A data-driven based modeling method for WPT system

Abstract

The application relates to the technical field of wireless power transmission, and particularly discloses a WPT system modeling method based on data driving, which comprises the following steps: firstly, determining the circuit structure and system parameters of the WPT system, establishing a differential equation, then constructing a GSSA model (large signal model) based on the system differential equation, and obtaining a linear small signal model of the system by adding disturbance, further establishing a Hammerstein model based on the large signal model and the small signal model through a data driving modeling method, and performing order reduction to obtain a second-order Hammerstein model, finally constructing an optimization problem based on the second-order Hammerstein model, and finally solving the optimization problem by adopting a method combining the least square method and Newton iteration search, so that the model offset parameters and system communication delay of the WPT system can be estimated more accurately.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless power transmission, and in particular to a data-driven WPT system modeling method. BACKGROUND

[0002] In recent years, wireless power transmission (WPT) technology has become a research hotspot. It can completely isolate the power supply and charging equipment. It has been widely used in electric vehicles, oil drilling, industrial production, biomedicine, aerospace, ocean, etc. Through non-contact mode, WPT technology can improve the safety, reliability and flexibility of power supply equipment, and enhance the working capacity of the equipment.

[0003] Generally, due to the change of system parameters caused by environmental factors, the output voltage of the system is unstable. Considering the safety of electrical equipment, a closed-loop control strategy needs to be taken for the output voltage. At present, the traditional control method uses a linear controller, which depends on an accurate system model. Therefore, it is very necessary to accurately obtain the control input and output model of the system. The WPT system is a special electric resonance conversion system, which has high-order nonlinearity, multiple circuit topologies and corresponding control models, and randomness of load size and type. The main modeling methods include generalized state space average (GSSA), expansion function description, discrete mapping time, and alternating current impedance analysis. These traditional methods depend on the real circuit topology, and most of the methods have strict requirements for the working state of the system. Even in the same system, the system model may have great difference under different working states. Through traditional modeling, the obtained model is often more complex. The model obtained by the traditional modeling method has the disadvantage of poor universality. In addition, the WPT system forms a closed loop through the communication link between the primary side and the secondary side to control the output voltage, as shown in Figure 2 Wireless communication, data sampling, processor calculation and model simplification in the system will cause time delay. The traditional modeling method cannot accurately describe the system with time delay.

[0004] The above method is mainly the circuit-level modeling of the WPT system, which only considers the steady-state running state of the system. There is little research on the system-level dynamic modeling required for the design of the control system. The circuit-level modeling method is effective, but it cannot truly reflect the shift of system parameters. The established model has high order, poor universality, no accurate time delay parameter, and is not convenient in the actual industrial control process. In addition, time delay will cause instability of the system and failure of the closed-loop system. SUMMARY

[0005] The present application provides a data-driven WPT system modeling method, which solves the technical problem of how to accurately estimate the model shift parameters and system communication delay of the WPT system.

[0006] To solve the above technical problems, the application provides a data-driven-based WPT system modeling method, which is characterized by comprising the following steps:

[0007] S1, determining the circuit structure and system parameters of the WPT system, and establishing the differential equation of the system based on the circuit structure and Kirchhoff's theorem;

[0008] S2, establishing the GSSA model of the system based on the differential equation of the system;

[0009] S3, adding a disturbance at a given steady-state operating point, converting the GSSA model of the system into a linear small-signal model, and obtaining the small-signal open-loop transfer function of the WPT system from the duty cycle to the output voltage;

[0010] S4, substituting the system parameters into the small-signal open-loop transfer function to obtain a linear high-order model;

[0011] S5, based on the GSSA model and the linear high-order model, constructing a Hammerstein model of the system by means of a data-driven modeling method and adding a time delay;

[0012] S6, obtaining a second-order model of the Hammerstein model, denoted as a second-order Hammerstein model;

[0013] S7, defining an optimization problem for estimating the model offset parameter and the system communication delay based on the second-order Hammerstein model;

[0014] S8, using a method combining the least square method and Newton iteration search to solve the optimization problem to estimate the model offset parameter and the system communication delay.

[0015] Further, in the step S5, the Hammerstein model is represented as:

[0016]

[0017] wherein t represents time, x(t) represents a generalized state variable vector containing the real part and the imaginary part of the state variable in the differential equation obtained in the step S1, τ represents a pure time delay describing the total time delay of the system, f(u(t-τ)) represents the nonlinear input of the system at t-τ, t k =kT represents a sampling time (k=1, 2, 3, …), T represents a sampling interval, x(t k ) represents the actual output of the system at the kth sampling time, v(t k ) represents the measurement noise of the output of the system at the kth sampling time, y(t k) represents the system output at the kth sampling time, G(s, θ) represents the rational transfer function of the system, B(s, θ) and A(s, θ) represent the following polynomials:

[0018]

[0019] where n a and n b are the polynomial degrees, n a ≥ n b , is a vector of model bias parameters.

[0020] Further, in the step S6, n a = 2 and n b = 1 are taken, obtaining the second-order Hammerstein model.

[0021] Further, in the step S7, the optimization problem is constructed as:

[0022]

[0023]

[0024] ε(t k ) = y(t k ) - x(t k ),

[0025] where represents the optimized solution of the estimated model bias parameters and system communication delay θ, τ, J(θ, τ) is the cost function of the prediction error, ε(t k ) is the error between the actual output and the estimated output at the kth sampling time, and N is the number of samples.

[0026] Further, define In step S8, the iterative estimation of the parameter vector ρ is as follows:

[0027]

[0028] where μ j represents the step factor at the jth iteration, and respectively represent the gradient vector and the Hessian matrix of the cost function, respectively represent the ρ estimation values at the jth and j+1th iterations.

[0029] Further, the step S8 specifically includes the steps of:

[0030] S81, obtaining sampling data where u(tk represents the control input at the kth sampling time;

[0031] S82, setting the initial value τ of the time delay τ 0 , the minimum time delay interval Δτ min , the minimum time delay τ min and the maximum time delay τ max , the initial training data quantity N0 and the iteration number Niter, and the cost function increment error parameter estimation error

[0032] S83, based on τ 0 estimating the initial value θ of θ 0 , and assigning [θ 0 ; τ 0 ] to the solution ρ* of ρ;

[0033] S84, starting iteration, in each iteration, first make μ=1, calculate Δρ * = (▽ 2 J(ρ * )) -1 ▽J(ρ * ), for each training data, through get the next iteration of ρ value if or the current delay then execute step S85; if or during the entire iteration, terminate the iteration, otherwise execute to the iteration number Niter to terminate the iteration;

[0034] S85, make μ decrease by half, further if then terminate the current training data to enter the next training data, otherwise assign to ρ* and terminate the current training data to enter the next training data.

[0035] Further, in step S3, by performing perturbation linearization on the state space equation of the system, a small signal model is obtained as follows:

[0036]

[0037] wherein, and represent the input voltage, output voltage and duty cycle of the steady state operating point, here the input voltage refers to the first order effective value of the inverter output voltage, the output voltage refers to the load voltage, and the duty cycle refers to the duty cycle of the high frequency inverter, and represents input voltage perturbation, output voltage perturbation and duty cycle perturbation corresponding to the execution around the steady state operating point, represents small signal of the generalized state variable vector, represents steady state value of the generalized state variable vector, x i , u ab , y, d respectively represent the generalized state variable vector, input voltage, system output, duty cycle of the phase shift angle;

[0038] and is calculated by the following formula:

[0039]

[0040]

[0041] wherein, U dc represents DC input voltage of the WPT system.

[0042] Further, in step S3, the state space equation of the small signal model is established as:

[0043]

[0044] represents input and output variable vector of the state space model, and represents coefficient matrix of the state, control input, output of the small signal model, represents small signal of the generalized state variable vector, represents differential of the small signal of the generalized state variable vector;

[0045] The small signal open loop transfer function is represented as:

[0046]

[0047] wherein, and represents small signal output and input of the system under the frequency domain model, I represents unit matrix.

[0048] Further, in the step S1, the circuit structure of the WPT system is composed of a primary side and a secondary side, the primary side includes sequentially connected DC power supply, inverter, LCC compensation network, transmitting coil L p , the secondary side includes sequentially connected receiving coil L s , series compensation capacitor C s , rectifier circuit, filter capacitor C d , load resistor R L, the LCC compensation network comprising a series compensation inductance L f , a series compensation capacitance C p , and a parallel compensation capacitance C f .

[0049] Further, in the step S1, the differential equation of the system is established as:

[0050]

[0051] where u ab represents the first order effective value of the inverter output voltage, i f , u cf represent the current and voltage of L f , respectively, i p , u cp represent the current and voltage of L p , respectively, u cf represents the voltage of C f , M represents the mutual inductance between L p and L s , i s , u cs represent the current and voltage of L s , respectively, i r , u r represent the current and voltage of the rectifier circuit, respectively, u o represents the voltage of R L , i.e. the system output voltage, R1, R2 and R3 represent the equivalent series resistance of L f , L p and L s , respectively;

[0052] The real and imaginary parts of the state variables u ab and i r are represented by the following equations:

[0053]

[0054] (·) d and (·) q represent the real and imaginary parts of the state variables;

[0055] In the step S2, the GSSA model of the system is represented as:

[0056]

[0057] where x(t) represents a generalized state variable vector comprising the real and imaginary parts of the state variables obtained from the differential equation in step S1; represents the differential of the generalized state variable vector; u(t) = [u ab(d)] represents the control input, d represents the duty cycle of the inverter phase shift angle; y(t) = [u o ] represents the output of the system; A, B and C represent the state, control input and output coefficient matrices, respectively.

[0058] The application provides a data-driven WPT system modeling method, which comprises the following steps: firstly, determining the circuit structure and system parameters of the WPT system, establishing a differential equation, then constructing a GSSA model (large signal model) based on the system differential equation, and obtaining a linear small signal model of the system by adding disturbance, further establishing a Hammerstein model based on the large signal model and the small signal model through a data-driven modeling method, and performing order reduction to obtain a second-order Hammerstein model, finally constructing an optimization problem based on the second-order Hammerstein model, and finally solving the optimization problem by combining the least square method and Newton iteration search, so that the model offset parameters and system communication delay of the WPT system can be accurately estimated. BRIEF DESCRIPTION OF DRAWINGS

[0059] Figure 1 is a flow chart of the data-driven WPT system modeling method provided by the background art of the application;

[0060] Figure 2 is a circuit structure diagram of the WPT system provided by the embodiment of the application;

[0061] Figure 3 is a switching schematic diagram of the PS control and the inverter output voltage at α provided by the embodiment of the application;

[0062] Figure 4 is an output characteristic curve of the system under different duty cycles provided by the embodiment of the application, wherein (a) corresponds to the steady-state output as a function of the duty cycle, and (b) corresponds to the step response of the increase of 2% of the duty cycle at different static points;

[0063] Figure 5 is an equivalent circuit diagram of the Figure 2 provided by the embodiment of the application;

[0064] Figure 6 is a singular value distribution diagram of the original high-order system provided by the embodiment of the application;

[0065] Figure 7 is a bode comparison diagram of the original model and the reduced-order model provided by the embodiment of the application, wherein (a) corresponds to the original model and the first-order model, and (b) corresponds to the original model and the second-order model;

[0066] Figure 8 is a WPT system block diagram based on the Hammerstein model provided by the embodiment of the application;

[0067] Figure 9 is a schematic diagram of a data-driven model provided by an embodiment of the present application;

[0068] Figure 10 is steady-state input and output data of a plurality of static operating points collected in an experiment provided by an embodiment of the present application, where (a) corresponds to steady-state output as a function of duty ratio, and (b) corresponds to a step response of a 2% increase in duty ratio at different static points;

[0069] Figure 11 is a part of an oscillogram of a perturbed output voltage and inverter current provided by an embodiment of the present application;

[0070] Figure 12 is a comparison diagram of measured output and estimated model output provided by an embodiment of the present application. DETAILED DESCRIPTION

[0071] Embodiments of the present application will be described in detail below with reference to the accompanying drawings, which are given for the purpose of illustration and description only and are not intended to be limiting, and the drawings comprise reference and illustrative use only, and do not constitute a limitation on the scope of patent protection of the present application, because many changes can be made to the present application without departing from the spirit and scope thereof.

[0072] A Hammerstein model is composed of a nonlinear static characteristic and a linear time-invariant autoregressive model (ARX model) with exogenous input. Data-driven modeling has been widely applied in industry. The structure and parameters of the model only need to be obtained by identifying the sampled input and output data, and are independent of specific circuit topology and parameters. The input and output sampling data required for model identification are very easy to obtain. At the same time, the system model can be optimized by relevant performance indicators. This method is superior to traditional modeling methods in various aspects, and has attracted more and more attention in the field of power electronics. WPT system modeling based on data-driven method can more accurately estimate the model parameters of the system after the system is offset and the communication delay of the system model.

[0073] Specifically, a data-driven WPT system modeling method provided by an embodiment of the present application, as shown in Figure 1 includes the following steps:

[0074] S1, determining the circuit structure and system parameters of the WPT system, and establishing a differential equation of the system based on the circuit structure and Kirchhoff's theorem;

[0075] S2, establishing a GSSA model of the system based on the differential equation of the system;

[0076] S3. Add a disturbance at the given steady-state operating point to transform the GSSA model of the system into a linear small-signal model, and obtain the small-signal open-loop transfer function of the WPT system from the duty cycle to the output voltage.

[0077] S4. Substitute the system parameters into the small-signal open-loop transfer function to obtain a linear high-order model;

[0078] S5. Based on the GSSA model and linear higher-order models, a Hammerstein model of the system is constructed by using a data-driven modeling method and adding a time delay.

[0079] S6. Obtain the second-order model of the Hammerstein model, denoted as the second-order Hammerstein model;

[0080] S7. An optimization problem for estimating model offset parameters and system communication delay is defined based on the second-order Hammerstein model.

[0081] S8. The optimization problem is solved by combining the least squares method and Newton's iterative search to estimate the model offset parameters and system communication delay.

[0082] Figure 2 This illustrates a typical closed-loop WPT system, consisting of a primary side and a secondary side. The primary side comprises a DC power supply, an inverter, an LCC compensation network, and a transmitting coil L, connected in sequence. p The secondary side includes sequentially connected receiving coils L s Series compensation capacitor C s 1. Rectifier circuit, 2. Filter capacitor C d Load resistance R L The LCC compensation network includes a series compensation inductor L f Series compensation capacitor C p and parallel compensation capacitor C f . Figure 2 Middle,U dc u represents the DC input voltage of the WPT system. ab i represents the first effective value of the inverter output voltage. f u cf L f The current and voltage, i p u cp L p The current and voltage, u cf C represents f The voltage, M represents L p and L s Mutual intuition between them, i s u cs L sThe current and voltage of the rectifier circuit, i r , u r , respectively o The voltage of R L , i.e., the system output voltage, R1, R2, and R3 represent the equivalent series resistance of L f , L p , and L s , respectively.

[0083] In the practical application of the WPT system, the secondary side or load can be removed, which will cause safety and stability problems of the system. The primary side of the selected LCC-S topology has a constant current characteristic. When the receiver or load is removed, the current of the primary side coil can be roughly kept unchanged, which reduces the complexity of system control and the current stress of the inverter circuit. The WPT system adopts the primary side LCC composite compensation mode and the secondary side LC series compensation mode. The working frequency of the system is denoted as f0, and the corresponding working angular frequency is ω0.

[0084] Generally, in order to meet the requirement of the stability of the system output voltage, the collected data is fed back to the primary side through wireless communication. In the primary side, the output voltage is adjusted through phase shift (PS). The principle of phase shift control and the output voltage of the inverter are shown in Figure 3 . d represents the duty ratio of the phase shift angle of the inverter. α represents the angle of the duration when switches S1 and S4 (or S2 and S3) are simultaneously turned off. The duty ratio d is calculated through the error between the output voltage and the set voltage. Previous studies show that Figure 2 the system shown in Figure 4 is nonlinear. Figure 1 The output characteristic curves of the system shown in Figure 4 under different duty ratios are shown, in which (a) corresponds to the steady-state output of the duty ratio function, and (b) corresponds to the output response of the increase of 2% of the duty ratio at different static points. In Figure 4 (a), the steady-state output voltage of the system is different under different duty ratios, and the steady-state output voltage increases with the increase of the duty ratio, but the trend is nonlinear. (b) shows the step response of different steady-state operating points, in which a small duty ratio disturbance is superimposed as an input. At different steady-state operating points, the response trend is similar, but the model gain is different. Therefore, the modeling of the WPT system facing control needs to be able to accurately describe the steady-state and transient behavior, and the embodiment is modeled based on the Hammerstein modeling method.

[0085] Figure 5 The simplified model of the WPT system is shown in Figure 5 . According to and Kirchhoff's theorem, the differential equation of the system can be established as:

[0086]

[0087] In particular, the state variable u ab and i r It can be calculated based on the law of conservation of energy, therefore u ab and i r The real and imaginary parts can be represented by the following equations:

[0088]

[0089] here(·) d and(·) q Let these represent the real and imaginary parts of the state variables. Then, the GSSA model of the system can be obtained as follows:

[0090]

[0091] x(t) represents the generalized state variable vector, which contains the real and imaginary parts of the state variables in equation (1); Represents the differential of the generalized state variable vector; u(t) = [u ab (d)] represents the control input, u ab (d) can be obtained through the following equation (4). y(t)=[u o ] indicates the system output.

[0092]

[0093] A, B, and C represent the state, control input, and output coefficient matrices of the large-signal model, respectively, as follows:

[0094]

[0095]

[0096] C=[0 0 0 0 0 0 0 0 0 0 0 0 1]

[0097] Where Δ=M 2 -L p L s .

[0098] For control system design purposes, a linear model is usually required. Therefore, equation (3) can be linearized at a given steady-state operating point to obtain a small-signal model. To obtain the small-signal model, the state-space equations of the system need to be linearized by perturbation as (5):

[0099]

[0100] in, and input voltage, output voltage and duty cycle, where input voltage refers to the first order effective value of the inverter output voltage, output voltage refers to the load voltage, and duty cycle refers to the duty cycle of the high frequency inverter, and represent input voltage perturbation, output voltage perturbation and duty cycle perturbation corresponding to performing around the steady state operating point, represents the small signal of the generalized state variable vector, represents the steady state value of the generalized state variable vector, x i , u ab , y, d represent the generalized state variable vector, input voltage, system output, duty cycle of phase shift angle, respectively.

[0101] All capital letter variables are steady state values, which are calculated by setting the derivative part of equation (3) to zero. and can be calculated by equations (6) and (7) as follows, respectively:

[0102]

[0103]

[0104] Therefore, the state space equation of the small signal model is established as:

[0105]

[0106] represents the input and output variable vector of the state space model, and represents the coefficient matrix of the state, control input, output of the small signal model, where and represents the small signal of the generalized state variable vector, represents the differential of the small signal of the generalized state variable vector.

[0107] Through equation (8), the small signal open loop transfer function of the WPT system from duty cycle to output voltage can be derived as:

[0108]

[0109] where, and represent the small signal output and input of the system under the frequency domain model, and I represents the unit matrix.

[0110] Then, the WPT system parameters in Table 1 are substituted into Equation (9) to obtain a linear high-order model with thirteen poles. Based on the balance theory and Hankel singular value truncation reduction method, a reduced-order model of the original high-order model is obtained. The singular value distribution of the original model is shown in Figure 6 . Most of the information in the system is mainly distributed in the first two states. The bode plots of the original model and the simplified model are shown in Figure 7 , where (a) is the bode plot of the original model and the first-order model, (b) is the bode plot of the original model and the second-order system model. In the frequency range of [0, 10 5 ] rad / s, the gain and phase curves of the second-order model and the original model are almost the same. Therefore, the second-order model with undetermined coefficients can accurately describe the linear part of the WPT system model. In previous work, a method of multiple second-order models is usually used to realize the design of the nonlinear system controller, but this method will increase the complexity of the controller. The Hammerstein model is composed of nonlinear and linear components, which can accurately represent the behavior of the nonlinear system and can solve the dynamic response characteristics of the large operating point that cannot be solved by the small signal model. By analyzing the large signal and small signal models of the WPT system, the Hammerstein model shown in Figure 8 can be obtained. Where f(d) is the nonlinear static characteristic of the WPT system, d is the duty ratio (control variable), G p (s) is a linear time-invariant model.

[0111] Obviously, the linear model G p (s) established by the GSSA method is very complex and inaccurate in describing high-order converters and parameter-varying systems. The data-driven modeling method based on Hammerstein is applied to solve this problem, which will be described in detail below.

[0112] Through the data-driven modeling method, the Hammerstein model can be easily obtained, as shown in Figure 8 . In this paper, the static nonlinearity of the Hammerstein model is f(d) = sin(πd / 2). In addition, this nonlinear function can also be identified from the static input and output data (measured after all transients disappear). The dynamic linear model can be identified from the dynamic input and output data related to the transient response generated by a suitable excitation signal (such as a pseudo-random binary sequence (PRBS)). The block diagram of the data-driven model is shown in Figure 9As shown, the discrete nonlinear input is passed through a zero-order hold to become a continuous nonlinear input, which acts on the plant model of the system to obtain the output, and the system is sampled at fixed time instants to obtain the discrete system output (containing measurement noise error), in which a time delay is added to illustrate the communication delay. Thus, the Hammerstein model can be written as:

[0113]

[0114] where t represents time, τ represents a pure time delay describing the total time delay of the system, f(u(t-τ)) represents a nonlinear input function of the system at t-τ, t k =kT represents a sampling time, where k=1, 2, 3…, T represents a sampling interval, x(t k ) represents the true output of the system at the kth sampling time, v(t k ) represents the measurement noise of the system output at the kth sampling time, y(t k ) represents the system output at the kth sampling time, G(s, θ) represents a rational transfer function of the system, and B(s, θ) and A(s, θ) represent the following polynomials:

[0115]

[0116] where n a and n b are polynomial degrees, n a ≥n b , and θ=[a1,…a na ,b0…b nb ] Τ is a vector of unknown parameters.

[0117] The conclusion of the circuit modeling analysis shows that a second-order model is more suitable for reflecting the characteristics of the WPT system. It is suggested to use a second-order model with n a =2 and n b =1 to describe the system.

[0118] The following assumptions are made:

[0119] 1) B(s, θ) and A(s, θ) are not common factors at any time; the roots of A(s, θ) are located in the left half plane;

[0120] 2) n a and n b are known;

[0121] 3) the continuous-time (CT) input u(t) is converted into a discrete-time (DT) sequence u(t k) is generated by a holding device designed to be independent of other input parameters of the system and has sufficient information to ensure the recognizability of the object model.

[0122] The purpose of the method modeling is to recursively estimate the parameters θ and time delay τ from the sampled input-output data where N is the number of samples, which increases by one at each recursion. Therefore, the following optimization problem is defined to estimate the unknown model parameters:

[0123]

[0124]

[0125] ε(t k ) = y(t k ) - x(t k ) (14)

[0126] where, represents the optimized solution of the estimated model offset parameters and system communication delay θ, τ, J(θ, τ) is the cost function of the prediction error, ε(t k ) is the error between the actual output and the estimated output at the kth sampling time, and N is the number of samples.

[0127] In this way, the time-invariant parameters of the system model at a single operating point can be obtained. Newton's steepest gradient descent method has the characteristics of fast convergence speed. The least squares method and Newton iterative search are combined to estimate the parameters θ and τ. For ease of annotation, define:

[0128]

[0129] Then in the optimization process, the iterative estimation of ρ is as follows:

[0130]

[0131] where μ represents the step factor, and represent the gradient vector and Hessian matrix of the cost function, respectively, and and are calculated as follows:

[0132]

[0133]

[0134] This embodiment uses a combination of least squares and Newton's iterative search to solve the optimization problem, in order to estimate the model offset parameters of the second-order Hammerstein model and the system communication delay. The corresponding solution process is based on Algorithm 1 below, which includes the following steps:

[0135] S81. Obtain sampling data Where u(t) k () represents the control input at the k-th sampling time;

[0136] S82. Set the initial value of the delay τ. 0 Minimum time delay interval Δτ min Minimum delay τ min and maximum delay τ max The initial training data size N0 and the number of iterations Niter, as well as the incremental error of the cost function. Parameter estimation error

[0137] S83, based on τ 0 Estimate the initial value of θ. 0 and [θ 0 ;τ 0 The solution ρ* is assigned to ρ;

[0138] S84. Begin iteration. In each iteration, first set μ = 1 and calculate Δρ. * =(▽ 2 J(ρ * )) -1 ▽J(ρ * For each training data point, through Get the value of ρ for the next iteration if Or the current delay Then proceed to step S85; throughout the entire iteration process, if or The iteration terminates if the iteration count is reached; otherwise, the iteration terminates after the specified number of iterations.

[0139] S85, reduce μ by half, further if If so, terminate the current training data and proceed to the next training data; otherwise, continue. Assign the value to ρ* and terminate the current training data, then proceed to the next training data.

[0140] The unknown parameters are estimated by Newton's iterative search, and the iterative calculation is repeated until the best parameter estimate is obtained.

[0141]

[0142] Theoretically, the application provides a data-driven WPT system modeling method, which firstly determines the circuit structure and system parameters of the WPT system, establishes a differential equation, then constructs a GSSA model (large signal model) based on the system differential equation, and obtains a linear small signal model of the system by adding disturbance, further establishes a Hammerstein model based on the large signal model and the small signal model through a data-driven modeling method, and performs order reduction to obtain a second-order Hammerstein model, and finally constructs an optimization problem based on the second-order Hammerstein model, and finally solves the optimization problem by combining the least square method and the Newton iterative search method, so that the model offset parameters and system communication delay of the WPT system can be accurately estimated.

[0143] Experimental results are provided below to verify the effectiveness of the proposed modeling method. In the experiment, on the primary side, an STM32H7 control board is used to realize IMC control, signal processing and communication functions. On the secondary side, an STM32F042 is used to realize sampling and communication functions. The main parameters of the system are shown in Table 1.

[0144] Table 1 Main parameters of the experiment

[0145]

[0146] In order to show the static input nonlinearity of the system, the steady-state input and output data of multiple static operating points are collected, as shown in Figure 10 . The steady-state output as a function of duty cycle is shown in Figure 10 (a), where the obvious nonlinearity close to 225sin(πd / 2) can be observed. Figure 10 The steady-state operating points (m1, m2, m3, m4) shown in Figure 10 (a) are superimposed with 2% duty cycle disturbances, and the dynamic responses (remove static values) to these disturbances are shown in Figure 10 (b). Obviously, all the dynamic responses have the same trend of change, but the benefits are different. This particularizes the static nonlinear characteristics of the system. It should be mentioned that the experimental and theoretical (i.e. 225sin(πd / 2)) results, as shown in Figure 11 (a), are due to the omission of higher harmonic components. In order to accurately describe the input nonlinearity, the lookup table (LUT) method is a good choice. The reasonable parameter estimation data of the Hammerstein model is generated at the steady-state operating point of D=0.8. The steady-state output at this operating point is measured as 210V. Then, a PRBS input with an amplitude of 1% duty cycle is superimposed on the steady-state input, and then a total of 3300 input-output data are sampled. The dynamic output response of the system to the PRBS input excitation is shown in Figure 11The average output is 209.92 V and the perturbation amplitude on the output is about 5 V. The tiny perturbation does not have much impact on the operation of the system. The comparison between the measured output and the estimated second-order model output is shown in Fig. 6. The fitness ratio calculated by the comparison program in the control system toolbox in Matlab reaches 90.32%, which specifically illustrates the accuracy of the data-driven modeling method. The estimated model parameters are shown in Table 2, in which the second-order model achieves a higher fitness ratio than the first-order model. This indicates that the second-order model is more accurate than the first-order model for the considered WPT system. Figure 12

[0147] Table 2 Estimated parameters at the steady-state operating point

[0148]

[0149] The present application considers the identification and control problem of LCC-S WPT systems. In order to solve the high-order nonlinear characteristics and large communication time delay problem of the considered system, a Hammerstein model is used and identified to describe the system dynamics. The research results show that the Hammerstein model is a global model that can describe the WPT system in a larger operating range, and the data-driven scheme for model identification leads to an accurate model of relatively low order. This solves the problem in the traditional circuit theory-based modeling method (the resulting models always have high order, and they cannot estimate time delay). The simulation and experimental results verify the good performance of the proposed data-driven modeling method.

[0150] The above embodiments are the preferred embodiments of the present application, but the embodiments of the present application are not limited to the above embodiments, and any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present application should be equivalent replacement methods, and are all included in the protection scope of the present application.​

Claims

1. A data-driven based WPT system modeling method, characterized in that, The method comprises the steps of: S1, determining the circuit structure and system parameters of the WPT system, and establishing a differential equation of the system based on the circuit structure and Kirchhoff's theorem; In the step S1, the circuit structure of the WPT system is composed of a primary side and a secondary side, the primary side includes sequentially connected DC power supply, inverter, LCC compensation network, transmitting coil L p , the secondary side includes sequentially connected receiving coil L s , series compensation capacitor C s , rectifier circuit, filter capacitor C d , load resistor R L , the LCC compensation network includes series compensation inductor L f , series compensation capacitor C p and parallel compensation capacitor C f ; S2, establishing a GSSA model of the system based on the differential equation of the system; S3, adding a disturbance at a given steady-state operating point, converting the GSSA model of the system into a linear small-signal model, and obtaining a small-signal open-loop transfer function of the WPT system from a duty cycle to an output voltage; S4, substituting the system parameters into the small-signal open-loop transfer function to obtain a linear high-order model; S5, based on the GSSA model and the linear high-order model, constructing a Hammerstein model of the system by a data-driven modeling method and adding a time delay; In the step S5, the Hammerstein model is represented as: Where t represents time, x(t) represents the generalized state variable vector containing the real and imaginary parts of the state variables in the differential equation obtained in step S1, τ represents the pure time delay describing the total system delay, and f(u(t-τ)) represents the nonlinear input function of the system at time t-τ. k =kT represents the sampling time, where k = 1, 2, 3…, and T represents the sampling interval, x(t) k ) represents the actual output of the system at the k-th sampling time, v(t) k ) represents the system output measurement noise at the k-th sampling time, y(t) k Let A(s,θ) represent the system output at the k-th sampling time, G(s,θ) represent the rational transfer function of the system, and B(s,θ) and A(s,θ) represent the following polynomials: where n a and n b are polynomial degrees, n a ≥ n b , is a vector of model bias parameters; S6, obtaining a second-order model of the Hammerstein model, denoted as a second-order Hammerstein model; S7, defining an optimization problem for estimating a model offset parameter and a system communication delay based on the second-order Hammerstein model; In the step S7, the optimization problem is constructed as: ε(t k ) = y(t k ) - x(t k ), wherein, represents the optimized solution of the estimated model offset parameters and system communication delay θ,τ, J(θ,τ) is the cost function of the prediction error, ε(t k ) is the error between the actual output and the estimated output at the kth sampling time, and N is the number of samples. S8, using a method combining least squares and Newton iterative search to solve the optimization problem to estimate the model offset parameter and the system communication delay.

2. The data-driven modeling method for a WPT system of claim 1, wherein: In the step S6, take n a = 2 and n b = 1, the second order Hammerstein model is obtained.

3. The data-driven based WPT system modeling method of claim 1, wherein, Definitions In step S8, the iterative estimate of the parameter vector p is as follows: where μ j denotes the step size factor at iteration j, and denote the gradient vector and Hessian matrix of the cost function, respectively, denote the estimates of p at iterations j, j + 1, respectively.

4. The data-driven WPT system modeling method according to claim 3, characterized in that, The step S8 specifically comprises the steps of: S81, obtaining sampling data where u(t k ) represents the control input at the kth sampling time; S82. Set the initial value of the delay τ. 0 Minimum time delay interval Δτ min Minimum delay τ min and maximum delay τ max The initial training data size N0 and the number of iterations Niter, as well as the incremental error of the cost function. Parameter estimation error S83、based on τ 0 an initial value θ 0 for θ and assigning [θ 0 ; τ 0 ] to the solution ρ* for ρ; S84, start iteration, in each iteration, first set μ = 1, calculate For each training data, by Get the next iteration of the value of ρ If Or the current delay Then execute step S85; in the whole iteration process, if Or Then terminate the iteration, otherwise execute to the iteration number Niter terminate the iteration; S85, reduce μ by half, further if then terminate this training data and enter the next training data, otherwise assign ρ* and terminate this training data and enter the next training data.

5. The data-driven based WPT system modeling method of claim 1, wherein, In step S3, the state space equation of the system is linearized by disturbance as follows to obtain a small-signal model: wherein and denote the input voltage, the output voltage and the duty cycle at the steady state operating point, where the input voltage refers to the first order effective value of the inverter output voltage, the output voltage refers to the load voltage and the duty cycle refers to the duty cycle of the high frequency inverter, and denote the input voltage perturbation, the output voltage perturbation and the duty cycle perturbation corresponding to the execution around the steady state operating point, denotes the small signal of the generalized state variable vector, denotes the steady state value of the generalized state variable vector, x i , u ab , y, d denote the generalized state variable vector, the input voltage, the system output, the duty cycle of the phase shift angle, respectively; and By the formula: wherein U dc represents the DC input voltage of the WPT system.

6. The data-driven based WPT system modeling method of claim 5, wherein, In step S3, the state space equation of the small-signal model is established as: and denote the input and output variable vectors of the state space model, and denote the coefficient matrices of the states, control inputs, outputs of the small signal model, denote the small signal of the generalized state variable vector, denote the differential of the small signal of the generalized state variable vector; The small-signal open-loop transfer function is represented as: wherein and denotes the small signal output and input of the system under the frequency domain model, and I denotes the unit matrix.

7. The data-driven based WPT system modeling method of claim 1, wherein, In the step S1, the differential equation of the system is established as: where u ab represents the first order effective value of the inverter output voltage, i f represents the current of L cf , and u f represents the voltage of L p , i cp represents the current of L p , and u cf represents the voltage of L f , M represents the mutual inductance between L p and L s , i s represents the current of L cs , and u s represents the voltage of L r , i r represents the current of the rectifier circuit, and u o represents the voltage of R L , i.e., the system output voltage, R1, R2 and R3 respectively represent the equivalent series resistances of L f , L p and L s ; State variable u ab and i r The real and imaginary parts of u are expressed by the following equations: (·) d and (·) q denotes the real and imaginary parts of the state variable; In the step S2, the GSSA model of the system is represented as: where x(t) represents a generalized state variable vector composed of real and imaginary parts of the state variable from the resulting differential equation in step S1 ; represents the differential of the generalized state variable vector; u(t) = [u ab (d)] represents the control input, d represents the duty ratio of the inverter phase shift angle; y(t) = [u o ] represents the output of the system; A, B, and C represent state, control input, and output coefficient matrices, respectively, where and

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