A low-voltage contactor dynamic characteristic autonomous simulation system and method

Abstract

The application provides a low-voltage contactor dynamic characteristic autonomous simulation system and method, and the system comprises a motion module, a circuit module and a finite element simulation module.The method comprises the following steps: the finite element simulation module is used for simulating and calculating the current position and current of the contactor moving iron core, the latest electromagnetic attraction data of the contactor moving iron core is transmitted to the motion module, and the latest coil inductance value calculated according to the magnetic field is transmitted to the circuit module.The motion module calculates the displacement of the next time step according to the current resultant force and transmits the displacement to the finite element simulation module for real-time updating.The circuit module calculates the current of the next time step according to the current inductance and current and outputs the current so as to perform the cycle iteration of the next time step.The application does not need to calculate all possible coil currents and moving iron core displacements, thereby greatly improving the calculation efficiency.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of contactors, and particularly relates to a low-voltage contactor dynamic characteristic autonomous simulation system and method. BACKGROUND

[0002] In recent years, under the driving of the strategic goal of "carbon peak and carbon neutralization", the new energy industry has rapidly risen in China. As a key electrical equipment in the field of automatic control, the contactor, which has high economic benefits and good effects, is widely used in the fields of power systems and new energy automobile manufacturing. The technology of the contactor is therefore replaced frequently. If a new reliable contactor is to be designed, the dynamic characteristics thereof need to be simulated. However, the current electromagnetic simulation software in China lacks in-depth research on the simulation module of the dynamic characteristics of the contactor, and the traditional interpolation method is usually used for simulation calculation of the dynamic characteristics of the contactor. This method has a long calculation time and poor flexibility. SUMMARY

[0003] To solve the above problems, the application proposes an autonomous electromagnetic contactor simulation calculation idea, designs a circuit-motion-electromagnetic mechanism full-coupling simulation method framework through an algorithm module developed autonomously, so as to achieve a contactor dynamic characteristic simulation method based on real-time calculation, and make up for the defects of long simulation time and poor flexibility of the interpolation method for calculating the dynamic characteristics of the contactor.

[0004] The technical solution adopted by the application to solve the technical problems is:

[0005] A low-voltage contactor dynamic characteristic autonomous simulation system, comprising: a finite element simulation module, a circuit module, and a motion module.

[0006] The finite element simulation module is used for simulation calculation of the current position and current of the contactor moving core, and respectively transmits the current position and current to the motion module and the circuit module.

[0007] The motion module is used for calculating the displacement of the next time step according to the current position of the contactor moving core and transmitting the displacement to the finite element simulation module for real-time updating.

[0008] The circuit module is used for calculating the current of the next time step according to the current and outputting, so as to perform a loop iteration of the next time step.

[0009] Preferably, the circuit module is excited by a current source.

[0010] Preferably, the current source excitation can calculate the current without inductors, capacitors, resistors and other elements.

[0011] Preferably, the circuit module is excited by a non-current source.

[0012] Preferably, the non-current source excitation exists a dynamic calculation process.

[0013] Preferably, the dynamic calculation process comprises:

[0014] The latest electromagnetic force and the latest inductance are calculated through electromagnetic field equations;

[0015] If the simulation time is less than the specified cutoff time at this time, the latest electromagnetic force and the latest current are substituted into the motion module and the circuit module respectively, the latest position at the current time is calculated according to the contactor moving iron core position at the last time, and the latest current value is obtained by iterative solution according to the contactor coil current value at the last time and the voltage value at the current time;

[0016] The latest current value and the latest position parameter of the contactor moving iron core are transmitted to the finite element simulation module again, the finite element simulation module updates the model according to the latest position of the contactor moving iron core, and the electromagnetic field simulation calculation is carried out according to the latest current value, and the process is repeated until the simulation time is less than the specified cutoff time.

[0017] The application also provides a low-voltage contactor dynamic characteristic self-own simulation method, which comprises:

[0018] The finite element simulation module simulates the current position and current of the contactor moving iron core, and transmits them to the motion module and the circuit module respectively;

[0019] The motion module calculates the displacement of the next time step according to the current position of the contactor moving iron core and transmits the displacement to the finite element simulation module for real-time updating;

[0020] The circuit module calculates the current of the next time step according to the current and outputs it for the next time step of the cycle iteration.

[0021] Preferably, the circuit module can be excited by a current source or a non-current source.

[0022] Preferably, the current source excitation can calculate the current without inductance, capacitance and resistance elements.

[0023] Preferably, the non-current source excitation exists a dynamic calculation process, comprising:

[0024] The latest electromagnetic force and the latest inductance are calculated through electromagnetic field equations;

[0025] If the simulation time is less than the specified cutoff time at this time, the latest electromagnetic force and the latest current are substituted into the motion module and the circuit module respectively, the latest position of the contactor moving iron core is calculated according to the position of the contactor moving iron core at the last time, and the latest current value is obtained by iterative solution according to the contactor coil current value at the last time and the voltage value at the current time;

[0026] The latest current value and the latest position parameter of the contactor moving iron core are transmitted to the finite element simulation module again, the finite element simulation module updates the model according to the latest position of the contactor moving iron core, and the electromagnetic field simulation calculation is carried out according to the latest current value, and the process is repeated until the simulation time is less than the specified cutoff time.

[0027] The application also discloses a computer storage medium, wherein the storage medium comprises computer instructions, and when the computer instructions are run on a computer, the computer instructions make the computer execute the method in any one of the preceding aspects.

[0028] The application also discloses an electronic device, wherein the electronic device comprises a memory, a processor and a computer program stored on the memory and executable on the processor, and when the processor executes the program, the method in any one of the preceding aspects is implemented.

[0029] The technical advantages of the application are as follows:

[0030] 1) Nowadays, interpolation method is mostly used in the dynamic simulation of contactors in China, and the interpolation method has the inherent defect of long calculation time. The dynamic simulation method based on real-time calculation of the application greatly speeds up the iterative calculation speed by combining real-time finite element calculation with circuit equations and motion equations, and well makes up for the defect.

[0031] 2) The application deeply considers the influence of the inductance of the coil on the loop current, the electromagnetic force and the movement state of the coil under the excitation of the voltage source, and builds a more accurate algorithm. Compared with the traditional interpolation method, the method is more accurate in calculation.

[0032] 3) The traditional interpolation method has the disadvantage of poor flexibility, and after the circuit parameters are changed, the cumbersome fitting calculation needs to be performed again. The application can quickly iterate as usual when the initial conditions are changed through real-time parameter output and reading, and well makes up for the defect.

[0033] 4) The application establishes different circuit equations for different types of different excitation sources such as current source circuit, first-order voltage source circuit, second-order capacitor power supply circuit and second-order double-winding voltage source circuit, considers comprehensively, and is suitable for most contactor coil circuits. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1This is a simulation logic diagram of the overall dynamic characteristics of a contactor based on real-time calculation in one embodiment of the present invention;

[0035] Figure 2 This is a basic finite element one-dimensional schematic diagram in one embodiment of the present invention;

[0036] Figure 3 This is a basic two-dimensional finite element diagram in one embodiment of the present invention;

[0037] Figure 4 This is a basic finite element three-dimensional schematic diagram in one embodiment of the present invention;

[0038] Figure 5 This is a flowchart of the overall process of contactor dynamic simulation current source excitation based on real-time calculation in one embodiment of the present invention;

[0039] Figure 6 This is a flowchart of the overall process of non-current source excitation for contactor dynamic simulation based on real-time calculation in one embodiment of the present invention;

[0040] Figure 7 This is a flowchart illustrating the motion module algorithm implementation in one embodiment of the present invention;

[0041] Figure 8 This is a flowchart illustrating the algorithm implementation of the circuit module in one embodiment of the present invention;

[0042] Figure 9 This is a current calculation result using different multiples of the time constant as the iteration step size in one embodiment of the present invention. Detailed Implementation

[0043] The following will refer to the appendix. Figures 1 to 9 Specific embodiments of the invention are described in detail below. While specific embodiments of the invention are shown in the accompanying drawings, it should be understood that the invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the invention and to fully convey the scope of the invention to those skilled in the art.

[0044] It should be noted that certain terms are used in the specification and claims to refer to specific components. Those skilled in the art will understand that different terms may be used to refer to the same component. This specification and claims do not distinguish components based on differences in terminology, but rather on differences in function. The terms "comprising" or "including" used throughout the specification and claims are open-ended and should be interpreted as "comprising but not limited to." The following descriptions are preferred embodiments for carrying out the invention; however, these descriptions are for the purpose of understanding the general principles of the specification and are not intended to limit the scope of the invention. The scope of protection of this invention is determined by the appended claims.

[0045] To facilitate understanding of the embodiments of the present invention, further explanations and descriptions will be provided below with reference to the accompanying drawings and specific embodiments. The accompanying drawings do not constitute a limitation on the embodiments of the present invention.

[0046] This invention provides an autonomous simulation system for the dynamic characteristics of low-voltage contactors, comprising: a finite element simulation module, a circuit module, and a motion module;

[0047] The finite element simulation module is used to simulate and calculate the current position and current of the contactor's moving iron core, and then transmits the data to the motion module and the circuit module, respectively.

[0048] The motion module is used to calculate the displacement of the next time step based on the current position of the contactor's moving iron core and transmit the displacement to the finite element simulation module for real-time updating.

[0049] The circuit module is used to calculate and output the current for the next time step based on the current, thereby performing a cyclic iteration for the next time step.

[0050] This invention also provides an autonomous simulation method for the dynamic characteristics of low-voltage contactors, such as... Figure 1 As shown, this method is jointly implemented by a motion module, a circuit module, and a finite element simulation module. The circuit and motion modules are implemented through independent compilation, and the algorithm is coupled with the finite element simulation module. The finite element simulation module is responsible for simulating and calculating the current position and current of the contactor's moving iron core using the finite element method, transmitting the latest electromagnetic attraction data of the contactor's moving iron core to the motion module, and transmitting the latest coil inductance value calculated based on the magnetic field to the circuit module. The motion module is responsible for calculating the displacement for the next time step based on the current resultant force (electromagnetic attraction + spring reaction force) and transmitting this displacement to the finite element simulation module for real-time updates. The circuit module needs to calculate the current for the next time step based on the current inductance and current and output it for iterative iteration of the next time step.

[0051] It should be noted that the development logic for current source excitation and non-current source excitation differs for different circuit modules.

[0052] For current source excitation, since the current is usually a function of time, it can be calculated without the need for components such as inductors, capacitors, and resistors. At the initial moment, the time can be directly substituted into the equation of current with respect to time to directly solve for the initial current.

[0053] In subsequent iterations, the latest current value is substituted into the electromagnetic field equation to calculate the latest electromagnetic attraction force under the current displacement value of the moving iron core. Then, it is determined whether the iteration time has exceeded the set total simulation time. If it has, the simulation process ends. If it has not, the latest electromagnetic attraction force is passed to the motion module. The motion module calculates the displacement value within the simulation step size, and the circuit module calculates the latest current value at the next moment. The latest current value and the latest displacement value of the moving iron core are passed to the finite element model again to update the position of the finite element model. Electromagnetic field simulation calculation is performed based on the latest current value. This process is repeated until the simulation time t exceeds the set total simulation time T.

[0054] In one embodiment, the finite element preprocessing section includes the following steps:

[0055] 1. Regional Discretization

[0056] Let the region be Ω. In any finite element analysis, region discretization is the first and most important step, as the method of discretization affects computer memory requirements, computation time, and the accuracy of numerical results. In this step, the global region Ω is divided into many smaller regions, denoted by I (e=1,2,3,…,M), where M represents the total number of subdomains. These subdomains are usually called elements. For a one-dimensional region that is actually a straight line or curve, the elements are typically short straight line segments that connect to form the original line domain (see…). Figure 1 For two-dimensional regions, the units are typically small triangles or rectangles (see...). Figure 2 In 3D solutions, the region can be divided into tetrahedral, triangular prism, or rectangular blocks (see...). Figure 3 ( ), among which the tetrahedron is the simplest and most suitable unit for discretizing arbitrary volume regions.

[0057] In most finite element solutions, the problem is expressed using unknown functions at the nodes associated with the element. For example, a linear wire element has two nodes, one at each endpoint; a linear triangular element has three nodes, one at each vertex; and a linear tetrahedral element has four nodes, one at each corner. A complete description of a node should include its coordinates, local code, and global code. The local code of a node indicates its position within the element, while the global code indicates its position within the entire system.

[0058] 2. Select the interpolation function

[0059] The second step in finite element analysis is to select an interpolation function that can approximate the unknown solutions in an element. Typically, the interpolation function can be a first-order (linear), second-order (quadratic), or higher-order polynomial. Although higher-order polynomials offer higher accuracy, the resulting formulas are usually more complex. Therefore, simple and basic linear interpolation is still widely used. Once the order of the polynomial is selected, we can derive an expression for the unknown solutions in an element. Taking element e as an example, we obtain the following form:

[0060] (1)

[0061] Where n is the number of nodes in the unit; The trial function representing the unit; It is the j node in the cell. value; It is an interpolation function, characterized by being non-zero only inside element e, and zero outside the element. N e φ represents the matrix formed by the interpolation functions. e This represents the matrix formed by the trial functions of the unit.

[0062] 3. Establish a system of equations

[0063] A typical programming problem can be defined using the governing differential equations within the region Ω and the boundary conditions on the boundary Γ enclosing the region Ω. The differential equations can be expressed as:

[0064] (2)

[0065] in Here, f is the differential operator, and f is the excitation or imposed function. These are unknowns. Boundary conditions include Dirichlet conditions, Norman conditions, or even more complex conditions. In engineering, it is difficult to obtain analytical solutions to the equations, so various approximation methods are sought, among which the Ritz method and the Galerkin method are the most widely used.

[0066] Derive the solution to the system of equations using the Galerkin method:

[0067] For equation (2), the weighted residual of the e-th unit is:

[0068] (3)

[0069] Substituting equation (1) into equation (3):

[0070] (4)

[0071] Written in matrix form:

[0072] (5)

[0073] Among them, [K e ] is called the element stiffness matrix, {b e} is related to the excitation. Since the expansion function related to a node covers all units directly connected to that node, we can extend equation (5) by utilizing the relationship between local and global encoding, and then sum it over each unit:

[0074] (6)

[0075] At this point, by setting the residual {R}={0}, we can obtain:

[0076] (7)

[0077] Therefore, it can be written as:

[0078] (8)

[0079] Here, [K] can be called the overall stiffness matrix.

[0080] Before a definite solution can be obtained from equation (8), the required boundary conditions must be applied. Two types of boundary conditions frequently appear: one is the Dirichlet boundary condition, which gives the boundary conditions at the boundary. Another type is the homogeneous Norman boundary condition, which requires that the boundary value be equal to the mean value. The normal derivative is zero. First-type boundary conditions are necessary boundary conditions and must be explicitly imposed in the calculation; second-type boundary conditions are usually implicitly satisfied during the solution process. For this reason, second-type boundary conditions are often called natural boundary conditions.

[0081] As can be seen, this step actually involves three sub-steps. First, the Galerkin method is applied to write the element equation (5). Second, the element equation is summed over all elements to obtain the system of equations; this process is called combination. Finally, boundary conditions are applied to obtain the final form of the system of equations. Note: In the process of implementing this calculation using a computer, these three sub-steps are usually not separate; on the contrary, they are intertwined. The generation of the element matrix and the imposition of boundary conditions usually occur during the combination process.

[0082] 4. Solve the system of equations

[0083] After solving equation (8), the following parameters are further calculated: capacitance, inductance, electromagnetic force, etc. Among them, in solving the three-dimensional static magnetic field, the unknown quantity to be solved is the vector magnetic potential A. After solving according to the above method, the magnetic potential [A] = [A] of each node is obtained. x Ay A z Post-processing is required to obtain the desired electromagnetic force and inductance.

[0084] like Figure 5 As shown, in one embodiment, the overall process of dynamic simulation current source excitation for contactors based on real-time calculation includes the following steps:

[0085] The first step is to perform initialization, setting the current time t=0 and the current displacement x=x0.

[0086] The second step is to substitute the current time t into the circuit equation to obtain i(t), and then output the value of i as a text file. For example, if a sinusoidal AC current source with a single-coil winding is required, only the current amplitude i needs to be given. m Given the frequency f and the initial phase angle θ, we can program i(t) = i m The function *sin(2*pi*f*t+θ) directly calculates the current value at the current moment. If it's the initial moment, substitute t=0.

[0087] The third step involves reading the current current and using the finite element method to calculate the electromagnetic field and electromagnetic force F based on the current model. For example, the vector magnetomotive force [A] = [A] at each finite element node at the current moment is solved using the finite element preprocessing step. x A y A z The magnetic flux density B at that moment can be obtained by taking the curl of the vector magnetic potential A:

[0088] (9)

[0089] in and Let j be the magnetic flux density and vector magnetomotive force of node j. After obtaining the magnetic flux density of each node, take the arithmetic mean as the average magnetic flux density of the element. :

[0090] (10)

[0091] For a homogeneous medium, the electromagnetic force f acting on the element e This can be simplified to the gradient of energy density W:

[0092] (11)

[0093] For a uniform object in an electromagnetic field, the total electromagnetic force can be obtained by integration, and its discrete form is:

[0094] (12)

[0095] Where f e For a single element subjected to force, V e Let F be the unit volume. From this, we can obtain the calculation results of the electromagnetic force F acting on the moving iron core at that moment.

[0096] The fourth step is to determine whether the current time t exceeds the specified deadline T. If it does not exceed the deadline T, the motion module algorithm reads the electromagnetic attraction force F calculated in the third step, calculates the displacement x of the moving iron core according to Newton's second law based on the spring reaction force, and updates the current time to t+Δt. If it exceeds the deadline T, the algorithm ends.

[0097] The fifth step is to update the geometric model based on the displacement x of the moving iron core at the current time step, and then return to the second step for iteration, repeating the process.

[0098] For non-current source excitation, the circuit module is typically excited by voltage sources or capacitor discharge, among other forms. The coil current is not only a function of time but also depends on other factors. Therefore, the current value cannot be obtained directly and must be calculated iteratively within the current time step. During the iteration process, since the permeability of the contactor core is usually nonlinear, the coil inductance also changes with the core saturation level and the relative position of the moving core. Therefore, for the iterative process of the coil current, the inductance at each moment needs to be calculated to ensure accuracy.

[0099] like Figure 6 As shown, in another embodiment, the overall process of non-current source excitation for contactor dynamic simulation based on real-time calculation includes the following steps:

[0100] The first step is to perform initialization: set the current time t=0, the current displacement x=x0, and the initial current i=0.

[0101] The second step involves calculating the electromagnetic field using the finite element method based on the current model and current i, obtaining the coil inductance L and electromagnetic force F. For example, the vector magnetomotive force [A] = [A] at each finite element node at the current moment is solved using the finite element preprocessing section. x A y A z The magnetic flux density B at that moment can be obtained by taking the curl of the vector magnetic potential A:

[0102] (13)

[0103] in and Let j be the magnetic flux density and vector magnetomotive force of node j. After obtaining the magnetic flux density of each node, take the arithmetic mean as the average magnetic flux density of the element. :

[0104] (14)

[0105] For a homogeneous medium, the electromagnetic force f acting on the element e This can be simplified to the gradient of energy density W:

[0106] (15)

[0107] For a uniform object in an electromagnetic field, the total electromagnetic force can be obtained by integration, and its discrete form is:

[0108] (16)

[0109] Where f e For a single element subjected to force, V e Let F be the unit volume. From this, we can obtain the calculation results of the electromagnetic force F acting on the moving iron core at that moment.

[0110] For example, the vector magnetomotive force [A] = [A] of each finite element node at the current time is solved based on the finite element preprocessing part. x A y A z The inductance L is usually calculated by dividing the magnetic flux of the coil by the current.

[0111] (17)

[0112] Where I is a known quantity, and the magnetic flux φ m Then it needs to be calculated. If there are s volume elements passing through a certain cross-section of the coil, and according to the formula... and The average magnetic flux density of each volume element, φ, can be obtained. m The calculation can be performed as follows:

[0113] (18)

[0114] Among them, B i Let S be the average magnetic flux density of the i-th volume element passing through the cross-section of the coil. i Let be the projected area of ​​the volume element passing through the cross-section of the coil on the interface. Combining the above two equations:

[0115] (19)

[0116] From this, the calculation result of the coil inductance L can be obtained.

[0117] The third step is to determine whether the current time t has exceeded the specified deadline T. If it has not, the circuit module algorithm reads the current current i. n The current inductance L and other necessary parameters (such as the inductance L in the previous step)last ), calculate the next current i n+1 Simultaneously, the motion module algorithm reads the current electromagnetic force F, calculates the displacement x of the moving iron core based on the spring reaction force, updates the geometric model, and finally updates the current time to t + Δt; if this time is exceeded, the algorithm terminates.

[0118] Fourth step: Return to second step and repeat the loop.

[0119] In summary, for the dynamic calculation process under non-current source excitation conditions, the latest electromagnetic attraction force F and the latest inductance L are first calculated using the electromagnetic field equations. Then, if the simulation time is less than the total simulation time, the latest electromagnetic attraction force and the latest current are substituted into the motion and circuit equation modules respectively. Based on the contactor's moving iron core position at the previous moment, the latest position at the current moment is calculated. The latest current value is obtained by iteratively solving based on the contactor coil current value at the previous moment and the voltage value at the current moment. Finally, the latest current value and the latest position parameters of the contactor's moving iron core are passed back to the simulation software. The simulation software updates the model based on the latest position of the contactor's moving iron core and performs electromagnetic field simulation calculations based on the latest current value. This process is repeated until the simulation time t is less than the total simulation time T.

[0120] It is worth noting that the order of iteration of the circuit equations differs between the two different power supply models of non-current source excitation and current source excitation. However, regardless of the two, it is necessary to ensure that each time corresponds to only one electromagnetic attraction force, one contactor coil inductance value, one contactor coil current value, and one moving iron core displacement value.

[0121] The purpose of building the motion module is to calculate the displacement and velocity changes of the model over time, thereby coupling it with the finite element model and the circuit model. There are two main motion modes of the contactor's moving iron core: linear translation and rotation around a fixed axis. Since the algorithms for these two motion modes are logically very similar, the following explanation will focus on the linear motion scenario.

[0122] The first step is for the algorithm script to read the parameter information from a text file (obtained from the initial parameters given by the user and the parameters output from the previous iteration), and import the displacement, velocity, end time of the previous iteration, the specified maximum and minimum displacement values, time step, deadline time, and electromagnetic attraction force of the previous iteration.

[0123] The second step is to determine whether the moving core meets the motion conditions before starting the iteration at the current time step. If the direction of the resultant force on the moving core is positive and the moving core has reached the maximum value of the positive displacement, the algorithm determines that it cannot continue moving. The same logic applies to the negative direction. At this time, the algorithm should set the velocity and displacement of the moving core to 0.

[0124] The third step, according to Newton's second law, can be listed as follows:

[0125] (1.2)

[0126] Where a is the acceleration of the moving iron core / m·s -2 λ is the damping coefficient / N·s·m -1 ;v n The current time is the speed of the stepping iron core in m·s. -1 ;v n+1 The next time stepping core speed / m·s -1 ;x n x represents the displacement of the moving core at the current time step in meters. n+1 F represents the displacement of the moving core in the next time step (in meters). f Δt is the spring reaction force in N; F is the electromagnetic attraction force in N; Δt is the current time step; m is the mass of the moving iron core in kg.

[0127] Except for the spring reaction force, which is fitted using a script in the algorithm by inputting data points from the user, all other parameters can be obtained from a text file. The spring reaction force is linearly related to the displacement magnitude; however, since the pre-defined spring reaction force coordinates are discrete, they usually cannot correspond to the current displacement. Therefore, a fitting function must be used to calculate the current spring reaction force. Here, a first-order linear interpolation fitting method is used to express the reaction force as a function of displacement x only:

[0128] (1.3)

[0129] Where x1 and x2 are the two displacement coordinate values ​​among the pre-set spring reaction force coordinate points that are closest to the current displacement, F f (x1), F f (x2) represents the magnitude of the spring reaction force corresponding to these two displacement coordinates. X represents the displacement at the current moment. From this, F can be fitted. f After the algorithm completes this iteration and obtains new displacement data, it updates the current time and transmits the displacement data to the finite element module. The finite element module should then update the model's position and proceed to the next iteration.

[0130] When setting iteration conditions, there may be cases where the deadline is not an integer multiple of the simulation step size. The following example illustrates how to handle this situation. If the simulation step size is 0.3s and the total simulation time is 1s, when the simulation time reaches 0.9s, since the simulation time is less than the total simulation time of 1s, another iteration will be performed, ultimately resulting in a total simulation time of 1.2s. This not only exceeds the user-set length but also causes more displacement of the contactor's moving iron core due to the extra 0.2s. To address this, the algorithm will determine whether the current time exceeds the simulation termination time during final processing. If it does, it needs to calculate the excess time and correct for the extra calculated moving iron core displacement and velocity during this period to obtain the data at the simulation termination time.

[0131] After calculating the motion equations, the displacement of the moving core at the current moment may exceed the range encompassed by the maximum positive or negative displacement. This not only fails to meet the user-defined displacement range for the moving core but may also cause the moving core component to overlap with other components of the model, leading to an overall simulation error. Therefore, it is necessary to compare the moving core displacement result calculated at the current step size with the previously set maximum positive and maximum negative displacements. If the moving core displacement is greater than the maximum positive displacement, its displacement value is reset to the maximum positive displacement value; if the moving core displacement is less than the maximum negative displacement, its displacement value is reset to the maximum negative displacement value, and the moving core velocity in both cases is reset to 0.

[0132] like Figure 7 As shown, in another embodiment, the motion module algorithm implementation process includes the following steps:

[0133] In the first step, the iterative algorithm obtains parameter information such as electromagnetic attraction force F and displacement x of the moving iron core from the finite element module and the text file saved from the previous iteration.

[0134] The second step is to determine whether the motion conditions are met based on the spring reaction force. If the position is at the maximum positive displacement and the resultant force is in the positive direction, or at the maximum negative displacement and the resultant force is in the negative direction, then the motion conditions are not met, the displacement remains unchanged, the velocity is set to 0, the time is updated to t+Δt, and finally, the process jumps to the fourth step. If the motion conditions are met, the process jumps to the third step.

[0135] The third step is to write the equation of motion based on Newton's second law, calculate the displacement x and velocity v at the next moment under the current force, and update the time t+Δt.

[0136] The fourth step is to perform post-processing of the calculated data to correct any overflowing displacement data.

[0137] The fifth step is to change the position of the moving iron core based on the calculated x data and update the geometric model.

[0138] The purpose of building the circuit module is to calculate the magnitude of the coil current, and then couple it with the algorithms of the finite element module and the motion module. After the algorithm reads the parameters from the text file (different circuit types will have different calculation methods, but the overall logic is the same), the algorithm script of the circuit module can then perform iterative calculations.

[0139] The flowchart of the circuit module algorithm implementation is as follows: Figure 8 As shown, after the algorithm obtains the necessary circuit parameter information, if it finds that the set time step is too long, the algorithm will refine the time step to pursue high-precision calculation. The current obtained through iteration is then passed to the finite element module and the motion module for subsequent inductance and electromagnetic attraction calculations. For example, the circuit module algorithm implementation process includes the following steps:

[0140] The first step involves the iterative algorithm obtaining the inductance L and the previous current i from the finite element module and the text file saved from the previous iteration. n Parameter information, etc.

[0141] The second step is to divide the specified time step Δt into segments based on the circuit time constant with Δm, and set the current time m=0.

[0142] The third step is to determine whether the time step size Δm is less than the time step size Δt to be divided. If Δm is less than Δt, then the current i is calculated using the fourth-order Runge-Kutta method with the time step size Δm as the time step. n+1 Then update the time m = m + Δm; if Δm is greater than Δt, then use Δt as the time step to perform the above Runge-Kutta method iteration and then jump to the fifth step.

[0143] The fourth step is to determine whether the iterative calculation for the current time step has been completed, i.e., m is greater than Δt. If m is less than Δt, the calculation is not complete, and the process returns to the third step to continue iterative calculation; if m is greater than Δt, the calculation is complete, and post-processing is performed to correct the overflowed time step.

[0144] The fifth step is to save the calculated current value to a local text file and then pass it to the finite element module.

[0145] For cases where a current source is used as the excitation, the current source is directly connected in series with the contactor coil, and the circuit module algorithm can solve the problem using the current analytical formula. However, the cases where capacitor discharge and voltage sources are used as the excitation are different. The circuit module algorithm script does not directly write out the circuit analytical formula for current calculation. Although this method is simpler, the main magnetic circuit of the coil is generally composed of nonlinear ferromagnetic materials, so the coil inductance will change with the current (changes in the saturation degree of the ferromagnetic material). Furthermore, second-order circuits also have critical damping, overdamping, and underdamping conditions, and the formula method cannot guarantee correct analysis for every case. This invention, based on first-order circuit voltage sources, second-order circuit capacitor discharge, and second-order circuit voltage source cases, has developed iterative programs for circuit equations under different conditions and uses the fourth-order Runge-Kutta method for iterative solution.

[0146] For certain circuit parameters, directly using the user-specified simulation time step for iterative calculation may lead to significant errors. Therefore, the iterative program in this circuit module needs to pre-divide the relatively long simulation time step given by the user. Although this adds an iterative calculation step, the iterative process only occurs within the circuit module algorithm, resulting in fast calculation speed and eliminating the need for additional static simulation. For loops with different parameters, the most common method for determining the iteration step is through the circuit's time constant. To determine the feasibility of this approach, tests were conducted using different multiples of the time constant as the iteration step. A circuit example with a 10V DC voltage source, a 0.3Ω resistor, and a 1.8H coil inductor was used for illustration. The time constant of this circuit was 6, iterating from 0s to 24s. The test results are as follows. Figure 9 As shown:

[0147] This case study employed five different time steps: 3 times the time constant, 2.5 times the time constant, 2 times the time constant, 1 time constant, and 0.1 times the time constant. Clearly, as the iteration step size decreases, the simulation results increasingly approximate the accurate curve, and 1 time constant is already quite accurate as a step size. Therefore, using 1 time constant as a reference standard is feasible when determining whether the specified iteration step size is too large. During the splitting process, the time constant can also be divided into multiples of 10 as the iteration time steps.

[0148] It should be noted that the small step size division is not based on the user-defined simulation time step, but on the time constant. Therefore, when using the divided small step size for iterative calculations, additional post-processing steps are required. For example, if the simulation time step is 0.5s and the divided small step size is 0.2s, the actual time of this simulation time step after normal iteration is 0.6s, which does not match the user-defined value. Therefore, similar to the post-processing of the motion module, the extra 0.1s iteration step needs to be corrected. In the last iteration, the time step should be changed to 0.1s to ensure that the current result is the result after 0.5s. Only by making this modification can the actual simulation time step that matches the user's settings be obtained.

[0149] Based on the above discussion, this patent designs iterative algorithms for current source circuits, first-order voltage source circuits, second-order capacitor power supply circuits, and second-order voltage source dual-winding circuits.

[0150] 1 Current source circuit

[0151] The solution for the current source circuit is relatively simple. As mentioned above, this invention has built three calculation algorithms for current source excitation: DC current, AC current, and custom current. When using current source excitation, since the current flows directly through the coil, the coil current can be solved directly by the current source analytical expression without iteration. In the case of DC current, the coil current i(t) is equal to the power supply current is; in the case of AC current source, the circuit module algorithm will obtain the current simulation time in the parameter transfer step before the iteration starts, and the coil current value can be obtained by substituting the current simulation time into the expression of AC current; for custom current, based on the one-to-one time-current coordinate points input by the user, find the two closest time points t1 and t2 that contain the current simulation time t, and the currents i(t1) and i(t2) corresponding to these time points. The coil current value i(t) of the current step size can be solved by formula (1.4). This solution method is almost the same as the idea of ​​the spring reaction force on the contactor mentioned above, both of which use interpolation to fit the curve.

[0152] (1.4)

[0153] 2. First-order voltage source circuit

[0154] As mentioned above, this invention constructs six solution algorithms under different excitations for the first-order voltage source circuit, including DC voltage, AC voltage, square wave voltage, triangular wave voltage, custom voltage waveform (periodic), and custom voltage waveform (non-periodic). The circuit elements of the first-order circuit consist of a power supply, coil resistance, and coil inductance. Since the contactor coil is usually made of nonlinear ferromagnetic material, and the proportion of the air magnetic circuit decreases during the closing process of the moving iron core, the coil inductance value is not constant. It changes continuously with the current and the spatial position of the moving iron core. The circuit equation of the first-order circuit is shown in formula (1.5):

[0155] (1.5)

[0156] in The magnetic flux linked to the coil is represented by ; u is the voltage provided by the voltage source; i is the current in the circuit; R is the total resistance of the circuit; and L is the current inductance value.

[0157] Simplifying the equations in (1.5), we get:

[0158] (1.6)

[0159] In summary, the coil inductance changes continuously with the current and the distance between the moving and stationary iron cores. The inductance value L is obtained through finite element simulation. For dL / dt, the current inductance L is subtracted from the inductance L at the previous moment. last Dividing this by the time step Δt gives an approximate rate of change of the inductance, dL / dt. After simplification, we obtain the common first-order differential equation expression, as shown below:

[0160] (1.7)

[0161] In equation (1.7), the coefficients of the independent variable *i* and its derivative term are already determined, allowing the differential equation to be solved numerically. This invention employs the fourth-order Runge-Kutta method for solution, and the iterative expression for this method is as follows:

[0162] (1.8)

[0163] Among them, i n It is the current after the nth time step iteration, u is the current value of the power supply at the current moment, R is the total resistance of the circuit, and L is the current after the nth time step iteration. n Let L be the inductance at the nth time step. n-1 Let Δt be the inductance at the (n-1)th time step, and Δt be the time step size.

[0164] 3. Second-order capacitor power supply circuit

[0165] When a charging capacitor is used to power the contactor coil, the circuit elements of the second-order circuit consist of the coil inductance, the total circuit resistance, and the capacitor power supply. According to Kirchhoff's laws, the circuit equations satisfy the following formula:

[0166] (1.9)

[0167] Among them, u C Indicates capacitor voltage in V; u L This indicates the inductor voltage in V.

[0168] Equation (1.9) can be transformed into a differential equation with respect to the independent variable i, resulting in:

[0169] (1.10)

[0170] Where C is the capacitance value.

[0171] Similar to the first-order circuit, the second-order circuit is also solved using the fourth-order Runge-Kutta method. Equation (1.10) needs to be rearranged into an iterable form, transforming the second-order differential equation into a joint solution of two first-order differential equations, as shown below:

[0172] (1.11)

[0173] Where y1 represents the coil current; y2 represents the first derivative of the coil current.

[0174] From the formula, it can be deduced that to solve for the capacitor discharge of a second-order circuit using the Runge-Kutta method, two initial values ​​are needed: the current and the first derivative of the current with time. Due to the inductance of the coil, according to the switching law, the initial current is 0 when the circuit is switched on, and the initial voltage of the capacitor is entirely applied across the coil inductance. Therefore, the initial value of the first derivative of the current with time is the ratio of the initial voltage of the capacitor to the coil inductance. Thus, the complete iterative expression for solving the current in a second-order circuit can be written, as shown in formula (1.12).

[0175] (1.12)

[0176] Where R is the total circuit resistance (in Ω), C is the power supply capacitance (in F), and L is the coil inductance at the current moment (in H). y1(n) and y2(n) represent the values ​​of y1 and y2 after the nth iteration, and y1(n+1) and y2(n+1) represent the values ​​of y1 and y2 after the (n+1)th iteration.

[0177] Each iteration of the capacitor discharge calculation for a second-order circuit requires two initial values: the current and the first derivative of the current with respect to time. The variables that the finite element simulation module can pass to the circuit module algorithm are the current, the initial capacitor voltage, and the coil inductance. However, only the initial value of the first derivative of the current with respect to time can be calculated using the initial capacitor voltage and the coil inductance. Therefore, after each time step iteration, the algorithm needs not only to output the current value but also to save the latest value of the first derivative of the current with respect to time within that step for use in the next circuit equation iteration.

[0178] 4. Second-order voltage source dual-winding circuit

[0179] A second-order voltage source dual-winding circuit refers to a circuit where the excitation is a voltage source and two coil windings are connected in parallel. Ignoring the mutual inductance between the two windings, according to Kirchhoff's laws, we can write:

[0180] (1.13)

[0181] Where L1 and L2 are the current inductance values ​​of the two coil windings, I1 and I2 are the current values ​​of the two coil windings, R1 and R2 are the resistance values ​​of the branches containing the two coil windings, and R L This represents the load resistance value.

[0182] The above formulas are rearranged into expressions for differential equations. Considering the similarity between the solutions for I1 and I2, only the differential equation for I2 is listed here, as shown in formula (1.14).

[0183] (1.14)

[0184] Finally, following the approach of formula (1.12), formula (1.14) is transformed into a joint solution of two differential equations. Thus, the complete iterative expression for solving the second-order circuit of the voltage source with two windings can be written, as shown in formula (1.15):

[0185] (1.15)

[0186] Where R is the total circuit resistance (in Ω), C is the power supply capacitance (in F), and L is the coil inductance at the current moment (in H). y1(n) and y2(n) represent the values ​​of y1 and y2 after the nth iteration, y1(n+1) and y2(n+1) represent the values ​​of y1 and y2 after the (n+1)th iteration, and u is the voltage at the current moment.

[0187] The foregoing general description of the invention and its specific embodiments should not be construed as limiting the technical solution of the invention. Those skilled in the art, based on the disclosure herein, may add, reduce, or combine the disclosed technical features in the foregoing general description and / or specific embodiments (including examples) without departing from the constituent elements of the invention, to form other technical solutions within the scope of protection of this invention.

Claims

1. An autonomous simulation system for the dynamic characteristics of low-voltage contactors, characterized in that, The system includes: a finite element simulation module, a circuit module, and a motion module; The finite element simulation module is used to simulate and calculate the current position and current of the contactor's moving iron core, and then transmits the data to the motion module and the circuit module, respectively. The motion module is used to calculate the displacement of the next time step based on the current position of the contactor's moving iron core and transmit the displacement to the finite element simulation module for real-time updating. The circuit module is used to calculate and output the current for the next time step based on the current, thereby performing a cyclical iteration for the next time step. The motion module algorithm implementation process includes the following steps: The first step is to obtain the electromagnetic attraction force F and the displacement x parameter information of the moving iron core from the finite element module and the text file saved from the previous iteration. The second step is to determine whether the motion conditions are met based on the spring reaction force. If the position is at the maximum positive displacement and the resultant force is in the positive direction, or at the maximum negative displacement and the resultant force is in the negative direction, then the motion conditions are not met. The displacement remains unchanged, the velocity is set to 0, the time is updated to t+Δt, and finally, the process jumps to the fourth step. If the motion conditions are met, the process jumps to the third step. The third step is to write the equation of motion according to Newton's second law, calculate the displacement x and velocity v at the next moment under the current force, and update the time t+Δt. The fourth step is to perform post-processing of the calculated data and correct any overflowing displacement data. Fifth, change the position of the moving core based on the calculated x data and update the geometric model; The algorithm implementation process for the circuit module includes the following steps: The first step involves the iterative algorithm obtaining the inductance L and the previous current i from the finite element module and the text file saved from the previous iteration. n Parameter information; The second step is to divide the specified time step Δt into segments based on the circuit time constant with Δm, and set the current time m=0; The third step is to determine whether the time step size Δm is less than the time step size Δt to be divided. If Δm is less than Δt, then the current i is calculated using the fourth-order Runge-Kutta method with the time step size Δm as the time step. n+1 Then update the time m = m + Δm; if Δm is greater than Δt, then use Δt as the time step to perform the above Runge-Kutta method iteration and then jump to the fifth step; The fourth step is to determine whether the iterative calculation for the current time step has been completed, i.e., m is greater than Δt. If m is less than Δt, the calculation is not completed, and the process returns to the third step to continue the iterative calculation. If m is greater than Δt, the calculation is completed, and post-processing is performed to correct the overflowed time step. The fifth step is to save the calculated current value to a local text file and then pass it to the finite element module.

2. The system according to claim 1, characterized in that, The circuit module is excited by a current source.

3. The system according to claim 2, characterized in that, The current source excitation can calculate the current without the need for inductors, capacitors, and resistors.

4. The system according to claim 1, characterized in that, The circuit module is excited by a non-current source.

5. The system according to claim 4, characterized in that, The non-current source excitation involves a dynamic calculation process.

6. An autonomous simulation method for the dynamic characteristics of low-voltage contactors, characterized in that, The method includes: The finite element simulation module performs simulation calculations on the current position and current of the contactor's moving iron core, and transmits the results to the motion module and circuit module, respectively. The motion module calculates the displacement for the next time step based on the current position of the contactor's moving iron core and transmits the displacement to the finite element simulation module for real-time updating. The circuit module calculates and outputs the current for the next time step based on the current, so as to perform cyclic iteration for the next time step. The motion module algorithm implementation process includes the following steps: The first step is to obtain the electromagnetic attraction force F and the displacement x parameter information of the moving iron core from the finite element module and the text file saved from the previous iteration. The second step is to determine whether the motion conditions are met based on the spring reaction force. If the position is at the maximum positive displacement and the resultant force is in the positive direction, or at the maximum negative displacement and the resultant force is in the negative direction, then the motion conditions are not met. The displacement remains unchanged, the velocity is set to 0, the time is updated to t+Δt, and finally, the process jumps to the fourth step. If the motion conditions are met, the process jumps to the third step. The third step is to write the equation of motion according to Newton's second law, calculate the displacement x and velocity v at the next moment under the current force, and update the time t+Δt. The fourth step is to perform post-processing of the calculated data and correct any overflowing displacement data. Fifth, change the position of the moving core based on the calculated x data and update the geometric model; The algorithm implementation process for the circuit module includes the following steps: The first step involves the iterative algorithm obtaining the inductance L and the previous current i from the finite element module and the text file saved from the previous iteration. n Parameter information; The second step is to divide the specified time step Δt into segments based on the circuit time constant with Δm, and set the current time m=0; The third step is to determine whether the time step size Δm is less than the time step size Δt to be divided. If Δm is less than Δt, then the current i is calculated using the fourth-order Runge-Kutta method with the time step size Δm as the time step. n+1 Then update the time m = m + Δm; if Δm is greater than Δt, then use Δt as the time step to perform the above Runge-Kutta method iteration and then jump to the fifth step; The fourth step is to determine whether the iterative calculation for the current time step has been completed, i.e., m is greater than Δt. If m is less than Δt, the calculation is not completed, and the process returns to the third step to continue the iterative calculation. If m is greater than Δt, the calculation is completed, and post-processing is performed to correct the overflowed time step. The fifth step is to save the calculated current value to a local text file and then pass it to the finite element module.

7. The method according to claim 6, characterized in that, The circuit module can be excited by a current source or by a non-current source.

8. The method according to claim 7, characterized in that, The current source excitation can calculate the current without the need for inductors, capacitors, and resistors.

9. A computer storage medium, characterized in that, The storage medium includes computer instructions that, when executed on a computer, cause the computer to perform the method of any one of claims 6 to 8.

10. An electronic device, characterized in that, The electronic device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the method according to any one of claims 6 to 8.

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