CN203827076U - Integer-order and fractional-order mixed-serial-connected resonance wireless power transmission system - Google Patents

Abstract

The utility model provides an integer-order and fractional-order mix-serial-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 integer order capacitor and a primary integer order inductor with primary resistor, the primary integer order capacitor and the primary integer order inductor being serially connected; and the reception portion comprises a secondary fractional order capacitor and a secondary fractional order inductor with secondary resistor, the primary fractional order capacitor and the primary fractional order inductor being serially connected. The wireless power transmission system employs integer-order and fractional-order elements to achieve wireless power transmission in a mixed way, is simple in structure 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 series 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 particularly a kind of integer rank and fractional order are mixed series 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 at 2m, apart from left and right, with 40% efficiency, to light the bulb of a 60W, 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, for the situation of fractional order, ignores completely.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 (as 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, so it is always in the theory analysis stage.In recent decades, development due to biotechnology, macromolecular material etc., it is found that integer rank calculus can not well explain the phenomenon that nature exists, 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 the application in wireless power transmission field is not mentioned especially.

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 series 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 series resonance radio energy transmission system.

The utility model is achieved through the following technical solutions:

Integer rank and fractional order are mixed a series resonance radio energy transmission system, comprise high frequency power source V _s, radiating portion, receiving unit and load R _l, radiating portion comprises integer rank, the former limit capacitor C being connected in series _pwith integer rank, former limit inductance L _p, integer rank, former limit inductance L _pthere is former limit resistance R _p; Receiving unit comprises the secondary fractional order electric capacity being connected in series with secondary fractional order inductance secondary fractional order inductance there is secondary resistance R _s.

Described a kind of integer rank and fractional order are mixed series resonance radio energy transmission system, former limit fractional order electric capacity secondary fractional order electric capacity voltage, 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 ^αvalue for fractional order electric capacity.Described integer rank electric capacity is the situation of exponent number α=1.

Described a kind of integer rank and fractional order are mixed series resonance radio energy transmission system, former limit fractional order inductance secondary fractional order inductance voltage, 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, and 0 < β≤2, L ^βvalue for fractional order inductance.Described integer rank inductance is the situation of β=1.

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

Operation principle of the present utility model is: 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 series resonant 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, simple in structure, adopt integer rank and fractional order element to mix the wireless power transmission realizing, be different from the radio energy transmission system of only being realized by integer rank device in the past completely, increased the degree of freedom of parameter designing.

2, by choosing suitable fractional order exponent number, can make through-put power larger.

Accompanying drawing explanation

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

Fig. 2 is α=1.1, the power output of β=0.9 o'clock embodiment and the relation curve of frequency.

Fig. 3 is α=0.8, the power output of β=0.9 o'clock embodiment and the relation curve of frequency.

Fig. 4 is α=1.1, the power output of β=1.2 o'clock embodiment and the relation curve of frequency.

Fig. 5 is α=0.8, the power output of β=1.2 o'clock embodiment and the relation curve of frequency.

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 V _s, integer rank, former limit capacitor C _p, integer rank, former limit inductance L _pwith former limit resistance R _pseries connection forms loop successively; Secondary integer rank electric capacity secondary integer rank inductance secondary resistance R _swith load R _lseries connection forms loop successively.By Fig. 1, can be obtained the Fractional Differential Equation of system:

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

$0=v_{C2}+M\frac{{\mathrm{di}}_1}{\mathrm{dt}}+L_S\frac{d^{\mathrm{\&beta;}}{i}_2}{{\mathrm{dt}}^{\mathrm{\&beta;}}}+i_2{R}_S+i_2{R}_L$

$i_1=C_P\frac{{\mathrm{dv}}_{c1}}{\mathrm{dt}}$

$i_2=C_S^{\mathrm{\&alpha;}}\frac{d^{\mathrm{\&alpha;}}{v}_{c2}}{{\mathrm{dt}}^{\mathrm{\&alpha;}}}$

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:

V _S(s)＝V _C1(s)+sL _PI ₁(s)+s ^βMI ₂(s)+I ₁(s)R _P

$0=V_{C2}\left(s\right)+{\mathrm{sMI}}_1\left(s\right)+s^{\mathrm{\&beta;}}{L}_s^{\mathrm{\&beta;}}{I}_2\left(s\right)+I_2\left(s\right)R_s+I_2\left(s\right)R_L$

I ₁(s)＝sC _PV _C1(s)

$I_2\left(s\right)=s^{\mathrm{\&alpha;}}{C}_s^{\mathrm{\&alpha;}}{V}_{C2}\left(s\right)$

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.In frequency domain, there is s=j ω.Defined loop impedance: in frequency domain, have s=j ω.Defined loop impedance:

$Z_{11}=R_P+\mathrm{j\&omega;}{L}_P+\frac{1}{\mathrm{j\&omega;}{C}_P}=1/Y_{11}$

$Z_{22}=R_S+R_L+{\left(\mathrm{j\&omega;}\right)}^{\mathrm{\&beta;}}{L}_S^{\mathrm{\&beta;}}+\frac{1}{{\left(\mathrm{j\&omega;}\right)}^{\mathrm{\&alpha;}}{C}_S^{\mathrm{\&alpha;}}}=1/Y_{22}$

Solve:

$I_1=\frac{V_S{Z}_{22}}{Z_{11}{Z}_{22}-{\left(\mathrm{j\&omega;}\right)}^{1+\mathrm{\&beta;}}{M}^2}=\frac{V_S}{Z_{11}-{\left(\mathrm{j\&omega;}\right)}^{1+\mathrm{\&beta;}}{M}^2{Y}_{22}}$

$I_2=\frac{\mathrm{j\&omega;M}{V}_S}{{-Z}_{11}{Z}_{22}+{\left(\mathrm{j\&omega;}\right)}^{1+\mathrm{\&beta;}}{M}^2}=\frac{\mathrm{j\&omega;M}{V}_S/Z_{11}}{Z_{22}-{\left(\mathrm{j\&omega;}\right)}^{1+\mathrm{\&beta;}}{M}^2{Y}_{11}}$

The expression formula that can obtain power output is:

$\begin{array}{c}{P}_0=I_2^2{R}_L={\left|\frac{\mathrm{j\&omega;M}{V}_S}{-Z_{11}{Z}_{22}+{\left(\mathrm{j\&omega;}\right)}^{1+\mathrm{\&beta;}}{M}^2}\right|}^2{R}_L\\ ={\left|\frac{\mathrm{j\&omega;}{\mathrm{MV}}_S}{\begin{array}{c}-(R_P+\mathrm{j\&omega;}{L}_P+\frac{1}{j{\mathrm{\&omega;}}^{\mathrm{\&alpha;}}{C}_P^{\mathrm{\&alpha;}}})g[R_S+R_L+{\mathrm{\&omega;}}^{\mathrm{\&beta;}}{L}_S^{\mathrm{\&beta;}}(\cos \frac{\mathrm{\&beta;\&pi;}}{2R_L}+j\sin \frac{\mathrm{\&beta;\&pi;}}{2})\\ +\frac{1}{{\mathrm{\&omega;}}^{\mathrm{\&alpha;}}{C}_S^{\mathrm{\&alpha;}}}(\cos \frac{\mathrm{\&alpha;\&pi;}}{2}+j\sin \frac{\mathrm{\&alpha;\&pi;}}{2})]+{\mathrm{\&omega;}}^{1+\mathrm{\&beta;}}{M}^2[\cos (1+\mathrm{\&beta;})\mathrm{\&pi;}+j\sin (1+\mathrm{\&beta;})\mathrm{\&pi;}]\end{array}}\right|}^2\end{array}$

Input power expression formula is:

$P_{\mathrm{in}}=\mathrm{Re}\left(V_S{I}_1^{*}\right)$

Or

$\begin{array}{c}{P}_{\mathrm{in}}=I_1^2\left|\mathrm{Re}\left(Z_{11}\right)\right|+I_2^2\left|\mathrm{Re}(Z_{22}-R_L)\right|+P_o\\ =I_1^2{R}_P+I_2^2(R_S+{\mathrm{\&omega;}}^{\mathrm{\&beta;}}{L}_S^{\mathrm{\&beta;}}\cos \frac{\mathrm{\&beta;\&pi;}}{2}+\frac{1}{{\mathrm{\&omega;}}^{\mathrm{\&alpha;}}{C}_S^{\mathrm{\&alpha;}}}\cos \frac{\mathrm{\&alpha;\&pi;}}{2})+P_o\end{array}$

System efficiency of transmission is:

$\begin{array}{c}\mathrm{\&eta;}=\frac{P_o}{P_{\mathrm{in}}}=\frac{I_2^2{R}_L}{I_1^2\mathrm{Re}\left(Z_{11}\right)+I_2^2\mathrm{Re}(Z_{22}-R_L)+P_o}\\ =\frac{I_2^2{R}_L}{I_1^2{R}_P+I_2^2(R_S+{\mathrm{\&omega;}}^{\mathrm{\&beta;}}{L}_S^{\mathrm{\&beta;}}\cos \frac{\mathrm{\&beta;\&pi;}}{2}+\frac{1}{{\mathrm{\&omega;}}^{\mathrm{\&alpha;}}{C}_S^{\mathrm{\&alpha;}}}\cos \frac{\mathrm{\&alpha;\&pi;}}{2})+P_o}\end{array}$

From the expression formula of power output, the size of power output is mainly relevant with β with mutual inductance M, operating frequency ω, fractional order exponent number α.Lower surface analysis, the impact of operating frequency on power output, other parameters remain unchanged.

1), as α >1, during β <1, as an example, a kind of integer rank and fractional order are mixed series resonance radio energy transmission system: V _s=10V, L=100 μ H, C=0.2533nF, R _l=50 Ω, coupling coefficient k=0.1(and mutual inductance ), α=1.1, β=0.9, R _p=R _s=0.5 Ω.The power output of embodiment and the relation curve of frequency (dotted portion) as shown in Figure 2.For advantage more of the present utility model, the power output of integer rank system (being α=1, the situation of β=1 o'clock) is (solid line part) also as shown in Figure 2.As seen from Figure 2, power output is in such cases greater than the situation of integer rank system, demonstrates huge superiority of the present utility model.

2), as α <1, during β <1, as an example, a kind of integer rank and fractional order are mixed series resonance radio energy transmission system: V _s=10V, L=100 μ H, C=0.2533nF, R _l=50 Ω, coupling coefficient k=0.1(and mutual inductance ), α=0.8, β=0.9, R _p=R _s=0.5 Ω.The power output of embodiment and the relation curve of frequency (dotted portion) as shown in Figure 3, the power output of integer rank system (being α=1, the situation of β=1 o'clock) is (solid line part) also as shown in Figure 3.As seen from Figure 3, this kind of situation power output is less, during design, should avoid.

3), as α >1, during β >1, as an example, a kind of integer rank and fractional order are mixed series resonance radio energy transmission system: V _s=10V, L=100 μ H, C=0.2533nF, R _l=50 Ω, coupling coefficient k=0.1(and mutual inductance ), α=1.1, β=1.2, R _p=R _s=0.5 Ω.The power output of embodiment and the relation curve of frequency (dotted portion) as shown in Figure 4, the power output of integer rank system (being α=1, the situation of β=1 o'clock) is (solid line part) also as shown in Figure 4.As seen from Figure 4, this kind of situation power output is less, during design, should avoid.

4), as α <1, during β >1, as an example, a kind of integer rank and fractional order are mixed series resonance radio energy transmission system: V _s=10V, L=100 μ H, C=0.2533nF, R _l=50 Ω, coupling coefficient k=0.1(and mutual inductance ), α=0.8, β=1.2, R _p=R _s=0.5 Ω.The power output of embodiment and the relation curve of frequency (dotted portion) as shown in Figure 5, the power output of integer rank system (being α=1, the situation of β=1 o'clock) is (solid line part) also as shown in Figure 5.As seen from Figure 5, this kind of situation power output is less, during design, should avoid.

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

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

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