Analysis method of lcc-lcc compensation topology based on fourier series model under tps mode

Abstract

The application discloses an analysis method of LCC-LCC compensation topology based on a Fourier series model in a TPS mode. The application comprises the following steps: A. inputting working conditions and parameters of a resonant cavity of LCC-LCC under a TPS control strategy; B. modeling a voltage excitation source of a phase-shifted full bridge; C. modeling characteristics of a circuit system; D. expressing and calculating a current vector of a wireless charging system under the TPS control strategy; and E. calculating power of the TPS wireless charging system. The application is applied to the technical field of power electronics.

Description

Technical Field

[0001] This invention applies to the field of power electronics technology, and particularly relates to an analysis method for LCC-LCC compensation topology based on Fourier series model in TPS mode. Background Technology

[0002] Wireless power transfer technology is a transmission mode that uses an invisible soft medium (such as electric field, magnetic field, sound wave, etc.) to transfer electrical energy from the power source to the device. In wireless power transfer technology, to optimize output power characteristics and facilitate control, a compensation topology for the resonant cavity is added. Currently, various compensation topologies are used in wireless power transfer technology. Common wireless charging systems have many primary-side (ground) and secondary-side (vehicle-side) resonant compensation topologies, mainly including four types: series resonant (S), parallel resonant (P), and hybrid series-parallel LCL and LCC. Various combinations can be formed based on these four resonant compensation topologies. Currently, various topologies have been developed, including ground-vehicle series (SS), ground-vehicle series-parallel (SP), ground-vehicle series-parallel (PS), ground-vehicle parallel (PP), ground-LCL-vehicle parallel (LCL-S), ground-vehicle LCL-LCL (LCL-LCL), ground-vehicle series (LCC-S), and ground-vehicle LCC-LCC (LCC-LCC). Each combination of topologies has unique characteristics and transmission features. Generally speaking, parameter design for high-order compensation topologies like LCL and LCC is quite difficult and currently suffers from the following drawbacks: 1) Parameter verification of wireless power transmission systems with such high-order compensation topologies requires numerous experimental verifications using testing machines and multiple modifications to the coil and compensation topology parameters, which is very time-consuming and labor-intensive; 2) Because wireless power transmission systems are very sensitive to mutual inductance parameters, the resonant parameters need to be very precise, and verification is difficult to perform; 3) Signal analysis under different operating states of the TPS control strategy is difficult, and it is also difficult to analyze problems and evaluate design parameters from actual experimental data; 4) Current SPICE and Saber models offer little advantage in analyzing circuit systems under this TPS control strategy (neither the mutual inductance model nor the control source model can adequately describe the voltage characteristics of TPS and the basic properties of the wireless charging system), and these methods cannot accurately model the electrical parameters under the TPS control strategy. The current design of high-order compensation topologies such as LCL and LCC requires consideration of numerous performance parameters and complex engineering conditions. Furthermore, the lack of structured and reliable evaluation methods after the design parameters are finalized necessitates more experimental and verification work in subsequent research and development. Therefore, a comprehensive and integrated parameter evaluation method is urgently needed for the design parameters of wireless power transmission compensation topologies. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide an analysis method for LCC-LCC compensation topology based on Fourier series model in TPS mode.

[0004] Fourier series models are a class of engineering mathematical methods commonly used in fields such as power electronics, communication engineering, and microelectronics. They decompose periodic signals into a series of sine and cosine functions. Specifically, they represent periodic signals as linear combinations of trigonometric functions, with each sine or cosine component called a harmonic. This model allows complex signals to be decomposed into a series of simple harmonic signals, which is helpful for analysis and research. This invention uses this engineering mathematical method to establish an analysis and evaluation method for high-order compensated topologies.

[0005] Furthermore, the design parameters evaluated in this invention are its operational performance and characteristics under the TPS control strategy. The TPS control strategy is a novel and practical control strategy for wireless power transmission. The TPS control strategy involves controlling three different phase shifts in the entire wireless power transmission system: the ground-end phase shift angle φp, the vehicle-end phase shift angle φs, and the system phase angle θc.

[0006] This invention relates to a method and its software algorithm for evaluating, analyzing, and optimizing the design parameters of the LCC-LCC compensation topology of a wireless transmission system under a TPS control strategy using a Fourier series model.

[0007] The technical solution adopted in this invention is as follows: This invention includes the following steps: A. Input the operating conditions and parameters of the LCC-LCC resonant cavity under the TPS control strategy; B. Model the voltage excitation source of the phase-shifted full-bridge, and obtain the ground-side full-bridge output voltage V by using the Fourier trigonometric function expression of the full-bridge output voltage under TPS. pi The output voltage V of the full bridge at the vehicle end si ; C. Model the characteristics of the circuit system. Based on the principle of LCC-LCC circuit, analyze the impedance characteristics under the premise that there are voltage pulse sources on both sides of the circuit. The impedance characteristics include the analysis and calculation of the impedance Z from the vehicle end to the ground end. p_in And analyze and calculate the impedance Z from the ground end to the vehicle end. s_in Next, the key parameters are converted, including the equivalent turns ratio n and the mutual inductance L. m Ground leakage magnetic field L pe , vehicle end leakage magnetic field L seAnd calculate the impedance Z on the opposite side from the vehicle end to the ground end. s_p and the impedance Z from the ground end to the vehicle end p_s ; D. Express and calculate the current vector of the wireless charging system under the TPS control strategy; obtain V from the Fourier trigonometric function expression. pi and V si and circuit impedance Z p_in and Z s_in The ground resonant current i is calculated. pi Resonant current i at the vehicle end si And through a calculation program, V of up to order N is calculated separately. pi and V si The corresponding ground resonant current i pi Resonant current i at the vehicle end si Then, their phasor diagrams are displayed separately and superimposed to form a superimposed effect diagram; E. Calculate the power of the TPS wireless charging system by simulating the voltage V at various orders under given operating conditions. pi and V s and current i pi and i si The components were analyzed, and the active power P of its output power was determined. s and reactive power Q s Furthermore, its power angle θ can be analyzed. power and system phase shift angle θ c The relationship between these parameters allows developers to directly evaluate and improve the design parameters based on the excitation effect under each harmonic component.

[0008] Furthermore, the input operating conditions in step A include the coupling coefficient k, load resistance RL, operating frequency fw, angular frequency ω, and system input voltage V. in Input resonant cavity ground voltage, ground phase angle φ p Angle value, system output voltage V out Input resonant cavity terminal voltage and terminal phase shift angle φ s Angle value, system phase angle θ c The angle value; the parameters of the resonant cavity include the ground coil inductance L. p Ground resonant inductor L rp , series capacitor C at ground terminal ps Ground parallel capacitor C p Ground coil internal resistance R p , Vehicle end coil inductance L s Vehicle-end resonant inductor L rs Series capacitor C at the vehicle end ss Parallel capacitor C at the vehicle ends and the internal resistance R of the coil at the vehicle end s .

[0009] Furthermore, in step B... The output voltage V of the ground-side full-bridge pi : ; The output voltage V of the full bridge at the vehicle end si :

[0010] Where V in It is the input voltage, V out It is the output voltage, w is the angular frequency, and φ is the output voltage. p It is the ground phase shift angle, φ s It is the phase shift angle at the vehicle end, θ c System phase angle.

[0011] Furthermore, the impedance Z from the vehicle end to the ground end in step C... p_in The calculation process includes the following steps: impedance calculation from the ground terminal. The schematic diagram of the LCC-LCC based circuit is shown from right to left as follows: Impedance of the resonant inductor branch at the vehicle end:

[0012] Impedance of the parallel capacitor branch from the vehicle end to the ground end:

[0013] The series capacitance at the vehicle end to the ground end and the impedance of the receiving leakage magnetic branch:

[0014] Equivalent turns ratio transformation impedance from vehicle end to ground:

[0015] Mutual inductance impedance from vehicle end to ground end:

[0016] The series capacitance from the vehicle end to the ground end and the impedance of the emission leakage magnetic branch:

[0017] Impedance of the parallel capacitor branch from the vehicle end to the ground end:

[0018] The impedance from the vehicle end to the ground end is the impedance seen from the ground end: ; The impedance Z from the ground end to the vehicle end in step C. s_in The calculation process includes the following steps: impedance calculation from the vehicle end, and the schematic diagram of the LCC-LCC circuit, from left to right: Ground resonant inductor branch impedance:

[0019] Impedance of the parallel capacitor branch from ground to vehicle end:

[0020] The ground series capacitor from the ground terminal to the vehicle terminal and the impedance of the receiving leakage magnetic branch:

[0021] Mutual inductance impedance from ground to vehicle:

[0022] Equivalent turns ratio transformation impedance from ground to vehicle:

[0023] The series capacitance from ground to vehicle end and the impedance of the emission leakage magnetic branch:

[0024] Impedance of the parallel capacitor branch from ground to vehicle end:

[0025] The impedance Z from the ground end to the vehicle end s_in That is, the impedance seen from the vehicle end:

[0026] The conversions for some of the key parameters mentioned above are as follows: Equivalent turns ratio:

[0027] Mutual intuition: (where k is the coupling coefficient) Ground leakage flux:

[0028] Vehicle-end magnetic leakage:

[0029] To calculate the current component reflected by the voltage pulse source on the opposite side, it is necessary to calculate the impedance on the opposite side from the vehicle end to the ground end separately:

[0030] The impedance from the ground end to the vehicle end on the opposite side: .

[0031] Furthermore, the magnitude and phasor direction of the current are calculated using a computer program. nth order ground resonant current:

[0032] The nth-order vehicle-end resonant current:

[0033] In the above formulas, the parameters are all expressed in phasor form, as follows: nth-order ground voltage:

[0034] nth-order vehicle terminal voltage:

[0035] nth order ground input impedance:

[0036] nth-order vehicle-end input impedance:

[0037] The impedance across the nth-order ground vehicle:

[0038] nth-order vehicle-to-ground cross impedance:

[0039] In this context, the absolute value of each expression represents its modulus, indicating the strength of the component, while the exponent of the natural base e of each expression represents the frequency and phase angle of that component.

[0040] Substituting into the phasor expression above, the resonant current can be expressed as:

[0041]

[0042] From the formulas for the two resonant currents, it can be seen that the nth-order resonant current mainly consists of two components because the entire circuit has two sources, namely: 1) The first current phasor of the ground resonant current: The current component induced by the ground terminal voltage as seen from the ground terminal has a magnitude of V. pi and Z p_in Divide the phase angle of the input impedance at ground by the phase angle of the input impedance at ground, while the phase angle of the input impedance at ground is zero (with the ground voltage as a reference). 2) The second current phasor of the ground resonant current: The magnitude of the current component of the vehicle terminal voltage reflected back to ground from the opposite side is V. si and Z s_p The phase angle is divided by the phase angle of the system phase angle, and the direction is the phase angle of the system phase angle minus the phase angle of the ground vehicle across the impedance; 3) The first current phasor of the resonant current at the vehicle end: The current component induced by the voltage at the vehicle terminals, as seen from the vehicle terminals, has a magnitude of V. si and Z s_in The phase angle is divided by the phase angle of the system phase angle minus the phase angle of the vehicle input impedance; 4) The second current phasor of the resonant current at the vehicle end: The ground voltage reflects the current component at the return terminal across the opposite side, and its magnitude is V. pi and Z p_s Divide the phase by the modulus, and subtract the phase angle of the vehicle-to-ground cross impedance when the direction is zero; By using computer programs to calculate and depict, we can obtain the phasor diagrams of ground voltage and vehicle voltage at any order, calculate the various current phasors they excite, synthesize them into resonant current phasors, and depict them on a phasor diagram in complex coordinates. According to the Fourier expression, the resonant current can actually be expressed as a linear superposition of multiple orders of resonant currents, which can be expressed as: Ground resonant current:

[0043] Vehicle-end resonant current:

[0044] Through computer programs, resonant currents of up to N orders can be calculated separately, their phasor diagrams can be displayed separately and superimposed to form a superimposed effect diagram.

[0045] Furthermore, The output power of the TPS wireless charging system can be expressed as:

[0046] The resonant current at the vehicle end needs to be taken as its conjugate complex number, which can be expressed as follows:

[0047] This is a complex expression for power, so active power and reactive power are its real and imaginary terms, respectively, as follows:

[0048]

[0049] The power angle of the system's output power can be expressed by the trigonometric function relationship between active power Ps and reactive power Qs.

[0050]

[0051] In fact, it can be derived from the Fourier series relationship:

[0052]

[0053] Therefore, there is a relationship between the power angle and the system phase angle:

[0054] The computer program MATLAB can be used to depict the relationship between the system phase shift angle and the power angle, calculate the corresponding active and reactive power content, and plot the results.

[0055] Furthermore, the computer program is a MATLAB program.

[0056] The beneficial effects of this invention are: 1. This invention allows for partial verification work to be carried out before the testing machine is manufactured; 2. Since wireless power transmission systems are very sensitive to mutual inductance parameters, the resonance parameters need to be very accurate, and the verification work is difficult to carry out. This invention can realize the verification work under some working conditions before the test machine is manufactured. 3. Signal analysis under different operating states of the TPS control strategy is very difficult, and it is also difficult to analyze problems and evaluate design parameters from actual experimental data; this invention can analyze the effect of each harmonic component one by one, and simplify the analysis steps and evaluation difficulty. 4. Existing SPICE and Saber models offer little advantage in analyzing circuit systems under this TPS control strategy. Neither the mutual inductance model nor the control source model can adequately describe the voltage characteristics of TPS and the fundamental properties of the wireless charging system. Furthermore, these methods struggle to accurately model the electrical parameters under the TPS control strategy. This invention effectively solves this problem because it uses first-principle programming for simulation, enabling precise description of the circuit model under the TPS control strategy. 5. It allows for intuitive evaluation of the design parameters of the LCC-LCC compensation topology. Attached Figure Description

[0057] Figure 1 This is a schematic diagram of a wireless power transmission system for an LCC-LCC compensation network; Figure 2 This is a schematic diagram of the entire wireless power transmission system that needs to be controlled under the TPS control strategy; Figure 3 This is a diagram showing the effect of synthesizing the full-bridge output voltage in Fourier series form under the TPS control strategy; Figure 4 This is the schematic diagram of an LCC-LCC circuit; Figure 5 This is a schematic diagram of the synthesis process of ground resonant current; Figure 6 These are all principal phasors in the fundamental order; Figure 7 This is a diagram showing the effect of synthesizing the ground resonant current in Fourier series form under the TPS control strategy. Figure 8 This is a diagram showing the effect of synthesizing the vehicle-end resonant current in the form of Fourier series under the TPS control strategy. Figure 9 The simulation results of the nth-order Fourier series model of a wireless charging system based on the TPS control strategy are shown. Figure 10 It is a transient waveform diagram of the vehicle-end resonant current and active power; Figure 11 It is the relationship between the system phase shift angle and the power angle. Detailed Implementation

[0058] In this embodiment, as Figure 1 The diagram shows a wireless power transmission system with an LCC-LCC compensation network. Both the vehicle-end and ground-end converters are phase-shifted full-bridge converters. The left side represents the ground end (transmitter) of the wireless power transmission system, while the right side represents the vehicle-end (receiver).

[0059] Figure 1 The parameters are represented as follows: Vdp is the input voltage, Vp is the full-bridge output voltage at ground, Lrp is the ground resonant inductance, Cp is the ground parallel compensation capacitor, Cps is the ground series compensation capacitor, Lp is the ground self-inductance, ILrp is the resonant current of the LCC compensation network, M is the mutual inductance coefficient, Ls is the vehicle self-inductance, Css is the vehicle series compensation capacitor, Cs is the vehicle parallel compensation capacitor, Lrs is the vehicle resonant inductance, Vs is the vehicle full-bridge output voltage, Vds is the output voltage, and Ids is the output current.

[0060] The three variables that need to be controlled under the TPS control strategy are: φp (ground phase shift angle), φs (vehicle phase shift angle), and θc (system phase angle). For example... Figure 2 As shown in the figure, Sp1~Sp4 are the switching signals at the ground terminal, Ss1~Ss4 are the switching signals at the vehicle terminal, Vp is the full-bridge output voltage at the ground terminal, Vs is the full-bridge output voltage at the vehicle terminal, iLrp is the resonant current at the ground terminal, and iLrs is the resonant current at the vehicle terminal.

[0061] To mathematically model a wireless power transfer system under the TPS strategy, the following steps are required: 1. First, mathematical models need to be performed on the excitation source (the phase-shifted full-bridge inverter located at the ground end and the phase-shifted full-bridge rectifier or other rectifier located at the vehicle end) and the characteristics of the circuit system itself (generally, an array of branch equations or an impedance characteristic model); 2. Then, the voltage phasors and current phasors are calculated using these models; 3. Next, the magnitude and direction of the power flow are analyzed; 4. Finally, the power angle relationship and the control characteristics and related properties of the system are determined.

[0062] In this embodiment, the present invention includes the following steps: Step S1. Input the operating conditions and parameters of the LCC-LCC resonant cavity under the TPS control strategy; the input operating conditions include the coupling coefficient k, load resistance RL, operating frequency fw, angular frequency ω, and system input voltage V. inInput resonant cavity ground voltage, ground phase angle φ p Angle value, system output voltage V out Input resonant cavity terminal voltage and terminal phase shift angle φ s Angle value, system phase angle θ c The angle value; the parameters of the resonant cavity include the ground coil inductance L. p Ground resonant inductor L rp , series capacitor C at ground terminal ps Ground parallel capacitor C p Ground coil internal resistance R p , Vehicle end coil inductance L s Vehicle-end resonant inductor L rs Series capacitor C at the vehicle end ss Parallel capacitor C at the vehicle end s and the internal resistance R of the coil at the vehicle end s .

[0063] Step S2. Model the voltage excitation source of the phase-shifted full-bridge and express the full-bridge output voltage in the Fourier trigonometric series form under TPS (the derivation process is omitted, but it can be directly obtained from the table, which refers to the Fourier transform formula table. The derivation process is not part of this patent. This Fourier formula is obtained by looking up and transforming it from the appendix of a mathematics book. It requires phase shifting and convolution on the Fourier form of a normal square wave signal): The output voltage V of the ground-side full-bridge pi : ; The output voltage V of the full bridge at the vehicle end si :

[0064] Where V in It is the input voltage, V out It is the output voltage, w is the angular frequency, and φ is the output voltage. p It is the ground phase shift angle, φ s It is the phase shift angle at the vehicle end, θ c System phase angle. In practical programming, it can also be expressed as an exponential Fourier series using Euler transform, which is more convenient in some situations. This invention uses a trigonometric function expression. This expression can fully represent the properties of the input / output resonant voltage under this TPS strategy, including the content of each component and phase angle changes, etc. Furthermore, it allows for convenient analysis and calculation. Figure 3The image shows the effect of implementing the Fourier series expression using MATLAB. The curves in the figure represent the output TPS (Three-phase shift control) drive voltage waveform data. It can output the drive voltage waveform under predetermined parameters (input / output voltage, ground / vehicle phase shift angle, and system phase angle, etc.) at a specified order. This waveform data will be used in subsequent automated design work. As can be seen from the figure, the waveform's state in the time domain can be adjusted through key control parameters, achieving an effect approximating the real waveform. The peaks appearing in the synthesized waveform are closer to the discontinuities of the original signal. This is because when a periodic function with discontinuities (usually referring to Type I discontinuities, sometimes Type II / III discontinuities may also satisfy the principle of absolute integrability) undergoes Fourier series expansion, a "Gibbs effect" may occur when synthesizing a finite number of terms. This is a purely mathematical phenomenon, not a real physical phenomenon.

[0065] Step S3. Model the characteristics of the circuit system, such as... Figure 4 The diagram shows the schematic of an LCC-LCC circuit. The impedance characteristics are analyzed under the premise of voltage pulse sources on both sides of the circuit. These impedance characteristics include the calculated impedance Z from the vehicle end to ground. p_in And analyze and calculate the impedance Z from the ground end to the vehicle end. s_in The impedance Z from the vehicle end to the ground end p_in The calculation process includes the following steps: impedance calculation from the ground terminal. The schematic diagram of the LCC-LCC based circuit is shown from right to left as follows: Impedance of the resonant inductor branch at the vehicle end:

[0066] Impedance of the parallel capacitor branch from the vehicle end to the ground end:

[0067] The series capacitance at the vehicle end to the ground end and the impedance of the receiving leakage magnetic branch:

[0068] Equivalent turns ratio transformation impedance from vehicle end to ground:

[0069] Mutual inductance impedance from vehicle end to ground end:

[0070] The series capacitance from the vehicle end to the ground end and the impedance of the emission leakage magnetic branch:

[0071] Impedance of the parallel capacitor branch from the vehicle end to the ground end:

[0072] The impedance from the vehicle end to the ground end is the impedance seen from the ground end: ; The impedance Z from the ground end to the vehicle end in step C. s_in The calculation process includes the following steps: impedance calculation from the vehicle end, and the schematic diagram of the LCC-LCC circuit, from left to right: Ground resonant inductor branch impedance:

[0073] Impedance of the parallel capacitor branch from ground to vehicle end:

[0074] The ground series capacitor from the ground terminal to the vehicle terminal and the impedance of the receiving leakage magnetic branch:

[0075] Mutual inductance impedance from ground to vehicle:

[0076] Equivalent turns ratio transformation impedance from ground to vehicle:

[0077] The series capacitance from ground to vehicle end and the impedance of the emission leakage magnetic branch:

[0078] Impedance of the parallel capacitor branch from ground to vehicle end:

[0079] The impedance Z from the ground end to the vehicle end s_in That is, the impedance seen from the vehicle end:

[0080] The conversions for some of the key parameters mentioned above are as follows: Equivalent turns ratio:

[0081] Mutual intuition: (where k is the coupling coefficient) Ground leakage flux:

[0082] Vehicle-end magnetic leakage:

[0083] To calculate the current component reflected by the voltage pulse source on the opposite side, it is necessary to calculate the impedance on the opposite side from the vehicle end to the ground end separately:

[0084] The impedance from the ground end to the vehicle end on the opposite side: .

[0085] Step S4. Express and calculate the current vector of the wireless charging system under the TPS control strategy; V is obtained from the Fourier trigonometric function expression form. pi and V si and circuit impedance Zp_in and Z s_in The magnitude and direction (phasor) of the current can then be calculated using a MATLAB program. The specific steps are as follows: nth order ground resonant current:

[0086] The nth-order vehicle-end resonant current:

[0087] In the above formulas, the parameters are all expressed in phasor form, as follows: nth-order ground voltage:

[0088] nth-order vehicle terminal voltage:

[0089] nth order ground input impedance:

[0090] nth-order vehicle-end input impedance:

[0091] The impedance across the nth-order ground vehicle:

[0092] nth-order vehicle-to-ground cross impedance:

[0093] In this context, the absolute value of each expression represents its modulus, indicating the strength of the component, while the exponent of the natural base e of each expression represents the frequency and phase angle of that component.

[0094] Substituting into the phasor expression above, the resonant current can be expressed as:

[0095]

[0096] From the formulas for the two resonant currents, it can be seen that the nth-order resonant current mainly consists of two components because the entire circuit has two sources, namely: 1) The first current phasor of the ground resonant current: The current component induced by the ground terminal voltage as seen from the ground terminal has a magnitude of V. pi and Z p_in Divide the phase angle of the input impedance at ground by the phase angle of the input impedance at ground, while the phase angle of the input impedance at ground is zero (with the ground voltage as a reference). 2) The second current phasor of the ground resonant current: The magnitude of the current component of the vehicle terminal voltage reflected back to ground from the opposite side is V. si and Z s_pThe phase angle is divided by the phase angle of the system phase angle, and the direction is the phase angle of the system phase angle minus the phase angle of the ground vehicle across the impedance; 3) The first current phasor of the resonant current at the vehicle end: The current component induced by the voltage at the vehicle terminals, as seen from the vehicle terminals, has a magnitude of V. si and Z s_in The phase angle is divided by the phase angle of the system phase angle minus the phase angle of the vehicle input impedance; 4) The second current phasor of the resonant current at the vehicle end: The ground voltage reflects the current component at the return terminal across the opposite side, and its magnitude is V. pi and Z p_s Divide the phase by the modulus, and subtract the phase angle of the vehicle-to-ground cross impedance when the direction is zero; By using computer programs to calculate and depict, we can obtain the phasor diagrams of ground voltage and vehicle voltage at any order, calculate the various current phasors they excite, synthesize them into resonant current phasors, and depict them on a phasor diagram in complex coordinates. like Figure 5 The diagram illustrates the synthesis process of the ground resonant current, a phasor diagram (a common analysis method in applications such as three-phase PFC and three-phase motors). This diagram can output the ground resonant current at any order and analyze the current magnitude and Euler angles (or phasor directions) for each component. The same method can also be used to synthesize other phasors, such as ground coil current, vehicle coil current, and vehicle resonant current. This phasor diagram can analyze current variations under different operating conditions and evaluate the rationality of the ground resonant state of the wireless system. The diagram represents the phasor synthesis process of the ground resonant circuit and includes the ground voltage phasor V. pi and vehicle terminal voltage phasor V si And the first term current phasor I1 and the second term current phasor I2 of the ground resonant current excited by them, and synthesize them into the ground resonant current phasor I. rp .

[0097] like Figure 6 The diagram shown combines all principal phasors of the same order into a single phasor diagram, adding the vehicle-end resonant current phasor I compared to the previous diagram. rs It is also obtained using a synthesis method where the ground resonant current phasors are roughly the same. This diagram shows all the principal phasors at the fundamental order, clearly displaying the magnitude and direction of each principal phasor. This invention... Figure 6 Is Figure 5 This is achieved on the basis of [previous technology / method]. After synthesizing and obtaining the phasors of the ground resonant circuit and the vehicle resonant current, [further steps are taken]. Figure 3The full-bridge output voltage data (also represented in phasor form) under the TPS control strategy can be synthesized into this figure. This figure can be used to analyze and evaluate whether the resonance state of the entire wireless system is reasonable.

[0098] According to the Fourier expression, the resonant current can actually be expressed as a linear superposition of multiple orders of resonant currents, which can be expressed as: Ground resonant current:

[0099] Vehicle-end resonant current:

[0100] Computer programs can calculate up to Nth order resonant currents individually, then display their phasor diagrams separately, and superimpose them to form a final superimposed image. For example... Figure 7 The figure shows the effect of synthesizing the ground resonant current in Fourier series form under the TPS control strategy. This figure represents the effect after synthesizing all ground resonant currents at a specified order. Figure 5 The superposition of ground resonant currents at various orders is nearly identical to the actual waveform, allowing for a clear view of detuning, phase, and peak value. This diagram is primarily used to study the magnitude and phase of the ground resonant current and can be used to derive data for further analysis (e.g., for system identification of control systems or verification of finite element analysis data).

[0101] like Figure 8 The figure shows the effect of synthesizing the vehicle-end resonant current in Fourier series form under the TPS control strategy. This figure represents the effect after synthesizing all vehicle-end resonant currents at a specified order. It is the effect of superimposing the vehicle-end resonant currents at various orders obtained from previous analyses, and it is very close to the actual waveform, allowing for a direct view of detuning, phase, and peak value. This figure is mainly used to study the magnitude and phase of the vehicle-end resonant current, and the data can be exported for further analysis (e.g., for system identification of the control system or verification of finite element analysis data).

[0102] The simulation results of the nth-order Fourier series model of the entire wireless charging system based on the TPS control strategy are as follows: Figure 9 As shown, this diagram is... Figure 3 , Figure 7 and Figure 8 The combined data visualization shows both the full-bridge drive voltage and resonant current at the ground vehicle end. This diagram is primarily used to study the magnitude and phase of the resonant current, and their relationship with the drive voltage. This diagram is mainly used to analyze the soft-switching conditions of the wireless charging system, because to achieve ZVS (Zero Voltage Switching), the voltage across the switch must be zero when it is turned off and on. This diagram provides a visual analysis of whether the parameters meet the ZVS conditions.

[0103] Step S5. Calculate the power of the TPS wireless charging system. The output power of the TPS wireless charging system can be expressed as:

[0104] The resonant current at the vehicle end needs to be taken as its conjugate complex number, which can be expressed as follows:

[0105] This is a complex expression for power, so active power and reactive power are its real and imaginary terms, respectively, as follows:

[0106]

[0107] The transient waveforms of the vehicle-end resonant current and active power are as follows: Figure 10 As shown, the power waveform is a multiple of the resonant current, which conforms to mathematical laws and also to the patterns observed in actual circuit sampling. This figure analyzes the waveform of the vehicle-end current and the transient waveform of the output active power; typically, the power change frequency is twice that of the current. This figure shows the output power and magnitude of the resonant cavity. It is mainly used to analyze whether this set of parameters meets the power rating requirements and can also, to some extent, analyze the stress on the phase-shifted full-bridge, helping hardware engineers select appropriate switching devices and auxiliary power topologies.

[0108] The power angle of the system's output power can be expressed by the trigonometric function relationship between active power Ps and reactive power Qs as follows:

[0109] In fact, it can be derived from the Fourier series relationship:

[0110]

[0111] Therefore, there is a relationship between the power angle and the system phase angle:

[0112] The computer program MATLAB can be used to depict the relationship between the system's phase shift angle and power angle, calculate the corresponding active and reactive power content, and plot the results. Figure 11 As shown, this figure analyzes the relationship between the system phase shift angle and the power angle. The upper figure is the curve of the system phase shift angle and the power angle, and the lower figure is the active power and reactive power content under the corresponding conditions.

[0113] The above evaluation method analyzes the behavior and characteristics of each harmonic component under the TPS control strategy based on the design parameters of the LCC-LCC. It simulates the voltage and current components at various orders under given operating conditions and analyzes the active power P of the output power. s and reactive power Q s Furthermore, it allows analysis of the relationship between the power angle θpower and the system phase shift angle θc. Developers can meticulously evaluate and improve these design parameters based on the excitation effect under each harmonic component.

[0114] This method is implemented using MATLAB, and the various effect diagrams in the preceding steps are also represented by MATLAB output diagrams. For clarity, each step will be introduced sequentially. Step S1. Input of given operating conditions under the TPS control strategy:

[0115] This code mainly takes into account the basic operating conditions under the TPS control strategy and the parameters of the LCC-LCC resonant cavity.

[0116] Step S2. Modeling the voltage excitation source of the phase-shifted full-bridge

[0117] This code mainly models the voltage excitation source of the phase-shifted full-bridge under the TPS control strategy.

[0118] Step S3. Characteristic modeling process of the circuit system

[0119] This code mainly models the impedance characteristics of the entire circuit system.

[0120] Step S4. Voltage and current phasor expression and calculation of the wireless charging system under the TPS control strategy.

[0121]

[0122]

[0123]

[0124] This code mainly models, expresses, and calculates the voltage and current phasors of a wireless charging system under the TPS control strategy.

[0125] Step S5. Power Calculation of the TPS Wireless Charging System

[0126] This code mainly models and calculates the power of the entire wireless charging system.

[0127] Although the embodiments of the present invention are described with reference to actual solutions, they do not constitute a limitation on the meaning of the present invention. Modifications to the embodiments and combinations with other solutions based on this specification will be obvious to those skilled in the art.

Claims

1. An analysis method for LCC-LCC compensated topology based on Fourier series model in TPS mode, characterized in that, It includes the following steps: A. Input the operating conditions and parameters of the LCC-LCC resonant cavity under the TPS control strategy; B. Model the voltage excitation source of the phase-shifted full-bridge, and obtain the ground-side full-bridge output voltage V by using the Fourier trigonometric function expression of the full-bridge output voltage under TPS. pi The output voltage V of the full bridge at the vehicle end si ; C. Model the characteristics of the circuit system. Based on the principle of LCC-LCC circuit, analyze the impedance characteristics under the premise that there are voltage pulse sources on both sides of the circuit. The impedance characteristics include the analysis and calculation of the impedance Z from the vehicle end to the ground end. p_in And analyze and calculate the impedance Z from the ground end to the vehicle end. s_in And calculate the impedance Z on the opposite side from the vehicle end to the ground end. s_p and the impedance Z from the ground end to the vehicle end p_s ; D. Express and calculate the current vector of the wireless charging system under the TPS control strategy; obtain V from the Fourier trigonometric series function expression. pi and V si and circuit impedance Z p_in and Z s_in The ground resonant current i is calculated. pi Resonant current i at the vehicle end si And through a calculation program, V of up to order N is calculated separately. pi and V si The corresponding ground resonant current i pi Resonant current i at the vehicle end si ; E. Calculate the power of the TPS wireless charging system by simulating the voltage V at various orders under given operating conditions. pi and V s and current i pi and i si The components were analyzed, and the active power P of its output power was determined. s and reactive power Q s Furthermore, it can analyze the relationship between its power angle θpower and the system phase shift angle θc.

2. The analysis method for LCC-LCC compensation topology based on Fourier series model in TPS mode according to claim 1, characterized in that: The input operating conditions in step A include the coupling coefficient k, load resistance RL, operating frequency fw, angular frequency w, and system input voltage V. in Input resonant cavity ground voltage, ground phase angle φ p Angle value, system output voltage V out Input resonant cavity terminal voltage and terminal phase shift angle φ s Angle value, system phase angle θ c The angle value; the parameters of the resonant cavity include the ground coil inductance L. p Ground resonant inductor L rp , series capacitor C at ground terminal ps Ground parallel capacitor C p Ground coil internal resistance R p , Vehicle end coil inductance L s Vehicle-end resonant inductor L rs Series capacitor C at the vehicle end ss Parallel capacitor C at the vehicle end s and the internal resistance R of the coil at the vehicle end s .

3. The analysis method for LCC-LCC compensation topology based on Fourier series model in TPS mode according to claim 2, characterized in that: In step B The output voltage V of the ground-side full-bridge pi : ; The output voltage V of the full bridge at the vehicle end si : ; Where V in It is the input voltage, V out It is the output voltage, w is the angular frequency, and φ is the output voltage. p It is the ground phase shift angle, φ s It is the phase shift angle at the vehicle end, θ c System phase angle.

4. The analysis method for LCC-LCC compensation topology based on Fourier series model in TPS mode according to claim 3, characterized in that: The impedance Z from the vehicle end to the ground end in step C. p_in The calculation process includes the following steps: impedance calculation from the ground end, including: Impedance of the resonant inductor branch at the vehicle end: ; Impedance of the parallel capacitor branch from the vehicle end to the ground end: ; The series capacitance at the vehicle end to the ground end and the impedance of the receiving leakage magnetic branch: ; Equivalent turns ratio transformation impedance from vehicle end to ground: ; Mutual inductance impedance from vehicle end to ground end: ; The series capacitance from the vehicle end to the ground end and the impedance of the emission leakage magnetic branch: ; Impedance of the parallel capacitor branch from the vehicle end to the ground end: ; The impedance from the vehicle end to the ground end is the impedance seen from the ground end: ; The impedance Z from the ground end to the vehicle end in step C. s_in The calculation process includes the following steps: impedance calculation from the vehicle end, including: Ground resonant inductor branch impedance: ; Impedance of the parallel capacitor branch from ground to vehicle end: ; The ground series capacitor from the ground terminal to the vehicle terminal and the impedance of the receiving leakage magnetic branch: ; Mutual inductance impedance from ground to vehicle: ; Equivalent turns ratio transformation impedance from ground to vehicle: ; The series capacitance from ground to vehicle end and the impedance of the emission leakage magnetic branch: ; Impedance of the parallel capacitor branch from ground to vehicle end: ; The impedance Z from the ground end to the vehicle end s_in That is, the impedance seen from the vehicle end: ; The conversions for some of the key parameters mentioned above are as follows: Equivalent turns ratio: ; Mutual intuition: Where k is the coupling coefficient; Ground leakage flux: ; Vehicle-end magnetic leakage: ; To calculate the current component reflected by the voltage pulse source on the opposite side, it is necessary to calculate the impedance on the opposite side from the vehicle end to the ground end separately: ; The impedance from the ground end to the vehicle end on the opposite side: .

5. The analysis method for LCC-LCC compensation topology based on Fourier series model in TPS mode according to claim 4, characterized in that: The magnitude and phasor direction of the current are calculated using a computer program. nth order ground resonant current: ; The nth-order vehicle-end resonant current: ; In the above formulas, the parameters are all expressed in phasor form, as follows: nth-order ground voltage: ; nth-order vehicle terminal voltage: ; nth order ground input impedance: ; nth-order vehicle-end input impedance: ; The impedance across the nth-order ground vehicle: ; nth-order vehicle-to-ground cross impedance: ; In this context, the absolute value of each expression represents its modulus, indicating the strength of the component, while the exponent of the natural base e of each expression represents the frequency and phase angle of that component. Substituting into the phasor expression above, the resonant current can be expressed as: ； ； From the formulas for the two resonant currents, it can be seen that the nth-order resonant current mainly consists of two components, namely: 1) The first current phasor of the ground resonant current: The current component induced by the ground terminal voltage as seen from the ground terminal has a magnitude of V. pi and Z p_in Divide the phase angle of the input impedance at ground by the phase angle of the input impedance at ground, while the phase angle of the input impedance at ground is zero (with the ground voltage as a reference). 2) The second current phasor of the ground resonant current: The magnitude of the current component of the vehicle terminal voltage reflected back to ground from the opposite side is V. si and Z s_p The phase angle is divided by the phase angle of the system phase angle, and the direction is the phase angle of the system phase angle minus the phase angle of the ground vehicle across the impedance; 3) The first current phasor of the resonant current at the vehicle end: The current component induced by the voltage at the vehicle terminals, as seen from the vehicle terminals, has a magnitude of V. si and Z s_in The phase angle is divided by the phase angle of the system phase angle minus the phase angle of the vehicle input impedance; 4) The second current phasor of the resonant current at the vehicle end: The ground voltage reflects the current component at the return terminal across the opposite side, and its magnitude is V. pi and Z p_s Divide the phase by the modulus, and subtract the phase angle of the vehicle-to-ground cross impedance when the direction is zero; The computer program is used to calculate and depict the phasor diagrams of the ground voltage and vehicle voltage at any order, and calculates the various current phasors excited by them. These are then combined into resonant current phasors and depicted on the phasor diagram in complex coordinates. According to the Fourier expression, the resonant current can actually be expressed as a linear superposition of multiple orders of resonant currents, as follows: Ground resonant current: ; Vehicle-end resonant current: ; The computer program calculates up to N resonant currents, displays their phasor diagrams separately, and then superimposes them to form a superimposed effect diagram.

6. The analysis method for LCC-LCC compensation topology based on Fourier series model in TPS mode according to claim 1, characterized in that: The output power of the TPS wireless charging system is expressed as: ； The resonant current at the vehicle end needs to be taken as its conjugate complex number, expressed as follows: ； This is a complex expression for power, so active power and reactive power are its real and imaginary terms, respectively, as follows: ； ； The power angle of the system's output power can be expressed by the trigonometric function relationship between active power Ps and reactive power Qs. ； In fact, based on the Fourier series relationship, we can derive: ； ； Therefore, there is a relationship between the power angle and the system phase angle: ； The relationship between the system phase shift angle and power angle was depicted using the computer program MATLAB, and the corresponding active and reactive power contents were calculated and plotted.

7. The analysis method for LCC-LCC compensation topology based on Fourier series model in TPS mode according to claim 6, characterized in that: The computer program used is MATLAB.

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