CN107528359A - The induction type wireless charging system of charging pile can be shared - Google Patents

The induction type wireless charging system of charging pile can be shared Download PDF

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Publication number
CN107528359A
CN107528359A CN201710569967.5A CN201710569967A CN107528359A CN 107528359 A CN107528359 A CN 107528359A CN 201710569967 A CN201710569967 A CN 201710569967A CN 107528359 A CN107528359 A CN 107528359A
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mrow
msub
mover
nodisjunction
mfrac
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CN107528359B (en
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何正友
寇志豪
陈阳
麦瑞坤
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Southwest Jiaotong University
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Southwest Jiaotong University
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    • H02J7/025
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J50/00Circuit arrangements or systems for wireless supply or distribution of electric power
    • H02J50/10Circuit arrangements or systems for wireless supply or distribution of electric power using inductive coupling
    • H02J7/0003
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J7/00Circuit arrangements for charging or depolarising batteries or for supplying loads from batteries
    • H02J7/0013Circuit arrangements for charging or depolarising batteries or for supplying loads from batteries acting upon several batteries simultaneously or sequentially
    • H02J7/0027

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Charge And Discharge Circuits For Batteries Or The Like (AREA)

Abstract

The invention discloses a kind of induction type wireless charging system for sharing charging pile, system is made up of transmitting portion and receiving portion, can set up constant current constant voltage switching circuit one in receiving portion and constant current constant voltage switching circuit two is realized jointly, and its composition is respectively:Secondary constant-current compensates inductance and the series connection of switching switch one, and the control terminal for switching switch one is connected with controller one;The composition of described constant current constant voltage switching circuit two is:Secondary constant-pressure compensation inductance and switching switch two are in parallel, and the control terminal for switching switch two is connected with controller one.The present invention can export the constant current unrelated with loading and constant voltage, it is suitable for more charging systems and shares an inverter, whole process input impedance is purely resistive, it is avoided that the input of reactive power, system effectiveness can be improved, so that the different equipment of charge requirement can share charging pile, the utilization rate of charging pile is improved.

Description

The induction type wireless charging system of charging pile can be shared
Technical field
The present invention relates to a kind of induction type wireless charging system for sharing charging pile.
Background technology
Induction type wireless power transmission technology is a kind of to realize the new of transmitting non-contact electric energy using soft-mediums such as magnetic fields Power supply technique, it is high and be widely used in medical treatment, consumption electricity the advantages that environment affinity is strong with flexible, the safe and stable property of powering The fields such as sub- product, underwater power, electric car charging and track traffic.Wherein, with induction type wireless power transmission technology pair Battery carries out wireless charging, and it is huge to avoid the drawback such as contact sparking and plug aging, development prospect existing for traditional plug-in system Greatly.
In order to realize that cell safety charges, extend the service life and discharge and recharge number of battery, generally mainly include constant current With two charging stages of constant pressure.Constant current mode is used in charging initial stage, cell voltage increases sharply;Filled when cell voltage reaches During electricity setting voltage, charged using constant voltage mode, charging current, which is progressively smaller until, reaches charge cutoff electric current, charging complete. Namely the induction type wireless charging system to be charged to battery should be able to provide constant electric current and voltage.
There is the rechargeable battery of plurality of specifications, the requirement of its charging current and voltage on Vehicles Collected from Market to also tend to phase not to the utmost Together, therefore, usually the charging pile of unique match can only be used to carry out one-to-one induction type wireless charging, charging pile utilization rate for it Very low, inconvenient, cost is also higher.
The main composition and the course of work of existing wireless charging system be:Industrial-frequency alternating current turns into direct current by rectification, DC inverter high frequency alternating current injection primary coil, produces high-frequency alternating magnetic field into high-frequency alternating current after inverter; Secondary coil induces induced electromotive force in high frequency magnetic field caused by primary coil, after the induced electromotive force is by high-frequency rectification Electric energy is provided to load.Equiva lent impedance due to loading (battery) is to change, so system is difficult under certain input voltage Constant current or voltage needed for output loading.To solve the problem, usual way has two kinds:First, draw in circuit system Enter close loop negative feedback control, controller is added such as before inverter and adjusts input voltage either using phase shifting control or secondary DC-DC converter is added after level coil rectification;Its defect is to add control cost and complexity, reduces the stability of a system. 2nd, using VFC, system is operated in two different frequency points and realizes constant current and constant pressure output, but frequency occurs in this method Rate bifurcation, cause system job insecurity.
The content of the invention
The purpose of the present invention be make induction type wireless charging system can output constant current can also export constant pressure, suitable for electricity Pond is charged, and the charging of multi-load under particularly single power supply, such as more electric cars is charged simultaneously;And its is easy to control, System working stability, input are idle almost nil;Only by the voltage that changes the i.e. configurable output different demands of secondary parameter and Electric current so that need the battery of different charging currents and voltage to share charging pile, improve the utilization rate of charging pile.
The technical scheme adopted by the invention for realizing the object of the invention is a kind of induction type wireless charging for sharing charging pile Electric system, it is made up of transmitting portion and receiving portion, high-frequency inverter H input connection dc source E, high-frequency inverter H Output end connect primary compensating electric capacity CPPrimary coil L is accessed afterwardsPForm the transmitting portion;The composition of the receiving portion For:Secondary coil LS, the P of secondary nodisjunction onee1, the P of secondary nodisjunction twoe2, the C of secondary compensation electric capacity twoS3, constant current constant voltage switching electricity The Q of road two2, current rectifying and wave filtering circuit D is sequentially connected;The C of secondary compensation electric capacity oneS1It is connected to the P of secondary nodisjunction onee1With secondary nodisjunction Two Pe2Tie point and secondary coil LSBetween current rectifying and wave filtering circuit D tie points;Current rectifying and wave filtering circuit D output ends connect battery Load Z.The described P of secondary nodisjunction twoe2With the C of secondary compensation electric capacity twoS3Tie point and the C of secondary compensation electric capacity oneS1Filtered with rectification The Q of constant current constant voltage switching circuit one is connected between wave circuit D tie points1, the described C of secondary compensation electric capacity twoS3With rectifying and wave-filtering The Q of constant current constant voltage switching circuit two is serially connected between circuit D2
The described Q of constant current constant voltage switching circuit one1Composition be:Secondary constant-current compensation inductance LS3A S is switched with switching1String Connection, and switch one S of switch1Control terminal and the K of controller one1It is connected.
The described Q of constant current constant voltage switching circuit two2Composition be:Secondary constant-pressure compensation inductance LVTwo S are switched with switching2And Connection, and switch two S of switch2Control terminal and the K of controller one1It is connected.
Further, the described P of secondary nodisjunction onee1And the P of secondary nodisjunction twoe2It is made up of inductance or electric capacity.Secondary is mended Repay the P of device onee1And the P of secondary nodisjunction twoe2It is made up of inductance or electric capacity, shares four kinds of situations:Pe1Inductance-Pe2Inductance, Pe1Inductance- Pe2Electric capacity, Pe1Electric capacity-Pe2Inductance, Pe1Electric capacity-Pe2Electric capacity.
Further, described primary compensating electric capacity CPCapacitanceDetermined by formula (1):
Wherein ω is system work angular frequency.
The described C of secondary compensation electric capacity oneS1CapacitanceDetermined by formula (2):
WhereinFor dc source E output voltage values, M is primary coil LPWith secondary coil LSMutual inductance value, VBFor Set charging voltage.
The described C of secondary compensation electric capacity twoS3CapacitanceDetermined by formula (3):
Wherein IBTo set charging current.
Described secondary constant-current compensation inductance LS3Inductance valueDetermined by formula (4):
Described secondary constant-pressure compensation inductance LVInductance valueDetermined by formula (5):
The described P of secondary nodisjunction onee1Determined by following formula:If the P of secondary nodisjunction onee1Impedance In perception, then inductance L is compensated by secondary coile1Form, its valueDetermined by formula (6):
If the P of secondary nodisjunction onee1ImpedanceIn capacitive, then by secondary coil compensating electric capacity Ce1Form, its valueDetermined by formula (7):
The described P of secondary nodisjunction twoe2Determined by following formula:If the P of secondary nodisjunction twoe2Impedance In perception, then inductance L is compensated by secondary coile2Form, its valueDetermined by formula (8):
If the P of secondary nodisjunction onee2ImpedanceIn capacitive, then by secondary coil compensating electric capacity Ce2Form, its valueDetermined by formula (9):
The application method of technical solution of the present invention is:
The closure of the control switching of controller one switch one and the closure of switching switch two, system works in constant current mode, to negative Output constant current is carried, i.e., the constant charge current I of setting is provided to batteryB;It is adapted to battery charging to use initial stage.
The control switching of controller one switch one disconnects and switching switch two disconnects, and system works in constant voltage mode, to negative Output constant voltage is carried, i.e., the constant charge voltage V of setting is provided to batteryB;It is adapted to battery charging later stage, cell voltage to reach Used during charging setting voltage.
System output constant current and the theory analysis of constant voltage are as follows in the present invention program:
Consider circuit as shown in Figure 1, wherein primary coil is LP, secondary coil LS.Its T-shaped equivalent circuit as shown in Fig. 2 Wherein magnetizing inductance L=M, primary, secondary leakage inductance are respectively:LP-M,LS- M, if CPMeet CSMeetI.e.
When, system input impedance is:
Output current, which can further be calculated, is:
It can draw under structure as Fig. 1, system input impedance is purely resistive, and the output current of system and load Size it is unrelated, i.e., under the operating mode of load change, system can keep constant current output, suitable for battery charging early stage.
Likewise, the structure shown in Fig. 3 is considered, if LS1And LS2Meet relation respectively:
Then system input impedance is:
Output voltage, which can further be calculated, is:
It can draw under structure as Fig. 3, system input impedance is purely resistive, and the output voltage of system and load Size it is unrelated, i.e., under the operating mode of load change, system can keep constant pressure to export, suitable for battery charging later stage.
Likewise, the structure shown in Fig. 4 is considered, if CS2And CS3Meet relation respectively:
Then system input impedance is:
Output current, which can further be calculated, is:
It can draw under structure as Fig. 4, system input impedance is purely resistive, and the output current of system and load Size it is unrelated, i.e., under the operating mode of load change, system can keep constant current output, suitable for battery charging early stage.
If the voltage source in Fig. 1 is replaced by dc source E and high-frequency inverter, high-frequency inverter input voltageWith output Voltage ViBetween relation be:
Current source in Fig. 3 is replaced by the system output current in Fig. 1, and the voltage source in Fig. 4 is exported by the system in Fig. 3 Voltage is replaced, and the load in Fig. 4 is replaced by cell load and rectifier bridge, the input voltage V of rectifier bridgeoWith output voltage VBBetween Relation be:
The input current I of rectifier bridgeoWith output current IBBetween relation be:
The structure shown in Fig. 5 can be then combined into, based on the analysis done above, it is clear that system is defeated under this structure It is purely resistive to enter impedance, and can realize voltage source input, the function of system constant current output, association type (12), (15), (18), (19), (21) can try to achieve its output current and be:
Suitable for the early stage of battery charging.In order to reduce element with cost-effective, by C in the structure shown in Fig. 5SWith LS1Group Synthesize a P of component secondary nodisjunction onee1、LS2With CS2It is combined into a P of component secondary nodisjunction twoe2, obtain Fig. 6 institutes The structure shown.
The circuit realiration principle of system constant current output is described above, is discussed below on the basis of the structure shown in Fig. 6 On the conversion of system constant pressure and flow outlet chamber is realized by secondary structure changes, to meet to export system in whole charging process The requirement of voltage x current.
Scheme as shown in fig. 7,
Phase before charging, to obtain system power constant current output, the K of controller one1One S of closure switching switch1, closure switching Switch two S2, now system architecture be changed into the structure shown in Fig. 6.
Phase after charging, to obtain the output of system voltage constant pressure, the K of controller one1Disconnect one S of switching switch1, disconnect switching Switch two S2, under such configuration when with CS3The secondary constant-pressure compensation inductance L of series connectionVImpedance valueMeet
When, based on the analysis done above, it is clear that system input impedance is purely resistive under this structure, and can be real Existing voltage source input, the function of system constant pressure output, association type (12), (15), (19), (20) can try to achieve its output voltage and be:
The load constant-voltage V then required in userB, input direct voltagePrimary coil LPSecondary coil LSInductance ValueUnder conditions of mutual inductance M and system operating frequency f between primary and secondary are certain, secondary compensation electricity is understood by formula (24) Hold a CS1CapacitanceCondition need to be met:
Primary compensating electric capacity C is understood by formula (10)PCapacitanceCondition need to be met:
Understood to form the P of secondary nodisjunction one by formula (10)e1CSCapacitanceCondition need to be met:
Understand to form the P of secondary nodisjunction one by formula (13), (25)e1LS1Inductance valueCondition need to be met:
The P of secondary nodisjunction one is can determine that by formula (27), (28)e1:If the P of secondary nodisjunction onee1Impedance In perception, then inductance L is compensated by secondary coile1Form, its valueDetermined by formula (29):
If the P of secondary nodisjunction onee1ImpedanceIn capacitive, then by secondary coil compensating electric capacity Ce1Form, its valueDetermined by formula (30):
Understood to form the P of secondary nodisjunction two by formula (13)e2LS2Inductance valueCondition need to be met:
To determine the parameter of other elements in Fig. 7 systems, the K of controller one1One S of closure switching switch1, disconnect switching switch Two S2, make system power constant current output.
Secondary constant-current compensation inductance L is understood by formula (22), (25)S3Inductance valueCondition need to be met:
Understand to form the P of secondary nodisjunction two by formula (16), (32)e2CS2CapacitanceCondition need to be met:
The P of secondary nodisjunction two is can determine that by formula (31), (33)e2:If the P of secondary nodisjunction twoe2Impedance In perception, then inductance L is compensated by secondary coile2Form, its valueDetermined by formula (34):
If the P of secondary nodisjunction onee2ImpedanceIn capacitive, then by secondary coil compensating electric capacity Ce2Form, its valueDetermined by formula (35):
The C of secondary compensation electric capacity two is understood by formula (16), (32)S3CapacitanceCondition need to be met:
Finally, secondary constant-pressure compensation inductance L is understood by formula (23), (25), (35), (36)VInductance valueCondition need to be met:
In summary, as the K of controller one1One S of closure switching switch1, closure switching switch two S2, then system output is constant Electric current, used early stage suitable for charging, and work as the K of controller one1Disconnect one S of switching switch1, disconnect switching switch two S2, then system Constant voltage is exported, is used suitable for the charging later stage.
Association type (22), (24) can be drawn when working in constant current output mode or the constant pressure way of output, its output current Or output voltage only can be changed by changing secondary parameter, so the equipment different to charging current, charging voltage demand During charging, the charging pile of same specification can be used, improve the compatibility of charging pile, be more convenient, manufacturing cost is also minimized.
In addition, association type (11), (14), (17) can be derived when working in constant current output mode, the input resistance of system Resist and be:In purely resistive, so during system constant current output, system almost inputs without reactive power, reduces Requirement of the system to inverter capacity.
Similarly, association type (11), (14) can derive work in the constant pressure way of output when, the input impedance of system For:In purely resistive, so during system constant current output, system almost inputs without reactive power, reduces system Requirement to inverter capacity.
Compared with prior art, the beneficial effects of the invention are as follows:
First, a kind of induction type wireless charging system for sharing charging pile proposed by the present invention, only two need to be set in secondary Individual switching switch, it just can change the circuit topological structure of secondary, so as to export the constant current unrelated with loading and constant Voltage, meet the requirement of battery constant-current charge at initial stage, later stage constant-voltage charge.System is operated under a Frequency point, is not in Frequency bifurcation, system working stability.Its circuit structure is simple, and cost is low, only needs cutting for simple controlling switch during work Change, without the control strategy of complexity, communicated without primary and secondary;It is controlled simply, conveniently, reliably.
2nd, after the circuit system parameter determines, the constant current unrelated with load and constant voltage of output and high frequency Inverter output voltage is relevant, therefore can be by the high-frequency inverter rear portion circuit in parallel of such multiple system in same high-frequency inversion On device, realize and multiple batteries or charging equipment are charged simultaneously, greatly reduce high-frequency inverter during more cell load chargings Quantity, reduce charging cost.
3rd, circuit topology of the invention is in system constant pressure and constant current output, inverter output voltage current in phase position, causes Inverter is almost not injected into reactive power, so system loss is smaller, and the capacity requirement of inverter is reduced.
4th, for circuit topology of the invention in system constant pressure or constant current output, its output voltage or output current can be only Changed by changing secondary parameter, so in the equipment charge different to charging current, charging voltage demand, can be used same The charging pile of one specification, the utilization rate of charging pile is improved, be more convenient, manufacturing cost is also minimized.
The present invention is further illustrated with reference to the accompanying drawings and detailed description.
Brief description of the drawings
Fig. 1 is the system circuit diagram of primary and secondary all series compensations.
Fig. 2 is the T-shaped equivalent circuit diagram of the circuit system of primary and secondary all series compensations.
Fig. 3 is the LCL type circuit diagram that driving source is current source.
Fig. 4 is the CLC type circuit diagrams that driving source is voltage source.
Fig. 5 is constant current output system circuit diagram.
Fig. 6 is the simplification figure of constant current output system circuit diagram.
Fig. 7 is system circuit diagram.
Label declaration in figure:E is dc source, and H is high-frequency inverter, Q1For constant current constant voltage switching circuit one, Q2For constant current Constant pressure switching circuit two, CPFor primary compensating electric capacity, LPFor primary coil, LSFor secondary coil, Pe1For secondary nodisjunction one, Pe2 For secondary nodisjunction two, CS1For secondary compensation electric capacity one, CS3For secondary compensation electric capacity two, LS3Inductance is compensated for secondary constant-current, LVFor secondary constant-pressure compensation inductance, D is current rectifying and wave filtering circuit, and Z is cell load, S1One, S is switched for switching2Switched for switching Two, K1For controller one, ViFor high-frequency inverter H equivalent output voltage, R is to enter in terms of current rectifying and wave filtering circuit input port Battery equivalent load, VBFor the voltage at battery both ends, IBThe electric current flowed through for battery.
Embodiment
Shown in Fig. 7, embodiment of the invention is a kind of induction type wireless charging system for sharing charging pile, It is made up of transmitting portion and receiving portion, high-frequency inverter H input connection dc source E, high-frequency inverter H output end Connect primary compensating electric capacity CPPrimary coil L is accessed afterwardsPForm the transmitting portion;The composition of the receiving portion is:Secondary wire Enclose LS, the P of secondary nodisjunction onee1, the P of secondary nodisjunction twoe2, the C of secondary compensation electric capacity twoS3, the Q of constant current constant voltage switching circuit two2, rectification Filter circuit D is sequentially connected;The described P of secondary nodisjunction onee1And the P of secondary nodisjunction twoe2It is made up of inductance or electric capacity;It is secondary The C of compensating electric capacity oneS1It is connected to the P of secondary nodisjunction onee1With the P of secondary nodisjunction twoe2Tie point and secondary coil LSFiltered with rectification Between wave circuit D tie points;Current rectifying and wave filtering circuit D output ends connection cell load Z.
The described P of secondary nodisjunction twoe2With the C of secondary compensation electric capacity twoS3Tie point and the C of secondary compensation electric capacity oneS1With it is whole The Q of constant current constant voltage switching circuit one is connected between stream filter circuit D tie points1, the described C of secondary compensation electric capacity twoS3With rectification The Q of constant current constant voltage switching circuit two is serially connected between filter circuit D2
The described Q of constant current constant voltage switching circuit one1Composition be:Secondary constant-current compensation inductance LS3A S is switched with switching1String Connection, and switch one S of switch1Control terminal and the K of controller one1It is connected.
The described Q of constant current constant voltage switching circuit two2Composition be:Secondary constant-pressure compensation inductance LVTwo S are switched with switching2And Connection, and switch two S of switch2Control terminal and the K of controller one1It is connected.
Described primary compensating electric capacity CPCapacitanceDetermined by formula (1):
Wherein ω is system work angular frequency.
The described C of secondary compensation electric capacity oneS1CapacitanceDetermined by formula (2):
WhereinFor dc source E output voltage values, M is primary coil LPWith secondary coil LSMutual inductance value, VBFor Set charging voltage.
The described C of secondary compensation electric capacity twoS3CapacitanceDetermined by formula (3):
Wherein IBTo set charging current.
Described secondary constant-current compensation inductance LS3Inductance valueDetermined by formula (4):
Described secondary constant-pressure compensation inductance LVInductance valueDetermined by formula (5):
The described P of secondary nodisjunction onee1Determined by following formula:If the P of secondary nodisjunction onee1Impedance In perception, then inductance L is compensated by secondary coile1Form, its valueDetermined by formula (6):
If the P of secondary nodisjunction onee1ImpedanceIn capacitive, then by secondary coil compensating electric capacity Ce1Form, its valueDetermined by formula (7):
The described P of secondary nodisjunction twoe2Determined by following formula:If the P of secondary nodisjunction twoe2Impedance In perception, then inductance L is compensated by secondary coile2Form, its valueDetermined by formula (8):
If the P of secondary nodisjunction onee2ImpedanceIn capacitive, then by secondary coil compensating electric capacity Ce2Form, its valueDetermined by formula (9):

Claims (6)

1. a kind of induction type wireless charging system for sharing charging pile, is made up of, high-frequency inversion transmitting portion and receiving portion The input connection dc source (E) of device (H), the primary compensating electric capacity (C of output end series connection of high-frequency inverter (H)P) access afterwards Primary coil (LP) form the transmitting portion;The composition of the receiving portion is:Secondary coil (LS), secondary nodisjunction one (Pe1), (P of secondary nodisjunction twoe2), (C of secondary compensation electric capacity twoS3), (Q of constant current constant voltage switching circuit two2), current rectifying and wave filtering circuit (D) it is sequentially connected;(the C of secondary compensation electric capacity oneS1) it is connected to (the P of secondary nodisjunction onee1) and (P of secondary nodisjunction twoe2) tie point With secondary coil (LS) between current rectifying and wave filtering circuit (D) tie point;Current rectifying and wave filtering circuit (D) output end connects cell load (Z);Characterized in that, described (the P of secondary nodisjunction twoe2) and (C of secondary compensation electric capacity twoS3) tie point and secondary compensation electricity Hold (a CS1) between current rectifying and wave filtering circuit (D) tie point it is connected with (the Q of constant current constant voltage switching circuit one1), described secondary benefit Repay (the C of electric capacity twoS3) (the Q of constant current constant voltage switching circuit two is serially connected between current rectifying and wave filtering circuit (D)2);
Described (the Q of constant current constant voltage switching circuit one1) composition be:Secondary constant-current compensation inductance (LS3) and one (S of switching switch1) Series connection, and switch one (S of switch1) control terminal and the (K of controller one1) be connected;
Described (the Q of constant current constant voltage switching circuit two2) composition be:Secondary constant-pressure compensation inductance (LV) and two (S of switching switch2) Parallel connection, and switch two (S of switch2) control terminal and the (K of controller one1) be connected.
2. the induction type wireless charging system according to claim 1 for sharing charging pile, it is characterised in that described time Level compensator one (Pe1) and (P of secondary nodisjunction twoe2) be made up of inductance.
3. the induction type wireless charging system according to claim 1 for sharing charging pile, it is characterised in that described time Level compensator one (Pe1) and (P of secondary nodisjunction twoe2) be made up of electric capacity.
4. the induction type wireless charging system according to claim 1 for sharing charging pile, it is characterised in that described time Level compensator one (Pe1) be made up of inductance;(the P of secondary nodisjunction twoe2) be made up of electric capacity.
5. the induction type wireless charging system according to claim 1 for sharing charging pile, it is characterised in that described time Level compensator one (Pe1) be made up of electric capacity and be made up of inductance;(the P of secondary nodisjunction twoe2) be made up of inductance.
6. the induction type wireless charging system according to claim 1 for sharing charging pile, it is characterised in that:
Described primary compensating electric capacity (CP) capacitanceDetermined by formula (1):
<mrow> <mover> <msub> <mi>C</mi> <mi>P</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msup> <mi>&amp;omega;</mi> <mn>2</mn> </msup> <mover> <msub> <mi>L</mi> <mi>P</mi> </msub> <mo>&amp;OverBar;</mo> </mover> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
Wherein ω is system work angular frequency;
Described (the C of secondary compensation electric capacity oneS1) capacitanceDetermined by formula (2):
<mrow> <mover> <msub> <mi>C</mi> <mrow> <mi>S</mi> <mn>1</mn> </mrow> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mover> <mi>E</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <msup> <mi>&amp;omega;</mi> <mn>2</mn> </msup> <msub> <mi>MV</mi> <mi>B</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
WhereinFor dc source (E) output voltage values, M is primary coil (LP) and secondary coil (LS) mutual inductance value, VBFor Set charging voltage;
Described (the C of secondary compensation electric capacity twoS3) capacitanceDetermined by formula (3):
<mrow> <mover> <msub> <mi>C</mi> <mrow> <mi>S</mi> <mn>3</mn> </mrow> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mrow> <msup> <mi>&amp;pi;</mi> <mn>2</mn> </msup> <msub> <mi>I</mi> <mi>B</mi> </msub> </mrow> <mrow> <mn>8</mn> <msub> <mi>&amp;omega;V</mi> <mi>B</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
Wherein IBTo set charging current;
Described secondary constant-current compensation inductance (LS3) inductance valueDetermined by formula (4):
<mrow> <mover> <msub> <mi>L</mi> <mrow> <mi>S</mi> <mn>3</mn> </mrow> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mrow> <mn>8</mn> <msub> <mi>V</mi> <mi>B</mi> </msub> </mrow> <mrow> <msup> <mi>&amp;pi;</mi> <mn>2</mn> </msup> <msub> <mi>&amp;omega;I</mi> <mi>B</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
Described secondary constant-pressure compensation inductance (LV) inductance valueDetermined by formula (5):
<mrow> <mover> <msub> <mi>L</mi> <mi>V</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mrow> <mn>16</mn> <msub> <mi>V</mi> <mi>B</mi> </msub> </mrow> <mrow> <msup> <mi>&amp;pi;</mi> <mn>2</mn> </msup> <msub> <mi>&amp;omega;I</mi> <mi>B</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
Described (the P of secondary nodisjunction onee1) determined by following formula:If the P of secondary nodisjunction onee1Impedance In perception, then inductance L is compensated by secondary coile1Form, its valueDetermined by formula (6):
<mrow> <mover> <msub> <mi>L</mi> <mrow> <mi>e</mi> <mn>1</mn> </mrow> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mrow> <msub> <mi>MV</mi> <mi>B</mi> </msub> </mrow> <mover> <mi>E</mi> <mo>&amp;OverBar;</mo> </mover> </mfrac> <mo>-</mo> <mover> <msub> <mi>L</mi> <mi>S</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
If the P of secondary nodisjunction onee1ImpedanceIn capacitive, then by secondary coil compensating electric capacity Ce1Structure Into its valueDetermined by formula (7):
<mrow> <mover> <msub> <mi>C</mi> <mrow> <mi>e</mi> <mn>1</mn> </mrow> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mover> <mi>E</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <msup> <mi>&amp;omega;</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mover> <mi>E</mi> <mo>&amp;OverBar;</mo> </mover> <mover> <msub> <mi>L</mi> <mi>S</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>-</mo> <msub> <mi>MV</mi> <mi>B</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
Described (the P of secondary nodisjunction twoe2) determined by following formula:If the P of secondary nodisjunction twoe2Impedance In perception, then inductance L is compensated by secondary coile2Form, its valueDetermined by formula (8):
<mrow> <mover> <msub> <mi>L</mi> <mrow> <mi>e</mi> <mn>2</mn> </mrow> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mrow> <msub> <mi>MV</mi> <mi>B</mi> </msub> </mrow> <mover> <mi>E</mi> <mo>&amp;OverBar;</mo> </mover> </mfrac> <mo>-</mo> <mfrac> <mrow> <mn>8</mn> <msub> <mi>V</mi> <mi>B</mi> </msub> </mrow> <mrow> <msup> <mi>&amp;pi;</mi> <mn>2</mn> </msup> <msub> <mi>&amp;omega;I</mi> <mi>B</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
If the P of secondary nodisjunction onee2ImpedanceIn capacitive, then by secondary coil compensating electric capacity Ce2Structure Into its valueDetermined by formula (9):
<mrow> <mover> <msub> <mi>C</mi> <mrow> <mi>e</mi> <mn>2</mn> </mrow> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mrow> <msup> <mi>&amp;pi;</mi> <mn>2</mn> </msup> <mover> <mi>E</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>I</mi> <mi>B</mi> </msub> </mrow> <mrow> <msub> <mi>&amp;omega;V</mi> <mi>B</mi> </msub> <mrow> <mo>(</mo> <mn>8</mn> <mover> <mi>E</mi> <mo>&amp;OverBar;</mo> </mover> <mo>-</mo> <msup> <mi>&amp;pi;</mi> <mn>2</mn> </msup> <msub> <mi>&amp;omega;MI</mi> <mi>B</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
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