A linear phase-shifting transformer equivalent circuit modeling and performance parameter acquisition method

Abstract

The application belongs to the field of transformers, and discloses a linear phase-shifting transformer equivalent circuit modeling and performance parameter obtaining method, analyzes the electromagnetic relationship between the primary side winding and the air gap when the linear phase-shifting transformer is in steady-state operation, and Maxwell equations of the linear phase-shifting transformer; based on the theory of one-dimensional field, the equivalent circuit of the linear phase-shifting transformer is established and solved when the longitudinal edge effect is considered. The performance parameter obtaining method is also disclosed, which comprises: solving the established equivalent circuit model to obtain the resistance and leakage reactance of the primary side winding, the excitation reactance, and the secondary side winding resistance; and calculating the performance parameters of the linear phase-shifting transformer based on the equivalent circuit solving result. The application considers the actual situation of the transformer in electromagnetic analysis, the model is more accurate, the calculation precision is high, the winding loss, efficiency and voltage regulation rate and other performance parameters of the transformer can be quickly and effectively calculated, the application is relatively convenient in actual calculation and analysis, and has high practical value.

Description

Technical Field

[0001] This invention belongs to the field of transformer technology, and in particular relates to a method for modeling the equivalent circuit of a linear phase-shifting transformer and obtaining its performance parameters. Background Technology

[0002] The linear phase-shifting transformer is a novel type of phase-shifting transformer that draws inspiration from the structure and principles of linear motors. Its primary and secondary sides have equal and fixed lengths. When three-phase alternating current is applied to the primary side, a traveling wave magnetic field is generated in the air gap, inducing a current in the secondary conductors. Phase shifting is achieved through the design of the control circuit and winding connection positions. Theoretically, phase shifting of any number of phases can be realized, greatly simplifying the structure of the phase-shifting transformer. Compared with traditional phase-shifting transformers, the linear phase-shifting transformer has the advantages of simple winding structure, easy modularization, and arbitrary angle phase shifting. It can be used in microgrid systems such as ship power supply, electric vehicles, and outdoor power supplies. Under the condition of meeting electrical isolation requirements, it can eliminate high-order harmonics and improve the waveform quality on the output side.

[0003] Linear phase-shifting transformers have three winding structures: unequal pitch, hairpin, and toroidal. The core volume and copper wire weight differ significantly depending on the winding structure, and the analysis of the air gap magnetic field is also affected by the winding structure. Therefore, when analyzing various performance parameters of linear phase-shifting transformers, such as efficiency, temperature rise, voltage regulation, three-phase asymmetry, and output voltage harmonic content, the differences in these parameters under different winding structures must be considered.

[0004] There are two main models for linear phase-shifting transformers: mathematical models and equivalent circuit models. Mathematical models primarily describe the transient processes of the transformer, while equivalent circuit models focus on the electrical and magnetic relationships within the transformer. These two models are related and can be converted to each other under certain conditions, but they also differ significantly. Mathematical models are often used to analyze the transient performance calculations of linear phase-shifting transformers, providing strategies for control research. Equivalent circuit models are primarily used to describe the steady-state electromagnetic relationships of linear phase-shifting transformers, analyzing their steady-state operating characteristics and providing guidance for the design optimization of linear phase-shifting transformers.

[0005] The commonly used T-type equivalent circuit model of a linear phase-shifting transformer assumes that the electromotive force (EMF) of each phase in the primary winding is symmetrical. In reality, due to various factors, the EMF of each phase is not symmetrical. Furthermore, it has the following shortcomings: first, it does not consider the influence of the asymmetry of the EMF of each phase winding in the primary side; second, it does not consider the influence of different winding structures in the linear phase-shifting transformer; and third, it does not consider the influence of end-effects, winding asymmetry, and magnetic circuit interruptions caused by the core structure of the linear phase-shifting transformer itself.

[0006] There are two main methods for establishing the equivalent circuit model of a linear phase-shifting transformer: 1) the equivalent circuit derived based on the air gap magnetic flux density distribution model; and 2) the equivalent circuit derived based on electromagnetic field theory. The first method has lower computational accuracy, and the analytical expression for the air gap magnetic field can only be calculated when the primary current is known, whereas in practice, only the primary input voltage is usually known. The second method, based on electromagnetic field theory and a practical transformer model, combined with boundary conditions, can solve for the analytical expressions of the field quantities in each region, resulting in higher computational accuracy, and the primary input voltage is usually known. Therefore, this paper uses electromagnetic field analysis to solve for the expression of the air gap magnetic field and derives the edge effect coefficient based on the principle of equal complex power in the field and circuit, thus obtaining the equivalent circuit of the linear phase-shifting transformer considering the edge effect.

[0007] Based on the above analysis, the problems and shortcomings of the existing technology are as follows:

[0008] (1) The commonly used T-type equivalent circuit model of linear phase-shifting transformer assumes that the electromotive force of each phase in the primary winding is symmetrical. In reality, due to the influence of various factors, the electromotive force of each phase is not symmetrical, and the influence of the asymmetry of the electromotive force of each phase winding in the primary side is not considered.

[0009] (2) Existing technology does not take into account the effects of different winding structures of linear phase-shifting transformers.

[0010] (3) Existing technology does not take into account the effects of edge effect, winding asymmetry and magnetic circuit interruption caused by the core structure of linear phase-shifting transformer. Summary of the Invention

[0011] To address the problems existing in the prior art, this invention provides a method for modeling the equivalent circuit of a linear phase-shifting transformer and obtaining its performance parameters.

[0012] This invention is implemented as follows: a method for modeling the equivalent circuit of a linear phase-shifting transformer, the method comprising:

[0013] Step 1: Analyze the electromagnetic relationship between the primary winding and the air gap during steady-state operation of the linear phase-shifting transformer, and analyze Maxwell's equations for the linear phase-shifting transformer.

[0014] Step 2: Based on the theory of one-dimensional fields, establish and solve the equivalent circuit of the linear phase-shifting transformer when considering the longitudinal end effect.

[0015] Furthermore, step one specifically includes the following process:

[0016] (1) Establish the electromagnetic field relationship and equations of the linear phase-shifting transformer based on Maxwell's equations.

[0017] (2) Introduce vector magnetic potential A to represent the magnetic flux density and induced electric field intensity of the air gap using vector magnetic potential.

[0018] (3) Based on the principle that the complex power of the field circuit is equal, it can be written that the input electrical energy on the primary side is equal to the sum of the complex power of the air gap part and the secondary side part.

[0019] Furthermore, the specific process includes the following:

[0020] (1.1) Establish Maxwell's equations for a linear phase-shifting transformer:

[0021]

[0022] In the formula, B is the magnetic flux density, H is the magnetic field strength, E is the electric field strength, j1 is the current density of the primary conductor, j2 is the current density induced in the secondary conductor from the traveling wave magnetic field, μ0 is the core permeability, and σ is the secondary conductivity.

[0023] (1.2) From the relationship that the complex power of the field circuit is equal, we can obtain

[0024]

[0025] In the formula, P2 represents the effective value of the phase potential of the air gap on the primary side, P3 represents the active power in the secondary side and air gap (equivalent to P3 = 0), and Q2 and Q3 represent the reactive power in the secondary side and air gap. Here, m1 represents the effective value of the primary phase current, and m1 represents the number of primary phases. The relationship between the amplitude of the primary phase current layer and the effective value of the primary phase current is as follows:

[0026]

[0027] In the formula, p is the number of pole pairs, τ is the pole pitch, J1 is the amplitude of the traveling wave current density, W1 is the number of turns in series per phase of the primary winding, and k w1 This represents the primary winding coefficient.

[0028] (1.3) Introducing the vector magnetic potential A, the following two equations are added.

[0029]

[0030]

[0031] In the formula, B 3y Let A be the component of the magnetic flux density in the air gap on the y-axis. 3z E represents the z-component of the vector magnetic potential in the air gap. 3z Let z be the z-component of the induced electric field intensity in the air gap.

[0032] Furthermore, the relevant assumptions include:

[0033] (2.1) The primary side magnetomotive force is represented by the surface current layer, and only the fundamental component is considered;

[0034] (2.2) The influence of primary side teeth and grooves is considered using the air gap coefficient;

[0035] (2.3) Core saturation, hysteresis loss and skin effect of secondary conductor are all negligible;

[0036] (2.4) The current flows along the Z-axis;

[0037] (2.5) All field quantities change with time according to a sinusoidal law.

[0038] Furthermore, the equivalent circuit includes: region 1, region 2, region 3, region 4, region 5, region 1 is the primary side branch, region 2 is the secondary side branch, region 3 is the air gap region, region 4 is the region with coordinate x=0, and region 5 is the end magnetic flux.

[0039] Furthermore, step two includes:

[0040] (1) Assume that the primary current layer is known, and write the expression for the line current density of the conductor in the primary winding, and establish the relationship between the magnetic flux density of the air gap and the primary and secondary current layers.

[0041] (2) Find the z-component of the vector magnetic potential in the air gap.

[0042] (3) Calculate the expressions for each coefficient based on the equality of the tangential components of the magnetic field strength on the boundary and the continuity theorem of magnetic flux.

[0043] (4) Ignore the transverse end effect and only consider the longitudinal end effect to find the z component of the electric field intensity in the air gap.

[0044] (5) The total complex power is the complex power per unit length in the z direction multiplied by the length in the z direction. The total complex power transmitted from the primary side to the secondary side stage and the air gap can be calculated.

[0045] Furthermore, the process of establishing and solving the equivalent circuit for the linear phase-shifting transformer and considering the longitudinal end effect specifically includes the following steps:

[0046] (1) Assume the transformer expression is:

[0047] j1 = J1e j(ωt-kx) (0 < x < 2pτ)

[0048]

[0049] In the formula, j1 is the primary side current layer density, and w is the angular velocity.

[0050] When the secondary side is under load, along the line in the figure

[0051]

[0052] In the formula, δ' is the effective length of the air gap, δ'=k δ k μ δ, k δ ,k μ Here, denoted by δ, represents the air gap coefficient and saturation coefficient of the transformer, and δ represents the air gap length of the transformer.

[0053] (2) Solving the equations in step (1) simultaneously yields:

[0054]

[0055] In the formula, A 3z Let z be the z-component of the vector magnetic potential in the air gap. τ e =πλ, Solving for C1 and C2 requires using boundary conditions and the flux continuity theorem.

[0056] (3) The analytical expression for the magnetic flux density distribution on the center line of y=0 on both sides of the transformer opening is:

[0057]

[0058]

[0059] In the formula, B 4y B 5y B represents the y-component of the air gap magnetic flux density at the ends of region 4 and region 5. 40 B 50 These are coefficients to be determined.

[0060] C1, C2, B 40 B 50 The following can be obtained from the boundary conditions and the flux continuity theorem:

[0061] Since the tangent components of the magnetic field strength on the boundary are equal, we can conclude that:

[0062]

[0063] According to the flux continuity theorem:

[0064]

[0065] Therefore, we obtain:

[0066]

[0067]

[0068]

[0069]

[0070] (4) Ignoring the transverse end effect and considering only the longitudinal end effect, the z-component of the electric field intensity in the air gap is:

[0071]

[0072] The total complex power is the complex power per unit length in the z-direction multiplied by the length in the z-direction. Therefore, the total complex power transmitted from the primary side to the secondary side stage and the air gap is:

[0073]

[0074] Another objective of this invention is to provide a method for obtaining the performance parameters of a linear phase-shifting transformer in implementing the aforementioned linear phase-shifting transformer equivalent circuit modeling method, the method comprising:

[0075] (1.1) An equivalent circuit modeling method based on one-dimensional field analysis and taking into account the edge effect of the Clem winding structure linear phase-shifting transformer is adopted.

[0076] (1.2) Solve the equivalent circuit model to obtain the secondary winding resistance, excitation reactance, primary winding resistance and primary winding leakage reactance.

[0077] (1.3) Calculate the performance parameters of the linear phase-shifting transformer based on the solution results of the equivalent circuit.

[0078] Furthermore, the expression for the secondary winding resistance is as follows:

[0079]

[0080] In the formula, This is the longitudinal end effect correction factor for the phase resistance of the secondary winding. This is the longitudinal end effect correction factor for the magnetizing reactance of each phase on the primary side. The phase resistance of the secondary winding on the secondary side is referred to as the primary side when the longitudinal dynamic end effect is ignored.

[0081] Furthermore, the excitation reactance is expressed as follows:

[0082]

[0083] In the formula, The magnetizing reactance per phase on the primary side is ignored when the longitudinal dynamic end effect is neglected.

[0084]

[0085]

[0086] Furthermore, the resistance expression of the primary winding is as follows:

[0087]

[0088] In the formula, ρ is the resistivity of the conductor at the reference temperature, and L cp W1 is the average half-turn length of the coil, W1 is the number of windings per phase, and A is the conductor cross-sectional area.

[0089] Solving for the leakage permeability of the primary side

[0090] (1) Slot leakage permeability, has

[0091]

[0092] In the formula, k Cu k K a is the coefficient caused by the short pitch of the winding. s1 a s2 The values ​​of h1 and b are all 1. s h2, h3, h0, and b0 are the specific slot parameters of the linear phase-shifting transformer.

[0093] (2) Leakage permeability at the tooth tip,

[0094]

[0095] In the formula, δ is the air gap length of the linear phase-shifting transformer.

[0096] (3) Leakage permeability at the winding ends,

[0097]

[0098] In the formula, L e The length of the primary winding end is [length missing]. y represents the short pitch of the primary winding, and k represents the short pitch of the primary winding. y This is the short-pitch factor for the primary winding.

[0099] (4) Harmonic leakage permeability,

[0100]

[0101] In the formula, k β It can be found in the design book of rotary induction motor.

[0102] The expression for the primary side leakage resistance is:

[0103]

[0104] In the formula, f is the operating frequency, a is the core thickness, q1 is the actual number of slots per pole per phase on the primary side, and p is the number of pole pairs. λ s For slot leakage permeability, λ t For tooth tip leakage permeability, λ e Leakage permeability at the winding end, λ d Harmonic leakage permeability.

[0105] Another object of the present invention is to provide a computer device including a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the linear phase-shifting transformer equivalent circuit modeling method.

[0106] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the linear phase-shifting transformer equivalent circuit modeling method.

[0107] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0108] (1) Based on the theory of one-dimensional field, this invention establishes and solves the equivalent circuit of linear phase-shifting transformer when considering longitudinal edge effect. To simplify the analysis, assumptions are made such as using the surface current layer to represent the primary magnetomotive force, only considering the fundamental component, and using the air gap coefficient to consider the influence of primary side teeth and slots.

[0109] (2) In this invention, the electromagnetic analysis takes into account the actual situation of the transformer, and takes into account the influence of the asymmetry of the electromotive force of each phase winding on the primary side; it also takes into account the influence of the side-end effect, winding asymmetry and magnetic circuit interruption caused by the core structure of the linear phase-shifting transformer.

[0110] (3) This invention uses electromagnetic field analysis to solve the expression of the air gap magnetic field and derives the edge effect coefficient based on the principle of equal complex power in the field and circuit, thus obtaining the equivalent circuit of the linear phase-shifting transformer considering the edge effect. The structure is simple and the calculation accuracy is high. It is convenient to directly apply the calculation of efficiency in linear phase-shifting transformer superimposed inverter system and linear phase-shifting transformer superimposed rectifier system, providing a reference for the efficient operation of the system.

[0111] (4) The expected benefits and commercial value of the technical solution of the present invention after transformation are as follows: Since the theoretical analysis and characteristic calculation of the linear phase-shifting transformer are relatively complex, obtaining an accurate equivalent circuit model of the linear phase-shifting transformer makes it easier to intuitively express the relationship between the electric field and magnetic field in each region of the transformer by the relationship between the various components in the circuit. It has the advantages of simple structure and high calculation accuracy. It can quickly and effectively calculate the winding loss, efficiency and voltage regulation rate of the transformer. It is also more convenient in actual calculation and analysis, has high practical value and huge commercial value.

[0112] (5) The technical solution of this invention fills a technical gap in the domestic and international industry: The commonly used T-type equivalent circuit model of a linear phase-shifting transformer assumes that the electromotive force of each phase in the primary winding is symmetrical. In reality, due to the influence of various factors, the electromotive force of each phase is not symmetrical. In addition, there are problems such as the influence of different winding structures, edge effects, asymmetrical winding distribution, and magnetic circuit interruption. This invention provides a modeling method for the equivalent circuit of a linear phase-shifting transformer with a Cramer winding structure based on one-dimensional field analysis and taking into account edge effects, thus filling the relevant technical gap.

[0113] (6) The technical solution of the present invention solves a technical problem that people have long wanted to solve but have never been able to solve successfully: when analyzing various performance parameters such as steady-state efficiency, voltage regulation rate, three-phase asymmetry and output voltage harmonic content of the T-type equivalent circuit model of the linear phase-shifting transformer, the equivalent circuit model is too simplified, resulting in low calculation accuracy. In view of the defects and deficiencies of the prior art, the present invention provides a modeling method for the equivalent circuit of the linear phase-shifting transformer based on one-dimensional field analysis and taking into account the edge effect of the Cramer winding structure, thus solving this technical problem.

[0114] (7) The technical solution of the present invention overcomes technical bias: Compared with the traditional T-type equivalent circuit of the linear phase-shifting transformer, the electromagnetic analysis in the present invention takes into account the actual situation of the transformer, the model is more accurate, and takes into account the influence of the asymmetry of the electromotive force of each phase winding on the primary side; it also takes into account the influence of the side-end effect, winding distribution asymmetry and magnetic circuit interruption caused by the linear phase-shifting transformer due to its own core structure. Attached Figure Description

[0115] Figure 1 This is a simplified two-dimensional physical model diagram of a linear phase-shifting transformer considering the edge effect provided in an embodiment of the present invention;

[0116] Figure 2 This invention provides a T-type equivalent circuit diagram for a linear phase-shifting transformer and its edge-end effect.

[0117] Figure 3 This is a two-dimensional simulation model diagram of a Clem winding structure linear phase-shifting transformer provided in an embodiment of the present invention;

[0118] Figure 4 This is a load voltage comparison diagram provided in an embodiment of the present invention;

[0119] Figure 5 This is a load voltage error percentage diagram provided in an embodiment of the present invention;

[0120] Figure 6 This is a load current comparison diagram provided in an embodiment of the present invention;

[0121] Figure 7 This is a load current error percentage diagram provided in an embodiment of the present invention. Detailed Implementation

[0122] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0123] To enable those skilled in the art to fully understand how the present invention is specifically implemented, this section provides an explanatory description of the embodiments that expand upon the technical solutions of the claims.

[0124] The method for modeling the equivalent circuit of a linear phase-shifting transformer provided in this invention includes:

[0125] S101, Analyze the electromagnetic relationship between the primary winding and the air gap during steady-state operation of a linear phase-shifting transformer, and analyze Maxwell's equations for the linear phase-shifting transformer;

[0126] S102, establish and solve the equivalent circuit of the linear phase-shifting transformer when considering the longitudinal end effect.

[0127] Furthermore, step S101 specifically includes the following process:

[0128] (1.1) Establish Maxwell's equations for a linear phase-shifting transformer:

[0129]

[0130] In the formula, B is the magnetic flux density, H is the magnetic field strength, E is the electric field strength, j1 is the current density of the primary conductor, j2 is the current density induced in the secondary conductor from the traveling wave magnetic field, μ0 is the core permeability, and σ is the secondary conductivity.

[0131] (1.2) From the relationship that the complex power of the field circuit is equal, we can obtain:

[0132]

[0133] In the formula, P2 represents the effective value of the phase potential of the air gap on the primary side, P3 represents the active power in the secondary side and air gap (equivalent to P3 = 0), and Q2 and Q3 represent the reactive power in the secondary side and air gap. m1 is the effective value of the primary phase current and m1 is the number of primary phases.

[0134] The relationship between the magnitude of the primary current layer and the effective value of the primary phase current is as follows:

[0135]

[0136] In the formula, p is the number of pole pairs, τ is the pole pitch, J1 is the amplitude of the traveling wave current density, W1 is the number of turns in series per phase of the primary winding, and k w1 This represents the primary winding coefficient.

[0137] (1.3) Introducing the vector magnetic potential A, the following two equations are added.

[0138]

[0139]

[0140] In the formula, B 3y Let A be the component of the magnetic flux density in the air gap on the y-axis. 3z E represents the z-component of the vector magnetic potential in the air gap. 3z Let z be the z-component of the induced electric field intensity in the air gap.

[0141] The relevant assumptions provided in the embodiments of the present invention include:

[0142] (2.1) The primary side magnetomotive force is represented by the surface current layer, and only the fundamental component is considered;

[0143] (2.2) The influence of primary side teeth and grooves is considered using the air gap coefficient;

[0144] (2.3) Core saturation, hysteresis loss and skin effect of secondary conductor are all negligible;

[0145] (2.4) The current flows along the Z-axis;

[0146] (2.5) All field quantities change with time according to a sinusoidal law.

[0147] like Figure 1 As shown, the simplified two-dimensional model of the linear phase-shifting transformer includes: region 1, region 2, region 3, and region 4. Region 1 is the primary core, region 2 is the secondary core, region 3 is the air gap region, region 4 is the region with coordinate x = 0, and region 5 is the region with coordinate x = 2pτ. The T-type equivalent circuit of the linear phase-shifting transformer considering the end-effect is shown below. Figure 2As shown, the components include the primary winding resistance, primary winding leakage reactance, magnetizing reactance, and the secondary winding resistance referred to the primary side. The two-dimensional simulation model of the Cramer winding structure linear phase-shifting transformer is shown below. Figure 3 As shown. The cores of the primary and secondary sides of the linear phase-shifting transformer are completely symmetrical and fixed. The primary winding adopts a full-pitch winding structure with twelve phases, while the secondary winding adopts a long-short pitch winding structure with three phases.

[0148] Assume the primary current layer of the transformer:

[0149] j1 = J1e j(ωt-kx) (0 < x < 2pτ)

[0150] In the formula, j1 is the primary side current layer density.

[0151] When the secondary side is under load, along the rectangular loop shown in the figure, from ▽×H=j1+j2, we get...

[0152]

[0153] In the formula, δ' is the effective length of the air gap, δ'=k δ k μ δ, k δ ,k μ Here, denoted by δ, represents the air gap coefficient and saturation coefficient of the transformer, and δ represents the air gap length of the transformer.

[0154] Solving the above equations simultaneously yields:

[0155]

[0156] In the formula, A 3z Let z be the z-component of the vector magnetic potential in the air gap. τ e =πλ, Solving for C1 and C2 requires using boundary conditions and the flux continuity theorem.

[0157] Due to the symmetrical structure of the linear phase-shifting transformer, the magnetic flux distribution at the end faces of regions 4 and 5 is symmetrical. The analytical expression for the magnetic flux density distribution along the center line at y=0 on both sides of the transformer opening can be approximately expressed as:

[0158]

[0159]

[0160] In the formula, B 4y B 5y B represents the y-component of the air gap magnetic flux density at the ends of region 4 and region 5. 40 B50 These are coefficients to be determined.

[0161] In the above formula, C1, C2, and B 40 B 50 The following can be obtained from the boundary conditions and the flux continuity theorem:

[0162] 1) From the fact that the tangential components of the magnetic field strength on the boundary are equal, we can obtain:

[0163]

[0164] 2) By the flux continuity theorem:

[0165]

[0166] We can obtain:

[0167]

[0168]

[0169]

[0170]

[0171] Neglecting lateral end effects and considering only longitudinal end effects, the z-component of the electric field intensity in the air gap is:

[0172]

[0173] The total complex power is the complex power per unit length in the z-direction multiplied by the length in the z-direction. Therefore, the total complex power transmitted from the primary side to the secondary side stage and the air gap is:

[0174]

[0175] This invention also provides a method for obtaining performance parameters of a Cramer-wound linear phase-shifting transformer that takes into account end-effects, including:

[0176] (1) The equivalent circuit modeling method of the linear phase-shifting transformer with Clem winding structure based on one-dimensional field analysis and taking into account the edge effect is adopted.

[0177] (2) Solve the equivalent circuit model to obtain the secondary winding resistance, magnetizing reactance, primary winding resistance and primary winding leakage reactance.

[0178] (3) Calculate the performance parameters of the linear phase-shifting transformer based on the solution results of the equivalent circuit.

[0179] Furthermore, the expression for the secondary winding resistance is as follows:

[0180]

[0181] In the formula, This is the longitudinal end effect correction factor for the phase resistance of the secondary winding. This is the longitudinal end effect correction factor for the magnetizing reactance of each phase on the primary side. The phase resistance of the secondary winding on the secondary side is referred to as the primary side when the longitudinal dynamic end effect is ignored.

[0182] Furthermore, the excitation reactance is expressed as follows:

[0183]

[0184] In the formula, The magnetizing reactance per phase on the primary side is ignored when the longitudinal dynamic end effect is neglected.

[0185]

[0186]

[0187] Furthermore, the resistance expression of the primary winding is as follows:

[0188]

[0189] In the formula, ρ is the resistivity of the conductor at the reference temperature, and L cp W1 is the average half-turn length of the coil, W1 is the number of windings per phase, and A is the conductor cross-sectional area.

[0190] Solving for the primary side leakage withstand

[0191] (2) Slot leakage permeability, has

[0192]

[0193] In the formula, k Cu k K a is the coefficient caused by the short pitch of the winding. s1 a s2 The values ​​of h1 and b are all 1. s h2, h3, h0, and b0 are the specific slot parameters of the linear phase-shifting transformer.

[0194] (2) Leakage permeability at the tooth tip,

[0195]

[0196] In the formula, δ is the air gap length of the linear phase-shifting transformer.

[0197] (3) Leakage permeability at the winding ends,

[0198]

[0199] In the formula, L e The length of the primary winding end is [length missing]. y represents the short pitch of the primary winding, and k represents the short pitch of the primary winding. y This is the short-pitch factor for the primary winding.

[0200] (4) Harmonic leakage permeability,

[0201]

[0202] In the formula, k β It can be found in the design book of rotary induction motor.

[0203] The leakage reactance expression is:

[0204]

[0205] In the formula, f is the operating frequency, a is the core thickness, q1 is the actual number of slots per pole per phase on the primary side, and p is the number of pole pairs. λ s For slot leakage permeability, λ t For tooth tip leakage permeability, λ e Leakage permeability at the winding end, λ d Harmonic leakage permeability.

[0206] To demonstrate the inventiveness and technical value of the technical solution of this invention, this section provides specific product or related technology application examples of the technical solution claimed.

[0207] This facilitates the direct application of calculations to the efficiency of multiple superimposed inverter systems and multiple superimposed rectifier systems of linear phase-shifting transformers in ships, providing a reference for the efficient operation of the systems.

[0208] The embodiments of the present invention have achieved some positive results during the research and development or use process, and have indeed great advantages compared with the prior art. The following content describes them in conjunction with the data, charts and other information of the experimental process.

[0209] A calculation program for the equivalent circuit was written using MATLAB, and a linear phase-shifting transformer system model based on finite element field-circuit coupling simulation was established. (A prototype model of the linear phase-shifting transformer was built in the finite element software, powered by an external circuit. The cores of the primary and secondary sides of the linear phase-shifting transformer are completely symmetrical and fixed. The primary winding adopts a full-pitch winding structure with twelve phases, and the secondary winding adopts a long-short pitch winding structure with three phases.) A multi-layer superimposed inverter system platform for the linear phase-shifting transformer was built (the external circuit providing the voltage source to the primary side consists of four sets of three-phase full-pitch external circuits). The system comprises a bridge inverter circuit, with each inverter circuit group separated by 15°. Each inverter circuit outputs a three-phase six-pulse AC current. After multiple superpositions, the twelve groups of six-pulse AC currents are equivalent to a three-phase twenty-four-pulse AC current, with a height approximately approximating a three-phase sinusoidal AC current. Thus, DC current achieves both inversion and superposition functions in the multi-superposition inverter system. When the three-phase AC current is input to the primary side of a linear phase-shifting transformer, a traveling wave magnetic field with a fixed velocity is induced in the air gap. Depending on the winding structure and number of turns on the secondary side, three-phase AC currents with different phase-shifting effects and amplitudes can be obtained. Finite element simulations of the transformer's operating characteristics under different conditions can verify the accuracy of the equivalent circuit model of the linear phase-shifting transformer in this invention.

[0210] The equivalent circuit model of the linear phase-shifting transformer with the Cramer winding structure calculated in this invention is applicable to loads between 60 and 100 ohms. Figure 4 , Figure 5 , Figure 6 , Figure 7 As shown, the voltage and current output from the secondary side have an error of less than 6.5% compared with the simulation results, indicating high accuracy.

[0211] Figure 4 This involves calculating and comparing the changes in load voltage using two methods: finite element simulation and equivalent circuit analysis, under a fixed input voltage, when the secondary load resistance of a linear phase-shifting transformer is changed.

[0212] Figure 5 It is the relationship between the load resistance and the load voltage difference between the equivalent circuit method and the finite element simulation results, and the ratio of the finite element method result to the load resistance.

[0213] Figure 6 This involves calculating and comparing the changes in load current using two methods: finite element simulation and equivalent circuit analysis, under a fixed input voltage, when the secondary load resistance of a linear phase-shifting transformer is changed.

[0214] Figure 7 It is the relationship between the load resistance and the ratio of the difference between the load current obtained by the equivalent circuit method and the finite element simulation results to the load resistance obtained by the finite element method.

[0215] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for modeling the equivalent circuit of a Cramer-wound linear phase-shifting transformer considering edge effects, characterized in that, The equivalent circuit modeling method for a Cramer-wound linear phase-shifting transformer that takes into account edge effects includes: Step 1: Analyze the electromagnetic relationship between the primary winding and the air gap during steady-state operation of the linear phase-shifting transformer, and analyze Maxwell's equations for the linear phase-shifting transformer. Step 2: Based on the theory of one-dimensional fields, establish and solve the equivalent circuit of the linear phase-shifting transformer when considering the longitudinal end effect; Step one specifically includes the following process: (1) Establish the electromagnetic field relationships and equations of a linear phase-shifting transformer based on Maxwell's equations; (2) Introduce vector magnetic potential A to represent the magnetic flux density and induced electric field intensity of the air gap using vector magnetic potential; (3) Based on the principle that the complex power of the field circuit is equal, it can be written that the input electrical energy on the primary side is equal to the sum of the complex power of the air gap part and the secondary side part; Step two specifically includes the following process: (1) Assume that the primary current layer is known, and write the expression for the line current density of the conductor in the primary winding, and establish the relationship between the magnetic flux density of the air gap and the primary and secondary current layers. (2) Determine the vector magnetic potential in the air gap. Quantity; (3) Calculate the expressions for each coefficient based on the equality of tangential components of magnetic field strength on the boundary and the continuity theorem of magnetic flux; (4) Ignore the transverse end effect and only consider the longitudinal end effect to find the z component of the electric field intensity in the air gap; (5) The total complex power is the complex power per unit length in the z direction multiplied by the length in the z direction. The total complex power transmitted from the primary side to the secondary side stage and the air gap can be calculated. The components of the T-type equivalent circuit of a linear phase-shifting transformer that takes into account the end effect include the primary winding resistance, the primary winding leakage reactance, the magnetizing reactance, and the resistance value of the secondary winding referred to the primary side. The excitation reactance is expressed as follows: ； In the formula, The magnetizing reactance per phase on the primary side is ignored when the longitudinal dynamic end effect is neglected. ； 。 2. The method for modeling the equivalent circuit of a Cramer-winding linear phase-shifting transformer considering edge effects as described in claim 1, characterized in that, The simplified two-dimensional model of the linear phase-shifting transformer includes: Region 1, Region 2, Region 3, and Region 4. Region 1 is the primary core, Region 2 is the secondary core, Region 3 is the air gap region, Region 4 is the region with coordinate x=0, and Region 5 is... area; The cores of the primary and secondary sides of the linear phase-shifting transformer are completely symmetrical and fixed. The primary winding adopts a full-pitch winding structure with twelve phases, while the secondary winding adopts a long-short pitch winding structure with three phases.

3. A method for obtaining performance parameters of a Cramer-winding linear phase-shifting transformer considering edge-end effects, implementing the equivalent circuit modeling method for a Cramer-winding linear phase-shifting transformer considering edge-end effects as described in any one of claims 1-2, characterized in that, The method for obtaining the performance parameters of the Cramer-wound linear phase-shifting transformer that takes into account the edge effect includes: (2.1) An equivalent circuit modeling method based on one-dimensional field analysis and taking into account the edge effect of the Cramer winding structure linear phase-shifting transformer is adopted; (2.2) Solve the equivalent circuit model to obtain the secondary winding resistance, magnetizing reactance, primary winding resistance and primary winding leakage reactance; (2.3) Calculate the efficiency, loss and temperature rise performance parameters of the linear phase-shifting transformer based on the solution results of the equivalent circuit.

4. The method for obtaining performance parameters of a Cramer-winding linear phase-shifting transformer considering edge effects as described in claim 3, characterized in that, The expression for the resistance of the secondary winding is: ； In the formula, This is the longitudinal end effect correction factor for the phase resistance of the secondary winding. This is the longitudinal end effect correction factor for the magnetizing reactance of each phase on the primary side. The phase resistance of the secondary winding on the secondary side is referred to as the primary side when the longitudinal dynamic end effect is ignored.

5. The method for obtaining performance parameters of a Cramer-winding linear phase-shifting transformer considering edge effects as described in claim 3, characterized in that, The resistance expression for the primary winding is: ； In the formula, The conductor resistivity at the reference temperature, The average half-turn length of the coil, Number of windings per phase The cross-sectional area of ​​the conductor; Solving for the leakage permeability of the primary side (1) Slot leakage permeability, has ； In the formula, , This is the coefficient caused by the short pitch of the winding. , The values ​​are all 1. , , , , , The specific cogging parameters of the linear phase-shifting transformer; (2) Leakage permeability at the tooth tip, with ； In the formula, The air gap length of the linear phase-shifting transformer (3) Leakage permeability at the winding ends, ； In the formula, The length of the primary winding end is [missing information]. , For the primary winding with short pitch, This refers to the short-pitch factor of the primary winding; (4) Harmonic leakage permeability, has ； In the formula, , , This information can be found in the design manual for rotary induction motors; The expression for the primary side leakage resistance is: ； In the formula, For operating frequency, Core thickness, This represents the actual number of slots per pole per phase on the primary side. For extreme logarithms, , For slot leakage permeability, For tooth tip leakage permeability, Leakage permeability at the winding ends Harmonic leakage permeability.

6. A computer device, characterized in that, The computer device includes a memory and a processor. The memory stores a computer program that, when executed by the processor, causes the processor to perform the steps of the equivalent circuit modeling method for a Cramer-wound linear phase-shifting transformer considering edge effects as described in any one of claims 1-2.

7. A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the method for modeling the equivalent circuit of a Cramer-wound linear phase-shifting transformer taking into account edge effects as described in any one of claims 1-2.

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