CN109655662A - A kind of k-factor calculation method calculating power by transformer core sectional area - Google Patents

A kind of k-factor calculation method calculating power by transformer core sectional area Download PDF

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CN109655662A
CN109655662A CN201810965676.2A CN201810965676A CN109655662A CN 109655662 A CN109655662 A CN 109655662A CN 201810965676 A CN201810965676 A CN 201810965676A CN 109655662 A CN109655662 A CN 109655662A
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formula
core
iron core
window
sectional area
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刘飞翠
冉瑞刚
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R21/00—Arrangements for measuring electric power or power factor
    • G01R21/006—Measuring power factor

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  • Power Engineering (AREA)
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  • General Physics & Mathematics (AREA)
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Abstract

The invention discloses a kind of k-factor calculation methods that power is calculated by transformer core sectional area; give the calculating formula of the power coefficient K of EI lamination silicon steel core; the calculating formula of other non-standard EI iron core power coefficient K can be equally released using this method; the shortcomings that avoiding traditional value for carrying out coefficient of determination K by experience, superfluous or off-capacity designed with bring.

Description

A kind of k-factor calculation method calculating power by transformer core sectional area
Technical field
The present invention relates to transformer technology fields, and in particular to a kind of K system that power is calculated by transformer core sectional area Number calculating method.
Background technique
Transformer (Transformer) is the device for changing alternating voltage using the principle of electromagnetic induction, transformer work For Cheng Shi when carrying out Preliminary design to product, what is often considered first is that corresponding iron core is chosen according to load capacity, one As design of transformer books or eelctrical engineering handbook in used following empirical equation:
P=(Sc/K)x
P: transformer output capacity (W)
Sc: iron core column cross-sectional area (cm2)
K: empirical coefficient
X: index, for EI lamination silicon steel core, index x generally takes 2
For empirical coefficient K, engineers respectively have viewpoint, and the depth of the industry according to involved by itself is for different types of Transformer, which has, identifies oneself most reasonable value range, and often this is under fixed mode or limited experimental data supports Under the data that obtain.For example, the small-sized single-phase Industrial Frequency Transformer of 50Hz, when using standard EI lamination silicon steel core, K value is most (actually this coefficient is also inaccurate) is taken between 0.8~1.2.The standard EI lamination silicon steel core piece is by E type and the punching of I type Piece composition is general using to intersecting lamination by the way of slotting.Standard EI chip size has formed seriation, standardization in the industry, such as: EI48, EI57, EI60, EI66, EI76.2, EI85.8, EI96, EI114, EI133.2, EI152.4 etc., if being marked with quasi- EI piece side Column width is n, then window width is n, window height 3n, iron core middle column's width are 2n, iron core beam overall is 6n, iron core is always a height of 5n；It is assumed herein that it is a*2n that iron core, which folds thickness, a is multiple.EI48 indicates that iron core beam overall is 48mm, i.e. 6n=48.
With the demand of marketing users, and it will also tend to encounter the change of some off-gauge EI shaped iron cores or higher frequency Depressor, such as 400Hz etc., that empirical coefficient K again this how to choose, often selected under the conditions of not similar experimental data Take iron core excessive or too small.
Therefore, for the specific algorithm of formula (1) empirical coefficient K, it is necessary to do further research.
Summary of the invention
The purpose of the present invention is being directed to above-mentioned deficiency in the prior art, one kind is provided by transformer core sectional area meter The k-factor calculation method of power is calculated, and provides the calculating formula of K, suitable for the EI iron core of standard, nonstandard EI iron core is also the same It can be derived with the method.
Steps are as follows:
Step 1 lists empirical equation:
P=(Sc/K)2--------------------------------------------(1)
P: transformer output capacity (W)
Sc: iron core column cross-sectional area (cm2)
K: empirical coefficient
Step 2: the relationship of transformer output power P2 Yu core area product Sc*Sm are sought
1), transformer input power:
P1=U1*I1---------------------------------------------(2)
In formula, P1: input power (VA), U1: input voltage (V), I1: input current (A)
2), the relationship of input current and conductor cross-section:
By j1=I1/Q1Export I1=j1Q1----------------------(3)
In formula, j1: current density (A/mm2), Q1: conducting wire effective sectional area (mm2)
3) it, is obtained by the law of electromagnetic induction:
U1=4.44W1BmScf*10-4--------------------------------(4)
In formula, W1: primary circle number, Bm: work flux density (T), Sc: iron core effective cross section product (cm2)
F: working frequency (Hz)
4) formula (4), are substituted into formula (2) to obtain:
P1=4.44W1BmScf*10-4I1--------------------------------(5)
5) formula (3), are substituted into formula (5) to obtain:
P1=4.44W1Q1Bmj1Scf*10-4-------------------------------(6)
W in formula1Q1Efficiently use area for core window then has if primary and secondary respectively accounts for half:
W1Q1=0.5Sm*102-------------------------------------(7)
In formula, SmFor iron core valid window area, i.e., copper section product in core window
6) formula (7), are substituted into formula (6) and obtain transformer input power:
P1=2.22Bmj1SmScf*10-2--------------------------------(8)
7), transformer output power P2:
P=P1* η=2.22fBmjSmScη*10-2--------------------------(9)
In formula, η: efficiency, j1: it is directly replaced with j, P2: directly replaced with P
Sm: iron core valid window area, i.e., copper section accumulates (cm in core window2)
Step 3: product of areas Sc*Sm is converted into iron core column cross-sectional area Sc
Sc*Sm=(2n*a2n*0.95) * (n*3n*0.35)
=(2n*a2n*0.95) * [(1.05/3.8a) * (2n*a2n*0.95)]
=(1.05/3.8a) * (2n*an*0.95)2
=(1.05/3.8a) * Sc2----------------------------(10)
In formula, 0.95 is lamination coefficient, and 0.35 is window effective utilization coefficients
Step 4: formula (10) are substituted into formula (9) and are converted to the format of formula (1)
Step 5: formula (11) is compared with formula (1) and obtains COEFFICIENT K
Above formula is the calculating formula of standard EI iron core empirical coefficient K
The standard EI lamination silicon steel core, is made of E type and the punching EI of I type structure, using to intersecting by the way of slotting Lamination, the EI piece side column width are n, then window width is n, window height 3n, iron core middle column's width are 2n, iron core beam overall is The total a height of 5n of 6n, iron core；Assuming that it is a*2n that iron core, which folds thickness, a is multiple.
Beneficial effects of the present invention: the present invention provides a kind of k-factor meters that power is calculated by transformer core sectional area Calculation method, is derived the calculating formula of empirical equation K, and lists its derivation process.Avoid the full extensive style transformation for leaning on experience Device design, can be such that calculating more refines.
Detailed description of the invention
Invention is described further using attached drawing, but the embodiments in the accompanying drawings do not constitute any limitation to the present invention, For those of ordinary skill in the art, without creative efforts, it can also be obtained according to the following drawings Its attached drawing.
Attached drawing 1 is a kind of derivation step for the k-factor that power is calculated by transformer core sectional area of the present invention；
Attached drawing 2 is EI lamination silicon steel core schematic diagram；
Attached drawing 3 be window width be 2n when EI lamination silicon steel core schematic diagram；
EI lamination silicon steel core schematic diagram when attached drawing 4 is window a height of 6n.
Specific embodiment
Below in conjunction with the embodiment of the present invention, technical scheme in the embodiment of the invention is clearly and completely described, Obviously, described embodiments are some of the embodiments of the present invention, instead of all the embodiments.Based on the implementation in the present invention Example, every other embodiment obtained by those of ordinary skill in the art without making creative efforts belong to The scope of protection of the invention.The present invention is further retouched according to Fig. 1, Fig. 2, Fig. 3 and Fig. 4, and with the following Examples It states.
Case study on implementation 1
Fig. 2 is EI lamination silicon steel core schematic diagram, usually names iron core model in the industry with iron core beam overall (6n), and unit is mm.Such as EI48, then n=48/6=8mm.Does is it much that this silicon steel laminations iron core capacity is sought in examination if folded thickness a2n=30mm?
First calculate folded thick coefficient a=a2n/2n=30/16=1.875, if setting f=50Hz, Bm=1.5T, j=5A/mm2, η=80%, by this parameter substitution formula (12) design factor K
Then transformer capacity P are as follows:
P=(Sc/K)2=(16*30*10-2/1.01)2=22.5W
Sc is iron core middle column's sectional area, the i.e. pillar of unwrapping wire circle, i.e. 2n*a2n herein.
Case study on implementation 2
Fig. 2 is standard EI chip size figure, such as EI114, then n=114/6=19mm.If folded thickness a2n=60mm, examination ask this Does is silicon steel laminations iron core capacity much?
First calculate folded thick coefficient a=a2n/2n=60/38=1.58, if setting f=50Hz, Bm=1.35T, j=3A/mm2, η=85%, by this parameter substitution formula (12) design factor K
Then transformer capacity P are as follows:
P=(Sc/K)2=(38*60*10-2/1.226)2=346W
Sc is iron core middle column's sectional area, the i.e. pillar of unwrapping wire circle, i.e. 2n*a2n herein.
Case study on implementation 3
Nonstandard iron core, as shown in Fig. 3, i.e., when window width is 2n, examination derives COEFFICIENT K.The same specification of step is derived, only from the 3 steps start core window area Sm being changed to 2n*3n*0.35 by n*3n*0.35, then the calculated result of formula (10) is by (1.05/ 3.8a)*Sc2Become (2.1/3.8a) * Sc2, only coefficient changes, until step 5 formula (12),
Case study on implementation 4
Nonstandard iron core, as shown in Fig. 4, i.e. when a height of 6n of window, examination derives COEFFICIENT K.The same specification of step is derived, only from the 3 steps start core window area Sm being changed to n*6n*0.35 by n*3n*0.35, then the calculated result of formula (10) is by (1.05/ 3.8a)*Sc2Become (2.1/3.8a) * Sc2, only coefficient changes, until step 5 formula (12),
The steps in the embodiment of the present invention can be sequentially adjusted, merged and deleted according to actual needs.
It is apparent to those skilled in the art that for convenience and simplicity of description, the system of foregoing description It with the specific work process of unit, can refer to corresponding processes in the foregoing method embodiment, details are not described herein.

Claims (4)

1. a kind of k-factor calculation method for calculating power by transformer core sectional area, which is characterized in that steps are as follows:
Step 1 lists empirical equation:
P=(Sc/K)2--------------------------------------------(1)
P: transformer output capacity (W)
Sc: iron core column cross-sectional area (cm2)
K: empirical coefficient；
Step 2: the relationship of transformer output power P2 Yu core area product Sc*Sm are sought
1), transformer input power:
P1=U1*I1---------------------------------------------(2)
In formula, P1: input power (VA), U1: input voltage (V), I1: input current (A)
2), the relationship of input current and conductor cross-section:
By j1=I1/Q1Export I1=j1Q1----------------------(3)
In formula, j1: current density (A/mm2), Q1: conducting wire effective sectional area (mm2)
3) it, is obtained by the law of electromagnetic induction:
U1=4.44W1BmScf*10-4--------------------------------(4)
In formula, W1: primary circle number, Bm: work flux density (T), Sc: iron core effective cross section product (cm2)
F: working frequency (Hz)
4) formula (4), are substituted into formula (2) to obtain:
P1=4.44W1BmScf*10-4I1--------------------------------(5)
5) formula (3), are substituted into formula (5) to obtain:
P1=4.44W1Q1Bmj1Scf*10-4-------------------------------(6)
W in formula1Q1Efficiently use area for core window then has if primary and secondary respectively accounts for half:
W1Q1=0.5Sm*102-------------------------------------(7)
In formula, SmFor iron core valid window area, i.e., copper section product in core window
6) formula (7), are substituted into formula (6) and obtain transformer input power:
P1=2.22Bmj1SmScf*10-2--------------------------------(8)；
7), transformer output power P2:
P=P1* η=2.22fBmjSmScη*10-2--------------------------(9)
In formula, η: efficiency, j1: it is directly replaced with j, P2: directly replaced with P
Sm: iron core valid window area, i.e., copper section accumulates (cm in core window2)；
Step 3: product of areas Sc*Sm is converted into iron core column cross-sectional area Sc
Sc*Sm=(2n*a2n*0.95) * (n*3n*0.35)
=(2n*a2n*0.95) * [(1.05/3.8a) * (2n*a2n*0.95)]
=(1.05/3.8a) * (2n*an*0.95)2
=(1.05/3.8a) * Sc2----------------------------(10)
In formula, 0.95 is lamination coefficient, and 0.35 is window effective utilization coefficients；
Step 4: formula (10) are substituted into formula (9) and are converted to the format of formula (1)
Step 5: formula (11) is compared with formula (1) and obtains COEFFICIENT K
Above formula is the calculating formula of EI lamination silicon steel core empirical coefficient K.
2. a kind of k-factor calculation method for calculating power by transformer core sectional area according to claim 1, feature It is, the EI lamination silicon steel core is made of E type and the punching EI of I type structure, using to intersecting lamination by the way of slotting, institute Stating EI piece side column width is n, then window width is n, window height 3n, iron core middle column's width are 2n, iron core beam overall is 6n, iron core Total a height of 5n；If it is a*2n that iron core, which folds thickness, a is multiple.
3. a kind of k-factor calculation method for calculating power by transformer core sectional area according to claim 1, feature It is, the EI lamination silicon steel core, when window width is 2n,
4. a kind of k-factor calculation method for calculating power by transformer core sectional area according to claim 1, feature It is, the EI lamination silicon steel core, as a height of 6n of window,
CN201810965676.2A 2018-08-23 2018-08-23 A kind of k-factor calculation method calculating power by transformer core sectional area Pending CN109655662A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110118904A (en) * 2019-04-28 2019-08-13 东莞市大忠电子有限公司 A kind of k-factor transformer equivalent load conversion method
WO2023053479A1 (en) * 2021-09-29 2023-04-06 三菱重工サーマルシステムズ株式会社 Reactor

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Publication number Priority date Publication date Assignee Title
GB2034054B (en) * 1978-11-10 1982-11-17 Huen Yeang Kong Powermeasuring device
CN101029914A (en) * 2006-02-28 2007-09-05 魏营隆 Method for measuring iron-core parameter, designing transformer iron-core parameter and coil parameter by frequency impedance
CN105183992A (en) * 2015-09-08 2015-12-23 国网智能电网研究院 Determining method for maximum design capacity of high-frequency transformer
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

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB2034054B (en) * 1978-11-10 1982-11-17 Huen Yeang Kong Powermeasuring device
CN101029914A (en) * 2006-02-28 2007-09-05 魏营隆 Method for measuring iron-core parameter, designing transformer iron-core parameter and coil parameter by frequency impedance
CN105183992A (en) * 2015-09-08 2015-12-23 国网智能电网研究院 Determining method for maximum design capacity of high-frequency transformer
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

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
冉瑞刚: "关于EI迭片铁心经验公式中的"P=(Sc/k)2"中的"k"值", 《国际电子变压器》 *
***加工贸易及保税监管司: "《加工贸易单耗标准实务手册》", 30 September 2009 *

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110118904A (en) * 2019-04-28 2019-08-13 东莞市大忠电子有限公司 A kind of k-factor transformer equivalent load conversion method
CN110118904B (en) * 2019-04-28 2021-12-14 东莞市大忠电子有限公司 K-coefficient transformer equivalent load conversion method
WO2023053479A1 (en) * 2021-09-29 2023-04-06 三菱重工サーマルシステムズ株式会社 Reactor

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