CN116720377A - Electromagnetic structure optimization method of high-frequency transformer based on intelligent optimization algorithm - Google Patents
Electromagnetic structure optimization method of high-frequency transformer based on intelligent optimization algorithm Download PDFInfo
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Abstract
The application relates to an electromagnetic structure optimization technology of a high-frequency transformer, in particular to an electromagnetic structure optimization method of the high-frequency transformer based on an intelligent optimization algorithm, which comprises the following steps of firstly, setting system parameters, selecting fixed parameters and decision variables, and obtaining a minimum voltage shift angle of a zero-voltage switch based on an equivalent circuit of a BDA converter; step two, carrying out parameterization treatment on a magnetic core and a winding structure in the high-frequency transformer, calculating magnetic core loss and winding loss, constructing a leakage inductance calculation model, building a multiple insulation structure and calculating an insulation distance; step three, establishing a multi-objective optimized mathematical model of the high-frequency transformer; and step four, searching an optimal solution on the basis of a multi-objective optimized mathematical model of the high-frequency transformer, and manufacturing a high-frequency transformer prototype of 60kVA, 400V/400V and 10kHz according to the optimal solution. The application has the beneficial effects that the high-frequency transformer prototype with 60kVA/10kHz, 400V/400V can be optimized, the efficiency is 99.65 percent, and the power density is 71.7kW/m 3 。
Description
Technical Field
The application relates to the technical field of electromagnetic structure optimization of high-frequency transformers, in particular to an electromagnetic structure optimization method of a high-frequency transformer based on an intelligent optimization algorithm.
Background
Along with the continuous deep application of the power electronic transformer in the medium-high voltage alternating current/direct current power grid, the development and research of the high frequency transformer are in full play, and how to improve the efficiency, the power density and the reliability of the whole machine becomes the main trend of the development of power electronic equipment. The improvement of the performance of the switching device and the wide application of the novel magnetic materials such as nanocrystalline and the like make the power electronic device increasingly develop towards the high frequency and high power density. Nowadays, the high-frequency transformer is a core component in the fields of power conversion such as an alternating current-direct current hybrid power distribution network, electric traction and the like, plays a very key role in voltage conversion, isolation and the like, and is widely applied to new energy direct current collection systems such as photovoltaic power generation, offshore wind power and the like and railway electric traction systems. The accurate and effective high-frequency transformer design not only can improve efficiency and power density, but also can ensure the reliability and stability of equipment operation.
The high-frequency transformer provides more stringent requirements for overall evaluation of indexes such as loss, insulation, leakage inductance and the like. Since high frequency transformers are usually operated under complex excitation conditions, the optimization objectives are conflicting with each other and are difficult to balance. Therefore, the optimal design of the high-frequency transformer is a multi-objective optimization process which needs to consider the influence of a plurality of factors. The eddy current effect of the transformer is remarkable under the high-frequency condition, so that the loss of the magnetic core and the winding is increased, and the winding loss is difficult to calculate accurately due to the complex winding structure. And the high-frequency transformer has compact volume and structure, and the great improvement of the power density brings serious challenges to electromagnetic design.
At present, many research institutions and expert scholars at home and abroad have achieved certain results on the aspect of the optimal design of the high-power high-frequency transformer. Wang Jianing, jiang, hu Jiamen, pei Wei, zhao Yushun and the like in a medium voltage insulation high power medium frequency transformer]Technical journal of electrician, 2022,37 (12): 3048-3060. Multi-winding intermediate frequency transformers employing special core and winding structures for operation in LLC resonant converters are proposed, employing free parameter scanningA sample machine of the air-cooled intermediate frequency transformer with the efficiency of 200kW/30kHz is designed, the efficiency can reach 99.18 percent, and an insulation structure is not considered in the design process. Cao Xiaopeng of the university of Dongnan optimally designs a high-frequency transformer with the power of 3.52kW and the frequency of 20kHz based on a genetic algorithm, but the algorithm has the problems of uneven population distribution, easy local convergence and the like. Chen Bin team designs a 15kW/5kHz,500V/500V nanocrystalline alloy high-power medium-frequency three-phase transformer based on a free parameter scanning method, the efficiency can reach 98.6 percent, and the power density can reach 8.29MW/m 3 However, the influence of the end magnetic field component on the leakage inductance analysis method is not considered in the three-phase transformer, and when the optimization targets and the optimization parameters are more, the effective design schemes generated by the parameter scanning are more, and the optimal design schemes are difficult to screen. Therefore, a need exists for an electromagnetic field modeling method based on high frequency effect and structural effect analysis for multi-objective collaborative optimization of high frequency transformers.
Disclosure of Invention
The application aims to solve the problems, and designs an electromagnetic structure optimization method of a high-frequency transformer based on an intelligent optimization algorithm.
The technical scheme for achieving the purpose is that the electromagnetic structure optimization method of the high-frequency transformer based on the intelligent optimization algorithm comprises the following steps:
firstly, setting the system specification of a DAB converter, selecting fixed parameters and decision variables according to a magnetic core, a winding structure and insulating materials, establishing a design scheme of a square litz wire high-frequency transformer structure, carrying out parameterization treatment on the magnetic core and the winding structure in a magnetic core window, and calculating all structural parameters;
step two, according to the electrical and structural parameters determined in the step one, a calculation model of the core loss and the winding loss of the high-frequency transformer is established, a leakage inductance calculation model is established, a multiple insulation structure is established, and the insulation distance is calculated;
step three, establishing a multi-objective optimized mathematical model of the high-frequency transformer according to the calculation and analysis in the step two;
and step four, on the basis of a multi-objective optimized mathematical model of the high-frequency transformer, improving NSGA-II, searching a global optimal solution by combining a free parameter scanning method, and manufacturing a high-frequency transformer prototype according to the screened optimal solution.
In the step one, the DAB converter controls the input bridge and the output bridge and controls the inductanceL σ The mode of applying full voltage to make two square wave voltage waveforms on two sides of transformer shift to produce phase shift angleφWherein the leakage inductanceL σ As a shape of the power transmission element controlling the current,I T1 the effective value expression of the piecewise linear waveform comprises a fundamental wave component and a harmonic component as shown in the formula (1):
（1）
wherein ,
to achieve soft switching when on, the anti-parallel diode of each switch should start to conduct before the on time. To reduce the number of components, to achieve higher power density, the series inductance may be integrated as the leakage inductance of the high frequency transformer;
in the second step, all the structural parameters in the magnetic core window are calculated as follows:
the cross-sectional area of the magnetic core is:
（2）
in the formula ,Din order for the duty cycle to be a duty cycle,N 2 is the total number of turns of the secondary winding,N 2 =m 2 N l2 ，K c is the lamination factor of the magnetic core;
the length of the cross section of the magnetic core is as follows:
（3）
according to the turn ratio of the primary winding and the secondary winding of the transformernThe total number of turns of the primary winding of the high-frequency transformer can be obtained:
（4）
number of strands of single turn litz wire for primary and secondary windings:
（5）
wherein ,J max the resistance value and the cooling pattern of the litz wire selected according to the application are chosen in order to allow a maximum current density to pass,J max =3.82A/mm 2 ；
in order to improve the filling coefficient and reduce the volume of the high-frequency transformer, each turn of litz wire is considered to be square, so the number of sub-lines of the litz wires of a single turn of a primary winding and a secondary winding is as follows:
（6）
the side length of the single-turn litz wire of the primary winding and the secondary winding is as follows:
（7）
the number of layers of the primary winding is:
（8）
the heights of the primary winding and the secondary winding are as follows:
（9）
the height of the magnetic core window is:
（10）
the widths of the primary winding and the secondary winding are as follows:
（11）
the width of the magnetic core window is:
（12）
the average turn length of the primary winding is:
（13）
the average turn length of the secondary winding is:
（14）
the average turn length of the inter-winding magnetic leakage channel is as follows:
（15）
the magnetic core has the volume as follows:
（16）
the volume of the winding is as follows:
（17）。
the expression for calculating the magnetic core loss in the second step adopts a modified IGSE, and the formula of the IGSE before modification is as follows:
（18）
wherein ,
（19）
according toαIs obtained by the value range and curve fitting:
（20）
within one periodBThe rate of change of (2) is:
（21）
the expression of the modified IGSE is as follows:
（22）。
and in the second step, the winding loss calculation is performed according to the area equivalent principle and the linearization of a complex function, and an approximate Dowell model suitable for the litz wire winding is deduced. Firstly, replacing round strands with square strands under the condition of unchanged number of turns and layers of litz wire windings, and introducing an equivalent square strand side lengthd seq The relationship between the side length of the square strand and the diameter of the round strand is shown in the formula (23):
（23）
then ensuring the layer number of the litz wire winding is unchanged, and making the square stranded wire winding equivalent to an ideal foil winding, but the equivalent changes the effective conductive cross-sectional area of the winding, and considering a porosity in order to ensure that the direct current conductivity of the windings is the sameηCorrecting the conductivity of the winding wire, e.g.Formula (24):
（24）
since the copper foils of the foil-type winding are uniformly arranged, the interlayer insulation distance is equivalent to the insulation distance between the foilsd i ：
（25）
The winding loss of the high frequency transformer can be calculated as follows:
（26）
F r,n is the alternating current resistivity of the winding,R dc1 、R dc2 the direct current resistances of the wires of the primary winding and the secondary winding are respectively,I rms n, is thatnRoot mean square value of primary side excitation current of transformer under subharmonic;
（27）
（28）
（29）
in the formula (27), delta s For the penetration rate of the windings,ξ 1 、ξ 2 for skin and proximity correction factors of the windings,δ w skin depth of the winding at the operating frequency;
（30）
（31）
（32）
in the formula (32), the amino acid sequence of the compound,fin order to operate at the frequency of operation,μ 0 is vacuum magnetic permeability.
Due to the induction of eddy current under high frequency condition, the skin effect and proximity effect of the winding are enhanced, the current density is no longer uniform, and the alternating current resistivity is improvedF r And also increases. In order to realize more accurate calculation of the square litz wire winding at high frequency, the application derives an approximate Dowell model suitable for the square litz wire winding on the basis of area equivalence, and obtains alternating current resistivity by linearizing hyperbolic functions and trigonometric functions in the Dowell modelF r The approximate expression of (2) is shown in the formula (33):
（33）
in the second step, a Rogowski factor is introduced into the leakage inductance calculation model, and the winding height is corrected by correcting the path length of the magnetic field, as shown in the formula (34):
（34）
in the method, in the process of the application,K R in the case of the Rogowski factor,h weq is the equivalent height of the winding;
the leakage inductance calculation model considering the winding end effect and the structural effect is obtained based on the integration of magnetic field energy generated by a leakage magnetic field, and is specifically as follows:
the calculation of leakage inductance is divided into two parts, one part is the frequency-dependent region, namely the leakage inductance generated by the region where the winding is locatedL σb The method comprises the steps of carrying out a first treatment on the surface of the Another part is the frequency uncorrelated region, namely the leakage inductance generated by the winding interlayer insulation region and the leakage magnetic channel regionL σy ；
The total leakage inductance of the high-frequency transformerL σ It can be calculated as:
（35）
for leakage inductance of the frequency-dependent portion, a frequency-dependent factor is introduced that takes the effect of the winding structure into accountk f ThenL σb The following can be calculated:
（36）
（37）
in the method, in the process of the application,
（38）
wherein the method comprises the steps ofγIn order for the conductivity to be a factor,γ=（1+j）/δ w for leakage inductance of the frequency-uncorrelated part,L σy the following can be calculated:
（39）
the process of establishing the multi-objective optimized mathematical model of the high-frequency transformer in the third step is as follows:
first, the decision variables selected are:
number of blocks of core stackn c Side length of magnetic core cross sectionAStrand diameter of litz wire for primary and secondary windingsd s1 、d s2 Layer number of secondary windingsm 2 Turns of primary and secondary windingsN l1 、N l2 Maximum magnetic inductionB m The upper boundary of which is defined by the saturation magnetic flux density of the materialB sat Setting.
The second, two objective functions selected are:
objective function 1: the magnetic core loss and winding loss of the high-frequency transformer are minimum, the efficiency is maximized,
（40）
objective function 2: the volume of the high-frequency transformer is minimum, the power density is maximized,
（41）
at a level capable of withstanding a minimum insulation voltageU iso Under the condition of (1) to ensure that zero voltage switching can be realized, the leakage inductance is larger than the minimum leakage inductance value capable of meeting the minimum isolation requirementL σ-min Therefore, the constraint conditions selected by the application are as follows:
（42）
wherein,x l is the lower bound of the decision variable,x u is the upper bound of the decision variable;
thirdly, introducing a dynamic aggregation distance by an improved non-dominant ordering genetic algorithm, and improving the NSGA-II crossing operation by adopting an arithmetic crossing operator; wherein the arithmetic crossover operator is set upX i t 、X j t Respectively the firsttAnd (3) encoding real values of corresponding decision variables at the crossing points of the two individuals of the generation, wherein the decision variables corresponding to the two individuals after the crossing are respectively:
（43）
wherein,a、brespectively [0,1 ]]Random numbers uniformly distributed on the base; while dynamically aggregating individuals of distanceiThe dynamic aggregation distance of (2) is calculated as follows:
（44）
wherein,
（45）
（46）
in the method, in the process of the application,I i for individualsiIs used for the distance of aggregation of (a),Min order to be of the dimension of the target,I i,k is the firstiIndividual at the firstkAnd (5) maintaining the function values after sequencing on the targets.
And step four, carrying out 58 ten thousand parameter scans in the range of all decision variables based on a free parameter scanning method, generating 26 ten thousand effective designs in a specific range, obtaining a distributed cloud picture of the volume power density and the efficiency in the range of 10Hz-100kHz, wherein each point represents one design, carrying out iterative calculation by taking the point as an initial population in an improved NSGA-II, carrying out global optimization on all the designs obtained by the free parameter scanning by using the improved NSGA-II, and obtaining a global optimal design, and designing and manufacturing a high-frequency transformer prototype by using the design.
Compared with the prior art, the application has the following beneficial effects:
1. according to the application, a magnetic core loss calculation model with low cost and high efficiency is established by fitting a complex integral function in the IGSE under a high-frequency non-sinusoidal excitation waveform;
2. according to the application, an approximate Dowell model considering the winding structure effect and the eddy current effect is deduced according to the area equivalent principle and the complex function linearization, so that the high-precision calculation of the winding loss is realized.
3. The application provides a leakage inductance calculation model considering the winding end effect and the structural effect, which reduces the dependence of leakage inductance on geometry and frequency; on the basis of considering the long-term and short-term dielectric strength, a novel multiple insulation structure is adopted to improve the insulation voltage-withstanding level between windings in the running process of the high-frequency transformer;
4. the application introduces dynamic aggregation distance (DCD) and arithmetic crossover operator NSGA-II for improvement, uses ZDT1 and ZDT3 functions for testing, combines a free parameter scanning method to establish an optimal design flow of the high-frequency transformer, and prepares a high-frequency transformer prototype according to the screened optimal design scheme.
Drawings
FIG. 1 is a flow chart of an electromagnetic structure optimization method of a high-frequency transformer based on an intelligent optimization algorithm;
fig. 2 is a system parameter table of the DAB converter according to the present application;
fig. 3 is an equivalent circuit diagram of the DAB converter of the present application;
FIG. 4 is a graph of voltage and current waveforms for a DAB converter in accordance with the present application in steady state;
fig. 5 is a design of the structure of the high frequency transformer according to the present application;
FIG. 6 is a graph of a general three-level voltage waveform generated by the converter and a characteristic magnetic induction intensity waveform caused by the general three-level voltage waveform;
FIG. 7 is a physical diagram of a nanocrystalline magnetic ring loss data measurement platform according to the application;
FIG. 8 is a graph of the loss of a nanocrystalline magnetic ring measured under square waves of different frequencies according to the present application;
FIG. 9 is an equivalent process diagram of the litz wire winding of the present application;
FIG. 10 is a simulation of a two-dimensional finite element vortex field within a core window in accordance with the present application;
FIG. 11 is a graph of the current density profile of a litz wire winding at 110kHz in accordance with the present application;
FIG. 12 is a graph comparing primary winding alternating current resistivity curves obtained from a Dowell model and finite element simulations in accordance with the present application;
FIG. 13 is a schematic illustration of a variation of the present applicationmAc resistivity of litz wire windings at values belowF r With respect tod s /δ w Graph of variation (solid line: dowell equation, dashed line: approximate Dowell equation);
FIG. 14 shows a variation of the applicationηAc resistivity of litz wire windings at values belowF r With respect tod s /δ w A graph of the change;
FIG. 15 is a top cross-sectional view of a high frequency transformer core window according to the present application;
FIG. 16 is a finite element simulation result diagram of the leakage magnetic field in the 110kHz magnetic core window according to the present application;
FIG. 17 is a graph of leakage inductance comparisons obtained by analytical methods and finite element simulations in accordance with the present application;
FIG. 18 is a diagram of a novel multiple insulation structure according to the present application;
FIG. 19 is a Pareto front-edge graph of the test function before and after introducing DCD and arithmetic crossover operators according to the present application;
FIG. 20 is a cloud plot of the distribution of volumetric power density and efficiency in the range of 10Hz-100kHz according to the present application;
FIG. 21 is a pareto front-end plot of power density versus efficiency in accordance with the present application;
FIG. 22 is a three-dimensional block diagram and prototype physical diagram of the high frequency transformer of the application;
FIG. 23 is a pictorial view of the empty load loss and thermal measurement test platform of the present application;
FIG. 24 is a graph of voltage and current waveforms at the primary side of the transformer at 10kHz and corresponding hysteresis loops for the magnetic core in accordance with the present application;
FIG. 25 is a graph of hot spot temperature measured during a 5 hour hot run according to the present application;
FIG. 26 is a thermal imaging of a high frequency transformer in an unloaded steady state according to the present application;
FIG. 27 is a table of design parameters according to the present application;
fig. 28 is a table comparing core losses and winding losses of the high frequency transformer of the present application.
Detailed Description
The present application will now be described in detail with reference to the accompanying drawings, as shown in fig. 1-28;
the Dual-active Bridge (DAB) converter has the characteristics of easy implementation of soft switching, bidirectional power transmission, modularization and structural symmetry, and is increasingly applied to high-power occasions, and becomes an important component of a direct-current power distribution network. The system parameter table is shown in figure 2, the equivalent circuit of DAB converter is shown in figure 3, the voltage and current waveforms generated in steady state are shown in figure 4, the input bridge and the output bridge are controlled, and the voltage and current waveforms are controlled by the inductorL σ Applying full voltage to shift two square wave voltage waveforms at two sides of the transformer to generate phase shift angleφ. Wherein the leakage inductanceL σ As a shape of the power transmission element controlling the current,I T1 the effective value expression of the piecewise linear waveform comprises a fundamental wave component and a harmonic component as shown in the formula (1):
（1）
wherein,
to achieve soft switching when on, the anti-parallel diode of each switch should start to conduct before the on time. To reduce the number of components and achieve higher power density, the series inductance may be integrated as the leakage inductance of the high frequency transformer.
The design scheme of the square litz wire high frequency transformer structure is depicted, all structure dimensions within the core window are parameterized as shown in fig. 5 and calculated as follows:
the cross-sectional area of the magnetic core is:
（2）
in the method, in the process of the application,Din order for the duty cycle to be a duty cycle,N 2 is the total number of turns of the secondary winding,N 2 =m 2 N l2 ，K c is the lamination factor of the magnetic core;
the length of the cross section of the magnetic core is as follows:
（3）
according to the turn ratio of the primary winding and the secondary winding of the transformernThe total number of turns of the primary winding of the high-frequency transformer can be obtained:
（4）
the number of strands of the single-turn litz wire of the primary winding and the secondary winding is as follows:
（5）
wherein,J max the resistance value and the cooling pattern of the litz wire selected according to the application are chosen in order to allow a maximum current density to pass,J max =3.82A/mm 2 ；
in order to improve the filling coefficient and reduce the volume of the high-frequency transformer, each turn of litz wire is considered to be square, so the number of sub-lines of the litz wires of a single turn of a primary winding and a secondary winding is as follows:
（6）
the side length of the single-turn litz wire of the primary winding and the secondary winding is as follows:
（7）
the number of layers of the primary winding is:
（8）
the heights of the primary winding and the secondary winding are as follows:
（9）
the height of the magnetic core window is:
（10）
the widths of the primary winding and the secondary winding are as follows:
（11）
the width of the magnetic core window is:
（12）/>
the average turn length of the primary winding is:
（13）
the average turn length of the secondary winding is:
（14）
the average turn length of the inter-winding magnetic leakage channel is as follows:
（15）
the magnetic core has the volume as follows:
（16）
the volume of the winding is as follows:
（17）。
because IGSE is high in accuracy and good in fit in the working range, and only three empirical coefficients are needed, the IGSE is a more suitable expression for calculating the magnetic core loss under the high-frequency non-sinusoidal excitation waveform, and the voltage and magnetic induction intensity waveforms are shown in figure 6. In order to avoid increasing the calculation cost of the complex integral function in the IGSE, the formula is modified according to the application, and the process is as follows:
the formula before IGSE correction is:
（18）
wherein,
（19）
according toαIs obtained by the value range and curve fitting:
（20）
in FIG. 6, within one periodBThe rate of change of (2) is:
（21）
in summary, the modified IGSE expression is calculated as follows:
（22）
the measurement platform for the loss data of the nanocrystalline magnetic ring is built as shown in fig. 7. And measuring loss data of the nanocrystalline magnetic ring under the sine induction waveform. Matlab simulates the magnetic core loss to the working point of the magnetic materialf，B m ) Is according to (1)Depending on the relationship. The empirical coefficients for fitting IGSE are shown in Table 1. Table 1 is a table of empirical coefficients in IGSE, which is specifically described as follows:
| empirical coefficient | α | β | K |
| Numerical value | 1.397 | 2.296 | 4.229×10 -5 |
Meanwhile, loss data of the nanocrystalline magnetic ring at different frequencies were measured under the square wave condition, as shown in fig. 8. It can be seen that in the region smaller than the saturation magnetic flux density, the loss gradually increases as the magnetic flux density increases. Because hysteresis loss at low frequency accounts for a main part in a loss separation model of magnetic core loss, the hysteresis loss is in direct proportion to the first power of frequency, the eddy current loss is not obvious, the potential increase of the magnetic ring loss is slower, and the curve is flatter; the eddy current loss in the magnetic core is larger and larger along with the increase of the frequency and is proportional to the quadratic of the frequency, so that the higher the frequency is, the faster the potential increase of the loss is, and the steeper the curve is. Therefore, in the optimization design of the high-frequency transformer, selecting proper frequency and magnetic flux density has important significance for improving efficiency.
The Dowell unidimensional assumption of the electromagnetic field in the core window applies only to an ideal foil winding transformer, and for the case where the winding is litz wire, winding equivalence is also required, the equivalent process is shown in fig. 9.
According to the area equivalent principle, square stranded wires are used for replacing round stranded wires under the condition of unchanged number of turns and layers of the litz wire winding, and an equivalent square stranded wire side length is introducedd seq The relationship between the side length of the square strand and the diameter of the round strand is shown in the formula (23):
（23）
and then ensuring the number of layers of the litz wire winding to be unchanged, and enabling the square stranded wire winding to be equivalent to an ideal foil winding. However, this equivalent changes the effective conductive cross-sectional area of the winding, taking into account a porosity in order to ensure that the DC conductivity of the winding is the sameηThe conductivity of the winding wire is modified as shown in equation (24):
（24）
since the copper foils of the foil-type winding are uniformly arranged, the interlayer insulation distance is equivalent to the insulation distance between the foilsd i ：
（25）
The DAB converter contains a large number of higher harmonics, and the total winding loss is the sum of the winding losses at all individual harmonics. The winding loss of the high frequency transformer can be calculated as follows:
（26）
F r,n is the alternating current resistivity of the winding,R dc1 、R dc2 the direct current resistances of the wires of the primary winding and the secondary winding are respectively,I rms n, is thatnRoot mean square value of primary side excitation current of transformer under subharmonic;
（27）
（28）
（29）
in the formula (27), delta s For the penetration rate of the windings,ξ 1 、ξ 2 for skin and proximity correction factors of the windings,δ w skin depth of the winding at the operating frequency;
（30）
（31）
（32）
in the formula (32), the amino acid sequence of the compound,fin order to operate at the frequency of operation,μ 0 is vacuum magnetic permeability.
Due to the induction of eddy current under high frequency condition, the skin effect and proximity effect of the winding are enhanced, the current density is no longer uniform, and the alternating current resistivity is improvedF r And also increases. In order to realize more accurate calculation of square litz wire windings at high frequency, the application derives an approximate Dowell model suitable for the litz wire windings on the basis of area equivalence by linearizing hyperbolic functions and trigonometric functions in the Dowell modelObtaining the alternating current resistivityF r The approximate expression of (2) is shown in the formula (33):
（33）
in order to verify the validity and the estimation accuracy of the Dowell equivalent, the application carries out two-dimensional vortex field finite element simulation on the actual magnetic core window structure and the equivalent magnetic core window structure, and the simulation result is shown in fig. 10.
As can be seen from fig. 10, the magnetic field strength and magnetic energy of the equivalent magnetic core window structure are significantly smaller than those of the actual magnetic core window structure, and the magnetic field strength and magnetic energy distribution are also more uniform, so that the skin effect and the proximity effect are not obvious.
And adopting a finite element method to perform simulation calculation on the alternating current resistance of the square litz wire winding of the high-frequency transformer. The current density distribution of the winding at 110kHz is shown in fig. 11. The strand diameter of the square litz wire was 0.1mm and the strand count was 100 strands. At high frequencies, the current density of the litz wire is uniformly distributed, and the skin effect is not obvious.
FIG. 12 shows the AC resistivity curves of the broadband primary winding obtained by the Dowell model and finite element simulation. It can be seen that the ac resistivity calculated using the Dowell model is well matched with the simulation results, and the model can be used to derive an approximate Dowell model.
The skin effect and the proximity effect of the winding are enhanced under high frequency, so that the number of layers of the winding is enabled to be the number of layers for exploring the influence of the skin depth of the winding on the winding lossmVarying in the range of 1-20, porosityη=0.8, the obtained alternating current resistivityF r With respect tod s /δ w The curves of the changes are shown in fig. 13. Then the number of winding layers is maintainedm=1, let the porosity be unchangedηVarying from 0.6 to 1, to obtainF r With respect tod s /δ w The curves of the changes are shown in fig. 14.
From fig. 13-14, the following conclusions can be drawn: in designing a high frequency transformer, in order to approximate DowellThe winding loss calculated by the model and the calculation result of the Dowell model have smaller errors, and the winding loss calculated by the model and the calculation result of the Dowell model need to be as much as possibled s /δ w ≤2。
The porosity of the winding has a great influence on the uniformity of the leakage magnetic field distribution, and the reasonable design of the insulation distance is important to the calculation of the leakage inductance of the high-frequency transformer. Therefore, the application introduces the Rogowski factor, corrects the winding height by correcting the magnetic field path length, as shown in formula (34), thereby reducing the dependence of the magnetic field strength and magnetic energy distribution on the winding structure.
（34）
In the method, in the process of the application,K R in the case of the Rogowski factor,h weq is the equivalent height of the winding.
Such corrections enable more accurate estimation of parameter values when designing high frequency transformers than when directly applying the Dowell model. With the increase of the working frequency, the transverse magnetic field component can appear at the end of the winding, so that the calculation result of leakage inductance is lower. Therefore, the application provides a leakage inductance calculation model considering winding end effect and structural effect, which comprises the following specific steps:
the calculation of leakage inductance is divided into two parts, as shown in FIG. 15, one part is a frequency-dependent region, which is represented by blue, i.e. leakage inductance generated in the region where the windings are locatedL σb The method comprises the steps of carrying out a first treatment on the surface of the The other part is a frequency uncorrelated region, which is indicated by yellow, namely leakage inductance generated by an interlayer insulating region of the winding and a leakage magnetic channel regionL σy 。
The total leakage inductance of the high-frequency transformerL σ It can be calculated as:
（35）
for leakage inductance of frequency-dependent parts represented by blue regions, frequency-dependent factors taking into account winding geometry are introducedk f ThenL σb The following can be calculated:
（36）
（37），
in the method, in the process of the application,
（38）
wherein the method comprises the steps ofγIn order for the conductivity to be a factor,γ=（1+j）/δ w . For leakage inductance of the frequency uncorrelated part represented by the yellow area,L σy the following can be calculated:
（39）
fig. 16 shows the finite element simulation results of the leakage magnetic field of the high frequency transformer at 110 kHz. It can be seen that the maximum magnetic field strength of the high frequency transformer is located at the leakage magnetic path. Therefore, if the accurate value of leakage inductance is to be obtained, the width of the leakage flux path needs to be reasonably designedd iso . The leakage inductance curve results obtained by the analytical method and finite element simulation are shown in fig. 17. The leakage inductance calculated by the analytic method is basically consistent with the simulation result, and when the frequency is higher than 100kHz, the leakage inductance calculated by the analytic method is slightly lower than the finite element simulation result, but still within the error allowable range, and the model can be applied to the optimal design of the high-frequency transformer. In order to reduce the risk of reduced insulation reliability caused by thermal aging and other problems in the operation process of the high-frequency transformer and improve the insulation voltage-withstanding level between windings, the application adopts a novel multiple insulation structure in the design process, as shown in fig. 18, and semiconductor paint is brushed on the magnetic core and the outer layer of the windings to enhance the structural strength and reduce noise; epoxy resin with excellent dielectric property is poured into the window of the magnetic core, so that the required insulation distance is greatly reduced compared with air insulation, and the required insulation distance is reducedThe separation is greatly reduced compared with air insulation; the single-stranded wire is wound by using the polyurethane film, the litz wire adopts a double-layer insulation design, the inner layer is wrapped by the polyimide film, the outer layer is wrapped by the Nomex T410 insulating paper, and the electric stress is bound in the main insulating layer, so that the problem of partial discharge caused by overhigh field strength in the air outside the insulating layer can be avoided, and the electric stress of the main insulating layer can be softened. According to fig. 18, the respective insulation distances within the novel multiple insulation structure can be calculated as follows:
minimum insulation distance between primary and secondary windings:
to ensure zero voltage switching of DAB converter, safety factork saf =30%。
Horizontal and vertical insulation distance between winding and upper and lower yokes:
insulation distance between secondary winding and core center post:
wherein Eins-s is the short term dielectric strength, i.e., the breakdown field strength at power frequency.
The inter-turn insulation of the winding and the inter-layer insulation size are only related to the breakdown field strength of the inter-turn insulation material under the high-frequency square wave voltage, and can be calculated as follows:
wherein,E ins-l for long-term dielectric strength, i.e. insulating material at high frequencyBreakdown field strength at wave voltage.U t-t For the inter-turn voltage of the winding at long-term high frequency square wave voltages,U l-l respectively the interlayer voltages of the windings under long-term high-frequency square wave voltages.
The decision variables selected by the application are:
number of blocks of core stackn c Side length of magnetic core cross sectionAStrand diameter of litz wire for primary and secondary windingsd s1 、d s2 Layer number of secondary windingsm 2 Turns of primary and secondary windingsN l1 、N l2 Maximum magnetic inductionB m The upper boundary of which is defined by the saturation magnetic flux density of the materialB sat Setting.
The two objective functions selected by the application are:
objective function 1: the magnetic core loss and winding loss of the high-frequency transformer are minimum, and the efficiency is maximized.
（40）
Objective function 2: the volume of the high-frequency transformer is minimum, and the power density is maximized.
（41）
At a level capable of withstanding a minimum insulation voltageU iso Under the condition of (1) to ensure that zero voltage switching can be realized, the leakage inductance is larger than the minimum leakage inductance value capable of meeting the minimum isolation requirementL σ-min Therefore, the constraint conditions selected by the application are as follows:
（42）
wherein,x l is the lower bound of the decision variable,x u is the upper bound of the decision variable. Because NSGA-II still has the uneven, easy problem such as sinking local convergence of population distribution in the course of high-frequency transformer optimal design, in order to make this algorithm have better global searching ability, the application introduces DCD and arithmetic crossover operator to improve NSGA-II, promote population distribution breadth and homogeneity, raise the overall optimization efficiency.
Is provided withX i t 、X j t Respectively the firsttAnd (3) encoding real values of corresponding decision variables at the crossing points of the two individuals of the generation, wherein the decision variables corresponding to the two individuals after the crossing are respectively:
（43）/>
wherein,a、brespectively [0,1 ]]Random numbers uniformly distributed on the base.
Individual bodyiThe dynamic aggregation distance of (2) is calculated as follows:
（44）
wherein,
（45）
（46）
in the method, in the process of the application,I i for individualsiIs used for the distance of aggregation of (a),Min order to be of the dimension of the target,I i,k is the firstiIndividual at the firstkAnd (5) maintaining the function values after sequencing on the targets. The modified algorithm was debugged using Matlab platform and tested using the ZDT1 and ZDT3 functions. Population used in algorithmN p Number of generations =100GenNumber of tests =200trCross probability =8p c Probability of variation =0.8p m =1/n v Whereinn v Is the number of decision variables, cross distribution indexmu=80, mutation distribution indexmum=20. The Pareto front of the test function obtained before and after the algorithm improvement was compared as shown in fig. 19. As can be seen from fig. 19, after the NSGA-ii algorithm is improved, the Pareto front curve of the test function is smoother, the distribution of each solution is more uniform, and the improved NSGA-ii is more suitable for being applied to the multi-objective optimization design of the high-frequency transformer.
Based on a free parameter scanning method, the application makes the selected decision variables carry out 58 ten thousand parameter scans in the respective ranges, and generates 26 ten thousand effective design schemes in the specific range, thus obtaining a distribution cloud picture of the volume power density and the efficiency in the range of 10Hz-100kHz, as shown in figure 20. Wherein each point represents a design and is iteratively calculated as an initial population in the modified NSGA-ii. Fig. 27 summarizes the design parameters required in the design process of the high frequency transformer. According to the optimal design flow chart, all design schemes obtained by the free parameter scanning are globally optimized by using the improved NSGA-II, and the pareto front of the power density-efficiency is obtained as shown in figure 21. And searching a global optimal design scheme according to the power density maximization principle, wherein the global optimal design scheme is represented by a red asterisk. The design scheme is used for designing and manufacturing a high-frequency transformer prototype, and a three-dimensional structure diagram and a prototype picture of the high-frequency transformer prototype are shown in fig. 22. For the manufactured shell type high-frequency transformer prototype, the magnetic core uses Antainano nanocrystalline materials of the Antainano technology, and the specification is as follows: CN-154 x 87 x 28 x 35. The strand diameters of the square litz wire windings are all 0.2mm, the litz wire structure is 16×137 strands, namely 2192 strands are twisted into 16 sub-bundles in sequence, 137 strands are formed in each sub-bundle, and then the 16 sub-bundles are twisted into one turn of litz wire. The dimensions of the single turn litz wire were 11.65mm by 11.65mm and the insulation thickness was 0.3mm. The upper magnetic yoke of the magnetic core is connected with the front and the back by using Z-shaped stainless steel clamping plates, the lower magnetic yoke is connected with the front and the back by using U-shaped stainless steel plates as clamping pieces of the structure and is connected by a screw rod, so that the whole structure is fastened and formed.
Examples
And measuring leakage inductance and alternating current resistance of the high-frequency transformer prototype by using a Tonghui TH2840B impedance analyzer, short-circuiting a secondary winding of the high-frequency transformer prototype in the measuring process, opening a primary winding, and ignoring the influence of excitation inductance. The leakage inductance measurement result is 7.92 mu H, and the error is 2.2% compared with the leakage inductance value which is calculated to the primary side; the measurement result of the ac resistance was 3.1mΩ, and a measurement value of the winding loss was calculated from the measured ac resistance value and the root-mean-square value of the rated harmonic current. In the actual manufacturing process, certain difference exists between the insulation distance between the skeleton of the high-frequency transformer and the inside of the winding and the design value, so that the measured value of leakage inductance cannot be consistent with the design value. An empty load loss and thermal measurement experimental platform as shown in fig. 23 was constructed. The excitation source was a WF1974 signal generator with NF4520A power amplifier, generating a square wave voltage with an amplitude of 400V and operating frequency of 10kHz, while the secondary winding remained open, and using an LMG500 power analyzer to read the values of voltage, current and core loss. Fig. 24 shows the voltage and current waveforms at the primary side of the high frequency transformer and the corresponding hysteresis loop of the core in an unloaded condition. A three-dimensional model of the high-frequency transformer is built in the Solid works software, and is imported into the Ansys software for finite element analysis, and the calculated magnetic core loss and winding loss at the frequency of 10kHz are shown in figure 28. Fig. 28 is a table comparing core loss and winding loss of the high frequency transformer. In order to verify the thermal characteristics of the designed high-frequency transformer prototype, the high-frequency transformer prototype is thermally operated for 5 hours under no-load and rated voltage excitation until the high-frequency transformer prototype is in a stable state, and the ambient temperature is 20 ℃. The temperatures of each hot spot were recorded using a NAPUL TP230X temperature recorder and the measurement results are shown in fig. 25. Fig. 26 shows a thermal photograph taken by the FLUKE Ti32 infrared thermal imager at steady state operation of the high frequency transformer. The winding is mainly heated by thermal coupling under no-load condition, so that the magnetizing current in the winding is lower and the winding temperature is lower. At the moment, the core loss mainly exists in the high-frequency transformer, the temperature of the core is highest, the temperature can reach 135.7 ℃ in a stable operation state, the temperature is still in a safe operation range, and the temperature rise meets the expected design requirement.
The above technical solution only represents the preferred technical solution of the present application, and some changes that may be made by those skilled in the art to some parts of the technical solution represent the principles of the present application, and the technical solution falls within the scope of the present application.
Claims (8)
1. The electromagnetic structure optimization method of the high-frequency transformer based on the intelligent optimization algorithm is characterized by comprising the following steps of:
firstly, setting the system specification of a DAB converter, selecting fixed parameters and decision variables according to a magnetic core, a winding structure and insulating materials, establishing a design scheme of a square litz wire high-frequency transformer structure, carrying out parameterization treatment on the magnetic core and the winding structure in a magnetic core window, and calculating all structural parameters;
step two, according to the electrical and structural parameters determined in the step one, a calculation model of the core loss and the winding loss of the high-frequency transformer is established, a leakage inductance calculation model is established, a multiple insulation structure is established, and the insulation distance is calculated;
step three, establishing a multi-objective optimized mathematical model of the high-frequency transformer according to the calculation and analysis in the step two;
and step four, on the basis of a multi-objective optimized mathematical model of the high-frequency transformer, improving NSGA-II, searching a global optimal solution by combining a free parameter scanning method, and manufacturing a high-frequency transformer prototype according to the screened optimal solution.
2. The method for optimizing electromagnetic structure of high-frequency transformer based on intelligent optimization algorithm as claimed in claim 1, wherein in said step one, the DAB converter is controlled by an input bridge and an output bridge and is electrically connected with the inductorL σ The mode of applying full voltage to make two square wave voltage waveforms on two sides of transformer shift to produce phase shift angleφWherein the leakage inductanceL σ As a shape of the power transmission element controlling the current,I T1 the effective value expression of the piecewise linear waveform comprises a fundamental wave component and a harmonic component as shown in the formula (1):
（1）
wherein,
to achieve soft switching when on, the anti-parallel diode of each switch should start to conduct before the turn-on time;
to reduce the number of components and achieve higher power density, the series inductance may be integrated as the leakage inductance of the high frequency transformer.
3. The electromagnetic structure optimization method of the high-frequency transformer based on the intelligent optimization algorithm according to claim 1, wherein all the structural parameters in the magnetic core window in the second step are calculated as follows:
the cross-sectional area of the magnetic core is:
（2）
in the method, in the process of the application,Din order for the duty cycle to be a duty cycle,N 2 is the total number of turns of the secondary winding,N 2 =m 2 N l2 ，K c is the lamination factor of the magnetic core;
the length of the cross section of the magnetic core is as follows:
（3）
according to the turn ratio of the primary winding and the secondary winding of the transformernThe total number of turns of the primary winding of the high-frequency transformer can be obtained:
（4）
number of strands of single turn litz wire for primary and secondary windings:
（5）
wherein,J max the resistance value and the cooling pattern of the litz wire selected according to the application are chosen in order to allow a maximum current density to pass,J max =3.82A/mm 2 ；
in order to improve the filling coefficient and reduce the volume of the high-frequency transformer, each turn of litz wire is considered to be square, so the number of sub-lines of the litz wires of a single turn of a primary winding and a secondary winding is as follows:
（6）
the side length of the single-turn litz wire of the primary winding and the secondary winding is as follows:
（7）
the number of layers of the primary winding is:
（8）
the heights of the primary winding and the secondary winding are as follows:
（9）
the height of the magnetic core window is:
（10）
the widths of the primary winding and the secondary winding are as follows:
（11）
the width of the magnetic core window is:
（12）
the average turn length of the primary winding is:
（13）
the average turn length of the secondary winding is:
（14）
the average turn length of the inter-winding magnetic leakage channel is as follows:
（15）
the magnetic core has the volume as follows:
（16）
the volume of the winding is as follows:
（17）。
4. the electromagnetic structure optimization method of a high-frequency transformer based on an intelligent optimization algorithm according to claim 1, wherein the expression for calculating the core loss in the second step is a modified IGSE, and the formula of the IGSE before modification is:
（18）
wherein,
（19）
according toαIs obtained by the value range and curve fitting:
（20）
within one periodBThe rate of change of (2) is:
（21）
the expression of the modified IGSE is as follows:
（22）。
5. the electromagnetic structure optimization method of the high-frequency transformer based on the intelligent optimization algorithm according to claim 1, wherein winding loss calculation in the second step is linearization according to an area equivalent principle and a complex function, and an approximate Dowell model suitable for litz wire windings is deduced;
firstly, replacing round strands with square strands under the condition of unchanged number of turns and layers of litz wire windings, and introducing an equivalent square strand side lengthd seq The relationship between the side length of the square strand and the diameter of the round strand is shown in the formula (23):
（23）
then ensuring the layer number of the litz wire winding is unchanged, and making the square stranded wire winding equivalent to an ideal foil winding, but the equivalent changes the effective conductive cross-sectional area of the winding, and considering a porosity in order to ensure that the direct current conductivity of the windings is the sameηThe conductivity of the winding wire is modified as shown in equation (24):
（24）
since the copper foils of the foil-type winding are uniformly arranged, the interlayer insulation distance is equivalent to the insulation distance between the foilsd i ：
（25）
The winding loss of the high frequency transformer can be calculated as follows:
（26）
F r,n is the alternating current resistivity of the winding,R dc1 、R dc2 the direct current resistances of the wires of the primary winding and the secondary winding are respectively,I rms n, is thatnRoot mean square value of primary side excitation current of transformer under subharmonic;
（27）
（28）
（29）
in the formula (27), delta s For the penetration rate of the windings,ξ 1 、ξ 2 for skin and proximity correction factors of the windings,δ w skin depth of the winding at the operating frequency;
（30）
（31）
（32）
in the formula (32), the amino acid sequence of the compound,fin order to operate at the frequency of operation,μ 0 is vacuum magnetic permeability;
due to the induction of eddy current under high frequency condition, the skin effect and proximity effect of the winding are enhanced, the current density is no longer uniform, and the alternating current resistivity is improvedF r And also increases with it;
in order to realize more accurate calculation of the square litz wire winding at high frequency, the application derives an approximate Dowell model suitable for the square litz wire winding on the basis of area equivalence, and obtains alternating current resistivity by linearizing hyperbolic functions and trigonometric functions in the Dowell modelF r The approximate expression of (2) is shown in the formula (33):
（33）。
6. the electromagnetic structure optimization method of a high-frequency transformer based on an intelligent optimization algorithm according to claim 1, wherein in the second step, a Rogowski factor is introduced into a leakage inductance calculation model, and the winding height is corrected by correcting the path length of a magnetic field, as shown in formula (34):
（34）
in the method, in the process of the application,K R in the case of the Rogowski factor,h weq is the equivalent height of the winding;
the leakage inductance calculation model considering the winding end effect and the structural effect is obtained based on the integration of magnetic field energy generated by a leakage magnetic field, and is specifically as follows:
the calculation of leakage inductance is divided into two parts, one part is the frequency-dependent region, namely the leakage inductance generated by the region where the winding is locatedL σb The method comprises the steps of carrying out a first treatment on the surface of the Another part is the frequency uncorrelated region, namely the leakage inductance generated by the winding interlayer insulation region and the leakage magnetic channel regionL σy ；
The total leakage inductance of the high-frequency transformerL σ It can be calculated as:
（35）
for leakage inductance of the frequency-dependent portion, a frequency-dependent factor is introduced that takes the effect of the winding structure into accountk f ThenL σb The following can be calculated:
（36）
（37）
in the method, in the process of the application,
（38）
wherein the method comprises the steps ofγIn order for the conductivity to be a factor,γ=（1+j）/δ w for leakage inductance of the frequency-uncorrelated part,L σy the following can be calculated:
（39）。
7. the electromagnetic structure optimization method of the high-frequency transformer based on the intelligent optimization algorithm as claimed in claim 1, wherein the process of establishing the multi-objective optimization mathematical model of the high-frequency transformer in the third step is as follows:
first, the decision variables selected are:
number of blocks of core stackn c Side length of magnetic core cross sectionAStrand diameter of litz wire for primary and secondary windingsd s1 、d s2 Layer number of secondary windingsm 2 Turns of primary and secondary windingsN l1 、N l2 Maximum magnetic inductionB m The upper boundary of which is defined by the saturation magnetic flux density of the materialB sat Setting;
the two selected objective functions are:
objective function 1: the magnetic core loss and winding loss of the high-frequency transformer are minimum, the efficiency is maximized,
（40）
objective function 2: the volume of the high-frequency transformer is minimum, the power density is maximized,
（41）
at a level capable of withstanding a minimum insulation voltageU iso Under the condition of (a) and (b),to ensure zero voltage switching, the leakage inductance is greater than the minimum leakage inductance value that meets the minimum isolation requirementL σ-min Therefore, the constraint conditions selected by the application are as follows:
（42）
wherein,x l is the lower bound of the decision variable,x u is the upper bound of the decision variable;
thirdly, introducing a dynamic aggregation distance by an improved non-dominant ordering genetic algorithm, and improving the NSGA-II crossing operation by adopting an arithmetic crossing operator; wherein the arithmetic crossover operator is set upX i t 、X j t Respectively the firsttAnd (3) encoding real values of corresponding decision variables at the crossing points of the two individuals of the generation, wherein the decision variables corresponding to the two individuals after the crossing are respectively:
（43）
wherein,a、brespectively [0,1 ]]Random numbers uniformly distributed on the base; while dynamically aggregating individuals of distanceiThe dynamic aggregation distance of (2) is calculated as follows:
（44）
wherein,
（45）
（46）
in the method, in the process of the application,I i for individualsiIs of (3)The distance between the two adjacent substrates is determined,Min order to be of the dimension of the target,I i,k is the firstiIndividual at the firstkAnd (5) maintaining the function values after sequencing on the targets.
8. The electromagnetic structure optimization method of a high-frequency transformer based on an intelligent optimization algorithm according to claim 1, wherein the step four is characterized in that 58 ten thousand parameter scans are performed in the range of all decision variables based on a free parameter scanning method, 26 ten thousand effective design schemes are generated in a specific range, a distributed cloud chart of the volume power density and the efficiency in the range of 10Hz-100kHz is obtained, each point represents one design scheme and is used as an initial population in an improved NSGA-II for iterative calculation, global optimization is performed on all the design schemes obtained by the free parameter scanning by using the improved NSGA-II, and a global optimal design scheme is obtained, and a high-frequency transformer prototype is designed and manufactured by using the design scheme.
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