CN103915913B  Fractional order parallelseries resonance wireless power transmission system  Google Patents
Fractional order parallelseries resonance wireless power transmission system Download PDFInfo
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 CN103915913B CN103915913B CN201410129860.5A CN201410129860A CN103915913B CN 103915913 B CN103915913 B CN 103915913B CN 201410129860 A CN201410129860 A CN 201410129860A CN 103915913 B CN103915913 B CN 103915913B
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 fractional order
 inductance
 secondary
 former limit
 electric capacity
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Abstract
Description
Technical field
The invention belongs to wireless power transmission or the field of wireless power transmission technology, particularly to a kind of fractional order Seriesmultiple connection resonant radio can transmit system.
Background technology
Wireless power transmission or wireless power transmission technology before more than 100 years just by American inventor tesla (Nicola Tesla) is attempted experimentally.2006, the research of the Massachusetts Institute of Technology (MIT) Personnel utilize the resonance technique of physics successfully to light one in 2m distance left and right with the efficiency of 40% The bulb of 60W, this experiment is not only the reproduction of tesla's experiment, especially wireless power transmission technology Another new breakthrough, and started the upsurge of wireless power transmission research.
Wireless power transmission technology is the electric energy transmission means of a kind of wide application prospect, have safety, can Lean on, flexibly, the advantage such as convenient, be increasingly subject to the attention of countries in the world, and the most extensively applied In the various places be not suitable for or be inconvenient to use conductive contact transmission electric energy, as implantable medical device, Mobile electronic product, robot, rail electric car such as are powered at the occasion, and be expected in the near future can be Smallpower electronic product wireless charging aspect replaces traditional plug charging.
Current radio energy transmission system is all based on integer rank inductance, electric capacity realizes, its resonance frequency Rate is only determined by inductance value and capacitance, and therefore, the design of its system only need to consider parameter value, it is not necessary to considers The exponent number of element, the degree of freedom of design is fewer.Meanwhile, the element of real system is substantially fractional order , but the most exponent number in current reality is close to 1, neglects completely during for fractional order Slightly.Traditional modeling by integer rank designs radio energy transmission system, under certain conditions, and reason Opinion and actual error may be the biggest.
Fractional order device (such as fractional order electric capacity and fractional order inductance) concept derive from fractional calculus Generation, and the concept of fractional calculus has had the history of more than 300 year, almost microwith integer rank longpending Divide and be born simultaneously.But owing to fractional order is more complicated, and the most good numerical analysis tools, Therefore it is constantly in the theory analysis stage.In recent decades, due to biotechnology, macromolecular material etc. Development, it has been found that integer rank calculus can not well explain the phenomenon that nature exists, and therefore divides Number rank calculus starts to be paid attention to, and starts to be applied to engineering field, its control field research and Apply the most perfect.Meanwhile, the fractional order device at two ends is manufactured at laboratory.But point Number rank some special character of Circuits and Systems are studied, and the application in wireless power transmission field is more It is not to be mentioned.
In view of current fractional order element or fractional order circuit huge advantage in some aspects, and it is the most not It is applied to wireless power transmission field, it is therefore necessary to propose a kind of fractional order stringresonant radio energy Transmission system.
Summary of the invention
It is an object of the invention to overcome abovementioned the deficiencies in the prior art, it is provided that a kind of fractional order seriesmultiple connection is humorous Shake radio energy transmission system.
The present invention is achieved through the following technical solutions:
A kind of fractional order seriesmultiple connection resonant radio can transmit system, including high frequency power source V_{S}, emission part Point, receiving portion and load R_{L}；Emitting portion includes the former limit fractional order electric capacity being connected in seriesWith former limit Fractional order inductanceFormer limit fractional order inductanceThere is former limit resistance R_{P}；Receiving portion includes being connected in parallel Secondary fractional order electric capacityWith secondary fractional order inductanceSecondary fractional order inductanceThere is secondary resistance R_{S}。
Described a kind of fractional order seriesmultiple connection resonant radio can transmit system, former limit fractional order electric capacity、 Secondary fractional order electric capacityVoltage, current differential relation is satisfied by:Phase relation is full Foot:Wherein, i_{C}For fractional order capacitance current, v_{C}For fractional order capacitance voltage, α is mark The exponent number of rank electric capacity, and 0 ＜ α≤2, C^{α}Value for fractional order electric capacity.
Described a kind of fractional order seriesmultiple connection resonant radio can transmit system, former limit fractional order inductance、 Secondary fractional order inductanceVoltage, current differential relation is satisfied by:Phase relation meets:Wherein, v_{L}For the voltage of fractional order inductance, i_{L}For the electric current of fractional order inductance, β is mark The exponent number of rank inductance, and 0 ＜ β≤2, L^{β}Value for fractional order inductance.
Described a kind of fractional order seriesmultiple connection resonant radio can transmit system, emitting portion and receiving portion Between be the wireless power transmission that realizes by the way of the coupling of fractional order circuit seriesmultiple connection resonance.
The operation principle of the present invention is: emitting portion and receiving portion are respectively by former limit fractional order electric capacity C_{P}α、 Former limit fractional order inductance, former limit resistance R_{P}, secondary fractional order electric capacity, secondary fractional order inductance、 Secondary resistance R_{S}Constitute fractional order RLC seriesmultiple connection resonance circuit, emitting portion and receiving portion by humorous The mode of coupling of shaking realizes being wirelessly transferred of electric energy.
Compared with prior art, present invention have the advantage that
1, the wireless power transmission using fractional order element to realize, is different from conventional radio energy completely and passes Communication system, adds the degree of freedom of parameter designing.
2, by designing the exponent number of selection element, the resonance frequency of radio energy transmission system can be substantially reduced Rate, thus reduce the requirement to power electronic devices, it is very beneficial for the design of real system.
3, by designing suitable fractional order exponent number, throughput power can be made bigger.
Accompanying drawing explanation
Fig. 1 is the schematic diagram that the fractional order seriesmultiple connection resonant radio of the present invention can transmit system.
Fig. 2 is α=1.2, output during β=0.9 and the relation curve of frequency f.
Fig. 3 is α=0.8, efficiency of transmission during β=0.9 and the relation curve of frequency f.
Fig. 4 is α=1.2, output during β=1.5 and the relation curve of frequency f.
Fig. 5 is α=0.8, output during β=1.2 and the relation curve of frequency f.
Specific embodiments
It is embodied as being further described to invention below in conjunction with accompanying drawing, but the enforcement of the present invention and protection It is not limited to this.
Embodiment
As it is shown in figure 1, the signal of system can be transmitted for the fractional order seriesmultiple connection resonant radio of the present invention Figure, below in conjunction with the operation principle of this figure explanation present invention.In Fig. 1, high frequency power source V_{S}, former limit divides Number rank electric capacity, former limit fractional order inductanceWith former limit resistance R_{P}Connect and compose series resonance；Secondary mark Rank electric capacity, secondary fractional order inductance, secondary resistance R_{S}With load R_{L}Connect and compose parallel resonance；Send out Penetrate part and receiving portion realizes wireless power transmission by mutual inductance M.For the convenience analyzed, make former limit Fractional order electric capacityWith secondary fractional order electric capacityParameter is consistent, and omits upper and lower mark, is designated as C；Order Former limit fractional order inductanceWith secondary fractional order inductanceParameter is consistent, and omits upper and lower mark, is designated as L； Make former limit resistance R_{P}With secondary resistance R_{S}For R.Then can obtain the Fractional Differential Equation of system:
In formula, v_{S}For the transient expression form of high frequency power source, i_{1}For former limit fractional order inductive current,
For secondary fractional order inductive current, v_{C1}For former limit fractional order capacitance voltage, v_{C2}For secondary fractional order electricity
Voltage.The differential equation of said system can be obtained by Laplace transform:
V_{S}(s)=V_{C1}(s)+s^{β}LI_{1}(s)+s^{β}MI_{2}(s)+I_{1}(s)R
I_{1}(s)=s^{α}CV_{C1}(s)
V_{C2}(s)=s^{β}LI_{2}(s)+s^{β}MI_{1}(s)+I_{2}(s)R
Symbol in above equation group is Laplace transform form, has one by one with the differential equation of system Corresponding relation, i.e. I_{1}For former limit loop current, I_{2}For secondary loop electric current, V_{C1}For former limit fractional order electric capacity Voltage, V_{C2}For secondary fractional order capacitance voltage.Solve:
V_{C2}(s)=s^{β}MV_{S}(s)/
In a frequency domain, there is s=j ω.Then can be in the hope of output P_{o}For:
From the expression formula of output, the size of output is main and mutual inductance M, operating angle frequency Exponent number α with β is relevant for ω, fractional order.Analyze further below, the operating angle frequency shadow to output Ringing, other parameters keep constant.A kind of fractional order seriesmultiple connection resonant radio can transmit the concrete ginseng of system Number is: V_{S}=10V, L=100 μ H, C=0.2533nF, R_{L}=50 Ω, coefficient of coup k=0.1(and mutual inductance M=k × L), α=1.2, β=0.9, R=0.5 Ω.Then output and relation curve such as Fig. 2 of frequency f Shown in.Integer level system is the resonance frequency of (i.e. α=1, β=1, other parameter constants) under same parameter Rate is 1MHz, and as shown in Figure 2, the resonant frequency of system is less than 1MHz.As can be seen here, permissible The resonance frequency of fractional order circuit parallel resonance radio energy transmission system is reduced by choosing fractional order exponent number Rate, thus the design of beneficially radio energy transmission system.
1) α is worked as>1,<when 1, as an example, a kind of fractional order seriesmultiple connection resonant radio can transmit system to β The design parameter of system is: V_{S}=10V, L=100 μ H, C=0.2533nF, R_{L}=50 Ω, coefficient of coup k=0.1 (and mutual inductance M=k × L), α=1.2, β=0.9, R=0.5 Ω.Then output is bent with the relation of frequency f Line is as shown in Figure 2.Integer level is united under same parameter (i.e. α=1, β=1, other parameter constants) Resonant frequency be 1MHz, and as shown in Figure 2, the resonant frequency of system is less than 1MHz.Thus may be used See, fractional order circuit parallel resonance radio energy transmission system can be reduced by choosing fractional order exponent number Resonant frequency, thus the design of beneficially radio energy transmission system.
2) as α < 1, β, < when 1, as an example, a kind of fractional order seriesmultiple connection resonant radio can transmit system The design parameter of system is: V_{S}=10V, L=100 μ H, C=0.2533nF, R_{L}=50 Ω, coefficient of coup k=0.1 (and mutual inductance M=k × L), α=0.8, β=0.9, R=0.5 Ω.Then output is bent with the relation of frequency f Line is as it is shown on figure 3, this situation can be greatly improved the resonant frequency of system, and output is the least, Real system is not intended to this situation occur, should avoid during design.
3) work as α > 1, β > 1 time, as an example, a kind of fractional order seriesmultiple connection resonant radio can transmit system The design parameter of system is: V_{S}=10V, L=100 μ H, C=0.2533nF, R_{L}=50 Ω, coefficient of coup k=0.1 (and mutual inductance M=k × L), α=1.2, β=0.9, R=0.5 Ω.Then output is bent with the relation of frequency f Line is as shown in Figure 4.Although this situation reduces the resonant frequency of system, but output paying no attention to Think, therefore also should avoid during design.
4) as α<1, β>1, this situation is more complicated, and resonant frequency is with the change of fractional order exponent number Bigger.As an example, fractional order seriesmultiple connection resonant radio can transmit the design parameter of system and is: V_{S}=10V, L=100 μ H, C=0.2533nF, R_{L}=50 Ω, coefficient of coup k=0.1(and mutual inductance M=k × L), α=0.8, β=1.2, R=0.5 Ω.Then the relation curve of output and frequency f is as shown in Figure 5.This Although situation reduces the resonant frequency of system, but substantially can not realize the transmission of power, when therefore designing Also should avoid.
Situation described above is for equally applicable during α=β.
Abovedescribed embodiment is the present invention preferably embodiment, but embodiments of the present invention are not by described reality Execute the restriction of example, the change made under other any spirit without departing from the present invention and principle, modification, Substitute, combine, simplify, all should be the substitute mode of equivalence, within being included in protection scope of the present invention.
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