CN203827076U

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

Info

Publication number: CN203827076U
Application number: CN201420156452.4U
Authority: CN
Inventors: 张波; 黄润鸿; 丘东元
Original assignee: South China University of Technology SCUT
Current assignee: South China University of Technology SCUT
Priority date: 2014-03-31
Filing date: 2014-03-31
Publication date: 2014-09-10
Anticipated expiration: 2024-03-31

Abstract

The utility model provides an integer-order and fractional-order mixed series resonant wireless power transmission system, which includes a high-frequency power source, a transmitting part, a receiving part and a load. Inductance, the primary-side integer-order inductance has a primary-side resistance; the receiving part includes a secondary-side fractional-order capacitor and a secondary-side fractional-order inductance connected in series, and the secondary-side fractional-order inductance has a secondary-side resistance. The utility model uses a mixture of integer-order and fractional-order components to realize wireless power transmission, has a simple structure, increases the dimension of parameter design, and is completely different from the traditional wireless power transmission system realized only by integer-order components.

Description

A Hybrid Series Resonant Wireless Power Transfer System of Integer and Fractional Orders

技术领域technical field

本实用新型属于无线电能传输或无线输电技术的领域，特别涉及一种整数阶和分数阶混合串联谐振无线电能传输系统。The utility model belongs to the field of wireless power transmission or wireless power transmission technology, in particular to an integer-order and fractional-order mixed series resonant wireless power transmission system.

背景技术Background technique

无线电能传输或无线输电技术早在100多年前就由美国实用新型家特斯拉（Nicola Tesla）在实验上得到尝试。2006年，麻省理工学院（MIT）的研究人员利用物理的共振技术成功的在2m距离左右以40%的效率点亮了一个60W的灯泡，该实验不仅仅是特斯拉实验的重现，更是无线电能传输技术的又一个新突破，并且掀起了无线电能传输研究的热潮。Wireless power transmission or wireless power transmission technology was tried experimentally by the American utility model Tesla (Nicola Tesla) more than 100 years ago. In 2006, researchers at the Massachusetts Institute of Technology (MIT) used physical resonance technology to successfully light up a 60W light bulb with 40% efficiency at a distance of about 2m. This experiment is not just a reproduction of Tesla's experiment. It is another new breakthrough in wireless power transmission technology, and it has set off an upsurge in wireless power transmission research.

目前的无线电能传输系统都是基于整数阶电感、电容实现的，其谐振频率只由电感值和电容值决定，因此，其系统设计只需考虑参数值，无需考虑元件的阶数，设计的自由度比较少。同时，实际系统的元件本质上是分数阶的，但是目前实际中用的大部分的阶数接近于1，对于分数阶的情况完全忽略。传统的通过整数阶的建模来设计无线电能传输系统，在某些条件下，理论和实际的误差可能会很大。The current wireless power transfer system is based on integer-order inductors and capacitors, and its resonant frequency is only determined by the value of the inductor and capacitor. Therefore, the system design only needs to consider the parameter values, without considering the order of the components, and the design is free The degree is relatively small. At the same time, the components of the actual system are of fractional order in nature, but most of the orders used in practice are close to 1, and the case of fractional order is completely ignored. Traditionally, wireless power transfer systems are designed through integer-order modeling. Under certain conditions, the theoretical and practical errors may be large.

分数阶器件（如分数阶电容和分数阶电感）概念的来源于分数阶微积分的产生，而分数阶微积分的概念已经有300多年的历史，几乎与整数阶微积分同时诞生。但是由于分数阶比较复杂，并且一直没有很好的数值分析工具，因此其一直处于理论分析阶段。近几十年来，由于生物技术、高分子材料等的发展，人们发现整数阶微积分不能很好的解释自然界存在的现象，因此分数阶微积分开始得到重视，并开始应用于工程领域，其在控制领域的研究和应用已日益完善。同时，两端的分数阶器件已经在实验室被制造出来。但分数阶电路与系统一些特殊的性质未得到研究，在无线电能传输领域的应用更是未被提及。The concept of fractional-order devices (such as fractional-order capacitors and fractional-order inductors) comes from the generation of fractional-order calculus, and the concept of fractional-order calculus has a history of more than 300 years, almost at the same time as integer-order calculus. However, due to the complexity of the fractional order and the lack of good numerical analysis tools, it has been in the stage of theoretical analysis. In recent decades, due to the development of biotechnology, polymer materials, etc., people have found that integer order calculus cannot explain the phenomena in nature well, so fractional order calculus has begun to be valued and applied in the field of engineering. The research and application in the field of control has been perfected day by day. Meanwhile, fractional-order devices at both ends have been fabricated in the laboratory. However, some special properties of fractional-order circuits and systems have not been studied, and the application in the field of wireless power transmission has not been mentioned.

鉴于目前分数阶元件或分数阶电路在某些方面的巨大优势，并且其还未被应用于无线电能传输领域，因此有必要提出一种整数阶和分数阶混合串联谐振无线电能传输系统。In view of the great advantages of fractional-order components or fractional-order circuits in some aspects, and they have not been applied in the field of wireless power transmission, it is necessary to propose a hybrid series resonant wireless power transmission system of integer and fractional orders.

实用新型内容Utility model content

本实用新型的目的在于克服上述现有技术的不足，提供一种整数阶和分数阶混合串联谐振无线电能传输系统。The purpose of the utility model is to overcome the shortcomings of the above-mentioned prior art, and provide a hybrid series resonant wireless power transmission system of integer order and fractional order.

本实用新型通过如下技术方案实现：The utility model is realized through the following technical solutions:

一种整数阶和分数阶混合串联谐振无线电能传输系统，包括高频功率源V_S、发射部分、接收部分和负载R_L，发射部分包括串联连接的原边整数阶电容C_P和原边整数阶电感L_P，原边整数阶电感L_P具有原边电阻R_P；接收部分包括串联连接的副边分数阶电容和副边分数阶电感副边分数阶电感具有副边电阻R_S。An integer-order and fractional-order hybrid series resonant wireless power transmission system, including a high-frequency power source V _S , a transmitting part, a receiving part and a load R _L , and the transmitting part includes a series-connected primary-side integer-order capacitor C _P and a primary-side integer order inductance L _P , the primary-side integer-order inductance L _P has a primary-side resistance R _P ; the receiving part includes secondary-side fractional-order capacitances connected in series and secondary fractional inductance Secondary Fractional Inductance With secondary resistance R _S .

所述的一种整数阶和分数阶混合串联谐振无线电能传输系统，原边分数阶电容副边分数阶电容的电压、电流微分关系均满足：相位关系满足：其中，i_C为分数阶电容电流，v_C为分数阶电容电压，α为分数阶电容的阶数，并且0＜α≤2，C^α为分数阶电容的值。所述的整数阶电容即为阶数α＝1的情况。In the hybrid series resonant wireless power transmission system of integer order and fractional order, the fractional order capacitance of the primary side Secondary Fractional Capacitance The differential relations of voltage and current satisfy: The phase relationship satisfies: Among them, i _C is the fractional capacitor current, v _C is the fractional capacitor voltage, α is the order of the fractional capacitor, and 0<α≤2, and C ^α is the value of the fractional capacitor. The integer-order capacitance described above is the case where the order α=1.

所述的一种整数阶和分数阶混合串联谐振无线电能传输系统，原边分数阶电感副边分数阶电感的电压、电流微分关系均满足：相位关系满足：其中，v_L为分数阶电感的电压，i_L为分数阶电感的电流，β为分数阶电感的阶数，并且0＜β≤2，L^β为分数阶电感的值。所述的整数阶电感即为β＝1的情况。A hybrid series resonant wireless power transmission system of integer order and fractional order, the fractional order inductance of the primary side Secondary Fractional Inductance The differential relations of voltage and current satisfy: The phase relationship satisfies: Among them, v _L is the voltage of the fractional inductor, i _L is the current of the fractional inductor, β is the order of the fractional inductor, and 0<β≤2, L ^β is the value of the fractional inductor. The said integer order inductance is the case of β=1.

所述的一种整数阶和分数阶混合串联谐振无线电能传输系统，发射部分和接收部分之间是通过串联谐振耦合的方式实现的无线电能传输。In the integer-order and fractional-order mixed series resonant wireless power transmission system described above, the wireless power transmission is realized through series resonant coupling between the transmitting part and the receiving part.

本实用新型的工作原理为：发射部分和接收部分分别由原边整数阶电容C_P、原边整数阶电感L_P、原边电阻R_P、副边分数阶电容副边分数额阶电感副边电阻R_S构成RLC串联谐振电路，发射部分和接收部分通过谐振耦合的方式实现电能的无线传输。The working principle of the utility model is: the transmitting part and the receiving part are respectively composed of the primary side integer-order capacitance C _P , the primary side integer-order inductance L _P , the primary side resistance R _P , and the secondary side fractional-order capacitance Secondary side fractional order inductance The secondary resistance R _S constitutes an RLC series resonant circuit, and the transmitting part and the receiving part realize the wireless transmission of electric energy through resonant coupling.

与现有技术相比，本实用新型具有如下优点：Compared with the prior art, the utility model has the following advantages:

1、结构简单，采用整数阶和分数阶元件混合实现的无线电能传输，完全区别于以往的只由整数阶器件实现的无线电能传输系统，增加了参数设计的自由度。1. The structure is simple, and the wireless power transmission realized by a mixture of integer-order and fractional-order components is completely different from the previous wireless power transmission system realized only by integer-order devices, which increases the degree of freedom in parameter design.

2、通过选取适当的分数阶阶数，可以使传输功率更大。2. By selecting an appropriate fractional order, the transmission power can be increased.

附图说明Description of drawings

图1为本实用新型的具体实施电路。Fig. 1 is the specific implementation circuit of the present utility model.

图2为α=1.1，β=0.9时实施例的输出功率与频率的关系曲线。Fig. 2 is the relationship curve between output power and frequency of the embodiment when α=1.1 and β=0.9.

图3为α=0.8，β=0.9时实施例的输出功率与频率的关系曲线。Fig. 3 is the relationship curve between output power and frequency of the embodiment when α=0.8 and β=0.9.

图4为α=1.1，β=1.2时实施例的输出功率与频率的关系曲线。Fig. 4 is the relationship curve between output power and frequency of the embodiment when α=1.1 and β=1.2.

图5为α=0.8，β=1.2时实施例的输出功率与频率的关系曲线。Fig. 5 is the relationship curve between output power and frequency of the embodiment when α=0.8 and β=1.2.

具体实施方案specific implementation plan

以下结合附图对实用新型的具体实施作进一步描述，但本实用新型的实施和保护不限于此。The specific implementation of the utility model will be further described below in conjunction with the accompanying drawings, but the implementation and protection of the utility model are not limited thereto.

实施例Example

如图1所示，为本实用新型的具体实施电路，以下结合本图说明本实用新型的工作原理和设计方法。如图1所示，高频功率源V_S、原边整数阶电容C_P、原边整数阶电感L_P和原边电阻R_P依次串联形成回路；副边整数阶电容副边整数阶电感副边电阻R_S和负载R_L依次串联形成回路。由图1可以得到系统的分数阶微分方程：As shown in Figure 1, it is a concrete implementation circuit of the utility model, and the working principle and design method of the utility model are explained below in conjunction with this figure. As shown in Figure 1, the high-frequency power source V _S , the primary-side integer-order capacitor C _P , the primary-side integer-order inductance L _P and the primary-side resistor R _P are connected in series to form a loop; the secondary-side integer-order capacitor Secondary Integer Order Inductance The secondary resistor R _S and the load _RL are connected in series in turn to form a loop. From Figure 1, the fractional differential equation of the system can be obtained:

${v v}_{S S} = = {v v}_{C C 11} + + {L L}_{P P} \frac{{di di}_{11}}{dt dt} + + M m \frac{{d d}^{β β} {i i}_{22}}{{dt dt}^{β β}} + + {i i}_{11} {R R}_{P P}$

$00 = = {v v}_{C C 22} + + M m \frac{{di di}_{11}}{dt dt} + + {L L}_{S S} \frac{{d d}^{β β} {i i}_{22}}{{dt dt}^{β β}} + + {i i}_{22} {R R}_{S S} + + {i i}_{22} {R R}_{L L}$

${i i}_{11} = = {C C}_{P P} \frac{{dv dv}_{c c 11}}{dt dt}$

${i i}_{22} = = {C C}_{S S}^{α α} \frac{{d d}^{α α} {v v}_{c c 22}}{{dt dt}^{α α}}$

式中，i_S为高频功率源的暂态表达形式，i₁为原边分数阶电感电流，i₂为副边分数阶电感电流，v_C1为原边分数阶电容电压，v_C2为副边分数阶电容电压。上述系统的微分方程由拉普拉斯变换可以得到：In the formula, i _S is the transient expression form of the high-frequency power source, i ₁ is the fractional-order inductor current of the primary side, i ₂ is the fractional-order inductor current of the secondary side, v _C1 is the fractional-order capacitor voltage of the primary side, and v _C2 is the secondary side side fractional capacitance voltage. The differential equation of the above system can be obtained by Laplace transform:

V_S(s)＝V_C1(s)+sL_PI₁(s)+s^βMI₂(s)+I₁(s)R_P V _S (s)＝V _C1 (s)+sL _P I ₁ (s)+s ^β MI ₂ (s)+I ₁ (s)R _P

$00 = = {V V}_{C C 22} ((s the s)) + + {sMI sMI}_{11} ((s the s)) + + {s the s}^{β β} {L L}_{s the s}^{β β} {I I}_{22} ((s the s)) + + {I I}_{22} ((s the s)) {R R}_{s the s} + + {I I}_{22} ((s the s)) {R R}_{L L}$

I₁(s)＝sC_PV_C1(s)I ₁ (s) = sC _P V _C1 (s)

${I I}_{22} ((s the s)) = = {s the s}^{α α} {C C}_{s the s}^{α α} {V V}_{C C 22} ((s the s))$

以上方程组中的符号为拉普拉斯变换形式，与系统的微分方程具有一一对应关系，即I₁为原边分数阶电感电流，I₂为副边分数阶电感电流，V_C1为原边分数阶电容电压，V_C2为副边分数阶电容电压。在频域中，有s＝jω。定义回路阻抗：在频域中，有s＝jω。定义回路阻抗：The symbols in the above equations are Laplace transform forms, which have a one-to-one correspondence with the differential equations of the system, that is, I ₁ is the fractional inductor current on the primary side, I ₂ is the fractional inductor current on the secondary side, and V _C1 is the primary side fractional capacitor voltage, V _C2 is the secondary side fractional capacitor voltage. In the frequency domain, there is s=jω. Define the loop impedance: In the frequency domain, there is s=jω. Define the loop impedance:

${Z Z}_{1111} = = {R R}_{P P} + + jω jω {L L}_{P P} + + \frac{11}{jω jω {C C}_{P P}} = = 11 / / {Y Y}_{1111}$

${Z Z}_{22 twenty two} = = {R R}_{S S} + + {R R}_{L L} + + {((jω jω))}^{β β} {L L}_{S S}^{β β} + + \frac{11}{{((jω jω))}^{α α} {C C}_{S S}^{α α}} = = 11 / / {Y Y}_{22 twenty two}$

解得：Solutions have to:

${I I}_{11} = = \frac{{V V}_{S S} {Z Z}_{22 twenty two}}{{Z Z}_{1111} {Z Z}_{22 twenty two} - - {((jω jω))}^{11 + + β β} {M m}^{22}} = = \frac{{V V}_{S S}}{{Z Z}_{1111} - - {((jω jω))}^{11 + + β β} {M m}^{22} {Y Y}_{22 twenty two}}$

${I I}_{22} = = \frac{jωM jωM {V V}_{S S}}{{- - Z Z}_{1111} {Z Z}_{22 twenty two} + + {((jω jω))}^{11 + + β β} {M m}^{22}} = = \frac{jωM jωM {V V}_{S S} / / {Z Z}_{1111}}{{Z Z}_{22 twenty two} - - {((jω jω))}^{11 + + β β} {M m}^{22} {Y Y}_{1111}}$

则可以求出输出功率的表达式为：Then the expression of the output power can be obtained as:

$\begin{matrix} {P P}_{00} = = {I I}_{22}^{22} {R R}_{L L} = = {| | \frac{jωM jωM {V V}_{S S}}{- - {Z Z}_{1111} {Z Z}_{22 twenty two} + + {((jω jω))}^{11 + + β β} {M m}^{22}} | |}^{22} {R R}_{L L} \\ = = {| | \frac{jω jω {MV MV}_{S S}}{\begin{matrix} - - (({R R}_{P P} + + jω jω {L L}_{P P} + + \frac{11}{j j {ω ω}^{α α} {C C}_{P P}^{α α}})) g g [[{R R}_{S S} + + {R R}_{L L} + + {ω ω}^{β β} {L L}_{S S}^{β β} ((cos cos \frac{βπ βπ}{22 {R R}_{L L}} + + j j sin sin \frac{βπ βπ}{22})) \\ + + \frac{11}{{ω ω}^{α α} {C C}_{S S}^{α α}} ((cos cos \frac{απ απ}{22} + + j j sin sin \frac{απ απ}{22}))]] + + {ω ω}^{11 + + β β} {M m}^{22} [[cos cos ((11 + + β β)) π π + + j j sin sin ((11 + + β β)) π π]] \end{matrix}} | |}^{22} \end{matrix}$

输入功率表达式为：The input power expression is:

${P P}_{in in} = = Re Re (({V V}_{S S} {I I}_{11}^{* *}))$

或or

$\begin{matrix} {P P}_{in in} = = {I I}_{11}^{22} | | Re Re (({Z Z}_{1111})) | | + + {I I}_{22}^{22} | | Re Re (({Z Z}_{22 twenty two} - - {R R}_{L L})) | | + + {P P}_{o o} \\ = = {I I}_{11}^{22} {R R}_{P P} + + {I I}_{22}^{22} (({R R}_{S S} + + {ω ω}^{β β} {L L}_{S S}^{β β} cos cos \frac{βπ βπ}{22} + + \frac{11}{{ω ω}^{α α} {C C}_{S S}^{α α}} cos cos \frac{απ απ}{22})) + + {P P}_{o o} \end{matrix}$

则系统传输效率为：Then the transmission efficiency of the system is:

$\begin{matrix} η η = = \frac{{P P}_{o o}}{{P P}_{in in}} = = \frac{{I I}_{22}^{22} {R R}_{L L}}{{I I}_{11}^{22} Re Re (({Z Z}_{1111})) + + {I I}_{22}^{22} Re Re (({Z Z}_{22 twenty two} - - {R R}_{L L})) + + {P P}_{o o}} \\ = = \frac{{I I}_{22}^{22} {R R}_{L L}}{{I I}_{11}^{22} {R R}_{P P} + + {I I}_{22}^{22} (({R R}_{S S} + + {ω ω}^{β β} {L L}_{S S}^{β β} cos cos \frac{βπ βπ}{22} + + \frac{11}{{ω ω}^{α α} {C C}_{S S}^{α α}} cos cos \frac{απ απ}{22})) + + {P P}_{o o}} \end{matrix}$

由输出功率的表达式可知，输出功率的大小主要与互感M、工作频率ω、分数阶阶数α和β有关。下面分析，工作频率对输出功率的影响，其他参数保持不变。It can be seen from the expression of output power that the size of output power is mainly related to mutual inductance M, operating frequency ω, fractional order α and β. The following analysis shows the influence of operating frequency on output power, and other parameters remain unchanged.

1）当α>1，β<1时，作为举例，一种整数阶和分数阶混合串联谐振无线电能传输系统：V_S=10V，L=100μH，C=0.2533nF，R_L=50Ω，耦合系数k=0.1（且互感），α=1.1，β=0.9，R_P＝R_S＝0.5Ω。则实施例的输出功率与频率的关系曲线如图2所示（虚线部分）。为了比较本实用新型的优点，整数阶系统（即α=1，β=1时的情况）的输出功率也如图2所示（实线部分）。由图2可见，此种情况下的输出功率大于整数阶系统的情况，显示出本实用新型的巨大优越性。1) When α>1, β<1, as an example, an integer-order and fractional-order hybrid series resonant wireless power transfer system: V _S =10V, L=100μH, C=0.2533nF, R _L =50Ω, coupling Coefficient k=0.1 (and mutual inductance ), α=1.1, β=0.9, R _P ＝ _RS ＝0.5Ω. Then, the relationship curve between the output power and the frequency of the embodiment is shown in Fig. 2 (dotted line). In order to compare the advantages of the present utility model, the output power of the integer-order system (that is, when α=1, β=1) is also shown in Figure 2 (the solid line part). It can be seen from Fig. 2 that the output power in this case is greater than that of the integer-order system, showing the great advantages of the present invention.

2）当α<1，β<1时，作为举例，一种整数阶和分数阶混合串联谐振无线电能传输系统：V_S=10V，L=100μH，C=0.2533nF，R_L=50Ω，耦合系数k=0.1（且互感），α=0.8，β=0.9，R_P＝R_S＝0.5Ω。则实施例的输出功率与频率的关系曲线如图3所示（虚线部分），整数阶系统（即α=1，β=1时的情况）的输出功率也如图3所示（实线部分）。由图3可见，此种情况输出功率较小，设计时应避免。2) When α<1, β<1, as an example, an integer-order and fractional-order hybrid series resonant wireless power transmission system: V _S =10V, L=100μH, C=0.2533nF, R _L =50Ω, coupling Coefficient k=0.1 (and mutual inductance ), α=0.8, β=0.9, R _P ＝ _RS ＝0.5Ω. Then the relationship curve between the output power and frequency of the embodiment is shown in Figure 3 (dotted line part), and the output power of the integer order system (that is, when α=1, β=1) is also shown in Figure 3 (solid line part ). It can be seen from Figure 3 that the output power in this case is small and should be avoided during design.

3）当α>1，β>1时，作为举例，一种整数阶和分数阶混合串联谐振无线电能传输系统：V_S=10V，L=100μH，C=0.2533nF，R_L=50Ω，耦合系数k=0.1（且互感），α=1.1，β=1.2，R_P＝R_S＝0.5Ω。则实施例的输出功率与频率的关系曲线如图4所示（虚线部分），整数阶系统（即α=1，β=1时的情况）的输出功率也如图4所示（实线部分）。由图4可见，此种情况输出功率较小，设计时应避免。3) When α>1, β>1, as an example, an integer-order and fractional-order hybrid series resonant wireless power transfer system: V _S =10V, L=100μH, C=0.2533nF, R _L =50Ω, coupling Coefficient k=0.1 (and mutual inductance ), α=1.1, β=1.2, R _P ＝ _RS ＝0.5Ω. Then the relationship curve between the output power and frequency of the embodiment is shown in Figure 4 (dotted line part), and the output power of the integer order system (that is, when α=1, β=1) is also shown in Figure 4 (solid line part ). It can be seen from Figure 4 that the output power in this case is small and should be avoided during design.

4）当α<1，β>1时，作为举例，一种整数阶和分数阶混合串联谐振无线电能传输系统：V_S=10V，L=100μH，C=0.2533nF，R_L=50Ω，耦合系数k=0.1（且互感），α=0.8，β=1.2，R_P＝R_S＝0.5Ω。则实施例的输出功率与频率的关系曲线如图5所示（虚线部分），整数阶系统（即α=1，β=1时的情况）的输出功率也如图5所示（实线部分）。由图5可见，此种情况输出功率较小，设计时应避免。4) When α<1, β>1, as an example, an integer-order and fractional-order hybrid series resonant wireless power transfer system: V _S =10V, L=100μH, C=0.2533nF, R _L =50Ω, coupling Coefficient k=0.1 (and mutual inductance ), α=0.8, β=1.2, R _P ＝ _RS ＝0.5Ω. Then the relationship curve between output power and frequency of the embodiment is shown in Figure 5 (dotted line part), and the output power of the integer order system (that is, when α=1, β=1) is also shown in Figure 5 (solid line part ). It can be seen from Figure 5 that the output power in this case is small and should be avoided during design.

上述所述的情况对于α=β的情况同样适用。The situation described above is also applicable to the case of α=β.

上述实施例为本实用新型较佳的实施方式，但本实用新型的实施方式并不受所述实施例的限制，其他的任何未背离本实用新型的精神实质与原理下所作的改变、修饰、替代、组合、简化，均应为等效的置换方式，都包含在本实用新型的保护范围之内。The above-mentioned embodiment is the preferred implementation mode of the present utility model, but the implementation mode of the present utility model is not limited by the described embodiment, and any other changes, modifications, modifications made without departing from the spirit and principle of the present utility model Substitution, combination, and simplification should all be equivalent replacement methods, and are all included in the protection scope of the present utility model.

Claims

1. An integer-order and fractional-order hybrid series resonant wireless power transfer system, comprising a high-frequency power source (V _S ), a transmitting part, a receiving part and a load ( _RL ), characterized in that the transmitting part includes primary sides connected in series Integer-order capacitance (C _P ) and primary-side integer-order inductance (L _P ), the primary-side integer-order inductance (L _P ) has a primary-side resistance (R _P ); the receiving part consists of secondary-side fractional-order capacitance connected in series and secondary fractional inductance Secondary Fractional Inductance With secondary resistance (R _S ).

2. A kind of integer-order and fractional-order hybrid series resonant wireless power transmission system according to claim 1, characterized in that the primary side fractional-order capacitor Secondary Fractional Capacitance The differential relations of voltage and current satisfy: The phase relationship satisfies: Among them, i _C is the fractional-order capacitor current, v _C is the fractional-order capacitor voltage, α is the order of the fractional-order capacitor, and 0<α≤2, C ^α is the value of the fractional-order capacitor, when α=1 in the formula, that is It is the relationship satisfied by the integer-order capacitance.

3. A kind of integer-order and fractional-order hybrid series resonant wireless power transmission system according to claim 1, characterized in that the primary-side fractional-order inductance Secondary Fractional Inductance The differential relations of voltage and current satisfy: Among them, v _L is the voltage of the fractional inductor, i _L is the current of the fractional inductor, β is the order of the fractional inductor, and 0<β≤2, L ^β is the value of the fractional inductor, and β=1 in the formula It is the relationship satisfied by the integer-order inductance mentioned above.