CN105742047A - Control method for inductance parameter of high-frequency transformer body - Google Patents
Control method for inductance parameter of high-frequency transformer body Download PDFInfo
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Abstract
The invention provides a control method for an inductance parameter of a high-frequency transformer body. The control method comprises excitation inductance control and leakage inductance control of a high-frequency transformer; the rated voltage and the work frequency of the high-frequency transformer are known under the condition that the magnetic core structure and dimension are determined; the excitation inductance control method comprises the following steps: selecting a magnetic core material according to different magnetic core material magnetization characteristics and different saturation flux densities; controlling the work flux density to be Bm; and controlling an air-gap length to be lg under the condition of an open air gap of the magnetic core; and the leakage inductance control method comprises the following steps: controlling the number of turns of single-layer windings in primary and secondary windings; controlling the interlayer thickness of the primary winding, the interlayer thickness of the secondary winding and the thickness between the primary winding and the secondary winding; and changing the arrangement mode of the primary winding and the secondary winding in a separating manner, a sandwich manner and a complete coordinated transposition manner. The control method provided by the invention is used for controlling the inductance parameter, so that resonance on conversion topologies at two sides of the high-frequency transformer is achieved; and the voltage quality is improved.
Description
Technical field
The present invention relates to high frequency transformer technical field, be specifically related to the control method of a kind of high frequency transformer body inductance parameters.
Background technology
Electrically-based electronic technology, Chinese scholars starts exploratory development and realizes the Novel intelligent transformer-electric power electric transformer (PowerElectronicTransformer of transformation of electrical energy, it is called for short PET), also referred to as solid-state transformer (Solid-StateTransformer is called for short SST).Electric power electric transformer is as a kind of highly controllable novel power transformation equipment, and its outstanding feature is that by the flexible control to transformer primary secondary voltage amplitude with phase place, to meet many new demands of intelligent grid future development.
Development along with power electronic devices, IGBT and controllable silicon MOSFET application in power electronics topology, the switching speed and the make-break capacity that make power electronics topology (rectification side and inverter side) are greatly enhanced, and the performance boost for electric power electric transformer provides a lot of support.In the realization of the high-power topology of electric power electric transformer, middle high frequency transformer body is the most basic is also most important electromagnetic component.Along with design capacity improves constantly, volume of transformer constantly increases, and can pass through to promote the physical size of the method reduction high frequency transformer body of operating frequency.
In the future, a large amount of along with distributed power source access and grid-connected, such as wind energy, solar energy, tide energy etc., as shown in Figure 1, in order to improve power supply quality and reduce the threat to electrical network and broken evil, the quality of power supply of the distributed power source of grid integration is required by electrical network can be significantly high, and harmonic wave to lack, and this is most important.And the access of these distributed power sources, the participation of electric power electric transformer is requisite.
The harmonic effects access grid-connected in order to reduce distributed power source, improve power supply quality, will in electric power electric transformer, make the inductance parameters of high frequency transformer body and the parameter generation resonance of both sides converter topology, namely soft switch technique is achieved, to improve power supply quality and to reduce harmonic wave, as shown in Figure 2.
In fig 2, LrAnd CrFor the resonant inductance in the topology of both sides and capacitance parameter, and L1kAnd LmThe respectively leakage inductance of high frequency transformer and magnetizing inductance parameter, for the resonant inductance in the topology of the inductance parameters Yu both sides that realize high frequency transformer body and capacitance parameter generation resonance, to reduce harmonic wave, improve power supply quality, so it is necessary to controlling leakage inductance and the magnetizing inductance parameter of high frequency transformer body accurately.
At present, in the design cycle of existing high frequency transformer body, accurately do not control the inductance parameters of self, simply carry out Method of Spreading Design according to the design capacity of high frequency transformer, electric pressure and operating frequency, it is determined that magnetic core size, the number of turn and winding arrangement mode etc..
Summary of the invention
For solving above-mentioned deficiency of the prior art, determine under condition at core structure and size, derivation based on high frequency transformer inductance parameters is theoretical, start with from the derivation calculating formula of high frequency transformer inductance parameters, a kind of method proposing accurate control high frequency transformer body inductance parameters, to realize occurring resonance between the topology of both sides, it is achieved soft switch technique, improve quality of voltage.
It is an object of the invention to adopt following technical proposals to realize:
The present invention provides the control method of a kind of high frequency transformer (high frequency transformer includes dry type high frequency transformer and oil immersed type high frequency transformer) magnetizing inductance parameter (magnetizing inductance and leakage inductance), when the core structure of high frequency transformer is UU type and EE type, as shown in accompanying drawing 3 and accompanying drawing 4, described method includes following control mode:
(1): different with saturation magnetic induction according to the magnetization characteristic of different core materials, core material is selected;
(2): determine under condition at core structure and size, it is known that the rated voltage of former vice-side winding and operating frequency, the close B of work magnetic is controlledmSize, and then, control winding the number of turn;
(3): determine under condition at core structure and size, adopt the accurate insulating paper of thickness to be filled in air gap, control gas length by changing the number of the insulating paper being filled in air gap, it is achieved control gas length lgSize.
Further, in described (1) and (2), selecting after core structure, first determining magnetic core size according to minimum linear work magnetic is close;After magnetic core size is determined, at the linear segment of magnetization curve, select and control the close B of work magneticm, for different core materials, the close B of work magnetic of selectionmScope is different, and as shown in Figure 5, the close 0.2-1T that ranges for of linear work magnetic of nanocrystalline magnet core, the close 0.15-0.4T that ranges for of linear work magnetic of amorphous magnetic core, the linear work magnetic of FERRITE CORE is close ranges for 0.15-0.35T.
Further, described (1) is different with saturation magnetic induction in the magnetization characteristic according to different core materials, selects core material;For amorphous and the nanocrystalline magnetic core material of identical core structure, such as UU type structure, as shown in Figure 3, magnetic core size is a=24.3mm, b=40.1mm, c=85.2mm, d=70mm.The design parameter of high frequency transformer is 5kVA, 4.5kHz and 1.2/0.3kV, the design magnetic of both core materials is close all elects 0.2T as, amorphous magnetic core lamination coefficient is 0.82, the lamination coefficient of nanocrystalline magnet core is 0.75, and magnetic core air gap length takes 0.2mm, and the amorphous magnetic core high frequency transformer high-low pressure number of turn is 216/54, the nanocrystalline magnet core high frequency transformer high-low pressure number of turn is 236/59, the magnetization curve of 5 with reference to the accompanying drawings, during 0.3T, amorphous and nanocrystalline magnet core relative permeability urRespectively 19586.183 and 26233.224, so, according to formula (8), calculate and obtain high-pressure side magnetizing inductance respectively 377.252 and 414.146mH.Therefore, for same core structure and size, at the identical close B of work magneticmUnder, select different core materials can obtain different magnetizing inductance values.
Further, described (2) is determine under condition at core structure and size, it is known that the rated voltage of former vice-side winding and operating frequency, controls the close B of work magneticmSize, and then, control winding the number of turn;
For UU type nanocrystalline magnetic cored structure, as shown in Figure 3, magnetic core size is a=24.3mm, b=40.1mm, c=85.2mm, d=70mm.The design parameter of high frequency transformer is 5kVA, 4.5kHz and 1.2/0.3kV, and lamination coefficient is 0.75, and magnetic core air gap length takes 0.2mm, when controlling the close B of work magneticmSize, changes in the range of linearity of 0.2-1T, and other conditions are constant, calculates and obtains high-pressure side magnetizing inductance change curve, as shown in Figure 6.Therefore, the close value of work magnetic is controlled, it is possible to control magnetizing inductance value.
Further, described (3) are to determine under condition at core structure and size, adopt the accurate insulating paper of thickness to be filled in air gap, control gas length by changing the number of the insulating paper being filled in air gap, it is achieved control gas length size.At the work close B of magneticmTime constant, by controlling gas length, according to formula (2), thus it is possible to vary equivalent permeability ue, and then, change magnetizing inductance value.
For UU type nanocrystalline magnetic cored structure, magnetic core size is a=24.3mm, b=40.1mm, c=85.2mm, d=70mm.The design parameter of high frequency transformer is 5kVA, 4.5kHz and 1.2/0.3kV, and lamination coefficient is 0.75, and work the close B of magneticmFor 0.2T, change gas length lg, the high-pressure side magnetizing inductance value obtained is along with the change curve of gas length, as shown in Figure 7.Therefore, determine under condition at core structure and size, during by changing gas length, it is possible to substantially control magnetizing inductance value.
Further, when air gap left by magnetic core, comprising equivalent magnetic resistance calculating formula in the magnetic core of air gap is:
In formula, RmFor magnetic core equivalent magnetic resistance, RcFor magnetic resistance in magnetic core, RgFor magnetic resistance in air gap, lcFor the length of magnetic path in magnetic core, lgFor gas length in magnetic core, leIt is the magnetic circuit total length including gas length, AcAmass for core cross section, μ0For permeability of vacuum, μeFor equivalent permeability;μrFor magnetic core relative permeability;
According to formula (1), obtain out the equivalent permeability μ of magnetic core in air gapeCalculating formula is as follows:
According to the relation that magnetic flux and magnetic are close, obtaining the number of turn is N1The magnetic flux of Exciting Windings for Transverse Differential Protection is:
ψ=N1Φ=N1BAc=Lmi0(3)
In formula, ψ is excitation flux linkage, and Ф is magnetic flux, and B is that magnetic is close, AcAmass for core cross section, LmFor magnetizing inductance, i0For exciting current, N1For the Exciting Windings for Transverse Differential Protection number of turn.
As follows according to magnetomotive force calculating formula:
ΦRm=N1i0(4)
In formula, Ф is magnetic flux, and B is that magnetic is close, AcAmass for core cross section, LmFor magnetizing inductance, i0For exciting current, N1For the Exciting Windings for Transverse Differential Protection number of turn;
So, according to (1)~(4) formula, obtain such as following formula:
According to the law of electromagnetic induction, obtaining electromagnetic induction calculating formula is:
In formula, U is the voltage of flux change sensing, and ψ (t) is for changing over magnetic linkage, and Ф (t) is time dependent magnetic flux;
According to formula (6), and convolution (3), (4) and (5), obtain following formula:
According to formula (7), the calculating formula obtaining magnetizing inductance is:
In formula, LmFor magnetizing inductance;μeFor equivalent permeability, leFor the total length of magnetic path of magnetic core, N1For excitation side umber of turn, AcAmass for core cross section.
Further, in described (3), in dry type high frequency transformer, what insulating paper adopted is Nomex insulating paper, i.e. Nomex paper, and individual insulating paper thickness is 0.08mm-0.36mm.
The present invention provides the control method of a kind of high frequency transformer magnetizing inductance parameter, and when the core structure of high frequency transformer is air-gap-free ring-like, as shown in Figure 8, described method includes following control mode:
<1>: different with saturation magnetic induction according to the magnetization characteristic of different core materials, core material is selected;
<21>: when selecting ring type magnetic core size, control the size of internal diameter, external diameter and height, with reach to realize core cross section long-pending with the length of magnetic path between cooperation, control magnetizing inductance value;
<3>: determine under condition at core structure and size, it is known that the rated voltage of former vice-side winding and operating frequency, the close B of work magnetic is controlledmSize;And then, control the number of turn of winding.
Further, described<2>are when determining ring type magnetic core structure, control the size of internal diameter, external diameter and height, with reach to realize core cross section long-pending with the length of magnetic path between cooperation, control magnetizing inductance value;For ring type magnetic core, as shown in Figure 8, after internal diameter IR and height H determines, by changing the external diameter value OR of magnetic core, obtain different length of magnetic path value and the long-pending formula of different core cross section respectively as shown in formula (9) and (10), set up core cross section and amass the ratio between the length of magnetic path, as shown in formula (11), when obtaining different OR/IR ratio, (OR/IR-1) change curve of/(OR/IR+1), as shown in Figure 9, according to formula (11), obtain the ratio between different sectional areas and the length of magnetic path, according to formula (12), obtain different magnetizing inductance values;
When core structure is the ring type structure not opening air gap, the calculating formula of magnetizing inductance is:
In formula, LmFor magnetizing inductance;μ0For permeability of vacuum, μrFor the relative permeability of magnetic core, lcFor the length of magnetic path of magnetic core, N1For excitation side umber of turn, AcAmass for core cross section.
Further, the control mode of described<3>, it is the same with the control mode (3) of magnetizing inductance under UU and the EE type core structure having air gap, sees the explanation of mode (3) described in summary of the invention 1.
The present invention provides the control method of a kind of high frequency transformer leakage inductance parameter, when the core structure of high frequency transformer be UU type, EE type and ring-like time, described method includes following control mode:
1 >: control the number of turn of Single-layer Windings and then the number of plies of control winding, the distribution of the stray field intensity in change magnetic core window;
2 >: by controlling the number of insulating paper, controlling the one-tenth-value thickness 1/10 between primary side winding layer thickness and vice-side winding layer thickness value and former vice-side winding, the thickness of individual insulating paper is 0.05-0.36mm;
3 >: when the total number of turns of former vice-side winding and the Single-layer Windings number of turn of former vice-side winding are constant, change the arrangement mode of former vice-side winding, change the magnetic field distribution in magnetic core window, namely adopt winding separation coiling, sandwich style coiling or complete intersection transposition coiling.
Further, described 1 > being determine under condition at core structure and size, control the number of turn of Single-layer Windings, change the number of plies of winding, the amplitude adjusting leakage inductance is big, it is adaptable to core structure that magnetic core window area is bigger and size.
For ring-like nanocrystalline magnet core, wherein, ring type structure, as shown in Figure 8, magnetic core size is OR=120mm, IR=60mm, H=30mm.Design parameter is 5kVA, 4.5kHz and 1.2/0.3kV, and high-low pressure umber of turn is 140/35, high-pressure side adopt sub-thread reality wire, diameter of wire is 1.56mm, low-pressure side adopt 2 strands of real wires and around, per share real diameter of wire is 1.9mm, and layer thickness is 0.6mm.Changing the number of turn of Single-layer Windings respectively, change the winding number of plies, the winding number of plies and arrangement, as shown in Figure 10, (a) high-low pressure winding number of plies is all 2 layers, and (b) high-voltage winding layer number is 2 layers, and low voltage winding layer number is 1 layer.It is 51.27uH that calculating obtains reduction to high-pressure side leakage inductance, and it is 34.852uH that calculating obtains reduction to high-pressure side leakage inductance, and leakage inductance value reduces 32.023%.The dynamics that described mode 1 adjusts leakage inductance is very big.
Further, described 2 > it is determine under condition at core structure and size, by insulating paper, change layer thickness, the amplitude adjusting leakage inductance is big, it is adaptable to the control of high frequency transformer leakage inductance parameter when the winding number of plies is few.
For UU type amorphous magnetic core, wherein, UU type structure, as shown in Figure 3, magnetic core size is a=24.3mm, b=40.1mm, c=85.2mm, d=70mm.The design parameter of high frequency transformer is 5kVA, 4.5kHz and 1.2/0.3kV, high-low pressure umber of turn is 240/60, high-pressure side adopts sub-thread reality wire, diameter of wire is 1.56mm, low-pressure side adopt 2 strands of real wires and around, per share real diameter of wire is 1.9mm, the winding number of plies and arrangement, as shown in Figure 11, monolayer high-voltage winding layer thickness is 1.56mm, and monolayer low voltage winding layer thickness is 1.9mm.When other conditions are constant, when only changing layer thickness value, calculate and obtain the reduction change curve to high-pressure side leakage inductance value, as shown in Figure 12.When layer thickness increases to 3mm from 0, reduction increases to 1mH to high-pressure side leakage inductance value from 0.3mH, and when namely often increasing unit millimeter layer thickness, reduction is increased by 0.233mH to high-pressure side leakage inductance value.So, the dynamics that described mode 2 adjusts leakage inductance is very big.
Further, described 3 > determine under condition at core structure and size, adjust leakage inductance great efforts, it is adaptable to the control of the high frequency transformer leakage inductance parameter of the former vice-side winding number of plies all >=2 layers.
For UU type amorphous magnetic core, wherein, UU type structure, as shown in Figure 3, magnetic core size is a=24.3mm, b=40.1mm, c=85.2mm, d=70mm.The design parameter of high frequency transformer is 5kVA, 4.5kHz and 1.2/0.3kV, high-low pressure umber of turn is 240/60, high-pressure side adopts sub-thread reality wire, per share real diameter of wire is 1.56mm, low-pressure side adopt 2 strands of real wires and around, per share real diameter of wire is 1.9mm, layer thickness is 1.5mm, winding is arranged, as shown in Figure 13, the separation coiling of (a) winding, the sandwich style coiling of (b) winding, the complete intersection transposition coiling of (c) winding, calculating obtains under three kinds of winding arrangements, reduction is on high-tension side leakage inductance value respectively 0.621mH, 0.253mH and 0.0757mH.Separation coiling form is compared in sandwich style coiling, and reduction reduces 59.26% on high-tension side leakage inductance value, and separation coiling form is compared in complete intersection transposition coiling, and reduction reduces 87.81% on high-tension side leakage inductance value.So, described mode 4 adjusts the great efforts of leakage inductance.
Further, the leakage inductance of high frequency transformer body calculates and adopts leakage field energy method, including:
The mensuration calculating formula of magnetic core window internal hemorrhage due to trauma magnetic energy is
In formula, WmFor the leakage field energy in magnetic core window, H is the magnetic field intensity in magnetic core window, and B is the magnetic induction in magnetic core window, L1kFor the leakage inductance of reduction to primary side winding, I1For rated current virtual value in primary side winding;
The computation model of leakage inductance is monolayer double winding model, and as shown in Figure 14, wherein, P represents primary side winding, and S represents vice-side winding, and in x positive direction, primary side winding layer thickness is d1, former vice-side winding layer thickness is △12, vice-side winding layer thickness is d2, the height of magnetic core window is h;
If the whole magnetomotive force of coil all drops in the air path in magnetic core window, according to circuital law in Maxwell equation, have:
Ni=Hgl(15)
In formula, N is umber of turn, rated current in i winding, HgFor magnetic field intensity in air, l is air path length;
According to formula (15), obtain in magnetic core window as follows along the magnetic field intensity calculating formula in x positive direction:
Magnetic field intensity calculating formula in primary side winding, as shown in following formula (16):
Magnetic field intensity calculating formula between former vice-side winding, as shown in following formula (17)::
Magnetic field intensity calculating formula in vice-side winding, as shown in following formula (18)::
In formula, H1x、H12And H2xRespectively in magnetic core window in air section, the field strength values in primary side winding, between former vice-side winding and in vice-side winding, i1For load current value in primary side winding, N1The number of turn for primary side winding;
Formula (16), (17) and (18) being brought in formula (13), obtaining total leakage field energy meter formula in magnetic core window is:
Leakage field energy total in monolayer double winding is:
According to (14) formula, obtain reduction and be respectively as follows: to the leakage inductance of primary side winding and vice-side winding
In formula, μ0For permeability of vacuum, MLT1、MLT12And MLT2Respectively primary side winding, between former vice-side winding and the average turn of vice-side winding long, △12For thickness, d between former vice-side winding1And d2Respectively primary and secondary side winding thickness;
Compared with immediate prior art, the excellent effect that technical scheme provided by the invention has is:
The control method of a kind of high frequency transformer body inductance parameters provided by the invention, when core structure and size are determined, comprehensively, the control method proposing inductance parameters of system, the i.e. control method of magnetizing inductance and leakage inductance parameter, it is possible to accurately control the inductance parameters value of high frequency transformer body.Prior art is only intended to the inductance value design of inducer and reactor, and for high frequency transformer body, not it has been proposed that system, the method that controls inductance parameters accurately.And when the inventive method can be implemented in core structure and size determines, accurately control the inductance parameters of high frequency transformer body, at the same time it can also be according to different core structures, such as UU type, EE type, ring-like etc., it is proposed to the control method of corresponding inductance parameters.Therefore, the inventive method is the control method proposing high frequency transformer body inductance parameters comprehensive, system.
Accompanying drawing explanation
Fig. 1 is that high frequency transformer system is at the potential application drawing of power system in future;
Fig. 2 is electric power electric transformer application drawing in distributed power source accesses and be grid-connected;
Fig. 3 is UU type core structure figure in present invention;
Fig. 4 is EE type core structure figure in present invention;
Fig. 5 is the magnetization curve figure of different core materials in present invention;
Fig. 6 is the close B of different operating magnetic in present inventionmUnder, the change curve of high-pressure side magnetizing inductance;
Fig. 7 is in present invention under different air gap length, the change curve of high-pressure side magnetizing inductance;
Fig. 8 is ring-like core structure figure in present invention;
Fig. 9 is the graph of relation of (OR/IR-1) in ring type magnetic core/between (OR/IR+1) and OR/IR;
Figure 10 is ring-like nanocrystalline magnet core high frequency transformer winding layout viewing in present invention;A () high-low pressure winding number of plies is 2 layers;B () high-voltage winding layer number is 2 layers, low voltage winding layer number is 1 layer;
Figure 11 is UU type amorphous magnetic core high frequency transformer winding layout viewing in present invention;
Figure 12 is UU type amorphous magnetic core high frequency transformer in present invention, and during different layer thickness, reduction is to high-pressure side leakage inductance value change curve;
Figure 13 is UU type amorphous magnetic core high frequency transformer winding arrangement mode figure in present invention;A () separates coiling;The coiling of (b) sandwich style;(c) complete intersection transposition coiling;
Figure 14 is the leakage inductance computation model figure provided in present invention;
Figure 15 is the arrangement mode figure of embodiment Central Plains provided by the invention vice-side winding;A () separates coiling;The coiling of (b) sandwich style;(c) complete intersection shifting type coiling.
Detailed description of the invention
Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described in further detail.
The following description and drawings illustrate specific embodiments of the present invention fully, to enable those skilled in the art to put into practice them.Other embodiments can include structure, logic, electric, process and other change.Embodiment only represents possible change.Unless explicitly requested, otherwise independent assembly and function are optional, and the order operated can change.The part of some embodiments and feature can be included in or replace part and the feature of other embodiments.The scope of embodiment of the present invention includes the gamut of claims and all obtainable equivalent of claims.In this article, these embodiments of the present invention can be represented individually or generally with term " invention ", this is only used to conveniently, and if in fact disclose the invention of more than one, what be not meant to automatically to limit this application ranges for any single invention or inventive concept.
1, the derivation of the magnetizing inductance of high frequency transformer body is as follows:
When air gap left by magnetic core, as adopted UU type and EE type core structure, wherein, UU type and EE type core structure, see shown in accompanying drawing 6 and accompanying drawing 10, after air gap left by magnetic core, comprising equivalent magnetic resistance calculating formula in the magnetic core of air gap is:
In formula, RmFor magnetic core equivalent magnetic resistance, RcFor magnetic resistance in magnetic core, RgFor magnetic resistance in air gap, lcFor the length of magnetic path in magnetic core, lgFor gas length in magnetic core, leFor magnetic circuit total length, AcAmass for core cross section, μ0For permeability of vacuum, μeFor equivalent permeability.
According to formula (1), obtain out the equivalent permeability μ of magnetic core in air gapeCalculating formula is:
And according to the close relation of magnetic flux and magnetic, obtaining the number of turn is N1The excitation flux linkage of Exciting Windings for Transverse Differential Protection is:
ψ=N1Φ=N1BAc=Lmi0(3)
In formula, ψ is excitation flux linkage, and Ф is magnetic flux, and B is that magnetic is close, AcAmass for core cross section, LmFor magnetizing inductance, i0For exciting current, N1For the Exciting Windings for Transverse Differential Protection number of turn.
And have according to magnetomotive force calculating formula
ΦRm=N1i0(4)
In formula, Ф is magnetic flux, RmFor equivalent magnetic resistance, i0For exciting current, N1For the Exciting Windings for Transverse Differential Protection number of turn.
So, according to (1) to (4) formula, obtain:
According to the law of electromagnetic induction, obtaining electromagnetic induction calculating formula is:
In formula, U is that flux change induces voltage, i.e. induction electromotive force, and ψ (t) is time dependent magnetic linkage, and Ф (t) is for changing over magnetic flux.
So, according to formula (6), and convolution (3), (4) and (5), obtain following formula:
So, according to formula (7), the calculating formula obtaining magnetizing inductance is:
In formula, μeFor considering the magnetic core equivalent permeability after air gap, see formula (2), leFor magnetic circuit total length (including gas length), N1For excitation side umber of turn, AcAmass for core cross section.
If core structure does not open air gap, such as ring type structure, as shown in Figure 4, then, the calculating formula of magnetizing inductance is:
In formula, μ0For permeability of vacuum, μrFor the relative permeability of magnetic core, lcFor the length of magnetic path of magnetic core, N1For excitation side umber of turn, AcAmass for core cross section.
So, according to formula (8) and (9) magnetizing inductance calculating formula, it is possible to the method and measure obtaining controlling magnetizing inductance is as follows:
When core structure is UU type and EE type (opening air gap), the magnetizing inductance control method of high frequency transformer body is:
Mode 1: different with saturation magnetic induction according to the magnetization characteristic of different core materials, such as ferrite, amorphous and the core material such as nanocrystalline, selects suitable core material.
For amorphous and the nanocrystalline magnetic core material of identical core structure, such as UU type structure, as shown in Figure 3, magnetic core size is a=24.3mm, b=40.1mm, c=85.2mm, d=70mm.The design parameter of high frequency transformer is 5kVA, 4.5kHz and 1.2/0.3kV, the design magnetic of both core materials is close all elects 0.2T as, amorphous magnetic core lamination coefficient is 0.82, the lamination coefficient of nanocrystalline magnet core is 0.75, and magnetic core air gap length takes 0.2mm, and the amorphous magnetic core high frequency transformer high-low pressure number of turn is 216/54, the nanocrystalline magnet core high frequency transformer high-low pressure number of turn is 236/59, the magnetization curve of 5 with reference to the accompanying drawings, during 0.3T, amorphous and nanocrystalline magnet core relative permeability urRespectively 19586.183 and 26233.224, so, according to formula (8), calculate and obtain high-pressure side magnetizing inductance respectively 377.252 and 414.146mH.Therefore, for same core structure and size, at the identical close B of work magneticmUnder, select different core materials can obtain different magnetizing inductance values.
Mode 2: determine under condition at core structure and size, it is known that the rated voltage of former vice-side winding and operating frequency, controls the close B of work magneticmSize.And then, it is possible to control the number of turn of winding.
For UU type nanocrystalline magnetic cored structure, as shown in Figure 3, magnetic core size is a=24.3mm, b=40.1mm, c=85.2mm, d=70mm.The design parameter of high frequency transformer is 5kVA, 4.5kHz and 1.2/0.3kV, and lamination coefficient is 0.75, and magnetic core air gap length takes 0.2mm, when controlling the close B of work magneticmSize, changes in the range of linearity of 0.2-1T, and other conditions are constant, calculates and obtains high-pressure side magnetizing inductance change curve, as shown in Figure 6.Therefore, the close value of work magnetic is controlled, it is possible to control magnetizing inductance value.
Mode 3: determine under condition at core structure and size, adopts the accurate insulating paper of thickness to be filled in air gap, realizes controlling gas length lgSize.
For UU type nanocrystalline magnetic cored structure, magnetic core size is a=24.3mm, b=40.1mm, c=85.2mm, d=70mm.The design parameter of high frequency transformer is 5kVA, 4.5kHz and 1.2/0.3kV, and lamination coefficient is 0.75, and work the close B of magneticmFor 0.2T, change gas length lg, the high-pressure side magnetizing inductance value obtained is along with the change curve of gas length, as shown in Figure 7.Therefore, determine under condition at core structure and size, during by changing gas length, it is possible to substantially control magnetizing inductance value.
2, when core structure is ring-like (not having air gap), as shown in Figure 8, the magnetizing inductance control method of high frequency transformer body is:
Mode 1: different with saturation magnetic induction according to the magnetization characteristic of different core materials, such as ferrite, amorphous and the core material such as nanocrystalline, selects suitable core material.
Mode 2: when selecting ring type magnetic core size, controls the size of internal diameter, external diameter and height, to reach the cooperation realizing between sectional area and the length of magnetic path, controls magnetizing inductance value.
Mode 3: determine under condition at core structure and size, it is known that the rated voltage of former vice-side winding and operating frequency, controls the close B of work magneticmSize, and then, it is possible to control winding the number of turn.
Further, the control mode of described mode 1, it is the same with the control mode 1 of magnetizing inductance under UU and the EE type core structure having air gap, sees the explanation of mode 1 described in summary of the invention 1.
Further, described mode 2 is when determining ring type magnetic core structure, controls the size of internal diameter, external diameter and height, with reach to realize core cross section long-pending with the length of magnetic path between cooperation, control magnetizing inductance value;For ring type magnetic core, as shown in Figure 8, after internal diameter IR and height H determines, by changing the external diameter value OR of magnetic core, obtain different length of magnetic path value and the long-pending formula of different core cross section respectively as shown in formula (9) and (10), set up core cross section and amass the ratio between the length of magnetic path, as shown in formula (11), when obtaining different OR/IR ratio, (OR/IR-1) change curve of/(OR/IR+1), as shown in Figure 9, according to formula (12), obtain the ratio between different sectional areas and the length of magnetic path, according to formula (13), obtain different magnetizing inductance values;
When core structure is the ring type structure not opening air gap, the calculating formula of magnetizing inductance is:
In formula, LmFor magnetizing inductance;μ0For permeability of vacuum, μrFor the relative permeability of magnetic core, lcFor the length of magnetic path of magnetic core, N1For excitation side umber of turn, AcAmass for core cross section.
Further, the control mode of described mode 3, it is the same with the control mode 3 of magnetizing inductance under UU and the EE type core structure having air gap, sees the explanation of mode 3 described in summary of the invention 1.
3, the derivation of the leakage inductance of high frequency transformer body is as follows:
Calculating the leakage inductance computational methods of high frequency transformer body, main adopt leakage field energy method, the mensuration calculating formula of magnetic core window internal hemorrhage due to trauma magnetic energy is
In formula, WmFor the leakage field energy in magnetic core window, H is the magnetic field intensity in magnetic core window, and B is the magnetic induction in magnetic core window, L1kFor the leakage inductance of reduction to primary side winding, I1For rated current virtual value in primary side winding.
Below in conjunction with accompanying drawing 14, the leakage inductance computing formula of derivation high frequency transformer body.
From accompanying drawing 14, the computation model of leakage inductance is monolayer double winding model, and wherein, P represents primary side winding, and S represents vice-side winding, and in x positive direction, primary side winding layer thickness is d1, former vice-side winding layer thickness is △12, vice-side winding layer thickness is d2, the height of magnetic core window is h.
Because the pcrmeability that the pcrmeability of magnetic core compares air is much larger, so, the magneto resistive ratio air of magnetic core is little a lot, when there being high permeability magnetic core, coil outer magnetic field by high permeability magnetic core short circuit, the magnetic pressure ignored at this in magnetic core drops, it is assumed that the whole magnetomotive force of coil all drops in the air path in magnetic core window, according to circuital law in Maxwell equation, have:
Ni=Hgl(16)
In formula, N is umber of turn, rated current in i winding, HgFor magnetic field intensity in air, l is air path length.
So, according to formula (16), obtain in magnetic core window as follows along the magnetic field intensity calculating formula in x positive direction:
Magnetic field intensity calculating formula in primary side winding:
Magnetic field intensity calculating formula between former vice-side winding:
Magnetic field intensity calculating formula in vice-side winding:
In formula, H1x、H12And H2xRespectively in magnetic core window in air section, the field strength values in primary side winding, between former vice-side winding and in vice-side winding, i1For load current value in primary side winding, N1The number of turn for primary side winding.
According to formula (17), (18) and (19) magnetic field intensity calculating formula, obtain magnetic core window internal magnetic field intensity variation curve as shown in Figure 7.
Formula (17), (18) and (19) being brought in formula (14), obtaining total leakage field energy meter formula in magnetic core window is:
So, leakage field energy total in monolayer double winding in accompanying drawing 14 is:
So, according to (15) formula, it is possible to obtain reduction and be respectively as follows: to the leakage inductance of primary side winding and vice-side winding
In formula, μ0For permeability of vacuum, MLT1、MLT12And MLT2Respectively primary side winding, between former vice-side winding and the average turn of vice-side winding long, △12For thickness, d between former vice-side winding1And d2Respectively primary and secondary side winding thickness.
According to leakage inductance calculating formula (22) to (23), it is possible to the method obtaining controlling the leakage inductance of high frequency transformer body is:
Mode 1: control the number of turn of Single-layer Windings, and then, controlling the number of plies of winding, the distribution of the stray field intensity in change magnetic core window, to control leakage inductance value.
For ring-like nanocrystalline magnet core, wherein, ring type structure, as shown in Figure 8, magnetic core size is OR=120mm, IR=60mm, H=30mm.Design parameter is 5kVA, 4.5kHz and 1.2/0.3kV, and high-low pressure umber of turn is 140/35, high-pressure side adopt sub-thread reality wire, diameter of wire is 1.56mm, low-pressure side adopt 2 strands of real wires and around, per share real diameter of wire is 1.9mm, and layer thickness is 0.6mm.Changing the number of turn of Single-layer Windings respectively, change the winding number of plies, the winding number of plies and arrangement, as shown in Figure 10, (a) high-low pressure winding number of plies is all 2 layers, and (b) high-voltage winding layer number is 2 layers, and low voltage winding layer number is 1 layer.Shown in accompanying drawing 10 (a), it is 51.27uH that calculating obtains reduction to high-pressure side leakage inductance, shown in accompanying drawing 10 (b), it is 34.852uH that calculating obtains reduction to high-pressure side leakage inductance, accompanying drawing 10 (b) is relative to accompanying drawing 10 (a), and leakage inductance value reduces 32.023%.So, the dynamics that described mode 1 adjusts leakage inductance is very big.
Mode 2: by controlling the number of insulating paper, control the one-tenth-value thickness 1/10 (thickness of individual insulating paper is accurate fixed value) between primary side winding layer thickness and vice-side winding layer thickness value and former vice-side winding.
For UU type amorphous magnetic core, wherein, UU type structure, as shown in Figure 3, magnetic core size is a=24.3mm, b=40.1mm, c=85.2mm, d=70mm.The design parameter of high frequency transformer is 5kVA, 4.5kHz and 1.2/0.3kV, high-low pressure umber of turn is 240/60, high-pressure side adopts sub-thread reality wire, diameter of wire is 1.56mm, low-pressure side adopt 2 strands of real wires and around, per share real diameter of wire is 1.9mm, the winding number of plies and arrangement, as shown in Figure 11, monolayer high-voltage winding layer thickness is 1.56mm, and monolayer low voltage winding layer thickness is 1.9mm.When other conditions are constant, when only changing layer thickness value, calculate and obtain the reduction change curve to high-pressure side leakage inductance value, as shown in Figure 12.When layer thickness increases to 3mm from 0, reduction increases to 1mH to high-pressure side leakage inductance value from 0.3mH, and when namely often increasing unit millimeter layer thickness, reduction is increased by 0.233mH to high-pressure side leakage inductance value.So, the dynamics that described mode 2 adjusts leakage inductance is very big.
Mode 3: when the total number of turns of former vice-side winding and the Single-layer Windings number of turn of former vice-side winding are constant, change the arrangement mode of former vice-side winding, change the magnetic field distribution in magnetic core window, as adopted winding separation coiling, sandwich style coiling or coordinated transposition coiling, as shown in Figure 13.
For UU type amorphous magnetic core, wherein, UU type structure, as shown in Figure 3, magnetic core size is a=24.3mm, b=40.1mm, c=85.2mm, d=70mm.The design parameter of high frequency transformer is 5kVA, 4.5kHz and 1.2/0.3kV, high-low pressure umber of turn is 240/60, high-pressure side adopts sub-thread reality wire, per share real diameter of wire is 1.56mm, low-pressure side adopt 2 strands of real wires and around, per share real diameter of wire is 1.9mm, layer thickness is 1.5mm, winding is arranged, as shown in Figure 13, the separation coiling of (a) winding, the sandwich style coiling of (b) winding, the complete intersection transposition coiling of (c) winding, calculating obtains under three kinds of winding arrangements, reduction is on high-tension side leakage inductance value respectively 0.621mH, 0.253mH and 0.0757mH.Separation coiling form is compared in sandwich style coiling, and reduction reduces 59.26% on high-tension side leakage inductance value, and separation coiling form is compared in complete intersection transposition coiling, and reduction reduces 87.81% on high-tension side leakage inductance value.So, described mode 4 adjusts the great efforts of leakage inductance.
Embodiment
The present invention provides the control method of the inductance parameters of high frequency transformer body, i.e. the control method of magnetizing inductance and leakage inductance, and specific implementation is:
1, the control method embodiment of magnetizing inductance is as follows:
First, the electric pressure according to design capacity S, the operating frequency f of high frequency transformer and former secondary, it is determined that the size of magnetic core, the defining method of magnetic core size is the long-pending AP method of area, and formula is:
In formula, the area that AP is magnetic core amasss, and unit is cm4, AcFor the sectional area of magnetic core, unit is cm2, WaFor the window area of magnetic core, unit is cm2, KfFor form factor, it is 4.44 time sinusoidal wave, is 4, K during square waveuFor winding usage factor, for Litz line, it is generally 0.2-0.3, BmClose for work magnetic, unit is T, J is electric current density, is generally (2.5-4) × 106A/m2, S is design capacity, and unit is VA, f is operating frequency, and unit is Hz, η is efficiency, and unit is %.
In order to ensure certain nargin, according to the work close B of magnetic in realitym, select the long-pending AP value of area of magnetic core to be greater than and precalculate AP value.
The rated current of former vice-side winding and operating frequency f are design parameters, are usually given, so, the type of wire determines that according to the rated current of operating frequency and former vice-side winding, it is determined that mode is as follows:
In order to reduce Kelvin effect, the wire diameter of single cord is less than 2 times of skin depth, and wire skin depth calculating formula is:
In formula, δ is skin depth, and μ is winding pcrmeability, and ω is angular frequency, and σ is the electrical conductivity of winding.
The wire diameter of the single cord being typically chosen is less than 2 times of skin depth, and namely the wire diameter dc of single cord is:
dc=(0.8~0.9) × 2 δ (26)
So, it is determined that the number of share of stock of wire, calculating formula is:
In formula, AwFor the current carrying area of Litz line, Aw=S/ (UJ), NsNumber of share of stock for wire.
Determining under condition in design capacity, operating frequency, former vice-side winding electric pressure, magnetic core size and wire number of share of stock determine that, core cross section amasss AcDetermining that, know according to the calculating formula (8) of magnetizing inductance and (9), the method controlling magnetizing inductance controls the number of turn, magnetic permeability and the length of magnetic path exactly, and the calculating formula of the number of turn is:
In formula, N is umber of turn, BmClose for work magnetic, AcAmassing for core cross section, f is operating frequency, KfFor form factor.
In electric pressure, core cross section amasss, operating frequency is determined under condition, controls the close B of work magneticm, it is possible to control the number of turn of winding, and then, control magnetizing inductance value.The magnetization curve of different core materials, as shown in Figure 5, when selecting work magnetic close, in order to reduce the harmonic content in winding current, the magnetic selecting magnetization curve linear parts is close close as work magnetic, and as shown in Figure 7, the work magnetic of nanocrystalline magnet core is close ranges for 0.2-1T, the close 0.15-0.4T that ranges for of work magnetic of amorphous magnetic core, the work magnetic of FERRITE CORE is close ranges for 0.15-0.35T.So, in the range of linearity, the close B of work magnetic to be controlledmSize, namely according to the close scope of work magnetic of the range of linearity of different core materials above, control the close B of work magneticm, and then, it is possible to control magnetizing inductance value.
Adjusting the close B of work magneticmAfter, if magnetizing inductance does not also reach designing requirement, according to magnetizing inductance (8) and (9) two formulas, when adopting UU type and EE type when core structure, by adding the number (every insulating paper thickness is fixed) of insulation paper, adjust gas length value in magnetic core, by changing gas length value, adjust the equivalent permeability μ of magnetic coree, and then, control magnetizing inductance value.
2, the control method embodiment of leakage inductance is as follows:
Computing formula (22) and (23) according to leakage inductance are known, the leakage inductance value of high frequency transformer body is unrelated with the excitation added by high frequency transformer, only with magnetic core size and relevant around packet size and arrangement, when high frequency transformer designs, operating frequency, former vice-side winding rated current, electric current density parameter all determine that, so, the number of share of stock of wire determines that.Therefore, the leakage inductance method controlling high frequency transformer body is:
Method 1: be UU type and EE type for core structure, controls the number of turn (every layer of number of turn is the same) of Single-layer Windings, namely controls the height of Single-layer Windings, and then, it is possible to control the number of plies of winding, change leakage field energy value;Being ring-like for core structure, control the number of turn of each layer of winding, every layer of number of turn is generally unequal, and the number of turn of magnetic core innermost layer is maximum.
The method 1 implements, simple and convenient, it is easy to operation, when magnetic core height allows, controls the number of turn of Single-layer Windings, and then, it is possible to control the number of plies of winding, to change the magnetic field distribution in magnetic core window, control leakage inductance value.
Method 2: by controlling the number of insulating paper, control the one-tenth-value thickness 1/10 between primary side winding layer thickness, vice-side winding layer thickness and former vice-side winding;
The method 2 is the method controlling leakage inductance most critical, also it is the maximum method of adjustment dynamics, if actual requirement leakage inductance value is very big, can by increasing the thickness between former vice-side winding interlayer, and the thickness of primary side winding interlayer and vice-side winding interlayer, increase leakage inductance value.
Method 3: when the total number of turns of former vice-side winding and the Single-layer Windings number of turn of former vice-side winding are constant, change the arrangement mode of former vice-side winding, change the magnetic field distribution in magnetic core window, as adopted winding separation coiling, sandwich style coiling or coordinated transposition coiling.
It is relatively big that the method 3 adjusts leakage inductance value dynamics, and shown in accompanying drawing 15, black represents primary side winding, white represents vice-side winding, the arrangement mode of three kinds of former vice-side winding, the corresponding different change of magnetic field strength in magnetic core window, and then, thus it is possible to vary the value of leakage inductance, to reach to control the requirement of leakage inductance.Wherein, under former vice-side winding total number of turns and the former vice-side winding number of plies all the same terms, the arrangement of former vice-side winding is that the leakage inductance value of sandwich style is between former vice-side winding separation coiling and former vice-side winding coordinated transposition coiling.High for former vice-side winding electric pressure, the number of plies is more, and the method is conducive to adjustment leakage inductance value by a relatively large margin.
Above example is only in order to illustrate that technical scheme is not intended to limit; although the present invention being described in detail with reference to above-described embodiment; the specific embodiment of the present invention still can be modified or equivalent replacement by those of ordinary skill in the field; these are without departing from any amendment of spirit and scope of the invention or equivalent replace, within the claims of the present invention all awaited the reply in application.
Claims (11)
1. a control method for high frequency transformer magnetizing inductance parameter, when the core structure of high frequency transformer is UU type or EE type, described method includes:
1): different with saturation magnetic induction according to the magnetization characteristic of different core materials, core material is selected;
2): select core structure and determine magnetic core size;Determine under condition at core structure and size, it is known that the rated voltage of former vice-side winding and operating frequency, control the close B of work magneticmSize, and then, control umber of turn;
3): determine under condition at core structure and size, the accurate insulating paper of thickness is adopted to be filled in air gap, it is achieved to control gas length lgSize.
2. control method as claimed in claim 1, it is characterised in that described 1) and 2) in, after selecting core structure, elder generation determines magnetic core size according to minimum linear work magnetic is close;After magnetic core size is determined, at the linear segment of magnetization curve, select and control the close B of work magneticm, for different core materials, the close B of work magnetic of selectionmScope is different, and the close 0.2-1T that ranges for of linear work magnetic of nanocrystalline magnet core, the close 0.15-0.4T that ranges for of linear work magnetic of amorphous magnetic core, the linear work magnetic of FERRITE CORE is close ranges for 0.15-0.35T.
3. control method as claimed in claim 1, it is characterised in that when air gap left by magnetic core, comprising equivalent magnetic resistance calculating formula in the magnetic core of air gap is:
In formula, RmFor magnetic core equivalent magnetic resistance, RcFor magnetic resistance in magnetic core, RgFor magnetic resistance in air gap, lcFor the length of magnetic path in magnetic core, lgFor gas length in magnetic core, leIt is the magnetic circuit total length including gas length, AcAmass for core cross section, μ0For permeability of vacuum, μeFor equivalent permeability;μrRelative permeability for magnetic core;
According to formula (1), obtain out the equivalent permeability μ of magnetic core in air gapeCalculating formula is as follows:
According to the relation that magnetic flux and magnetic are close, obtaining the number of turn is N1The magnetic flux of Exciting Windings for Transverse Differential Protection is:
ψ=N1Φ=N1BAc=Lmi0(3)
In formula, ψ is excitation flux linkage, and Ф is magnetic flux, and B is that magnetic is close, AcAmass for core cross section, LmFor magnetizing inductance, i0For exciting current, N1For the Exciting Windings for Transverse Differential Protection number of turn;
As follows according to magnetomotive force calculating formula:
ΦRm=N1i0(4)
In formula, Ф is magnetic flux, and B is that magnetic is close, AcAmass for core cross section, LmFor magnetizing inductance, i0For exciting current, N1For the Exciting Windings for Transverse Differential Protection number of turn;
So, according to (1)~(4) formula, obtain such as following formula:
According to the law of electromagnetic induction, obtaining electromagnetic induction calculating formula is:
In formula, U is the voltage of flux change sensing, and ψ (t) is for changing over magnetic linkage, and Ф (t) is time dependent magnetic flux;
According to formula (6), and convolution (3), (4) and (5), obtain following formula:
According to formula (7), the calculating formula obtaining magnetizing inductance is:
In formula, LmFor magnetizing inductance;μeFor equivalent permeability, leFor the total length of magnetic path of magnetic core, N1For excitation side umber of turn, AcAmass for core cross section.
4. control method as claimed in claim 1, it is characterised in that described 3) in, in dry type high frequency transformer, what insulating paper adopted is Nomex insulating paper, i.e. Nomex paper, and individual insulating paper thickness is 0.08mm-0.36mm.
5. a control method for high frequency transformer magnetizing inductance parameter, when the core structure of high frequency transformer is ring-like, described method includes:
<1>: different with saturation magnetic induction according to the magnetization characteristic of different core materials, core material is selected;
<2>: when selecting ring type magnetic core size, control the size of internal diameter, external diameter and height, with reach to realize core cross section long-pending with the length of magnetic path between cooperation, control magnetizing inductance value;
<3>: determine under condition at core structure and size, it is known that the rated voltage of former vice-side winding and operating frequency, the close B of work magnetic is controlledmSize;And then, control the number of turn of winding.
6. control method as claimed in claim 5, it is characterized in that, in described<2>, for ring type magnetic core, after internal diameter IR and height H determines, by changing the external diameter value OR of magnetic core, obtain different length of magnetic path value and different core cross section amasss, formula is respectively as shown in formula (9) and (10), set up core cross section and amass the ratio between the length of magnetic path, as shown in formula (11), when obtaining different OR/IR ratio, (OR/IR-1) change curve of/(OR/IR+1), according to formula (11), obtain the ratio between different sectional areas and the length of magnetic path, according to formula (12), obtain different magnetizing inductance values;
When core structure is the ring type structure not opening air gap, the calculating formula of magnetizing inductance is:
In formula, LmFor magnetizing inductance;μ0For permeability of vacuum, μrFor the relative permeability of magnetic core, lcFor the length of magnetic path of magnetic core, N1For excitation side umber of turn, AcAmass for core cross section.
7. a control method for high frequency transformer leakage inductance parameter, when the core structure of high frequency transformer be UU type, EE type or ring-like time, described method includes:
1 >: control the number of turn of Single-layer Windings and then the number of plies of control winding, the distribution of the stray field intensity in change magnetic core window;
2 >: by controlling the number of insulating paper, controlling the one-tenth-value thickness 1/10 between primary side winding layer thickness and vice-side winding layer thickness value and former vice-side winding, the thickness of individual insulating paper is 0.05-0.36mm;
3 >: when the total number of turns of former vice-side winding and the Single-layer Windings number of turn of former vice-side winding are constant, change the arrangement mode of former vice-side winding, change the magnetic field distribution in magnetic core window, namely adopt winding separation coiling, sandwich style coiling or complete intersection transposition coiling.
8. control method as claimed in claim 7, it is characterised in that described 1 > it is determine under condition at core structure and size, control the number of turn of Single-layer Windings, changing the number of plies of winding, the amplitude adjusting leakage inductance is big, it is adaptable to core structure that magnetic core window area is bigger and size.
9. control method as claimed in claim 7, it is characterised in that described 2 > it is determine under condition at core structure and size, by insulating paper, change layer thickness, the amplitude adjusting leakage inductance is big, it is adaptable to the control of high frequency transformer leakage inductance parameter when the winding number of plies is few.
10. control method as claimed in claim 7, it is characterised in that described 3 > determine under condition at core structure and size, adjust leakage inductance great efforts, it is adaptable to the control of the high frequency transformer leakage inductance parameter of the former vice-side winding number of plies all >=2 layers.
11. control method as claimed in claim 7, it is characterised in that the leakage inductance calculating high frequency transformer body adopts leakage field energy method, including:
The mensuration calculating formula of magnetic core window internal hemorrhage due to trauma magnetic energy is
In formula, WmFor the leakage field energy in magnetic core window, H is the magnetic field intensity in magnetic core window, and B is the magnetic induction in magnetic core window, L1kFor the leakage inductance of reduction to primary side winding, I1For rated current virtual value in primary side winding;
The computation model of leakage inductance is monolayer double winding model, and wherein, P represents primary side winding, and S represents vice-side winding, and in x positive direction, primary side winding layer thickness is d1, former vice-side winding layer thickness is △12, vice-side winding layer thickness is d2, the height of magnetic core window is h;
If the whole magnetomotive force of coil all drops in the air path in magnetic core window, according to circuital law in Maxwell equation, have:
Ni=Hgl(15)
In formula, N is umber of turn, rated current in i winding, HgFor magnetic field intensity in air, l is air path length;
According to formula (15), obtain in magnetic core window as follows along the magnetic field intensity calculating formula in x positive direction:
Magnetic field intensity calculating formula in primary side winding, as shown in following formula (16):
Magnetic field intensity calculating formula between former vice-side winding, as shown in following formula (17)::
Magnetic field intensity calculating formula in vice-side winding, as shown in following formula (18)::
In formula, H1x、H12And H2xRespectively in magnetic core window in air section, the field strength values in primary side winding, between former vice-side winding and in vice-side winding, i1For load current value in primary side winding, N1The number of turn for primary side winding;
Formula (16), (17) and (18) being brought in formula (13), obtaining total leakage field energy meter formula in magnetic core window is:
Leakage field energy total in monolayer double winding is:
According to (14) formula, obtain reduction and be respectively as follows: to the leakage inductance of primary side winding and vice-side winding
In formula, μ0For permeability of vacuum, MLT1、MLT12And MLT2Respectively primary side winding, between former vice-side winding and the average turn of vice-side winding long, △12For thickness, d between former vice-side winding1And d2Respectively primary and secondary side winding thickness.
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