CN107844624A - A kind of modeling method of shared core type multiwinding transformer - Google Patents

A kind of modeling method of shared core type multiwinding transformer Download PDF

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CN107844624A
CN107844624A CN201710816460.5A CN201710816460A CN107844624A CN 107844624 A CN107844624 A CN 107844624A CN 201710816460 A CN201710816460 A CN 201710816460A CN 107844624 A CN107844624 A CN 107844624A
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msub
mrow
mfrac
mover
msubsup
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武琳
姜�远
王兰香
杨林
赵守忠
刘军
赵泓博
李凤羽
李文文
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State Grid Corp of China SGCC
Beijing Kedong Electric Power Control System Co Ltd
State Grid Liaoning Electric Power Co Ltd
Nanjing NARI Group Corp
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State Grid Corp of China SGCC
Beijing Kedong Electric Power Control System Co Ltd
State Grid Liaoning Electric Power Co Ltd
Nanjing NARI Group Corp
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Publication of CN107844624A publication Critical patent/CN107844624A/en
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/36—Circuit design at the analogue level
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Abstract

The present invention relates to electrical technology field, more particularly to a kind of modeling method of shared core type multiwinding transformer.The present invention shares the mathematical modeling of iron core Multiple coil (height) frequency power transformer by establishing, common appendiron core transformer winding power transmission equation is derived, the winding power transmission feature of common appendiron core transformer is analyzed, is that basis is established in the application of the type transformer.This method can accurately illustrate the power transmission feature between common each winding of core type multiwinding transformer.It is that basis is established in application of the type transformer in power equipment by establishing the mathematical modeling of core type multiwinding transformer altogether.

Description

A kind of modeling method of shared core type multiwinding transformer
Technical field
The present invention relates to electrical technology field, more particularly to altogether in core type Multiple coil (height) frequency power transformer mathematical modeling Power transmission feature modeling method between method and primary side-secondary.
Background technology
For the mathematical modeling of two-winding transformer inside (height) frequency power transformer in independent core type, typically using radial type Equivalent-circuit model, derive primary side-vice-side winding power transmission feature.And for share core type multiwinding transformer and Speech, because power coupled relation is complicated between winding, there has been no similar modeling method at present.
The modeling of (height) frequency power transformer in common core type Multiple coil, existing method be for winding voltage and Electric current conversion relation is deployed, not yet to the power coupled relation between (height) frequency power transformer winding in common core type Multiple coil Carry out analysis and modeling.To employing in common core type Multiple coil for the electric device of (height) frequency power transformer, if can not be accurate Really power transmission feature between the winding of assurance multiwinding transformer, just can not accurately be controlled electric device.This is shadow Ring one of factor of the application of the type electric device and development.
The content of the invention
The problem of in background technology, it is an object of the invention to provide a kind of shared core type multiwinding transformer Modeling method.This method can accurately illustrate the power transmission feature between common each winding of core type multiwinding transformer.Pass through The mathematical modeling of core type multiwinding transformer altogether is established, is that basis is established in application of the type transformer in power equipment.
To achieve these goals, the present invention proposes following technical scheme：
A kind of modeling method of shared core type multiwinding transformer, it is characterised in that methods described comprises the following steps：
Step 1：Physical quantity is defined, if appendiron core transformer has n independent winding altogether, wherein 11 and 12,21 and 22nd ..., a pair each other of n1 and n2, be transformer T1, T2 ..., Tn former vice-side winding, u11And u12、u21And u22、……、 un1And un2Respectively transformer T1, T2 ..., Tn former vice-side winding voltage, i11And i12、i21And i22、……、in1And in2 Respectively transformer T1, T2 ..., Tn former secondary winding current, Rk1、Lk1、Ck1And Rk2、Lk2、Ck2Respectively k-th of transformation Resistance, inductance and the capacitance of device original vice-side winding series connection, k=1,2 ... n；
Step 2：The voltage equation for establishing kth transformer primary vice-side winding is：
K=1 in formula, 2 ... n, Lh_jFor the mutual inductance between h-th of winding of transformer and j-th of winding, wherein, transformer The h=11 of primary side, 21 ... n1, the h=12 of transformer secondary, 22 ... n2；If h=j, namely Lh_hFor h windings master from Sense, leakage inductance is in Lh1And Lh2Middle consideration；If it is considered to each umber of turn is equal, then have：Lh_j=Lj_h, namely transformer respectively around The main self-induction of group and the mutual inductance between them are equal, are Lm, then have：
According to voltage equation (2), and ignore exciting current influence, draw simple equivalent circuit；
Step 3：Row write out Multiple coil, and the steady state voltage equation of appendiron core transformer is altogether：
Wherein：WithRepresent the n-th winding primary and secondary side voltage phasor, Zn1And Zn2Represent the n-th winding primary side and pair The equiva lent impedance on side, then calculate factor ZGExpression formula is：
In formula, j and ωsRespectively plural empty unit and switch angular frequency；
Then the conjugate of the complex power of the winding of transformer 12 is：
Wherein,Represent voltage U12The conjugation of phasor value；
Step 4：Order
WhereinWithRespectively 11,21,22 ..., n1 and n2 around The electrical angle of the group advanced 12 winding voltage phase of voltage-phase, U11、U12、U21、U22…Un1、Un2Respectively 11,12,21, 22nd ..., the equivalent sine fundamental voltage virtual value of n1 and n2 winding voltages；
Consider resonant frequency and the unequal situation of switching frequency, i.e.,The then active power of the winding of transformer 12 For：
The real part of the winding complex power of Re indication transformers 12 conjugation；
Can equally derive 11 windings, the n-th 1 and the active power of n2 windings be：
Step 5：Because transformer primary secondary voltage waveform is that frequency is ωs50% square wave, primary side square-wave voltage width It is worth for UCk(k=1,2 ... n)=UC1, the amplitude of secondary square-wave voltage is UCo, then the equivalent fundamental wave sinusoidal voltage of former secondary is effective It is worth and is：
And can keeping primary side 11,12 in control ..., the phase of .., 1n winding voltage is just the same, namely：
Step 6：Formula (11) and (12) are substituted into (7)~(10), the wattful power for, the n2 windings that obtain transformer 12,22 ... Rate is：
It is written as using the active power of the DC-DC converter of n independent appendiron core transformers：
And becauseThen formula (13) and (14) can be written as：
Compared with prior art, beneficial effects of the present invention are：
(height) frequency power transformer in common core type Multiple coil, power coupling be present between primary side-vice-side winding, bring this The problem of type transformer mathematical modeling is analyzed with Power Control difficulty, the present invention, which passes through to establish, shares iron core Multiple coil (height) frequency The mathematical modeling of transformer, common appendiron core transformer winding power transmission equation is derived, analyzed the winding of common appendiron core transformer Power transmission feature, it is that basis is established in the application of the type transformer.
The present invention establishes the mathematical modeling of (height) frequency power transformer in core type Multiple coil altogether, being capable of the change of in-depth explanation the type Power transmission relation between depressor primary side-secondary.By the theoretical modeling to the type transformer, exist for the type transformer Basis is established in the application of electric device.
Brief description of the drawings
Fig. 1 is Multiple coil appendiron core transformer altogether.
Fig. 2 is the simple equivalent circuit of the common appendiron core transformer of Multiple coil.
Embodiment
With reference to the accompanying drawings and detailed description, specific embodiments of the present invention are made with detailed elaboration.These tools Body embodiment is only not used for limiting the scope of the present invention or implementation principle for narration, and protection scope of the present invention is still with power Profit requires to be defined, including obvious changes or variations made on this basis etc..
(height) frequency power transformer in common core type Multiple coil, power coupling be present between primary side-vice-side winding, bring this The problem of type transformer mathematical modeling is analyzed with Power Control difficulty, the present invention, which passes through to establish, shares iron core Multiple coil (height) frequency The mathematical modeling of transformer, common appendiron core transformer winding power transmission equation is derived, analyzed the winding of common appendiron core transformer Power transmission feature, it is that basis is established in the application of the type transformer.
In order to achieve the above object, technical solution of the invention is as follows：
The present invention proposes a kind of Mathematical Modeling Methods of (height) frequency power transformer in core type Multiple coil altogether.Fig. 1 is with n The common appendiron core transformer of individual independent winding, wherein 11 and 12,21 and 22 ..., a pair each other of n1 and n2, be transformer T1, T2 ..., Tn former vice-side winding, u11And u12、u21And u22、……、un1And un2Respectively transformer T1, T2 ..., Tn Former vice-side winding voltage, i11And i12、i21And i22、……、in1And in2Respectively transformer T1, T2 ..., Tn former secondary around Group electric current, Rk1、Lk1、Ck1And Rk2、Lk2、Ck2Resistance, inductance and the electric capacity of respectively k-th transformer primary vice-side winding series connection Value, k=1,2 ... n.
The voltage equation for establishing its kth transformer primary vice-side winding is：
K=1 in formula, 2 ... n, Lh_jmFor the mutual inductance between h-th of winding of transformer and j-th of winding, wherein, transformer The h=11 of primary side, 21 ... n1, the h=12 of transformer secondary, 22 ... n2.If h=j, namely Lh_hmFor the master of h windings Self-induction, leakage inductance is in Lh1And Lh2Middle consideration.If it is considered to each umber of turn is equal, then have：Lh_jm=Lj_hm, namely transformer is each The main self-induction of winding and the mutual inductance between them are equal, are Lm, then have：
According to above voltage equation, and ignore exciting current influence, can show that simple equivalent circuit is as shown in Figure 2.
Due to transformer T1、T2、……、TnFormer vice-side winding voltage be that frequency is ωsDutycycle is 50% square wave Voltage, only consider that frequency is ωsFundamental wave effect and negligible resistance influence when, can arrange write out Multiple coil altogether appendiron core transformer it is steady State voltage equation is：
Wherein：WithRepresent the n-th winding primary and secondary side voltage phasor, Zn1And Zn2Represent the n-th winding primary side and pair The equiva lent impedance on side, then calculate factor ZGExpression formula is
In formula, j and ω s are respectively the empty unit of plural number and switch angular frequency.
Then the conjugate of the complex power of the winding of transformer 12 is：
Wherein,Represent voltage U12The conjugation of phasor value.
Order
WhereinWithRespectively 11,21,22 ..., n1 and n2 around The electrical angle of the group advanced 12 winding voltage phase of voltage-phase, U11、U12、U21、U22…Un1、Un2Respectively 11,12,21, 22nd ..., the equivalent sine fundamental voltage virtual value of n1 and n2 winding voltages.
Consider resonant frequency and the unequal situation of switching frequency, i.e.,The now wattful power of the winding of transformer 12 Rate is：
The real part of the winding complex power of Re indication transformers 12 conjugation.
Can equally derive 11 windings, the n-th 1 and the active power of n2 windings be：
Because transformer primary secondary voltage waveform is that frequency is ωs50% square wave, primary side square-wave voltage amplitude is UCk (k=1,2 ... n)=UC1, the amplitude of secondary square-wave voltage is UCo, then the equivalent fundamental wave sinusoidal voltage virtual value of former secondary be：
And can keeping primary side 11,12 in control ..., the phase of .., 1n winding voltage is just the same, namely：
Formula (11) and (12) are substituted into (7)~(10), the active power for, the n2 windings that obtain transformer 12,22 ... is：
It can be written as using the active power of the DC-DC converter of n independent appendiron core transformers：
And becauseThen formula (13) and (14) can be written as：
From formula (16), the active power of each vice-side winding of common appendiron core transformer is made up of two parts, and one Part is power of each primary side winding to the vice-side winding transmission, and another part is work(of other vice-side windings to the winding transmission Rate.The active power of each vice-side winding of appendiron core transformer is the nonlinear function of primary side-vice-side winding phase difference of voltage altogether, i.e., each There is stronger Non-linear coupling between winding power.

Claims (1)

  1. A kind of 1. modeling method of shared core type multiwinding transformer, it is characterised in that
    Methods described comprises the following steps：
    Step 1：Define physical quantity, if altogether appendiron core transformer there is n independent winding, wherein 11 and 12,21 and 22 ..., n1 With a pair each other of n2, be transformer T1, T2 ..., Tn former vice-side winding, u11And u12、u21And u22、……、un1And un2Point Not Wei transformer T1, T2 ..., Tn former vice-side winding voltage, i11And i12、i21And i22、……、in1And in2Respectively transformation Device T1, T2 ..., Tn former secondary winding current, Rk1、Lk1、Ck1And Rk2、Lk2、Ck2Respectively k-th of transformer primary secondary around Resistance, inductance and the capacitance of group series connection, k=1,2 ... n；
    Step 2：The voltage equation for establishing kth transformer primary vice-side winding is：
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    K=1 in formula, 2 ... n, Lh_jFor the mutual inductance between h-th of winding of transformer and j-th of winding, wherein, transformer primary side H=11,21 ... n1, the h=12 of transformer secondary, 22 ... n2；If h=j, namely Lh_hFor the main self-induction of h windings, Leakage inductance is in Lh1And Lh2Middle consideration；If it is considered to each umber of turn is equal, then have：Lh_j=Lj_h, namely each winding of transformer Main self-induction and mutual inductance between them are equal, are Lm, then have：
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    According to voltage equation (2), and ignore exciting current influence, draw simple equivalent circuit；
    Step 3：Row write out Multiple coil, and the steady state voltage equation of appendiron core transformer is altogether：
    <mrow> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>m</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mfrac> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>11</mn> </msub> <msub> <mi>Z</mi> <mn>11</mn> </msub> </mfrac> <mo>+</mo> <mfrac> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>12</mn> </msub> <msub> <mi>Z</mi> <mn>12</mn> </msub> </mfrac> <mo>+</mo> <mfrac> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>21</mn> </msub> <msub> <mi>Z</mi> <mn>21</mn> </msub> </mfrac> <mo>+</mo> <mfrac> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>22</mn> </msub> <msub> <mi>Z</mi> <mn>22</mn> </msub> </mfrac> <mo>+</mo> <mo>...</mo> <mo>+</mo> <mfrac> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>n</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>Z</mi> <mrow> <mi>n</mi> <mn>1</mn> </mrow> </msub> </mfrac> <mo>+</mo> <mfrac> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>n</mi> <mn>2</mn> </mrow> </msub> <msub> <mi>Z</mi> <mrow> <mi>n</mi> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mrow> <mfrac> <mn>1</mn> <msub> <mi>Z</mi> <mn>11</mn> </msub> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>Z</mi> <mn>12</mn> </msub> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>Z</mi> <mn>21</mn> </msub> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>Z</mi> <mn>22</mn> </msub> </mfrac> <mo>+</mo> <mo>...</mo> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>Z</mi> <mrow> <mi>n</mi> <mn>1</mn> </mrow> </msub> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>Z</mi> <mrow> <mi>n</mi> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> </mfrac> </mrow>
    <mrow> <mo>=</mo> <mfrac> <msub> <mi>Z</mi> <mi>G</mi> </msub> <msub> <mi>Z</mi> <mn>11</mn> </msub> </mfrac> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>11</mn> </msub> <mo>+</mo> <mfrac> <msub> <mi>Z</mi> <mi>G</mi> </msub> <msub> <mi>Z</mi> <mn>12</mn> </msub> </mfrac> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>12</mn> </msub> <mo>+</mo> <mfrac> <msub> <mi>Z</mi> <mi>G</mi> </msub> <msub> <mi>Z</mi> <mn>21</mn> </msub> </mfrac> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>21</mn> </msub> <mo>+</mo> <mfrac> <msub> <mi>Z</mi> <mi>G</mi> </msub> <msub> <mi>Z</mi> <mn>22</mn> </msub> </mfrac> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>22</mn> </msub> <mo>+</mo> <mo>...</mo> <mo>+</mo> <mfrac> <msub> <mi>Z</mi> <mi>G</mi> </msub> <msub> <mi>Z</mi> <mrow> <mi>n</mi> <mn>1</mn> </mrow> </msub> </mfrac> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>n</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mfrac> <msub> <mi>Z</mi> <mi>G</mi> </msub> <msub> <mi>Z</mi> <mrow> <mi>n</mi> <mn>2</mn> </mrow> </msub> </mfrac> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>n</mi> <mn>2</mn> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    Wherein：WithRepresent the n-th winding primary and secondary side voltage phasor, Zn1And Zn2Represent the n-th winding primary and secondary side Equiva lent impedance, then calculate factor ZGExpression formula is：
    <mrow> <msub> <mi>Z</mi> <mi>G</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mfrac> <mn>1</mn> <msub> <mi>Z</mi> <mn>11</mn> </msub> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>Z</mi> <mn>12</mn> </msub> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>Z</mi> <mn>21</mn> </msub> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>Z</mi> <mn>22</mn> </msub> </mfrac> <mo>+</mo> <mo>...</mo> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>Z</mi> <mrow> <mi>n</mi> <mn>1</mn> </mrow> </msub> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>Z</mi> <mrow> <mi>n</mi> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>Z</mi> <mn>11</mn> </msub> <mo>=</mo> <msub> <mi>Z</mi> <mn>12</mn> </msub> <mo>=</mo> <msub> <mi>j&amp;omega;</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>L</mi> <mn>11</mn> </msub> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <msubsup> <mi>&amp;omega;</mi> <mi>s</mi> <mn>2</mn> </msubsup> <msub> <mi>C</mi> <mn>11</mn> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Z</mi> <mn>21</mn> </msub> <mo>=</mo> <msub> <mi>Z</mi> <mn>22</mn> </msub> <mo>=</mo> <msub> <mi>j&amp;omega;</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>L</mi> <mn>21</mn> </msub> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <msubsup> <mi>&amp;omega;</mi> <mi>s</mi> <mn>2</mn> </msubsup> <msub> <mi>C</mi> <mn>21</mn> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Z</mi> <mrow> <mi>n</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>Z</mi> <mrow> <mi>n</mi> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>j&amp;omega;</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>L</mi> <mrow> <mi>n</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <msubsup> <mi>&amp;omega;</mi> <mi>s</mi> <mn>2</mn> </msubsup> <msub> <mi>C</mi> <mrow> <mi>n</mi> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>
    <mrow> <msub> <mi>Z</mi> <mi>G</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>j&amp;omega;</mi> <mi>s</mi> </msub> </mrow> <mrow> <mfrac> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>L</mi> <mn>11</mn> </msub> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <msubsup> <mi>&amp;omega;</mi> <mi>s</mi> <mn>2</mn> </msubsup> <msub> <mi>C</mi> <mn>11</mn> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> </mfrac> <mo>+</mo> <mfrac> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>L</mi> <mn>21</mn> </msub> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <msubsup> <mi>&amp;omega;</mi> <mi>s</mi> <mn>2</mn> </msubsup> <msub> <mi>C</mi> <mn>21</mn> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> </mfrac> <mo>+</mo> <mn>...</mn> <mo>+</mo> <mfrac> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>L</mi> <mrow> <mi>n</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <msubsup> <mi>&amp;omega;</mi> <mi>s</mi> <mn>2</mn> </msubsup> <msub> <mi>C</mi> <mrow> <mi>n</mi> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> </mfrac> </mrow> </mfrac> </mrow>
    In formula, j and ωsRespectively plural empty unit and switch angular frequency；
    Then the conjugate of the complex power of the winding of transformer 12 is：
    <mrow> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>S</mi> <mn>12</mn> <mo>*</mo> </msubsup> <mo>=</mo> <mo>-</mo> <msub> <mover> <mi>I</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>12</mn> </msub> <msubsup> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>12</mn> <mo>*</mo> </msubsup> <mo>=</mo> <mfrac> <mrow> <mo>(</mo> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>m</mi> </msub> <mo>-</mo> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>12</mn> </msub> <mo>)</mo> <msubsup> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>12</mn> <mo>*</mo> </msubsup> </mrow> <msub> <mi>Z</mi> <mn>12</mn> </msub> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <msub> <mi>Z</mi> <mi>G</mi> </msub> <mrow> <msub> <mi>Z</mi> <mn>11</mn> </msub> <msub> <mi>Z</mi> <mn>12</mn> </msub> </mrow> </mfrac> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>11</mn> </msub> <msubsup> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>12</mn> <mo>*</mo> </msubsup> <mo>+</mo> <mrow> <mo>(</mo> <mfrac> <msub> <mi>Z</mi> <mi>G</mi> </msub> <mrow> <msub> <mi>Z</mi> <mn>12</mn> </msub> <msub> <mi>Z</mi> <mn>12</mn> </msub> </mrow> </mfrac> <mo>-</mo> <mfrac> <mn>1</mn> <msub> <mi>Z</mi> <mn>12</mn> </msub> </mfrac> <mo>)</mo> </mrow> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>12</mn> </msub> <msubsup> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>12</mn> <mo>*</mo> </msubsup> <mo>+</mo> <mfrac> <msub> <mi>Z</mi> <mi>G</mi> </msub> <mrow> <msub> <mi>Z</mi> <mn>21</mn> </msub> <msub> <mi>Z</mi> <mn>12</mn> </msub> </mrow> </mfrac> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>21</mn> </msub> <msubsup> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>12</mn> <mo>*</mo> </msubsup> <mo>+</mo> <mfrac> <msub> <mi>Z</mi> <mi>G</mi> </msub> <mrow> <msub> <mi>Z</mi> <mn>22</mn> </msub> <msub> <mi>Z</mi> <mn>12</mn> </msub> </mrow> </mfrac> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>22</mn> </msub> <msubsup> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>12</mn> <mo>*</mo> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mn>...</mn> <mo>+</mo> <mfrac> <msub> <mi>Z</mi> <mi>G</mi> </msub> <mrow> <msub> <mi>Z</mi> <mrow> <mi>n</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>Z</mi> <mn>12</mn> </msub> </mrow> </mfrac> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>n</mi> <mn>1</mn> </mrow> </msub> <msubsup> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>12</mn> <mo>*</mo> </msubsup> <mo>+</mo> <mfrac> <msub> <mi>Z</mi> <mi>G</mi> </msub> <mrow> <msub> <mi>Z</mi> <mrow> <mi>n</mi> <mn>2</mn> </mrow> </msub> <msub> <mi>Z</mi> <mn>12</mn> </msub> </mrow> </mfrac> <msub> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>n</mi> <mn>2</mn> </mrow> </msub> <msubsup> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>12</mn> <mo>*</mo> </msubsup> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,Represent voltage U12The conjugation of phasor value；
    Step 4：Order
    WhereinWithRespectively 11,21,22 ..., n1 and n2 windings electricity Press the electrical angle of the advanced 12 winding voltage phase of phase, U11、U12、U21、U22…Un1、Un2Respectively 11,12,21,22 ..., The equivalent sine fundamental voltage virtual value of n1 and n2 winding voltages；
    Consider resonant frequency and the unequal situation of switching frequency, i.e.,Then the active power of the winding of transformer 12 is：
    The real part of the winding complex power of Re indication transformers 12 conjugation；
    Can equally derive 11 windings, the n-th 1 and the active power of n2 windings be：
    Step 5：Because transformer primary secondary voltage waveform is that frequency is ωs50% square wave, primary side square-wave voltage amplitude is UCk(k=1,2 ... n)=UC1, the amplitude of secondary square-wave voltage is UCo, then the equivalent fundamental wave sinusoidal voltage virtual value of former secondary For：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>U</mi> <mn>11</mn> </msub> <mo>=</mo> <msub> <mi>U</mi> <mn>21</mn> </msub> <mo>=</mo> <msub> <mi>U</mi> <mn>31</mn> </msub> <mo>=</mo> <mn>...</mn> <mo>=</mo> <msub> <mi>U</mi> <mrow> <mi>n</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mn>4</mn> <mrow> <mi>&amp;pi;</mi> <msqrt> <mn>2</mn> </msqrt> </mrow> </mfrac> <msub> <mi>U</mi> <mrow> <mi>C</mi> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>U</mi> <mn>12</mn> </msub> <mo>=</mo> <msub> <mi>U</mi> <mn>22</mn> </msub> <mo>=</mo> <msub> <mi>U</mi> <mn>32</mn> </msub> <mo>=</mo> <mn>...</mn> <mo>=</mo> <msub> <mi>U</mi> <mrow> <mi>n</mi> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mn>4</mn> <mrow> <mi>&amp;pi;</mi> <msqrt> <mn>2</mn> </msqrt> </mrow> </mfrac> <msub> <mi>U</mi> <mrow> <mi>C</mi> <mi>o</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
    And can keeping primary side 11,12 in control ..., the phase of .., 1n winding voltage is just the same, namely：
    Step 6：Formula (11) and (12) are substituted into (7)~(10), obtain transformer 12,22 ... the active power of, n2 windings For：
    It is written as using the active power of the DC-DC converter of n independent appendiron core transformers：
    And becauseThen formula (13) and (14) It can be written as：
CN201710816460.5A 2017-09-12 2017-09-12 A kind of modeling method of shared core type multiwinding transformer Pending CN107844624A (en)

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CN114244139A (en) * 2021-12-23 2022-03-25 西安交通大学 Multi-winding high-frequency magnetic coupling current transformer and power decoupling control method thereof

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114244139A (en) * 2021-12-23 2022-03-25 西安交通大学 Multi-winding high-frequency magnetic coupling current transformer and power decoupling control method thereof
CN114244139B (en) * 2021-12-23 2024-05-14 西安交通大学 Multi-winding high-frequency magnetic coupling converter and power decoupling control method thereof

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