A WPT system control method based on nonlinear model reduction

Abstract

The application relates to the wireless power transmission (WPT) technical field and particularly discloses a WPT system control method based on nonlinear model reduction, which comprises the following steps: firstly, a complex full-order mathematical model of the WPT system is constructed; then, the complex full-order mathematical model is reduced by using an LPV-Hammerstein model to obtain an LPV-Hammerstein model of the WPT system; next, different order reduced models are generated according to the LPV-Hammerstein model of the WPT system, and system identification is performed on the reduced models to obtain identification parameters; then, corresponding low-order models are established according to the identification parameters; finally, one of the low-order models with the highest fitting degree with the complex full-order mathematical model is taken as the optimal low-order model of the WPT system. The application reduces the high-order complex full-order mathematical model of nonlinear output by using the LPV-Hammerstein model, and obtains the parameters most matched with the original model through system identification. Without obtaining all circuit element parameters, a simple and accurate model can be obtained, and the dynamic characteristics of the system can be accurately described by using a first-order or second-order model.

Description

Technical Field

[0001] This invention relates to the field of wireless power transfer (WPT) technology, and in particular to a WPT system control method based on order reduction of a nonlinear model. Background Technology

[0002] To reduce greenhouse gas emissions and conserve energy, electric vehicles (EVs) have been widely adopted. EV charging methods include contact and wireless charging. Compared to traditional wired contact power transfer, wireless power transfer (WPT) is portable, safe, and reliable, and has seen rapid development in the field of EV dynamic charging.

[0003] In dynamic applications, WPT systems require performance analysis and output control; therefore, the dynamic mathematical model of the controlled object is particularly important for system analysis and controller design. Currently, for WPT system controller design, to obtain better dynamic performance, system modeling needs to be closer to the actual model.

[0004] To address this problem, some scholars have employed a systematic and intuitive time-domain dynamic phasor modeling method and proposed a reduced-order model by applying an appropriate s-domain approximation to the linear part of the system. This model uses field amplitude and field phase to describe the equivalent inductor element, successfully reducing the 9th-order small-signal model to a 5th-order system. Other scholars have used a reduced-order time-domain model to provide a precise time-domain and frequency-domain description of the converter, successfully reducing the 11th-order small-signal model to a 6th-order system. However, this method has a complex theoretical framework, lacks certain applicability, and the reduced order of the system remains relatively high.

[0005] Some scholars have used the closed-loop dominant pole method to convert the 11th-order WPT system into a 2nd-order system. However, since only the dominant pole is considered, it cannot guarantee a high degree of matching with the original system in terms of dynamic characteristics and steady-state error. Furthermore, the closed-loop dominant pole method originates from classical control theory, so it is only applicable to single-input single-output systems and has certain limitations in application.

[0006] Scholars have proposed a method for establishing a dynamic control output model for a SS-compensated wireless power transfer (WPT) system under phased or frequency-converted control. Based on a complex-valued full-order mathematical model derived from low-order Taylor series expansion and circuit theory, a polynomial approximation technique is used to reduce the order of the model. After reducing the order of the signals in the model and decomposing them into real and imaginary forms, it can be converted into real-valued models of orders 1, 3, and 5.

[0007] However, the above methods generate nonlinear system models of too high an order or cannot obtain large signal models of arbitrary order. Summary of the Invention

[0008] This invention provides a control method for WPT systems based on nonlinear model order reduction. The technical problem it solves is: how to reduce the order of a high-order complex-valued WPT system model with nonlinear output, obtain the parameters that best match the original model through system identification, and obtain a simple and accurate low-order model that can accurately describe the dynamic characteristics of the system.

[0009] To address the above technical problems, this invention provides a WPT system control method based on nonlinear model order reduction, characterized by the following steps:

[0010] S1. Construct a complex-valued full-order mathematical model of the WPT system;

[0011] S2. The complex-valued full-order mathematical model is reduced in order using the LPV-Hammerstein model to obtain the LPV-Hammerstein model of the WPT system.

[0012] S3. Generate reduced-order models of different orders based on the WPT system LPV-Hammerstein model, perform system identification on these reduced-order models to obtain identification parameters, and establish corresponding low-order models based on the identification parameters.

[0013] S4. The low-order model that has the highest fitting degree with the complex-valued full-order mathematical model is taken as the optimal low-order model of the WPT system.

[0014] S5. Control the WPT system based on the optimal low-order model.

[0015] Further, in step S1, the complex-valued full-order mathematical model is expressed as:

[0016]

[0017] Among them, I 2d I 2q Z represents the real and imaginary parts of the first harmonic approximation value I2 of the receiving coil current i2 through real-imaginary decomposition, respectively; Ad (p,r e Z Aq (p,r e ) represent Z respectively A (p,r e Z is obtained by decomposing Z into its real and imaginary parts. A (p,r e () represents the coefficients related to I² in the complex-valued full-order mathematical model after calculation; Z Bd (p,M), Z Bq (p, M) represent Z respectively. B (p,M) is decomposed into its real and imaginary parts, Z B(p,M) represents the coefficients related to cos(U / 2) in the complex-valued full-order mathematical model after calculation; U represents the input phase shift angle, C d R represents the filter capacitor located on the secondary side connected to the rectifier. o Indicates the load resistance, V o The load voltage is represented by ||, which represents the absolute value; p is the differential operator, p(·) = d(·) / dt; the mutual inductance coefficient M of the primary and secondary sides is Z. B The scheduling variable (p,M), the instantaneous equivalent resistance r of the secondary rectified load. e For Z A (p,r e The scheduling variable.

[0018] Further, in step S2, the WPT system LPV-Hammerstein model is expressed as:

[0019]

[0020] Where A(p,r) e ) indicates that there is a scheduling variable r e =4V o A linear polynomial of / (π|I2|), B(p,M) represents a linear polynomial with scheduling variable M, and f(U) represents a nonlinear function.

[0021] Furthermore, A(p,r) e B(p,M) is specifically represented as:

[0022]

[0023]

[0024] Among them, a i,0 a i,1 They are A(p,r) e The real constant coefficient to be estimated, b j,0 b j,1 These are the real-valued constant coefficients of B(p,M) to be estimated, and n a and n b They are respectively A(p,r) e The polynomial degree of B(p,M) and n a >n b ;

[0025] f(U) is specifically represented as:

[0026] f(U) = cos(U / 2).

[0027] Furthermore, in step S3, dynamic input and output data are used. The real-valued constant coefficients of each reduced-order model are obtained, where (·) m This represents the observation value in the m-th sampling interval.

[0028] Furthermore, in step S3, a state variable filtering method based on working variables is used for parameter identification.

[0029] Furthermore, this WPT system is an LCC-S type WPT system, n a =6,n b =3, Z A (p,r e Z B (p,M) is specifically represented as follows:

[0030]

[0031]

[0032] Where α0 is the real-valued coefficient, β j α i,0 α i,1 The coefficient is a complex number.

[0033] Further, step S1 specifically includes the following steps:

[0034] S11. Based on Kirchhoff's voltage law, establish a model for the LCC-S type WPT system:

[0035]

[0036] Where L1 and L2 represent the transmitting coil and receiving coil, respectively, L f C f C1 represents the compensation inductor, primary-side parallel resonant capacitor, and primary-side series resonant capacitor in the primary-side LCC compensation network, respectively; C2 represents the secondary-side series resonant capacitor; k represents the coupling coefficient between the transmitting coil and the receiving coil; R1, R2, and R3 represent the internal resistance of the compensation inductor, the internal resistance of the transmitting coil, and the internal resistance of the receiving coil, respectively; i f For L f Current, v1, v2, i1, i2, I r These are the inverter output voltage, rectifier input voltage, transmitter current, receiver current, and rectifier output current, respectively.

[0037] S12. Apply the following first harmonic approximation to the AC signals i1 and i2 to obtain the corresponding approximate values ​​I1 and I2:

[0038]

[0039] Where Y = Y d +jYq It is a response to the alternating current signal y in terms of Y d For the real part, Y q ω0 is the inverter switching frequency, e is the natural base, Re{} denotes taking the real part, and t represents time.

[0040] S13. Utilizing the principles of full-bridge inverter and full-bridge rectification, v1, v2, and I... r Make the following approximation:

[0041]

[0042] Among them, V d φ and φ are the phase differences between the input DC voltage and the inverter modulation signal, respectively;

[0043] S14. Substitute the approximate formulas obtained in steps S12 and S13 into the model obtained in step S1, and eliminate I1 and I2. f This yields a sixth-order complex-valued equation:

[0044]

[0045] S15. Perform virtual-real decomposition on the complex-valued equation obtained in step S14 to obtain a thirteenth-order large-signal full-order model:

[0046]

[0047] Furthermore, α i,1 α i,0 β j Represented as:

[0048]

[0049]

[0050]

[0051]

[0052]

[0053] Among them, the K matrix and the J matrix are custom matrices defined for simplification.

[0054] Further, in step S4:

[0055] S21. The optimal low-order model is a second-order model.

[0056] This invention provides a control method for WPT systems based on nonlinear model order reduction. First, a complex-valued full-order mathematical model of the WPT system is constructed. Then, the LPV-Hammerstein model is used to reduce the order of the complex-valued full-order mathematical model, resulting in the LPV-Hammerstein model of the WPT system. Next, reduced-order models of different orders are generated based on the LPV-Hammerstein model of the WPT system. System identification is performed on these reduced-order models to obtain identification parameters. Corresponding low-order models are then established based on the identification parameters. Finally, the low-order model with the highest fit to the complex-valued full-order mathematical model is taken as the optimal low-order model of the WPT system. This invention utilizes the LPV-Hammerstein model to reduce the order of a high-order complex-valued full-order mathematical model with nonlinear output and obtains the parameters that best match the original model through system identification. It obtains a simple and accurate model without needing all circuit component parameters; only a first-order or second-order model is required to accurately describe the dynamic characteristics of the system. Attached Figure Description

[0057] Figure 1 This is a flowchart of a WPT system control method based on nonlinear model order reduction provided by an embodiment of the present invention;

[0058] Figure 2 This is a circuit topology diagram of the LCC-S type WPT system provided in an embodiment of the present invention;

[0059] Figure 3 This is provided by the embodiments of the present invention. Figure 2 First-order equivalent circuit diagram;

[0060] Figure 4 This is a dynamic input / output waveform diagram of the system in the simulation provided in this embodiment of the invention;

[0061] Figure 5 This is a comparison diagram of the original system, the first-order LPV-Hamm model, and the second-order LPV-Hamm model provided in the embodiments of the present invention on the load voltage. Detailed Implementation

[0062] The embodiments of the present invention are described in detail below with reference to the accompanying drawings. The embodiments are given for illustrative purposes only and should not be construed as limiting the present invention. The accompanying drawings are for reference and illustration only and do not constitute a limitation on the scope of patent protection of the present invention, because many changes can be made to the present invention without departing from the spirit and scope of the present invention.

[0063] A linear parameter varying (LPV) system is a time-varying parameter system that depends on a scheduling variable. It approximates the model structure of a linear system, and LPV models have lower model order and higher accuracy.

[0064] The Hammerstein model (H model for short) is a typical nonlinear model with a specific structure, consisting of a static nonlinear element and a dynamic linear element connected in series. This model can well reflect the characteristics of a process and can describe a large class of nonlinear processes, such as neutralization processes, distillation columns, heat exchangers, polymerization reactors, drying processes, noise suppressors, nonlinear predictors, biological systems, hydraulic automatic generation control (AGC) systems, multi-sensor systems, power systems, physiological and nervous systems, etc. More importantly, the special structure of this model can be used to simplify nonlinear control problems into linear model predictive control problems.

[0065] This invention combines the LPV model and the Hammerstein model to obtain a low-order (first-order or second-order) model that can accurately describe the dynamic characteristics of the WPT system.

[0066] like Figure 1 As shown in the flowchart, an embodiment of the present invention provides a WPT system control method based on nonlinear model order reduction, comprising the following steps:

[0067] S1. Construct a complex-valued full-order mathematical model of the WPT system;

[0068] S2. The LPV-Hammerstein model is used to reduce the order of the complex-valued full-order mathematical model to obtain the LPV-Hammerstein model of the WPT system.

[0069] S3. Generate reduced-order models of different orders based on the WPT system LPV-Hammerstein model, perform system identification on these reduced-order models, obtain identification parameters, and establish corresponding low-order models based on the identification parameters.

[0070] S4. The low-order model that has the highest fitting degree to the complex-valued full-order mathematical model is taken as the optimal low-order model of the WPT system.

[0071] S5. Control the WPT system based on the optimal low-order model.

[0072] Taking the LCC-S resonant topology variable coupling coefficient wireless power transfer system as an example, this invention specifically illustrates how to achieve order reduction.

[0073] A typical circuit topology for a WPT system employing an LCC-S resonant topology is as follows: Figure 2 As shown, the transmitter of this WPT system includes a DC power supply V connected in sequence. dHigh-frequency inverter (composed of four MOSFETs S1, S2, S3, and S4), primary-side LCC compensation network (including compensation inductor L) f Primary-side parallel resonant capacitor C f The receiver includes a primary-side series resonant capacitor C1, a transmitting coil L1, and a receiving coil L2, a secondary-side series resonant capacitor C2, a rectifier (composed of four diodes D1, D2, D3, and D4), and a filter capacitor C1 connected in sequence. d and load resistance R o v1, v2, i1, i2, I r These represent the inverter output voltage, rectifier input voltage, transmitter current, receiver current, and rectifier output current, respectively, with M being the mutual inductance coefficient between the primary and secondary sides. Points A and B are the output terminals of the left and right half-bridge arms of the high-frequency inverter, respectively, while points C and D represent the input terminals of the left and right half-bridge arms of the rectifier, respectively.

[0074] Figure 2 The first-order equivalent circuit diagram is as follows: Figure 3 As shown, R1, R2, and R3 represent the internal resistances of the compensating inductor, the transmitting coil, and the receiving coil, respectively, and p is the differential operator, p(·) = d(·) / dt. According to Kirchhoff's voltage law, based on... Figure 3 The following system model can be established:

[0075]

[0076] Where k represents the coupling coefficient between the transmitting coil and the receiving coil, i f For L f Current. Due to the presence of Therefore, M can replace the coupling coefficient k as the scheduling variable in the following text.

[0077] Under ideal resonance conditions, the AC signals i1 and i2 can be approximated by the following first harmonic approximation to obtain the corresponding approximate values ​​I1 and I2:

[0078]

[0079] Where Y = Y d +jY q It is a response to the alternating current signal y in terms of Y d For the real part, Y q ω0 is the inverter switching frequency, e is the natural base, Re{} denotes taking the real part, and t represents time.

[0080] Furthermore, by utilizing the principles of full-bridge inverter and full-bridge rectification, it is possible to control v1, v2, and I. r Make the following approximation:

[0081]

[0082] Among them, V d φ and φ are the phase differences between the input DC voltage and the inverter modulation signal, respectively.

[0083] Substitute equations (2) and (3) into equation (1), and eliminate I1 and I f We can obtain:

[0084]

[0085] in

[0086] r e =4V o / (π|I2|)(5)

[0087] For Z A (p,r e The scheduling variable of ) can be understood as the instantaneous equivalent resistance of the rectified load; in addition, the mutual inductance coefficient M is Z B The scheduling variable for (p,M). Z A (p,r e ) and Z B (p, M) are defined as the coefficients of the complex-valued full-order mathematical model with respect to I² and cos(U / 2), respectively, after calculation. And Z A (p,r e ) and Z B (p,M) can be derived as follows:

[0088]

[0089]

[0090] Where α0 is the real-valued coefficient, β j α i,0 α i,1 For complex coefficients, specifically:

[0091]

[0092]

[0093]

[0094]

[0095]

[0096] Among them, the K matrix and the J matrix are custom matrices defined for simplification.

[0097] Equation (4) is a sixth-order complex-valued equation. To obtain a complete large-signal full-order model, the equation needs to be decomposed into real and imaginary components to obtain a thirteenth-order large-signal full-order model.

[0098]

[0099] Among them, Z Ad (p,r e Z Aq (p,r e ) represent Z respectively A (p,r e Z is decomposed into real and imaginary parts through the decomposition of real and imaginary components. Bd (p,M), Z Bq (p, M) represent Z respectively. B (p,M) is the real and imaginary parts decomposed by the real-imaginary decomposition.

[0100] The high order of the LCC-S large-signal real-valued model leads to a greater computational burden. Therefore, this invention utilizes the LPV-Hammerstein model to reduce the order of the system. It consists of a statically input nonlinear function f(U) and a scheduling variable r. e A(p,r) e The linear polynomial and the B(p,M) linear polynomial of the scheduling variable M are composed of a linear polynomial, which is a polynomial with a similar structure to equation (13):

[0101] A(p,r e V o =B(p,M)f(U)(14)

[0102]

[0103]

[0104] a i,0 a i,1 They are A(p,r) e The real constant coefficient to be estimated, b j,0 b j,1 These are the real-valued constant coefficients of B(p,M) to be estimated, and n a and n b They are respectively A(p,r) e The polynomial degree of B(p,M) and n a >n b When n a With n bWhen the value is relatively small, the LPV-Hammerstein model has a relatively low order and can fit the output of a 13th-order system relatively well. That is, the low-order LPV-Hammerstein model can fit the actual 13th-order model very well, achieving the effect of order reduction.

[0105] This model can generate models of different orders, systematically identify them, and select the best model from the identification results as the final model. Additionally, f(U) = cos(U / 2).

[0106] Finally, based on equations (4) and (14)-(16), the LPV-Hammerstein model of the LCC-S large-signal model can be derived:

[0107]

[0108] The parameters of equations (15), (16), and (17) can be obtained from dynamic input and output data. We obtain, among which (·) m This represents the observation value in the m-th sampling interval. Parameter identification can be performed using the Instrumental-Variable-based State Variable Filter (IVSVF) method. Simply add the filter F(p) to equation (14) to obtain the new formula:

[0109] A f (p,r e V o =B f (p,M)f(U)(18)

[0110] in

[0111]

[0112]

[0113]

[0114]

[0115] λ represents the hyperparameters A estimated by the model. f (p,r e ) indicates that filter F has been added. i A(p,r) after (p) e ) value, B f (p,M) indicates that filter F has been added. j The value of B(p,M) after (p).

[0116] Equation (18) can be used to express the system in linear regression form as follows:

[0117]

[0118]

[0119]

[0120] in (k) represents the observation value in the k-th sampling interval, and r represents the value for V. o The order of the differential operator is denoted by s, which represents the order of the differential operator for f(U).

[0121] By performing linear least squares (LS) parameter estimation on equation (25), we can obtain:

[0122]

[0123] In CT system identification, even if the equation error is white noise, the LS estimator in equation (26) is still biased. This asymptotic bias problem can be mitigated by using the IVSF estimator:

[0124]

[0125]

[0126]

[0127] in Estimate the output value for LS:

[0128]

[0129] B(p,M,θ ls ) represents the B(p,M) coefficient obtained by estimating the parameters using the LS method, and A(p,r) represents the coefficient. e ,θ ls ) represents A(p,r) obtained by estimating the parameters using the LS method. e )coefficient.

[0130] In summary, the WPT system control method based on nonlinear model order reduction provided by this invention first constructs a complex-valued full-order mathematical model of the WPT system. Then, it uses the LPV-Hammerstein model to reduce the order of the complex-valued full-order mathematical model, obtaining the LPV-Hammerstein model of the WPT system. Next, it generates reduced-order models of different orders based on the LPV-Hammerstein model of the WPT system, performs system identification on these reduced-order models to obtain identification parameters, and establishes corresponding low-order models based on the identification parameters. Finally, the low-order model with the highest fitting degree to the complex-valued full-order mathematical model is taken as the optimal low-order model of the WPT system. This invention utilizes the LPV-Hammerstein model to reduce the order of a high-order complex-valued full-order mathematical model with nonlinear output, and obtains the parameters that best match the original model through system identification. It can obtain a simple and accurate model without needing all circuit element parameters; only a first-order or second-order model is needed to accurately describe the dynamic characteristics of the system.

[0131] To verify the effectiveness of the invention, the input phase shift angle U of the system was set to a pseudo-random number to fully stimulate the dynamic characteristics of the system. Figure 4 As shown in (a), the coupling coefficient k, secondary coil current I2, and load voltage V are obtained. o The curves showing the changes over time are as follows: Figure 4 As shown in (b), (c) and (d), Figure 4 This represents the system's dynamic input and output data. Simultaneously, a Simscape simulation model was established to simulate the original system and a first-order LPV-Hamm model. a =1, n b =0) and the second-order LPV-Hamm model (n a =2,n b =0) at load voltage V o The comparative analysis is shown in Figure 5. Figure 5 It can be seen that when the large signal model is reduced to a second-order model through the LPV-Hammerstein model, the output of the second-order model has a very high accuracy (fit = 0.9787). Therefore, it is believed that the reduction can effectively simulate the full-order model with nonlinear output, verifying the effectiveness and accuracy of the reduced-order model, and laying the model foundation for the design of the WPT control system.

[0132] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A WPT system control method based on nonlinear model reduction, characterized in that, Including the following steps: S1. Construct the complex-valued full-order mathematical model of the WPT system; the complex-valued full-order mathematical model is expressed as: ， in, , These represent the current in the receiving coil, respectively. Approximate value of the first harmonic By decomposing the real and imaginary parts; , They represent By decomposing the real and imaginary parts, This indicates that, after calculation, the complex-valued full-order mathematical model is related to... Correlation coefficient; , They represent By decomposing the real and imaginary parts, This indicates that, after calculation, the complex-valued full-order mathematical model is related to... Correlation coefficient; Indicates the input phase shift angle. This refers to the filter capacitor located on the secondary side connected to the rectifier. Indicates the load resistance. Indicates the load voltage. This indicates the absolute value; For differential operators, Mutual inductance coefficient between primary and secondary sides for The scheduling variable, the instantaneous equivalent resistance of the secondary rectifier load. for The scheduling variable; S2. The complex-valued full-order mathematical model is reduced in order using the LPV-Hammerstein model to obtain the WPT system LPV-Hammerstein model; the WPT system LPV-Hammerstein model is expressed as: ， in, Indicates having scheduling variables linear polynomials, Indicates having scheduling variables linear polynomials, Represents a nonlinear function; , Specifically, it is expressed as follows: ， ， in, They are The real constant coefficients to be estimated They are The real constant coefficients to be estimated and They are respectively and polynomial degree, ; Specifically, it is expressed as follows: ； This WPT system is an LCC-S type WPT system. , , , Specifically, it is expressed as follows: ， ， in, For real-valued coefficients, , The coefficients are complex numbers; S3. Generate reduced-order models of different orders based on the WPT system LPV-Hammerstein model, perform system identification on these reduced-order models to obtain identification parameters, and establish corresponding low-order models based on the identification parameters. S4. The low-order model that has the highest fitting degree with the complex-valued full-order mathematical model is taken as the optimal low-order model of the WPT system. S5. Control the WPT system based on the optimal low-order model.

2. The WPT system control method based on nonlinear model order reduction according to claim 1, characterized in that, In step S3, dynamic input and output data are generated. The real-valued constant coefficients of each reduced-order model are obtained, where This represents the observation value in the m-th sampling interval.

3. The control method for a WPT system based on nonlinear model order reduction according to claim 2, characterized in that, In step S3, a state variable filtering method based on working variables is used for parameter identification.

4. The control method for a WPT system based on order reduction of a nonlinear model according to claim 1, characterized in that, Step S1 specifically includes the following steps: S11. Based on Kirchhoff's voltage law, establish a model for the LCC-S type WPT system: ， in, and These represent the transmitting coil and the receiving coil, respectively. , These represent the compensation inductor, the primary-side parallel resonant capacitor, and the primary-side series resonant capacitor in the primary-side LCC compensation network, respectively. This represents the secondary-side series resonant capacitor. This represents the coupling coefficient between the transmitting coil and the receiving coil. , , These represent the internal resistance of the compensating inductor, the internal resistance of the transmitting coil, and the internal resistance of the receiving coil, respectively. for Current, , , , , These are the inverter output voltage, rectifier input voltage, transmitter current, receiver current, and rectifier output current, respectively. S12, for AC signals , By making the following first harmonic approximation, we obtain the corresponding approximate value. : ， in, It is a response to the AC signal y. For the actual part, The complex-valued envelope of the imaginary part. It is the inverter switching frequency. Let Re be the natural base, Re{} denote the real part, and t denote time; S13. Utilizing the principles of full-bridge inverter and full-bridge rectification, for , , Make the following approximation: ， in, and These are the phase differences between the input DC voltage and the inverter modulation signal, respectively. S14. Substitute the approximate formulas obtained in steps S12 and S13 into the model obtained in step S1, and eliminate... , This yields a sixth-order complex-valued equation: ； S15. Perform virtual-real decomposition on the complex-valued equation obtained in step S14 to obtain a thirteenth-order large-signal full-order model: 。 5. The WPT system control method based on nonlinear model order reduction according to claim 4, characterized in that, , , Represented as: ， ， ， ， ， Among them, the K matrix and the J matrix are custom matrices defined for simplification.

6. The control method for a WPT system based on order reduction of a nonlinear model according to claim 1, characterized in that, In step S4: The optimal low-order model is a second-order model.

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