CN103915909B - A kind of integer rank and fractional order series-multiple connection resonance radio energy transmission system - Google Patents

Abstract

The invention provides a kind of integer rank and fractional order series-multiple connection resonance radio energy transmission system, comprise high frequency power source, radiating portion, receiving unit and load, radiating portion comprises the former limit fractional order electric capacity and the former limit fractional order inductance that are connected in series, and former limit fractional order inductance has former limit resistance; Receiving unit comprises the secondary integer rank electric capacity and the secondary fractional order inductance that are connected in parallel, and secondary fractional order inductance has secondary resistance. The present invention adopts integer rank and fractional order element to realize wireless power transmission, has increased the dimension of parameter designing, is different from traditional radio energy transmission system of only being realized by integer rank element completely.

Description

A kind of integer rank and fractional order series-multiple connection resonance radio energy transmission system

Technical field

The invention belongs to the field of wireless power transmission or wireless technology of transmission of electricity, particularly a kind of integer rank and fractional orderSeries-multiple connection resonance radio energy transmission system.

Background technology

Wireless power transmission or wireless technology of transmission of electricity before more than 100 years just by the (Nicola of American inventor teslaTesla) attempted experimentally. 2006, the researcher of the Massachusetts Institute of Technology (MIT) utilized the resonance technique of physics to becomeThe bulb of having lighted a 60W at 2m apart from left and right with 40% efficiency of merit, this experiment is not only the weight of tesla's experimentExisting, another new breakthrough of wireless power transmission technology especially, and started the upsurge of wireless power transmission research.

Current radio energy transmission system is all realized based on integer rank inductance, electric capacity, and its resonant frequency is only by electricitySense value and capacitance decision, therefore, its system only need be considered parameter value, without the exponent number of considering element, the freedom of designSpend fewer. Meanwhile, the element of real system is fractional order in essence, but the most exponent number of using in current reality connectsBe bordering on 1, ignore completely for the situation of fractional order. Traditional modeling of passing through integer rank designs radio energy transmission system,Under certain conditions, theoretical and actual error may be very large.

The generation that derives from fractional calculus of fractional order device (for example fractional order electric capacity and fractional order inductance) concept,And the concept of fractional calculus has had the history of more than 300 year, be almost born with integer rank calculus simultaneously. But owing to dividingNumber rank more complicated, and never have good numerical analysis tools, therefore it is always in the theory analysis stage. Nearly tensNian Lai, due to the development of biotechnology, macromolecular material etc., it is found that integer rank calculus can not well explain natureThe phenomenon existing, therefore fractional calculus starts to be paid attention to, and starts to be applied to engineering field, and it grinds control fieldStudy carefully and apply day by day perfect. Meanwhile, the fractional order device at two ends is out manufactured in laboratory. But fractional order circuit withSome special character of system are studied, and are not mentioned especially in the application in wireless power transmission field.

In view of current fractional order element or fractional order circuit huge advantage in some aspects, and it is not also applied toWireless power transmission field, is therefore necessary to propose a kind of integer rank and fractional order series-multiple connection resonance radio energy transmission system.

Summary of the invention

The object of the invention is to overcome above-mentioned the deficiencies in the prior art, a kind of integer rank and fractional order series-multiple connection are providedResonance radio energy transmission system.

The present invention is achieved through the following technical solutions:

A kind of integer rank and fractional order series-multiple connection resonance radio energy transmission system, comprise high frequency power source V_S, emission partPoint, receiving unit and load R_L, radiating portion comprises 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 unit comprises the secondary integer rank capacitor C being connected in parallel_SAnd pairLimit fractional order inductance L_S, secondary fractional order inductance L_SThere is secondary resistance R_S。

Described a kind of integer rank and fractional order series-multiple connection resonance radio energy transmission system, former limit fractional order electric capacitySecondary fractional order electric capacityVoltage, current differential relation all meet:Phase relation meets:Wherein, i_CFor fractional order capacitance current, v_CFor fractional order capacitance voltage, α is the exponent number of fractional order electric capacity, and 0 < α≤2, C^αFor the value of fractional order electric capacity. In formula, α=1 o'clock is the described satisfied relation of integer rank electric capacity.

Described a kind of integer rank and fractional order series-multiple connection resonance radio energy transmission system, former limit fractional order inductanceSecondary fractional order inductanceVoltage, current differential relation all meet:Phase relation meets:Wherein, v_LFor the voltage of fractional order inductance, i_LFor the electric current of fractional order inductance, β is the exponent number of fractional order inductance, andAnd 0 < β≤2, L^βFor the value of fractional order inductance. In formula, β=1 o'clock is the described satisfied relation of integer rank inductance.

In described a kind of integer rank and fractional order series-multiple connection resonance radio energy transmission system, radiating portion and receptionIt between part, is the wireless power transmission realizing by the mode of fractional order series-multiple connection resonance coupling.

Operation principle of the present invention is: radiating portion is by former limit fractional order electric capacityFormer limit fractional order inductanceFormer limitResistance R_PForm RLC series resonant circuit, receiving unit is by secondary integer rank capacitor C_S, secondary integer rank inductance L_S, secondary resistanceR_SForm RLC antiresonant circuit, or radiating portion is by integer rank, former limit capacitor C_P, integer rank, former limit inductance L_P, former limit resistance R_PForm RLC series resonant circuit, receiving unit is by secondary fractional order electric capacitySecondary fractional order inductanceSecondary resistance R_SStructureBecome RLC antiresonant circuit. The mode that radiating portion and receiving unit are coupled by resonance realizes the wireless transmission of electric energy.

Compared with prior art, tool of the present invention has the following advantages:

1, the wireless power transmission that adopts fractional order element to realize, is different from radio energy transmission system in the past completely,Increase the free degree of parameter designing.

2,, by the exponent number of selection element, can greatly reduce the resonant frequency of radio energy transmission system, thereby reduceTo the requirement of power electronic devices, be very beneficial for the design of real system.

Brief description of the drawings

Fig. 1 is specific embodiment of the invention circuit.

Fig. 2 is α=1.2, the power output of β=0.9 o'clock embodiment 1 and the relation curve of frequency f.

Fig. 3 is α=0.8, the efficiency of transmission of β=0.9 o'clock embodiment 1 and the relation curve of frequency f.

Fig. 4 is α=1.2, the power output of β=1.5 o'clock embodiment 1 and the relation curve of frequency f.

Fig. 5 is α=0.8, the power output of β=1.5 o'clock embodiment 1 and the relation curve of frequency f.

Specific embodiments

Below in conjunction with accompanying drawing, the concrete enforcement of invention is further described, but enforcement of the present invention and protection are not limited toThis.

Embodiment

As shown in Figure 1, be specific embodiment of the invention circuit, operation principle of the present invention is described and establishes below in conjunction with this figureMeter method. As shown in Figure 1, high frequency power source V_S, former limit fractional order electric capacityFormer limit fractional order inductanceWith former limit resistance R_PStructureBecome series resonance; Secondary integer rank capacitor C_S, secondary integer rank inductance L_SWith secondary resistance R_SWith load R_LForm parallel resonance.Radiating portion and receiving unit are realized wireless power transmission by mutual inductance M. Can be obtained the fractional order differential side of system by Fig. 1Journey:

$v_S=v_{C1}+L_P^{\mathrm{\&beta;}}\frac{d^{\mathrm{\&beta;}}{i}_1}{{\mathrm{dt}}^{\mathrm{\&beta;}}}+M\frac{{\mathrm{di}}_2}{\mathrm{dt}}+i_1{R}_P$

$0=i_2+C_S\frac{{\mathrm{dv}}_{C2}}{\mathrm{dt}}+\frac{v_{C2}}{R_L}$

$i_1=C_P^{\mathrm{\&alpha;}}\frac{d^{\mathrm{\&alpha;}}{v}_{c1}}{{\mathrm{dt}}^{\mathrm{\&alpha;}}}$

$v_{C2}=L_S\frac{{\mathrm{di}}_2}{\mathrm{dt}}+M\frac{d^{\mathrm{\&beta;}}{i}_1}{{\mathrm{dt}}^{\mathrm{\&beta;}}}+i_2{R}_S$

In formula, v_SFor the transient expression form of high frequency power source, i₁For former limit fractional order inductive current, i₂For secondary markRank inductive current, v_C1For former limit fractional order capacitance voltage, v_C2For secondary fractional order capacitance voltage. The differential equation of said systemCan be obtained by Laplace transform:

$V_S\left(s\right)=V_{C1}\left(s\right)+s^{\mathrm{\&beta;}}{L}_P^{\mathrm{\&beta;}}{I}_1\left(s\right)+s{\mathrm{MI}}_2\left(s\right)+I_1\left(s\right)R_P$

$0=I_2\left(s\right)+s{C}_S{V}_{C2}\left(s\right)+\frac{V_{C2}\left(s\right)}{R_L}$

$I_1\left(s\right)={s^{\mathrm{\&alpha;}}C}_P^{\mathrm{\&alpha;}}{V}_{C1}\left(s\right)$

$V_{C2}\left(s\right)=s{L}_S{I}_2\left(s\right)+s^{\mathrm{\&beta;}}{\mathrm{MI}}_1\left(s\right)+I_2\left(s\right)R_S$

Symbol in above equation group is Laplace transform form, has corresponding pass one by one with the differential equation of systemSystem, i.e. I₁For former limit loop current, I₂For secondary loop current, V_C1For former limit fractional order capacitance voltage, V_C2For secondary fractional orderCapacitance voltage. Solve:

$\begin{array}{c}{V}_{C2}\left(s\right)=s^{\mathrm{\&beta;}}{\mathrm{MV}}_S\left(s\right)/\\ [(R_P+s^{\mathrm{\&beta;}}{L}_P^{\mathrm{\&beta;}}+\frac{1}{s^{\mathrm{\&alpha;}}{C}_P^{\mathrm{\&alpha;}}})g(1+s^2{L}_S{C}_S+\frac{s{L}_S}{R_L}+s{R}_S{C}_S+\frac{R_S}{R_L})-s^{1+\mathrm{\&beta;}}{M}^2(s{C}_S+\frac{1}{R_L})]\end{array}$

In frequency domain, there is s=j ω. Can be in the hope of power output P_oFor:

$P_o=V_{C2}^2/R_L$

From the expression formula of power output, the main and mutual inductance M of the size of power output, operating angle frequencies omega, fractional orderExponent number α is relevant with β. Further analyze below, the impact of operating angle frequency on power output, other parameters remain unchanged.

The design parameter of embodiment system is: V_S=10V， $L_P^{\mathrm{\&beta;}}=L_S^{\mathrm{\&beta;}}=L_P=L_S=100\mathrm{\&mu;H},$ $C_P^{\mathrm{\&alpha;}}=C_S^{\mathrm{\&alpha;}}=C_P=C_S=0.2533\mathrm{nF},$ R_L=50 Ω, coefficient of coup k=0.1(and mutual inductance $M=k\sqrt{L_P^{\mathrm{\&beta;}}{L}_S}$ ），α=1.2，β=0.9，R_S＝R_P＝0.5Ω。

1) work as α>1, β<1 o'clock, as an example, a kind of integer rank and fractional order series-multiple connection resonance radio energy transmission system:V_S=10V， $L_P^{\mathrm{\&beta;}}=L_S^{\mathrm{\&beta;}}=L_P=L_S=100\mathrm{\&mu;H},C_P^{\mathrm{\&alpha;}}=C_S^{\mathrm{\&alpha;}}=C_P=C_S=0.2533\mathrm{nF},$ R_L=50 Ω, coefficient of coup k=0.1(and mutual inductance），α=1.2，β=0.9，R_S＝R_P=0.5 Ω. The relation curve of power output and frequency fAs shown in Figure 2. System resonant frequency of (being α=1, β=1, other parameter constants) under same parameter in integer rank is 1MHz, andAs shown in Figure 2, the resonant frequency of system is less than 1MHz. As can be seen here, can reduce fractional order by choosing fractional order exponent numberThe resonant frequency of circuit parallel resonance radio energy transmission system, thus be conducive to the design of radio energy transmission system.

2) when α < 1, β < 1 o'clock, as an example, a kind of integer rank and fractional order series-multiple connection resonance radio energy transmission system:V_S=10V， $L_P^{\mathrm{\&beta;}}=L_S^{\mathrm{\&beta;}}=L_P=L_S=100\mathrm{\&mu;H},C_P^{\mathrm{\&alpha;}}=C_S^{\mathrm{\&alpha;}}=C_P=C_S=0.2533\mathrm{nF},$ R_L=50 Ω, coefficient of coup k=0.1(and mutual inductance），α=0.8，β=0.9，R_S＝R_P=0.5 Ω. The relation curve of power output and frequency f asShown in Fig. 3, this situation can improve the resonant frequency of system greatly, and substantially can not realize the transmission of power, real systemIn do not wish to occur this situation.

3) work as α > 1, β > 1 o'clock, as an example, a kind of integer rank and fractional order series-multiple connection resonance radio energy transmission system:V_S=10V， $L_P^{\mathrm{\&beta;}}=L_S^{\mathrm{\&beta;}}=L_P=L_S=100\mathrm{\&mu;H},C_P^{\mathrm{\&alpha;}}=C_S^{\mathrm{\&alpha;}}=C_P=C_S=0.2533\mathrm{nF},$ R_L=50 Ω, coefficient of coup k=0.1(and mutual inductance），α=1.2，β=1.5，R_S＝R_P=0.5 Ω. The relation curve of power output and frequency fAs shown in Figure 4. This situation has reduced the resonant frequency of system, is conducive to the design of radio energy transmission system.

4) when α<1, β>1 o'clock, as an example, a kind of integer rank and fractional order series-multiple connection resonance radio energy transmission system:VS=10V， $L_P^{\mathrm{\&beta;}}=L_S^{\mathrm{\&beta;}}=L_P=L_S=100\mathrm{\&mu;H},C_P^{\mathrm{\&alpha;}}=C_S^{\mathrm{\&alpha;}}=C_P=C_S=0.2533\mathrm{nF},$ R_L=50 Ω, coefficient of coup k=0.1(and mutual inductance），α=0.8，β=1.5，R_S＝R_P=0.5 Ω. The relation curve of power output and frequency f asShown in Fig. 5. This situation has reduced the resonant frequency of system, is conducive to the design of radio energy transmission system. Meanwhile, due to humorousVibration frequency is irregular with the variation of fractional order exponent number, but resonant frequency totally reduces in this case.

Situation described above is applicable equally for the situation of α=β.

Above-described embodiment is preferably embodiment of the present invention, but embodiments of the present invention are not subject to described embodiment'sRestriction, other any do not deviate from change, the modification done under Spirit Essence of the present invention and principle, substitutes, combination, simplification,All should be equivalent substitute mode, within being included in protection scope of the present invention.

Claims (1)

1. integer rank and a fractional order series-multiple connection resonance radio energy transmission system, comprise high frequency power source (V_S), emission partPoint, receiving unit and load (R_L), it is characterized in that radiating portion comprises the former limit fractional order electric capacity being connected in seriesWith formerLimit fractional order inductanceFormer limit fractional order inductanceThere is former limit resistance (R_P); Receiving unit comprises and being connected in parallelSecondary integer rank electric capacity (C_S) and secondary integer rank inductance (L_S), secondary integer rank inductance (L_S) there is secondary resistance (R_S); Former limitFractional order electric capacitySecondary integer rank electric capacity (C_S) voltage, current differential relation all meet:Phase placeRelation meets:Wherein, i_CFor fractional order capacitance current, v_CFor fractional order capacitance voltage, α is the rank of fractional order electric capacityNumber, and 0 < α≤2, C^αFor the value of fractional order electric capacity, in formula, α=1 o'clock is the described satisfied pass of electric capacity, integer rankSystem; Former limit fractional order inductanceSecondary integer rank inductance (L_S) voltage, current differential relation all meet:Phase relation meets:Wherein, v_LFor the voltage of fractional order inductance, i_LFor the electricity of fractional order inductanceStream, β is the exponent number of fractional order inductance, and 0 < β≤2, L^βFor the value of fractional order inductance, in formula, β=1 o'clock is describedThe satisfied relation of integer rank inductance.