CN118171530A - Conductor eccentricity self-adaptive correction method of array type single-axis TMR current sensor - Google Patents

Abstract

The invention provides a conductor eccentric self-adaptive correction method of an array type single-axis TMR current sensor, which belongs to the technical field of power systems, and comprises the following steps: analyzing the principle and the error of the TMR current sensor, establishing a self-correction algorithm model, and setting an experimental platform for verification based on comsol finite element simulation analysis. The TMR current sensor eccentricity compensation model of the BP neural network is optimized based on a sparrow search algorithm, training and learning are carried out by adopting the sparrow search algorithm to optimize the weight and the threshold of the BP neural network, the relation of the change between the conductor eccentricity position and the sensor output is searched, the influence of the conductor eccentricity is eliminated by feeding back a correction factor, and the remarkable performance of the method in the aspect of resisting the eccentricity error is proved through finite element simulation and experimental verification, so that the accuracy of current measurement is greatly improved.

Description

Conductor eccentricity adaptive correction method for array single-axis TMR current sensor

Technical Field

The present invention relates to the technical field of power systems, and in particular to a conductor eccentricity adaptive correction method for an array-type single-axis TMR current sensor.

Background technique

With the continuous modernization of power systems, smart grids that rely on real-time and accurate current information have become the development goal of modern power systems, and high-precision current measurement plays an indispensable role in it.

Traditional electromagnetic induction current sensors improve their anti-interference ability by concentrating magnetism through the magnetic core. However, when a fault occurs in the power system, the sudden increase in current causes the magnetic core to saturate, limiting the current measurement range and resulting in poor transient performance. They also have the problems of large weight and volume, which prevents them from being widely used in power systems in different environments.

In recent years, with the update and iteration of micro magnetic sensor technology in integrated circuits, Hall Effect, Anisotropic Magnetoresistance (AMR), Giant Magnetoresistance (GMR) and the latest generation of Tunnel Magnetoresistance (TMR) effect current sensors have emerged. Compared with the previous three generations of magnetic sensors, TMR current sensors have very high sensitivity and can sense tiny magnetic field changes, which makes them perform well in low current measurement and high-precision applications; at the same time, they have fast response time and are suitable for applications that require real-time monitoring and control, such as fault detection and fast response in power systems. TMR current sensors are divided into closed-loop and open-loop categories. Since open-loop TMR current sensors have no feedback link and have a faster response time, and the coreless structure does not have saturation problems, which greatly improves transient performance, open-loop TMR current sensors are often used on transmission lines.

Open-loop current sensors based on magnetic rings often have problems such as core saturation and DC bias when measuring large currents and DC. In order to solve this problem, J.T.Scoville first proposed an array current sensor solution in 1990. Multiple magnetic sensors are arranged in a closed loop of a current-carrying conductor. The sum of the magnetic sensors simulates the integral of the magnetic field generated by the current-carrying conductor in the closed loop, and then the measured current is obtained by inverting Ampere's loop law.

When analyzing the measurement errors of array TMR current sensors in practical applications, in addition to temperature drift and crosstalk, conductor position eccentricity is the main source of error. However, in practical applications, due to the certain distance between multi-axis sensor elements, the field strength at the same point cannot be accurately measured, and the conductor eccentricity error cannot be completely eliminated.

Summary of the invention

The object of the present invention is to provide a conductor eccentricity adaptive correction method for an array-type single-axis TMR current sensor to solve the technical problems mentioned in the background technology.

Theoretical and error analysis are carried out on the problem of conductor eccentricity, and a measurement method based on array single-axis TMR sensor is proposed. The relationship between the eccentric position of the conductor and the transformation ratio of the sensor output is found by optimizing the BP neural network (SSA-BP) through the sparrow algorithm, and then the correction factor is fed back to eliminate the eccentricity error of the conductor. The theoretical simulation and experimental verification of the current measurement method are given.

In order to achieve the above object, the technical solution adopted by the present invention is as follows:

A conductor eccentricity adaptive correction method for an array-type single-axis TMR current sensor, the method comprising the following steps:

Step 1: Analyze the principle and error of TMR current sensor;

Step 2: Establish a self-correction algorithm model;

Step 3: Finite element simulation analysis based on comsol;

Step 4: Set up the experimental platform for verification.

Furthermore, the specific process of step 1 is:

Step 1.1: Analysis of the principle of TMR current sensor. The basic structure of the magnetic tunnel junction of the TMR element is a triangular structure, which consists of two ferromagnetic material layers sandwiching a non-magnetic insulating layer. The two ferromagnetic material layers are the free layer and the pinned layer. The magnetization direction of the pinned layer remains unchanged under a fixed magnetic field, while the magnetization direction of the free layer rotates under the influence of the magnetic field. When the magnetic moments of the two magnetic layers are parallel, the resistance is small, and when the directions are anti-parallel, the resistance is large. The change of TMR magnetoresistance reflects the influence of the external magnetic field on the TMR structure, causing the imbalance of the Wheatstone bridge to output the differential signal voltage to achieve current measurement;

An equivalent Wheatstone bridge model is established. R1, R2, R3 and R4 are magnetoresistances. The directions of the magnetic moments of R1 and R3 are the same, and the directions of the magnetic moments of R2 and R4 are the same. When there is no external magnetic field, the magnetoresistance values on the bridge are equal, that is, R1＝R2＝R3＝R4, and the output signal of the bridge is 0. When an external magnetic field acts, the magnetoresistance changes by the same amount due to the effect of the magnetic field. The directions of R1 and R3 are opposite to those of R2 and R4, and the magnetic signal is converted into a differential voltage signal. The voltage output by the bridge needs to be amplified by the signal conditioning circuit, which is expressed as:

V _out =G _op ·V _tmr (1)

Where V _out represents the output voltage after differential amplification, G _op is the amplification factor of the operational amplifier, and V _tmr is the output voltage of a single TMR sensor;

Step 1.2: Analysis of the measurement principle of the annular TMR array. According to Ampere's loop law, the line integral of the magnetic induction intensity B along a closed path is equal to the algebraic sum of the currents enclosed by the path multiplied by the magnetic permeability. Therefore, the line integral of the closed loop approximate path can be formed by the annular TMR array.

∫ _l Bdl＝μ ₀ ∑I (3)

Where μ ₀ is the vacuum magnetic permeability, usually 4π*10 ^-7 . At the same time, since the transmission line can be approximated as an infinitely long straight conductor, according to the Biot-Savart law, the TMR sensor output V _tmr is:

Where k _s and B _s are the sensitivity and magnetic induction intensity measurement value of the TMR sensor, respectively. is the magnetic induction intensity vector of the magnetic field generated by the conductor at the sensor,/> is the current vector flowing through the conductor, /> is the sensor sensitive axis unit vector, /> is the radius vector from the center of the wire to the center of the sensor. The total output of N sensors is as follows:

The average value V _mean of the array sensor output is:

The measured value of the conductor current Im _is obtained by combining equations (3)-(6):

Step 1.3: Eccentricity error analysis. The intersection of the current-carrying conductor and the array TMR current sensor is not at the center point, resulting in measurement error. The measured current _I0 flows perpendicular to the xy plane from inside to outside. The azimuth angle α is the eccentric distance vector between the y-axis and the eccentric conductor. The angle between the two, β is the magnetic induction intensity generated at the sensor S1/> and sensitive axis/> From formula (4), we can know that the output voltage of the TMR sensor is related to the dot product of the magnetic induction intensity vector generated by the conductor on the sensor and the unit direction vector of the sensitive axis. Through geometric decomposition, we can get:

From the cosine theorem we can get:

r ₁ ² = r ₀ ² + d ² - 2r ₀ dcos α (10)

Combining equations (4), (8), (9) and (10) we can obtain:

Continuing to deduce, we can get the output voltage V _i of sensor S _i :

After adding and averaging V _mean , the eccentric current measurement value _Im can be obtained:

Where N = 3, It is known that the relative measurement error ε _u caused by eccentricity can be further obtained:

From the above formula, we can know that the measurement error is related to the two eccentric variables, eccentric distance d and azimuth angle α, and has nothing to do with the magnitude of the measured current. Using MATLAB for numerical simulation, _tp is defined as the ratio of the conductor eccentric distance to the array radius, that is:

By changing t _p and taking the azimuth angle α as the coordinate axis, the relationship of the conductor eccentricity error can be obtained.

Furthermore, the specific process of step 2 is:

Step 2.1: Establish BP neural network and SSA algorithm;

Step 2.2: Establish the SSA-BP self-correction algorithm based on the BP neural network and the SSA algorithm;

Step 2.3: Establish SSA-BP neural network.

Furthermore, the specific process of step 2.2 is:

Since the eccentricity causes the distance r and azimuth angle α _i of each TMR sensor to change from the conductor, the measured values of each TMR sensor are no longer equal, and the ratio between the outputs of each TMR sensor changes accordingly. The ratio between the measured values of the magnetic induction intensity of TMR sensors at different positions is set as the input of the neural network, as shown in the following formula:

Among them, _BS1 , _BS2 and _BS3 are the magnetic induction intensity measurement values of TMR sensors S1, S2 and S3 respectively. The BP neural network generation process requires standard output for training. The ratio of the magnetic induction intensity _Bt generated by the conductor on the TMR sensor when there is no eccentricity to the sensor measurement value _BSi is the theoretical correction factor _kti as the output of the training process:

The BP neural network is trained with x ₁ , x ₂ and x ₃ as input and k _t1 , k _t2 and k _t3 as output. The network is transplanted to obtain the output of correction factors k ₁ , k ₂ and k ₃ to eliminate the eccentricity error, thereby obtaining the corrected measured current value I _a :

The error value of BP neural network is used as the fitness function of SSA algorithm, and the optimal weight and threshold in BP neural network model are directly determined by integrating global search and local search mechanism.

Furthermore, the specific process of step 2.3 is:

The input and output data of different positions of the conductor derived from the theory are used as the training set of the network. First, the measured current I ₀ = 100A and the radius of the ring array r ₀ = 50mm are set. Then, equation 4 and equation 12 are combined to obtain the measured values of the magnetic induction intensity of the three TMR sensors at different positions evenly distributed in the ring array. Finally, 400 training data sets are established according to the method in step 2.3.

The neural network parameters were set, and a 3-input 3-output BP neural network topology was established. The hidden layer activation function used the logsig function, and the output layer activation function used the pureline function. The hidden layer nodes and the training error were cyclically analyzed to determine the best hidden layer nodes. The network parameters were set, the maximum number of neural network training times was 100, the learning rate was set to 0.01, the minimum training target error was 1e-10, and other parameters were set to default values. The initial parameters of the SSA algorithm were initialized, the initial population size was 50, the maximum number of iterations was 10, the upper and lower limits of the independent variables were 5 and -5 respectively, and the safety value ST was set to 0.8.

After 57 trainings, the network reached the best performance, with a mean square error (MSE) of 0.00072, close to 0.

The neural network automatically calculates and plots the correlation coefficient R between the target value and the predicted value and its fitting effect. The data is divided into four parts: training, validation, testing and overall. The horizontal and vertical axes represent the actual value of the sample and the output value of the network respectively. The closer the correlation coefficient R is to 1, the higher the degree of linearization and the better the training effect. The scattered points fit the regression line and the overall correlation coefficient R is 0.9886, indicating that the network performance is excellent.

The learning result evaluation indicators of BP neural network and SSA-BP neural network are compared. The mean absolute error E _MAE of BP and SSA-BP prediction models are 0.0062 and 0.0048, the root mean square error E _RMSE is 0.0532 and 0.0268, and the mean absolute percentage error E _MAPE is 0.5568% and 0.4446%, respectively. It can be seen that the prediction effect of SSA-BP is superior.

Furthermore, the specific process of step 3 is:

Step 3.1: Use Comsol finite element simulation software to simulate the magnetic field of the TMR annular array current sensor. The circumferential radius of the TMR sensing unit is 50 mm, the radius of the current-carrying conductor is 10 mm, the length is 200 mm, and a DC current of 100 A is applied. It should be noted that the TMR sensing unit is only sensitive to the magnetic field component in the tangential direction of the circle. The magnetic field simulation is performed on the conductor at different eccentric positions uniformly in the annular array. The magnetic induction intensity values B _Si of the three TMR sensing units are collected respectively, and the simulation test data set is organized and imported into the neural network established in step 2.4 for test verification.

Step 3.2: Substituting the correction factor k _i output by the neural network into equation 21, the measured value of the conductor current after correction I _a can be obtained. The measurement error after correction is calculated for effect analysis. The distribution diagram of the eccentricity error before correction and after correction by the self-correction algorithm based on SSA-BP is compared. After SSA-BP correction, it presents a uniform distribution close to 0, and its maximum error is reduced from 33.86% before correction to 0.92%. The adaptive correction algorithm can perform predictive measurement for eccentricity conditions;

The eccentricity error ε _u increases with the increase of the conductor eccentricity distance d, and changes periodically with the azimuth angle α. Therefore, the eccentricity ratio t _p = 0.4 and the step size of the azimuth angle α are set to 10°. The measurement errors without correction, after BP neural network correction and after SSA-BP neural network correction are compared. The addition of the self-correction algorithm can effectively reduce the eccentricity error. At the same time, the measurement value after SSA-BP neural network correction has better robustness than that of BP neural network.

Furthermore, the specific process of step 4 is:

Step 4.1: Experimental platform design: design an open array current sensor based on uniaxial TMR2901, with a circular array radius of r = 50 mm. Three uniaxial TMR current sensors are evenly fixed on the acrylic board at 120° on the xy axis.

From formula 14, it can be seen that the error of the eccentricity measurement value has nothing to do with the magnitude of the measured current. The DC power supply KPS6020D is selected and adjusted to the constant voltage mode CV to output a constant voltage of 30V. It is connected in series with the electronic load meter IT8512A set to the 2Ω constant resistance mode to output a DC power of 15A. The eccentricity position of the conductor is changed by adjusting the movable buckle on the wire fixing seat. The waveform and output voltage measurement value of the TMR current sensor are collected on the oscilloscope Tektronix MSO56B, and the collected data set is imported into the computer for processing and calculation;

Step 4.2: TMR current sensor calibration. To accurately measure the current, the sensitivity k _s of the TMR current sensor must be known. Therefore, 5 basic accuracy measurement experiments were carried out without eccentricity and interference of the conductor. The standard input current value and the output voltage value of the TMR current sensor were fitted by the least square method. The sensitivity k _s and bias voltage of the sensor were obtained by taking the average of the slope and intercept. The bias voltage was eliminated and a mathematical model between the input current and the sensor output voltage was established. The measured current value can be inverted through the output voltage of the sensor. When the conductor current changes from 0A to 20A, the average relative error E _MRE is 0.14%, of which the input current is 0.12% when it is 15A. The error is caused by the internal noise of the sensor and the measurement error.

Step 4.3: Convert the collected TMR current sensor output voltage value V _i into the corresponding magnetic induction intensity measurement value B _si through formula 4 to establish an experimental test data set, import the neural network generated in step 3.4, and then feed back the correction factor k _i and substitute it into formula 21 to obtain the corrected current measurement value I _a , and analyze the correction effect;

Before the experimental correction, the error curve derived from the theory shows a trend consistent with that of the azimuth angle α. At the same time, the test set is imported into the self-correction algorithm model and compared with the measurement error before correction. After adding the BP and SSA-BP self-correction algorithms for correction, the average relative error _EMRE of 4.03% before correction can be reduced to 1.02% and 0.47% respectively. It can be seen that the SSA-BP self-correction algorithm can eliminate the eccentricity error.

The present invention has the following beneficial effects due to the adoption of the above technical solution:

The present invention is based on a TMR current sensor eccentricity compensation model of a BP neural network optimized by a sparrow search algorithm (SSA). The weights and thresholds of the BP neural network are optimized by the sparrow search algorithm (SSA) for training and learning, and the relationship between the eccentric position of the conductor and the change of the sensor output is found, and then the correction factor is fed back to eliminate the influence of the conductor eccentricity. Through finite element simulation and experimental verification, it is proved that the method has significant performance in resisting eccentricity errors, and the accuracy of current measurement is greatly improved. This not only provides strong support for the reliability and stability of the TMR current sensor in practical engineering applications, but also provides an effective method and idea for the study of eccentricity adaptive correction of other sensors.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a diagram of an equivalent Wheatstone bridge model of the present invention;

FIG2 is a structural diagram of the annular array TMR of the present invention;

FIG3 is a diagram showing an analysis of conductor eccentricity measurement errors according to the present invention;

FIG4 is a diagram showing the relationship between conductor eccentricity errors of the present invention;

FIG5 is a topological diagram of the Bp neural network structure of the present invention;

FIG6 is a schematic diagram of a conductor eccentricity simulation of the present invention;

FIG7 is a flow chart of the SSA-BP neural network of the present invention;

FIG8 is a training performance diagram of the SSA-BP neural network of the present invention;

FIG9 is a diagram showing the fitting effect of the SSA-BP neural network of the present invention;

FIG10 is a diagram showing the establishment of a comsol model of the present invention;

FIG11 is a distribution diagram of eccentricity error before correction of the present invention;

12 is a distribution diagram of eccentricity error after SSA-BP correction of the present invention;

FIG13 is an eccentricity error analysis diagram of simulation data of the present invention;

FIG14 is a schematic diagram of an experimental system of the present invention;

FIG15 is a physical diagram of the experimental system of the present invention;

FIG16 is a diagram showing the calibration results of the TMR current sensor of the present invention;

FIG. 17 is an analysis diagram of eccentricity error of experimental data of the present invention.

Detailed ways

In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and preferred embodiments. However, it should be noted that many details listed in the specification are only for the purpose of enabling the reader to have a thorough understanding of one or more aspects of the present invention, and these aspects of the present invention can be implemented even without these specific details.

A conductor eccentricity adaptive correction method for an array-type single-axis TMR current sensor, the method comprising the following steps:

1 Basic principles and error analysis

1.1 Introduction to the principle of TMR current sensor

The basic structure of the magnetic tunnel junction of the TMR element is a "sandwich" structure, which consists of two ferromagnetic material layers (free layer and pinned layer) sandwiching a non-magnetic insulating layer (tunnel junction). Under a certain magnetic field, the magnetization direction of the pinned layer remains unchanged, while the magnetization direction of the free layer rotates under the influence of the magnetic field. When the magnetic moments of the two magnetic layers are parallel, the resistance is small; when the directions are anti-parallel, the resistance is large. Therefore, the change of TMR magnetoresistance reflects the influence of the external magnetic field on the TMR structure, causing the imbalance of the Wheatstone bridge to output the differential change signal voltage to achieve the measurement of current.

The equivalent Wheatstone bridge model is shown in Figure 1. R1, R2, R3 and R4 are magnetoresistances. The directions of the magnetic moments of R1 and R3 are the same, and the directions of the magnetic moments of R2 and R4 are the same. When there is no external magnetic field, the magnetoresistance values on the bridge are equal, that is, R1 = R2 = R3 = R4, and the output signal of the bridge is 0; when the external magnetic field acts, the magnetoresistance changes by the same amount under the action of the magnetic field. The directions of R1 and R3 are opposite to those of R2 and R4, and the magnetic signal is converted into a differential voltage signal. The voltage output by the bridge needs to be amplified by the signal conditioning circuit, which can be expressed as:

V _out =G _op ·V _tmr (1)

Where _Vout represents the output voltage after differential amplification, _Gop is the amplification factor of the operational amplifier, and _Vtmr is the output voltage of a single TMR sensor.

1.2 Annular TMR array measurement principle

The structure of the annular TMR array is shown in FIG2 . According to Ampere's loop law, as shown in the formula, the line integral of the magnetic induction intensity B along the closed path is equal to the algebraic sum of the currents enclosed by the path multiplied by the magnetic permeability. Therefore, the line integral of the closed loop approximate path can be formed by the annular TMR array.

∫ _l Bdl＝μ ₀ ∑I (3)

Where μ ₀ is the vacuum magnetic permeability, usually 4π*10 ^-7 . At the same time, since the transmission line can be approximated as an infinitely long straight conductor, according to the Biot-Savart law, the TMR sensor output V _tmr is:

Where k _s and B _s are the sensitivity and magnetic induction intensity measurement value of the TMR sensor, respectively. is the magnetic induction intensity vector of the magnetic field generated by the conductor at the sensor,/> is the current vector flowing through the conductor, /> is the sensor sensitive axis unit vector, /> is the radius vector from the center of the wire to the center of the sensor. The total output of N sensors is as follows:

The average value V _mean of the array sensor output is:

Combining the above four equations, we can invert the measured value of the conductor current, _Im :

1.3 Eccentricity error analysis

The long-term operation of the transmission line will be affected by the environment or the sensor installation will cause the conductor eccentricity problem, that is, the intersection of the current-carrying conductor and the array TMR current sensor is not at the center point, resulting in a large measurement error. This section will take sensor S1 as an example to analyze in detail the error effect of conductor eccentricity on current measurement.

As shown in Figure 3, the measured current _I0 flows perpendicular to the xy plane from the inside to the outside, and the azimuth angle α is the eccentric distance vector between the y axis and the eccentric conductor. The angle between the two, β is the magnetic induction intensity generated at the sensor S1/> and sensitive axis/> The parameters are defined in Table 1.

Table 1 Definition of parameters in Figure 3

It can be seen from formula (4) that the output voltage of the TMR sensor is related to the dot product of the magnetic induction intensity vector generated by the conductor on the sensor and the unit direction vector of the sensitive axis. Through geometric decomposition, it can be obtained:

From the cosine theorem we can get:

r ₁ ² = r ₀ ² + d ² - 2r ₀ dcos α (10)

Combining equations (4), (8), (9) and (10) we can obtain:

Continuing to deduce, we can get the output voltage V _i of sensor S _i :

After adding and averaging V _mean , the eccentric current measurement value _Im can be obtained:

Where N = 3, It is known that the relative measurement error ε _u caused by eccentricity can be further obtained:

From the above formula, we can know that the measurement error is related to the two eccentric variables, eccentric distance d and azimuth angle α, and has nothing to do with the magnitude of the measured current. Using MATLAB for numerical simulation, _tp is defined as the ratio of the conductor eccentric distance to the array radius, that is:

By changing t _p and taking the azimuth angle α as the coordinate axis, the relationship of the conductor eccentricity error can be obtained as shown in Figure 4.

2 Self-correction algorithm model establishment

The BP neural network has the ability to learn and store a large number of input-output pattern mapping relationships, so that it can directly establish an eccentricity compensation model by training the network of TMR sensor unit measurements under different eccentricity states of the conductor. At the same time, the sparrow optimization algorithm (SSA) can adjust the hyperparameters of the BP neural network to further improve the model performance. Therefore, in order to deal with the measurement error caused by eccentricity, this paper designs an eccentricity self-correction algorithm based on SSA-BP, which provides an effective solution to the eccentricity problem.

2.1 BP Neural Network

As a multi-layer feedforward neural network that optimizes weights and bias parameters based on the error back propagation algorithm, BP neural network can minimize the error between the network output value and the target value. It is often used to deal with nonlinear problems with high accuracy.

2.1 Sparrow Search Algorithm (SSA)

Although the BP neural network has powerful nonlinear mapping capabilities, it relies on the gradient descent method to adjust the network connection weights and thresholds, and optimizes them through the back propagation of errors. This method has a potential risk, that is, the network may fall into a local optimal solution, thereby reducing the accuracy of the prediction, so it is necessary to optimize the weights and thresholds of the BP neural network to reduce the diagnostic error.

The SSA algorithm is a heuristic optimization algorithm, and its design is inspired by the group behavior of sparrows in nature in hunting and avoiding predators. During the hunting process, sparrows will constantly adjust their positions according to the level of their own energy to ensure the highest efficiency in obtaining food. The algorithm has a strong optimization ability and a fast convergence speed. The entire algorithm process divides the group into two sub-groups: discoverers and joiners, to be closer to the group behavior in nature. Individuals with higher individual energy are discoverers and play a leading role in the search space, and the rest are called joiners. The specific implementation steps of the algorithm are as follows:

Step 1: Initialize the position and fitness of the sparrow population, and set the initial values of the maximum number of iterations N, population size n, number of discoverers PD, number of sparrows that sense danger SD, and safety value ST parameters.

Step 2: Start the loop and exit when the number of iterations is greater than N and return the value.

Step 3: Sort the population to separate the discoverers and joiners, and determine the position of the current optimal sparrow individual and the corresponding optimal fitness value.

Step 4: During the foraging process, the position of the discoverer is continuously updated to maximize the energy acquisition rate. When the alarm threshold R ₂ is less than the safety value AT, it means that the surrounding is safe. Otherwise, the discoverer issues a warning and randomly moves to the current optimal position. The expression for the discoverer's position update is as follows:

Among them, Q is a random number (subject to normal distribution); is a unit row vector; a is a random number between [0,1].

Step 5: Update the joiner's location based on the discoverer's location and group information:

Where X _worst is the position of the sparrow with the lowest fitness; X _p is the optimal position in the population iteration process; A row vector containing two randomly arranged elements, 1 and -1.

Step 6: In the anti-predator process, a small number of sparrows are randomly selected to serve as sentinels. When they find danger, they abandon food and move randomly. When the individual fitness _fi is greater than the global optimal fitness _fg , it indicates that the sparrows at the edge of the population are vulnerable to predators; when the two are equal, it means that when the sparrows in the middle feel the approach of predators, they will fly to other sparrows to reduce the risk of being hunted by predators. The position update is as follows:

In the formula, β is a random number that follows a normal distribution to control the step size of the updated position. K is a random number between [-1,1], _fw is the global worst fitness, and ε is a constant close to 0 to avoid the denominator being zero.

Step 7: Update the historical optimal fitness (equivalent to updating the fitness bulletin board).

Step 8: Execute steps 3-7, and end the loop when the maximum number of iterations N is reached, and output the optimal individual position X _best and fitness value.

2.3 Self-correction algorithm based on SSA-BP. From Figure 6 above, we can see that due to the eccentricity, the distance r and azimuth angle α _i between each TMR sensor and the conductor change, and the measured values of each TMR sensor are no longer equal. At the same time, the ratio between the outputs of each TMR sensor changes accordingly. Through this phenomenon, we use the ratio between the magnetic induction intensity measurement values of TMR sensors at different positions as the input of the neural network, as follows:

Where _BS1 , _BS2 and _BS3 are the measured values of magnetic induction intensity of TMR sensors S1, S2 and S3 respectively. The BP neural network generation process requires standard output for training, so the ratio of the magnetic induction intensity _Bt generated by the conductor on the TMR sensor when there is no eccentricity to the sensor measurement value _BSi is the theoretical correction factor _kti as the output of the training process:

The BP neural network is trained with x ₁ , x ₂ and x ₃ as input and k _t1 , k _t2 and k _t3 as output. In practical applications, transplanting this network can obtain the output of correction factors k ₁ , k ₂ and k ₃ to eliminate the eccentricity error, thereby obtaining the corrected measured current value I _a :

The error value of the BP neural network is used as the fitness function of the sparrow search algorithm (SSA), and the optimal weights and thresholds in the BP neural network model are directly determined by integrating the global search and local search mechanisms. The SSA algorithm helps to overcome the problem that the BP neural network is prone to fall into the local optimal solution, thereby significantly improving the accuracy of optimization. The process flow chart is shown in Figure 7.

2.4SSA-BP neural network establishment

The establishment of a neural network requires a data set for training. In order to make the network more accurate, the input and output data of different positions of the conductor derived from the theory are used as the training set of the network. First, the measured current I ₀ = 100A and the radius of the circular array r ₀ = 50mm are set. Then, equations 4 and 12 are combined to obtain the measured values of the magnetic induction intensity of the three TMR sensors at different positions evenly distributed in the circular array. Finally, 400 training data sets are established according to the method described in Section 2.3.

Set the neural network parameters. Establish a 3-input 3-output BP neural network topology; the hidden layer activation function uses the logsig function, the output layer activation function uses the pureline function, and the hidden layer nodes and training errors are looped to determine the best hidden layer nodes. Set the network parameters; the maximum number of neural network training is 100 times, the learning rate is set to 0.01, the minimum training target error is 1e-10, and other parameters are set to default values. Initialize the initial parameters of the sparrow search algorithm (SSA); the initial population size is 50, the maximum number of iterations is 10, the upper and lower limits of the independent variable are 5 and -5 respectively, and the safety value ST is set to 0.8.

The network is trained and learned. Its training performance is shown in Figure 8. The network reaches the best after 57 trainings, and its mean square error MSE is 0.00072, close to 0.

The neural network automatically calculates and plots the correlation coefficient R between the target value and the predicted value. The fitting effect is shown in Figure 9. The data is divided into four parts: training, validation, testing and overall. The horizontal and vertical axes represent the actual sample values and the output values of the network respectively. The closer the correlation coefficient R is to 1, the higher the degree of linearization and the better the training effect. It can be seen from the figure that the scattered points fit the regression line and the overall correlation coefficient R is 0.9886, indicating that the network has excellent performance.

The evaluation indicators of the learning results of the BP neural network and the SSA-BP neural network are compared, as shown in Table 2. As can be seen from the table, the mean absolute error E _MAE of the BP and SSA-BP prediction models are 0.0062 and 0.0048, the root mean square error E _RMSE are 0.0532 and 0.0268, and the mean absolute percentage error E _MAPE are 0.5568% and 0.4446%, respectively. It can be seen that the prediction effect of SSA-BP is superior.

Table 2 shows the evaluation indicators of the two models

3 Simulation Analysis

3.1 Finite element simulation based on Comsol

This paper uses COMSO finite element simulation software to simulate the magnetic field of the TMR annular array current sensor. As shown in Figure 10, the circumferential radius of the TMR sensor unit is 50 mm, the radius of the current-carrying conductor is 10 mm, the length is 200 mm, and the DC current is 100 A. It should be noted that the TMR sensor unit is only sensitive to the magnetic field component in the tangential direction of the circle. The magnetic field simulation is performed on the conductor at different eccentric positions in the annular array, and the magnetic induction intensity values BS _i of the three TMR sensor units are collected respectively. The simulation test data set is organized and imported into the neural network established in Section 2.4 for test verification.

3.2 Results Analysis

Substituting the correction factor k _i output by the neural network into equation 21, the measured value I _a of the conductor current after correction can be obtained, and the measurement error after correction can be calculated for effect analysis. As shown in Figures 11 and 12, the distribution diagrams of the eccentricity error before correction and after correction by the self-correction algorithm based on SSA-BP are compared. After SSA-BP correction, the distribution is uniform and close to 0, and the maximum error value is reduced from 33.86% before correction to 0.92%, indicating that the adaptive correction algorithm can perform good prediction and measurement for various eccentricity conditions.

From the distribution diagram of eccentricity error before correction, it can be seen that the eccentricity error _εu increases with the increase of conductor eccentricity distance d, and changes periodically with azimuth angle α. Therefore, let the eccentricity ratio _tp and azimuth angle α step length be 10° for further detailed analysis. As shown in Table 3 and Figure 13, the measurement errors after uncorrected, BP neural network correction and SSA-BP neural network correction are compared. It can be seen from Table 3 that the addition of self-correction algorithm can effectively reduce the eccentricity error. At the same time, it can be seen from Figure 13 that the measurement value after SSA-BP neural network correction is more robust than BP neural network.

Table 3 Mean relative error K _MRE /%

1 Experimental verification

4. Experimental platform design

4.1 This paper designs an open array current sensor based on uniaxial TMR2901. The radius of the annular array is r = 50 mm, and three uniaxial TMR current sensors are evenly fixed on the acrylic plate at 120° on the xy axis.

The test system is shown in Figures 14 and 15. From the above formula 14, it can be seen that the eccentricity measurement error has nothing to do with the magnitude of the measured current. Therefore, this paper selects the DC power supply KPS6020D to adjust to the constant voltage mode CV output 30V constant voltage, and connects it in series with the electronic load meter IT8512A set to the 2Ω constant resistance mode to output 15A DC. The eccentric position of the conductor is changed by adjusting the movable buckle on the wire fixing seat, and the waveform and output voltage measurement value of the TMR current sensor are collected on the oscilloscope Tektronix MSO56B, and the collected data set is imported into the computer for processing and calculation.

4.2 TMR Current Sensor Calibration

To accurately measure the current, the sensitivity k _s of the TMR current sensor must be known, so five basic accuracy measurement experiments were conducted without eccentricity and interference on the conductor. The standard input current value and the output voltage value of the TMR current sensor were fitted by the least square method, and the average of the slope and intercept was taken to obtain the sensitivity k _s and bias voltage of the sensor. The bias voltage was eliminated and a mathematical model between the input current and the sensor output voltage was established, so that the measured current value can be inverted through the output voltage of the sensor. As shown in Figure 16, when the conductor current changes from 0A to 20A, the average relative error E _MRE is 0.14%, of which 0.12% when the input current is 15A. The main causes of this error are sensor internal noise and measurement errors.

4.3 Results Analysis

The collected TMR current sensor output voltage value Vi _is converted into the corresponding magnetic induction intensity measurement value _Bsi through formula 4 to establish an experimental test data set. The neural network generated in Section 3.4 is imported and the correction factor k _is fed back and substituted into formula 21 to obtain the corrected current measurement value _Ia , so as to analyze the correction effect.

This paper discusses the case of eccentricity ratio _tp = 0.4. The eccentricity error analysis is shown in the uncorrected curve in Figure 17. The error curves before experimental correction and theoretical derivation (as shown in Figure 5) are consistent with the trend of the change of azimuth angle α. At the same time, the test set is imported into the self-correction algorithm model and the measurement error before correction is compared as shown in Table 4. After adding BP and SSA-BP self-correction algorithms, the average relative error E _MRE before correction can be reduced from 4.03% to 1.02% and 0.47% respectively. Combined with Figure 17 and Table 4, it can be seen that the self-correction algorithms based on BP and SSA-BP can better eliminate the eccentricity error, but the self-correction algorithm based on SSA-BP has better accuracy and stability.

Table 4 Experimental average relative error E _MRE /%

A TMR current sensor eccentricity compensation model based on sparrow search algorithm (SSA) optimized BP neural network is proposed. The weights and thresholds of the BP neural network are optimized by sparrow search algorithm (SSA) for training and learning, and the relationship between the conductor eccentricity position and the sensor output is found, and then the correction factor is fed back to eliminate the influence of conductor eccentricity. Through finite element simulation and experimental verification, it is proved that this method has significant performance in resisting eccentricity error and greatly improves the accuracy of current measurement. This not only provides strong support for the reliability and stability of TMR current sensors in practical engineering applications, but also provides an effective method and idea for the study of eccentricity adaptive correction of other sensors.

The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims (7)

1. A conductor eccentricity adaptive correction method for an array type single-axis TMR current sensor, characterized in that the method comprises the following steps: Step 1: Analyze the principle and error of TMR current sensor; Step 2: Establish a self-correction algorithm model; Step 3: Finite element simulation analysis based on comsol; Step 4: Set up the experimental platform for verification. 2. The conductor eccentricity adaptive correction method of an array-type single-axis TMR current sensor according to claim 1 is characterized in that the specific process of step 1 is: Step 1.1: Analysis of the principle of TMR current sensor. The basic structure of the magnetic tunnel junction of the TMR element is a triangular structure, which consists of two ferromagnetic material layers sandwiching a non-magnetic insulating layer. The two ferromagnetic material layers are the free layer and the pinned layer. The magnetization direction of the pinned layer remains unchanged under a fixed magnetic field, while the magnetization direction of the free layer rotates under the influence of the magnetic field. When the magnetic moments of the two magnetic layers are parallel, the resistance is small, and when the directions are anti-parallel, the resistance is large. The change of TMR magnetoresistance reflects the influence of the external magnetic field on the TMR structure, causing the imbalance of the Wheatstone bridge to output the differential signal voltage to achieve the current measurement; An equivalent Wheatstone bridge model is established. R1, R2, R3 and R4 are magnetoresistances. The directions of the magnetic moments of R1 and R3 are the same, and the directions of the magnetic moments of R2 and R4 are the same. When there is no external magnetic field, the magnetoresistance values on the bridge are equal, that is, R1＝R2＝R3＝R4, and the output signal of the bridge is 0. When an external magnetic field acts, the magnetoresistance changes by the same amount due to the effect of the magnetic field. The directions of R1 and R3 are opposite to those of R2 and R4, and the magnetic signal is converted into a differential voltage signal. The voltage output by the bridge needs to be amplified by the signal conditioning circuit, which is expressed as: V _out =G _op ·V _tmr (1) Where V _out represents the output voltage after differential amplification, G _op is the amplification factor of the operational amplifier, and V _tmr is the output voltage of a single TMR sensor; Step 1.2: Analysis of the measurement principle of the annular TMR array. According to Ampere's loop law, the line integral of the magnetic induction intensity B along a closed path is equal to the algebraic sum of the currents enclosed by the path multiplied by the magnetic permeability. Therefore, the line integral of the closed loop approximate path can be formed by the annular TMR array. ∫ _l Bdl＝μ ₀ ∑I (3) Where μ ₀ is the vacuum magnetic permeability, usually 4π*10 ^-7 . At the same time, since the transmission line can be approximated as an infinitely long straight conductor, according to the Biot-Savart law, the TMR sensor output V _tmr is: Where k _s and B _s are the sensitivity and magnetic induction intensity measurement value of the TMR sensor, respectively. is the magnetic induction intensity vector of the magnetic field generated by the conductor at the sensor,/> is the current vector flowing through the conductor, /> is the sensor sensitive axis unit vector, /> is the radius vector from the center of the wire to the center of the sensor. The total output of N sensors is as follows: The average value V _mean of the array sensor output is: The measured value of the conductor current Im _is obtained by combining equations (3)-(6): Step 1.3: Eccentricity error analysis. The intersection of the current-carrying conductor and the array TMR current sensor is not at the center point, resulting in measurement error. The measured current _I0 flows perpendicular to the xy plane from inside to outside. The azimuth angle α is the eccentric distance vector between the y-axis and the eccentric conductor. The angle between the two, β is the magnetic induction intensity generated at the sensor S1/> and sensitive axis/> From formula (4), we can know that the output voltage of the TMR sensor is related to the dot product of the magnetic induction intensity vector generated by the conductor on the sensor and the unit direction vector of the sensitive axis. Through geometric decomposition, we can get: From the cosine theorem we can get: r ₁ ² = r ₀ ² + d ² - 2r ₀ dcos α (10) Combining equations (4), (8), (9) and (10) we can obtain: Continuing to deduce, we can get the output voltage V _i of sensor S _i : After adding and averaging V _mean , the eccentric current measurement value _Im can be obtained: Where N = 3, It is known that the relative measurement error ε _u caused by eccentricity can be further obtained: It can be seen from the above formula that the size of the measurement error is related to the two eccentric variables of eccentric distance d and azimuth angle α, and has nothing to do with the size of the measured current value and other factors. Using MATLAB for numerical simulation, _tp is defined as the ratio of the conductor eccentric distance to the array radius, that is: By changing t _p and taking the azimuth angle α as the coordinate axis, the relationship of the conductor eccentricity error can be obtained. 3. The conductor eccentricity adaptive correction method of an array-type single-axis TMR current sensor according to claim 1 is characterized in that the specific process of step 2 is: Step 2.1: Establish BP neural network and SSA algorithm; Step 2.2: Establish the SSA-BP self-correction algorithm based on the BP neural network and the SSA algorithm; Step 2.3: Establish SSA-BP neural network. 4. The conductor eccentricity adaptive correction method of an array type single-axis TMR current sensor according to claim 3 is characterized in that: the specific process of step 2.2 is: Since the eccentricity causes the distance r and azimuth angle α _i of each TMR sensor to change from the conductor, the measured values of each TMR sensor are no longer equal, and the ratio between the outputs of each TMR sensor changes accordingly. The ratio between the measured values of the magnetic induction intensity of TMR sensors at different positions is set as the input of the neural network, as shown in the following formula: Among them, _BS1 , _BS2 and _BS3 are the magnetic induction intensity measurement values of TMR sensors S1, S2 and S3 respectively. The BP neural network generation process requires standard output for training. The ratio of the magnetic induction intensity _Bt generated by the conductor on the TMR sensor when there is no eccentricity to the sensor measurement value _BSi is the theoretical correction factor _kti as the output of the training process: The BP neural network is trained with x ₁ , x ₂ and x ₃ as input and k _t1 , k _t2 and k _t3 as output. The network is transplanted to obtain the output of correction factors k ₁ , k ₂ and k ₃ to eliminate the eccentricity error, thereby obtaining the corrected measured current value I _a : The error value of BP neural network is used as the fitness function of SSA algorithm, and the optimal weight and threshold in BP neural network model are directly determined by integrating global search and local search mechanism. 5. The conductor eccentricity adaptive correction method of an array type single-axis TMR current sensor according to claim 4 is characterized in that: the specific process of step 2.3 is: The input and output data of different positions of the conductor derived from the theory are used as the training set of the network. First, the measured current I ₀ =100A and the radius of the ring array r ₀ =50mm are set. Then, equation 4 and equation 12 are combined to obtain the measured values of the magnetic induction intensity of the three TMR sensors at different positions evenly distributed in the ring array. Finally, 400 training data sets are established according to the method in step 2.3. Set the neural network parameters, establish a 3-input 3-output BP neural network topology, use the logsig function as the hidden layer activation function, and the pureline function as the output layer activation function. Loop the hidden layer nodes and the training error to determine the best hidden layer nodes. Set the network parameters. The maximum number of neural network training is 100 times. The learning rate is set to 0.01. The minimum training target error is 1e-10. Other parameters are set to default values. Initialize the initial parameters of the SSA algorithm. The initial population size is 50, the maximum number of iterations is 10, the upper and lower limits of the independent variable are 5 and -5 respectively, and the safety value ST is set to 0.8. After 57 trainings, the network reached the best performance, with a mean square error (MSE) of 0.00072, close to 0. The neural network automatically calculates and plots the correlation coefficient R between the target value and the predicted value and its fitting effect. The data is divided into four parts: training, validation, testing and overall. The horizontal and vertical axes represent the actual value of the sample and the output value of the network respectively. The closer the correlation coefficient R is to 1, the higher the degree of linearization and the better the training effect. The scattered points fit the regression line and the overall correlation coefficient R is 0.9886, indicating that the network performance is excellent. The learning result evaluation indicators of BP neural network and SSA-BP neural network are compared. The mean absolute error E _MAE of BP and SSA-BP prediction models are 0.0062 and 0.0048, the root mean square error E _RMSE is 0.0532 and 0.0268, and the mean absolute percentage error E _MAPE is 0.5568% and 0.4446%, respectively. It can be seen that the prediction effect of SSA-BP is superior. 6. The conductor eccentricity adaptive correction method of an array type single-axis TMR current sensor according to claim 5, characterized in that the specific process of step 3 is: Step 3.1: Use COMSO finite element simulation software to simulate the magnetic field of the TMR annular array current sensor. The circumferential radius of the TMR sensing unit is 50 mm, the radius of the current-carrying conductor is 10 mm, and the length is 200 mm. A DC current of 100 A is applied. It should be noted that the TMR sensing unit is only sensitive to the magnetic field component in the tangential direction of the circle. The conductor is uniformly positioned at different eccentric positions in the annular array for magnetic field simulation. The magnetic induction intensity values B _Si of the three TMR sensing units are collected respectively. The simulation test data set is organized and imported into the neural network established in step 2.4 for test verification. Step 3.2: Substituting the correction factor k _i output by the neural network into equation 21, the measured value of the conductor current after correction I _a can be obtained. The measurement error after correction is calculated for effect analysis. The distribution diagram of the eccentricity error before correction and after correction by the self-correction algorithm based on SSA-BP is compared. After SSA-BP correction, it presents a uniform distribution close to 0, and its maximum error is reduced from 33.86% before correction to 0.92%. The adaptive correction algorithm can perform predictive measurement for eccentricity conditions; The eccentricity error ε _u increases with the increase of the conductor eccentricity distance d, and changes periodically with the azimuth angle α. Therefore, the eccentricity ratio t _p = 0.4 and the step size of the azimuth angle α are set to 10°. The measurement errors without correction, after BP neural network correction and after SSA-BP neural network correction are compared. The addition of the self-correction algorithm can effectively reduce the eccentricity error. At the same time, the measurement value after SSA-BP neural network correction has better robustness than that of BP neural network. 7. The conductor eccentricity adaptive correction method of an array type single-axis TMR current sensor according to claim 6, characterized in that the specific process of step 4 is: Step 4.1: Experimental platform design: design an open array current sensor based on uniaxial TMR2901, with a circular array radius of r = 50 mm. Three uniaxial TMR current sensors are evenly fixed on the acrylic board at 120° on the xy axis. From formula 14, it can be seen that the error of the eccentricity measurement value has nothing to do with the magnitude of the measured current. The DC power supply KPS6020D is selected and adjusted to the constant voltage mode CV to output a constant voltage of 30V. It is connected in series with the electronic load meter IT8512A set to the 2Ω constant resistance mode to output a DC power of 15A. The eccentricity position of the conductor is changed by adjusting the movable buckle on the wire fixing seat, and the waveform and output voltage measurement value of the TMR current sensor are collected on the oscilloscope TektronixMSO56B. The collected data set is imported into the computer for processing and calculation; Step 4.2: TMR current sensor calibration. To accurately measure the current, the sensitivity k _s of the TMR current sensor must be known. Therefore, 5 basic accuracy measurement experiments were carried out without eccentricity and interference of the conductor. The standard input current value and the output voltage value of the TMR current sensor were fitted by the least square method. The sensitivity k _s and bias voltage of the sensor were obtained by taking the average of the slope and intercept. The bias voltage was eliminated and a mathematical model between the input current and the sensor output voltage was established. The measured current value can be inverted through the output voltage of the sensor. When the conductor current changes from 0A to 20A, the average relative error E _MRE is 0.14%, of which the input current is 0.12% when it is 15A. The error is caused by the internal noise of the sensor and the measurement error. Step 4.3: Convert the collected TMR current sensor output voltage value V _i into the corresponding magnetic induction intensity measurement value B _si through formula 4 to establish an experimental test data set, import the neural network generated in step 3.4, and then feed back the correction factor k _i and substitute it into formula 21 to obtain the corrected current measurement value I _a , and analyze the correction effect; Before the experimental correction, the error curve derived from the theory shows a trend consistent with that of the azimuth angle α. At the same time, the test set is imported into the self-correction algorithm model and compared with the measurement error before correction. After adding the BP and SSA-BP self-correction algorithms for correction, the average relative error _EMRE of 4.03% before correction can be reduced to 1.02% and 0.47% respectively. It can be seen that the SSA-BP self-correction algorithm can eliminate the eccentricity error.