CN104317979A - High-frequency high-voltage transformer design optimization method based on genetic algorithm - Google Patents

Abstract

The invention discloses a high-frequency high-voltage transformer design optimization method based on a genetic algorithm. On the basis of a minimum loss formula of a transformer and the insulation dimension and the iron core shape of the transformer, a mathematical model is established, a genetic algorithm is adopted for optimizing the transformer by taking the number of turns of primary sides and the layer number of secondary sides as optimization variables and taking efficiency as an optimization target, so that the efficiency of the transformer is maximized, the loss of the transformer is minimized, temperature rise is minimized under an equal condition, the leakage inductance and the distribution capacitance of the transformer are fully utilized to participate in the work of a power system to form an LCC (Life Cycle Costs) resonance circuit, and the loss of the transformer is reduced so as to lower the temperature rise. Compared with the prior art, the invention introduces the genetic algorithm, the genetic algorithm exhibits a problem non-relevant quick and random search capability, searches by starting from a group and has the characteristic of concurrency, and a plurality of individuals can be simultaneously compared to greatly quicken optimal solution search speed.

Description

Based on the high frequency high voltage transformer design optimization method of genetic algorithm

Technical field

The present invention relates to a kind of method for designing of high frequency high voltage transformer, particularly relate to a kind of method for designing of the static dust-removing power high frequency high voltage transformer based on genetic algorithm.

Background technology

Along with domestic industry fast development, people are lived more and more convenient, but thing followed problem of environmental pollution is more and more serious, particularly serious haze weather creates serious impact to our health and trip, and the formulation of new atmospheric emission standard brings new requirement and opportunity to dedusting industry.High-frequency high-voltage electrostatic dust removal power obtains applying more and more widely in dedusting industry, simultaneously also more and more higher to its performance requirement.

High-frequency transformer is the core component of whole static dust-removing power; but transformer temperature is too high, heat radiation abnormal conditions not in time often can occur; particularly high-frequency transformer is along with the high frequency of input; the characteristic showed and Industrial Frequency Transformer are greatly different; the too high insulation life that not only can affect transformer of temperature; the serious stable operation even affecting electrical network; unnecessary loss is brought, so high frequency high voltage transformer temperature must be controlled in a rational scope to the productive life of people.Because the self-radiating of transformer is limited in one's ability, therefore the optimal design of transformer is absolutely necessary for reduction transformer temperature with increase auxiliary radiating device.

Summary of the invention

The object of the present invention is to provide a kind of high frequency high voltage transformer design optimization method based on genetic algorithm, make full use of the leakage inductance of high-frequency transformer and the resonant process of distributed capacitance participation circuit, make power work under discontinuous conduct mode (DCM), based on the minimal losses formula of transformer, the insulation size of transformer and core configuration founding mathematical models, with the former limit number of turn of transformer and the secondary number of plies for optimized variable, take efficiency as optimization aim, genetic algorithm is adopted to be optimized transformer, make the maximizing efficiency of transformer, loss minimizes, temperature rise minimizes, transformer is run more stable, longer service life.

Object of the present invention is achieved by the following technical programs:

Based on a high frequency high voltage transformer design optimization method for genetic algorithm, comprise the following steps:

Step 1: based on the minimal losses formula of transformer, the insulation size of transformer and core configuration founding mathematical models, mathematical model is:

U in formula _pfor original edge voltage, K is form factor, and f is frequency of operation, B _moperating magnetic field flux density, ρ _cfor iron core density, ρ _wthe resistivity of winding conductor, n ₁the former limit number of turn, n _2cbe the secondary number of plies, η is transformer efficiency, l _p, l _sformer and deputy limit winding length respectively, S _p, S _sthat former and deputy limit winding cross section amasss respectively, P _oit is winding output power;

Step 2: the majorized function being built genetic algorithm by Transformer Model, considers the complicacy of mathematical model, sets up two majorized function W ₁, W ₂, and W ₁, W ₂with efficiency eta positive correlation:

$W_1=\frac{2P_o}{2P_o+A_c\×(2h_1+2L_w+4\sqrt{A_c}){\mathrm{\ρ}}_c{K}_c{f}^{\mathrm{\α}}{B_m}^{\mathrm{\β}}(2+\mathrm{\β})}$

$W_2=\frac{1}{|2\×(\frac{{\left(\frac{P_o}{W_1{U}_p}\right)}^2{\mathrm{\ρ}}_w{k}_{p-s}{k}_{p-x}{l}_p}{S_p}+\frac{{I_s}^2{\mathrm{\ρ}}_w{k}_{s-s}{k}_{s-x}{l}_s}{S_s})-\frac{\mathrm{\β}}{2}{V}_c{\mathrm{\ρ}}_c{K}_c{f}^{\mathrm{\α}}{B_m}^{\mathrm{\β}}|}$

Wherein P _othe output power of indication transformer; U _prepresent former limit input voltage; A _crepresent that core cross section amasss; h ₁represent magnetic core window height; L _wrepresent magnetic core window width; ρ _crepresent magnetic core density; K _c, α, β be the dissipation constant of core material, by acquisition of tabling look-up; The frequency of f indication transformer; B _mthe magnetic flux density of indication transformer; ρ _wrepresent the resistivity of copper conductor; k _p-s, k _p-xrepresent skin effect coefficient and the proximity effect coefficient of former limit winding respectively; k _s-s, k _s-xrepresent skin effect coefficient and the proximity effect coefficient of vice-side winding respectively; l _p, l _srepresent the winding length on former and deputy limit respectively; S _p, S _srepresent the sectional area of the winding on former and deputy limit respectively; V _crepresent the volume of magnetic core;

L _w＝2×(L ₁+n ₁×L ₂+L ₃+n _2c×L ₄)+L ₅

A _c＝U _p/Kfn ₁k _fB _m

Step 3: definition iterations and the parameter for optimizing high frequency high voltage transformer, and treat to deal with problems and encode; The former limit number of turn n of initialization transformer ₁with vice-side winding number of plies n _2cand iterations N;

n _1-min＜n ₁＜n _1-max，n _2c-min＜n _2c＜n _2c-max，N≤N _max

Step 4: random initializtion colony P (0)=(p ₁, p ₂, p ₃p _n);

Step 5: set up fitness function according to objective function, and the fitness value (F) calculating each individuality in colony;

max1＝max(W ₁)

min1＝min(W ₁)

max2＝max(W ₂)

min2＝min(W ₂)

M1＝1/(max1-min1)

M2＝1/(max2-min2)

Then fitness function is: F=(W ₁-min1) × M1+ (W ₂-min2) × M2;

Step 6: assessment fitness, to individual p each in current group P (t) _icalculate its fitness F (i), fitness illustrates the performance quality of this individuality; Adopt the fitness that formula p (i)=F (i)/sum (F) assessment is individual, the larger fitness of proportion accounted in every generation colony is higher;

Step 7: for Pr (t) in the middle of producing by the regular application choice operator determined by ideal adaptation angle value;

Step 8: according to P _cindividuality is selected to carry out interlace operation;

Step 9: according to P _mmutation operation is carried out to breeding individuality;

Step 10: judge whether end condition meets, if met, optimizes and terminates, saving result, if do not met, turn back to step 5;

Rule of judgment: $\left\{\begin{array}{c}{n}_{1-\min }<n_1<n_{1-\max }\\ n_{2c-\min }<n_{2c}<n_{2c-\max }\\ N>N_{\max }\end{array}\right.$

Just terminate if satisfy condition to optimize, otherwise continue iteration, until reach maximum iteration time;

Step 11: the individuality exporting fitness value optimum in population.

Object of the present invention can also be realized further by following technical measures:

The aforementioned high frequency high voltage transformer design optimization method based on genetic algorithm, wherein P (0)=(p of step 4 ₁, p ₂, p ₃p _n), n gets 20 ~ 200.

The aforementioned high frequency high voltage transformer design optimization method based on genetic algorithm, wherein the selection opertor of step 7 is Wheel-type selection opertor or random unanimously selection opertor or algorithm of tournament selection operator.

The aforementioned high frequency high voltage transformer design optimization method based on genetic algorithm, the wherein P of step 8 _c=0.6 ~ 1.0.

The aforementioned high frequency high voltage transformer design optimization method based on genetic algorithm, the wherein P of step 9 _m=0.005 ~ 0.05.

Compared with prior art, the invention has the beneficial effects as follows: the design optimization method of a kind of high frequency high voltage transformer that the present invention proposes, the distribution parameter of high frequency high voltage transformer to be incorporated in whole power-supply system and to be optimized design, substantially increase the utilization ratio of high frequency high voltage transformer, adopt genetic Optimization Algorithm, solve the strong coupling problem between each parameter of transformer, comprehensive optimizing in the feature of the strong coupling and dynamic between each parameter of transformer, substantially increase the operational efficiency of transformer, transformer temperature rise obviously declines, transformer runs more stable, longer service life.

Accompanying drawing explanation

Fig. 1 is high-frequency electrostatic duster system block diagram;

Fig. 2 is high-frequency electrostatic duster system LCC resonant circuit topology figure;

Fig. 3 is high frequency high voltage transformer design optimization process flow diagram;

Fig. 4 is the physical dimension schematic diagram of microcrystalline iron core;

Fig. 5 is genetic algorithm optimization process flow diagram.

Embodiment

Below in conjunction with the drawings and specific embodiments, the invention will be further described.

Compared with Industrial Frequency Transformer, high frequency high voltage transformer has the feature of high frequency and high-pressure trend, wherein high frequency brings serious problem to transformer, the design of high frequency high voltage transformer also must will take into account the problems such as core loss, distribution parameter, proximity effect and the kelvin effect that high frequency brings, in Industrial Frequency Transformer design, these problems can be ignored.

As depicted in figs. 1 and 2, the design optimization method of a kind of high frequency high voltage transformer that the present invention proposes, is incorporated into the distribution parameter of high frequency high voltage transformer in whole power-supply system and is optimized design.This power-supply system have employed LCC resonance principle, participates in circuit resonance by the leakage inductance of transformer and distributed capacitance, makes power work in discontinuous conduct mode f _s< 1/2f _r(f _sfor switching frequency, f _rfor resonance natural frequency), thus make switching tube work in no-voltage to open zero-current switching, wherein

$f_r=1/2\mathrm{\&pi;}\sqrt{L_s{C}_s{C}_p}$

L in formula _s---the leakage inductance on former limit converted by transformer;

C _s---the resonant capacitance of system;

C _p---the electric capacity on former limit converted by transformer.

The frequency of transformer can be known according to the designing requirement of power-supply system, analyzed leakage inductance and the distributed capacitance of transformer by frequency, and in design of transformer, adjust the leakage inductance of transformer and the size of distributed capacitance.

Described series parallel resonance circuit feature is the leakage inductance L making full use of transformer _swith distributed capacitance C _pparticipate in the work of power-supply system, form LCC resonant circuit, reduce the loss of transformer, thus reduce temperature rise.

As shown in Figure 3, for being applied in the design flow diagram based on high-frequency and high-voltage transformation on electrostatic precipitation, concrete steps are:

1) according to the designing requirement of power-supply system, the distribution parameter of analysis of high frequency high-tension transformer

This power-supply system have employed LCC resonance principle, participates in circuit resonance by the leakage inductance of transformer and distributed capacitance, makes power work in discontinuous conduct mode f _s< 1/2f _r(f _sfor switching frequency, f _rfor resonance natural frequency), thus make switching tube work in no-voltage to open zero-current switching, wherein

$f_r=1/2\mathrm{\&pi;}\sqrt{L_s{C}_s{C}_p}---(1-1)$

L in formula _s---the leakage inductance on former limit converted by transformer;

C _s---the resonant capacitance of system;

C _p---the electric capacity on former limit converted by transformer.

2) as requested, determine the former vice-side winding turn ratio, determine former secondary rated current.In order to the requirement of output voltage can be reached, when designing, the turn ratio is determined in certain scope.

$n=\frac{U_s}{U_p}---(1-2)$

By the anticipating power P of dust pelletizing system ₀, the capacity of calculating transformer:

$S_n=\frac{P_0}{\mathrm{\&eta;}}---(1-3)$

The efficiency of η in formula---transformer.

Then the rated current of transformer primary side winding is:

$I_p=\frac{S_n}{U_P}---(1-4)$

3) core material and core structure form is selected

Bipolarity switching mode power supply transformer requires that magnetic material has high magnetic induction density and dynamic permeadility, lower high-frequency loss, and conventional material has: permalloy, FERRITE CORE, non-crystaline amorphous metal and ultramicro-crystal alloy.High frequency high voltage transformer of the present invention is the high-frequency and high-voltage high-power transformer be used in above electrostatic precipitation, and selected iron core is the ultracrystalline magnetic core (non-crystaline amorphous metal) that 0.8mil (Mill) is thick.

4) core section sum core dimensions is calculated

The determination of transformer applied power Pt:

P _t＝S _n (1-5)

Then the power handling capability of magnetic core and area amass A _prelation can be represented by formula below:

$A_p=W_a{A}_c=\frac{P_t\&times;{10}^4}{K{k}_u{B}_m\mathrm{Jf}}---(1-6)$

K in formula---form factor;

K _u---window utilization factor;

B _m---magnetic flux density;

J---current density;

W _a---iron core skeleton window area;

A _c---core section amasss.

Iron core of the present invention is of a size of: 270*170*60*60, and namely core window area is 270*170, and core section amasss as 60*60, as shown in Figure 4.

5) the former vice-side winding number of turn is determined

In given frequency, determine the cross section of magnetic core and magnetic close after obtain transformer primary side umber of turn by following formula:

$n_1=\frac{U_p}{\mathrm{Kf}{B}_m{A}_m}---(1-7)$

And then obtain transformer secondary umber of turn by n2=n*n1.

According to above formula, the electric current and voltage sum of products with all windings of transformer of n winding is:

$\mathrm{\&Sigma;VA}=\mathrm{Kf}{B}_m{A}_m\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i{I}_i---(1-8)$

Make k _ufor the usage factor of transformer core window, i.e. the effective conductive area sum W of all winding conductors _cwindow area W whole with iron core _aratio.

$\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i{A}_{\mathrm{wi}}=k_u{W}_a=W_c---(1-9)$

Wherein A _wibe the sectional area of the i-th winding conductor, then the current density of each winding conducting wire is J _i, then J _i=I _i/ A _wi

Suppose that the current density, J in each winding conductor is identical, (1-8) formula and (1-9) formula are merged, then:

$\mathrm{\&Sigma;VA}=\mathrm{Kf}{B}_m{k}_f{A}_{c}J{k}_u{W}_a---(1-10)$

Definition magnetic core area amasss as A _p, i.e. the product A of the core section sum core window area of transformer core _p=A _cw _a, then:

∑VA＝KfB _mk _fJk _uA _p (1-11)

6) winding and principal and subordinate's insulating structure design

Due in oil-immersed power transformer, between high pressure with low pressure winding and each mutually between and winding to mailbox, more uniform electric field is belonged to substantially to iron core, winding, so their major insulation all adopts oil to carry out barrier insulation system, comprising the square ring and phase partition etc. of the insulating cylinder between winding, winding overhang.According to the resistance to voltage of the potential difference (PD) between adjacent belts electric conductor and insulating material, determine the insulation distance L of former limit winding to iron core ₁, former limit winding every layer thickness (comprising insulation distance) L ₂, transformer primary side secondary insulation distance L ₃, the every layer thickness of vice-side winding (comprising insulation distance) L ₄if the winding number of plies of secondary is n _2c, transformer secondary is to the insulation distance L of secondary ₅, wherein in the present invention, adopt two-layer some gummed paper between former boundary layer, secondary interlayer adopts one deck point gummed paper, and some gummed paper thickness is 0.08mm.

If the window width of transformer core is L _w, the geometry system of equations (sectional area of general microcrystalline iron core material is square) of transformer can be expressed as follows

$\left\{\begin{array}{c}{L}_w=2\&times;(L_1+n_1\&times;L_2+L_3+n_{2c}\&times;L_4)+L_5\\ V_c=A_c\&times;(2h_1+2L_w+4\sqrt{A_c})\end{array}\right.---(1-12)$

7) former vice-side winding design: due in HF link, there is kelvin effect, the electric current of high frequency high voltage transformer is close to be asked for by following formula: $J=(2.5~4.5)f^{-\frac{1}{2}}(A/{\mathrm{mm}}^2)---(1-13)$

Wire gauge is calculated herein with above-mentioned J value (cps is for kHz, is the desirable coefficient 2.5 of 10kHz).The bare conductor sectional area of former and deputy limit winding is calculated again according to the rated current on former and deputy limit:

$S_p=\frac{I_p}{J},S_s=\frac{I_s}{J}---(1-14)$

If δ is the penetration depth of copper conductor, then $\mathrm{\&delta;}=\sqrt{{\mathrm{\&rho;}}_w/\mathrm{\&pi;f\&mu;}}\left(m\right)---(1-15)$

ρ in formula _w---the resistivity of winding conductor;

The magnetic permeability of μ---conductor, gets permeability of vacuum μ herein ₀.

Under general condition, former and deputy limit winding should adopt thickness (or diameter) to be less than the Copper Foil (or round wire) of the penetration depth of 2 times of copper conductors, can determine the thickness d of former limit Copper Foil accordingly _p.

Then former limit Copper Foil height is: $h_p=\frac{S_p}{d_p}---(1-16)$

Vice-side winding diameter of wire is: $d_s=2\sqrt{\frac{I_s}{\mathrm{J\&pi;}}}---(1-17)$

What in the present invention, first side winding adopted is Copper Foil, and specification is 0.5 × 186, and what secondary side winding adopted is three anti-copper conductors, and specification is φ 0.85.

8) adjust core window area, if core window meets the demands, then perform step (9), otherwise get back to step (4) application following formula and check window area, determine winding can around under:

S _d1n ₁+S _d2n ₂≤0.2D _i ² (1-18)

S in formula _d1, S _d2---a secondary side sectional area of wire;

D _i---magnetic core window width.

9) calculate the copper loss of former vice-side winding, if copper loss meets the demands, then perform step (10), otherwise the copper loss getting back to step (7) Transformer Winding can be expressed as follows:

$P_{\mathrm{cu}}=\mathrm{\&Sigma;}{\mathrm{RI}}^2={\mathrm{\&rho;}}_w\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{N_i\left(\mathrm{MLT}\right){\left({\mathrm{JA}}_{\mathrm{wi}}\right)}^2}{A_{\mathrm{wi}}}---(1-19)$

Wherein ρ _wthe resistivity of winding conductor and the average length of every circle winding is represented respectively, A with MLT _wiit is the sectional area of the i-th winding conducting wire.Then winding volume is V _w=MLT × W _a, effective conduction volume of winding conductor is V _w× k _u, then:

P _cu＝ρ _wV _wk _uJ ² (1-20)

Each winding copper loss is calculated by following formula: P _cu.i=I _i ²r _ac.i(1-21)

P in formula _cu.i---the copper loss of each winding;

R _ac.i---the AC resistance of each winding;

I _i---the effective value of each winding current.

If former limit winding average turn is long is MLT _p, k _p-sand k _p-xfor skin effect coefficient and the proximity effect coefficient of former limit winding,

Then: $R_{\mathrm{ac}-p}={\mathrm{\&rho;}}_w\frac{\mathrm{ML}{T}_p{n}_1}{S_p}{k}_{p-s}{k}_{p-x}---(1-22)$

ρ in formula _w---winding conductor resistivity;

$k_{p-s}=1+\frac{{(r_0/\mathrm{\&delta;})}^4}{48+0.8{(r_0/\mathrm{\&delta;})}^4}---(1-23)$

$k_{p-x}=1+\frac{5{n^2}_1-1}{45}{{\mathrm{\&Delta;}}_0}^4---(1-24)$

r ₀＝d _p/1.772 (1-25)

Δ ₀＝d _p/δ (1-26)

Former limit winding copper loss is: P _p-cu=2I _p ²r _ac-p(1-27)

In like manner can obtain vice-side winding AC resistance is:

$R_{\mathrm{ac}-s}={\mathrm{\&rho;}}_w\frac{\mathrm{ML}{T}_s{n}_2}{S_s}{k}_{s-s}{k}_{s-x}---(1-28)$

MLT in formula _s---vice-side winding average turn is long;

K _s-s, k _s-x---the skin effect coefficient of vice-side winding and proximity effect coefficient;

$k_{s-s}=1+\frac{{(r_1/\mathrm{\&delta;})}^4}{48+0.8{(r_1/\mathrm{\&delta;})}^4}---(1-29)$

$k_{s-x}=1+\frac{5{n^2}_{2c}-1}{45}{{\mathrm{\&Delta;}}_1}^4---(1-30)$

r ₁＝d _s/2 (1-31)

Δ ₁＝d _s/δ (1-32)

N _2cfor the vice-side winding number of plies.

Vice-side winding copper loss is: P _s-cu=2I _s ²r _ac-s(1-33)

The total copper loss of transformer is: P _cu=P _p-cu+ P _s-cu(1-34)

10) calculate core loss, if core loss meets the demands, then perform step (11), otherwise the core loss formula getting back to step (3) unit mass be:

W/kg (watt/kg)=K _cf ^αb _m ^β(1-35)

K in formula _c, α, β---the dissipation constant (by acquisition of tabling look-up) that core material is given;

F---unit is Hz.

Then core loss is: P _fe=mK _cf ^αb _m ^β=ρ _cv _ck _cf ^αb _m ^β(1-36)

Total losses of transformer is: P _∑=P _cu+ P _fe(1-37)

Formula (1-11) is substituted into formula (1-20) cancellation current density, J, then

$P_{\mathrm{cu}}={\mathrm{\&rho;}}_w{V}_w{k}_u{\left(\frac{\mathrm{\&Sigma;VA}}{\mathrm{Kf}{B}_m{k}_f{k}_u{A}_p}\right)}^2=\frac{a}{f^2{B_m}^2}---(1-38)$

Can be reduced to by formula (1-36)

P _fe＝bf ^αB _m ^β (1-39)

Then total losses are $P_{\mathrm{\&Sigma;}}=P_0(\frac{1}{\mathrm{\&eta;}}-1)=\frac{a}{f^2{B_m}^2}+{\mathrm{bf}}^{\mathrm{\&alpha;}}{B_m}^{\mathrm{\&beta;}}---(1-40)$

When frequency f gives timing, to the close B of magnetic in formula (1-40) _mask partial derivative, and make it equal 0, namely

$\frac{\&PartialD;P_{\mathrm{\&Sigma;}}}{\&PartialD;B_m}=0---(1-41)$

Solve, when time, the loss of transformer is minimum, and transformer is most effective, and under equal conditions temperature rise is minimum.

$P_{\mathrm{cu}}=\frac{\mathrm{\&beta;}}{2}{P}_{\mathrm{fe}}---(1-42)$

11) based on the minimal losses formula of transformer, the insulation size of transformer and core configuration founding mathematical models, with the former limit number of turn and the secondary number of plies for optimized variable, efficiency is optimization aim, genetic algorithm is adopted to be optimized transformer, if meet the requirements, perform step (12), otherwise get back to step (3), optimization method:

Formula (1-3), (1-4) are substituted into formula (1-27), formula (1-27), (1-33), (1-23), (1-24), (1-29), (1-30) are substituted into equation (1-34) and obtain

$\begin{array}{c}{P}_{\mathrm{cu}}=2{\left(\frac{P_o/\mathrm{\&eta;}}{U_p}\right)}^2{\mathrm{\&rho;}}_w\frac{(1+\frac{{\left(\frac{r_0}{\mathrm{\&delta;}}\right)}^4}{48+0.8{\left(\frac{r_0}{\mathrm{\&delta;}}\right)}^4})(1+\frac{5{n_1}^2-1}{45}{{\mathrm{\&Delta;}}_0}^4)l_p}{S_p}\\ +2{I_s}^2{\mathrm{\&rho;}}_w\frac{(1+\frac{{\left(\frac{r_1}{\mathrm{\&delta;}}\right)}^4}{48+0.8{\left(\frac{r_1}{\mathrm{\&delta;}}\right)}^4})(1+\frac{5{n_{2c}}^2-1}{45}{{\mathrm{\&Delta;}}_0}^4)l_s}{S_s}\end{array}---(1-43)$

Equation (1-36), (1-43) are substituted into formula (1-42) and obtain

$\begin{array}{c}\frac{\mathrm{\&beta;}}{2}{V}_c{\mathrm{\&rho;}}_c{K}_c{f}^{\mathrm{\&alpha;}}{B_m}^{\mathrm{\&beta;}}=2{\left(\frac{P_o/\mathrm{\&eta;}}{U_p}\right)}^2{\mathrm{\&rho;}}_w\frac{(1+\frac{{\left(\frac{r_0}{\mathrm{\&delta;}}\right)}^4}{48+0.8{\left(\frac{r_0}{\mathrm{\&delta;}}\right)}^4})(1+\frac{5{n_1}^2-1}{45}{{\mathrm{\&Delta;}}_0}^4)l_p}{S_p}\\ +2{I_s}^2{\mathrm{\&rho;}}_w\frac{(1+\frac{{\left(\frac{r_1}{\mathrm{\&delta;}}\right)}^4}{48+0.8{\left(\frac{r_1}{\mathrm{\&delta;}}\right)}^4})(1+\frac{5{n_{2c}}^2-1}{45}{{\mathrm{\&Delta;}}_0}^4)l_s}{S_s}\end{array}---(1-44)$

Obtained by formula (1-40) and (1-42)

${2P}_{\mathrm{cu}}/\mathrm{\&beta;}+P_{\mathrm{cu}}=(\frac{1}{\mathrm{\&eta;}}-1)P_o---(1-45)$

Formula (1-43) is substituted into formula (1-45) to obtain

$(\frac{1}{\mathrm{\&eta;}}-1)P_o=(\frac{2}{\mathrm{\&beta;}}+1)\left(\begin{array}{c}2{\left(\frac{P_o/\mathrm{\&eta;}}{U_p}\right)}^2{\mathrm{\&rho;}}_w\frac{(1+\frac{{\left(\frac{r_0}{\mathrm{\&delta;}}\right)}^4}{48+0.8{\left(\frac{r_0}{\mathrm{\&delta;}}\right)}^4})(1+\frac{5{n_1}^2-1}{45}{{\mathrm{\&Delta;}}_0}^4)l_p}{S_p}\\ +2{I_s}^2{\mathrm{\&rho;}}_w\frac{(1+\frac{{\left(\frac{r_1}{\mathrm{\&delta;}}\right)}^4}{48+0.8{\left(\frac{r_1}{\mathrm{\&delta;}}\right)}^4})(1+\frac{5{n_{2c}}^2-1}{45}{{\mathrm{\&Delta;}}_0}^4)l_s}{S_s}\end{array}\right)---(1-46)$

Structural equation model (1-12) simultaneous of equation (1-7), (1-44), (1-46) and transformer is obtained

Five equations, six unknown number L are had in system of equations (1-47) _w, A _c, n ₁, V _c, η, n _2c, its limit, Central Plains number of turn n ₁, secondary number of plies n _2cwith transformer efficiency η value within the specific limits, set up majorized function based on system of equations:

$\left\{\begin{array}{c}\max \mathrm{\&eta;}(n_1,n_{2c},L_w,A_c,V_c)\\ G_i(n_1,n_{2c})<0,i=\mathrm{1,2},...m\\ H_j(n_1,n_{2c})=0,j=\mathrm{1,2}...s\end{array}\right.$

η (n ₁, n _2c, L _w, A _c, V _c) be objective function;

G _i(n ₁, n _2c) < 0 is m inequality constrain condition, as by power and cost limit former limit number of turn n ₁within the specific limits etc.;

H _j(n ₁, n _2c)=0 is about condition for s equation, as magnetic core active volume, window width computing formula etc.

With former limit number of turn n ₁, secondary number of plies n _2cfor optimized variable, transformer efficiency η is optimization aim, adopts genetic function to be optimized transformer, makes the maximizing efficiency of transformer, this system of equations is the minimal losses establishing equation based on transformer, also just means that the temperature rise of transformer is minimum under equal conditions.

Through genetic algorithm optimization optimizing in the present invention, as former limit number of turn n ₁=7, secondary number of plies n _2cwhen=10, the efficiency of transformer is maximum, coincide with the high frequency high voltage transformer actual parameter in the present invention.

12) determine the distribution parameter of transformer, if leakage inductance, distributed capacitance satisfy condition perform step (13), otherwise get back to step (1);

Conversion is to transformer primary side leakage inductance L _rcomputing formula:

$L_r=\frac{4\mathrm{\&pi;}\left(\mathrm{MTL}\right){n_1}^2}{h}\&times;(c+\frac{b+d}{3})\&times;{10}^{-9}---(1-48)$

The average turn of MTL in formula---winding is long;

The height of h---winding;

B---former limit winding thickness;

C---former and deputy limit winding spacing;

D---vice-side winding thickness.

Conversion is to transformer primary side leakage inductance Cp computing formula:

13) Temperature Rise Analysis of transformer and heat dissipation design

Heat loss through convection calculates:

For oil-filled transformer, when fluid is air, because the heat dissipation capacity of the per surface area of natural convection and the relation of temperature rise have the reference of following empirical formula:

Q _k＝2.5Q ₁ ^1.25(W/m ²) (1-50)

Q in formula _k---the Natural Heat Convection amount of per surface area, W/m ²;

Q ₁---temperature rise, K.

In addition, in heat loss through convection, the cooling effectiveness of oil is high a lot of air, and such as, when temperature is upgraded to 5K, the heat loss through convection coefficient of oil is 65W/m ²dEG C, and air is 3.74W/m ²dEG C.The heat that oil sheds in unit area because of heat loss through convection can calculate with following empirical formula:

Q _k＝38Q ₁ ^1.25(W/m ²) (1-51)

Heat loss through radiation calculates:

Experimentally and radiation law, the pass spilt between heat air and radiator color temperatures and surrounding objects (or air) temperature from tank wall by radiation is:

$q_{\mathrm{\&lambda;}}=C\frac{{(T_1/100)}^4-{(T_2/100)}^4}{T_1-T_2}(W/m^2)---(1-52)$

Q in formula _λ---when the temperature difference is 1 degree Celsius, by the heat that radiator per surface gives off;

T ₁, T ₂---the absolute temperature (K) of radiator and air or surrounding objects, that is:

T ₁＝273+t ₁，T ₂＝273+t ₂；

C---constant, relevant with the surface condition of radiating object, can adopt oil tank of transformer

C＝5W/m ²·K。

In order to convenience of calculation, experimentally above formula can be reduced to:

$q_{\mathrm{\&lambda;}}=2.8\sqrt[4]{Q_1}(W/m^2)---(1-53)$

Q in formula ₁=T ₁-T ₂, i.e. mailbox wall surface temperature (T ₁) and ambient air temperature (T ₂) difference.

For oil-filled transformer, the heat given off from mailbox all surfaces is:

Q _n＝q _λQ ₁F _λ(W) (1-54)

F in formula _λ---fuel tank radiation surface area, (m ²), be whole external surface area when fuel tank is plain tank; When fuel tank be tubular type tank or refrigeratory fuel tank time then for outer perimeter.

By formula $q_{\mathrm{\&lambda;}}=2.8\sqrt[4]{Q_1}(W/m^2)$ Substitute into above formula can obtain:

$Q_n=2.8\sqrt[4]{Q_1}{Q}_1{F}_{\mathrm{\&lambda;}}=2.8{Q_1}^{1.25}{F}_{\mathrm{\&lambda;}}\left(W\right)---(1-55)$

Therefore, total heat dissipation capacity that can obtain transformer is:

Q＝Q _k+Q _n＝2.5Q ₁ ^1.25F _k+2.8Q ₁ ^1.25F _λ＝(2.5F _k+2.8F _λ)Q ₁ ^1.25(W) (1-56)

Q in formula _k---heat loss through convection amount;

F _λ---heat loss through convection area.

Because the total area of dissipation of transformer is that heat loss through convection area adds heat loss through radiation area, that is:

F＝F _k+F _λ (1-57)

Simplified style obtains total heat dissipation capacity: Q=C ₁fQ ₁ ^1.25(1-58)

Coefficient of heat transfer C ₁relevant with temperature, but when the change of transformer temperature range of operation is little, its impact is negligible.

14) fuel tank size and cooling device is determined

The present invention adopts the gelled fuel tank of band, increases the area of dissipation of fuel tank, and adopts the type of cooling of Natural Oil Circulation Power, if temperature rise is undesirable, increases heat radiator quantity.

15) calculate temperature rise and with finite element analysis software (ANSYS), modeling and simulating carried out to transformer, if transformer temperature rise meets the demands, continuing next step, otherwise get back to step (13)

In transformer temperature rise calculates, usually core loss and winding loss are combined, i.e. P _∑=P _cu+ P _fe, and suppose that heat is evenly dissipated by the whole surface area of magnetic core and winding, then temperature rise is approximately:

$\mathrm{\&Delta;t}=\frac{P_{\mathrm{\&Sigma;}}}{K_k{S}_t}---(1-59)$

Wherein Δ t is for allowing temperature rise;

P _∑for total losses of transformer;

K _kfor heat transfer coefficient, to oil-filled transformer, K _k=5 × 10 ^-3w/ (DEG C cm ²); For dry-type transformer,

K _k＝1.25×10 ^-3W/(℃·cm ²)；

S _tfor the total surface area of transformer.

Air-cooled with under circulation oil-cooling condition, the temperature rise of transformer can reduce 40 ~ 50%.

16) calculating of transformer weight and physical dimension are drawn;

17) transformer material is selected and transformer assembling.

As shown in Figure 5, be genetic algorithm optimization process flow diagram, concrete steps are as follows:

Step 1: the majorized function being built genetic algorithm by Transformer Model, considers the complicacy of mathematical model, sets up two majorized function W ₁, W ₂, and W ₁, W ₂with efficiency eta positive correlation:

$W_1=\frac{2P_o}{2P_o+A_c\&times;(2h_1+2L_w+4\sqrt{A_c}){\mathrm{\&rho;}}_c{K}_c{f}^{\mathrm{\&alpha;}}{B_m}^{\mathrm{\&beta;}}(2+\mathrm{\&beta;})}$

$W_2=\frac{1}{|2\&times;(\frac{{\left(\frac{P_o}{W_1{U}_p}\right)}^2{\mathrm{\&rho;}}_w{k}_{p-s}{k}_{p-x}{l}_p}{S_p}+\frac{{I_s}^2{\mathrm{\&rho;}}_w{k}_{s-s}{k}_{s-x}{l}_s}{S_s})-\frac{\mathrm{\&beta;}}{2}{V}_c{\mathrm{\&rho;}}_c{K}_c{f}^{\mathrm{\&alpha;}}{B_m}^{\mathrm{\&beta;}}|}$

Wherein P _othe output power of indication transformer; U _prepresent former limit input voltage; A _crepresent that core cross section amasss; h ₁represent magnetic core window height; L _wrepresent magnetic core window width; ρ _crepresent magnetic core density; K _c, α, β be the dissipation constant of core material, by acquisition of tabling look-up; The frequency of f indication transformer; B _mthe magnetic flux density of indication transformer; ρ _wrepresent the resistivity of copper conductor; k _p-s, k _p-xrepresent skin effect coefficient and the proximity effect coefficient of former limit winding respectively; k _s-s, k _s-xrepresent skin effect coefficient and the proximity effect coefficient of vice-side winding respectively; l _p, l _srepresent the winding length of former secondary respectively; S _p, S _srepresent the sectional area of the winding of former secondary respectively; V _crepresent the volume of magnetic core.

L _w＝2×(L ₁+n ₁×L ₂+L ₃+n _2c×L ₄)+L ₅

A _c＝U _p/Kfn ₁k _fB _m

Step 2: definition iterations and the parameter for optimizing high frequency high voltage transformer, and treat to deal with problems and encode;

The former limit number of turn n of initialization transformer ₁with vice-side winding number of plies n _2cand iterations N.

n _1-min＜n ₁＜n _1-max，n _2c-min＜n _2c＜n _2c-max，N≤N _max

Step 3: random initializtion colony P (0)=(p ₁, p ₂, p ₃p _m), generally N=20 ~ 200;

Step 4: set up fitness function according to objective function, and the fitness value (F) calculating each individuality in colony;

max1＝max(W ₁)

min1＝min(W ₁)

max2＝max(W ₂)

min2＝min(W ₂)

M1＝1/(max1-min1)

M2＝1/(max2-min2)

Then fitness function is: F=(W ₁-min1) × M1+ (W ₂-min2) × M2

Step 5: assessment fitness, to individual p each in current group P (t) _icalculate its fitness F (i), fitness illustrates the performance quality of this individuality; Adopt with the individual fitness of formula p (i)=F (i)/sum (F) assessment, the larger fitness of proportion accounted in every generation colony is higher.

Step 6: for Pr (t) in the middle of producing by certain the regular application choice operator determined by ideal adaptation angle value;

Step 7: according to P _cselect individuality to carry out interlace operation, generally get P _c=0.6 ~ 1.0;

Step 8: according to P _mmutation operation is carried out to breeding individuality; Generally get P _m=0.005 ~ 0.05;

Step 9: judge whether end condition meets, if met, optimizes and terminates, saving result, if do not met, turn back to step 4;

Rule of judgment: $\left\{\begin{array}{c}{n}_{1-\min }<n_1<n_{1-\max }\\ n_{2c-\min }<n_{2c}<n_{2c-\max }\\ N>N_{\max }\end{array}\right.$

Just terminate if satisfy condition to optimize, otherwise continue iteration, until reach maximum iteration time.

Step 10: the individuality exporting fitness value optimum in population.

In addition to the implementation, the present invention can also have other embodiments, and all employings are equal to the technical scheme of replacement or equivalent transformation formation, all drop in the protection domain of application claims.

Claims (5)

1., based on a high frequency high voltage transformer design optimization method for genetic algorithm, it is characterized in that, comprise the following steps:

Step 1: based on the minimal losses formula of transformer, the insulation size of transformer and core configuration founding mathematical models, mathematical model is:

U in formula _pfor original edge voltage, K is form factor, and f is frequency of operation, B _moperating magnetic field flux density, ρ _cfor iron core density, ρ _wthe resistivity of winding conductor, n ₁the former limit number of turn, n _2cbe the secondary number of plies, η is transformer efficiency, l _p, l _sformer and deputy limit winding length respectively, S _p, S _sthat former and deputy limit winding cross section amasss respectively, P _oit is winding output power;

Step 2: the majorized function being built genetic algorithm by Transformer Model, considers the complicacy of mathematical model, sets up two majorized function W ₁, W ₂, and W ₁, W ₂with efficiency eta positive correlation:

$W_1=\frac{2P_o}{2P_o+A_c\&times;(2h_1+2L_w+4\sqrt{A_c}){\mathrm{\&rho;}}_c{K}_c{f}^{\mathrm{\&alpha;}}{B_m}^{\mathrm{\&beta;}}(2+\mathrm{\&beta;})}$

$W_2=\frac{1}{|2\&times;(\frac{{\left(\frac{P_o}{W_1{U}_p}\right)}^2{\mathrm{\&rho;}}_w{k}_{p-s}{k}_{p-x}{l}_p}{S_p}+\frac{{I_s}^2{\mathrm{\&rho;}}_w{k}_{s-s}{k}_{s-x}{l}_s}{S_s})-\frac{\mathrm{\&beta;}}{2}{V}_c{\mathrm{\&rho;}}_c{K}_c{f}^{\mathrm{\&alpha;}}{B_m}^{\mathrm{\&beta;}}|}$

Wherein P _othe output power of indication transformer; U _prepresent former limit input voltage; A _crepresent that core cross section amasss; h ₁represent magnetic core window height; L _wrepresent magnetic core window width; ρ _crepresent magnetic core density; K _c, α, β be the dissipation constant of core material, by acquisition of tabling look-up; The frequency of f indication transformer; B _mthe magnetic flux density of indication transformer; ρ _wrepresent the resistivity of copper conductor; k _p-s, k _p-xrepresent skin effect coefficient and the proximity effect coefficient of former limit winding respectively; k _s-s, k _s-xrepresent skin effect coefficient and the proximity effect coefficient of vice-side winding respectively; l _p, l _srepresent the winding length on former and deputy limit respectively; S _p, S _srepresent the sectional area of the winding on former and deputy limit respectively; V _crepresent the volume of magnetic core;

L _w＝2×(L ₁+n ₁×L ₂+L ₃+n _2c×L ₄)+L ₅

A _c＝U _p/Kfn ₁k _fB _m

Step 3: definition iterations and the parameter for optimizing high frequency high voltage transformer, and treat to deal with problems and encode; The former limit number of turn n of initialization transformer ₁with vice-side winding number of plies n _2cand iterations N;

n _1-min＜n ₁＜n _1-max，n _2c-min＜n _2c＜n _2c-max，N≤N _max

Step 4: random initializtion colony P (0)=(p ₁, p ₂, p ₃p _n);

Step 5: set up fitness function according to objective function, and the fitness value (F) calculating each individuality in colony;

max1＝max(W ₁)

min1＝min(W ₁)

max2＝max(W ₂)

min2＝min(W ₂)

M1＝1/(max1-min1)

M2＝1/(max2-min2)

Then fitness function is: F=(W ₁-min1) × M1+ (W ₂-min2) × M2;

Step 6: assessment fitness, to individual p each in current group P (t) _icalculate its fitness F (i), fitness illustrates the performance quality of this individuality; Adopt the fitness that formula p (i)=F (i)/sum (F) assessment is individual, the larger fitness of proportion accounted in every generation colony is higher;

Step 7: for Pr (t) in the middle of producing by the regular application choice operator determined by ideal adaptation angle value;

Step 8: according to P _cindividuality is selected to carry out interlace operation;

Step 9: according to P _mmutation operation is carried out to breeding individuality;

Step 10: judge whether end condition meets, if met, optimizes and terminates, saving result, if do not met, turn back to step 5;

Rule of judgment: $\left\{\begin{array}{c}{n}_{1-\min }<n_1<n_{1-\max }\\ n_{2c-\min }<n_{2c}<n_{2c-\max }\\ N>N_{\max }\end{array}\right.$

Just terminate if satisfy condition to optimize, otherwise continue iteration, until reach maximum iteration time;

Step 11: the individuality exporting fitness value optimum in population.

2., as claimed in claim 1 based on the high frequency high voltage transformer design optimization method of genetic algorithm, it is characterized in that, P (0)=(p of described step 4 ₁, p ₂, p ₃p _n), n gets 20 ~ 200.

3. as claimed in claim 1 based on the high frequency high voltage transformer design optimization method of genetic algorithm, it is characterized in that, the selection opertor of described step 7 is Wheel-type selection opertor or random unanimously selection opertor or algorithm of tournament selection operator.

4., as claimed in claim 1 based on the high frequency high voltage transformer design optimization method of genetic algorithm, it is characterized in that, the P of described step 8 _c=0.6 ~ 1.0.

5., as claimed in claim 1 based on the high frequency high voltage transformer design optimization method of genetic algorithm, it is characterized in that, the P of described step 9 _m=0.005 ~ 0.05.