CN105118647B - The determination method of Large Copacity high frequency transformer optimum working frequency - Google Patents
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Abstract
The invention belongs to high frequency transformer design field, more particularly to a kind of determination method of Large Copacity high frequency transformer optimum working frequency.It is characterized in that：Determine material, the primary election working frequency f of magnetic core of transformer, obtain relevant parameter, calculate the area product value A of high frequency transformerp, according to ApDetermine the size of primary election magnetic core；Set up the work magnetic relational expression of close B and current in wire density J on frequency；Set up under particular design capacity S and the close B of work magnetic, the relational expression of the equivalent dimension SF and primary election working frequency f of high frequency transformer volume, derivation obtains the primary election optimum working frequency value f of transformeropt；Calculate primary election optimum working frequency value foptUnder high frequency transformer area product value A 'p, it is determined that corresponding magnetic core size value.Present invention can apply to the determination of optimum working frequency in the high frequency transformer design of different core materials voltage class different with former secondary, when the design volume of transformer is substantially reduced, amount of calculation can be efficiently reduced, save the calculating time.
Description
Technical field
The invention belongs to high frequency transformer design field, more particularly to a kind of Large Copacity high frequency transformer optimum working frequency
Determination method.
Background technology
Based on Power Electronic Technique, domestic and foreign scholars start exploratory development realize the Novel intelligent transformer of transformation of electrical energy-
Electric power electric transformer (Power Elecronic Transformer, abbreviation PET), also referred to as solid-state transformer (Solid-
State Transformer, abbreviation SST).Electric power electric transformer is equipped as a kind of highly controllable new power transformation, and it is dashed forward
Go out the flexible control that feature is that by transformer primary secondary voltage amplitude and phase, to meet intelligent grid future development
Many new demands.And in the realization of the high-power topology of electric power electric transformer, middle high frequency transformer body is most
Basis is also most important electromagnetic component.As design capacity is improved constantly, volume of transformer constantly increases, can be by lifting work
The method of working 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, the thing of high frequency transformer
Reason volume is substantially reduced；Magnetic core used is lighter, and wire is less, and dielectric is less；Application field is more extensive, such as：Match somebody with somebody
Electrical network field, direct current transportation field, and following intelligent grid field.In power electronics topology, the power electronics of composition
Transformer can realize the flexible control to former secondary voltage amplitude and phase, can meet many new of intelligent grid future development
It is required that.
With the development of Power Electronic Technique, following electric power electric transformer capacity can be bigger, and volume can be smaller, more
Realize that device is integrated, can be smaller for high frequency transformer volume requirement therein.Thus, it is necessary in particular design capacity
Under close with work magnetic, a kind of determination method of Large Copacity high frequency transformer optimum working frequency is found so that high frequency transformer
Design volume is minimum, to meet the growth requirement of following high frequency transformer.
Prior art does not determine method for the volume for reducing transformer using optimum working frequency.And prior art
It is：In the case where particular design capacity and work magnetic are close, working frequency is stepped up, it is determined that the magnetic core size under working frequency each time
With winding arrangement, core loss and winding loss value are calculated, and calculate the temperature rise value under working frequency each time, see whether exceed
Temperature rise limits value, if not above temperature rise limits value, then continue to improve working frequency, if improving work frequently next time
During rate, temperature rise exceedes limits value, then operating frequency value when just selecting last is used as final working frequency.So, it is existing
Technology is for the volume for reducing transformer, and amount of calculation is big, cumbersome, it is necessary to take a lot of time, and is unfavorable for engineer applied.And
The inventive method, effectively reduces amount of calculation, saves the calculating time, convenient and swift, is conducive to engineer applied.
The content of the invention
Regarding to the issue above, the present invention proposes a kind of determination method of Large Copacity high frequency transformer optimum working frequency,
Including：
Step 1：Determine the material of magnetic core of transformer, according to core material, determine core loss coefficient value Km, α and β
Value；Wire using multiply and around litz wire；
Step 2：Determine primary election working frequency f, according to primary election working frequency f and wire GB or AWG line gauge tables, it is determined that
The diameter d of single cord in wirec, the conductivityσ of wire；According to primary side winding rated current I1, vice-side winding rated current I2
With the current density, J of wire, the number of share of stock N of primary side wire is calculated1With the number of share of stock N of secondary wire2；
Step 3：Calculate the area product value A of high frequency transformerp, according to ApDetermine magnetic core size；According to winding loss PwTable
Up to unit volume core loss PcExpression formula, respectively obtain the pass of the current density, J on frequency of the close B of work magnetic and wire
It is expression formula；
Step 4：Under the conditions of particular design capacity S and the close B of work magnetic being set up according to step 3, high frequency transformer volume etc.
The relational expression of effect size SF and primary election working frequency f；Derivation is carried out to the primary election working frequency f in this formula, particular design is obtained
Under the conditions of capacity and work magnetic are close, the primary election optimum working frequency f of transformeropt；
Step 5：Calculate primary election optimum working frequency value foptUnder high frequency transformer area product value A 'p, according to high frequency transformation
Device area product value A 'p, it is determined that corresponding magnetic core size value；
Step 6：According to the primary election optimum working frequency f obtained in step 4 and step 5optAfter magnetic core size, it is determined that becoming
The winding arrangement of depressor, calculates core loss P ' respectivelycWith winding loss P 'w, determine the temperature rise of high frequency transformer in the limit for allowing
In value processed；If the temperature rise value for calculating has exceeded the temperature rise limits value for allowing, return to step 2 and redefine primary election work frequency
Rate f；If the temperature rise of high frequency transformer is in the limits value of permission, primary election optimum working frequency f nowoptFor specific
The optimum working frequency f ' of design capacity and the work close lower high frequency transformer of magneticopt, now the volume of corresponding transformer is minimum.
Winding loss P in the step 3wCalculating formula be
The gross area of primary side winding conducting wire in formulaThe gross area of vice-side winding wireMLT1For the average turn of primary side winding is long, MLT2For the average turn of vice-side winding is long, n1For primary side around
The group number of turn, n2It is the vice-side winding number of turn.
Relational expressions of the current in wire density J on frequency in the step 3 be
Under particular design capacity S in the step 4 and the close B of work magnetic, the equivalent dimension SF of high frequency transformer volume with
The relational expression of primary election working frequency f is
According to Steinmetz empirical equations, for essentially all of magnetic core, its loss factor relation is 3.5>β>α>1, η
It is high frequency transformer efficiency.
Under particular design capacity S and the close B of work magnetic in the step 4, the primary election optimum working frequency value f of transformeropt
Expression formula be
Intermediate variable in formulakcuIt is the fill factor of winding, μ0It is space permeability,
cwIt is winding height.
The fill factor k of the winding of the litz wirecuIt is 0.2-0.3, the electrical conductivity of wire is with the line of sub-thread litz wire
Footpath is different and different, and the current density, J of wire is 3-4A/mm2。
The structure of the magnetic core is UU types, determines that magnetic core window height value keeps constant during magnetic core size.
Beneficial effect
The inventive method can apply in the high frequency transformer design of different core materials voltage class different with former secondary
The determination of optimum working frequency, can substantially reduce the design volume of transformer.Prior art is for diminution transformer
Volume, amount of calculation is big, cumbersome, it is necessary to take a lot of time, and is unfavorable for engineer applied；And the inventive method, effectively reduce
Amount of calculation, saves the calculating time, convenient and swift, is conducive to engineer applied
Brief description of the drawings
Fig. 1 is Litz wire figures
Fig. 2 is UU type core structure figures
Fig. 3 is UU type core transformers Central Plains vice-side winding layout drawing
Fig. 4 is the determination method flow diagram of Large Copacity high frequency transformer optimum working frequency of the present invention
Specific embodiment
It is as follows that the present invention will be further described with reference to the accompanying drawings and detailed description：
Fig. 4 is the determination method flow diagram of Large Copacity high frequency transformer optimum working frequency of the present invention.
A kind of determination method of Large Copacity high frequency transformer optimum working frequency, it is characterised in that：
Step 1：Determine the material of magnetic core of transformer, according to core material, determine core loss coefficient value Km, α and β
Value；Wire using multiply and around litz wire；
Step 2：Determine primary election working frequency f, according to primary election working frequency f and wire GB or AWG line gauge tables, it is determined that
The diameter d of single cord in wirec, the conductivityσ of wire；According to primary side winding rated current I1, vice-side winding rated current I2
With the current density, J of wire, the number of share of stock N of primary side wire is calculated1With the number of share of stock N of secondary wire2；
Step 3：Calculate the area product value A of high frequency transformerp, according to ApDetermine magnetic core size；According to winding loss PwTable
Up to unit volume core loss PcExpression formula, respectively obtain the pass of the current density, J on frequency of the close B of work magnetic and wire
It is expression formula；
Step 4：Under the conditions of particular design capacity S and the close B of work magnetic being set up according to step 3, high frequency transformer volume etc.
The relational expression of effect size SF and primary election working frequency f；Derivation is carried out to the primary election working frequency f in this formula, particular design is obtained
Under the conditions of capacity and work magnetic are close, the primary election optimum working frequency f of transformeropt；
Step 5：Calculate primary election optimum working frequency value foptUnder high frequency transformer area product value A 'p, according to high frequency transformation
Device area product value A 'p, it is determined that corresponding magnetic core size value；As shown in Fig. 2 core structure is UU types
Step 6：According to the primary election optimum working frequency f obtained in step 4 and step 5optAfter magnetic core size, it is determined that becoming
The winding arrangement of depressor, as shown in Figure 3；Core loss P ' is calculated respectivelycWith winding loss P 'w, determine the temperature rise of high frequency transformer
In the limits value for allowing；If the temperature rise value for calculating has exceeded the temperature rise limits value for allowing, return to step 2 and redefine
Primary election working frequency f；If the temperature rise of high frequency transformer is in the limits value of permission, primary election optimum working frequency now
foptIt is particular design capacity and the optimum working frequency f ' of the work close lower high frequency transformer of magneticopt, now corresponding transformer
Volume is minimum.
Because design of transformer volume is not only relevant with core structure, winding arrangement, and with the radiating mode of transformer
It is closely related with insulation mode etc., therefore, if simple calculates volume of transformer with actual length, then
The volume of transformer expression formula for arriving will be extremely complex, is unfavorable for theory analysis.Thus, it is necessary to finding one can replace transformation
The parameter of body product.Assuming that magnetic core of transformer shape and winding fill factor are constant, then the length of transformer can
To be replaced with same equivalent dimension SF, then the expression formula for having volume of transformer is：
V∝SF3 (1)
In classical design of transformer theory, transformer area product ApIt is the selection standard of transformer core size, it is real
The magnetic core area product value of border selection is a little bigger than the magnetic core area product for calculating.The area product A of transformerpValue is bigger, then most
Whole design of transformer volume is also bigger, and the expression formula of transformer area product is：
Wherein, AcAnd AwHigh frequency transformer magnetic core sectional area and window area, K are represented respectivelyfForm factor is represented, it is sinusoidal
During ripple, Kf=4.44, during square wave, Kf=4, KuRepresent the usage factor of winding, generally for using Litz line wire types around
Group form, its KuIt is 0.2-0.3, B is that work magnetic is close, and f is working 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, then transformer loss is inversely proportional with the equivalent dimension SF of transformer,
That is P ∝ 1/SF.
Using Steinmetz empirical equations, under sinusoidal excitation, for magnetic core of transformer, unit volume core loss
Expression formula is：
Wherein, Km, α and β be core loss coefficient, for specific core material, Km, α and β be constant.
For Large Copacity high frequency transformer, wire has Kelvin effect, so, the diameter of wire of use is less than skin depth
2 times of degree.The current carrying area total for wire, wire using multiply and around Litz lines (wherein, the single cord line footpath of the inside
It is less than 2 times of skin depth), required total current carrying area on the one hand can be reached, on the other hand it is to reduce wire
The eddy-current loss that Kelvin effect causes.Shown in multiply Litz as accompanying drawing 1, the exchange winding coefficient of transformer primary vice-side winding is calculated
Formula is respectively：
Wherein, N1And N2The number of share of stock of respectively former vice-side winding Litz lines, n1And n2The number of turn of respectively former vice-side winding, dc
It is single cord diameter, μ in multiply Litz lines0It is space permeability, ρ is the resistivity of wire, and ω is angular frequency, and k is transformation
The breadth coefficient in device multi-layer winding magnetic field, usual its value 1.
Assuming that former vice-side winding is highly identical, after simplifying to (4) and (5) formula, the exchange of former vice-side winding is around system
Number is equal, that is, the former secondary exchange winding coefficient after simplifying is：
Fr1=Fr2=1+af2 (6)
Wherein, kcuIt is the fill factor of winding, σ is the electrical conductivity of winding, μ0It is space permeability, cwIt is winding height, dc
It is the diameter of single cord, bcIt is magnetic core window width, as shown in accompanying drawing 3.
Winding loss calculating formula is as follows：
Pw=Fr1I1 2Rdc1+Fr2I2 2Rdc2 (8)
Wherein, Fr1And Fr2It is the exchange winding coefficient of former vice-side winding, I1And I2It is former vice-side winding load current value,
Rdc1And Rdc2The DC resistance of respectively former vice-side winding.
Former secondary winding current and D.C. resistance calculating formula are as follows：
Wherein, J is the current density of wire, N1It is primary side winding Litz strand counts, N2It is vice-side winding Litz strand counts,
n1It is the primary side winding number of turn, n2It is the vice-side winding number of turn, MLT1For the average turn of primary side winding is long, MLT2It is putting down for vice-side winding
Equal circle is long.
(9) to (12) formula is brought into (8) formula, being calculated winding loss calculating formula is：
Wherein, W1And W2The gross area of primary side winding and vice-side winding copper conductor is represented respectively.
According to formula (3) and (13), the work magnetic relationship expression of close B and current in wire density J on frequency f is calculated
Formula：
Formula (16) and (17) are brought into formula (2), be calculated particular design capacity and work magnetic it is close under, high frequency transformer
The relational expression of the equivalent dimension SF and frequency f of volume：
In view of for essentially all of magnetic core, loss factor relation is in Steinmetz empirical equations：3.5>β>α>
1.By high frequency transformer volume V ∝ SF3, i.e., when SF has minimum value, volume V there is minimum value.Be can be seen that from formula (18)
Equivalent dimension SF has minimum value under a certain frequency f.So, formula (18) is carried out into derivation to frequency f, it is calculated spy
Determine design capacity and work magnetic it is close under, transformer when there is minimum volume corresponding optimum working frequency be：
Wherein, α and β is core loss coefficient, kcuIt is the fill factor of winding, σ is the electrical conductivity of winding conducting wire, μ0It is true
Empty magnetic conductivity, cwIt is winding height, dcIt is the diameter of single cord.
From formula (19) and (20) as can be seen that particular design capacity and the work close lower high frequency transformer of magnetic have minimal design
Optimum working frequency f during volumeoptLoss characteristic, winding construction and conductor material characteristic with high frequency magnetic core is relevant.
The above, a kind of specific embodiment that only present invention is calculated, it is impossible to be interpreted as to protection model of the invention
The limitation enclosed, the person skilled in the art in the field without departing from the spirit and scope of the present invention, can also make one
A little modifications and adaptations.Therefore all equivalent technical schemes fall within scope of the invention, and protection scope of the present invention should be with
Scope of the claims is defined.
Claims (7)
1. a kind of determination method of Large Copacity high frequency transformer optimum working frequency, it is characterised in that：
Step 1：The material of magnetic core of transformer is determined, according to core material, using Steinmetz empirical equations, in sinusoidal excitation
Under, for magnetic core of transformer, unit volume core lossDetermine core loss coefficient：Km, α and β；
Wire using multiply and around litz wire；
Step 2：Determine primary election working frequency f, according to primary election working frequency f and wire GB or AWG line gauge tables, determine wire
The diameter d of middle single cordc, the conductivityσ of wire；According to primary side winding rated current I1, vice-side winding rated current I2With lead
The current density, J of line, calculates the number of share of stock N of primary side wire1With the number of share of stock N of secondary wire2；
Step 3：Calculate the area product value A of high frequency transformerp, according to ApDetermine magnetic core size；According to winding loss PwExpression with
Unit volume core loss PcExpression formula, respectively obtain the relation table of the current density, J on frequency of the close B of work magnetic and wire
Up to formula；
Step 4：Under the conditions of particular design capacity S and the close B of work magnetic being set up according to step 3, the equivalent chi of high frequency transformer volume
The relational expression of very little SF and primary election working frequency f；Derivation is carried out to the primary election working frequency f in this formula, particular design capacity is obtained
Under the conditions of close with work magnetic, the primary election optimum working frequency f of transformeropt；
Step 5：Calculate primary election optimum working frequency value foptUnder high frequency transformer area product value A 'p, according to high frequency transformer face
Product product value A 'p, it is determined that corresponding magnetic core size value；
Step 6：According to the primary election optimum working frequency f obtained in step 4 and step 5optAfter magnetic core size, transformer is determined
Winding arrangement, core loss P ' is calculated respectivelycWith winding loss P 'w, determine the temperature rise of high frequency transformer in the limits value for allowing
It is interior；If the temperature rise value for calculating has exceeded the temperature rise limits value for allowing, return to step 2 and redefine primary election working frequency f；
If the temperature rise of high frequency transformer is in the limits value of permission, primary election optimum working frequency f nowoptIt is particular design
The optimum working frequency f ' of capacity and the work close lower high frequency transformer of magneticopt, now the volume of corresponding transformer is minimum.
2. method according to claim 1, it is characterised in that：Winding loss P in the step 3wCalculating formula be
The gross area of primary side winding conducting wire in formulaThe gross area of vice-side winding wireMLT1For the average turn of primary side winding is long, MLT2For the average turn of vice-side winding is long, n1For primary side around
The group number of turn, n2It is the vice-side winding number of turn.
3. method according to claim 1, it is characterised in that：Passes of the current in wire density J on frequency in the step 3
It is that expression formula is
4. method according to claim 1, it is characterised in that：Particular design capacity S and the close B of work magnetic in the step 4
Under, equivalent dimension SF and the relational expression of primary election working frequency f of high frequency transformer volume are
According to Steinmetz empirical equations, for essentially all of magnetic core, its loss factor relation is 3.5>β>α>1, η is height
Frequency power transformer efficiency.
5. method according to claim 1, it is characterised in that：Particular design capacity S and the close B of work magnetic in the step 4
Under, the primary election optimum working frequency value f of transformeroptExpression formula be
Intermediate variable in formulakcuIt is the fill factor of winding, μ0It is space permeability, cwBe around
Group height.
6. method according to claim 1, it is characterised in that：The fill factor k of the winding of the litz wirecuIt is 0.2-0.3,
The electrical conductivity of wire is different with the line footpath difference of sub-thread litz wire, and the current density, J of wire is 3-4A/mm2。
7. method according to claim 1, it is characterised in that：The structure of the magnetic core is UU types, determines magnetic during magnetic core size
Core window height value keeps constant.
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| CN105742047A (en) * | 2015-12-30 | 2016-07-06 | 国网智能电网研究院 | Control method for inductance parameter of high-frequency transformer body |
| CN106898487B (en) * | 2017-01-16 | 2019-02-22 | 湖北文理学院 | A kind of design method of multichannel intermediate-frequency transformer |
| CN106981995B (en) * | 2017-04-24 | 2019-04-02 | 华北电力大学 | The minute design method of high frequency transformer voltage, current transfer ratio |
| CN109920619A (en) * | 2019-01-31 | 2019-06-21 | 张欣 | The method for helping silicon carbide MOSFET in parallel to realize current balance using differential mode inductance |
| CN109992739A (en) * | 2019-02-25 | 2019-07-09 | 华北电力大学 | The optimal sub-thread diameter of rectangular litz wire and number of share of stock calculation method under non-sinusoidal current waveform stimulus |
| CN113962094B (en) * | 2021-10-26 | 2022-04-26 | 中国矿业大学(北京) | High-frequency transformer optimization design method comprehensively considering vibration noise |
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