Post-processing method for flux-current model identification

Abstract

The application relates to a post-processing method of a flux-current model identification, and relates to the field of motor parameter identification. The application is used to solve the problems of the existing flux-current model, large fitting error of the magnetic saturation grid and low identification accuracy. The application injects a voltage into the motor to make the motor flux change, and obtains the flux data points corresponding to the motor current under different working conditions based on a flux equation; the flux data points are divided into different zones according to the change amount of the motor flux, and a polynomial is used to describe the flux-current relationship in each zone; the coefficients of the polynomial are updated by using a recursive least square method, and then an optimal flux-current curve is obtained; and a two-dimensional bilinear interpolation method is used to extend the flux-current curve into a flux-current surface.

Description

Technical Field

[0001] This application belongs to the field of motor parameter identification. Background Technology

[0002] Permanent magnet-assisted synchronous reluctance motors (PMaSynRMs) have advantages such as low cost, high power density, and high efficiency, and have been widely used in industrial drives and electric vehicles in recent years. However, their nonlinear magnetic saturation characteristics make accurate modeling difficult. Motor parameters change significantly during motor operation, with the quadrature-axis inductance and flux linkage exhibiting significant nonlinearity with current. Traditional analytical models struggle to balance global fitting accuracy with local saturation characteristics, thus requiring data post-processing techniques to optimize model parameters and obtain an accurate flux linkage-current model. However, existing data post-processing techniques for identifying the flux linkage-current model of PMaSynRMs are not mature enough, resulting in a relative scarcity of suitable flux linkage-current models for this motor. This leads to large fitting errors and low identification accuracy of the identified magnetic saturation mesh surface. Summary of the Invention

[0003] This application aims to address the problems of insufficient existing flux linkage-current models, large fitting errors of identified magnetic saturation grid surfaces, and low identification accuracy. It provides a post-processing method for identifying the flux linkage-current model of a permanent magnet assisted synchronous reluctance motor.

[0004] This application provides a post-processing method for flux linkage-current model identification, including:

[0005] A voltage is injected into the motor to cause a change in the motor flux linkage, and flux linkage data points corresponding to the current of the motor under different operating conditions are obtained based on the flux linkage equation.

[0006] The flux linkage data points are partitioned according to the change in motor flux linkage, and the flux linkage-current relationship in each interval is described by a polynomial.

[0007] The coefficients of the polynomial are updated using the recursive least squares method, thereby obtaining the optimal flux linkage-current curve;

[0008] The flux linkage-current curve is extended into a flux linkage-current surface using a two-dimensional bilinear interpolation method.

[0009] In one possible design, obtaining the flux linkage data points corresponding to the motor current under different operating conditions based on the flux linkage equation includes:

[0010] The motor's dq-axis current is collected in real time, and a mathematical model of the motor is constructed. The mathematical model includes voltage equations and torque equations.

[0011] The magnetic flux linkage equation is derived based on the mathematical model described above.

[0012] The flux linkage data points corresponding to the motor current under different operating conditions are obtained by voltage signal injection method and the flux linkage equation.

[0013] In one possible design, the voltage equation is expressed as:

[0014] ,

[0015] ,

[0016] in, , These are the d-axis and q-axis voltages of the motor, respectively. , These are the d-axis and q-axis currents of the motor, respectively. , These are the magnetic flux linkages on the d and q axes of the motor, respectively. For stator resistance, Electric angular velocity;

[0017] The expression for the torque equation is as follows:

[0018] ,

[0019] in, This represents the number of pole pairs of the motor. Electromagnetic torque;

[0020] The expression for the magnetic flux linkage equation is:

[0021] ,

[0022] ,

[0023] in, It is a permanent magnet flux linkage;

[0024] In the Injected motor in each sampling period shaft voltage The expression is:

[0025] ,

[0026] in, , For the first Each sampling period Shaft magnetization voltage, For the first Each sampling period Shaft current sampling value.

[0027] In one possible design, the first Each sampling period The expression for the shaft magnetization voltage is:

[0028] ,

[0029] in, for The constant amplitude of the shaft magnetization voltage This is the current threshold of the hysteresis current controller.

[0030] In one possible design, partitioning the flux linkage data points based on the change in motor flux linkage includes:

[0031] The data partitioning interval is twice the absolute value of the change in motor flux linkage, and the flux linkage data points are partitioned using the data partitioning interval.

[0032] In one possible design, the absolute value expression for the change in motor flux linkage is:

[0033] ,

[0034] in, , For motor The change in axial flux linkage and The first and Motor in each sampling period Axial magnetic flux, for The constant amplitude of the shaft magnetization voltage For signal injection period;

[0035] The data partitioning interval expression is:

[0036] ,

[0037] in, For motor Axis data partitioning interval.

[0038] In one possible design, the use of polynomials to describe the flux linkage-current relationship within each interval includes:

[0039] The fitting polynomial for each flux linkage data point within each interval is:

[0040] ,

[0041] ,

[0042] in, , The first Within each interval , The corresponding current, , These are the magnetic flux linkages on the d and q axes of the motor, respectively. , Let these represent the orders of the polynomials fitted along the d and q axes, respectively. For the d-axis Index within a certain range The corresponding polynomial coefficients, For the q-axis Index within a certain range The corresponding polynomial coefficients, , .

[0043] In one possible design, updating the coefficients of the polynomial using the recursive least squares method includes:

[0044] Initialize the coefficient vector of the polynomial to a zero vector;

[0045] The coefficients of the updated polynomial are calculated according to the following formula:

[0046] ,

[0047] in, For the first Within the interval, the first Each magnetic flux linkage data point corresponds to an updated polynomial coefficient. , for Axis No. Index within a certain range The corresponding polynomial coefficients, , , for The order of the axis-fitting polynomial, For the first Within the interval, the first Gain matrix of each magnetic flux linkage data point For the first Within the interval, the first The current value corresponding to each magnetic flux linkage data point For the first Within the interval, the first The input vector corresponding to each magnetic flux linkage data point.

[0048] In one possible design, the first Within the interval, the first The expression for the gain matrix of each magnetic flux linkage data point is:

[0049] ,

[0050] in, For the input vector, for Axial magnetic flux, Forgetting factor, Let be the covariance matrix.

[0051] In one possible design, the flux-current lookup table is generated by processing the flux-current surface into an equally spaced grid.

[0052] The beneficial effects of this application are:

[0053] In this application, the partitioning of flux linkage data points is a quantitative calculation based on the injected voltage amplitude and the number of injection points. This partitioning method avoids empirical design, ensuring both the number of fitted data points within the partition and the consistency between the fitted curve and the fitted data points within the partition. This is beneficial for using piecewise linear fitting to obtain the local characteristics and global trends of the data, providing a foundation for accurately identifying the flux linkage-current model.

[0054] The polynomial fitting proposed in this application adopts a linear polynomial model, which can avoid overfitting or oscillation problems caused by higher-order polynomials. It can also be combined with the recursive least squares method for digital implementation. This process does not require a complete sample dataset and has the advantages of low computational cost and small memory footprint.

[0055] This application does not require complex controller design and calculation, has a simple principle, can be implemented based on low-cost digital processing chips, and has the advantages of high efficiency and economy. Attached Figure Description

[0056] Figure 1 A schematic diagram of data partitioning intervals determined based on the absolute value of the change in magnetic flux generated by the injection voltage;

[0057] Figure 2 A schematic diagram showing the results of piecewise linear fitting of the flux linkage-current relationship curve;

[0058] Figure 3 This is a schematic diagram illustrating the implementation of the two-dimensional bilinear interpolation method.

[0059] Figure 4The diagram shows the fitted curve based on piecewise linear regression, the equally spaced flux-current grid surface obtained from the fitting results, and the fitting error. In this diagram, (a) and (b) represent the original data and their corresponding d-axis and q-axis flux-current fitted curves, respectively; (c) and (d) represent the uniformly spaced flux-current grid surfaces, respectively; and (e) and (f) represent the errors between the fitted flux-current grid surfaces and the original data points, respectively.

[0060] Figure 5 The flowchart shows the implementation of the piecewise linear flux linkage-current model identification method.

[0061] Figure 6 This is a flowchart of the post-processing method for identifying the flux linkage-current model as described in Specific Implementation Method 1. Detailed Implementation

[0062] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other.

[0063] Data post-processing is a key technical step in the flux linkage-current model identification process. It involves processing and optimizing discrete data points acquired during the motor injection signal process to improve the reliability and applicability of the flux linkage-current identification plane. Model fitting is a common method in data post-processing, aiming to establish a functional relationship between flux linkage and current using mathematical methods. It selects a suitable fitting model based on the characteristics of the discrete data and optimizes its parameters to predict the complete flux linkage-current relationship. Therefore, selecting a suitable fitting model is crucial for improving the identification accuracy of the flux linkage-current model.

[0064] Existing fitting models are mainly based on traditional analytical equations proposed from the flux linkage-current model of synchronous reluctance motors (SynRM), including polynomial plane models, arctangent models, exponential function models, and sign function models. Due to the unique structure of permanent magnet assisted synchronous reluctance motors, their magnetic circuits exhibit strong nonlinearity. Directly applying fitting models of synchronous reluctance motors can lead to poor local fitting results, decreased accuracy of identification results, and negative impacts on motor control performance. Therefore, designing a fitting model suitable for the characteristics of permanent magnet assisted synchronous reluctance motors is crucial.

[0065] As described in the background section, the post-processing technology for identifying the flux linkage-current model of a permanent magnet assisted synchronous reluctance motor (PMSM) is not mature enough, and suitable flux linkage-current models for this motor are relatively scarce. This results in a large fitting error and low identification accuracy of the identified magnetic saturation grid surface. Therefore, to improve the identification accuracy of the flux linkage-current model, considering the strong nonlinearity of the magnetic circuit, proposing a piecewise linear regression fitting model suitable for PMSM is of great significance.

[0066] In view of this, this application provides a post-processing method for identifying the flux linkage-current model of a permanent magnet assisted synchronous reluctance motor, in order to solve the above-mentioned problems. The following will be discussed in conjunction with the attached... Figures 1 to 6 The implementation scheme of this application will be described in detail.

[0067] Specific implementation method one: Refer to Figure 6 Specifically, the post-processing method for flux linkage-current model identification described in this embodiment includes:

[0068] A voltage is injected into the motor to cause a change in the motor flux linkage, and flux linkage data points corresponding to the current of the motor under different operating conditions are obtained based on the flux linkage equation.

[0069] The flux linkage data points are partitioned according to the change in motor flux linkage, and the flux linkage-current relationship in each interval is described by a polynomial.

[0070] The coefficients of the polynomial are updated using the recursive least squares method, thereby obtaining the optimal flux linkage-current curve;

[0071] The flux linkage-current curve is extended into a flux linkage-current surface using a two-dimensional bilinear interpolation method.

[0072] In one embodiment, obtaining the flux linkage data points corresponding to the motor current under different operating conditions based on the flux linkage equation includes:

[0073] The motor's dq-axis current is collected in real time, and a mathematical model of the motor is constructed. The mathematical model includes voltage equations and torque equations.

[0074] The magnetic flux linkage equation is derived based on the mathematical model described above.

[0075] The flux linkage data points corresponding to the motor current under different operating conditions are obtained by voltage signal injection method and the flux linkage equation.

[0076] In one embodiment, the voltage equation is expressed as:

[0077] ,

[0078] ,

[0079] in, , These are the d-axis and q-axis voltages of the motor, respectively. , These are the d-axis and q-axis currents of the motor, respectively. , These are the magnetic flux linkages on the d and q axes of the motor, respectively. For stator resistance, Electric angular velocity;

[0080] The expression for the torque equation is as follows:

[0081] ,

[0082] in, This represents the number of pole pairs of the motor. Electromagnetic torque;

[0083] The expression for the magnetic flux linkage equation is:

[0084] ,

[0085] ,

[0086] in, It is a permanent magnet flux linkage;

[0087] In the Injected motor in each sampling period shaft voltage The expression is:

[0088] ,

[0089] in, , For the first Each sampling period Shaft magnetization voltage, For the first Each sampling period Shaft current sampling value.

[0090] In one implementation, the first Each sampling period The expression for the shaft magnetization voltage is:

[0091] ,

[0092] in, for The constant amplitude of the shaft magnetization voltage This is the current threshold of the hysteresis current controller.

[0093] In one embodiment, partitioning the flux linkage data points according to the change in motor flux linkage includes:

[0094] The data partitioning interval is twice the absolute value of the change in motor flux linkage, and the flux linkage data points are partitioned using the data partitioning interval.

[0095] In one embodiment, the absolute value expression of the change in motor flux linkage is:

[0096] ,

[0097] in, , For motor The change in axial flux linkage and The first and Motor in each sampling period Axial magnetic flux, for The constant amplitude of the shaft magnetization voltage For signal injection period;

[0098] The data partitioning interval expression is:

[0099] ,

[0100] in, For motor Axis data partitioning interval.

[0101] In one implementation, the description of the flux linkage-current relationship within each interval using a polynomial includes:

[0102] The fitting polynomial for each flux linkage data point within each interval is:

[0103] ,

[0104] ,

[0105] in, , The first Within each interval , The corresponding current, , These are the magnetic flux linkages on the d and q axes of the motor, respectively. , Let these represent the orders of the polynomials fitted along the d and q axes, respectively. For the d-axis Index within a certain range The corresponding polynomial coefficients, For the q-axis Index within a certain range The corresponding polynomial coefficients, , .

[0106] In one implementation, updating the coefficients of the polynomial using the recursive least squares method includes:

[0107] Initialize the coefficient vector of the polynomial to a zero vector;

[0108] The coefficients of the updated polynomial are calculated according to the following formula:

[0109] ,

[0110] in, For the first Within the interval, the first Each magnetic flux linkage data point corresponds to an updated polynomial coefficient. , for Axis No. Index within a certain range The corresponding polynomial coefficients, , , for The order of the axis-fitting polynomial, For the first Within the interval, the first Gain matrix of each magnetic flux linkage data point For the first Within the interval, the first The current value corresponding to each magnetic flux linkage data point For the first Within the interval, the first The input vector corresponding to each magnetic flux linkage data point.

[0111] In one implementation, the first Within the interval, the first The expression for the gain matrix of each magnetic flux linkage data point is:

[0112] ,

[0113] in, For the input vector, for Axial magnetic flux, Forgetting factor, Let be the covariance matrix.

[0114] In one implementation, a flux-current lookup table is generated by processing the flux-current surface into an equally spaced grid.

[0115] To further illustrate the implementation scheme of this application, steps 1 to 5 are included, wherein the numbering of each step does not necessarily limit the order in which they are executed. Each step is described in detail below:

[0116] Step 1: The current sensor samples and acquires the d-axis and q-axis currents in real time. , :

[0117] ,

[0118] in, , , The three-phase current obtained from sampling, This is the motor position angle.

[0119] A mathematical model of a permanent magnet assisted synchronous reluctance motor is established, including voltage equations and torque equations.

[0120] The specific expression for the voltage equation is:

[0121] ,

[0122] ,

[0123] in, , These are the d-axis and q-axis voltages, respectively. For stator resistance, Electric angular velocity, , These are the magnetic flux linkages along the d and q axes, respectively.

[0124] The specific expression for the torque equation is as follows:

[0125] ,

[0126] in, This represents the number of pole pairs of the motor. It is electromagnetic torque.

[0127] Based on the voltage and torque equations, the flux linkage calculation equations based on static constraints are derived as follows:

[0128] ,

[0129] ,

[0130] in, It is a permanent magnet flux linkage.

[0131] By selecting an appropriate injection voltage, the flux linkage will change. The flux linkage-current data points of the motor under different operating conditions can be obtained by using the signal injection method and the flux linkage calculation equation.

[0132] No. Each sampling period Shaft reference injection voltage The specific expression is:

[0133] ,

[0134] in, For the first Each sampling period Shaft current sampling value; For the first Each sampling period The shaft magnetization voltage is expressed as follows:

[0135] ,

[0136] in, for In this embodiment, the constant amplitude of the shaft magnetization voltage is maintained. and All were set to 80V; The current threshold of the hysteresis current controller. For the first Each sampling period Shaft magnetization voltage value.

[0137] In this embodiment, to ensure that the test results cover the rated operating range of the motor, a [specific method is provided]. Peak current 1.2 times that. Based on the selected 5.5kW permanent magnet assisted synchronous reluctance motor, the rated current... If it is 14.7A, then and They are respectively:

[0138] ,

[0139] .

[0140] Step 2: Calculate the data partition interval based on the absolute value of the change in magnetic flux generated by the injected voltage in Step 1.

[0141] In this embodiment, the signal injection period Set to 100µs. In one signal injection cycle. Changes in flux linkage along the inner d and q axes The absolute value of this can be obtained from the discrete flux linkage calculation equation, and its specific expression is as follows:

[0142] ,

[0143] .

[0144] Based on the 5.5kW permanent magnet assisted synchronous reluctance motor selected in this embodiment, the data of the d-axis and q-axis models are partitioned and spaced. Set to twice the absolute value of the flux change within one injection cycle:

[0145] ,

[0146] .

[0147] Figure 1 The data partitioning interval is given based on the absolute value of the change in magnetic flux caused by the injection voltage.

[0148] Step 3: Divide the data into partitions based on the partition intervals obtained in Step 2, and fit the flux linkage-current relationship within each partition using an nth-order polynomial.

[0149] In this embodiment, the fitting polynomial of the piecewise linear regression flux linkage-current model in each partition is:

[0150] ,

[0151] ,

[0152] in, , In the piecewise linear regression flux linkage-current model, the first... The d-axis and q-axis currents corresponding to the d-axis flux linkages within each partition. and Let these represent the orders of the polynomials fitted along the d and q axes, respectively. For the d-axis Index within each partition The corresponding polynomial coefficients, For the q-axis Index within each partition The corresponding polynomial coefficients, , .

[0153] Step 4: Based on the flux linkage-current data points obtained in Step 1 and the nth-order polynomial described in Step 3, initialize the covariance matrix for each partition. and parameter vector The parameter vector is updated by recursive least squares (RLS) to obtain the fitting polynomial coefficient matrix of the flux linkage-current model in each partition.

[0154] Initialize the covariance matrix Typically, this is represented by a large diagonal matrix, indicating the uncertainty in the initial parameter estimation; the parameter vector... It can usually be set as the zero vector.

[0155] In this embodiment, the recursive least squares (RLS) method is used to determine the polynomial coefficients in different partitions. Taking the d-axis flux linkage-current curve calculation process as an example, the recursive least squares method in the d-axis region... In the partition, the th The calculation equation for the next update is:

[0156] ,

[0157] ,

[0158] in, Let be the parameter vector to be estimated. The sample current value, Here is the gain matrix. , Let be the covariance matrix, and its initial value be... , As a scale factor, for An identity matrix of order 1. The input vector is composed of sample inputs. This is the forgetting factor. In this example, the scaling factor... =10000; Forgetting factor .

[0159] and The specific values ​​are shown in the table below:

[0160]

[0161] Figure 2 A schematic diagram of the results of piecewise linear fitting of the flux linkage-current relationship curve is given.

[0162] Step 5: Based on the fitting results of the partitioned fitting polynomial in Step 4, the flux linkage-current curve is extended into a flux linkage-current surface using a two-dimensional bilinear interpolation method, and the fitting results are processed by equal-spacing gridding to generate a high-precision lookup table.

[0163] In this embodiment, taking the d-axis flux linkage-current plane as an example, for calculating arbitrary Interpolation current point at the flux linkage point The expression for the two-dimensional bilinear interpolation method is:

[0164] ,

[0165] ,

[0166] ,

[0167] in, Interpolation calculations for data points The four known data points within the neighborhood can be obtained based on the fitting polynomial described in step 4. All of these are intermediate interpolation points.

[0168] Figure 3 A schematic diagram illustrating the implementation of the two-dimensional bilinear interpolation method is provided. Figure 4 The fitted curve based on piecewise linear regression, the equally spaced flux-current grid surface obtained from the fitting results, and the fitting error are presented.

[0169] While specific embodiments of this application have been described herein with reference to them, it should be understood that these embodiments are merely examples of the principles and applications of this application. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of this application as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A post-processing method for identifying flux linkage-current models, characterized in that, include: Injecting voltage into the motor causes a change in the motor flux linkage, and obtaining flux linkage data points corresponding to the motor current under different operating conditions based on the flux linkage equation; The flux linkage data points are partitioned according to the change in motor flux linkage, and the flux linkage-current relationship in each interval is described by a polynomial. The coefficients of the polynomial are updated using the recursive least squares method, thereby obtaining the optimal flux linkage-current curve; The flux linkage-current curve is extended into a flux linkage-current surface using a two-dimensional bilinear interpolation method. The step of partitioning the flux linkage data points according to the change in motor flux linkage includes: The data partitioning interval is twice the absolute value of the change in motor flux linkage, and the flux linkage data points are partitioned using the data partitioning interval. The expression for the absolute value of the change in the motor flux linkage is: ， in, , For motor The change in axial flux linkage and The first and Motor in each sampling period Axial magnetic flux, for The constant amplitude of the shaft magnetization voltage For signal injection period; The data partitioning interval expression is: ， in, For motor Axis data partitioning interval.

2. The post-processing method for flux linkage-current model identification according to claim 1, characterized in that, The process of obtaining flux linkage data points corresponding to the motor current under different operating conditions based on the flux linkage equation includes: The motor's dq-axis current is collected in real time, and a mathematical model of the motor is constructed. The mathematical model includes voltage equations and torque equations. The magnetic flux linkage equation is derived based on the mathematical model described above. The flux linkage data points corresponding to the motor current under different operating conditions are obtained by voltage signal injection method and the flux linkage equation.

3. The post-processing method for flux linkage-current model identification according to claim 2, characterized in that, The expression for the voltage equation is: ， ， in, , These are the d-axis and q-axis voltages of the motor, respectively. , These are the d-axis and q-axis currents of the motor, respectively. , These are the magnetic flux linkages on the d and q axes of the motor, respectively. For stator resistance, Electric angular velocity; The expression for the torque equation is as follows: ， in, This represents the number of pole pairs of the motor. Electromagnetic torque; The expression for the magnetic flux linkage equation is: ， ， in, It is a permanent magnet flux linkage; In the Injected motor in each sampling period shaft voltage The expression is: ， in, , For the first Each sampling period Shaft magnetization voltage, For the first Each sampling period Shaft current sampling value.

4. The post-processing method for flux linkage-current model identification according to claim 3, characterized in that, The first Each sampling period The expression for the shaft magnetization voltage is: ， in, for The constant amplitude of the shaft magnetization voltage This is the current threshold of the hysteresis current controller.

5. The post-processing method for flux linkage-current model identification according to claim 1, characterized in that, The description of the flux linkage-current relationship within each interval using polynomials includes: The fitting polynomial for each flux linkage data point within each interval is: ， ， in, , The first Within each interval , The corresponding current, , These are the magnetic flux linkages on the d and q axes of the motor, respectively. , Let these represent the orders of the polynomials fitted along the d and q axes, respectively. For the d-axis Index within a certain range The corresponding polynomial coefficients, For the q-axis Index within a certain range The corresponding polynomial coefficients, , .

6. The post-processing method for identifying the flux linkage-current model according to claim 1, characterized in that, The method of updating the coefficients of the polynomial using recursive least squares includes: Initialize the coefficient vector of the polynomial to a zero vector; The coefficients of the updated polynomial are calculated according to the following formula: ， in, For the first Within the interval, the first Each magnetic flux linkage data point corresponds to an updated polynomial coefficient. , for Axis No. Index within a certain range The corresponding polynomial coefficients, , , for The order of the axis-fitting polynomial, For the first Within the interval, the first Gain matrix of each magnetic flux linkage data point For the first Within the interval, the first The current value corresponding to each magnetic flux linkage data point For the first Within the interval, the first The input vector corresponding to each magnetic flux linkage data point.

7. The post-processing method for flux linkage-current model identification according to claim 6, characterized in that, The first Within the interval, the first The expression for the gain matrix of each magnetic flux linkage data point is: ， in, For the input vector, for Axial magnetic flux, Forgetting factor, Let be the covariance matrix.

8. The post-processing method for flux linkage-current model identification according to any one of claims 1 to 7, characterized in that, The flux linkage-current surface is processed by equal-spacing meshing to generate a flux linkage-current lookup table.

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