CN103378598A - Filter and designing method thereof - Google Patents

Filter and designing method thereof Download PDF

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CN103378598A
CN103378598A CN2012101196369A CN201210119636A CN103378598A CN 103378598 A CN103378598 A CN 103378598A CN 2012101196369 A CN2012101196369 A CN 2012101196369A CN 201210119636 A CN201210119636 A CN 201210119636A CN 103378598 A CN103378598 A CN 103378598A
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reactance
filter
inverter
damping resistance
equivalent capacity
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高成海
李江
吕海英
孙强
李广军
陈彬
杨飞
孙彦虎
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Siemens AG
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Abstract

The invention provides a filter and a designing method of the filter, wherein the filter is used for filtering harmonic waves of an inverter. The filter comprises at least one set of filtering units. Each filtering unit comprises a first electric reactor Li, a second electric reactor Lg, a damping resistor and an equivalent capacitor, wherein the second electric reactor Lg is connected with the first electric reactor Li in series, one end of the damping resistor is equivalently connected with the second electric reactor Lg in parallel, and one end of the equivalent capacitor is connected with the other end of the damping resistor. The electrical resistance value of the first electric reactor Li and the electrical resistance value of the second electric reactor Lg can be expressed by the following formula: 12%pu<=Li+Lg<=15%pu and 2<=Li/Lg<=3, wherein C is equivalent capacitance, f1 is output fundamental frequency of the inverter, fsw is switching frequency of an IGBT inside the inverter, and pu is phase voltage drop. The filter is high in converting efficiency, low in total harmonic distortion and capable of meeting governing standards of various harmonic waves.

Description

Filter and method for designing thereof
Technical field
The present invention relates to a kind of filter and method for designing thereof, relate in particular to a kind of filter for the novel energy electricity generation system.
Background technology
The exploitation of novel energy is global key subjects.Can not only progressively solve the lack of energy problem with novel energy generating (for example wind power generation and photovoltaic generation), also help to solve problem of environmental pollution.But the novel energy generating tends to inject a large amount of harmonic waves and reactive power to electrical network.For one of the solution problem, usually filter is connected to a large amount of harmonic waves of elimination between electrical network and the inverter.Fig. 1 is used for illustrating the topological structure schematic diagram of a kind of novel energy generating convertor assembly system.As shown in the figure, convertor assembly 30 comprises inverter 305.The input of convertor assembly 30 connects novel energy generator 40, and the output of convertor assembly 30 connects three-phase alternating current electrical network 10.Three-phase alternating current electrical network 10 comprises U a, U bAnd U cThree-phase.Filter 20 is connected between electrical network 10 and the convertor assembly 30, in order to reduce the harmonic wave quantity of input electrical network.Filter 20 comprises filter unit F a, F bAnd F c, respectively with U a, U bAnd U cBe connected.
In the generation of electricity by new energy field, line voltage is comparatively stable under normal conditions, and its harmonic content is less, so in this field, need choosing to the filter of current harmonics successful.In the design of existing filter, lack theoretical model and standard design method, usually, the relevant parameter in the filter need to determine according to engineer's experience repetition test.In addition, the energy conversion efficiency of existing filter is not high enough, and (hereinafter to be referred as THD) is not little for total harmonic distortion, and system is reliable and stable not, produces easily resonance phenomena.
Summary of the invention
The purpose of this invention is to provide a kind of energy conversion efficiency and approximate 1% up to 99%, THD, meet filter and the method for designing thereof of each harmonic wave control standard.
The invention provides a kind of filter for filtering inverter, comprising: at least one group of filter unit, described filter unit comprises: the first reactance L iThe the second reactance L that connects with described the first reactance gOne end and described the second reactance L gThe damping resistance of equivalent parallel; And equivalent capacity, an end is connected with the other end of described damping resistance, and its other end is connected with the equivalent capacity of another group filter unit; Wherein, described the first reactance L iReactance value and described the second reactance L gReactance value in following scope:
20 f 1 &le; 1 2 &pi; L g + L i L g L i C &le; f sw / 2 ,
12%pu≤L i+L g≤15%pu,
2≤L i/L g≤3,
Wherein, C is equivalent capacity, f 1Be inverter output fundamental frequency, f SwBe the switching frequency of igbt in the inverter, pu is the phase voltage pressure drop.
The present invention also provides a kind of method for designing of filter, and this filter comprises: the first reactance L iThe the second reactance L that connects with described the first reactance gOne end and described the second reactance L gThe damping resistance of equivalent parallel; And the equivalent capacity that is connected with the other end of described damping resistance of end, the first reactance L iReactance value and the second reactance L gReactance value determined by following formula:
20 f 1 &le; 1 2 &pi; L g + L i L g L i C &le; f sw / 2 ,
12%pu≤L i+L g≤15%pu,
2≤L i/L g≤3,
Wherein, C is equivalent capacity, f 1Be inverter output fundamental frequency, f SwBe the switching frequency of igbt in the inverter, pu is the phase voltage pressure drop.
The invention has the advantages that:
1. the present invention has very high energy conversion efficiency, and power factor reaches 1, and efficient all can reach 99% under semi-load and nominal load, and because generation of electricity by new energy efficient itself is not high, it is particularly important that the energy conversion efficiency of system becomes;
2. the present invention has less electric current, voltage harmonic aberration rate, is about 1% at fully loaded lower THD, and the harmonic attenuation rate is high, meets the harmonic wave control standards such as IEEE1547, IEEE519, VDE4105 and BDEW;
3. the present invention takes the multiple-protection measure, such as over voltage, and overcurrent, short circuit, overheated, reactance supersaturation and precharge loop guarantee that thus the reliable and secure operation of system stability and robustness are better;
4. the present invention avoids resonance phenomena to occur; And
5. the present invention provides the novel fruitful theory of a cover to calculate and method for designing for the exploitation of new-energy grid-connected filter, and emulation and experimental result have all been verified its feasibility and correctness, have improved accuracy and the reliability of development and Design.
Description of drawings
Hereinafter will also come by reference to the accompanying drawings the above-mentioned characteristic of the present invention, technical characterictic, advantage and implementation thereof are further described by description of a preferred embodiment in clear and definite understandable mode, wherein:
Fig. 1 is the topological structure schematic diagram of a kind of existing novel energy generating convertor assembly system;
Fig. 2 is the existing equivalent capacity that Star topology connects that is;
Fig. 3 exemplarily shows the topological structure schematic diagram of the convertor assembly system that comprises one embodiment of the present of invention;
Fig. 4 show exemplarily that the present invention adopts an embodiment in the equivalent capacity that connects of topology triangular in shape;
Fig. 5 is for showing the energy conversion efficiency of under different loads (5%, 10%, 20%, 30%, 50%, 100%) based on chart 2;
Fig. 6 exemplarily shows the related root locus of one embodiment of the present of invention;
Fig. 7 exemplarily shows the related Bode diagram of one embodiment of the present of invention;
Fig. 8 exemplarily shows the analogous diagram of the current waveform of non-filtered device;
Fig. 9 exemplarily shows the analogous diagram of the current waveform behind filter;
Figure 10 exemplarily shows the current spectrum of non-filtered device;
Figure 11 exemplarily shows the current spectrum behind filter;
Figure 12 exemplarily shows the analogous diagram of the current waveform of the equivalent capacity branch road of flowing through;
Figure 13 exemplarily shows the analogous diagram of the current spectrum of the equivalent capacity branch road of flowing through;
Figure 14 exemplarily shows the contrast experiment figure of harmonic current frequency spectrum and IEEE 1547 standards;
Figure 15 exemplarily shows the analogous diagram of the comparison of one embodiment of the present of invention and IEEE1547/IEEE519, VDE4105 and BDEW standard room.
Embodiment
Understand for technical characterictic, purpose and effect to invention have more clearly, now contrast description of drawings the specific embodiment of the present invention, identical label represents identical part in each figure.
Fig. 3 exemplarily shows the topological structure schematic diagram of the convertor assembly system that comprises one embodiment of the present of invention.As shown in Figure 3, filter 200 is connected between electrical network 100 and the inverter 300.400 represent the novel energy generating.Filter 200 in the present embodiment contains three groups of filter units.It should be noted that the present invention is not limited to three groups of filter units.Take first group of filter unit as example, first group of filter unit comprises the first reactance Li 1, the second reactance Lg 1, damping resistance
Figure BDA0000155709740000051
Equivalent capacity C 1And grading resistor
Figure BDA0000155709740000052
The first reactance Li 1With the second reactance Lg 1Be and be connected in series.Damping resistance
Figure BDA0000155709740000053
An end and the second reactance Lg 1Equivalent parallel.So-called equivalent parallel refers to from inverter 300 sides to be observed, because the impedance of electrical network 100 is very little, is equivalent to electrical network 100 and is short-circuit condition under the high frequency state, therefore is equivalent to the second reactance Lg 1With damping resistance
Figure BDA0000155709740000061
An end parallel connection after again with the first reactance Li 1Series connection.Work as damping resistance
Figure BDA0000155709740000062
An end and the second reactance Lg 1During equivalent parallel, its other end and equivalent capacity C 1An end connect.
The first reactance Li plays the effect that reduces ripple current and field fluctuation, need choose larger reactance value, but easily causes flux loss and system saturated, reduces real-time response.The introducing of the second reactance Lg can cooperate the Li effect, obviously reduces harmonics level, and reduces flux loss, if whole electricity generation system band electric power transformer, its leakage inductance can replace Lg.
The first reactance L iReactance value and the second reactance L gReactance value determined by following formula 1-4.Formula 5 can further be retrained.
The expression formula of resonance frequency is:
f res = I g V i = 1 2 &pi; L g + L i L g L i C 1 ---------------(formula 1),
Wherein, I gBe the output current of electrical network, V iBe inverter output voltage, L iBe the reactance of the first reactance, L gBe the reactance of the second reactance, C 1Be equivalent capacity.
For the characteristic of the inverter that is used for generation of electricity by new energy, f ResUsually the scope of choosing is:
20f 1≤ f Res≤ f Sw/ 2---------------------(formula 2),
Wherein, f ResBe resonance frequency, f 1Be inverter output fundamental frequency, f SwSwitching frequency for insulated gate bipolar transistor IGBT in the described inverter.Resonance frequency f ResChoose very crucially, select conference to cause the filter effect of filter poor, select I to cause inverter to burn, thereby cause electrical network to come off, produce " island effect ".
Should be noted in the discussion above that the filter that the present invention designs can not only be used in the grid-connected power generation system, also can be used in the traditional energy electricity generation system.
In addition, definition L Total=L i+ L g, L TotalUsually the scope of choosing is:
12%pu≤L Total≤ 15%pu-----------------(formula 3),
Wherein, pu is the phase voltage pressure drop.
In addition, L i/ L gUsually the scope of choosing is:
2≤L i/ L g≤ 3-----------------(formula 4),
In order to determine more accurately L gAnd L i, also need satisfy following constraints:
&Delta; i max = U dc 8 L total f sw &ap; K 1 * I N ---------------(formula 5),
Wherein, Δ i MaxBe the maximum of output current fluctuation, U DcBe DC side photovoltaic battery panel voltage, L Total=L i+ L g, I NBe described inverter output-current rating, k 1Be coefficient, it is worth in 15% to 25% scope.
In sum, the first reactance L iReactance value and the second reactance L gReactance value determined by said method.
The first reactance L iWith the second reactance L gRated current I LChoose and can meet:
I L=k 2* I N-------------(formula 6),
Wherein, I NBe inverter 300 output-current ratings, k 2Be coefficient, its output characteristic according to inverter 300 determines that its value can be in 1.1 to 1.2 scope.
Equivalent capacity C 1With and rated voltage determine please refer to following method.
As shown in Figure 3, equivalent capacity C 1Can be by four capacitor C ΔBe formed in parallel.It should be noted that shunt capacitance C ΔNumber be not limited to four, any amount of capacitor C such as two five ΔAll can and be unified into equivalent capacity C 1Electric capacity quantity depends on inverter switching frequency and its cut-off frequency.Then, equivalent capacity C 1Respectively with second group of filter unit in equivalent capacity C 2And the equivalent capacity C in the 3rd group of filter unit 3Join end to end, topology triangular in shape connects.(seeing also Fig. 4).Then, every end of triangular form more respectively with every group of filter unit in damping resistance R DampConnect.
The advantage that equivalent capacity topology triangular in shape connects is, compares with Y-connection (seeing also Fig. 2), and triangle topology can reduce capacitance to 1/3 times, and electric pressure is corresponding can be improved
Figure BDA0000155709740000081
Doubly.
U &Delta; = 3 * U Y C &Delta; = 1 3 * C Y ------------------------(formula 7),
Wherein, U Δ, U YBe voltage, C Δ, C YBe electric capacity.When reaching the required voltage grade, reduce cost and device volume thus, provide than large space and be beneficial to heat radiation.
Equivalent capacity C 1Value can meet
C 1 &le; 5 % P E 2 * 2 &pi; f 1 ----------------(formula 8),
Wherein, p is described inverter power output, and E is inverter output rated line voltage, f 1Be inverter output fundamental frequency.Formula 8 by
Q c≤ 5%P---------------(formula 9),
And
Q c = 3 * ( E / 3 ) 2 * 2 &pi; f 1 * C 1 ----------------(formula 10),
Determine, wherein, Q cBe total First Harmonic Reactive Power, p is described inverter power output, and E is inverter output rated line voltage, f 1Be inverter output fundamental frequency.
The rated voltage U of equivalent capacity CChoose and can meet:
U C=k 3* U N---------------(formula 11),
Wherein, U NBe inverter amount of exports phasing voltage, k 3Be coefficient, determine that according to output characteristic and the electrical network specific requirement of inverter 300 its value can be in 1.5 to 2 scope.
The connection of dihedral topology is prone to by the unbalanced phenomenon of the voltage drop of equivalent capacity, so all can a grading resistor R in parallel on each equivalent capacity Balence, its electric pressure and equivalent capacity are equal to, and power is chosen and is about 2W to prevent too much power loss, reduces filter efficient.
Damping resistance R DampResistance with and total current determine please refer to following method.
Damping resistance
Figure BDA0000155709740000091
Value can meet:
R damp 1 &le; 1 3 * 1 2 &pi; f res C 1 --------------(formula 12),
Wherein, f ResBe resonance frequency, C 1Be equivalent capacity.Damping resistance needs enough large to prevent the generation of resonance, and simultaneously, the excessive reduction that then can cause efficient is so the R value is less than or equal to 1/3 of resonance frequency place capacitive reactance usually.
The total current of damping resistance can meet:
I R damp &ap; ( U N + U Lg ) 2 R damp 2 + [ 1 / ( 2 &pi; f 1 C 1 ) ] 2 + k 4 2 * I N 2 ------------(formula 13),
Wherein, U NBe inverter amount of exports phasing voltage, U LgBe the second reactance pressure drop, R DampBe damping resistance, f 1Be inverter output fundamental frequency, C 1Be equivalent capacity, k 4Be the coefficient relevant with inverter, I NBe the inverter output-current rating.Formula 13 by
I 1 = U N + U Lg R damp 2 + [ 1 / ( 2 &pi; f 1 C 1 ) ] 2 ------------(formula 14),
I Sw=k 4* I N------------(formula 15),
And I R damp &ap; I 1 2 + I sw 2 ------------(formula 16),
Determine, wherein, I 1For resulting from damping resistance R DampOn fundamental current, U NBe inverter amount of exports phasing voltage, U LgBe the second reactance pressure drop, R DampBe damping resistance, f 1Be inverter output fundamental frequency, C 1Be equivalent capacity, I SwFor resulting from damping resistance R DampOn the switching frequency subharmonic current, k 4Be the coefficient relevant with inverter, I NBe the inverter output-current rating,
Figure BDA0000155709740000101
Total current for damping resistance.For certain photovoltaic DC-to-AC converter attribute, k 4Be about 10%, formula 15 all injects damping resistance R based on whole harmonic currents DampThe supposition of place branch road.
Following chart 1 has disclosed the concrete data of two embodiment of the present invention.
Chart 1
P(kW) Un(V) In(A) f(Hz) ΔUL(%)total f-res(kHz) f-cutoff(kHz) Li/Lg CY(uF) Ltotal(mH) Li(mH) Lg(mH) R(Ohm) Qc/P(%)
300 400 490 50 12.26% 1.71 2.42 3 252.00 0.035 0.138 0.046 0.09 4
300 400 490 50 15.99% 1.37 1.94 2 252.00 0.053 0.160 0.080 0.12 4
Following chart 2 illustrates the remarkable technique effect that one embodiment of the invention can obtain.In this embodiment, the first reactance L i=0.16mH, the second reactance L g=0.08mH, capacitor C=252uF.
Chart 2
Chart 2 is THD and the energy conversion efficiency of an embodiment under different loads (5%, 10%, 20%, 30%, 50%, 100%).
Fig. 5 is for showing under different loads the energy conversion efficiency of (5% 10% 20% 30% 50%100%) based on chart 2.As seen, under 50% load and 100% load energy conversion efficiency all on 99%.Electric current THD under 100% load less than 1%.
Fig. 6 exemplarily shows the related root locus of one embodiment of the present of invention.Transverse axis is real axis, and the longitudinal axis is the imaginary axis.Fig. 7 exemplarily shows the related Bode diagram of one embodiment of the present of invention.Transverse axis is frequency, and the longitudinal axis 1 is amplitude, and the longitudinal axis 2 is phase angle.Can find out that on scheming system is in the Asymptotic Stability state, effectively avoid the generation of resonance phenomena, the harmonic attenuation rate reaches-60dB/dec, thereby effectively reduces current harmonic content, improves the quality of power supply.
Fig. 8 exemplarily shows the analogous diagram of the current waveform of non-filtered device.Its transverse axis is the time, and the longitudinal axis is electric current.Fig. 9 exemplarily shows the analogous diagram of the current waveform behind filter.Its transverse axis is the time, and the longitudinal axis is electric current.Figure 10 exemplarily shows the analogous diagram of the current spectrum of non-filtered device.Its transverse axis is frequency, and the longitudinal axis is electric current.Figure 11 exemplarily shows the analogous diagram of the current spectrum behind filter.Its transverse axis is frequency, and the longitudinal axis is electric current.Can be found out the filter effect of filter involved in the present invention by Fig. 8-11.
Figure 12 exemplarily shows the analogous diagram of the current waveform of the equivalent capacity branch road of flowing through, and its transverse axis is the time, and the longitudinal axis is electric current; Figure 13 exemplarily shows the analogous diagram of the current spectrum of the equivalent capacity branch road of flowing through, and its transverse axis is frequency, and the longitudinal axis is electric current.Upper two figure show that the current harmonics of inverter output is absorbed by capacitive branch, thereby guarantees that its output waveform presents the sinusoidal waveform of perfect harmony under the effect of filter.
Figure 14 exemplarily shows the lab diagram of the comparison of harmonic current frequency spectrum and IEEE1547 standard.Its transverse axis is harmonic number, and the longitudinal axis is electric current.Under the EEE1547 standard, THD is less than or equal to 5%.THD of the present invention is about 1%.
Figure 15 exemplarily shows the analogous diagram of the comparison of one embodiment of the present of invention and IEEE1547/IEEE519, VDE4105 and BDEW standard room.Shown that by figure the present invention is high to the harmonic attenuation rate, meets the harmonic wave control standards such as IEEE1547/IEEE519, VDE4105 and BDEW, thereby has reduced ' pollution ' to the electrical network quality of power supply.
Above-mentioned listed detailed description only is specifying for feasibility embodiment of the present invention; be not to limit protection scope of the present invention; protection range is as the criterion with claim, and all equivalence or changes that does not break away from the embodiment that spirit of the present invention does all should be included within protection scope of the present invention.

Claims (14)

1. harmonic filter that be used for to filter inverter comprises:
At least one group of filter unit, every group of described filter unit comprises:
The first reactance L i
The the second reactance L that connects with described the first reactance g
One end and described the second reactance L gThe damping resistance of equivalent parallel; And
The equivalent capacity that one end is connected with the other end of described damping resistance; Wherein, institute
State the first reactance L iReactance value and described the second reactance L gReactance value in following scope:
20 f 1 &le; 1 2 &pi; L g + L i L g L i C &le; f sw / 2 ,
12%pu≤L i+ L g≤ 15%pu, and
2≤L i/L g≤3,
Wherein, C is equivalent capacity, f 1Be the fundamental frequency of described inverter output, f SwBe igbt switching frequency in the described inverter, pu is the phase voltage pressure drop.
2. filter as claimed in claim 1 or 2 is characterized in that, described the first reactance L iReactance value and described the second reactance L gReactance value also by constraints
Figure FDA0000155709730000021
Revise, wherein, U DcBe the DC bus-bar voltage of described inverter, I NBe described inverter output-current rating, k 1Be coefficient, it is worth in 15% to 25% scope.
3. filter as claimed in claim 1 or 2 is characterized in that described filter is used for wind power generation or photovoltaic generation.
4. filter as claimed in claim 1 or 2, it is characterized in that, described filter comprises three groups of filter units, the first filter unit that contains the first equivalent capacity and the first damping resistance, the second filter unit that contains the second equivalent capacity and the second damping resistance, and the 3rd filter unit that contains C grade effect electric capacity and the 3rd damping resistance, described first, second, third, etc. effect electric capacity joins end to end separately, topology triangular in shape connects, and three tie points of described electric capacity are connected with an end of described first, second, third damping resistance respectively.
5. filter as claimed in claim 1 or 2 is characterized in that, the total current of described damping resistance I R damp &ap; ( U N + U Lg ) 2 R damp 2 + [ 1 / ( 2 &pi; f 1 C ] ) 2 + k 4 2 * I N 2 , Wherein,
U NBe described inverter amount of exports phasing voltage, U LgBe described the second reactance pressure drop, R DampBe described damping resistance resistance, f 1Be the fundamental frequency of described inverter output, C is described equivalent capacity, k 4Be the coefficient relevant with described inverter, I NBe described inverter output-current rating.
6. filter as claimed in claim 1 or 2 is characterized in that, described equivalent capacity C value meets
Figure FDA0000155709730000031
P is described inverter power output, and E is described inverter output rated line voltage, f 1Fundamental frequency for described inverter output.
7. filter as claimed in claim 1 or 2 is characterized in that, described equivalent capacity is in parallel with a grading resistor.
8. filter as claimed in claim 1 or 2 is characterized in that, described the second reactance is the leakage inductance of power transformer of the system at described filter place.
9. method for designing of filtering the filter of inverter harmonic, this filter comprises: the first reactance L iThe the second reactance L that connects with described the first reactance gOne end and described the second reactance L gThe damping resistance of equivalent parallel; And the equivalent capacity that is connected with the other end of described damping resistance of end, the first reactance L iReactance value and the second reactance L gReactance value determined by following formula:
20 f 1 &le; 1 2 &pi; L g + L i L g L i C &le; f sw / 2 ,
12%pu≤L i+ L g≤ 15%pu, and
2≤L i/L g≤3,
Wherein, C is equivalent capacity, f 1Be the fundamental frequency of described inverter output, f SwBe the switching frequency of igbt in the described inverter, pu is the phase voltage pressure drop.
10. the method for designing of filter as claimed in claim 9 is characterized in that, described the first reactance L iReactance value and described the second reactance L gReactance value also by constraints
Figure FDA0000155709730000042
Revise, wherein, U DcBe the DC bus-bar voltage of described inverter, I NBe described inverter output-current rating, k 1Be coefficient, it is worth in 15% to 25% scope.
11. the method for designing such as claim 9 or 10 described filters is characterized in that, described filter is used for wind power generation or photovoltaic generation.
12. the method for designing such as claim 9 or 10 described filters is characterized in that, described damping resistance R value meets f ResBe resonance frequency, C is described equivalent capacity.
13. the method for designing such as claim 9 or 10 described filters is characterized in that the total current of described damping resistance meets
I R damp &ap; ( U N + U Lg ) 2 R damp 2 + [ 1 / ( 2 &pi; f 1 C ] ) 2 + k 4 2 * I N 2 , Wherein, U NBe described inverter amount of exports phasing voltage, U LgBe described the second reactance pressure drop, R DampBe described damping resistance resistance, f 1Be the fundamental frequency of described inverter output, C is described equivalent capacity, k 4Be the coefficient relevant with described inverter, I NBe described inverter output-current rating.
14. the method for designing such as claim 9 or 10 described filters is characterized in that, described equivalent capacity C value meets
Figure FDA0000155709730000052
P is described inverter power output, and E is described inverter output rated line voltage, f 1Fundamental frequency for described inverter output.
CN2012101196369A 2012-04-20 2012-04-20 Filter and designing method thereof Pending CN103378598A (en)

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CN112069655A (en) * 2020-08-04 2020-12-11 三峡大学 Loss calculation method for high-frequency high-power three-phase transformer
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CN113872208B (en) * 2021-09-30 2024-04-26 国网江苏省电力有限公司电力科学研究院 DC side capacitor design method of bidirectional energy flow impedance measuring device

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