CN115758485A - Method for modeling equivalent circuit of linear phase-shifting transformer and obtaining performance parameters of equivalent circuit - Google Patents
Method for modeling equivalent circuit of linear phase-shifting transformer and obtaining performance parameters of equivalent circuit Download PDFInfo
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Abstract
The invention belongs to the field of transformers, and discloses a method for modeling an equivalent circuit of a linear phase-shifting transformer and acquiring performance parameters of the equivalent circuit, which is used for analyzing the electromagnetic relation between a primary side winding and an air gap of the linear phase-shifting transformer in steady-state operation and a Maxwell equation set of the linear phase-shifting transformer; based on the theory of one-dimensional field, the equivalent circuit of the linear phase-shifting transformer and the longitudinal side effect is established and solved. Meanwhile, a performance parameter acquisition method is also disclosed, which comprises the following steps: solving the established equivalent circuit model to obtain the resistance and leakage reactance of the primary side winding, the excitation reactance and the resistance of the secondary side winding; and calculating the performance parameters of the linear phase-shifting transformer based on the equivalent circuit solving result. The invention considers the actual condition of the transformer in the electromagnetic analysis, has more accurate model and high calculation precision, can quickly and effectively calculate the performance parameters of the transformer, such as the winding loss, the efficiency, the voltage regulation rate and the like, is more convenient in the actual calculation analysis and has high practical value.
Description
Technical Field
The invention belongs to the technical field of transformers, and particularly relates to a method for modeling an equivalent circuit of a linear phase-shifting transformer and acquiring performance parameters of the equivalent circuit.
Background
The linear phase-shifting transformer is a novel phase-shifting transformer provided by taking the structure and the principle of a linear motor as reference, the lengths of the primary side and the secondary side of the linear motor are equal and fixed, a traveling wave magnetic field is generated in an air gap after three-phase alternating current is introduced to the primary side, a conductor on the secondary side generates induced current, the phase-shifting effect is realized by designing the access positions of a control circuit and a winding, the phase shifting of any phase number can be realized theoretically, and the structure of the phase-shifting transformer is greatly simplified. Compared with the traditional phase-shifting transformer, the linear phase-shifting transformer has the advantages of simple winding structure, easy modularization and phase shifting at any angle, can be used in micro-grid systems of ship power supply, electric vehicles, outdoor power supplies and the like, and can eliminate higher harmonics and improve the waveform quality of an output side under the condition of meeting the electrical isolation.
The winding structure of the linear phase-shifting transformer has three types of unequal pitch type, hairpin type and annular type, the volume of iron cores of different winding structures is greatly different from the weight of copper wires, and the analysis of an air gap magnetic field is also influenced by the winding structure. Therefore, the difference of each parameter under different winding structures needs to be considered when analyzing various performance parameters of the linear phase-shifting transformer, such as efficiency, temperature rise, voltage regulation rate, three-phase asymmetry, harmonic content of output voltage and the like.
The linear phase-shifting transformer mainly comprises a mathematical model and an equivalent circuit, wherein the mathematical model is mainly used for describing the transient process of the transformer, and the equivalent circuit is mainly concerned with the relation between electricity and magnetism of the linear phase-shifting transformer. The two models are mutually linked and can be mutually converted under certain conditions, but the two models are greatly different, the former is mainly used for analyzing the transient performance calculation of the linear phase-shifting transformer and providing a strategy for control research, and the latter is mainly used for describing the steady electromagnetic relationship of the linear phase-shifting transformer and analyzing the steady operation characteristics and providing guidance for the design optimization of the linear phase-shifting transformer.
The T-type equivalent circuit model of the current commonly used linear phase-shifting transformer assumes that the electromotive force of each phase in the primary side winding is symmetrical, and actually, the electromotive force of each phase is not symmetrical due to the influence of various factors. In addition, the following disadvantages exist: firstly, the influence of asymmetry of electromotive force of each phase winding on the primary side is not considered; secondly, the influence generated by different winding structures of the linear phase-shifting transformer is not considered; and thirdly, the influence of the problems of side end effect, asymmetric winding distribution, disconnection of a magnetic circuit and the like of the linear phase-shifting transformer due to the iron core structure of the linear phase-shifting transformer is not considered.
The establishment of the equivalent circuit model of the linear phase-shifting transformer mainly comprises two methods, namely 1) an equivalent circuit deduced based on an air gap flux density distribution model. 2) An equivalent circuit is derived based on electromagnetic field theory. The first method has low calculation accuracy, and the analytic expression of the air-gap magnetic field can be calculated only when the primary-side current is known, and only the input voltage of the primary side is known actually. The second method is based on an electromagnetic field theory and an actual transformer model, and can solve the analytical expression of each region field quantity by combining boundary conditions, the calculation precision is high, and the input voltage of the primary side is generally known. Therefore, the expression of the air gap magnetic field is solved by adopting an electromagnetic field analysis method, the side effect coefficient is deduced according to the principle that the complex power of a field path is equal, and the equivalent circuit of the linear phase-shifting transformer in consideration of the side effect is obtained.
Through the above analysis, the problems and defects of the prior art are as follows:
(1) The T-type equivalent circuit model of the conventional linear phase-shifting transformer assumes that the electromotive force of each phase in the primary side winding is symmetrical, actually, the electromotive force of each phase is asymmetrical due to the influence of various factors, and the influence of asymmetry of the electromotive force of each phase of the primary side winding is not considered.
(2) The prior art does not consider the influence generated by different winding structures of the linear phase-shifting transformer.
(3) In the prior art, the influence of the problems of side end effect, asymmetric winding distribution, disconnection of a magnetic circuit and the like of the linear phase-shifting transformer due to the iron core structure of the linear phase-shifting transformer is not considered.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a method for modeling an equivalent circuit of a linear phase-shifting transformer and acquiring performance parameters of the equivalent circuit.
The invention is realized in this way, a method for modeling an equivalent circuit of a linear phase-shifting transformer, the method for modeling the equivalent circuit of the linear phase-shifting transformer comprises the following steps:
analyzing the electromagnetic relation between a primary side winding and an air gap when the linear phase-shifting transformer operates in a steady state, and analyzing a Maxwell equation set of the linear phase-shifting transformer;
and step two, establishing and solving a linear phase-shifting transformer and an equivalent circuit in the longitudinal side effect based on the theory of the one-dimensional field.
Further, the step one specifically includes the following steps:
(1) And establishing the electromagnetic field relation and the equation of the linear phase-shifting transformer according to the Maxwell equation set.
(2) And introducing a vector magnetic potential A, and expressing the magnetic flux density and the induced electric field strength of the air gap by using the vector magnetic potential.
(3) According to the principle that the field circuit complex power is equal, the sum of the complex power of the air gap part and the secondary side part of the primary side input electric energy can be written.
Further, the method specifically comprises the following steps:
(1.1) establishing a Maxwell equation set of the linear phase-shifting transformer:
wherein B is the magnetic flux density, H is the magnetic field intensity, E is the electric field intensity, j 1 Is the primary side conductor current density j 2 Current density, μ induced from a travelling-wave magnetic field for a secondary side conductor 0 Is the permeability of the core, σSecondary side conductivity;
(1.2) the relationship of field-path complex power equality can be obtained
In the formula (I), the compound is shown in the specification,
is the primary side of the effective value of the air gap phase potential, P 2 、P 3 Is the active power in the secondary side and air gap, equivalent to P 3 ＝0，Q 2 、Q 3 Is the reactive power in the secondary side and the air gap,
is an effective value of the primary side phase current, m 1 Is the number of primary side phases; the relationship between the amplitude of the primary side current layer and the effective value of the primary side phase current is
Wherein p is the polar logarithm, τ is the polar distance, J 1 Is the traveling wave current density amplitude, W 1 For each phase of the primary winding, k w1 Is the primary winding coefficient.
(1.3) introducing vector magnetic potential A, adding the following two formulas
In the formula, B 3y The component of the flux density in the air gap on the coordinate y, A 3z Is the z-component of the vector magnetic potential in the air gap, E 3z Is the z-component of the induced electric field strength in the air gap.
Further, the correlation hypothesis includes:
(2.1) representing the primary side magnetic potential by using a surface current layer, and only considering a fundamental component;
(2.2) considering the influence of the primary side teeth and the grooves by using the air gap coefficient;
(2.3) iron core saturation, hysteresis loss and skin effect of a secondary side conductor are ignored;
(2.4) the current flows along the direction of the coordinate Z;
(2.5) the various field quantities vary sinusoidally with time.
Further, the equivalent circuit includes: the magnetic field generating device comprises a region 1, a region 2, a region 3, a region 4 and a region 4, wherein the region 1 is a primary side branch, the region 2 is a secondary side branch, the region three is an air gap region, the region 4 is a region with the coordinate x =0, and the region 5 is an end magnetic flux.
Further, the second step comprises:
(1) Assuming the primary current layer is a known condition, and writing a line current density expression of a conductor in the primary winding, a relationship between the magnetic flux density of the air gap and the primary and secondary current layers is established.
(2) The z-component of the vector magnetic potential in the air gap is determined.
(3) And calculating the expression of each coefficient according to the tangential component equality of the magnetic field intensity on the boundary and the magnetic flux continuity theorem.
(4) Neglecting the transverse end effect, only considering the longitudinal end effect, the z-component of the electric field intensity in the air gap is obtained.
(5) The total complex power is the complex power of unit length in the z direction multiplied by the length in the z direction, and the total complex power transmitted from the primary side to the secondary side and the air gap can be obtained.
Further, the establishing and solving of the equivalent circuit of the linear phase-shifting transformer in consideration of the longitudinal side effect specifically includes the following procedures:
(1) Assume that the transformer expression is:
j 1 ＝J 1 e j(ωt-kx) (0＜x＜2pτ)
in the formula, j 1 W is the primary current layer density and w is the angular velocity.
When the secondary side is loaded, along the diagram
Wherein δ 'is the effective length of the air gap, δ' = k δ k μ δ，k δ ,k μ Is the air gap coefficient and saturation coefficient of the transformer, and delta is the transformer air gap length.
(2) The formula solution in the simultaneous step (1) can be obtained as follows:
in the formula, A 3z Is the z-component of the vector magnetic bit in the air gap,
τ e ＝πλ，
C 1 、C 2 the solution of (2) needs to use boundary conditions and flux continuity theorem.
(3) The analytic expression of the flux density distribution on the center line of y =0 on both sides of the transformer opening is expressed as:
in the formula, B 4y 、B 5y Is the y-component of the air gap flux density at the ends of zone 4 and zone 5, B 40 、B 50 Is the undetermined coefficient.
C 1 、C 2 、B 40 、B 50 The following are obtained from the boundary conditions and the flux continuity theorem:
from the equal tangential components of the magnetic field strength at the boundary:
according to the magnetic flux continuity theorem, the following steps are obtained:
thus, we find:
(4) Ignoring the lateral end effect, only the longitudinal end effect is considered, the z-component of the electric field strength in the air gap being:
the total complex power is the complex power of the unit length in the z direction multiplied by the length in the z direction, and then the total complex power transmitted from the primary side to the secondary side and the air gap is:
another objective of the present invention is to provide a method for obtaining performance parameters of a linear phase-shifting transformer, which implements the method for modeling an equivalent circuit of a linear phase-shifting transformer, the method comprising:
(1.1) adopting an equivalent circuit modeling method based on one-dimensional field analysis and considering the edge effect Cramer winding structural type linear phase-shifting transformer.
And (1.2) solving the equivalent circuit model to obtain the resistance of the secondary side winding, the excitation reactance, the resistance of the primary side winding and the leakage reactance of the primary side winding.
And (1.3) calculating the performance parameters of the linear phase-shifting transformer based on the equivalent circuit solving result.
Further, the expression of the secondary side winding resistance is as follows:
in the formula (I), the compound is shown in the specification,
is a longitudinal end effect correction coefficient of a phase resistance of a secondary side winding,
the longitudinal end effect correction coefficient of each phase of the primary side magnetizing reactance,
the phase resistance of the secondary winding on the secondary side of the primary side is reduced to ignore the longitudinal dynamic end effect.
Further, the excitation reactance is expressed as:
in the formula (I), the compound is shown in the specification,
neglecting each phase magnetization reactance of the primary side when the longitudinal dynamic end effect;
further, the resistance expression of the primary side winding is:
where ρ is the conductor resistivity at the reference temperature, L cp Is the average half turn length of the coil, W 1 The number of windings of each phase, A is the sectional area of the conductor;
solving for primary side leakage magnetic conductance
(1) Magnetic leakage of the slot is provided with
In the formula, k Cu 、k K Coefficient due to winding short distance, a s1 、a s2 All have a value of 1,h 1 、b s 、h 2 、h 3 、h 0 、b 0 Is the specific tooth space parameter of the linear phase-shifting transformer.
(2) The magnetic leakage of the tooth end is provided with
Wherein δ is the air gap length of the linear phase-shifting transformer
(3) Magnetic leakage flux at the end of the winding, have
In the formula, L e The end of the primary side winding is long,
y is the primary winding short pitch, k y Is the primary winding short pitch coefficient.
(4) Harmonic magnetic leakage conductor, has
In the formula (I), the compound is shown in the specification,
k β can be found in the design book of the rotary induction motor
The primary side leakage reactance expression is:
wherein f is the operating frequency, a is the thickness of the iron core, q 1 Is the actual number of slots per pole per phase on the primary side, p is the number of pole pairs,
λ s is a slot leakage flux, λ t For magnetic flux leakage at the tooth tip, λ e Magnetic flux leakage of winding head, λ d And harmonic magnetic leakage flux.
It is a further object of the invention to provide a computer arrangement comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to carry out the steps of the method for modeling an equivalent circuit of a linear phase shifting transformer.
It is a further object of the present invention 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 method for modeling an equivalent circuit of a linear phase-shifting transformer.
By combining the technical scheme and the technical problem to be solved, the technical scheme to be protected by the invention has the advantages and positive effects that:
(1) The invention establishes and solves the equivalent circuit of the linear phase-shifting transformer and the longitudinal side effect based on the theory of one-dimensional field, and makes the assumptions of representing the primary side magnetic potential by a surface current layer, only considering the fundamental component, considering the influence of primary side teeth and slots by air gap coefficients and the like for simplifying analysis.
(2) According to the invention, the electromagnetic analysis considers the actual condition of the transformer and the influence of asymmetry of electromotive force of each phase winding on the primary side; the influence of the problems of side end effect, asymmetric winding distribution, disconnection of a magnetic circuit and the like of the linear phase-shifting transformer due to the iron core structure of the linear phase-shifting transformer is considered.
(3) The invention adopts the electromagnetic field analysis method to solve the expression of the air gap magnetic field, and deduces the side effect coefficient according to the principle that the complex power of the field path is equal, so as to obtain the equivalent circuit of the linear phase-shifting transformer in consideration of the side effect, and the equivalent circuit has simple structure and high calculation precision. The method is convenient for directly applying and calculating the efficiency calculation in the linear phase-shifting transformer multiple superposition inversion system and the linear phase-shifting transformer multiple superposition rectification system, and provides reference for the high-efficiency operation of the system.
(4) The expected income and commercial value after the technical scheme of the invention is converted are as follows: because the theoretical analysis and the characteristic calculation of the linear phase-shifting transformer are complex, the calculation of the accurate equivalent circuit model of the linear phase-shifting transformer is convenient for visually representing the relationship between the electric field and the magnetic field of each region of the transformer by using the relationship among elements in the circuit, has the advantages of simple structure, high calculation precision and the like, can quickly and effectively calculate the performance parameters of the transformer, such as winding loss, efficiency, voltage regulation rate and the like, is also convenient in practical calculation and analysis, has high practical value and has great commercial value.
(5) The technical scheme of the invention fills the technical blank in the industry at home and abroad: the T-type equivalent circuit model of the conventional linear phase-shifting transformer assumes that the electromotive force of each phase in the primary winding is symmetrical, and actually, the electromotive force of each phase is asymmetrical due to the influence of various factors. In addition, the problems of influence, edge effect, asymmetric winding distribution, magnetic circuit disconnection and the like caused by different winding structures exist, the invention provides a linear phase-shifting transformer equivalent circuit modeling method of a Cramer winding structure based on one-dimensional field analysis and considering the edge effect, and the method fills the blank of the related technology.
(6) The technical scheme of the invention solves the technical problems which are always desired to be solved but are not successfully achieved: the invention provides a linear phase-shifting transformer equivalent circuit modeling method based on a Cramer winding structure with one-dimensional field analysis and side effect consideration, which solves the technical problem that the calculation precision is low due to the fact that an equivalent circuit model is too simplified when various performance parameters such as steady-state efficiency, voltage regulation rate, three-phase asymmetry and harmonic content of output voltage are analyzed by a T-shaped equivalent circuit model of a linear phase-shifting transformer.
(7) The technical scheme of the invention overcomes the technical prejudice that: compared with the traditional general T-shaped equivalent circuit of the linear phase-shifting transformer, the electromagnetic analysis in the invention considers the actual situation of the transformer, the model is more accurate, and the influence of asymmetry of electromotive force of each phase winding on the primary side is considered; the influence of the problems of side end effect, asymmetric winding distribution, disconnection of a magnetic circuit and the like of the linear phase-shifting transformer due to the iron core structure of the linear phase-shifting transformer is considered.
Drawings
FIG. 1 is a simplified two-dimensional physical model diagram of a linear phase-shifting transformer and side-effect measurement according to an embodiment of the present invention;
FIG. 2 is a T-shaped equivalent circuit diagram of a linear phase-shifting transformer and side effect according to an embodiment of the present invention;
FIG. 3 is a two-dimensional simulation model diagram of a Cramer winding structure type linear phase-shifting transformer provided by the embodiment of the present invention;
FIG. 4 is a graph comparing load voltages provided by embodiments of the present invention;
FIG. 5 is a graph of load voltage error percentages provided by an embodiment of the present invention;
FIG. 6 is a graph comparing load currents provided by embodiments of the present invention;
fig. 7 is a graph of load current error percentage provided by an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
This section is an explanatory embodiment expanding on the claims so as to fully understand how the present invention is embodied by those skilled in the art.
The method for modeling the equivalent circuit of the linear phase-shifting transformer provided by the embodiment of the invention comprises the following steps:
s101, analyzing an electromagnetic relation between a primary side winding and an air gap when the linear phase-shifting transformer operates in a steady state, and analyzing a Maxwell equation set of the linear phase-shifting transformer;
and S102, establishing and solving an equivalent circuit of the linear phase-shifting transformer in consideration of longitudinal side effect.
Further, the S101 specifically includes the following steps:
(1.1) establishing a Maxwell equation set of the linear phase-shifting transformer:
wherein B is magnetic flux density, H is magnetic field intensity, and E is electric fieldStrength, j 1 Is the primary side conductor current density j 2 Current density, μ induced from a travelling-wave magnetic field for a secondary side conductor 0 The magnetic conductivity of the iron core, wherein sigma is the secondary side conductivity;
(1.2) obtaining the relation of field path complex power equality:
in the formula (I), the compound is shown in the specification,
is the primary side of the effective value of the air gap phase potential, P 2 、P 3 Is the active power in the secondary side and air gap, equivalent to P 3 ＝0，Q 2 、Q 3 Is the reactive power in the secondary side and the air gap,
effective value of phase current on the primary side, m 1 Is the number of primary phase.
The relationship between the amplitude of the primary side current layer and the effective value of the primary side phase current is
Wherein p is the number of pole pairs, τ is the pole pitch, J 1 Is the traveling wave current density amplitude, W 1 Each phase of the primary winding is connected in series with a number of turns, k w1 Is the primary winding coefficient.
(1.3) introducing vector magnetic potential A, adding the following two formulas
In the formula, B 3y The component of the flux density in the air gap on the coordinate y, A 3z Is the z-component of the vector magnetic potential in the air gap, E 3z Is the z-component of the induced electric field strength in the air gap.
The related assumptions provided by the embodiment of the invention comprise:
(2.1) representing the primary side magnetic potential by using a surface current layer, and only considering a fundamental component;
(2.2) considering the influence of the primary side teeth and the grooves by using the air gap coefficient;
(2.3) iron core saturation, hysteresis loss and skin effect of a secondary side conductor are ignored;
(2.4) the current flows along the direction of the coordinate Z;
(2.5) the various field quantities vary sinusoidally with time.
As shown in fig. 1, the simplified two-dimensional model of the linear phase-shifting transformer includes: the magnetic core comprises a region 1, a region 2, a region 3 and a region 4, wherein the region 1 is a primary side core, the region 2 is a secondary side core, the region three is an air gap region, the region 4 is a region with a coordinate x =0, and the region 5 is a region with a coordinate x =2p τ. The linear phase-shifting transformer and the side-effect T-type equivalent circuit are shown in FIG. 2, and the components include a primary winding resistor, a primary winding leakage reactance, an excitation reactance, and a secondary winding value calculated to the primary resistance value. The two-dimensional simulation model of the Cramer winding structure type linear phase-shifting transformer is shown in figure 3. The iron cores of the primary side winding and the secondary side winding of the linear phase-shifting transformer are completely symmetrical and fixed, the primary side winding adopts a full-pitch winding structure and has twelve phases in total, and the secondary side winding adopts a long-short-pitch matched winding structure and has three phases in total.
Assuming a transformer primary side current layer:
j 1 ＝J 1 e j(ωt-kx) (0＜x＜2pτ)
in the formula (I), the compound is shown in the specification,
j 1 the primary current layer density.
When the secondary side is loaded, pass through a rectangular loop in the figure by × H = j 1 +j 2 To obtain
Wherein δ 'is the effective length of the air gap, δ' = k δ k μ δ，k δ ,k μ Is the air gap coefficient and saturation coefficient of the transformer, and delta is the transformer air gap length.
The above formula is solved simultaneously to obtain:
in the formula, A 3z Is the z-component of the vector magnetic bit in the air gap,
τ e ＝πλ，
C 1 、C 2 the solution of (2) needs to use boundary conditions and flux continuity theorem.
Due to the symmetrical characteristic of the linear phase-shifting transformer structure, the distribution of the end-face magnetic fluxes of the region 4 and the region 5 is symmetrical. The analytic expression of the flux density distribution on the center line of y =0 on both sides of the transformer opening can be approximately expressed as:
in the formula, B 4y 、B 5y Is the y-component of the air gap flux density at the ends of zone 4 and zone 5, B 40 、B 50 Is the undetermined coefficient.
In the above formula C 1 、C 2 、B 40 、B 50 The following conditions were obtained from the boundary conditions and the flux continuity theorem:
1) From the equal tangential components of the magnetic field strength at the boundary:
2) By the magnetic flux continuity theorem:
the following can be obtained:
neglecting the transverse end effect, only the longitudinal end effect is considered, the z-component of the electric field strength in the air gap being
The total complex power is the complex power of the unit length in the z direction multiplied by the length in the z direction, and then the total complex power transmitted from the primary side to the secondary side and the air gap is:
the invention also provides a method for acquiring the performance parameters of the Cramer winding type linear phase-shifting transformer considering the edge effect, which comprises the following steps:
(1) The equivalent circuit modeling method based on the one-dimensional field analysis and considering the edge effect Cramer winding structure type linear phase-shifting transformer is adopted.
(2) And solving the equivalent circuit model to obtain the resistance of the secondary side winding, the excitation reactance, the resistance of the primary side winding and the leakage reactance of the primary side winding.
(3) And calculating the performance parameters of the linear phase-shifting transformer based on the equivalent circuit solving result.
Further, the expression of the secondary side winding resistance is as follows:
in the formula (I), the compound is shown in the specification,
is a longitudinal end effect correction coefficient of a phase resistance of a secondary side winding,
the longitudinal end effect correction coefficient of each phase of the primary side magnetizing reactance,
the phase resistance of the secondary winding on the secondary side of the primary side is reduced to ignore the longitudinal dynamic end effect.
Further, the excitation reactance is expressed as:
in the formula (I), the compound is shown in the specification,
neglecting the magnetization reactance of each phase of the primary side when the longitudinal dynamic end effect exists;
further, the resistance expression of the primary side winding is:
where ρ is the conductor resistivity at the reference temperature, L cp Is the average half turn length of the coil, W 1 The number of windings of each phase, A is the sectional area of the conductor;
solving for primary side leakage reactance
(2) Magnetic leakage of the slot is provided with
In the formula, k Cu 、k K Coefficient due to winding short distance, a s1 、a s2 All have a value of 1,h 1 、b s 、h 2 、h 3 、h 0 、b 0 Is the specific tooth space parameter of the linear phase-shifting transformer.
(2) The magnetic leakage at the tooth end is provided with
Wherein δ is the air gap length of the linear phase-shifting transformer
(3) Magnetic leakage flux at the end of the winding, have
In the formula, L e The end of the primary side winding is long,
y is the primary winding short pitch, k y Is the primary winding short pitch coefficient.
(4) Harmonic magnetic leakage conductor, has
In the formula (I), the compound is shown in the specification,
k β can be found in the design book of the rotary induction motor
The leakage reactance expression is:
wherein f is the operating frequency, a is the thickness of the iron core, q 1 P is the number of pole pairs as the actual number of slots per pole per phase at the primary side,
λ s is a slot leakage flux, λ t For magnetic flux leakage at the tooth tip, λ e Magnetic flux leakage of winding head, λ d And harmonic magnetic leakage flux guide.
In order to prove the creativity and the technical value of the technical scheme of the invention, the part is the application example of the technical scheme of the claims on specific products or related technologies.
The method is convenient for directly applying and calculating the efficiency calculation in the linear phase-shifting transformer multiple superposition inversion system and the linear phase-shifting transformer multiple superposition rectification system in the ship, and provides reference for the high-efficiency operation of the system.
The embodiment of the invention achieves some positive effects in the process of research and development or use, and has great advantages compared with the prior art, and the following contents are described by combining data, diagrams and the like in the test process.
The method comprises the steps of compiling a calculation program of an equivalent circuit based on MATLAB, establishing a linear phase-shifting transformer system model based on finite element field circuit coupling simulation, (establishing a model of a linear phase-shifting transformer prototype in finite element software, and supplying power by an external circuit, wherein iron cores of a first side and a second side of the linear phase-shifting transformer are completely symmetrical and fixed, a primary side winding adopts a winding structure with a whole pitch, twelve phases are totally provided, a secondary side winding adopts a winding structure with a long-short pitch matched, and three phases are totally provided), and a linear phase-shifting transformer multi-superposition inversion system platform is established (the external circuit for providing a voltage source for a primary side is composed of four groups of three-phase full-bridge inversion circuits, each group of inversion circuits has a difference of 15 degrees in sequence, each group of inversion circuits outputs three-phase six-pulse alternating current, the twelve groups of six-pulse alternating current are subjected to multi-superposition to be equivalent to three-phase twenty-four-pulse multiple alternating current, the height is approximate to three-phase sine alternating current, and direct current realizes inversion and superposition functions in the primary side of a three-phase alternating current superposition inversion system. The accuracy of the equivalent circuit model of the linear phase-shifting transformer can be verified by simulating the running characteristics of the transformer under different working conditions through finite elements.
The calculated equivalent circuit model of the linear phase-shifting transformer with the Cramer winding structure is loaded between 60 and 100 ohms as shown in figures 4, 5, 6 and 7, and compared with a simulation result, the voltage and the current output by the secondary side have errors within 6.5 percent and have higher accuracy.
FIG. 4 is a diagram of a linear phase-shifting transformer with a fixed input voltage, a variable of a secondary side load resistance, a finite element simulation and an equivalent circuit.
FIG. 5 is a graph showing the relationship between the ratio of the difference between the load voltages of the equivalent circuit method and the finite element simulation results and the finite element method results and the load resistance, with the load resistance varied.
FIG. 6 is a diagram illustrating the change of the load current calculated and compared by the two methods of changing the secondary side load resistance, finite element simulation and equivalent circuit of the linear phase-shifting transformer under the fixed input voltage.
FIG. 7 is a graph showing the relationship between the ratio of the difference between the load currents obtained by the equivalent circuit method and the finite element method to the result of the finite element method and the load resistance, with the load resistance being changed.
The above description is only for the purpose of illustrating the present invention and the appended claims are not to be construed as limiting the scope of the invention, which is intended to cover all modifications, equivalents and improvements that are within the spirit and scope of the invention as defined by the appended claims.
Claims (10)
1. A method for modeling an equivalent circuit of a Cramer winding type linear phase-shifting transformer considering an edge effect is characterized by comprising the following steps of:
analyzing the electromagnetic relation between a primary side winding and an air gap when the linear phase-shifting transformer operates in a steady state, and analyzing a Maxwell equation set of the linear phase-shifting transformer;
and step two, establishing and solving a linear phase-shifting transformer and an equivalent circuit in the longitudinal side effect based on the theory of the one-dimensional field.
2. The method for modeling an equivalent circuit of a Cramer-wound linear phase-shifting transformer taking into account the edge effect as claimed in claim 1, wherein said first step specifically comprises the following steps:
(1) Establishing an electromagnetic field relation and an equation of the linear phase-shifting transformer according to a Maxwell equation set;
(2) Introducing a vector magnetic potential A, and expressing the magnetic flux density of an air gap and the strength of an induced electric field by using the vector magnetic potential;
(3) According to the principle that the field circuit complex power is equal, the sum of the complex power of the air gap part and the secondary side part of the primary side input electric energy can be written.
3. The method for modeling an equivalent circuit of a Cramer-wound linear phase-shifting transformer taking into account the edge effect as recited in claim 1, wherein said simplified two-dimensional model of said linear phase-shifting transformer comprises: the core-cooling core comprises a region 1, a region 2, a region 3 and a region 4, wherein the region 1 is a primary side core, the region 2 is a secondary side core, the region three is an air gap region, the region 4 is a region with coordinates x =0, and the region 5 is a region with coordinates x =2p τ;
the linear phase-shifting transformer and the side-effect T-type equivalent circuit are composed of a primary side winding resistor, a primary side winding leakage reactance, an excitation reactance and a secondary side winding which are reduced to a primary side resistance value;
the iron cores of the primary side winding and the secondary side winding of the linear phase-shifting transformer are completely symmetrical and fixed, the primary side winding adopts a winding structure with the integral pitch, twelve phases are shared, and the secondary side winding adopts a winding structure with the long and short pitches matched, three phases are shared.
4. The method for modeling the equivalent circuit of the Cramer winding type linear phase-shifting transformer considering the edge-to-end effect according to claim 1, wherein the second step specifically comprises the following steps:
(1) Assuming that a primary side current layer is a known condition, writing a line current density expression of a conductor in a primary side winding, and establishing a relation between the magnetic flux density of an air gap and a primary side current layer and a secondary side current layer;
(2) Solving the z component of the vector magnetic potential in the air gap;
(3) Calculating the expression of each coefficient according to the tangential component equality of the magnetic field intensity on the boundary and the magnetic flux continuity theorem;
(4) Neglecting the transverse end effect, only considering the longitudinal end effect, and calculating the z component of the electric field intensity in the air gap;
(5) The total complex power is the complex power of unit length in the z direction multiplied by the length in the z direction, and the total complex power transmitted from the primary side to the secondary side and the air gap can be obtained.
5. A method for obtaining performance parameters of a Cramer-wound linear phase-shifting transformer taking into account an edge effect, which implements the method for modeling an equivalent circuit of a Cramer-wound linear phase-shifting transformer taking into account an edge effect according to any one of claims 1 to 4, wherein the method for obtaining the performance parameters of the Cramer-wound linear phase-shifting transformer taking into account an edge effect comprises:
(2.1) adopting an equivalent circuit modeling method based on one-dimensional field analysis and considering an edge effect Cramer winding structural type linear phase-shifting transformer;
(2.2) solving the equivalent circuit model to obtain secondary side winding resistance, excitation reactance, primary side winding resistance and primary side winding leakage reactance;
and (2.3) calculating performance parameters such as efficiency, loss, temperature rise and the like of the linear phase-shifting transformer based on the equivalent circuit solving result.
6. The method for obtaining the performance parameters of the Cramer winding type linear phase-shifting transformer considering the edge-termination effect according to claim 5, wherein the expression of the secondary side winding resistance is as follows:
in the formula (I), the compound is shown in the specification,
is a longitudinal end effect correction coefficient of a phase resistance of a secondary side winding,
the longitudinal end effect correction coefficient of each phase of the primary side magnetizing reactance,
the phase resistance of the secondary winding on the secondary side of the primary side is reduced to ignore the longitudinal dynamic end effect.
7. The method for obtaining the performance parameters of the Cramer-wound linear phase-shifting transformer considering the edge-end effect according to claim 5, wherein the excitation reactance is expressed as:
in the formula (I), the compound is shown in the specification,
neglecting the magnetization reactance of each phase of the primary side when the longitudinal dynamic end effect exists;
8. the method for obtaining the performance parameters of the Cramer winding type linear phase-shifting transformer considering the edge-termination effect according to claim 5, wherein the resistance expression of the primary side winding is as follows:
where ρ is the conductor resistivity at the reference temperature, L cp Is the average half turn length of the coil, W 1 The number of windings of each phase, A is the sectional area of the conductor;
solving for primary side leakage magnetic conductance
(3) Magnetic leakage of the slot is provided with
In the formula, k Cu 、k K Coefficient due to short winding run, a s1 、a s2 All have a value of 1,h 1 、b s 、h 2 、h 3 、h 0 、b 0 The parameters are specific tooth space parameters of the linear phase-shifting transformer;
(2) The magnetic leakage of the tooth end is provided with
Wherein δ is the air gap length of the linear phase-shifting transformer
(3) Magnetic leakage conductors at the end of the winding are
In the formula, L e The end of the primary side winding is long,
y is the primary winding short pitch, k y Is a short pitch coefficient of the primary side winding;
(4) Harmonic magnetic leakage conductor, has
In the formula (I), the compound is shown in the specification,
k β the method can be found in a design book of the rotary induction motor;
the primary side leakage reactance expression is:
wherein f is the operating frequency, a is the thickness of the iron core, q 1 P is the number of pole pairs as the actual number of slots per pole per phase at the primary side,
λ s is a slot leakage flux, λ t For magnetic flux leakage at the tooth tip, λ e Magnetic flux leakage at the end of winding, λ d And harmonic magnetic leakage flux.
9. A computer arrangement, characterized in that the computer arrangement comprises a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to carry out the steps of the method of modeling a chlamer-wound linear phase-shifting transformer equivalent circuit taking into account the side-end effect according to any one of claims 1 to 4.
10. 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 of modeling an equivalent circuit of a cramer-wound linear phase-shifting transformer taking into account the edge-end effect according to any one of claims 1 to 4.
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| CN117828244A (en) * | 2024-03-06 | 2024-04-05 | 华中科技大学 | Linear induction motor chain type equivalent circuit and characteristic analysis method |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117828244A (en) * | 2024-03-06 | 2024-04-05 | 华中科技大学 | Linear induction motor chain type equivalent circuit and characteristic analysis method |
| CN117828244B (en) * | 2024-03-06 | 2024-05-14 | 华中科技大学 | Linear induction motor chain type equivalent circuit and characteristic analysis method |
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