CN203827072U - Integer-order and fractional-order mixed-parallel connected resonance wireless power transmission system - Google Patents

Abstract

The utility model provides an integer-order and fractional-order mixed-parallel connected resonance wireless power transmission system which comprises a high-frequency power source, an emission portion, a reception portion and a load. The emission portion comprises a primary fractional order capacitor and a primary fractional order inductor with primary resistor, the primary fractional order capacitor and the primary fractional order inductor being parallelly connected; and the reception portion comprises a secondary integer order capacitor and a secondary integer order inductor with secondary resistor, the secondary integer order capacitor and a secondary integer order inductor being parallelly connected. The wireless power transmission system employs integer-order and fractional-order elements to achieve wireless power transmission, and increases dimensions for parameter design. The wireless power transmission system is completely different from a conventional power transmission system which is only achieved through integer order elements.

Description

A kind of integer rank and fractional order are mixed parallel resonance radio energy transmission system

Technical field

The utility model belongs to the field of wireless power transmission or wireless technology of transmission of electricity, and a kind of especially integer rank and fractional order are mixed parallel resonance radio energy transmission system.

Background technology

Wireless power transmission or wireless technology of transmission of electricity were just attempted experimentally by novel tesla of U.S. utility (Nicola Tesla) before more than 100 years.2006, the researcher of the Massachusetts Institute of Technology (MIT) utilizes the resonance technique of physics successfully to light the bulb of a 60W with 40% efficiency apart from left and right at 2m, this experiment is not only the reproduction of tesla's experiment, 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 resonance frequency only determines by inductance value and capacitance, and therefore, its system only need be considered parameter value, and without the exponent number of considering element, the degree of freedom of design is fewer.Meanwhile, the element of real system is fractional order in essence, but the most exponent number of using in current reality is close to 1, ignores completely for the situation of fractional order.Traditional modeling of passing through integer rank designs radio energy transmission system, and 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, is almost born with integer rank calculus simultaneously.But due to fractional order more complicated, and never have good numerical analysis tools, therefore it is always in the theory analysis stage.In recent decades, due to the development of biotechnology, macromolecular material etc., it is found that integer rank calculus can not well explain nature exist phenomenon, therefore fractional calculus starts to be paid attention to, and starting to be applied to engineering field, its research at control field and application are day by day perfect.Meanwhile, the fractional order device at two ends is out manufactured in laboratory.But some special character of fractional order circuit and 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 to wireless power transmission field, is therefore necessary to propose a kind of integer rank and fractional order and mixes parallel resonance radio energy transmission system.

Utility model content

The purpose of this utility model is to overcome above-mentioned the deficiencies in the prior art, provides a kind of integer rank and fractional order to mix parallel resonance radio energy transmission system.

The utility model is achieved through the following technical solutions:

A kind of integer rank and fractional order are mixed parallel resonance radio energy transmission system, comprise high frequency power source I _s, radiating portion, receiving unit and load R _l; Radiating portion comprises the former limit fractional order electric capacity being connected in parallel with former limit fractional order inductance former limit fractional order inductance there is former limit resistance R _p; Receiving unit comprises the secondary integer rank capacitor C being connected in parallel _swith secondary integer rank inductance L _s, secondary integer rank inductance L _sthere is secondary resistance R _s.

Described a kind of integer rank and fractional order are mixed parallel resonance radio energy transmission system, former limit fractional order electric capacity with secondary fractional order electric capacity voltage, current differential relation 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 are mixed parallel resonance radio energy transmission system, former limit fractional order inductance with secondary integer rank inductance voltage, current differential relation 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, and 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.

Described a kind of integer rank and fractional order are mixed in parallel resonance radio energy transmission system, are the wireless power transmission that the mode that is coupled by parallel resonance realizes between radiating portion and receiving unit.

Operation principle of the present utility model is: radiating portion and receiving unit are respectively by former limit fractional order electric capacity former limit fractional order inductance former limit resistance R _p, secondary integer rank capacitor C _s, secondary integer rank inductance L _s, secondary resistance R _sform RLC antiresonant circuit, or radiating portion and receiving unit are respectively by integer rank, former limit capacitor C _p, integer rank, former limit inductance L _p, former limit resistance R _p, secondary fractional order electric capacity secondary divides number rank inductance secondary resistance R _sform 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, the utlity model has following advantage:

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

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

Brief description of the drawings

Fig. 1 is concrete implementing circuit of the present utility model.

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=1.1, the power output of β=1.2 o'clock embodiment 1 and the relation curve of frequency f.

Fig. 5 is α=0.9, the power output of β=1.2 o'clock embodiment 1 and the relation curve of frequency f.

Specific embodiments

Below in conjunction with accompanying drawing, the concrete enforcement of utility model is further described, but enforcement of the present utility model and protection are not limited to this.

Embodiment

As shown in Figure 1, for concrete implementing circuit of the present utility model, below in conjunction with this figure, operation principle of the present utility model and method for designing are described.As shown in Figure 1, high frequency power source I _s, former limit fractional order electric capacity former limit fractional order inductance with former limit resistance R _pform parallel 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 Differential Equation of system by Fig. 1:

$i_S=C_P^{\mathrm{\&alpha;}}\frac{d^{\mathrm{\&alpha;}}{v}_{C1}}{{\mathrm{dt}}^{\mathrm{\&alpha;}}}+i_1$

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

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

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

In formula, i _sfor the transient expression form of high frequency power source, i ₁for former limit fractional order inductive current, i ₂for secondary fractional order inductive current, v _c1for former limit fractional order capacitance voltage, v _c2for secondary fractional order capacitance voltage.The differential equation of said system can be obtained by Laplace transform:

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

$0=I_2\left(s\right)+{\mathrm{sC}}_S{V}_{C2}\left(s\right)+\frac{1}{R_L}{V}_{C2}\left(s\right)$

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

V _C2(s)＝sL _SI ₂(s)+s ^βMI ₁(s)+I ₂(s)R _S

Symbol in above equation group is Laplace transform form, has one-to-one relationship, i.e. I with the differential equation of system ₁for former limit fractional order inductive current, I ₂for secondary fractional order inductive current, V _c1for former limit fractional order capacitance voltage, V _c2for secondary fractional order capacitance voltage.Solve:

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

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 size of power output is mainly relevant with β with mutual inductance M, operating angle frequencies omega, fractional order exponent number α.Further analyze again below, the impact of operating angle frequency on power output, other parameters remain unchanged.

The design parameter of embodiment system is: IS=1A, r _l=10 Ω, coupling coefficient k=0.01(and mutual inductance ), α=0.9, β=1.2, R=0.5 Ω.The relation curve of power output and frequency f as shown in Figure 2.As shown in Figure 2, the resonance frequency of system is for being less than 10MHz.And integer rank system (is α=1 under same parameter, β=1, other parameter constants) resonance frequency be 10MHz, as can be seen here, can reduce by choosing fractional order exponent number the resonance frequency of fractional order circuit parallel resonance radio energy transmission system, thereby be conducive to the design of radio energy transmission system.

1), as α >1, when β <1, as an example, a kind of integer rank and fractional order are mixed parallel resonance radio energy transmission system: I _s=1A, $L_P^{\mathrm{\&beta;}}=L_S^{\mathrm{\&beta;}}=L_P=L_S=20\mathrm{\&mu;H},C_P^{\mathrm{\&alpha;}}=C_S^{\mathrm{\&alpha;}}=C_P=C_S=12.67\mathrm{pF},$ R _l=10 Ω, coupling coefficient k=0.1(and mutual inductance ), α=1.2, β=0.9, R=0.5 Ω.The relation curve of power output and frequency f as shown in Figure 2.As shown in Figure 2, the resonance frequency of system is for being less than 10MHz.And integer rank system (is α=1 under same parameter, β=1, other parameter constants) resonance frequency be 10MHz, as can be seen here, can reduce by choosing fractional order exponent number the resonance frequency of fractional order circuit parallel resonance radio energy transmission system, thereby be conducive to the design of radio energy transmission system.

2), as α <1, when β <1, as an example, a kind of integer rank and fractional order are mixed parallel resonance radio energy transmission system: I _s=1A, $L_P^{\mathrm{\&beta;}}=L_S^{\mathrm{\&beta;}}=L_P=L_S=20\mathrm{\&mu;H},C_P^{\mathrm{\&alpha;}}=C_S^{\mathrm{\&alpha;}}=C_P=C_S=12.67\mathrm{pF},$ R _l=10 Ω, coupling coefficient k=0.01(and mutual inductance ), α=0.8, β=0.9, R=0.5 Ω.As shown in Figure 3, although this situation has reduced the resonance frequency of system, power output is unsatisfactory for the relation curve of power output and frequency f, while therefore design, also should avoid.

3), as α >1, when β >1, as an example, a kind of integer rank and fractional order are mixed parallel resonance radio energy transmission system: I _s=1A, $L_P^{\mathrm{\&beta;}}=L_S^{\mathrm{\&beta;}}=L_P=L_S=20\mathrm{\&mu;H},C_P^{\mathrm{\&alpha;}}=C_S^{\mathrm{\&alpha;}}=C_P=C_S=12.67\mathrm{pF},$ R _l=10 Ω, coupling coefficient k=0.1(and mutual inductance ), α=1.1, β=1.2, R=0.5 Ω.The relation curve of power output and frequency f as shown in Figure 4.Although this situation has reduced the resonance frequency of system, power output is also more satisfactory.Along with the further increase of fractional order exponent number, resonance frequency can further reduce, and is conducive to the design of radio energy transmission system.

4), as α <1, when β >1, as an example, a kind of integer rank and fractional order are mixed parallel resonance radio energy transmission system: I _s=1A, $L_P^{\mathrm{\&beta;}}=L_S^{\mathrm{\&beta;}}=L_P=L_S=20\mathrm{\&mu;H},C_P^{\mathrm{\&alpha;}}=C_S^{\mathrm{\&alpha;}}=C_P=C_S=12.67\mathrm{pF},$ R _l=10 Ω, coupling coefficient k=0.01(and mutual inductance ), α=0.9, β=1.2, R=0.5 Ω.The relation curve of power output and frequency f as shown in Figure 5, has reduced resonance frequency, is conducive to the design of radio energy transmission system.Meanwhile, due to the variation of fractional order exponent number, resonance frequency changes irregular, but has reduced in general resonance frequency.

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

Above-described embodiment is preferably execution mode of the utility model; but execution mode of the present utility model is not limited by the examples; other any do not deviate from change, the modification done under Spirit Essence of the present utility model and principle, substitutes, combination, simplify; all should be equivalent substitute mode, within being included in protection range of the present utility model.

Claims (3)

1. integer rank and fractional order are mixed a parallel resonance radio energy transmission system, comprise high frequency power source (I _s), radiating portion, receiving unit and load (R _l), it is characterized in that radiating portion comprises the former limit fractional order electric capacity being connected in parallel with former limit fractional order inductance former limit fractional order inductance there is former limit resistance (R _p); Receiving unit comprises the secondary integer rank electric capacity (C being connected in parallel _s) and secondary integer rank inductance (L _s), secondary integer rank inductance (L _s) there is secondary resistance (R _s).

2. a kind of integer rank according to claim 1 and fractional order are mixed parallel resonance radio energy transmission system, it is characterized in that former limit fractional order electric capacity with secondary fractional order electric capacity voltage, current differential relation 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.

3. a kind of integer rank according to claim 1 and fractional order are mixed parallel resonance radio energy transmission system, it is characterized in that former limit fractional order inductance with secondary integer rank inductance voltage, current differential relation 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, and 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.