CN105118647A - Determining method for optimal working frequency of large-capacity high-frequency transformer - Google Patents

Abstract

The invention belongs to the field of design of high-frequency transformers and particularly relates to a determining method for the optimal working frequency of a large-capacity high-frequency transformer. The determining method is characterized in that the material of a transformer core is determined, the working frequency f is initially selected, relevant parameters are obtained, the area value Ap of the high-frequency transformer is calculated, and the dimension of the initially-selected core is determined according to Ap; the relational expression of the working magnetic flux density B and the wire current density J relative to the frequency is established; the relation of the equivalent dimension SF and the initially-selected working frequency f of the size of the high-frequency transformer is established, and the initially-selected optimal working frequency value fopt of the transformer is derived; the area value A'p of the high-frequency transformer under the initially-selected optimal working frequency value fopt is calculated, and the corresponding core size value is determined. The determining method for the optimal working frequency of the large-capacity high-frequency transformer can be applied to determining of optimal working frequency in designing high-frequency transformers with different magnetic core materials and different voltage grades on primary and secondary sides, the workload can be effectively reduced when the design sizes of the transformer is reduced to the maximum, and the calculating time is saved.

Description

The defining method of Large Copacity high frequency transformer optimum working frequency

Technical field

The invention belongs to high frequency transformer design field, particularly a kind of defining method of Large Copacity high frequency transformer optimum working frequency.

Background technology

Based on power electronic technology, Chinese scholars start exploratory development realize transformation of electrical energy novel intelligent Bian Ya Qi ?electric power electric transformer (PowerElecronicTransformer, be called for short PET), also claim solid-state transformer (Solid ?StateTransformer, be called for short SST).Electric power electric transformer is equipped as the novel power transformation that a kind of height is controlled, and its outstanding feature is the flexible control that can realize transformer primary secondary voltage amplitude and phase place, to meet many new demands of intelligent grid future development.And in the realization of the high-power topology of electric power electric transformer, middle high frequency transformer body is the most basic is also most important electromagnetic component.Along with design capacity improves constantly, volume of transformer constantly increases, and the method by promoting operating frequency reduces the physical size of high frequency transformer body.

High frequency transformer, compared with traditional transformer, it is advantageous that: during same design capacity, and the physical size of high frequency transformer significantly reduces; Magnetic core used is lighter, and wire is less, and dielectric is less; Application is more extensive, such as: field of distribution network, and direct current transportation field, and following intelligent grid field.Be used in power electronics topology, the electric power electric transformer of composition can realize the flexible control to former secondary voltage amplitude and phase place, can meet many new demands of intelligent grid future development.

Along with the development of power electronic technology, following electric power electric transformer capacity can be larger, and volume can be less, and implement device is integrated more, can be less for high frequency transformer volume requirement wherein.So, be necessary, under particular design capacity and work magnetic are close, find a kind of defining method of Large Copacity high frequency transformer optimum working frequency, make the design volume of high frequency transformer minimum, with the growth requirement of satisfied following high frequency transformer.

Prior art does not adopt optimum working frequency defining method for the volume reducing transformer.And prior art is: under particular design capacity and work magnetic are close, progressively improve operating frequency, determine the magnetic core size under operating frequency each time and winding arrangement, calculate core loss and winding loss value, and the temperature rise value under calculating operating frequency each time, see and whether exceed temperature rise limits value, if do not exceed temperature rise limits value, so just continue to improve operating frequency, if upper once improve operating frequency time, temperature rise exceedes limits value, and operating frequency value when so just selecting last is as final operating frequency.So prior art is for the volume reducing transformer, and amount of calculation is large, loaded down with trivial details, needs the expensive time, is unfavorable for engineer applied.And the inventive method, effectively reduce amount of calculation, save computing time, convenient and swift, be conducive to engineer applied.

Summary of the invention

For the problems referred to above, the present invention proposes a kind of defining method of Large Copacity high frequency transformer optimum working frequency, comprising:

Step 1: the material determining magnetic core of transformer, according to core material, determines core loss coefficient value K _m, α and β value; Wire adopt multiply and around litz wire;

Step 2: determine primary election operating frequency f, according to primary election operating frequency f and wire GB or AWG wire gauge table, determines the diameter d of single cord in wire _c, the conductivityσ of wire; According to former limit winding rated current I ₁, vice-side winding rated current I ₂with the current density, J of wire, calculate the number of share of stock N of former limit wire ₁with the number of share of stock N of secondary wire ₂;

Step 3: the area product value A calculating high frequency transformer _p, according to A _pdetermine magnetic core size; According to winding loss P _wexpression and unit volume core loss P _cexpression formula, obtain the relational expression of current density, J about frequency of the close B of work magnetic and wire respectively;

Step 4: under setting up particular design capacity S and the close B condition of work magnetic according to step 3, the equivalent dimension SF of high frequency transformer volume and the relational expression of primary election operating frequency f; Differentiate is carried out to the primary election operating frequency f in this formula, under obtaining particular design capacity and the close condition of work magnetic, the primary election optimum working frequency f of transformer _opt;

Step 5: calculate primary election optimum working frequency value f _optunder high frequency transformer area product value A ' _p, according to high frequency transformer area product value A ' _p, determine corresponding magnetic core size value;

Step 6: according to the primary election optimum working frequency f obtained in step 4 and step 5 _optafter magnetic core size, determine that the winding of transformer is arranged, calculate core loss P ' respectively _cwith winding loss P ' _w, determine that the temperature rise of high frequency transformer is in the limits value allowed; If the temperature rise value calculated has exceeded the temperature rise limits value allowed, then turn back to step 2 and redefined primary election operating frequency f; If the temperature rise of high frequency transformer is in the limits value of permission, then primary election optimum working frequency f now _optfor particular design capacity and the optimum working frequency f ' of the close lower high frequency transformer of work magnetic _opt, the volume of now corresponding transformer is minimum.

Winding loss P in described step 3 _wcalculating formula be

$P_w=\frac{(W_1{\mathrm{MLT}}_1+W_2{\mathrm{MLT}}_2)J^2}{\mathrm{\σ}}\×(1+{\mathrm{\αf}}^2)\∝\frac{1}{SF}$

The gross area of limit, formula Central Plains winding conducting wire the gross area of vice-side winding wire mLT ₁for the average turn of former limit winding is long, MLT ₂for the average turn of vice-side winding is long, n ₁for former limit umber of turn, n ₂for the vice-side winding number of turn.

Current in wire density J in described step 3 about the relational expression of frequency is

$J\∝{(1+{\mathrm{\αf}}^2)}^{-\frac{1}{2}}\·{\mathrm{SF}}^{-\frac{1}{2}}.$

Under particular design capacity S in described the step 4 and close B of work magnetic, the equivalent dimension SF of high frequency transformer volume and the relational expression of primary election operating frequency f are

${\mathrm{SF}}^{\frac{7}{2}-\frac{1}{\mathrm{\β}}}\∝\[\frac{(1+\mathrm{\η})S}{f^{1-\frac{\mathrm{\α}}{\mathrm{\β}}}\·{(1+{\mathrm{\αf}}^2)}^{-\frac{1}{2}}}\]$

According to Steinmetz empirical equation, closing for its loss factor of substantially all magnetic cores is 3.5> β > α >1, and η is high frequency transformer efficiency.

Under particular design capacity S in described the step 4 and close B of work magnetic, the primary election optimum working frequency value f of transformer _optexpression formula be

$f_{opt}=\sqrt{\frac{1}{b}\left(\frac{\mathrm{\β}}{\mathrm{\α}}-1\right)}$

Intermediate variable in formula k _cufor the activity coefficient of winding, μ ₀for permeability of vacuum, c _wfor winding height.

The activity coefficient k of the winding of described litz wire _cufor 0.2-0.3, the conductivity of wire is different along with the wire diameter difference of sub-thread litz wire, and the current density, J of wire is 3-4A/mm ².

The structure of described magnetic core is UU type, and when determining magnetic core size, magnetic core window height value remains unchanged.

Beneficial effect

The inventive method can be applied to the determination of optimum working frequency in the high frequency transformer design of different core material electric pressure different from former secondary, can reduce the design volume of transformer substantially.Prior art is for the volume reducing transformer, and amount of calculation is large, loaded down with trivial details, needs the expensive time, is unfavorable for engineer applied; And the inventive method, effectively reduce amount of calculation, save computing time, convenient and swift, be conducive to engineer applied

Accompanying drawing explanation

Fig. 1 is Litz wire figure

Fig. 2 is UU type core structure figure

Fig. 3 is UU type core transformers Central Plains vice-side winding layout plan

Fig. 4 is the determination method flow diagram of Large Copacity high frequency transformer optimum working frequency of the present invention

Embodiment

Below in conjunction with the drawings and specific embodiments, that the present invention will be further described is as follows:

Fig. 4 is the determination method flow diagram of Large Copacity high frequency transformer optimum working frequency of the present invention.

A defining method for Large Copacity high frequency transformer optimum working frequency, is characterized in that:

Step 1: the material determining magnetic core of transformer, according to core material, determines core loss coefficient value K _m, α and β value; Wire adopt multiply and around litz wire;

Step 2: determine primary election operating frequency f, according to primary election operating frequency f and wire GB or AWG wire gauge table, determines the diameter d of single cord in wire _c, the conductivityσ of wire; According to former limit winding rated current I ₁, vice-side winding rated current I ₂with the current density, J of wire, calculate the number of share of stock N of former limit wire ₁with the number of share of stock N of secondary wire ₂;

Step 3: the area product value A calculating high frequency transformer _p, according to A _pdetermine magnetic core size; According to winding loss P _wexpression and unit volume core loss P _cexpression formula, obtain the relational expression of current density, J about frequency of the close B of work magnetic and wire respectively;

Step 4: under setting up particular design capacity S and the close B condition of work magnetic according to step 3, the equivalent dimension SF of high frequency transformer volume and the relational expression of primary election operating frequency f; Differentiate is carried out to the primary election operating frequency f in this formula, under obtaining particular design capacity and the close condition of work magnetic, the primary election optimum working frequency f of transformer _opt;

Step 5: calculate primary election optimum working frequency value f _optunder high frequency transformer area product value A ' _p, according to high frequency transformer area product value A ' _p, determine corresponding magnetic core size value; As shown in Figure 2, core structure is UU type

Step 6: according to the primary election optimum working frequency f obtained in step 4 and step 5 _optafter magnetic core size, determine that the winding of transformer is arranged, as shown in Figure 3; Calculate core loss P ' respectively _cwith winding loss P ' _w, determine that the temperature rise of high frequency transformer is in the limits value allowed; If the temperature rise value calculated has exceeded the temperature rise limits value allowed, then turn back to step 2 and redefined primary election operating frequency f; If the temperature rise of high frequency transformer is in the limits value of permission, then primary election optimum working frequency f now _optfor particular design capacity and the optimum working frequency f ' of the close lower high frequency transformer of work magnetic _opt, the volume of now corresponding transformer is minimum.

Because design of transformer volume is not only arranged relevant with core structure, winding, and it is closely related with the radiating mode and insulation mode etc. of transformer, therefore, if the simple length that volume of transformer is actual calculates, the volume of transformer expression formula so obtained will be very complicated, be unfavorable for theory analysis.So, be necessary to find a parameter that can replace volume of transformer.Suppose that magnetic core of transformer shape and winding activity coefficient are constant, so the length of transformer can replace with same equivalent dimension SF, so has the expression formula of volume of transformer to be:

V∝SF ³(1)

In the design of transformer theory of classics, transformer area amasss A _pbe the selection standard of transformer core size, the magnetic core area product value of actual selection is more long-pending than the magnetic core area calculated greatly a bit.The area of transformer amasss A _pbe worth larger, so final design of transformer volume is also larger, and the expression formula that transformer area amasss is:

$A_p=A_c\×A_w=\frac{(1+\frac{1}{\mathrm{\η}})}{K_f{K}_{u}BJf}\∝{\mathrm{SF}}^4---\left(2\right)$

Wherein, A _cand A _wrepresent high frequency transformer magnetic core sectional area and window area respectively, K _frepresent form factor, time sinusoidal wave, K _f=4.44, during square wave, K _f=4, K _urepresent the usage factor of winding, generally for the winding configuration utilizing Litz line wire type, its K _ube 0.2 ?0.3, B be that work magnetic is close, f is operating frequency, and J is current in wire density, and S is design capacity, and η is high frequency transformer efficiency.

When the radiating mode of transformer does not change, so the equivalent dimension SF of transformer loss and transformer is inversely proportional to, i.e. P ∝ 1/SF.

Utilize Steinmetz empirical equation, under sinusoidal excitation, for magnetic core of transformer, the expression formula of unit volume core loss is:

$P_c=K_m{f}^{\mathrm{\α}}{B}^{\mathrm{\β}}\∝\frac{1}{SF}---\left(3\right)$

Wherein, K _m, α and β be core loss coefficient, for specific core material, K _m, α and β be constant.

For Large Copacity high frequency transformer, wire has skin effect, so the diameter of wire of employing is less than 2 times of skin depth.For the current carrying area that wire is total, wire adopt multiply and around Litz line (wherein, the single cord wire diameter of the inside is 2 times that are less than skin depth), can reach required total current carrying area on the one hand, be the eddy current loss caused to reduce conductor skin effect on the other hand.Multiply Litz is shown in shown in accompanying drawing 1, and the interchange winding coefficient calculating formula of transformer primary vice-side winding is respectively:

$F_{r1}=1+\frac{{\mathrm{\π}}^2{\mathrm{\ω}}^2{{\mathrm{\μ}}_0}^2{N_1}^2{n_1}^2{d_c}^{6}k}{768{\mathrm{\ρ}}^2{b_c}^2}---\left(4\right)$

$F_{r2}=1+\frac{{\mathrm{\π}}^2{\mathrm{\ω}}^2{{\mathrm{\μ}}_0}^2{N_2}^2{n_2}^2{d_c}^{6}k}{768{\mathrm{\ρ}}^2{b_c}^2}---\left(5\right)$

Wherein, N ₁and N ₂be respectively the number of share of stock of former vice-side winding Litz line, n ₁and n ₂be respectively the number of turn of former vice-side winding, d _cfor single cord diameter in multiply Litz line, μ ₀for permeability of vacuum, ρ is the resistivity of wire, and ω is angular frequency, and k is the breadth coefficient in transformer multi-layer winding magnetic field, usually its value 1.

Suppose that former vice-side winding height is identical, after simplifying (4) and (5) formula, the interchange winding coefficient of former vice-side winding is equal, and the former secondary after namely simplifying exchanges winding coefficient and is:

F _r1＝F _r2＝1+af ²(6)

$a=\frac{1}{48}{\left({\mathrm{\πk}}_{cu}{\mathrm{\σ\μ}}_0{c}_w{d}_c\right)}^2---\left(7\right)$

Wherein, k _cufor the activity coefficient of winding, σ is the conductivity of winding, μ ₀for permeability of vacuum, c _wfor winding height, d _cfor the diameter of single cord, b _cfor magnetic core window width, see shown in accompanying drawing 3.

Winding loss calculating formula is as follows:

P _w＝F _r1I ₁ ²R _dc1+F _r2I ₂ ²R _dc2(8)

Wherein, F _r1and F _r2for the interchange winding coefficient of former vice-side winding, I ₁and I ₂for former vice-side winding load current value, R _dc1and R _dc2be respectively the DC resistance of former vice-side winding.

Former secondary winding current and D.C. resistance calculating formula as follows:

$I_1=J\×\mathrm{\π}{\left(\frac{d_c}{2}\right)}^2{N}_1---\left(9\right)$

$I_2=J\×\mathrm{\π}{\left(\frac{d_c}{2}\right)}^2{N}_2---\left(10\right)$

$R_{dc1}=\frac{1}{\mathrm{\σ}}\frac{{\mathrm{MLT}}_1\×n_1}{\mathrm{\π}{\left(\frac{d_c}{2}\right)}^2{N}_1}---\left(11\right)$

$R_{dc2}=\frac{1}{\mathrm{\σ}}\frac{{\mathrm{MLT}}_2\×n_2}{\mathrm{\π}{\left(\frac{d_c}{2}\right)}^2{N}_2}---\left(12\right)$

Wherein, J is the current density of wire, N ₁for former limit winding L itz strand count, N ₂for vice-side winding Litz strand count, n ₁for former limit umber of turn, n ₂for the vice-side winding number of turn, MLT ₁for the average turn of former limit winding is long, MLT ₂for the average turn of vice-side winding is long.

(9) to (12) formula is brought into (8) formula, and calculating winding loss calculating formula is:

$P_w=\frac{(W_1{\mathrm{MLT}}_1+W_2{\mathrm{MLT}}_2)J^2}{\mathrm{\σ}}\×(1+{\mathrm{\αf}}^2)\∝\frac{1}{SF}---\left(13\right)$

$W_1=\mathrm{\π}{\left(\frac{d_c}{2}\right)}^2{N}_1{n}_1---\left(14\right)$

$W_2=\mathrm{\π}{\left(\frac{d_c}{2}\right)}^2{N}_2{n}_2---\left(15\right)$

Wherein, W ₁and W ₂represent the gross area of former limit winding and vice-side winding copper conductor respectively.

According to formula (3) and (13), calculate the relational expression of the close B of work magnetic and current in wire density J about frequency f:

$B\∝{\mathrm{SF}}^{-\frac{1}{\mathrm{\β}}}\·f^{-\frac{\mathrm{\α}}{\mathrm{\β}}}---\left(16\right)$

$J\∝{(1+{\mathrm{af}}^2)}^{-\frac{1}{2}}\·{\mathrm{SF}}^{-\frac{1}{2}}---\left(17\right)$

Formula (16) and (17) are brought in formula (2), calculate particular design capacity and work magnetic close under, the equivalent dimension SF of high frequency transformer volume and the relational expression of frequency f:

${\mathrm{SF}}^{\frac{7}{2}-\frac{1}{\mathrm{\β}}}\∝\[\frac{(1+\mathrm{\η})S}{f^{1-\frac{\mathrm{\α}}{\mathrm{\β}}}\·{(1+{\mathrm{\αf}}^2)}^{-\frac{1}{2}}}\]---\left(18\right)$

Consider that, for substantially all magnetic cores, in Steinmetz empirical equation, loss factor relation is: 3.5> β > α >1.By high frequency transformer volume V ∝ SF ³, when namely SF exists minimum value, just there is minimum value in volume V.As can be seen from formula (18), equivalent dimension SF, under a certain frequency f, also exists minimum value.So, formula (18) is carried out differentiate to frequency f, calculate particular design capacity and work magnetic close under, when transformer exists minimum volume, corresponding optimum working frequency is:

$f_{opt}=\sqrt{\frac{1}{b}\left(\frac{\mathrm{\β}}{\mathrm{\α}}-1\right)}---\left(19\right)$

$a=\frac{1}{48}{\left({\mathrm{\πk}}_{cu}{\mathrm{\σ\μ}}_0{c}_w{d}_c\right)}^2---\left(20\right)$

Wherein, α and β is core loss coefficient, k _cufor the activity coefficient of winding, σ is the conductivity of winding conducting wire, μ ₀for permeability of vacuum, c _wfor winding height, d _cfor the diameter of single cord.

As can be seen from formula (19) and (20), there is optimum working frequency f during minimal design volume in particular design capacity and the close lower high frequency transformer of work magnetic _optrelevant with the loss characteristic of high frequency magnetic core, winding construction and conductor material characteristic.

The above, be only a kind of embodiment that the present invention calculates, can not be interpreted as the restriction to protection scope of the present invention, and the person skilled in the art in this field without departing from the spirit and scope of the present invention, can also make some and improve and adjustment.Therefore all equivalent technical schemes also belong to category of the present invention, and protection scope of the present invention should be as the criterion with the protection range of claim.

Claims (7)

1. a defining method for Large Copacity high frequency transformer optimum working frequency, is characterized in that:

Step 1: the material determining magnetic core of transformer, according to core material, determines core loss coefficient value K _m, α and β value; Wire adopt multiply and around litz wire;

Step 2: determine primary election operating frequency f, according to primary election operating frequency f and wire GB or AWG wire gauge table, determines the diameter d of single cord in wire _c, the conductivityσ of wire; According to former limit winding rated current I ₁, vice-side winding rated current I ₂with the current density, J of wire, calculate the number of share of stock N of former limit wire ₁with the number of share of stock N of secondary wire ₂;

Step 3: the area product value A calculating high frequency transformer _p, according to A _pdetermine magnetic core size; According to winding loss P _wexpression and unit volume core loss P _cexpression formula, obtain the relational expression of current density, J about frequency of the close B of work magnetic and wire respectively;

Step 4: under setting up particular design capacity S and the close B condition of work magnetic according to step 3, the equivalent dimension SF of high frequency transformer volume and the relational expression of primary election operating frequency f; Differentiate is carried out to the primary election operating frequency f in this formula, under obtaining particular design capacity and the close condition of work magnetic, the primary election optimum working frequency f of transformer _opt;

Step 5: calculate primary election optimum working frequency value f _optunder high frequency transformer area product value A ' _p, according to high frequency transformer area product value A ' _p, determine corresponding magnetic core size value;

Step 6: according to the primary election optimum working frequency f obtained in step 4 and step 5 _optafter magnetic core size, determine that the winding of transformer is arranged, calculate core loss P ' respectively _cwith winding loss P ' _w, determine that the temperature rise of high frequency transformer is in the limits value allowed; If the temperature rise value calculated has exceeded the temperature rise limits value allowed, then turn back to step 2 and redefined primary election operating frequency f; If the temperature rise of high frequency transformer is in the limits value of permission, then primary election optimum working frequency f now _optfor particular design capacity and the optimum working frequency f ' of the close lower high frequency transformer of work magnetic _opt, the volume of now corresponding transformer is minimum.

2. method according to claim 1, is characterized in that: the winding loss P in described step 3 _wcalculating formula be

$P_w=\frac{(W_1{\mathrm{MLT}}_1+W_2{\mathrm{MLT}}_2)J^2}{\mathrm{\σ}}\×(1+{\mathrm{\αf}}^2)\∝\frac{1}{SF}$

The gross area of limit, formula Central Plains winding conducting wire the gross area of vice-side winding wire mLT ₁for the average turn of former limit winding is long, MLT ₂for the average turn of vice-side winding is long, n ₁for former limit umber of turn, n ₂for the vice-side winding number of turn.

3. method according to claim 1, is characterized in that: the current in wire density J in described step 3 about the relational expression of frequency is

$J\∝{(1+{\mathrm{\αf}}^2)}^{-\frac{1}{2}}\·{\mathrm{SF}}^{-\frac{1}{2}}.$

4. method according to claim 1, is characterized in that: under the particular design capacity S in described the step 4 and close B of work magnetic, the equivalent dimension SF of high frequency transformer volume and the relational expression of primary election operating frequency f are

${\mathrm{SF}}^{\frac{7}{2}-\frac{1}{\mathrm{\β}}}\∝\[\frac{(1+\mathrm{\η})S}{f^{1-\frac{\mathrm{\α}}{\mathrm{\β}}}\·{(1+{\mathrm{\αf}}^2)}^{-\frac{1}{2}}}\]$

According to Steinmetz empirical equation, closing for its loss factor of substantially all magnetic cores is 3.5> β > α >1, and η is high frequency transformer efficiency.

5. method according to claim 1, is characterized in that: under the particular design capacity S in described the step 4 and close B of work magnetic, the primary election optimum working frequency value f of transformer _optexpression formula be

$f_{opt}=\sqrt{\frac{1}{b}\left(\frac{\mathrm{\β}}{\mathrm{\α}}-1\right)}$

Intermediate variable in formula k _cufor the activity coefficient of winding, μ ₀for permeability of vacuum, c _wfor winding height.

6. method according to claim 1, is characterized in that: the activity coefficient k of the winding of described litz wire _cufor 0.2-0.3, the conductivity of wire is different along with the wire diameter difference of sub-thread litz wire, and the current density, J of wire is 3-4A/mm ².

7. method according to claim 1, is characterized in that: the structure of described magnetic core is UU type, and when determining magnetic core size, magnetic core window height value remains unchanged.