CN116110709B - Round conductor type high-frequency transformer design method and device considering actual turn length - Google Patents
Round conductor type high-frequency transformer design method and device considering actual turn length Download PDFInfo
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Abstract
The invention relates to the technical field of power electronics and power transmission, in particular to a design method and a device for a circular conductor type high-frequency transformer taking actual turn length into consideration. The invention obtains the instantaneous power consumed by the inside of the p-th layer winding by calculating the difference value of the integral areas of the outer side surface and the inner side surface Potential vector of the p-th layer winding, and the integral area of the outer side surface or the inner side surface Potential vector of the p-th layer winding is the product of the porosity, the power flow density at the outer side surface or the inner side surface of the p-th layer winding, the total height of the winding and the inner perimeter of the outer Zhou Changhuo of the p-th layer winding; the invention makes it possible to consider the actual turn length by means of the Potentilla vector calculation method, and compared with the previous method using average turn length, the invention makes the calculation results of leakage inductance, AC resistance and DC resistance more accurate, thereby accurately adjusting the primary winding specification parameters and designing the high-frequency transformer meeting the circuit requirements.
Description
Technical Field
The invention relates to the technical field of power electronics and power transmission, in particular to a design method and a device for a circular conductor type high-frequency transformer taking actual turn length into consideration.
Background
High frequency transformers are one of the most commonly used components in high frequency switching power supplies. With the increase of the working frequency, skin effect and proximity effect are generated in the windings of the high-frequency transformer, which causes the resistance of the high-frequency transformer to deviate from the direct current resistance to generate alternating current resistance, and the leakage inductance of the transformer is also affected by the frequency. The relation of the leakage inductance of the transformer with the change of frequency needs to be strictly determined, because the relation affects important technical indexes such as resonance technology, soft switching technology, volume and the like of the whole switching power supply. At the same time, the prediction of the dc resistance and ac resistance of the transformer is also particularly important, since it is directly related to the calculation of the power loss or efficiency of the switching power supply under high frequency operating conditions. Any switching power supply designer needs to predict the performance of the high frequency transformer by measuring these three parasitic elements before designing the high frequency transformer to substantially increase the efficiency and power density of the overall system.
However, the current research results face the problem that the calculated expressions of leakage inductance, ac resistance and dc resistance of the high frequency transformer all use the average winding length. In practice, as the number of winding layers increases, the turn lengths between the layers will be greatly different, and the average turn length used in calculation will only bring errors to the prediction result, thereby affecting the adjustment of the primary winding specification parameters based on leakage inductance, ac resistance and dc resistance.
Disclosure of Invention
Therefore, the invention aims to solve the technical problem that the leakage inductance, the alternating current resistance and the direct current resistance are inaccurately measured due to the fact that the actual turn length is not considered in the prior art, and further the designed specification parameters of the high-frequency transformer are not in accordance with the circuit requirements.
In order to solve the technical problems, the invention provides a design method of a circular conductor type high-frequency transformer considering actual turn length, which comprises the following steps:
The specification parameters of the primary winding of the circular wire type high-frequency transformer and the working frequency of the input alternating current are obtained, and the specification parameters and the working frequency of the input alternating current are input into an alternating current resistance calculation model and a leakage inductance calculation model to obtain an alternating current resistance value and a leakage inductance value generated by the primary winding under the current working frequency;
the specification parameters of the primary winding of the circular wire type high-frequency transformer and the current value of the input direct current are obtained, and the direct current resistance value generated by the primary winding is obtained by inputting the specification parameters and the current value of the input direct current into a direct current resistance calculation model;
According to the alternating current resistance, the leakage inductance and the direct current resistance, the specification parameters of the primary winding are regulated so as to design a high-frequency transformer meeting the requirements of an electronic power circuit;
the alternating current resistance calculation model, the leakage inductance calculation model and the direct current resistance calculation model acquisition process comprise the following steps:
the round wire type primary winding is equivalent to a rectangular wire winding with the same cross section area;
When alternating current is applied to the primary winding, calculating the magnetic field intensity and the electric field intensity at the outer side surface or the inner side surface of the p-th layer winding in a phasor form of Maxwell equation set;
When direct current is applied to the primary winding, calculating the magnetic field intensity and the electric field intensity at the outer side surface or the inner side surface of the p-th layer winding by using a Maxwell equation set in a time domain;
obtaining the power flow density of the p-th layer winding at the outer side surface or the inner side surface according to the product of the magnetic field intensity and the electric field intensity of the p-th layer winding at the outer side surface or the inner side surface;
Obtaining the micro-element area of the outer side surface or the inner side surface of the p-th layer winding according to the product of the line integral, the porosity and the outer perimeter or the inner perimeter of the p-th layer winding in the vertical direction of the winding;
Calculating the integral area of the Potention vector of the outer side surface or the inner side surface of the p-th layer winding according to the power flow density and the infinitesimal area of the outer side surface or the inner side surface of the p-th layer winding, and obtaining the instantaneous power flowing into the outer side surface or flowing out of the inner side surface of the p-th layer winding, wherein the instantaneous power is the product of the porosity, the power flow density, the total height and the outer Zhou Changhuo inner perimeter of the p-th layer winding;
Obtaining the instantaneous power consumed by the inside of the p-th layer winding according to the difference value between the integral area of the p-th layer winding outside surface Potention vector and the integral area of the p-th layer winding inside surface Potention vector;
When alternating current is applied, calculating total instantaneous power consumed by the primary winding, and acquiring an alternating current resistance calculation model according to the real part of the total instantaneous power, wherein the alternating current resistance calculation model is expressed as:
Obtaining a leakage inductance calculation model according to the imaginary part of the total instantaneous power, wherein the leakage inductance calculation model is expressed as:
when direct current is supplied, calculating total instantaneous power consumed by the primary winding, and acquiring a direct current resistance calculation model according to the total instantaneous power, wherein the calculation model is expressed as:
Where m represents the number of layers of the primary winding, N l represents the number of turns per layer of the primary winding, and l T represents the actual length of each turn of the primary winding; σ represents the conductivity of the primary winding wire, b represents the total height of the primary winding, h represents the total thickness of the primary winding, Let δ' w denote the skin depth, ω denote the angular frequency, satisfying ω=2pi f, f being the operating frequency of the input ac current; h represents the width of the p-th rectangular wire winding, and u represents the thickness of the insulating layer between the windings.
Preferably, when alternating current is applied to the windings, the magnetic field intensity at the outer side surface or the inner side surface of the p-th layer winding is calculated by using the phasor form of Maxwell equation setAnd electric field strength
Wherein, Indicating the ac current level, N l indicating the number of turns of the wire in each layer of winding, b indicating the total height of the winding,The method is characterized in that the method comprises the steps of calculating the magnetic field intensity and the electric field intensity at the inner side surface of a p-th layer winding when x=0, and calculating the magnetic field intensity and the electric field intensity at the outer side surface of the p-th layer winding when x=h, wherein f is the skin depth of a round wire winding, f is the working frequency of alternating current, mu cu is the magnetic permeability of a primary winding wire, eta is the porosity, sigma is the conductivity, j is x=0/h, h is the width of the p-th layer rectangular wire winding.
Preferably, when the windings are subjected to direct current, the magnetic field strength H z (x) and the electric field strength E y at the outer side surface or the inner side surface of the p-th layer winding are calculated by using maxwell's equations in the time domain:
Wherein η represents porosity, J represents current density, σ represents conductivity, H 0 represents magnetic field strength of the outer side surface of the primary winding of the first layer, N l represents the number of turns of the wire in each layer of winding, I represents direct current magnitude, b represents total height of the winding, x=0/H, H represents the width of the winding of the rectangular wire of the p-th layer, when x=0, the magnetic field strength and the electric field strength at the inner side surface of the winding of the p-th layer are calculated, and when x=h, the magnetic field strength and the electric field strength at the outer side surface of the winding of the p-th layer are calculated.
Preferably, the infinitesimal area of the outer side surface or the inner side surface of the p-th layer winding is obtained according to the product of the line integral, the porosity and the outer perimeter or the inner perimeter of the p-th layer winding in the vertical direction of the winding:
Infinitesimal area of inner side surface of p-th layer winding
Infinitesimal area of outer surface of p-th layer winding
Wherein a x is a unit vector in the horizontal direction, the inner circumference l x＝0 of the p-th layer winding=2pi [ r+ (p-1) (h+u) ], the outer circumference l x＝h of the p-th layer winding=2pi [ r+ph+ (p-1) u ], r is the radius of the magnetic core, h represents the width of the p-th layer rectangular wire winding, and u represents the thickness of the insulating layer between the windings.
Preferably, the instantaneous power consumed inside the p-th layer winding is obtained according to the difference between the integral area of the p-th layer winding outer side surface poynting vector and the integral area of the p-th layer winding inner side surface poynting vector:
Wherein, For the Potentilla vector of the outer or inner surface of the winding of the p-th layer when AC or DC is applied,For the power flow density at the outer or inner surface of the p-th layer winding when ac or dc is applied, η is the porosity and b is the total height of the winding.
Preferably, the calculating the total instantaneous power consumed by the primary winding when the ac current is applied, obtaining an ac resistance calculation model according to the real part of the total instantaneous power, and obtaining a leakage inductance calculation model according to the imaginary part of the total instantaneous power includes:
When alternating current is applied, the total instantaneous power consumed by the primary winding is calculated:
Wherein, For the penetration rate, m is the number of winding layers of the primary winding;
According to the active power expression The real part of the total instantaneous power is used for obtaining an alternating current resistance calculation model:
according to reactive power expression And (3) obtaining a leakage inductance calculation model with an imaginary part of the total instantaneous power:
Preferably, the calculating the total instantaneous power consumed by the primary winding when the direct current is applied, and obtaining the direct current resistance calculation model according to the total instantaneous power includes:
when direct current is applied, the total instantaneous power consumed by the primary winding is calculated:
Obtaining a direct current resistance calculation model according to R dc_a＝P/I2 and the total instantaneous power:
The invention also provides a round wire type high-frequency transformer design device considering actual turn length, which comprises:
The parameter acquisition module is used for acquiring the number of layers, the total height, the total thickness and the porosity of the primary winding of the round wire type, the number of turns of the wire in each layer of winding, the actual length of each turn of winding, the resistivity, the conductivity and the magnetic permeability of the round wire and the current value of the input direct current and the alternating current power supply;
The parameter calculation module is used for calculating leakage inductance, alternating current resistance and direct current resistance of the primary winding according to the parameters acquired by the parameter acquisition module;
and the high-frequency transformer design module is used for changing the specification parameters of the primary winding according to the leakage inductance, the alternating current resistance and the direct current resistance value to design the high-frequency transformer meeting the requirements of the power electronic circuit.
Preferably, the parameter calculation module includes:
the equivalent conversion module is used for equivalent of the round wire type primary winding into a rectangular wire winding with the same cross section area;
The magnetic field intensity and electric field intensity calculation module is used for calculating the magnetic field intensity and the electric field intensity at the outer side surface or the inner side surface of the p-th layer winding in a phasor form of Maxwell's equations when alternating current is applied to the primary winding; when direct current is applied to the primary winding, calculating the magnetic field intensity and the electric field intensity at the outer side surface or the inner side surface of the p-th layer winding by using a Maxwell equation set in a time domain;
The power flow density calculation module is used for obtaining the power flow density of the outer side surface or the inner side surface of the p-th layer winding according to the product of the magnetic field intensity and the electric field intensity of the p-th layer winding at the outer side surface or the inner side surface;
the side surface infinitesimal area calculation module is used for obtaining infinitesimal area of the outer side surface or the inner side surface of the p-th layer winding according to the product of the line integral, the porosity and the outer perimeter or the inner perimeter of the p-th layer winding in the vertical direction of the winding;
The inflow and outflow instantaneous power calculation module is used for calculating the integral area of the PointTeth layer winding outer side surface or inner side surface PointTeth layer winding inner side surface according to the power flow density and the infinitesimal area at the p layer winding outer side surface or inner side surface to obtain the instantaneous power flowing into the p layer winding outer side surface or flowing out of the p layer winding inner side surface, wherein the instantaneous power is the product of the porosity, the power flow density at the p layer winding outer side surface or inner side surface, the total winding height and the p layer winding outer Zhou Changhuo inner perimeter;
the power consumption calculation module is used for obtaining the instantaneous power consumed in the p-th layer winding according to the difference value between the integral area of the p-th layer winding outer side surface Potention vector and the integral area of the p-th layer winding inner side surface Potention vector;
The alternating current resistance and leakage inductance calculation module is used for calculating total instantaneous power consumed by the primary winding when alternating current is supplied, acquiring an alternating current resistance calculation model according to the real part of the total instantaneous power, calculating the alternating current resistance, and acquiring a leakage inductance calculation model according to the imaginary part of the total instantaneous power, and calculating the leakage inductance;
And the direct current resistance calculation module is used for calculating the total instantaneous power consumed by the primary winding when direct current is supplied, and obtaining a direct current resistance calculation model according to the total instantaneous power to calculate the direct current resistance.
Compared with the prior art, the technical scheme of the invention has the following advantages:
According to the design method of the circular conductor type high-frequency transformer considering the actual turn length, the instant power consumed by the inside of the p-th layer winding is obtained by calculating the difference value of the integral area of the p-th layer winding outside surface and the inside surface Pointn vector, and the integral area of the p-th layer winding outside surface or the inside surface Pointn vector is the product of the porosity, the power flow density at the p-th layer winding outside surface or inside surface, the total height of the winding and the outer Zhou Changhuo inner perimeter of the p-th layer winding, namely the perimeter of the winding of each layer of the transformer, namely the turn length of each layer of winding; compared with the prior method using the average turn length, the method considers the thickness of the primary winding, calculates the actual turn length, and ensures that the calculation results of leakage inductance, alternating current resistance and direct current resistance are more accurate; so as to regulate the specification parameters of the primary winding according to accurate leakage inductance, alternating current resistance and direct current resistance and design the high-frequency transformer meeting the requirements of the electronic power circuit.
Drawings
In order that the invention may be more readily understood, a more particular description of the invention will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings, in which:
FIG. 1 is a flow chart of the acquisition of an alternating current resistance calculation model, a leakage inductance calculation model and a direct current resistance calculation model provided by the invention;
FIG. 2 is a block diagram of a high frequency transformer with a round wire winding in the ZX plane;
FIG. 3 is a schematic diagram of a round wire winding equivalent to a rectangular wire winding having an equal cross-sectional area;
FIG. 4 is a schematic diagram of boundary conditions;
FIG. 5 is an integral path schematic;
FIG. 6 is a three-dimensional perspective view of a transformer core and primary and secondary windings;
FIG. 7 is a top view of a transformer core and primary and secondary windings;
fig. 8 is a block diagram of a design apparatus for a circular conductor type high frequency transformer, which considers the actual turn length according to an embodiment of the present invention.
Detailed Description
The core of the invention is to provide a design method and a device for a circular conductor type high-frequency transformer taking the actual turn length into consideration, and the actual turn length is calculated by taking the thickness of a winding into consideration, so that the calculation results of leakage inductance, alternating current resistance and direct current resistance calculated based on the actual turn length are more accurate, the specification parameters of a primary winding are accurately regulated, and the high-frequency transformer which meets the requirements of an electronic power circuit better is designed.
In order to better understand the aspects of the present invention, the present invention will be described in further detail with reference to the accompanying drawings and detailed description. It will be apparent that the described embodiments are only some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention provides a design method of a circular conductor type high-frequency transformer taking actual turn length into consideration, which comprises the following specific steps:
The specification parameters of the primary winding of the circular wire type high-frequency transformer and the working frequency of the input alternating current are obtained, and the specification parameters and the working frequency of the input alternating current are input into an alternating current resistance calculation model and a leakage inductance calculation model to obtain an alternating current resistance value and a leakage inductance value generated by the primary winding under the current working frequency;
the specification parameters of the primary winding of the circular wire type high-frequency transformer and the current value of the input direct current are obtained, and the direct current resistance value generated by the primary winding is obtained by inputting the specification parameters and the current value of the input direct current into a direct current resistance calculation model;
According to the alternating current resistance, the leakage inductance and the direct current resistance, the specification parameters of the primary winding are regulated so as to design a high-frequency transformer meeting the requirements of an electronic power circuit;
Specifically, referring to fig. 1, fig. 1 is a flowchart of an ac resistance calculation model, a leakage inductance calculation model and a dc resistance calculation model according to the present invention, and the specific operation steps are as follows:
fig. 2 is a structural diagram of a high-frequency transformer with a round wire winding on a ZX plane, wherein the magnetic core is an EE magnetic core, the inner three-layer coil represents a primary winding of the round wire winding, and the outer two-layer coil represents a secondary winding. The points in the windings represent the direction in which current flows. The crosses in the windings represent the direction in which the current flows.
S1, equivalent to a round wire winding to be detected as a rectangular wire winding with the same cross-sectional area;
For convenience of analysis, we equivalent the round wire type winding to a rectangular wire winding with the same cross-sectional area, so that a gap appears between the rectangular windings, as shown in fig. 3, c is the height of the single-turn rectangular winding, b is the total height of the primary winding, u is the thickness of the insulating layer between windings, d is the diameter of the single-turn round wire winding, and h is the width of the rectangular winding. And l T is the length of the single turn winding. Thus, for an equivalent rectangular wire winding, its porosity is:
S2, when alternating current is applied to the winding, calculating the magnetic field intensity and the electric field intensity at the outer side surface or the inner side surface of the p-th layer winding in a phasor form of a Maxwell equation set;
Wherein, Indicating the ac current level, N l indicating the number of turns of the wire in each layer of winding, b indicating the total height of the primary winding,The method is characterized in that the method comprises the steps of (1) the skin depth of a round wire type winding, f represents the working frequency of alternating current, mu cu represents the magnetic permeability of a primary winding wire, eta represents the porosity, sigma represents the conductivity, j represents the imaginary number unit in a complex number, x=0/h, h represents the width of a p-th layer rectangular wire winding, when x=0, the magnetic field intensity and the electric field intensity at the inner side surface of the p-th layer winding are calculated, and when x=h, the magnetic field intensity and the electric field intensity at the outer side surface of the p-th layer winding are calculated.
S3, when direct current is conducted in the winding, calculating the magnetic field intensity and the electric field intensity at the outer side surface or the inner side surface of the p-th layer winding by using a Maxwell equation set in a time domain;
When the circular wire winding is supplied with direct current, the current is uniformly distributed over the cross-sectional area of the wire. The current density J in the wire can then be calculated by dividing the total current N l I by the total cross-sectional area ηbh, and we can derive the field strength in the p-th layer winding from ampere-loop law. According to the boundary conditions as shown in FIG. 4, we derive the magnetic field strength in the p-th layer winding as Where η represents the porosity, x=0/H, H represents the p-th layer rectangular winding width, as shown in fig. 4, H0 represents the magnetic field strength of the outer surface of the primary winding of the first layer, nl represents the number of turns of the wire in each layer of winding, I represents the current magnitude, and b represents the total height of the winding, where this formula represents the change in magnetic field strength in the p-th layer winding with the thickness of the winding, i.e. the change in magnetic field strength with the x-axis.
As shown in FIG. 5, the circumference in the anticlockwise direction of the cross section is the integral path with the apex of the lower left corner of the cross section of the p-th layer winding as the originThe line integral of the magnetic field intensity H (x) of the p-th layer winding along the circumference of the cross section of the p-th layer winding is calculated according to Maxwell's equation set and is converted into the conduction current passing through the total cross section s c of the rectangular wires in the p-th layer windingJ represents the current density, and since there is no displacement current in the case of direct current, the effect of the displacement current is not included in the equation, which converts the line integral of the magnetic field strength into the area integral of the current density. Such transformation facilitates later solutions.
The line integral of the field strength of the p-th layer winding along the circumference of the cross-section of the p-th layer winding is also equal to the field curl according to Stokes' theoremCurved integration over the p-th layer winding cross section sCalculating the magnetic field rotation as the product of porosity and conduction current density
Due to the density of the conducted currentFor conductivity sigma and electric field strengthProduct of (2)The magnetic field rotation is calculated as the product of porosity, conductivity and electric field strength
The rotation due to the magnetic field strength can be expressed as Calculating the electric field intensity in the p-th layer winding
S4: depending on the product of the magnetic field strength and the electric field strength of the p-th layer winding at the outer or inner side surface, obtaining a power flow density at an outer or inner surface of the p-th layer winding (E yHz)x＝h/0;
potin vector in the p-th layer winding of the primary winding is Indicating that the direction of the poynting vector is the negative direction of the x-axis. Thus, the instantaneous power flows from the outer boundary of the p-th layer conductor, from the inner boundary of the p-th layer conductor, the inner and outer boundaries of the p-th layer winding being shown in FIG. 4, the boundary of the p-th layer winding adjacent to the core side being called the inner boundary (inner side surface) and the magnetic field strength beingThe boundary of the p-th layer winding far from the magnetic core is called as the outer boundary (outer side surface) and has the magnetic field strength of
S5, obtaining the infinitesimal area of the outer side surface or the inner side surface of the p-th layer winding according to the product of the line integral, the porosity and the outer perimeter or the inner perimeter of the p-th layer winding in the vertical direction of the winding;
Infinitesimal area of inner side surface of p-th layer winding
Infinitesimal area of outer surface of p-th layer winding
Wherein a x is a unit vector in the horizontal direction, the inner circumference l x＝0 of the p-th layer winding=2pi [ r+ (p-1) (h+u) ], the outer circumference l x＝h of the p-th layer winding=2pi [ r+ph+ (p-1) u ], r is the radius of the magnetic core, h represents the width of the p-th layer rectangular wire winding, and u represents the thickness of the insulating layer between the windings.
S6, calculating the integral area of the Pointh vector of the outer side surface or the inner side surface of the p-th winding according to the power flow density and the infinitesimal area of the outer side surface or the inner side surface of the p-th winding, and obtaining the instantaneous power flowing into the outer side surface or flowing out of the inner side surface of the p-th winding, wherein the instantaneous power is the product of the porosity, the power flow density, the total height of the winding and the inner perimeter of the outer Zhou Changhuo of the p-th winding;
s7, obtaining the instantaneous power consumed in the p-th layer winding according to the difference value between the integral area of the p-th layer winding outer side surface Potention vector and the integral area of the p-th layer winding inner side surface Potention vector;
Wherein, For the Potentilla vector of the outer or inner surface of the winding of the p-th layer when AC or DC is applied,For the power flow density at the outer or inner surface of the p-th layer winding when ac or dc is applied, η is the porosity and b is the total height of the winding.
S8, when alternating current is conducted, calculating total instantaneous power consumed by the primary winding, calculating alternating current resistance according to the real part of the total instantaneous power, and calculating leakage inductance according to the imaginary part of the total instantaneous power;
When alternating current is applied, the total instantaneous power consumed by the primary winding is calculated:
Wherein, For the penetration rate, m is the number of winding layers of the primary winding;
The real part of the instantaneous power represents the active power, and an alternating current resistance calculation model is obtained according to the real part of the total instantaneous power:
the imaginary part of the instantaneous power represents reactive power, and the leakage inductance calculation model is obtained according to the imaginary part of the total instantaneous power:
S9, when direct current is conducted, calculating total instantaneous power consumed by the primary winding, and acquiring a direct current resistance calculation model according to the total instantaneous power;
when direct current is applied, the total instantaneous power consumed by the primary winding is calculated:
obtaining a direct current resistance calculation model according to the total instantaneous power:
Fig. 6 and 7 show three-dimensional perspective and top views of the high-frequency transformer core, primary winding and secondary winding. We can observe from fig. 6 that the circumferences of the windings of each layer of the transformer, i.e. the turn lengths of the windings of each layer, are not equal. Especially for a multi-layer winding transformer, the turn length of the outermost layer winding and the turn length of the innermost layer winding are obviously different, so that a mode of using an average turn length in the existing calculation expression leads to larger error of a calculation result; therefore, the invention provides a design method of a circular conductor type high-frequency transformer taking actual turn length into consideration, which obtains the instantaneous power consumed by the inside of a p-th layer winding by calculating the difference value of the integral area of the outer side surface and the inner side surface Pointn vector of the p-th layer winding, and the integral area of the outer side surface or the inner side surface Pointn vector of the p-th layer winding is the product of porosity, the power flow density at the outer side surface or the inner side surface of the p-th layer winding, the total height of the winding and the outer Zhou Changhuo inner perimeter of the p-th layer winding, namely the perimeter of the winding of each layer of the transformer, namely the turn length of each layer of winding; compared with the prior method using the average turn length, the method considers the thickness of the primary winding, calculates the actual turn length, and ensures that the calculation results of leakage inductance, alternating current resistance and direct current resistance are more accurate; so as to regulate the specification parameters of the primary winding according to accurate leakage inductance, alternating current resistance and direct current resistance and design the high-frequency transformer meeting the requirements of the electronic power circuit.
Referring to fig. 8, fig. 8 is a block diagram of a design apparatus for a circular conductor type high frequency transformer, which considers actual turn length according to an embodiment of the present invention, and the specific apparatus may include:
The parameter acquisition module is used for acquiring the number of layers, the total height, the total thickness and the porosity of the primary winding of the round wire type, the number of turns of the wire in each layer of winding, the actual length of each turn of winding, the resistivity, the conductivity and the magnetic permeability of the round wire and the current value of the input direct current and the alternating current power supply;
a parameter calculation module, comprising:
an equivalent conversion module 100 for equivalent-converting a round wire type primary winding into a rectangular wire winding having an equivalent cross-sectional area;
a magnetic field strength and electric field strength calculation module 200 for calculating the magnetic field strength and electric field strength at the outer side surface or the inner side surface of the p-th layer winding using the phasor form of maxwell's equations when alternating current is applied to the primary winding; when direct current is applied to the primary winding, calculating the magnetic field intensity and the electric field intensity at the outer side surface or the inner side surface of the p-th layer winding by using a Maxwell equation set in a time domain;
The power flow density calculating module 300 is configured to obtain the power flow density at the outer side surface or the inner side surface of the p-th layer winding according to the product of the magnetic field strength and the electric field strength of the p-th layer winding at the outer side surface or the inner side surface;
The side surface infinitesimal area calculating module 400 is configured to obtain an infinitesimal area of an outside surface or an inside surface of the p-th layer winding according to a product of a line integral, a porosity and an outer perimeter or an inner perimeter of the p-th layer winding in a vertical direction of the winding;
An inflow and outflow instantaneous power calculation module 500, configured to calculate an integral area of a potentilla vector of an outer side surface or an inner side surface of the p-th layer winding according to a power flow density and a infinitesimal area at the outer side surface or the inner side surface of the p-th layer winding, to obtain instantaneous power flowing into the outer side surface or flowing out of the inner side surface of the p-th layer winding, where the instantaneous power is a product of a porosity, the power flow density at the outer side surface or the inner side surface of the p-th layer winding, a total height of the winding, and an inner perimeter of the outer Zhou Changhuo of the p-th layer winding;
the power consumption calculation module 600 obtains the instantaneous power consumed inside the p-th layer winding according to the difference value between the integral area of the p-th layer winding outer side surface Potention vector and the integral area of the p-th layer winding inner side surface Potention vector;
The alternating current resistance and leakage inductance calculation module 700 is used for calculating total instantaneous power consumed by the primary winding when alternating current is supplied, calculating alternating current resistance according to the real part of the total instantaneous power, and calculating leakage inductance according to the imaginary part of the total instantaneous power;
The direct current resistance calculation module 800 is configured to calculate total instantaneous power consumed by the primary winding when a direct current is applied, and calculate a direct current resistance according to the total instantaneous power;
and the high-frequency transformer design module is used for adjusting the specification parameters of the primary winding according to the leakage inductance, the alternating current resistance and the direct current resistance value to design the high-frequency transformer meeting the requirements of the electronic power circuit.
The circular-conductor-type high-frequency transformer design apparatus with consideration of actual turn length of the present embodiment is used to implement the foregoing circular-conductor-type high-frequency transformer design method with consideration of actual turn length, so that the specific embodiments in the circular-conductor-type high-frequency transformer design apparatus with consideration of actual turn length can be seen from the foregoing example portions of the circular-conductor-type high-frequency transformer design method with consideration of actual turn length, for example, the equivalent conversion module 100, the power flow density calculation module 300, the side surface infinitesimal area calculation module 400, the inflow and outflow instantaneous power calculation module 500, the power consumption calculation module 600, the alternating current resistance and leakage inductance calculation module 700, and the direct current resistance calculation module 800 are respectively used to implement steps S1, S4, S5, S6, S7, S8 and S9 in the foregoing circular-conductor-type high-frequency transformer design method with consideration of actual turn length; the magnetic field strength and electric field strength calculation module 200 is configured to implement steps S2 and S3 in the design method of the circular conductor type high frequency transformer with the actual turn length considered; therefore, the specific embodiments thereof may refer to the descriptions of the corresponding examples of the respective parts, and will not be repeated herein.
With the increase of the number of winding layers, the turn lengths between layers are greatly different, and the average turn length is used for calculation, so that only errors are brought to a prediction result; compared with the traditional method using average turn length, the design method of the circular lead type high-frequency transformer taking the actual turn length into consideration, based on the Porphan vector method, calculates the actual turn length by considering the thickness of the primary winding, calculates leakage inductance, alternating current resistance and direct current resistance, and ensures more accurate calculation result; so as to regulate the specification parameters of the primary winding according to accurate leakage inductance, alternating current resistance and direct current resistance and design the high-frequency transformer meeting the requirements of the electronic power circuit.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It is apparent that the above examples are given by way of illustration only and are not limiting of the embodiments. Other variations and modifications of the present invention will be apparent to those of ordinary skill in the art in light of the foregoing description. It is not necessary here nor is it exhaustive of all embodiments. While still being apparent from variations or modifications that may be made by those skilled in the art are within the scope of the invention.
Claims (9)
1. A design method of a circular conductor type high-frequency transformer taking actual turn length into consideration is characterized by comprising the following steps:
The specification parameters of the primary winding of the circular wire type high-frequency transformer and the working frequency of the input alternating current are obtained, and the specification parameters and the working frequency of the input alternating current are input into an alternating current resistance calculation model and a leakage inductance calculation model to obtain an alternating current resistance value and a leakage inductance value generated by the primary winding under the current working frequency;
the specification parameters of the primary winding of the circular wire type high-frequency transformer and the current value of the input direct current are obtained, and the direct current resistance value generated by the primary winding is obtained by inputting the specification parameters and the current value of the input direct current into a direct current resistance calculation model;
According to the alternating current resistance, the leakage inductance and the direct current resistance, the specification parameters of the primary winding are regulated so as to design a high-frequency transformer meeting the requirements of an electronic power circuit;
the alternating current resistance calculation model, the leakage inductance calculation model and the direct current resistance calculation model acquisition process comprise the following steps:
the round wire type primary winding is equivalent to a rectangular wire winding with the same cross section area;
When alternating current is applied to the primary winding, calculating the magnetic field intensity and the electric field intensity at the outer side surface or the inner side surface of the p-th layer winding in a phasor form of Maxwell equation set;
When direct current is applied to the primary winding, calculating the magnetic field intensity and the electric field intensity at the outer side surface or the inner side surface of the p-th layer winding by using a Maxwell equation set in a time domain;
obtaining the power flow density of the p-th layer winding at the outer side surface or the inner side surface according to the product of the magnetic field intensity and the electric field intensity of the p-th layer winding at the outer side surface or the inner side surface;
Obtaining the micro-element area of the outer side surface or the inner side surface of the p-th layer winding according to the product of the line integral, the porosity and the outer perimeter or the inner perimeter of the p-th layer winding in the vertical direction of the winding;
Calculating the integral area of the Potention vector of the outer side surface or the inner side surface of the p-th layer winding according to the power flow density and the infinitesimal area of the outer side surface or the inner side surface of the p-th layer winding, and obtaining the instantaneous power flowing into the outer side surface or flowing out of the inner side surface of the p-th layer winding, wherein the instantaneous power is the product of the porosity, the power flow density, the total height and the outer Zhou Changhuo inner perimeter of the p-th layer winding;
Obtaining the instantaneous power consumed by the inside of the p-th layer winding according to the difference value between the integral area of the p-th layer winding outside surface Potention vector and the integral area of the p-th layer winding inside surface Potention vector;
When alternating current is applied, calculating total instantaneous power consumed by the primary winding, and acquiring an alternating current resistance calculation model according to the real part of the total instantaneous power, wherein the alternating current resistance calculation model is expressed as:
Obtaining a leakage inductance calculation model according to the imaginary part of the total instantaneous power, wherein the leakage inductance calculation model is expressed as:
when direct current is supplied, calculating total instantaneous power consumed by the primary winding, and acquiring a direct current resistance calculation model according to the total instantaneous power, wherein the calculation model is expressed as:
Where m represents the number of layers of the primary winding, N l represents the number of turns per layer of the primary winding, and l T represents the actual length of each turn of the primary winding; σ represents the conductivity of the primary winding wire, b represents the total height of the primary winding, h represents the total thickness of the primary winding, Let δ' w denote the skin depth, ω denote the angular frequency, satisfying ω=2pi f, f being the operating frequency of the input ac current; h represents the width of the p-th rectangular wire winding, and u represents the thickness of the insulating layer between the windings.
2. The method for designing a circular conductor type high frequency transformer taking into consideration actual turn length as set forth in claim 1, wherein when alternating current is applied to the windings, the magnetic field strength at the outer side surface or the inner side surface of the p-th layer winding is calculated by using the phasor form of maxwell's equationsAnd electric field strength
Wherein, Indicating the ac current level, N l indicating the number of turns of the wire in each layer of winding, b indicating the total height of the winding,The method is characterized in that the method comprises the steps of (1) the skin depth of a round wire type winding, f represents the working frequency of alternating current, mu cu represents the magnetic permeability of a primary winding wire, eta represents the porosity, sigma represents the conductivity, j represents the imaginary number unit in a complex number, x=0/h, h represents the width of a p-th layer rectangular wire winding, when x=0, the magnetic field intensity and the electric field intensity at the inner side surface of the p-th layer winding are calculated, and when x=h, the magnetic field intensity and the electric field intensity at the outer side surface of the p-th layer winding are calculated.
3. The method for designing a circular conductor type high frequency transformer taking into account actual turn lengths according to claim 1, wherein when direct current is applied to the windings, magnetic field strength H z (x) and electric field strength E y at the outer side surface or inner side surface of the p-th layer winding are calculated using maxwell's equations in a time domain:
Wherein η represents porosity, J represents current density, σ represents conductivity, H 0 represents magnetic field strength of the outer side surface of the first layer primary winding, N l represents the number of turns of the wire in each layer of winding, I represents direct current magnitude, b represents total height of the primary winding, x=0/H, H represents the width of the p layer rectangular wire winding, when x=0, the magnetic field strength and the electric field strength at the inner side surface of the p layer winding are calculated, and when x=h, the magnetic field strength and the electric field strength at the outer side surface of the p layer winding are calculated.
4. The method for designing a circular conductor type high frequency transformer according to claim 1, wherein the obtaining the infinitesimal area of the outer side surface or the inner side surface of the p-th layer winding according to the product of the line integral, the porosity and the outer perimeter or the inner perimeter of the p-th layer winding in the vertical direction of the winding is:
Infinitesimal area of inner side surface of p-th layer winding
Infinitesimal area of outer surface of p-th layer winding
Wherein a x is a unit vector in the horizontal direction, the inner circumference l x＝0 of the p-th layer winding is equal to 2pi [ r+ (p-1) (h+u) ], the outer circumference l x＝h of the p-th layer winding is equal to 2pi [ r+ph+ (p-1) u ], r is the radius of the magnetic core, and h represents the width of the p-th layer rectangular wire winding.
5. The method for designing a circular conductor type high frequency transformer according to claim 1, wherein the instantaneous power consumed inside the p-th layer winding is obtained according to the difference between the integrated area of the p-th layer winding outside surface poynting vector and the integrated area of the p-th layer winding inside surface poynting vector:
Wherein, For the Potentilla vector of the outer or inner surface of the winding of the p-th layer when AC or DC is applied,For the power flow density at the outer or inner surface of the p-th layer winding when ac or dc is applied, η is the porosity and b is the total height of the primary winding.
6. The method for designing a circular conductor type high frequency transformer with actual turn length considered as claimed in claim 5, wherein calculating total instantaneous power consumed by the primary winding when the ac current is applied, obtaining an ac resistance calculation model from a real part of the total instantaneous power, and obtaining a leakage inductance calculation model from an imaginary part of the total instantaneous power comprises:
When alternating current is applied, the total instantaneous power consumed by the primary winding is calculated:
Wherein, For the penetration rate, m is the number of winding layers of the primary winding;
According to the active power expression The real part of the total instantaneous power is used for obtaining an alternating current resistance calculation model:
according to reactive power expression And (3) obtaining a leakage inductance calculation model with an imaginary part of the total instantaneous power:
7. The method for designing a circular conductor type high frequency transformer taking into account actual turn lengths according to claim 5, wherein calculating total instantaneous power consumed by the primary winding when the direct current is applied, and obtaining a direct current resistance calculation model based on the total instantaneous power comprises:
when direct current is applied, the total instantaneous power consumed by the primary winding is calculated:
Obtaining a direct current resistance calculation model according to R dc_a＝P/I2 and the total instantaneous power:
8. the method of designing a circular conductor type high frequency transformer taking into account actual turn lengths as set forth in claim 7, wherein when the porosity is taken into the dc resistance calculation model, another expression of the dc resistance calculation model is obtained:
wherein the porosity is C represents the height of the p-th layer of windings in the primary winding, b represents the total height of the primary winding, and N l represents the number of turns of the wire in each layer of windings.
9. A circular conductor type high frequency transformer design apparatus taking into consideration actual turn lengths, comprising:
The parameter acquisition module is used for acquiring the number of layers, the total height, the total thickness and the porosity of the primary winding of the round wire type, the number of turns of the wire in each layer of winding, the actual length of each turn of winding, the resistivity, the conductivity and the magnetic permeability of the round wire and the current value of the input direct current and the alternating current power supply;
The parameter calculation module is used for calculating leakage inductance, alternating current resistance and direct current resistance of the primary winding according to the parameters acquired by the parameter acquisition module, and comprises the following steps:
the equivalent conversion module is used for equivalent of the round wire type primary winding into a rectangular wire winding with the same cross section area;
The magnetic field intensity and electric field intensity calculation module is used for calculating the magnetic field intensity and the electric field intensity at the outer side surface or the inner side surface of the p-th layer winding in a phasor form of Maxwell's equations when alternating current is applied to the primary winding; when direct current is applied to the primary winding, calculating the magnetic field intensity and the electric field intensity at the outer side surface or the inner side surface of the p-th layer winding by using a Maxwell equation set in a time domain;
The power flow density calculation module is used for obtaining the power flow density of the outer side surface or the inner side surface of the p-th layer winding according to the product of the magnetic field intensity and the electric field intensity of the p-th layer winding at the outer side surface or the inner side surface;
the side surface infinitesimal area calculation module is used for obtaining infinitesimal area of the outer side surface or the inner side surface of the p-th layer winding according to the product of the line integral, the porosity and the outer perimeter or the inner perimeter of the p-th layer winding in the vertical direction of the winding;
The inflow and outflow instantaneous power calculation module is used for calculating the integral area of the PointTeth layer winding outer side surface or inner side surface PointTeth layer winding inner side surface according to the power flow density and the infinitesimal area at the p layer winding outer side surface or inner side surface to obtain the instantaneous power flowing into the p layer winding outer side surface or flowing out of the p layer winding inner side surface, wherein the instantaneous power is the product of the porosity, the power flow density at the p layer winding outer side surface or inner side surface, the total winding height and the p layer winding outer Zhou Changhuo inner perimeter;
the power consumption calculation module is used for obtaining the instantaneous power consumed in the p-th layer winding according to the difference value between the integral area of the p-th layer winding outer side surface Potention vector and the integral area of the p-th layer winding inner side surface Potention vector;
The alternating current resistance and leakage inductance calculation module is used for calculating total instantaneous power consumed by the primary winding when alternating current is supplied, acquiring an alternating current resistance calculation model according to the real part of the total instantaneous power, and acquiring a leakage inductance calculation model according to the imaginary part of the total instantaneous power to calculate leakage inductance;
An alternating current resistance calculation model, expressed as:
The leakage inductance calculation model is expressed as:
the direct current resistance calculation module is used for calculating the total instantaneous power consumed by the primary winding when direct current is supplied, and obtaining a direct current resistance calculation model according to the total instantaneous power to calculate the direct current resistance;
a dc resistance calculation model, expressed as:
Where m represents the number of layers of the primary winding, N l represents the number of turns per layer of the primary winding, and l T represents the actual length of each turn of the primary winding; σ represents the conductivity of the primary winding wire, b represents the total height of the primary winding, h represents the total thickness of the primary winding, Let delta w' denote penetration rate, omega denote skin depth, omega denote angular frequency, satisfying omega = 2pi f, f being the operating frequency of the input alternating current; h represents the width of the p-th rectangular wire winding, and u represents the thickness of the insulating layer between the windings;
and the high-frequency transformer design module is used for adjusting the specification parameters of the primary winding according to the leakage inductance, the alternating current resistance and the direct current resistance value to design the high-frequency transformer meeting the requirements of the electronic power circuit.
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