equivalent winding, k p This represents the total number of layers in the primary winding.

[0011] Optionally, the first leakage magnetic energy of the insulation layer between adjacent primary windings is determined by integrating the magnetic energy density based on the following formula: ; The second leakage magnetic energy of the insulation layer between adjacent secondary windings is determined by integrating the magnetic energy density using the following formula: ; The third leakage magnetic energy of the insulation layer between the primary and secondary windings is determined by integrating the magnetic energy density using the following formula: ; in, W 1 represents the first leakage magnetic energy. W 2 represents the second leakage magnetic energy. W 3 represents the third leakage magnetic energy. l px ’ The equivalent winding height on the primary side is corrected using the Rogowski coefficient. l sx ’ The equivalent secondary winding height is calculated using the Rogowski coefficient correction. μ 0 is the permeability of free space. N sx This refers to the actual number of turns in the equivalent winding of the secondary winding. I p For primary side current, I s This is the secondary side current. k p This represents the total number of layers in the primary winding. k s This represents the total number of layers in the secondary winding. d px The equivalent thickness of a single-layer winding on the primary side. d sx The equivalent thickness of the secondary side single-layer winding. l px The height of the equivalent winding on the primary side. l sx The height of the equivalent winding on the secondary side. H ins1 The magnetic field strength within the insulation layer surrounding the primary winding. H ins2 This represents the magnetic field strength within the insulation layer surrounding the secondary winding.

[0012] Optionally, based on the transformer turns ratio of the primary and secondary windings, the second leakage flux energy is converted to the primary winding to obtain the equivalent leakage flux energy: ; in, This is the equivalent leakage magnetic energy. μ 0 is the permeability of free space. l2 represents the average magnetic path length of the secondary winding. l sx The height of the equivalent winding on the secondary side. k p This represents the total number of layers in the primary winding. N px This refers to the actual number of turns in the equivalent winding of the primary winding. I p For primary side current, d ins2 The thickness of the insulation layer around the secondary winding. k s This represents the total number of layers in the secondary winding. d sx It represents the equivalent thickness of a single-layer winding on the secondary side.

[0013] Optionally, the total equivalent leakage magnetic energy of the primary winding is converted into equivalent leakage inductance based on the following formula according to the conversion relationship between electromagnetic energy and inductance parameters: ; Based on the following equation, the magnetizing inductance of a four-winding transformer is modeled as an equivalent self-inductance located on the secondary side, resulting in an equivalent circuit model describing the leakage inductance and magnetizing characteristics of the four-winding transformer in power transmission: ; ; in, L Tx For the equivalent leakage inductance of the first-order x-phase of QAB, I p For primary side current, W 1 represents the first leakage magnetic energy. This is the equivalent leakage magnetic energy. W 3 represents the third leakage magnetic energy. L M For magnetizing inductance, L s For secondary self-inductance, Φ ms For the magnetic flux flowing through the secondary winding, I s This refers to the secondary winding current. N s This refers to the number of turns in the secondary winding. R s The magnetic reluctance in the magnetic circuit. l e The length of the magnetic circuit. A e This is the effective cross-sectional area of ​​the magnetic core. μ 0 is the permeability of free space. μ r denoted as ρ, where ρ is the relative permeability of the core material.

[0014] The equivalent modeling method for a four-winding transformer with CHB-QAB topology provided in this embodiment of the invention has the following advantages compared with the prior art: This invention combines a leakage magnetic field intensity distribution model with energy equivalent conversion, replacing the complex magnetic circuit network dual conversion with a clear physical field model. It bypasses the process of specific magnetoresistance modeling and network simplification for complex leakage magnetic paths, directly starting from the overall energy results of electromagnetic field simulation. This allows leakage magnetic energies from different sides and locations to be linearly superimposed under the same voltage reference, yielding the total equivalent leakage magnetic energy on the primary side. Based on the square-proportional relationship between electromagnetic energy and inductance, the equivalent leakage inductance on the primary side is directly derived. This process fundamentally simplifies the model structure of the equivalent circuit model, eliminating the need to handle numerous off-diagonal inductance coupling terms and the need to establish equivalent circuits with many nodes. It compresses the complex multidimensional cross-linked leakage magnetic network into a single leakage inductance parameter, greatly improving the establishment speed of the equivalent model of a four-winding transformer. Attached Figure Description

[0015] Figure 1 A topology diagram of an equivalent modeling method for a four-winding transformer with CHB-QAB topology provided in one embodiment; Figure 2 An insulation structure diagram of a high-voltage, high-power, high-frequency transformer is provided as an example of an equivalent modeling method for a four-winding transformer with a CHB-QAB topology in one embodiment. Figure 3 The leakage magnetic field intensity distribution of a four-winding transformer is shown in one embodiment of an equivalent modeling method for a CHB-QAB topology four-winding transformer. Figure 4 A magnetomotive force distribution diagram of a four-winding transformer provided in one embodiment of an equivalent modeling method for a CHB-QAB topology four-winding transformer; Figure 5 The diagram shows the distribution of leakage magnetic field strength in the windings and insulation layer of an equivalent modeling method for a four-winding transformer with CHB-QAB topology provided in one embodiment. Figure 6 An equivalent circuit diagram of a four-winding transformer is provided in one embodiment of an equivalent modeling method for a four-winding transformer with a CHB-QAB topology. Figure 7 An open-loop phase-shifting modulation strategy diagram for an equivalent modeling method of a four-winding transformer with CHB-QAB topology provided in one embodiment; Figure 8 A Maxwell and Simplier co-simulation model diagram of an equivalent modeling method for a four-winding transformer with CHB-QAB topology provided in one embodiment; Figure 9 This is a diagram of the secondary port output voltage of an equivalent modeling method for a four-winding transformer with a CHB-QAB topology provided in one embodiment. Figure 9 (a) in the figure represents the joint simulation results of the secondary port output voltage. Figure 9 (b) in the figure shows the equivalent circuit simulation results of the output voltage at the secondary side port; Figure 10 Here are the midpoint voltage diagrams of the primary and secondary arms of a four-winding transformer in a CHB-QAB topology, provided in one embodiment. Figure 10 (a) in the figure represents the joint simulation results of the midpoint voltages of the primary and secondary side bridge arms. Figure 10 (b) in the figure shows the equivalent circuit simulation results of the midpoint voltages of the primary and secondary side bridge arms; Figure 11 This is a transformer primary and secondary current diagram provided in one embodiment of an equivalent modeling method for a four-winding transformer with a CHB-QAB topology. Figure 11 (a) in the figure shows the joint simulation results of the primary and secondary currents of the transformer. Figure 11 (b) in the figure shows the simulation results of the equivalent circuit of the primary and secondary currents of the transformer. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0017] This invention provides an equivalent modeling method for a four-winding transformer with a CHB-QAB topology, the method comprising: A four-winding transformer includes: multiple primary windings, multiple secondary windings, and an insulation layer surrounding the primary and secondary windings.

[0018] Equivalent modeling methods include: Obtain the structural parameters of the four-winding transformer in the CHB-QAB topology.

[0019] Based on structural parameters, and according to Ampere's circuital law and the assumption of linear distribution of the magnetic field inside the winding under low-frequency operating conditions, leakage magnetic field intensity distribution models of the primary winding, secondary winding and their corresponding insulation layer regions are constructed respectively.

[0020] Based on the leakage magnetic field intensity distribution model, the first leakage magnetic energy of the insulation layer between adjacent primary windings, the second leakage magnetic energy of the insulation layer between adjacent secondary windings, and the third leakage magnetic energy of the insulation layer between the primary and secondary windings are determined by the magnetic energy density integral.

[0021] Based on the transformer turns ratio of the primary and secondary windings, the second leakage flux energy is converted to the primary winding to obtain the equivalent leakage flux energy. This equivalent leakage flux energy is then added to the first and third leakage flux energies to obtain the total equivalent leakage flux energy of the primary winding. Finally, based on the conversion relationship between electromagnetic energy and inductance parameters, the total equivalent leakage flux energy of the primary winding is converted into equivalent leakage inductance.

[0022] Based on the equivalent leakage flux energy and equivalent leakage inductance, the magnetizing inductance of the four-winding transformer is modeled as the equivalent self-inductance located in the secondary winding, resulting in an equivalent circuit model that describes the leakage inductance characteristics and magnetizing characteristics of the four-winding transformer in power transmission.

[0023] Preferably, the structural parameters of the four-winding transformer in the CHB-QAB topology include: the actual number of turns in the equivalent windings of the primary and secondary windings, the number of layers in the primary and secondary windings, the height of the equivalent windings of the primary and secondary windings, the insulation layer thickness and average magnetic circuit length of the primary and secondary windings, the equivalent thickness of the single-layer windings of the primary and secondary windings, and the average magnetic circuit length of the insulation layer between the primary and secondary windings.

[0024] Preferably, the leakage magnetic field intensity distribution model includes: a leakage magnetic field intensity distribution model of the leakage magnetic field region inside the primary winding and inside the insulation layer, a leakage magnetic field intensity distribution model of the leakage magnetic field region inside the secondary winding and inside the insulation layer, and a leakage magnetic field intensity distribution model of the leakage magnetic field region inside the insulation layer between the primary winding and the secondary winding.

[0025] A specific embodiment of the present invention is provided: 1. The topology of cascaded H-bridges connected in series with four active bridges CHB-QAB, such as... Figure 1 As shown.

[0026] 1.1 Insulation structure design of medium- and high-voltage high-power four-winding transformer.

[0027] In the design of high-power high-frequency transformers, especially in cascaded power electronic transformer topologies with three-phase ports, the insulation voltage level of medium- and high-voltage high-power isolated four-winding transformers must be considered according to the voltage level of the medium- and high-voltage AC power grid. Therefore, the high-voltage insulation design of the transformer is of paramount importance. Figure 2 This is a commonly used insulation structure for high-power high-frequency transformers, defined as a concentric parallel structure. In this structure, the magnetic core material is nanocrystalline, and the structure is UU or square. Nanocrystalline materials help improve the efficiency of high-power high-frequency transformers because they have high permeability and can generate greater magnetic induction intensity under the same magnetic field strength, thereby reducing excitation power and copper loss and improving energy transmission efficiency.

[0028] In addition, the low coercivity and low iron loss of nanocrystalline materials also reduce the energy loss of transformers, further improving efficiency. Figure 2 middle, d cw It is the insulation distance between the upper and lower yokes and the windings. d ps It is the insulation distance between the primary and secondary windings. d pp It is the insulation distance between adjacent primary three-phase windings. d sg It is the insulation distance between the secondary winding and ground.

[0029] In addition, while ensuring that the magnetic core has sufficient window area, d gap and d cp They can be set to their minimum values ​​to reduce the volume of the insulation. The total number of turns of the primary and secondary windings are respectively... N p and N s It means, and k p and k s These refer to the number of layers in the primary and secondary windings, respectively.

[0030] The expression for calculating the insulation distance to meet the required insulation level of the transformer is Equation (1): (1) in, V ins This is the low-frequency voltage isolation level that must be met to ensure long-term stable operation. For indicators under different AC power grid levels, please refer to IEEE Std. C C57.12.01. E ins The dielectric strength of the insulating medium, taking epoxy resin as an example, is typically between 30 and 50 kV / mm, with a typical value of about 38 kV / mm. K ins It is the insulation margin factor, ranging from 0 to 1.

[0031] 1.2 Establishment of the equivalent model of a four-winding transformer.

[0032] The high-frequency transformer structure in a multi-bus interconnection structure was designed. Inductance parameters are one of the important indicators of high-frequency transformers. In the manufacturing of medium- and high-voltage high-power transformers, since their materials are mostly high-permeability materials such as nanocrystalline materials, their excitation inductance is often tens of millihenries. Therefore, their excitation current is often very small and the overall impact on the peripheral circuit is negligible. However, due to the limitations of their insulation process, a large insulation distance often produces a non-negligible leakage inductance. The leakage inductance participates in the power transfer in a four-active-bridge converter and affects the response characteristics of the peripheral circuit. Therefore, it is necessary to perform detailed modeling of the inductance parameters of the high-frequency transformer.

[0033] The modeling of leakage inductance is related to the geometric parameters of the transformer. In Figure 2 In the structural design of the four-winding transformer with a concentric parallel structure, the finite element simulation of the leakage magnetic field strength is shown as follows: Figure 3 As shown in the figure. Through simulation, it can be seen that the main leakage magnetic field distribution can be divided into three regions: (1) inside the three-phase primary winding and inside the insulation layer, (2) inside the secondary winding and inside the insulation layer, and (3) inside the insulation material between the primary winding and the secondary winding.

[0034] Figure 4 This describes the equivalent winding structure and internal magnetomotive force distribution of a four-winding transformer. l px It is the height of the primary side equivalent winding. l sx It is the height of the equivalent winding on the secondary side. d ins1 and d ins2 These refer to the thickness of the insulation layer around the primary and secondary windings, respectively. d px and d sx These are the equivalent thicknesses of the primary and secondary single-layer windings, respectively. l 1 and l 2 is the average magnetic circuit length of the primary and secondary windings, while l i It is the average magnetic circuit length of the main insulation between the primary and secondary windings.

[0035] Since the magnetic field strength within the insulating layer remains constant, its value can be estimated using Ampere's circuital law. Therefore, the primary side... n The magnetic field strength in the insulation layers on both sides of the equivalent winding is given by equation (2):

[0036] (2) High-power transformers used in CHB-QAB systems typically operate below 100 kHz, where the influence of frequency variations on the internal magnetic field strength of the windings is negligible. Therefore, the change in leakage magnetic field strength within the windings can be approximated as linear, greatly simplifying the system modeling and calculation process.

[0037] The distribution of leakage magnetic field strength within the primary winding and the winding insulation layer is as follows: Figure 5 As shown, the leakage magnetic field energy distribution of the winding section can be divided into two parts: the insulation layer and the conductor. The leakage magnetic field strength remains constant inside the insulation layer and increases inside the winding conductor. In non-high frequency environments, its rate of increase can be approximated as linear, and the leakage magnetic field strength increases with the number of winding layers. Therefore, the mathematical expression for the leakage magnetic field strength at different locations is as shown in equation (3):

[0038] (3) in, l px The height of the equivalent winding on the primary side. l sx The height of the equivalent winding on the secondary side. d ins1 The thickness of the insulation layer around the primary winding. d ins2 The thickness of the insulation layer around the secondary winding. d px The equivalent thickness of a single-layer winding on the primary side. d sx The equivalent thickness of the secondary side single-layer winding. l 1 represents the average magnetic path length of the primary winding. l 2 represents the average magnetic path length of the secondary winding. l i The average magnetic path length of the insulation layer between the primary and secondary windings. H wind The magnetic field strength in the winding. H ins1 The magnetic field strength within the insulation layer surrounding the primary winding. H ins2 This refers to the magnetic field strength within the insulation layer surrounding the secondary winding. N px This refers to the actual number of turns in the equivalent winding of the primary winding. I p For primary side current, n For the first n Layer equivalent winding, k p This represents the total number of layers in the primary winding.

[0039] according to Figure 3The simulation of the leakage magnetic field intensity distribution shown can be seen from the fact that the equivalent length of the winding and the height of the core window are related. l c The difference between phases a and c is that the leakage magnetic field of phase a and phase c diffuses towards the yoke. In the winding structure of a high-power four-winding transformer, the three-phase windings a, b and c are arranged from top to bottom. The windings of phases a and c are closer to the yoke of the magnetic core, so the leakage magnetic field of phases a and c diffuses towards the yoke. In the equivalent model, the actual equivalent winding height can be corrected by combining the Rogowski coefficient with the actual winding height and the leakage magnetic path width, as shown in equation (4):

[0040] (4) in, l avg It is the average winding height. λ This is the width of the leakage magnetic field path. The leakage magnetic field distribution paths of the windings at phases a and c are symmetrical, so they can be corrected using the same Rochelle coefficient. In contrast, the leakage magnetic field distribution in the phase b winding is uniform, so its equivalent winding height does not require correction using the Rochelle coefficient.

[0041] The magnetic energy density at a point in space is proportional to the square of the magnetic induction intensity at that point. Therefore, the energy of the leakage magnetic field can be obtained by integrating the leakage magnetic field intensity as shown in equation (5): (5) By combining equations (3), (4), and (5), the leakage magnetic energy of the primary winding on a single-sided column and within the insulation layer is given by equation (6): (6) Similarly, the leakage flux energy between the equivalent secondary winding with the same ampere-turns as the primary winding and the surrounding insulation layer is calculated by equation (7): (7) The leakage magnetic field strength within the insulation layer between the primary and secondary windings is shown in equation (8): (8) in, W 1 represents the first leakage magnetic energy. W 2 represents the second leakage magnetic energy. W 3 represents the third leakage magnetic energy. l px ’ The equivalent winding height on the primary side is corrected using the Rogowski coefficient. l sx ’ The equivalent secondary winding height is calculated using the Rogowski coefficient correction. μ 0 is the permeability of free space. N sxThis refers to the actual number of turns in the equivalent winding of the secondary winding. I s This is the secondary side current. k s This represents the total number of layers in the secondary winding.

[0042] According to electromagnetic theory, inductance is a parameter characterizing the ability of a coil to store magnetic field energy. It is defined as the ratio of the magnetic flux linkage to the current in the coil, and the stored energy is (1 / 2)L*I². For leakage inductance, the corresponding magnetic field energy is the energy stored in the portion of the leakage magnetic field that is confined near the coil and fails to couple with another coil. Therefore, the leakage magnetic energy generated by the primary and secondary windings can be converted into leakage inductance through equation (9):

[0043] L =2 W / I p / s 2 (9) To simplify the analysis, the leakage magnetic energy in the insulation layer between the primary windings is... W 1, and the third leakage magnetic energy in the insulation layer between the primary and secondary windings. W 3. It is converted into a primary leakage inductance. L δpx The second leakage magnetic energy in the insulation layer between the secondary windings. W 2 is converted into secondary leakage inductance L δsx .

[0044] The second leakage flux energy is directly related to the secondary current. Therefore, the transformer turns ratio can be used to convert the secondary current to the primary current, thus obtaining the relationship between the second leakage flux energy and the primary current. To simplify the analysis of power transfer between the primary and secondary sides, the leakage inductance of the transformer secondary side can be converted to the primary side according to equation (10) to obtain the equivalent circuit of the four-winding transformer (e.g., Figure 6 (as shown)

[0045] (10) in, L Tx ( L Ta , L Tb and L Tc The equivalent leakage inductance of the first-order x-phase of QAB; W 1 represents the first leakage magnetic energy, which can be calculated according to formula (4); For the equivalent leakage magnetic energy, combine equation (7). Equation (11) represents: (11) W 3 represents the third leakage magnetic energy, which can be calculated using equation (8).

[0046] Because in the equivalent circuit of this model, the magnetizing inductance L M Located in the secondary winding, and the leakage inductance of each secondary winding has been fully converted to the primary side through the aforementioned analysis. Therefore, the magnetizing inductance here... L M Physically, this can be considered as secondary self-inductance. L s Its value can be solved based on the definition formula of self-inductance, and the specific expression is shown in equation (12). Where Φ ms For the magnetic flux flowing through the secondary winding, I s This refers to the secondary winding current. N s This refers to the number of turns in the secondary winding.

[0047] (12) Regarding the magnetic flux Φ flowing through the secondary winding ms The solution can be obtained using equation (13), where, R s The magnetic reluctance in the magnetic circuit. l e The length of the magnetic circuit. A e This is the effective cross-sectional area of ​​the magnetic core. μ 0 represents the permeability of free space. μ r This indicates the relative permeability of the core material.

[0048] (13) At this point, the inductance parameters in the equivalent circuit of the four-winding transformer have all been solved.

[0049] 2. Verification strategy for the equivalent model of a four-winding transformer.

[0050] The following is a verification scheme for the proposed four-winding transformer equivalent model. The inductance parameters in the four-winding transformer equivalent model are calculated according to equations (10) and (11). To verify the accuracy of the equivalent circuit model of the four-winding transformer and the precision of the equivalent leakage inductance modeling, a comparison and verification are performed using multi-bus isolated interconnection structure circuit simulation and co-simulation.

[0051] The control method used in the multi-bus isolated interconnection structure is open-loop phase-shift control, such as... Figure 7 As shown, where u px(x=a,b,c) and u s These are the midpoint voltages of the primary and secondary bridge arms, respectively. Power transmission is achieved using the equivalent leakage inductance of the primary side of the transformer. The simulation conditions are shown in Table 1.

[0052] In the Simpliorer simulation environment, a full-bridge circuit with primary and secondary sides of a multi-bus isolated interconnect structure was constructed, and co-simulated with Maxwell to simulate the actual operating conditions of the multi-bus interconnect structure. Figure 8 As shown. Construct a QAB full-bridge circuit in PLECS and Figure 6 The equivalent circuit of the four-winding transformer shown forms a multi-bus isolated interconnection circuit, and the equivalent leakage inductance of the primary side port is set as the parameter calculation value in the equivalent model. The PLECS circuit simulation and co-simulation results are compared to verify the accuracy of the equivalent circuit model and the equivalent leakage inductance modeling.

[0053] Table 1. Comparison of co-simulation and equivalent circuit simulation in verifying the operating condition design. The comparison between equivalent circuit simulation and co-simulation includes the output voltage at the secondary side ports of the multi-bus isolated interconnect structure, the midpoint voltages of the bridge arms on the primary and secondary sides, and the transformer currents on the primary and secondary sides. By comparing the output voltages, the output characteristics of the equivalent model are verified. By comparing the midpoint voltages of the bridge arms, the power transfer characteristics of the equivalent leakage inductance are verified. By comparing the transformer currents, the accuracy of the equivalent leakage inductance model is confirmed.

[0054] Figure 9 , Figure 10 and Figure 11 This is a comparison chart of the results of co-simulation and equivalent circuit simulation. Figure 9 (a) in the figure represents the joint simulation results of the secondary port output voltage. Figure 10 (a) in the figure represents the joint simulation results of the midpoint voltages of the primary and secondary side bridge arms. Figure 11 (a) shows the joint simulation results of the primary and secondary currents of the transformer, which simulates the actual operating conditions of a four-winding transformer in a multi-busbar isolated interconnection structure. Figure 9 (b) in the figure shows the equivalent circuit simulation results of the output voltage at the secondary side port. Figure 10 (b) shows the equivalent circuit simulation results of the midpoint voltages of the primary and secondary bridge arms. Figure 11 (b) in the figure shows the equivalent circuit simulation results of the primary and secondary currents of the transformer. These results are used to evaluate the correctness of the equivalent model and the accuracy of the leakage inductance modeling.

[0055] Figure 9This represents the output voltage at the secondary port. The output voltage and voltage ripple in the equivalent circuit are very close to the results of the co-simulation. Figure 10 The midpoint voltage waveforms of the primary and secondary bridge arms are shown in the simulations, and both simulations show a high degree of similarity. Figure 11 Let represent the transformer currents on the primary and secondary sides. Joint simulation results show that the currents in phases a and c on the primary side are consistent and higher than the current in phase b. This indicates that the equivalent leakage inductances of phases a and c are consistent and lower than the equivalent leakage inductance of phase b. This finding is consistent with the equivalent results obtained using the leakage magnetic energy method.

[0056] The difference in transformer current amplitude between the two simulations is within a reasonable range. These comparative simulations verify that the proposed equivalent circuit model of the four-winding transformer and the equivalent leakage inductance model can accurately reflect actual operating conditions.

[0057] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. An equivalent modeling method for a four-winding transformer with a CHB-QAB topology, wherein the four-winding transformer comprises: The system comprises multiple primary windings, multiple secondary windings, and an insulating layer surrounding the primary and secondary windings; characterized in that the equivalent modeling method includes: Obtain the structural parameters of the four-winding transformer in the CHB-QAB topology; Based on the structural parameters, leakage magnetic field intensity distribution models of the primary winding, secondary winding and their corresponding insulation layer regions are constructed according to Ampere's circuital law and the assumption of linear distribution of the magnetic field inside the winding under low-frequency operation conditions. Based on the leakage magnetic field intensity distribution model, the first leakage magnetic energy of the insulation layer between adjacent primary windings, the second leakage magnetic energy of the insulation layer between adjacent secondary windings, and the third leakage magnetic energy of the insulation layer between the primary winding and the secondary winding are determined by the magnetic energy density integral. Based on the transformer turns ratio of the primary and secondary windings, the second leakage flux energy is converted to the primary winding to obtain the equivalent leakage flux energy; the equivalent leakage flux energy is added to the first and third leakage flux energy to obtain the total equivalent leakage flux energy of the primary winding, and the total equivalent leakage flux energy of the primary winding is converted into equivalent leakage inductance according to the conversion relationship between electromagnetic energy and inductance parameters. Based on the equivalent leakage magnetic energy and the equivalent leakage inductance, the excitation inductance of the four-winding transformer is modeled as the equivalent self-inductance located in the secondary winding, resulting in an equivalent circuit model that describes the leakage inductance characteristics and excitation characteristics of the four-winding transformer in power transmission.

2. The equivalent modeling method for a four-winding transformer with CHB-QAB topology as described in claim 1, characterized in that, The structural parameters of the four-winding transformer in the CHB-QAB topology include: the actual number of turns in the equivalent windings of the primary and secondary windings, the number of layers in the primary and secondary windings, the height of the equivalent windings of the primary and secondary windings, the insulation layer thickness and average magnetic circuit length of the primary and secondary windings, the equivalent thickness of the single-layer windings of the primary and secondary windings, and the average magnetic circuit length of the insulation layer between the primary and secondary windings.

3. The equivalent modeling method for a four-winding transformer with CHB-QAB topology as described in claim 1, characterized in that, The leakage magnetic field intensity distribution model includes: A model of leakage magnetic field intensity distribution in the leakage magnetic field region inside the primary winding and the insulation layer; Model of leakage magnetic field intensity distribution in the leakage magnetic field region inside the secondary winding and the insulation layer; A model of the leakage magnetic field intensity distribution in the leakage magnetic field region inside the insulation layer between the primary and secondary windings.

4. The equivalent modeling method for a four-winding transformer with CHB-QAB topology as described in claim 3, characterized in that, Based on the following formula, and according to Ampere's circuital law and the assumption of linear distribution of the magnetic field inside the winding under low-frequency operating conditions, leakage magnetic field intensity distribution models are constructed for the primary winding, secondary winding, and their corresponding insulation layer regions: ； in, l px The height of the equivalent winding on the primary side. l sx The height of the equivalent winding on the secondary side. d ins1 The thickness of the insulation layer around the primary winding. d ins2 The thickness of the insulation layer around the secondary winding. d px The equivalent thickness of a single-layer winding on the primary side. d sx The equivalent thickness of the secondary side single-layer winding. l 1 represents the average magnetic path length of the primary winding. l 2 represents the average magnetic path length of the secondary winding. l i The average magnetic path length of the insulation layer between the primary and secondary windings. H wind The magnetic field strength in the winding. H ins1 The magnetic field strength within the insulation layer surrounding the primary winding. H ins2 This refers to the magnetic field strength within the insulation layer surrounding the secondary winding. N px This refers to the actual number of turns in the equivalent winding of the primary winding. I p For primary side current, n For the first n Layer equivalent winding, k p This represents the total number of layers in the primary winding.

5. The equivalent modeling method for a four-winding transformer with CHB-QAB topology as described in claim 1, characterized in that, The first leakage magnetic energy of the insulation layer between adjacent primary windings is determined by integrating the magnetic energy density using the following formula: ； The second leakage magnetic energy of the insulation layer between adjacent secondary windings is determined by integrating the magnetic energy density using the following formula: ； The third leakage magnetic energy of the insulation layer between the primary and secondary windings is determined by integrating the magnetic energy density using the following formula: ； in, W 1 represents the first leakage magnetic energy. W 2 represents the second leakage magnetic energy. W 3 represents the third leakage magnetic energy. l px ’ The equivalent winding height on the primary side is corrected using the Rogowski coefficient. l sx ’ The equivalent secondary winding height is calculated using the Rogowski coefficient correction. μ 0 is the permeability of free space. N sx This refers to the actual number of turns in the equivalent winding of the secondary winding. I p For primary side current, I s This is the secondary side current. k p This represents the total number of layers in the primary winding. k s This represents the total number of layers in the secondary winding. d px The equivalent thickness of a single-layer winding on the primary side. d sx The equivalent thickness of the secondary side single-layer winding. l px The height of the equivalent winding on the primary side. l sx The height of the equivalent winding on the secondary side. H ins1 The magnetic field strength within the insulation layer surrounding the primary winding. H ins2 This represents the magnetic field strength within the insulation layer surrounding the secondary winding.

6. The equivalent modeling method for a four-winding transformer with CHB-QAB topology as described in claim 1, characterized in that, Based on the transformer turns ratio of the primary and secondary windings, the second leakage flux energy is converted to the primary winding to obtain the equivalent leakage flux energy: ； in, This is the equivalent leakage magnetic energy. μ 0 is the permeability of free space. l 2 represents the average magnetic path length of the secondary winding. l sx The height of the equivalent winding on the secondary side. k p This represents the total number of layers in the primary winding. N px This refers to the actual number of turns in the equivalent winding of the primary winding. I p For primary side current, d ins2 The thickness of the insulation layer around the secondary winding. k s This represents the total number of layers in the secondary winding. d sx It represents the equivalent thickness of a single-layer winding on the secondary side.

7. The equivalent modeling method for a four-winding transformer with CHB-QAB topology as described in claim 1, characterized in that, Based on the following formula, the total equivalent leakage magnetic energy of the primary winding is converted into equivalent leakage inductance according to the conversion relationship between electromagnetic energy and inductance parameters: ； Based on the following equation, the magnetizing inductance of a four-winding transformer is modeled as an equivalent self-inductance located on the secondary side, resulting in an equivalent circuit model describing the leakage inductance and magnetizing characteristics of the four-winding transformer in power transmission: ； ； in, L Tx For the equivalent leakage inductance of the first-order x-phase of QAB, I p For primary side current, W 1 represents the first leakage magnetic energy. This is the equivalent leakage magnetic energy. W 3 represents the third leakage magnetic energy. L M For magnetizing inductance, L s For secondary self-inductance, Φ ms For the magnetic flux flowing through the secondary winding, I s This refers to the secondary winding current. N s This refers to the number of turns in the secondary winding. R s The magnetic reluctance in the magnetic circuit. l e The length of the magnetic circuit. A e This is the effective cross-sectional area of ​​the magnetic core. μ 0 is the permeability of free space. μ r denoted as ρ, where ρ is the relative permeability of the core material.

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