[Abstract]: This paper introduces the working principle and magnetic circuit of a magnetically compensated Hall current sensor. Based on the characteristics of the sensor's magnetic field circuit, the classical electromagnetic equations are derived using assumptions to solve the finite element method for the magnetic field of the current sensor. The modeling function, mesh weaving characteristics, magnetic field simulation solver principle, and the entire simulation and analysis process of the FLUX software are studied and analyzed. Finally, a comprehensive magnetic field simulation analysis is conducted using a general-purpose LEM industrial magnetically compensated current sensor as an example, based on FLUX software. This magnetic field simulation research and analysis method is beneficial for improving the efficiency and quality of sensor design.
Keywords : 3D finite element simulation; FLUX; LEM current sensor; magnetic field simulation
1. Introduction
With the deepening energy crisis, the utilization of electricity is becoming increasingly important and widespread. To improve the efficiency of electricity use, meet environmental protection requirements, and reduce power grid and electrical equipment pollution, monitoring electricity is crucial, and the HALL sensor, which monitors electricity consumption, is a core component. Designing high-precision, accurate, and long-life HALL sensors is of great significance and importance to the improvement of the power industry. Traditional design methods rely heavily on the experience of designers, leading to significant uncertainties and difficulties in guaranteeing product quality. This paper addresses the shortcomings of traditional designs by using advanced simulation technology to study and analyze key magnetic field factors in HALL sensors. Combined with excellent simulation software, this effectively improves several key design parameters of the HALL sensor, significantly enhancing the product's design quality.
2. Working principle of magnetically compensated hall current sensor
Based on the working principle of the HALL sensor and the relationship between magnetoresistance, self-inductance, and mutual inductance, a magnetic circuit model of the sensor can be established. During Flux simulation analysis, the magnetic circuit model of the associated system needs to be considered (as shown in Figure 2).
NSIS: Ampere-turns generated by the coil (NP, S: Number of turns in the primary and secondary coils) φ: Main magnetic flux generated by the coil φσ: Leakage magnetic flux of the coil φσS: Air gap leakage magnetic flux (edge effect) φδs: Magnetic flux through the air gap Rf: Core reluctance Rδ1: Air gap reluctance Rσ1: Leakage reluctance
Figure 2 Magnetic circuit model of HALL current sensor
3. Finite Element Method for Solving the Three-Dimensional Static Magnetic Field of a Sensor
Based on the unique electromagnetic field characteristics of the HALL current sensor, and considering the worst-case scenario of application conditions and environment, the following assumptions are made that will not affect the simulation analysis results.
Assumption 1: The magnetic equilibrium system is a time-invariant system, and the state variables have certain assumptions about time.
2: The magnetic field simulation only associates the magnetic field quantities B and H, while the electric field quantities E and D are decoupled from the system.
Based on the assumptions, Maxwell's electromagnetic field equations [2] can be rewritten as follows:
----（1）
The magnetic materials used in HALL current sensors include:
----（2）
Based on equations (1) and (2), combined with Biot-Savart's law, the Possion vector equation, and boundary conditions, the magnetic field variables can be solved. The resulting finite element solution equation for the HALL sensor magnetic field is:
----（3）
Where: [υr]: Relative magnetic reluctance tensor of the magnetic material (m/H)
4. Simulation Analysis of Sensor Magnetic Field Based on FLUX
4.1 Finite Element Analysis of FLUX Electromagnetic Field
FLUX is a powerful field finite element analysis tool produced by the French company CEDRAT. It can perform simulation analysis of magnetic field, electric field, thermal field and the coupling field between them, and is widely used in various industrial fields. Its magnetic field simulation analysis function is particularly powerful, providing a complete set of simulation optimization schemes [3].
Figure 3. Flowchart of FLUX magnetic field simulation analysis
The magnetic field simulation process of FLUX is shown in Figure 3. The software itself has bottom-up 3D modeling capabilities and can also import models created by other 3D software. There are various methods and types for meshing and dividing 3D models. The software provides various mesh element elements such as point elements, line elements, and volume elements, and allows designers to select specific meshing methods based on their focus. Different application environments require different magnetic materials. The HALL sensor has strict material requirements; to improve the simulation accuracy, multiple parameters need to be configured during the physical property setting process to fit the B(H) variation curve. Materials can also be imported from an existing material library into the analysis program. FLUX has a powerful and flexible customizable PyFlux programming language, providing programming capabilities from model creation and mesh creation to setting physical property boundary conditions. Designers can flexibly develop programs to implement specific functions according to requirements.
The FLUX software solves equations (1), (2), and (3) in both linear and nonlinear forms. For time-varying systems (ignoring assumption 1), the Euler solver is used. The magnetic circuit of the HALL sensor typically operates in the linear region. The software provides the SuperLU linear direct solver, a free Gaussian elimination algorithm module written in ANSI/C that can solve 2D and 3D models. Furthermore, FLUX offers various adaptive iterative solvers to address the symmetry and asymmetry of the model: CG, BiCG, BiCGStab, and GMRES, along with corresponding solver parameter adjustments.
To accurately reflect the distribution of the sensor's magnetic field, nonlinear solutions are often used for verification analysis. The Newton-Rapsen algorithm is widely used for solving nonlinear magnetic fields, but its convergence cannot be guaranteed. FLUX uses an improved Newton-Rapsen algorithm to efficiently perform magnetic field analysis and calculation.
To facilitate the study and analysis of the calculation results, the software provides powerful post-processing functions, offering various display processing options for spatial vector values of points, lines, surfaces, volumes, and domains: cross-sections, grids, paths, charts, and more.
4.2 Example of Hall Sensor Simulation Analysis [3][4]
Figure 4. Structure and finite element mesh of the VV200-P current sensor.
The magnetic circuit of a magnetically compensated hall current sensor is crucial for its effective operation. Its core material is permalloy, characterized by high permeability and low BS saturation. When the measured current IP is large, the magnetic material easily saturates. At this point, the sensor's output can no longer maintain a linear relationship with the measured current on the primary side, and may even become severely distorted, causing various performance indicators to exceed tolerances. This provides erroneous and distorted signals to the control system of the entire electrical equipment, leading to malfunctions. The magnetic analysis method described above can effectively avoid this situation, allowing for the design of sensors that meet application requirements. The following analysis uses a series of hall current sensors from LEM Company as an example to illustrate the magnetic circuit and magnetic field.
LEM is a renowned international multinational corporation, a pioneer and inventor of power electronic sensors, specializing in the design, development, and production of electrical sensors. The sensor used in this example is a widely used LEM sensor in industrial control, with a measurement range of 200A. Figure 4 shows its 3D core structure and finite element mesh. Its initial design was a rectangular, uniform cross-sectional area structure. However, magnetic field analysis revealed that the core was already saturated when measuring the rated IPN, causing the sensor parameters to exceed specifications. The improved design adopted an approximately rectangular, variable cross-sectional area structure, as shown in Figure 4-A.
In the analysis of the magnetic field distribution of the sensor, it is necessary to correlate the sensor's magnetic circuit. Due to the structural requirements of the sensor's manufacturing process, there are through holes in the magnetic core structure, forming a local magnetic loop, which is different from the main magnetic circuit of the system (Figure 2). This complicates the analysis process and affects the accuracy of the analysis results. Therefore, it is necessary to cut the magnetic core model into magnetic circuits, as shown in Figure 4-B, where the red curved surface is the cutting surface.
Based on the characteristics of the magnetic core structure, an appropriate infinite boundary volume is selected to constrain the solution region, as shown in the cuboid in Figure 4-C. This represents the boundary region, and its size can be set according to visual proportions. The mesh division should vary depending on the object of study. For the compensation coil and the measured current conductor, FLUX calculates based on the magnetomotive force source without considering the magnetic field distribution inside the conductor. This greatly optimizes the calculation process (Figure 4-D).
The linear solver was used to solve the 200-ampere sensor problem, and the calculation results are shown in Figure 5. From the color map of the magnetic field distribution in the sensor core (Figure 5-A), it can be seen that the maximum magnetic field in the core is 0.7 < 0.8 T, which does not reach saturation and meets the measurement range requirements. Simultaneously, the FLUX post-processing provides a color map of the magnetic field cross-section distribution. The XY and XZ cross-sectional magnetic fields in Figure 5-B can be used to analyze the magnetic field distribution characteristics inside and around the magnet. The magnetic field distribution trend diagram in the XYZ direction of the HALL device air gap (Figure 5-C) shows that the magnetic field is very weak, verifying that the HALL device plays the role of inducing zero magnetic flux. The above simulation analysis results are completely consistent with the actual experimental application of the sensor.
Figure 5. Post-processing diagram of sensor magnetic field calculation results.
5. Conclusion
FLUX software boasts powerful magnetic field analysis capabilities, offering comprehensive simulation analysis and post-processing functions. Magnetic simulation analysis based on this software effectively addresses the inefficiency and limitations of traditional current sensor design relying on experience. The effectiveness of this simulation process was verified through magnetic field simulation analysis of a LEM 200-ampere magnetically compensated current sensor. This demonstrates its significant role in improving the quality and reliability of current sensors, enhancing the efficiency and speed of product design and development, and strengthening the company's responsiveness to the market. Furthermore, it improves the reliability of electrical equipment using these sensors, which is of great importance to the entire power application field.
About the author:
Yan Siyu, male, born on November 29, 1975, from Luoyang, ID number: 410305197511292516.
Master's degree, major research area: industrial control and simulation
Five papers have been published.
Contact information: 15202931250 (M). [email protected]
