CN110674597A - Method for optimizing quality factor of non-ideal Litz coil - Google Patents
Method for optimizing quality factor of non-ideal Litz coil Download PDFInfo
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Abstract
The invention belongs to the technical field of power electronic systems and control thereof, in particular to a method for optimizing the quality factor of a non-ideal Litz coil, which aims at the problem that the high-frequency resistance of the non-ideal Litz coil is far higher than that of the ideal Litz coil and the transmission efficiency of wireless electric energy is hindered, and provides the following scheme, wherein the method comprises the following steps of modeling the high-frequency loss resistance of the non-ideal Litz coil, including inter-strand current distribution modeling and solving; modeling and solving the on-resistance component in the high-frequency loss resistor; modeling and solving a proximity effect resistance component in the high-frequency loss resistance. The distribution of a plurality of strands of insulated wires led out from the known position of the head end welding head at the tail end is solved according to the probability, the probability distribution of each strand of insulated thin wire current is further modeled and solved, and the current between the insulated wire strands is uniformized again to reduce the high-frequency loss resistance by designing the welding head base body with a specific shape and carrying out multiple connection and welding the strands on the surface of the Litz wire harness together at a specific length position.
Description
Technical Field
The invention relates to the technical field of power electronic systems and control thereof, in particular to a method for optimizing the quality factor of a non-ideal Litz coil.
Background
The Litz wire is formed by twisting a plurality of strands of thin insulated wires, can effectively reduce skin loss, and is widely applied to manufacturing high-frequency coils.
In high-power application occasions such as wireless charging of electric automobile, in order to reach great current-carrying cross sectional area, the strand number of thin insulated wires in the Litz wire is usually more than thousands of strands, the increase of the strand number and the increase of the external diameter of a welding head lead to serious uneven distribution of current among the thin insulated wires, and the increase of high-frequency loss resistance of a coil and the deterioration of quality factor are brought, so that the high-frequency resistance of the non-ideal Litz wire coil is far higher than that of the ideal Litz wire coil, and the further improvement of the efficiency of a wireless power transmission system is hindered.
Disclosure of Invention
The invention provides a quality factor optimization method of a non-ideal Litz wire coil, which is based on the technical problem that the high-frequency resistance of the non-ideal Litz wire coil is far higher than that of the ideal Litz wire coil, so that the efficiency of a wireless power transmission system is prevented from being further improved.
The invention provides a method for optimizing the quality factor of a non-ideal Litz coil, which comprises the following steps:
s1: firstly, modeling of non-ideal Litz coil high-frequency loss resistance, including modeling and solving of inter-strand current distribution; modeling and solving the on-resistance component in the high-frequency loss resistor; modeling and solving a proximity effect resistance component in the high-frequency loss resistance; solving a high-frequency loss resistance based on the non-uniform coefficient of the current among the strands;
s2: loss reduction of the nonideal Litz coil comprises the steps of constructing a three-dimensional model of a flow equalizing fusion joint such as a hemisphere, a cone, a fan and a hollow thin-wall cylinder; fusing and equalizing flow of the Litz wire harness surface strands; wire turn magnetic field mitigation at non-uniform inter-turn spacing; optimizing a fusion method with minimum loss;
s3: finally, obtaining a method for optimizing the quality factor of the Litz coil, and establishing an analytical expression of the quality factor of the coil depending on the frequency; and solving the optimal operation frequency and the maximum quality factor.
Preferably, in S1, when modeling and solving the current distribution between strands:
in a common welding method, a cylindrical conductor is formed at a Litz wire welding head, and an insulating thin conducting wire is connected to the cross section of one end of the cylindrical conductor, so that the whole Litz wire can be divided into three parts for modeling, namely a head-end cylindrical welding head, a Litz wire harness consisting of the insulating thin conducting wires and a tail-end cylindrical welding head, and due to the stranding characteristic of the Litz wire during manufacturing, the establishment of a three-dimensional model of stranding of thousands of strands of insulating thin conducting wires is basically impossible;
n (i) at the known position of the same circle of the Litz line head end fusion head in the cross section, wherein i is the number of turns of the insulated thin wires contained in the cross section of the wire harness, i is more than or equal to 1 and less than or equal to 3, a finite element model cannot be established because the positions of the cross section of the Litz line tail end fusion head are unknown, but the positions meet certain probability distribution, and if p (j) is the probability of the insulated thin wires in the jth circle (1 and less than or equal to j and less than or equal to 3) of the cross section of the tail end of the insulated thin wires, p (j) is approximately proportional to the radius of the jth circle (because the number of the thin wires distributed in the jth circle is 2 pi r of thejApproximately proportional), and the areas occupied by one thin wire are all equal, p (j) is solvable, so that the number of n (i) strands of insulated wires led out from the ith turn at the head end on the jth turn of the cross section at the tail end of the Litz wire is equal to
n(j)＝n(i)p(j)
Therefore, the probability distribution condition of all the n strands of insulating fine wires in all the Litz wire harnesses at the welding joints at the two ends of the Litz wire harnesses can be determined, and the current distribution of the Litz wire harnesses is solved by utilizing finite element modeling.
Preferably, in S1, when modeling and solving the on-resistance component in the high-frequency loss resistor:
the equivalent resistance of the high frequency loss can be expressed as the sum of the on-resistance and the proximity effect resistance, i.e.
R(ω)＝Rcond(ω)+Rprox(ω), and therefore the calculation of the high-frequency resistance, can be divided intoTwo parts, namely on-resistance calculation and proximity effect resistance calculation;
on the premise that the current distribution among strands of the insulating thin wires is known, the insulating thin wires can be directly equivalent to long straight wires with equal length to establish a finite element model, the on-resistance of the insulating thin wires is solved, and the on-resistance expression of the thin wires is established by an analytic method as follows
And:
wherein i represents the ith insulated thin wire, l is the length of the single thin wire, Rcond_u,lIs the resistance of a single strand of insulated thin wire per unit length, and ξ is a quantity related to the skin depth δ; mu.s0Is the free space permeability (mu)0＝4π×10-7H/m)；μrIs the relative permeability of the material (for copper mu)r＝1)；r0Is the radius of a single-stranded external insulation thin copper wire; ber, bei ', bei and ber' are Kelvin functions, if the currents flowing through the thin wires of the strands are the same, the equivalent on-resistance of the whole Litz wire bundle is 1/n of each strand (n is the number of strands of the insulated thin wires in the Litz wire bundle), but when the currents flowing through the thin wires of the strands are different, the equivalent resistance can be calculated according to the total loss of the n strands of Litz wires and the currents of the strands as follows
Wherein IiIs the firsti current flowing in the insulating thin wire and
preferably, in S1, when modeling and solving the proximity effect resistance component in the high-frequency loss resistance:
the proximity effect loss includes an internal loss and an external loss, i.e.
Rprox(ω)＝Rprox_int(ω)+Rprox_ext(ω)
Internal loss Rprox_intThe method is characterized in that loss caused by nonuniform current of the cross section in the insulated thin wires is caused in a Litz wire harness consisting of n strands of insulated thin wires under the action of a magnetic field caused by current carrying of the thin wires, a three-dimensional finite element model is established under the condition that the current distribution among the strands of the thin insulated wires is known, so that the internal proximity loss can be solved more accurately, meanwhile, the proximity effect magnetic field at a certain radius in the cross section is only related to the current contained in the circle of the radius and is not related to the distribution of the current, and due to the winding characteristic of Litz wires, when the number of the insulated thin wires in the Litz wire harness is large enough, the current can be considered to be uniformly distributed in the whole Litz wire harness according to the area, so that the internal proximity effect loss can be solved by an analytic method;
external loss Rprox_extThe loss caused by the uneven current distribution on a certain bundle of Litz turns caused by the magnetic field generated by turns except for the bundle of Litz turns in a multi-turn coil can be solved by establishing a three-dimensional finite element simulation model under the condition that the current distribution among strands of each insulated fine wire is known, and when the number of strands is large or the frequency is high, only one part of the whole coil can be modeled by a partial element equivalent circuit method to solve the whole loss.
Preferably, in S1, when solving for the high-frequency loss resistance based on the inter-strand current non-uniformity coefficient:
let I equal to 1, IiRepresenting the ratio of the current of the ith insulated thin wire to the total current, the inter-strand current non-uniformity coefficient can be extracted:
when the inter-strand current is uniformly distributed, the value of e is minimal (is 1/n), and the total on-resistance can be calculated as:
Rcond＝eRcond_i
in particular, when the specific value of each current is unknown, but the probability distribution f (x) is solvable in the current density distribution of the two-end weld joint, the inter-strand current non-uniformity coefficient can be calculated as follows:
wherein f (x) represents the number of strands with x current in the strands, and based on the non-uniform current coefficient among the strands, the on-resistance and the proximity effect resistance under the condition of uniform current distribution can be calculated firstly, and then the non-uniform current coefficient among the strands is multiplied, so that the total high-frequency resistance can be obtained.
Preferably, in S2, when a three-dimensional model is constructed to analyze the effect of multiple uniform flows using the fusion joint, wherein the welding head uses a thin-wall cylindrical ring, and current leading-out columns are uniformly distributed at the circumferential positions with equal radius at the top end of the thin-wall cylindrical ring, the current density distribution at the circumferential positions with equal radius of the thin-wall cylindrical ring is the same as that at the circumferential positions with equal radius of the thin-wall cylindrical ring according to the characteristic of skin effect, so that the current leading-out columns connected to the circumferential position can obtain the same current, a three-dimensional finite element method is used for establishing multiple welding models with different sizes, different numbers of current leading-out columns and different current-sharing weight numbers, the current density distribution in the base body of the cylindrical ring welding head at different frequencies and the current homogenization condition when the welding head uses all or part of the current leading-out columns are solved, according to the simulation result, extracting a current non-uniform coefficient depending on the frequency for an analytical method to calculate the on-resistance and the proximity effect resistance;
fusing together strands of insulating filaments on the Litz wire bundle surface enables redistribution of current among the insulating filaments, while considering only the skin effect, since the filaments are on the Litz wire bundle surface, the axial current density is the same, so that the current is uniformly redistributed among the welded together thin wires, in addition to the skin effect, however, there is also an external proximity effect, which, due to its influence, in the thin-wall conductor ring formed by welding on the cross section of the Litz wire harness, the current in the insulating thin wire on one side is higher than that on the other side, therefore, new current distribution is not uniform, a three-dimensional finite element simulation method is adopted to simulate the welding and current sharing effects of the surfaces of the Litz wire harnesses, only a small segment of Litz wires including the surface welding part needs to be simulated to improve the simulation speed, and the initial current of each strand of insulating thin wire in the Litz wire harnesses is randomly given according to the probability; the initial magnetic field distribution of the Litz wire harness cross section respectively considers the magnetic field conditions of a zero external magnetic field (single-turn coil) and a planar circular spiral coil with the diameter of 20 turns and 50cm in the first turn, the 5 th turn, the 10 th turn, the 15 th turn and the 20 th turn, and based on the result of three-dimensional finite element simulation, an analytic algorithm is used for modeling and simplifying the three-dimensional circular spiral coil so as to improve the resolving speed;
when the diameter of the thin insulating wire is small enough that the skin effect is negligible, the loss caused by the proximity effect accounts for a large proportion of the total loss, and the proximity effect loss is proportional to the square of the external magnetic field applied to the turns, the Litz wire coil has larger square magnetic fields of the turns of the coils at the inner and outer edges and smaller square magnetic fields of the turns at the middle position, because the electromagnetic fields generated by the turns at the two sides near the middle turn can cancel part of each other out, therefore, the distance between the turns of the wire is not uniform any more by adjusting the distance between the turns of the wire, so as to better utilize the cancellation effect of the magnetic field vectors of the turns of the inner and outer coils to reduce the magnetic field to achieve the minimum external proximity effect loss, and for the round turns, the average values of the square magnetic fields of the same turns at different cross sections are approximately considered to be the same based on the symmetry, therefore, the square magnetic field value at a cross section of each turn is calculated, for a rectangular coil, because of incomplete symmetry, the square magnetic field values of the turns at different cross sections are different, so that the total loss of the rectangular coil needs to be calculated by an integration method, and certainly, when the turn interval of the coil is adjusted, the coil is performed under the condition that the inductance of the coil and the maximum outer dimension of the coil need to be kept unchanged;
the optimization of the welding method comprises two aspects, namely, the optimization of a welding head base body, including the shape, the size, the number of current extraction columns and the like of the base body; secondly, optimizing multiple current sharing, including current sharing weight number and leading out all or part of a current leading-out column, on the other hand, when fusing the Litz wire harness surface strand, an external adjacent magnetic field can cause current to be concentrated to one side of a fusing ring, so that uneven distribution of current density among insulated thin wires fused together is caused, therefore, the surface strand fusing is required to be carried out at a position with a smaller external adjacent magnetic field, meanwhile, one-time surface fusing can only achieve current sharing in a part of insulated thin wires on the surface in the whole Litz wire bundle, therefore, the required times of surface fusing are analyzed and the optimal loss is solved under the condition of certain confidence coefficient from the angle of probability, finally, the current sharing effect of the surface fusing of a fusing joint and the Litz wire harness is considered, the optimal fusing current sharing loss reduction method is selected, three-dimensional finite element simulation is used, and models under the conditions of current sharing and Litz surface strand fusing of the fusing joint and the Litz wire harness are established, and solving the current distribution and current sharing effect of the insulating thin wire.
Preferably, the Litz coil quality factor optimization method comprises the following steps:
s21: establishing an analytical expression for the frequency-dependent coil quality factor in the quality factor equation Q of the coil ω L/R (ω), the resistance may be expressed as R (ω) Rcond(ω)+Rprox(ω) wherein Rcond(omega) on-resistance to account for skin effect, Rprox(ω) is the proximity effect resistance (including internal proximity loss and external proximity loss) caused by proximity loss, and in order to find the maximum quality factor, an analytical expression of the two resistances needs to be established, and meanwhile, different situations such as an air coil, a base coil with different types of magnetic materials need to be considered;
s22: optimal operating frequency and maximum quality factor solving order
The operating frequency (set to ω) at which the maximum quality factor is solved0) Changing ω to ω0The optimal quality factor at this operating frequency can be solved by substituting the expression Q of the quality factor ω L/R (ω).
The beneficial effects of the invention are as follows:
1. the method for winding the Litz wire can ensure that the insulating thin wire is in a certain probability p (i), according to the probability, the distribution of a plurality of strands of insulating wires led out from known positions of the cross section of the head end welding head on the cross section of the tail end welding head can be solved, then the probability distribution of each strand of insulating thin wire current can be solved through modeling, thousands of strands of insulating wires are considered as a whole according to the theory, local single-stranded wires do not need to be considered one by one, and therefore a feasible scheme is provided for fast solving the problems of inter-strand current distribution, high-frequency loss and resistance of the non-ideal Litz wire.
2. By designing the welding head base body with a specific shape and carrying out multiple connection and welding the Litz wire harness surface strands together at a specific length position, the current between the insulated strand strands is homogenized again to reduce the high-frequency loss resistance, and a new thought is provided for reducing the high-frequency loss of the Litz wire coil with high power and large insulated strand number.
Drawings
Fig. 1 is an overall flowchart of the method for optimizing the quality factor of a non-ideal Litz coil according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments.
Referring to fig. 1, a method for optimizing quality factor of a non-ideal Litz coil includes the following steps:
s1: firstly, modeling of non-ideal Litz coil high-frequency loss resistance, including modeling and solving of inter-strand current distribution; modeling and solving the on-resistance component in the high-frequency loss resistor; modeling and solving a proximity effect resistance component in the high-frequency loss resistance; solving a high-frequency loss resistance based on the non-uniform coefficient of the current among the strands;
s2: loss reduction of the nonideal Litz coil comprises the steps of constructing a three-dimensional model of a flow equalizing fusion joint such as a hemisphere, a cone, a fan and a hollow thin-wall cylinder; fusing and equalizing flow of the Litz wire harness surface strands; wire turn magnetic field mitigation at non-uniform inter-turn spacing; optimizing a fusion method with minimum loss;
s3: finally, obtaining a method for optimizing the quality factor of the Litz coil, and establishing an analytical expression of the quality factor of the coil depending on the frequency; and solving the optimal operation frequency and the maximum quality factor.
In S1, when modeling and solving the current distribution between strands:
in a common welding method, a cylindrical conductor is formed at a Litz wire welding head, and an insulating thin conducting wire is connected to the cross section of one end of the cylindrical conductor, so that the whole Litz wire can be divided into three parts for modeling, namely a head-end cylindrical welding head, a Litz wire harness consisting of the insulating thin conducting wires and a tail-end cylindrical welding head, and due to the stranding characteristic of the Litz wire during manufacturing, the establishment of a three-dimensional model of stranding of thousands of strands of insulating thin conducting wires is basically impossible;
n (i) at the known position of the same circle of the Litz line head end fusion head in the cross section, wherein i is the number of turns of the insulated thin wires contained in the cross section of the wire harness, i is more than or equal to 1 and less than or equal to 3, a finite element model cannot be established because the positions of the cross section of the Litz line tail end fusion head are unknown, but the positions meet certain probability distribution, and if p (j) is the probability of the insulated thin wires in the jth circle (1 and less than or equal to j and less than or equal to 3) of the cross section of the tail end of the insulated thin wires, p (j) is approximately proportional to the radius of the jth circle (because the number of the thin wires distributed in the jth circle is 2 pi r of thejApproximately proportional), and when the areas occupied by one thin wire are all equal, p (j) is solvable, so that the n (i) strand of insulated wire led out from the ith turn at the head end is at the end of the Litz wireHas a cross section of the number of jth turns of
n(j)＝n(i)p(j)
Therefore, the probability distribution condition of all the n strands of insulating fine wires in all the Litz wire harnesses at the welding joints at the two ends of the Litz wire harnesses can be determined, and the current distribution of the Litz wire harnesses is solved by utilizing finite element modeling.
In S1, when the on-resistance component in the high-frequency loss resistance is modeled and solved:
the equivalent resistance of the high frequency loss can be expressed as the sum of the on-resistance and the proximity effect resistance, i.e.
R(ω)＝Rcond(ω)+Rprox(ω), therefore the calculation of the high frequency resistance can be divided into two parts, namely the on-resistance calculation and the proximity effect resistance calculation;
on the premise that the current distribution among strands of the insulating thin wires is known, the insulating thin wires can be directly equivalent to long straight wires with equal length to establish a finite element model, the on-resistance of the insulating thin wires is solved, and the on-resistance expression of the thin wires is established by an analytic method as follows
And:
wherein i represents the ith insulated thin wire, l is the length of the single thin wire, Rcond_u,lIs the resistance of a single strand of insulated thin wire per unit length, and ξ is a quantity related to the skin depth δ; mu.s0Is the free space permeability (mu)0＝4π×10-7H/m)；μrIs the relative permeability of the material (for copper mu)r＝1)；r0Is the radius of a single-stranded external insulation thin copper wire; ber, bei ', bei and ber' are Kelvin functions, if the currents flowing through the thin wires of the strands are the same, the equivalent on-resistance of the whole Litz wire bundle is 1/n of each strand (n is the number of strands of the insulated thin wires in the Litz wire bundle), but when the currents flowing through the thin wires of the strands are different, the equivalent resistance can be calculated according to the total loss of the n strands of Litz wires and the currents of the strands as follows
Wherein IiIs a current flowing through the ith insulated thin wire
In S1, when modeling and solving the proximity effect resistance component in the high-frequency loss resistance:
the proximity effect loss includes an internal loss and an external loss, i.e.
Rprox(ω)＝Rprox_int(ω)+Rprox_ext(ω)
Internal loss Rprox_intThe method is characterized in that loss caused by nonuniform current of the cross section in the insulated thin wires is caused in a Litz wire harness consisting of n strands of insulated thin wires under the action of a magnetic field caused by current carrying of the thin wires, a three-dimensional finite element model is established under the condition that the current distribution among the strands of the thin insulated wires is known, so that the internal proximity loss can be solved more accurately, meanwhile, the proximity effect magnetic field at a certain radius in the cross section is only related to the current contained in the circle of the radius and is not related to the distribution of the current, and due to the winding characteristic of Litz wires, when the number of the insulated thin wires in the Litz wire harness is large enough, the current can be considered to be uniformly distributed in the whole Litz wire harness according to the area, so that the internal proximity effect loss can be solved by an analytic method;
external loss Rprox_extRefers to a multi-turn coil in which the magnetic field due to turns other than a bundle of Litz turns isLosses due to uneven distribution of current caused on the Litz wire turns of the bundle can be solved by establishing a three-dimensional finite element simulation model under the condition that the current distribution among strands of each insulated fine wire is known, and when the number of strands is large or the frequency is high, only a part of the whole coil can be modeled by a partial element equivalent circuit method to solve the whole loss.
In S1, when solving for the high-frequency loss resistance based on the inter-strand current unevenness coefficient:
let I equal to 1, IiRepresenting the ratio of the current of the ith insulated thin wire to the total current, the inter-strand current non-uniformity coefficient can be extracted:
when the inter-strand current is uniformly distributed, the value of e is minimal (is 1/n), and the total on-resistance can be calculated as:
Rcond＝eRcond_i
in particular, when the specific value of each current is unknown, but the probability distribution f (x) is solvable in the current density distribution of the two-end weld joint, the inter-strand current non-uniformity coefficient can be calculated as follows:
wherein f (x) represents the number of strands with x current in the strands, and based on the non-uniform current coefficient among the strands, the on-resistance and the proximity effect resistance under the condition of uniform current distribution can be calculated firstly, and then the non-uniform current coefficient among the strands is multiplied, so that the total high-frequency resistance can be obtained.
In S2, when a three-dimensional model is constructed to analyze the effect of multiple uniform flow by using the welding head, wherein the welding head uses a thin-wall cylindrical ring, and current extraction columns are uniformly distributed at the equal-radius circumferential positions at the top end of the thin-wall cylindrical ring, and the current density distribution at the equal-radius circumferential positions of the thin-wall cylindrical ring is the same as known from the skin effect, so that the current leading-out columns connected to the circumferential position can obtain the same current, a three-dimensional finite element method is used for establishing multiple welding models with different sizes, different numbers of current leading-out columns and different current-sharing weight numbers, the current density distribution in the base body of the cylindrical ring welding head at different frequencies and the current homogenization condition when the welding head uses all or part of the current leading-out columns are solved, according to the simulation result, extracting a current non-uniform coefficient depending on the frequency for an analytical method to calculate the on-resistance and the proximity effect resistance;
fusing together strands of insulating filaments on the Litz wire bundle surface enables redistribution of current among the insulating filaments, while considering only the skin effect, since the filaments are on the Litz wire bundle surface, the axial current density is the same, so that the current is uniformly redistributed among the welded together thin wires, in addition to the skin effect, however, there is also an external proximity effect, which, due to its influence, in the thin-wall conductor ring formed by welding on the cross section of the Litz wire harness, the current in the insulating thin wire on one side is higher than that on the other side, therefore, new current distribution is not uniform, a three-dimensional finite element simulation method is adopted to simulate the welding and current sharing effects of the surfaces of the Litz wire harnesses, only a small segment of Litz wires including the surface welding part needs to be simulated to improve the simulation speed, and the initial current of each strand of insulating thin wire in the Litz wire harnesses is randomly given according to the probability; the initial magnetic field distribution of the Litz wire harness cross section respectively considers the magnetic field conditions of a zero external magnetic field (single-turn coil) and a planar circular spiral coil with the diameter of 20 turns and 50cm in the first turn, the 5 th turn, the 10 th turn, the 15 th turn and the 20 th turn, and based on the result of three-dimensional finite element simulation, an analytic algorithm is used for modeling and simplifying the three-dimensional circular spiral coil so as to improve the resolving speed;
when the diameter of the thin insulating wire is small enough that the skin effect is negligible, the loss caused by the proximity effect accounts for a large proportion of the total loss, and the proximity effect loss is proportional to the square of the external magnetic field applied to the turns, the Litz wire coil has larger square magnetic fields of the turns of the coils at the inner and outer edges and smaller square magnetic fields of the turns at the middle position, because the electromagnetic fields generated by the turns at the two sides near the middle turn can cancel part of each other out, therefore, the distance between the turns of the wire is not uniform any more by adjusting the distance between the turns of the wire, so as to better utilize the cancellation effect of the magnetic field vectors of the turns of the inner and outer coils to reduce the magnetic field to achieve the minimum external proximity effect loss, and for the round turns, the average values of the square magnetic fields of the same turns at different cross sections are approximately considered to be the same based on the symmetry, therefore, the square magnetic field value at a cross section of each turn is calculated, for a rectangular coil, because of incomplete symmetry, the square magnetic field values of the turns at different cross sections are different, so that the total loss of the rectangular coil needs to be calculated by an integration method, and certainly, when the turn interval of the coil is adjusted, the coil is performed under the condition that the inductance of the coil and the maximum outer dimension of the coil need to be kept unchanged;
the optimization of the welding method comprises two aspects, namely, the optimization of a welding head base body, including the shape, the size, the number of current extraction columns and the like of the base body; secondly, optimizing multiple current sharing, including current sharing weight number and leading out all or part of a current leading-out column, on the other hand, when fusing the Litz wire harness surface strand, an external adjacent magnetic field can cause current to be concentrated to one side of a fusing ring, so that uneven distribution of current density among insulated thin wires fused together is caused, therefore, the surface strand fusing is required to be carried out at a position with a smaller external adjacent magnetic field, meanwhile, one-time surface fusing can only achieve current sharing in a part of insulated thin wires on the surface in the whole Litz wire bundle, therefore, the required times of surface fusing are analyzed and the optimal loss is solved under the condition of certain confidence coefficient from the angle of probability, finally, the current sharing effect of the surface fusing of a fusing joint and the Litz wire harness is considered, the optimal fusing current sharing loss reduction method is selected, three-dimensional finite element simulation is used, and models under the conditions of current sharing and Litz surface strand fusing of the fusing joint and the Litz wire harness are established, and solving the current distribution and current sharing effect of the insulating thin wire.
The Litz coil quality factor optimization method comprises the following steps:
s21: establishing an analytical expression for the frequency-dependent coil quality factor in the quality factor equation Q of the coil ω L/R (ω), the resistance may be expressed as R (ω) Rcond(ω)+Rprox(ω) wherein Rcond(omega) on-resistance to account for skin effect, Rprox(ω) is the proximity effect resistance (including internal proximity loss and external proximity loss) caused by proximity loss, and in order to find the maximum quality factor, an analytical expression of the two resistances needs to be established, and meanwhile, different situations such as an air coil, a base coil with different types of magnetic materials need to be considered;
s22: optimal operating frequency and maximum quality factor solving order
The operating frequency (set to ω) at which the maximum quality factor is solved0) Changing ω to ω0The optimal quality factor at this operating frequency can be solved by substituting the expression Q of the quality factor ω L/R (ω).
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.
Claims (7)
1. The method for optimizing the quality factor of the non-ideal Litz coil is characterized by comprising the following steps of:
s1: firstly, modeling of non-ideal Litz coil high-frequency loss resistance, including modeling and solving of inter-strand current distribution; modeling and solving the on-resistance component in the high-frequency loss resistor; modeling and solving a proximity effect resistance component in the high-frequency loss resistance; solving a high-frequency loss resistance based on the non-uniform coefficient of the current among the strands;
s2: loss reduction of the nonideal Litz coil comprises the steps of constructing a three-dimensional model of a flow equalizing fusion joint such as a hemisphere, a cone, a fan and a hollow thin-wall cylinder; fusing and equalizing flow of the Litz wire harness surface strands; wire turn magnetic field mitigation at non-uniform inter-turn spacing; optimizing a fusion method with minimum loss;
s3: finally, obtaining a method for optimizing the quality factor of the Litz coil, and establishing an analytical expression of the quality factor of the coil depending on the frequency; and solving the optimal operation frequency and the maximum quality factor.
2. The method for optimizing the quality factor of the non-ideal Litz coil according to claim 1, wherein in the step S1, when modeling and solving the inter-strand current distribution:
in a common welding method, a cylindrical conductor is formed at a Litz wire welding head, and an insulating thin conducting wire is connected to the cross section of one end of the cylindrical conductor, so that the whole Litz wire can be divided into three parts for modeling, namely a head-end cylindrical welding head, a Litz wire harness consisting of the insulating thin conducting wires and a tail-end cylindrical welding head, and due to the stranding characteristic of the Litz wire during manufacturing, the establishment of a three-dimensional model of stranding of thousands of strands of insulating thin conducting wires is basically impossible;
n (i) at the known position of the same circle of the Litz line head end fusion head in the cross section, wherein i is the number of turns of the insulated thin wires contained in the cross section of the wire harness, i is more than or equal to 1 and less than or equal to 3, a finite element model cannot be established because the positions of the cross section of the Litz line tail end fusion head are unknown, but the positions meet certain probability distribution, and if p (j) is the probability of the insulated thin wires in the jth circle (1 and less than or equal to j and less than or equal to 3) of the cross section of the tail end of the insulated thin wires, p (j) is approximately proportional to the radius of the jth circle (because the number of the thin wires distributed in the jth circle is 2 pi r of thejApproximately proportional), and the areas occupied by one thin wire are all equal, p (j) is solvable, so that the number of n (i) strands of insulated wires led out from the ith turn at the head end on the jth turn of the cross section at the tail end of the Litz wire is equal to
n(j)＝n(i)p(j)
Therefore, the probability distribution condition of all the n strands of insulating fine wires in all the Litz wire harnesses at the welding joints at the two ends of the Litz wire harnesses can be determined, and the current distribution of the Litz wire harnesses is solved by utilizing finite element modeling.
3. The method for optimizing the quality factor of the non-ideal Litz coil according to claim 2, wherein in the step S1, when the on-resistance component in the high-frequency loss resistance is modeled and solved:
the equivalent resistance of the high frequency loss can be expressed as the sum of the on-resistance and the proximity effect resistance, i.e.
R(ω)＝Rcond(ω)+Rprox(ω), therefore the calculation of the high frequency resistance can be divided into two parts, namely the on-resistance calculation and the proximity effect resistance calculation;
on the premise that the current distribution among strands of the insulating thin wires is known, the insulating thin wires can be directly equivalent to long straight wires with equal length to establish a finite element model, the on-resistance of the insulating thin wires is solved, and the on-resistance expression of the thin wires is established by an analytic method as follows
And:
wherein i represents the ith insulated thin wire, l is the length of the single thin wire, Rcond_u,lIs the resistance of a single strand of insulated thin wire per unit length, and ξ is a quantity related to the skin depth δ; mu.s0Is the free space permeability (mu)0＝4π×10-7H/m)；μrIs the relative permeability of the material (for copper mu)r＝1)；r0Is the radius of a single-stranded external insulation thin copper wire; ber, bei ', bei, ber' are Kelvin functions if strands of thin wire flowIf the currents are the same, the equivalent on-resistance of the whole Litz wire harness is 1/n (n is the number of strands of the thin insulated wires in the Litz wire harness) of each strand, but if the currents flowing in the strands of thin wires are different, the equivalent resistance can be calculated according to the total loss of the n strands of Litz wires and the currents of the strands as follows
Wherein IiIs a current flowing through the ith insulated thin wire
4. The method for optimizing the quality factor of the non-ideal Litz wire coil according to claim 3, wherein in the step S1, when the modeling and solving of the proximity effect resistance component in the high-frequency loss resistance are carried out:
the proximity effect loss includes an internal loss and an external loss, i.e.
Rprox(ω)＝Rprox_int(ω)+Rprox_ext(ω)
Internal loss Rprox_intThe method is characterized in that loss caused by nonuniform current of the cross section in the insulated thin wires is caused in a Litz wire harness consisting of n strands of insulated thin wires under the action of a magnetic field caused by current carrying of the thin wires, a three-dimensional finite element model is established under the condition that the current distribution among the strands of the thin insulated wires is known, so that the internal proximity loss can be solved more accurately, meanwhile, the proximity effect magnetic field at a certain radius in the cross section is only related to the current contained in the circle of the radius and is not related to the distribution of the current, and due to the winding characteristic of Litz wires, when the number of the insulated thin wires in the Litz wire harness is large enough, the current can be considered to be uniformly distributed in the whole Litz wire harness according to the area, so that the internal proximity effect loss can be solved by an analytic method;
external loss Rprox_extRefers to a multi-turn coil that is generated by turns other than a certain bundle of Litz turnsThe loss generated by the uneven distribution of current caused by the magnetic field on the Litz wire turns of the beam can be solved by establishing a three-dimensional finite element simulation model under the condition that the current distribution among strands of each insulated fine wire is known, and when the number of strands is large or the frequency is high, only a part of the whole coil can be modeled by a partial element equivalent circuit method so as to solve the whole loss.
5. The method for optimizing the quality factor of the non-ideal Litz coil according to claim 4, wherein in the step S1, when solving the high-frequency loss resistance based on the uneven coefficient of the inter-strand current:
let I equal to 1, IiRepresenting the ratio of the current of the ith insulated thin wire to the total current, the inter-strand current non-uniformity coefficient can be extracted:
when the inter-strand current is uniformly distributed, the value of e is minimal (is 1/n), and the total on-resistance can be calculated as:
Rcond＝eRcond_i
in particular, when the specific value of each current is unknown, but the probability distribution f (x) is solvable in the current density distribution of the two-end weld joint, the inter-strand current non-uniformity coefficient can be calculated as follows:
wherein f (x) represents the number of strands with x current in the strands, and based on the non-uniform current coefficient among the strands, the on-resistance and the proximity effect resistance under the condition of uniform current distribution can be calculated firstly, and then the non-uniform current coefficient among the strands is multiplied, so that the total high-frequency resistance can be obtained.
6. The method for optimizing the quality factor of the non-ideal Litz wire coil according to claim 5, wherein in S2, when constructing a three-dimensional model to analyze the effect of multiple current sharing using the fusion joint, the fusion joint uses a thin-walled cylindrical ring, and current leading-out pillars are uniformly arranged at the top end of the thin-walled cylindrical ring at the same radial circumference position, as can be seen from the skin effect, the current density distribution at the same radial circumference position of the thin-walled cylindrical ring is the same, so that the current leading-out pillars connected to the circumference position can obtain the same current, using a three-dimensional finite element method, a multiple fusion joint model with different sizes, different numbers of current leading-out pillars and different current sharing numbers is established, the current density distribution in the matrix of the fusion joint of the cylindrical ring at different frequencies is solved, and the current homogenization condition when the fusion joint uses all or part of the current leading-out pillars, according to the simulation result, extracting a current non-uniform coefficient depending on the frequency for an analytical method to calculate the on-resistance and the proximity effect resistance;
fusing together strands of insulating filaments on the Litz wire bundle surface enables redistribution of current among the insulating filaments, while considering only the skin effect, since the filaments are on the Litz wire bundle surface, the axial current density is the same, so that the current is uniformly redistributed among the welded together thin wires, but in addition to the skin effect, there is also the presence of an external proximity effect, which, due to its influence, in the thin-wall conductor ring formed by welding on the cross section of the Litz wire harness, the current in the insulating thin wire on one side is higher than that on the other side, therefore, new current distribution is not uniform, a three-dimensional finite element simulation method is adopted to simulate the welding and current sharing effects of the surfaces of the Litz wire harnesses, only a small segment of Litz wires including the surface welding part needs to be simulated to improve the simulation speed, and the initial current of each strand of insulating thin wire in the Litz wire harnesses is randomly given according to the probability; the initial magnetic field distribution of the Litz wire harness cross section respectively considers the magnetic field conditions of a zero external magnetic field (single-turn coil) and a planar circular spiral coil with the diameter of 20 turns and 50cm in the first turn, the 5 th turn, the 10 th turn, the 15 th turn and the 20 th turn, and based on the result of three-dimensional finite element simulation, an analytic algorithm is used for modeling and simplifying the three-dimensional circular spiral coil so as to improve the resolving speed;
when the diameter of the thin insulating wire is small enough that the skin effect is negligible, the loss caused by the proximity effect accounts for a large proportion of the total loss, and the proximity effect loss is proportional to the square of the external magnetic field applied to the turns, the Litz wire coil has larger square magnetic fields of the turns of the coils at the inner and outer edges and smaller square magnetic fields of the turns at the middle position, because the electromagnetic fields generated by the turns at the two sides near the middle turn can cancel part of each other out, therefore, the distance between the turns of the wire is not uniform any more by adjusting the distance between the turns of the wire, so as to better utilize the cancellation effect of the magnetic field vectors of the turns of the inner and outer coils to reduce the magnetic field to achieve the minimum external proximity effect loss, and for the round turns, the average values of the square magnetic fields of the same turns at different cross sections are approximately considered to be the same based on the symmetry, therefore, the square magnetic field value at a cross section of each turn is calculated, for a rectangular coil, because of incomplete symmetry, the square magnetic field values of the turns at different cross sections are different, so that the total loss of the rectangular coil needs to be calculated by an integration method, and certainly, when the turn interval of the coil is adjusted, the coil is performed under the condition that the inductance of the coil and the maximum outer dimension of the coil need to be kept unchanged;
the optimization of the welding method comprises two aspects, namely, the optimization of a welding head base body, including the shape, the size, the number of current extraction columns and the like of the base body; secondly, optimizing multiple current sharing, including current sharing weight number and leading out all or part of a current leading-out column, on the other hand, when fusing the Litz wire harness surface strand, an external adjacent magnetic field can cause current to be concentrated to one side of a fusing ring, so that uneven distribution of current density among insulated thin wires fused together is caused, therefore, the surface strand fusing is required to be carried out at a position with a smaller external adjacent magnetic field, meanwhile, one-time surface fusing can only achieve current sharing in a part of insulated thin wires on the surface in the whole Litz wire bundle, therefore, the required times of surface fusing are analyzed and the optimal loss is solved under the condition of certain confidence coefficient from the angle of probability, finally, the current sharing effect of the surface fusing of a fusing joint and the Litz wire harness is considered, the optimal fusing current sharing loss reduction method is selected, three-dimensional finite element simulation is used, and models under the conditions of current sharing and Litz surface strand fusing of the fusing joint and the Litz wire harness are established, and solving the current distribution and current sharing effect of the insulating thin wire.
7. The method of non-ideal Litz coil quality factor optimization according to claim 6, characterized in that the Litz coil quality factor optimization steps are:
s21: establishing an analytical expression for the frequency-dependent coil quality factor in the quality factor equation Q of the coil ω L/R (ω), the resistance may be expressed as R (ω) Rcond(ω)+Rprox(ω) wherein Rcond(omega) on-resistance to account for skin effect, Rprox(ω) is the proximity effect resistance due to proximity loss, and in order to find the maximum quality factor, analytical expressions of the two resistances need to be established, and meanwhile, different situations such as an air coil, a base coil with different types of magnetic materials, and the like need to be considered;
s22: optimal operating frequency and maximum quality factor solving order
The operating frequency (set to ω) at which the maximum quality factor is solved0) Changing ω to ω0The optimal quality factor at this operating frequency can be solved by substituting the expression Q of the quality factor ω L/R (ω).
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