Method for determining dynamic response characteristics of current-limiting resonance elimination device

Abstract

The invention provides a method for determining the dynamic response characteristic of a current-limiting resonance elimination device, and belongs to the technical field of current-limiting resonance elimination devices, and the method comprises the steps: firstly, setting an initial condition for an experimental test, and obtaining experimental data including current-limiting current, resonance elimination voltage, temperature rise and the like; and generating comprehensive current-limiting resonance elimination data by changing initial conditions for multiple times. Then, establishing a dynamic response characteristic equation set covering electrical, mechanical, thermal, magnetic and other characteristics, and fitting experimental data to obtain an analytical solution and a numerical range solution; and finally, by taking the analytical solution as a dynamic response characteristic expression and the numerical range solution as a constraint condition, establishing a dynamic response characteristic model of the current-limiting resonance elimination device for performance evaluation and optimization design. The method solves the technical problem that a dynamic response characteristic model of an existing current-limiting resonance elimination device is usually designed and evaluated by adopting a simplified model or an empirical formula, and the actual performance of the device in a complex power grid environment is difficult to reflect accurately.

Description

Technical Field

[0001] The present invention belongs to the technical field of current limiting and harmonic elimination devices, and in particular, relates to a method for determining dynamic response characteristics of a current limiting and harmonic elimination device. Background Art

[0002] In modern power systems, current limiting and harmonic elimination devices play a vital role. They are mainly used to suppress overcurrent during system failures, eliminate harmonic interference, and improve the stability and reliability of the power grid. With the continuous expansion of the power system and the massive access to new energy sources, the short-circuit current level faced by the power grid continues to rise, and traditional current limiting and harmonic elimination devices can no longer meet the increasingly complex power grid needs.

[0003] At present, common current limiting and detuning devices mainly include superconducting current limiters, solid-state current limiters and saturable reactors. Superconducting current limiters use the fast normal-conductor transition characteristics of superconductors to achieve current limiting. They have the advantages of fast response speed and large impedance change, but they are expensive and have strict requirements on the cooling system. Solid-state current limiters use power electronic devices to quickly cut in current limiting resistors. They are flexible and controllable, but they have problems of large power loss and low reliability. Saturable reactors use the magnetic saturation characteristics of the iron core to achieve current limiting. They have a simple structure and high reliability, but their dynamic response speed is slow and it is difficult to achieve precise control.

[0004] In practical applications, these current limiting and harmonic elimination devices face many challenges. First, the operating environment of the power grid is complex and changeable, and the device needs to maintain good performance under different voltage levels, fault types and environmental conditions, which places high demands on its dynamic response characteristics. Secondly, as the power grid's requirements for power quality increase, the current limiting and harmonic elimination device must not only have good current limiting capabilities, but also play a role in harmonic suppression and power factor improvement. Furthermore, the large-scale access of new energy power generation has made the impedance characteristics of the power grid more complex, and traditional devices are difficult to adapt to such changes.

[0005] In addition, the existing current limiting and harmonic elimination devices have obvious deficiencies in determining the dynamic response characteristics. The dynamic response characteristic models of existing current limiting and harmonic elimination devices are usually designed and evaluated using simplified models or empirical formulas, which are difficult to accurately reflect the actual performance of the device in a complex power grid environment. This method ignores the coupling of multiple physical fields such as electrical, mechanical, thermal, and magnetic fields within the device, resulting in a large deviation between the design results and the actual operating conditions, affecting the performance optimization and reliability improvement of the device. Summary of the invention

[0006] In view of this, the present invention provides a method for determining the dynamic response characteristics of a current limiting and harmonic elimination device, which can solve the technical problem that the dynamic response characteristic model of the existing current limiting and harmonic elimination device is usually designed and evaluated using a simplified model or empirical formula, and it is difficult to accurately reflect the actual performance of the device in a complex power grid environment.

[0007] The present invention is achieved in that:

[0008] The present invention provides a method for determining the dynamic response characteristics of a current limiting and harmonic elimination device, comprising the following steps:

[0009] S10, setting initial conditions, conducting experimental tests on the current limiting and harmonic elimination device, and obtaining experimental data, wherein the initial conditions include system voltage, system frequency, fault type, fault duration, ambient temperature, and initial magnetic flux, and the experimental data include current limiting current, harmonic elimination voltage, temperature rise, displacement, vibration, harmonic content, response time, and energy loss;

[0010] S20, changing the initial conditions multiple times to obtain experimental data of the experimental test of the current limiting and harmonic elimination device, and merging each set of experimental conditions and corresponding experimental data into current limiting and harmonic elimination data;

[0011] S30, establishing a group of dynamic response characteristic equations of the current limiting and harmonic elimination device including all parameters in the current limiting and harmonic elimination data, including electrical characteristic equations, mechanical characteristic equations, thermal characteristic equations, magnetic characteristic equations, impedance characteristic equations, energy conversion equations, harmonic characteristic equations and dynamic stability equations;

[0012] S40, fitting the current limiting and harmonic elimination data to the dynamic response characteristic equation group to obtain a fitted equation group;

[0013] S50, analytically solving the fitted equation group to obtain an analytical solution of the dynamic response characteristics of the current limiting and harmonic elimination device;

[0014] S60, solving the fitted equation group using a numerical method to obtain a numerical range solution of the dynamic response characteristics;

[0015] S70, using the analytical solution as a dynamic response characteristic expression of the current limiting and harmonic elimination device, using the numerical range solution as a constraint condition of the dynamic response characteristic expression, and establishing a dynamic response characteristic model of the current limiting and harmonic elimination device for equipment performance evaluation and optimization design.

[0016] Specifically, the dynamic response characteristic equation group is specifically expressed as follows:

[0017] 1. Electrical characteristic equation:

[0018]

[0019] Where i(t) is the current limiting current, in A; t is the time, in s; L(t) is the instantaneous inductance of the current limiting and detuning device, in H; V s is the system voltage peak value, in V; ω is the system angular frequency, equal to 2πf, where f is the system frequency, in Hz; R(t) is the instantaneous resistance of the current limiting and detuning device, in Ω; V c (t) is the detuning voltage, in V;

[0020] Calculation of inductance L(t):

[0021]

[0022] Where, L0 is the initial inductance value, in H; ΔL is the inductance change, in H; Φ(t) is the instantaneous magnetic flux, in Wb; Φ sat is the saturation flux, unit is Wb;

[0023] Calculation of resistance R(t):

[0024] R(t)=R0[1+α(T(t)-T0)];

[0025] Where R0 is the initial resistance value, in Ω; α is the temperature coefficient, in K^(-1); T(t) is the instantaneous temperature, in K; T0 is the initial temperature, in K.

[0026] 2. Mechanical characteristic equation:

[0027]

[0028] Where m is the mass of the movable part, in kg; x(t) is the displacement, in m; c is the damping coefficient, in N·s / m; k is the elastic coefficient, in N / m; F e (t) is the electromagnetic force, unit is N; F m (t) is the external mechanical force, in N.

[0029] Electromagnetic force F e Calculation of (t):

[0030]

[0031] 3. Thermal characteristic equation:

[0032]

[0033] Where ρ is the material density, in kg / m^3; C pis the specific heat capacity, in J / (kg·K); T(x,y,z,t) is the temperature field distribution function, in K; k is the thermal conductivity, in W / (m·K); Q(x,y,z,t) is the heat source distribution function, in W / m^3;

[0034] Calculation of heat source Q(x,y,z,t):

[0035] Q(x,y,z,t)=J 2 (x,y,z,t) / σ(T)

[0036] Among them, J(x,y,z,t) is the current density distribution function, the unit is A / m^2; σ(T) is the conductivity, which is a function of temperature, the unit is S / m.

[0037] 4. Magnetic characteristic equation:

[0038]

[0039]

[0040] B = μ0(H+M);

[0041] Where H is the magnetic field intensity, in A / m; J is the current density, in A / m^2; D is the electric displacement, in C / m^2; B is the magnetic induction intensity, in T; μ0 is the vacuum permeability, equal to 4π×10 ；7 H / m; M is the magnetization intensity, the unit is A / m.

[0042] Calculation of magnetization M (using Jiles-Atherton model):

[0043]

[0044] Among them, M an is the magnetization curve without hysteresis; k is the domain wall pinning coefficient; δ is the direction parameter (+1 or -1); α is the interaction parameter between magnetic domains.

[0045] 5. Impedance characteristic equation:

[0046]

[0047] Among them, Z(jω) is the complex impedance, the unit is Ω; R(jω) is the resistance component, the unit is Ω; X(jω) is the reactance component, the unit is Ω; V(jω) is the complex representation of voltage, the unit is V; I(jω) is the complex representation of current, the unit is A.

[0048] Calculation of the reactance component X(jω):

[0049]

[0050] Among them, L(jω) is the frequency-dependent equivalent inductance, unit is H; C(jω) is the frequency-dependent equivalent capacitance, unit is F.

[0051] 6. Energy conversion equation:

[0052]

[0053] Among them, E total is the total energy of the system, in J; P in (t) is the input power, in W; P out (t) is the output power, in W; P loss (t) is the power loss, in W.

[0054] Power loss P loss Calculation of (t):

[0055] P loss (t) = P copper (t)+P core (t)+P mech (t);

[0056] in:

[0057] P copper (t) = R(t)i 2 (t) is copper loss, unit is W;

[0058] is the iron loss (considering hysteresis loss and eddy current loss), unit is W;

[0059] is the mechanical loss, unit is W;

[0060] 7. Harmonic characteristic equation:

[0061]

[0062] Among them, I0 is the DC component, the unit is A; I n is the amplitude of the nth harmonic component, in A; φ n is the nth harmonic phase angle, in rad.

[0063] Calculation of Total Harmonic Distortion (THD):

[0064]

[0065] 8. Dynamic stability equation:

[0066]

[0067] Among them, δ is the power angle, the unit is rad; M is the moment of inertia, the unit is kg·m^2; P m is the mechanical power, in W; P e is the electromagnetic power, the unit is W; D is the damping coefficient, the unit is N·m·s / rad.

[0068] Electromagnetic power P e Calculation:

[0069]

[0070] Among them, E is the internal potential of the generator, in V; V is the infinite bus voltage, in V; X is the equivalent reactance, in Ω; these equations constitute the dynamic response characteristic equation group of the current limiting and detuning device.

[0071] Each equation contains multiple parameters and variables, involving multiple physical domains such as electrical, mechanical, thermal, and magnetic, reflecting the complexity and coupling of the system. In practical applications, further parameter determination and model correction may be required based on specific device characteristics and experimental data.

[0072] The dynamic response characteristic expression of the current limiting and detuning device is finally obtained as follows:

[0073]

[0074] Among them, i(t)=I m sin(ωt+φ)e ；t / τ For calculation of current limiting, Used for calculation of current limiting current peak value, For calculation of detuning voltage, Used for calculation of the peak value of the detuning voltage, For calculation of temperature change, For calculation of displacement, For the calculation of harmonic content, For calculation of energy loss, Used for calculation of instantaneous power loss;

[0075] Where i(t) is the current limiting current, in A; t is the time, in s; I m is the current limiting current peak value, in A; ω is the system angular frequency, in rad / s; φ is the initial phase angle, in rad; τ is the time constant, in s; k1 is the fitting constant, dimensionless; V s is the system voltage, in V; L is the equivalent inductance, in H; R is the equivalent resistance, in Ω; v c(t) is the detuning voltage, in V; V cm is the peak value of the detuning voltage, in V; θ is the initial phase angle of the detuning voltage, in rad; τ v is the detuning voltage time constant, in seconds; k3 is the fitting constant, dimensionless; R c is the detuning resistance, in Ω; ΔT(t) is the temperature rise, in K; ΔT max is the maximum temperature rise, in K; τ T is the thermal time constant, in seconds; x(t) is the displacement, in meters; X m is the maximum displacement, in m; ω n is the natural angular frequency, in rad / s; ψ is the initial phase angle of displacement, in rad; ζ is the damping ratio, dimensionless; THD is the total harmonic distortion, in %; I n is the effective value of the nth harmonic current, in A; I1 is the effective value of the fundamental current, in A; E loss is energy loss, unit is J; P loss (t) is the instantaneous power loss, in W; k9, k 10 is the fitting constant; f is the system frequency, in Hz; B m is the maximum magnetic induction intensity, unit is T; n is the iron loss coefficient.

[0076] Specifically, step S10 includes the following steps:

[0077] Step 101, selecting a system voltage, including one of standard voltage values ​​such as 110V, 220V or 380V;

[0078] Step 102, setting the system frequency, including 50 Hz or 60 Hz;

[0079] Step 103, determining the fault type, including single-phase grounding, two-phase short circuit or three-phase short circuit;

[0080] Step 104, set the fault duration, and select between 0.1 seconds and 5 seconds;

[0081] Step 105, record the ambient temperature, measured in the range of -20 degrees Celsius to 40 degrees Celsius;

[0082] Step 106, measuring the initial magnetic flux, obtained by a Hall sensor or a flux meter;

[0083] Step 107, preparing test equipment, including an oscilloscope, a current transformer, a voltage transformer, a temperature sensor, a displacement sensor, a vibration sensor and a power analyzer;

[0084] Step 108, connect the test circuit and ensure that all measuring devices are correctly connected;

[0085] Step 109, simulating a fault condition, which is achieved by a program-controlled switch or a fault simulator;

[0086] Step 110, record the experimental data, including limiting current, detuning voltage, temperature rise, displacement, vibration, harmonic content, response time and energy loss.

[0087] Wherein, the step S20 specifically includes:

[0088] Step 201, designing an experimental matrix, determining the initial conditions that need to be changed and their value ranges;

[0089] Step 202, adjusting the system voltage to vary between 80% and 120% of the rated value;

[0090] Step 203, changing the system frequency, adjusting between 45 Hz and 65 Hz;

[0091] Step 204, changing the fault type, including single-phase grounding, two-phase short circuit, three-phase short circuit;

[0092] Step 205, changing the fault duration from 0.1 seconds to 5 seconds;

[0093] Step 206, adjusting the ambient temperature to vary between -20 degrees Celsius and 40 degrees Celsius;

[0094] Step 207, changing the initial magnetic flux to adjust between 0 and saturation magnetic flux;

[0095] Step 208: According to the experimental matrix, the initial conditions are changed one by one, and the experimental test process in step S10 is repeatedly performed;

[0096] Step 209: Repeat each group of experiments at least 3 times to ensure the reliability of the data;

[0097] Step 210, recording the initial conditions and corresponding experimental data of each set of experiments;

[0098] Step 211, calculating the mean value and standard deviation of each set of experimental data, and eliminating obviously abnormal data points;

[0099] Step 212: Integrate the processed experimental conditions and corresponding experimental data into a complete data set, which is called current limiting and detuning data.

[0100] Wherein, the step S30 specifically includes:

[0101] Step 301: Determine the type of equation to be established according to the parameters included in the current limiting and harmonic elimination data;

[0102] Step 302: Establish an electrical characteristic equation based on Kirchhoff's voltage law to describe the relationship between current, voltage, inductance and resistance;

[0103] Step 303: Establish a mechanical characteristic equation based on Newton's second law to describe the relationship between displacement, velocity, acceleration and external force;

[0104] Step 304: Establish a thermal characteristic equation based on the heat conduction equation to describe the change of temperature distribution over time and space;

[0105] Step 305: Establish a magnetic characteristic equation based on Maxwell's equations to describe the relationship between the magnetic field, electric field and current density;

[0106] Step 306: Establish an impedance characteristic equation based on the complex form of Ohm's law to describe the complex ratio of voltage and current;

[0107] Step 307: Establish an energy conversion equation based on the law of conservation of energy to describe the input, output and loss of system energy;

[0108] Step 308: Establish a harmonic characteristic equation based on Fourier series expansion to describe the harmonic components in the nonlinear system;

[0109] Step 309: Establish a dynamic stability equation based on the power angle equation to describe the stability of the system under disturbance;

[0110] Step 310: Determine the variables and parameters in each equation based on physical principles and experimental observations;

[0111] Step 311, establishing a coupling relationship between various equations;

[0112] Step 312: combine all equations into a complete set of equations to form a set of dynamic response characteristic equations of the current limiting and detuning device.

[0113] Wherein, the step S40 specifically includes:

[0114] Step 401, preprocessing the dynamic response characteristic equation group, discretizing the differential equations and partial differential equations in the equation group, and converting them into algebraic equation groups;

[0115] Step 402: For ordinary differential equations, discretization is performed using the Runge-Kutta method;

[0116] Step 403: For the partial differential equation, discretize using finite difference method or finite element method;

[0117] Step 404: Select a suitable fitting algorithm. For the linear part, use the least squares method.

[0118] Step 405: For the nonlinear part, use an optimization method such as Levenberg-Marquardt algorithm or genetic algorithm;

[0119] Step 406, dividing the current limiting and harmonic elimination data into a training set and a verification set in a ratio of 7:3;

[0120] Step 407, using the training set data to fit the equation system;

[0121] Step 408, setting initial parameter values ​​and parameter value ranges, the initial parameter values ​​are obtained based on physical meaning or empirical estimation, and the parameter value ranges take into account physical feasibility;

[0122] Step 409: Use an optimization algorithm to iteratively adjust parameter values ​​so as to minimize the error between the prediction results of the equation group and the experimental data;

[0123] Step 410, in each iteration, calculating the root mean square error and the coefficient of determination between the predicted value and the experimental value;

[0124] Step 411: When the root mean square error is less than a preset threshold or the determination coefficient is greater than a preset threshold, or when the maximum number of iterations is reached, stop the iteration;

[0125] Step 412: Use the validation set data to validate the fitting results, and calculate the root mean square error and determination coefficient of the validation set;

[0126] Step 413: If the verification result is not ideal, adjust the equation form, add or delete parameters, change the fitting algorithm, etc., and then re-fit;

[0127] Step 414: Obtain the fitted equation group, including the specific form and parameter values ​​of each equation.

[0128] Wherein, the step S50 specifically includes:

[0129] Step 501, simplifying and transforming the fitted equation group;

[0130] Step 502, linearize the nonlinear equation using Taylor expansion or small signal analysis method;

[0131] Step 503: For coupled equations, use decoupling techniques, such as variable substitution or coordinate transformation;

[0132] Step 504: Select a suitable analytical solution method. For ordinary differential equations, use the Laplace transform method.

[0133] Step 505: For partial differential equations, use separation of variables method or Green's function method;

[0134] Step 506: For the algebraic equation system, use Cramer's rule or matrix inversion method;

[0135] Step 507, solving each equation one by one, taking into account initial conditions and boundary conditions;

[0136] Step 508: For nonlinear equations, use approximate methods such as perturbation method or asymptotic expansion method;

[0137] Step 509: The expression obtained by solving may contain special functions, such as Bessel function, Legendre function, etc., which are simplified using a mathematics manual or a computer algebra system;

[0138] Step 510: verify the analytical solution by substituting the analytical solution into the original equation to check whether the equation and boundary conditions are satisfied;

[0139] Step 511, using limit analysis to check whether the asymptotic behavior of the solution conforms to the physical meaning;

[0140] Step 512: Compare the analytical solution with the numerical solution and the experimental data to verify their accuracy.

[0141] Wherein, the step S60 specifically includes:

[0142] Step 601: Select a suitable numerical method. For ordinary differential equations, use the Runge-Kutta method or the adaptive step-size method.

[0143] Step 602: for partial differential equations, use finite difference method, finite element method or finite volume method;

[0144] Step 603: For the algebraic equation system, use the Newton-Raphson method or the quasi-Newton method;

[0145] Step 604, determine the computational domain and grid division, and determine the size and shape of the computational domain according to the physical characteristics of the problem;

[0146] Step 605, meshing the computational domain, using a denser mesh in areas with large gradient changes;

[0147] Step 606: Perform grid independence analysis to ensure that the results are not affected by the grid size;

[0148] Step 607: setting initial conditions and boundary conditions, where the initial conditions are obtained from experimental data or theoretical analysis;

[0149] Step 608: The boundary conditions are determined according to the physical model, including the first type of boundary conditions, the second type of boundary conditions or the third type of boundary conditions;

[0150] Step 609, write a solution program or use an existing numerical calculation software package;

[0151] Step 610: Perform numerical solution to obtain the distribution of each variable over time and space;

[0152] Step 611: During the solution process, monitor the residual error and convergence, and adjust the solution parameters or re-divide the grid if necessary;

[0153] Step 612: post-process the solution results, including data analysis, visualization, etc.;

[0154] Step 613, calculating the physical quantities of interest, such as maximum current limiting current, peak temperature, response time, etc.;

[0155] Step 614, drawing time history curves, spatial distribution diagrams, etc. of various physical quantities;

[0156] Step 615: perform error analysis and result verification to estimate the error of the numerical solution, including truncation error and rounding error;

[0157] Step 616, comparing the numerical solution with the analytical solution and the experimental data to verify the accuracy of the numerical method;

[0158] Step 617: If the result is not satisfactory, adjust the numerical method, refine the grid or improve the physical model;

[0159] Step 618: Through multiple calculations, a numerical range solution of the dynamic response characteristics is obtained, including the maximum value, minimum value and average value of each physical quantity.

[0160] Wherein, the step S70 specifically includes:

[0161] Step 701, sorting and analyzing analytical solutions and numerical range solutions;

[0162] Step 702: Express the analytical solution as a function expression of each physical quantity over time and space;

[0163] Step 703, expressing the numerical range solution as the value interval of each physical quantity;

[0164] Step 704, establish a dynamic response characteristic expression, and express the constants in the analytical solution with system parameters;

[0165] Step 705: For complex nonlinear relationships, use Taylor expansion for approximation and retain the main terms;

[0166] Step 706, determining constraint conditions, and using the numerical range solution as the constraint condition of the dynamic response characteristic expression;

[0167] Step 707: Establish a complete dynamic response characteristic model, and combine the dynamic response characteristic expression and constraint conditions into a complete mathematical model;

[0168] Step 708: Verify and optimize the model, use experimental data to verify the model and check the accuracy of the model prediction;

[0169] Step 709: Use sensitivity analysis method to study the influence of each parameter on system performance;

[0170] Step 710: Based on the sensitivity analysis results, further optimize the model, highlight key parameters, and simplify minor parameters.

[0171] Compared with the prior art, the method for determining the dynamic response characteristics of a current limiting and detuning device provided by the present invention achieves a comprehensive and accurate description of the dynamic response characteristics of the device through systematic experimental design, data acquisition, multi-physical field coupling modeling and numerical analysis, providing strong support for the optimal design and performance evaluation of the device.

[0172] This method has the following significant technical effects:

[0173] 1. Comprehensiveness: This method takes into account the mutual coupling of the current limiting and detuning device in multiple physical domains such as electrical, mechanical, thermal, and magnetic, and establishes a complete set of equations including electrical characteristics, mechanical characteristics, thermal characteristics, magnetic characteristics, impedance characteristics, energy conversion, harmonic characteristics, and dynamic stability. This comprehensive modeling method can more accurately reflect the complex behavior of the device in actual operation and overcome the limitations of traditional simplified models.

[0174] 2. Accuracy: Through the collection and fitting of multiple sets of experimental data, this method obtains a highly accurate dynamic response characteristic model. The model not only contains analytical solution expressions, but also gives numerical range solutions as constraints, which effectively improves the applicability and reliability of the model. This dual representation method enables the model to adapt to different application scenarios and computing requirements while ensuring accuracy.

[0175] 3. Adaptability: This method conducts multiple experiments by changing the initial conditions to obtain the response data of the device under different system voltages, frequencies, fault types, ambient temperatures, etc. This extensive data base makes the established model highly adaptable and can accurately predict the performance of the device in various complex power grid environments.

[0176] 4. Guidance: The dynamic response characteristic model established based on this method can provide powerful guidance for the design optimization of the current limiting and harmonic elimination device. By analyzing the sensitivity and interaction of each parameter in the model, the designer can adjust the device structure and parameters in a targeted manner to obtain the best current limiting and harmonic elimination effect. This optimization design method based on an accurate model can significantly improve the performance and reliability of the device.

[0177] In summary, the method of the present invention solves the technical problem that the dynamic response characteristic model of the existing current limiting and harmonic elimination device is usually designed and evaluated using a simplified model or empirical formula, which is difficult to accurately reflect the actual performance of the device in a complex power grid environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0178] Figure 1 A flow chart of the method provided by the present invention. DETAILED DESCRIPTION

[0179] In order to make the purpose, technical solution and advantages of the embodiments of the present invention more clear, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0180] like Figure 1 FIG. 1 is a flow chart of a method for determining the dynamic response characteristics of a current limiting and harmonic elimination device provided by the present invention. The method comprises the following steps:

[0181] S10, setting initial conditions, conducting experimental tests on the current limiting and harmonic elimination device, and obtaining experimental data, the initial conditions including system voltage, system frequency, fault type, fault duration, ambient temperature, and initial magnetic flux, and the experimental data including current limiting current, harmonic elimination voltage, temperature rise, displacement, vibration, harmonic content, response time, and energy loss;

[0182] S20, changing the initial conditions multiple times to obtain experimental data of the experimental test of the current limiting and harmonic elimination device, and merging each set of experimental conditions and corresponding experimental data into current limiting and harmonic elimination data;

[0183] S30, establishing a group of dynamic response characteristic equations of the current limiting and harmonic elimination device including all parameters in the current limiting and harmonic elimination data, including electrical characteristic equations, mechanical characteristic equations, thermal characteristic equations, magnetic characteristic equations, impedance characteristic equations, energy conversion equations, harmonic characteristic equations, and dynamic stability equations;

[0184] S40, fitting the current limiting and detuning data to the dynamic response characteristic equation group to obtain a fitted equation group;

[0185] S50, analytically solving the fitted equation group to obtain an analytical solution of the dynamic response characteristics of the current limiting and harmonic elimination device;

[0186] S60, solving the fitted equation group using a numerical method to obtain a numerical range solution of the dynamic response characteristics;

[0187] S70. Using the analytical solution as the dynamic response characteristic expression of the current limiting and harmonic elimination device, using the numerical range solution as the constraint condition of the dynamic response characteristic expression, and establishing a dynamic response characteristic model of the current limiting and harmonic elimination device for equipment performance evaluation and optimization design.

[0188] The specific implementation methods of the above steps are described in detail below:

[0189] The specific implementation method of step S10 is: first, set the system voltage, usually select standard voltage values ​​such as 110V, 220V or 380V; set the system frequency, usually 50Hz or 60Hz; select the fault type, such as single-phase grounding, two-phase short circuit or three-phase short circuit; determine the fault duration, usually between 0.1 seconds and 5 seconds; record the ambient temperature, usually in the range of -20℃ to 40℃; measure the initial magnetic flux, which can be measured by a Hall sensor or a fluxmeter. Then, conduct an experimental test of the current limiting and harmonic elimination device, including the following steps: prepare test equipment, such as an oscilloscope, current transformer, voltage transformer, temperature sensor, displacement sensor, vibration sensor and power analyzer; connect the test circuit to ensure that all measuring equipment is correctly connected; simulate fault conditions, which can be achieved by a programmable switch or a fault simulator; record experimental data, including current limiting current, harmonic elimination voltage, temperature rise, displacement, vibration, harmonic content, response time and energy loss. Among them, the current limiting current is measured by a current transformer, the harmonic elimination voltage is measured by a voltage transformer, the temperature rise is measured using a thermocouple or an infrared thermal imager, the displacement is measured by a laser displacement sensor, the vibration is measured by an acceleration sensor, the harmonic content and response time are obtained by a power analyzer, and the energy loss is calculated by the voltage and current product integral. The purpose of this step is to obtain the performance data of the current limiting and harmonic elimination device under specific working conditions to provide a basis for subsequent analysis and modeling.

[0190] The specific implementation of step S20 is: first, design an experimental matrix to determine the initial conditions that need to be changed and their value ranges. For example, the system voltage can vary between 80% and 120% of the rated value, the system frequency can be adjusted between 45Hz and 65Hz, the fault type can include single-phase grounding, two-phase short circuit, three-phase short circuit, etc., the fault duration can vary from 0.1 seconds to 5 seconds, the ambient temperature can vary between -20°C and 40°C, and the initial magnetic flux can be adjusted between 0 and saturation magnetic flux. Then, according to the experimental matrix, the initial conditions are changed one by one, and the experimental test process in step S10 is repeated. Each group of experiments is repeated at least 3 times to ensure the reliability of the data. The initial conditions and corresponding experimental data of each group of experiments are recorded, including current limiting current, detuning voltage, temperature rise, displacement, vibration, harmonic content, response time and energy loss. For each group of experimental data, the average value and standard deviation are calculated, and the obviously abnormal data points are eliminated. The processed experimental conditions and corresponding experimental data are integrated into a complete data set, which is called current limiting detuning data. This step uses the orthogonal experimental design method to obtain the response characteristics of the system under different conditions by changing multiple factors in a planned manner. At the same time, statistical methods are used to pre-process the data to improve the data quality. The purpose of this step is to obtain the performance data of the current limiting and detuning device under various possible working conditions, laying the foundation for the subsequent establishment of a comprehensive dynamic response characteristic model.

[0191] The specific implementation of step S30 is: first, according to the parameters contained in the current limiting and harmonic elimination data, determine the type of equation to be established. The electrical characteristic equation is based on Kirchhoff's voltage law and describes the relationship between current, voltage, inductance and resistance. The mechanical characteristic equation is based on Newton's second law and describes the relationship between displacement, velocity, acceleration and external force. The thermal characteristic equation is based on the heat conduction equation and describes the change of temperature distribution over time and space. The magnetic characteristic equation is based on Maxwell's equations and describes the relationship between magnetic field, electric field and current density. The impedance characteristic equation is based on the complex form of Ohm's law and describes the complex ratio of voltage and current. The energy conversion equation is based on the law of conservation of energy and describes the input, output and loss of system energy. The harmonic characteristic equation is based on Fourier series expansion and describes the harmonic components in nonlinear systems. The dynamic stability equation is based on the power angle equation and describes the stability of the system under disturbance. Then, according to physical principles and experimental observations, the variables and parameters in each equation are determined. For example, in the electrical characteristic equation, the inductance L(t) and resistance R(t) may be functions of temperature and magnetic flux; in the mechanical characteristic equation, the electromagnetic force F e(t) is a function of current. Next, the coupling relationship between the various equations is established. For example, the current in the electrical equation affects the electromagnetic force in the mechanical equation, and the temperature in the thermal characteristic equation affects the resistance in the electrical equation. Finally, all equations are combined into a complete set of equations to form a set of dynamic response characteristic equations for the current limiting and detuning device. This step uses a multi-physics coupling modeling method that takes into account the interactions of multiple physical fields such as electricity, magnetism, heat, and force. At the same time, differential equations and partial differential equations are used to describe the dynamic characteristics of the system.

[0192] The dynamic response characteristic equation group of the current limiting and harmonic elimination device specifically includes:

[0193] 1. Electrical characteristic equation:

[0194]

[0195] Where i(t) is the current limiting current, in A; t is the time, in s; L(t) is the instantaneous inductance of the current limiting and detuning device, in H; V s is the system voltage peak value, in V; ω is the system angular frequency, equal to 2πf, where f is the system frequency, in Hz; R(t) is the instantaneous resistance of the current limiting and detuning device, in Ω; V c (t) is the detuning voltage, in V;

[0196] Calculation of inductance L(t):

[0197] Where, L0 is the initial inductance value, in H; ΔL is the inductance change, in H; Φ(t) is the instantaneous magnetic flux, in Wb; Φ sat is the saturation flux, unit is Wb;

[0198] Calculation of resistance R(t): R(t)=R0[1+α(T(t)-T0)];

[0199] Where R0 is the initial resistance value, in Ω; α is the temperature coefficient, in K^(-1); T(t) is the instantaneous temperature, in K; T0 is the initial temperature, in K.

[0200] 2. Mechanical characteristic equation:

[0201]

[0202] Where m is the mass of the movable part, in kg; x(t) is the displacement, in m; c is the damping coefficient, in N·s / m; k is the elastic coefficient, in N / m; F e (t) is the electromagnetic force, unit is N; F m (t) is the external mechanical force, in N.

[0203] Electromagnetic force F e Calculation of (t):

[0204] 3. Thermal characteristic equation:

[0205]

[0206] Where ρ is the material density, in kg / m^3; C p is the specific heat capacity, in J / (kg·K); T(x,y,z,t) is the temperature field distribution function, in K; k is the thermal conductivity, in W / (m·K); Q(x,y,z,t) is the heat source distribution function, in W / m^3;

[0207] Calculation of heat source Q(x,y,z,t): Q(x,y,z,t)=J 2 (x,y,z,t) / σ(T)

[0208] Among them, J(x,y,z,t) is the current density distribution function, the unit is A / m^2; σ(T) is the conductivity, which is a function of temperature, the unit is S / m.

[0209] 4. Magnetic characteristic equation:

[0210]

[0211]

[0212] B = μ0(H+M);

[0213] Where H is the magnetic field intensity, in A / m; J is the current density, in A / m^2; D is the electric displacement, in C / m^2; B is the magnetic induction intensity, in T; μ0 is the vacuum permeability, equal to 4π×10 ；7 H / m; M is the magnetization intensity, the unit is A / m.

[0214] Calculation of magnetization M (using Jiles-Atherton model):

[0215]

[0216] Among them, M an is the magnetization curve without hysteresis; k is the domain wall pinning coefficient; δ is the direction parameter (+1 or -1); α is the interaction parameter between magnetic domains.

[0217] 5. Impedance characteristic equation:

[0218]

[0219] Among them, Z(jω) is the complex impedance, the unit is Ω; R(jω) is the resistance component, the unit is Ω; X(jω) is the reactance component, the unit is Ω; V(jω) is the complex representation of voltage, the unit is V; I(jω) is the complex representation of current, the unit is A.

[0220] Calculation of the reactance component X(jω):

[0221] Among them, L(jω) is the frequency-dependent equivalent inductance, unit is H; C(jω) is the frequency-dependent equivalent capacitance, unit is F.

[0222] 6. Energy conversion equation:

[0223]

[0224] Among them, E total is the total energy of the system, in J; P in (t) is the input power, in W; P out (t) is the output power, in W; P loss (t) is the power loss, in W.

[0225] Power loss P loss Calculation of (t):

[0226] P loss (t) = P copper (t)+P core (t)+P mech (t);

[0227] in:

[0228] P copper (t) = R(t)i 2 (t) is copper loss, unit is W;

[0229] is the iron loss (considering hysteresis loss and eddy current loss), unit is W;

[0230] is the mechanical loss, unit is W;

[0231] 7. Harmonic characteristic equation:

[0232]

[0233] Among them, I0 is the DC component, the unit is A; I n is the amplitude of the nth harmonic component, in A; φ n is the nth harmonic phase angle, in rad.

[0234] Calculation of Total Harmonic Distortion (THD):

[0235]

[0236] 8. Dynamic stability equation:

[0237]

[0238] Among them, δ is the power angle, the unit is rad; M is the moment of inertia, the unit is kg·m^2; P m is the mechanical power, in W; P e is the electromagnetic power, the unit is W; D is the damping coefficient, the unit is N·m·s / rad.

[0239] Electromagnetic power P e Calculation:

[0240] Among them, E is the internal potential of the generator, in V; V is the infinite bus voltage, in V; X is the equivalent reactance, in Ω; these equations constitute the dynamic response characteristic equation group of the current limiting and detuning device.

[0241] Each equation contains multiple parameters and variables, involving multiple physical domains such as electrical, mechanical, thermal, and magnetic, reflecting the complexity and coupling of the system. In practical applications, further parameter determination and model correction may be required based on specific device characteristics and experimental data.

[0242] The purpose of this step is to establish a comprehensive mathematical model that can accurately describe the dynamic response characteristics of the current limiting and detuning device under various operating conditions.

[0243] The specific implementation of step S40 is: first, pre-process the dynamic response characteristic equation group. Discretize the differential equations and partial differential equations in the equation group and convert them into algebraic equations. For ordinary differential equations, the Runge-Kutta method can be used for discretization; for partial differential equations, the finite difference method or the finite element method can be used for discretization. Then, select a suitable fitting algorithm. For the linear part, the least squares method can be used; for the nonlinear part, optimization methods such as the Levenberg-Marquardt algorithm or the genetic algorithm can be used. Next, the current limiting detuning data is divided into a training set and a validation set, usually divided in a ratio of 7:3. Use the training set data to fit the equation group. During the fitting process, it is necessary to set the initial parameter value and the parameter value range. The initial parameter value can be obtained based on physical meaning or empirical estimation, and the parameter value range needs to consider physical feasibility. The optimization algorithm iteratively adjusts the parameter value to minimize the error between the predicted results of the equation group and the experimental data. In each iteration, the root mean square error (RMSE) and the coefficient of determination (R 2). When RMSE is less than a preset threshold (e.g. 0.05) or R 2 When it is greater than the preset threshold (e.g. 0.95) or reaches the maximum number of iterations (e.g. 1000), the iteration is stopped. The fitting results are verified using the validation set data, and the RMSE and R of the validation set are calculated. 2 . If the verification result is not ideal, it may be necessary to adjust the equation form, add or delete parameters, change the fitting algorithm, etc., and then re-fit. Finally, the fitted equation set is obtained, including the specific form and parameter values ​​of each equation. This step uses the discretization method and optimization algorithm in numerical analysis to convert the continuous differential equation into a discrete form that can be solved by a computer, and find the optimal parameter value through the optimization algorithm. At the same time, the idea of ​​cross-validation is adopted to avoid overfitting problems by dividing the training set and the validation set. The purpose of this step is to combine the theoretical model with the actual data to obtain a mathematical model that can accurately describe the dynamic response characteristics of the current limiting and detuning device.

[0244] The specific implementation method of step S50 is: first, simplify and transform the fitted equation group. To linearize the nonlinear equation, Taylor expansion or small signal analysis method can be used. For coupled equations, decoupling techniques such as variable substitution or coordinate transformation can be used. Then, select a suitable analytical solution method. For ordinary differential equations, Laplace transform method can be used; for partial differential equations, separation of variables method or Green's function method can be used. For algebraic equations, Cramer's rule or matrix inversion method can be used. Next, solve each equation one by one. For example, for electrical characteristic equations, Laplace transform can be used to convert time domain equations into s domain equations, then solve s domain equations, and finally obtain time domain solutions through inverse Laplace transform. For thermal characteristic equations, separation of variables method can be used to separate space and time variables, then solve eigenvalue problems, and finally superimpose special solutions to obtain general solutions. In the solution process, initial conditions and boundary conditions need to be considered. Initial conditions are usually given by experimental data, and boundary conditions need to be determined based on physical models. For nonlinear equations, approximate methods such as perturbation method or asymptotic expansion method may need to be used. The expression obtained by the solution may contain special functions, such as Bessel functions, Legendre functions, etc., which need to be simplified using a mathematical manual or a computer algebra system. Finally, the analytical solution is verified. Substitute the analytical solution into the original equation to check whether the equation and boundary conditions are satisfied. Use limit analysis to check whether the asymptotic behavior of the solution conforms to the physical meaning. Compare the analytical solution with the numerical solution and experimental data to verify its accuracy. This step uses the differential equation solution method in higher mathematics and the mathematical physics equation solution techniques. At the same time, the ideas of approximate analysis and asymptotic analysis are used to simplify the problem while ensuring accuracy.

[0245] The following is the analytical solution process:

[0246] 1. Analytical solution of electrical characteristic equations:

[0247] First, there are the electrical characteristic equations:

[0248]

[0249] To simplify the solution, assume that L(t), R(t), and V c (t) can be regarded as a constant in a short time. Let L(t)=L, R(t)=R, V c (t) = V c .

[0250] Rewriting the equation into standard form:

[0251]

[0252] This is a first-order linear nonhomogeneous differential equation whose general solution is the sum of homogeneous solutions and particular solutions.

[0253] Solutions of homogeneous equations:

[0254]

[0255] Where C is the integration constant.

[0256] The particular solution can be assumed to be:

[0257] i p (t)=A sin (ωt)+B cos (ωt)+D

[0258] Substituting the special solution into the original equation, we get:

[0259]

[0260]

[0261]

[0262] Therefore, the complete solution for the current i(t) is:

[0263]

[0264] The initial condition i(0) = I0 can determine the constant C:

[0265]

[0266] 2. Analytical solution of mechanical characteristic equations:

[0267] The mechanical characteristic equation is:

[0268]

[0269] This is a second-order nonhomogeneous differential equation. To simplify the solution, assume that F e (t)+F m (t) = Fsin(Ωt), where F is the magnitude of the force and Ω is the angular frequency of the force.

[0270] Standard form:

[0271]

[0272] in is the natural frequency, is the damping ratio.

[0273] The homogeneous solution is:

[0274]

[0275] in is the damped vibration frequency, A and B are constants to be determined.

[0276] The particular solution can be assumed to be:

[0277] x p (t)=C sin(Ωt)+D cos(Ωt)

[0278] Substituting into the original equation, we get:

[0279]

[0280]

[0281] The complete solution is:

[0282]

[0283] Initial conditions x(0) = x0 and The constants A and B can be determined:

[0284] A=x0-D

[0285]

[0286] 3. Analytical solution of thermal characteristic equation:

[0287] The thermal characteristic equation is:

[0288]

[0289] This is a partial differential equation, and the analytical solution is relatively complicated. We can simplify the problem by considering the one-dimensional case and assuming that the heat source Q is a constant:

[0290]

[0291] make (thermal diffusion coefficient), the equation becomes:

[0292]

[0293] Assume the initial condition T(x,0)=T0 and the boundary condition T(0,t)=T(L,t)=T0, where L is the material length.

[0294] Using the separation of variables method, let T(x,t) = X(x)Y(t) and substitute into the equation:

[0295]

[0296] Separate variables:

[0297]

[0298] We get two ordinary differential equations:

[0299] Y′(t)+λ 2 αY(t)=0

[0300] X″(x)+λ 2 X(x)=0

[0301] Solving these two equations and taking into account the boundary conditions, we obtain:

[0302]

[0303]

[0304] Where n=1,2,3,...

[0305] The particular solution can be assumed to be:

[0306]

[0307] The complete solution is:

[0308]

[0309] Among them A n It can be determined from the initial conditions:

[0310]

[0311] 4. Analytical solution of magnetic characteristic equations:

[0312] For the magnetic characteristic equations:

[0313]

[0314]

[0315] B=μ0(H+M)

[0316] The static situation can be considered and the displacement current can be ignored. Assume that in one dimension, the current density J is uniformly distributed along the z direction, and the magnetic field H and the magnetic induction intensity B only change in the xy plane.

[0317] The simplified equation is:

[0318]

[0319]

[0320] B x =μ0(H x +M x )

[0321] B y =μ0(H y +M y )

[0322] Assume that the magnetization intensity M is proportional to the magnetic field H, that is, M = χH, where χ is the magnetic susceptibility.

[0323] Substituting into the third and fourth equations:

[0324] B x =μ0(1+χ)H x =μH x

[0325] B y =μ0(1+χ)H y =μH y

[0326] Where μ = μ0(1+χ) is the magnetic permeability of the material.

[0327] Substituting these relations into the first two equations:

[0328]

[0329]

[0330] Introduce the magnetic vector potential A, so that In the one-dimensional case, we can assume Then we have:

[0331]

[0332]

[0333] Substituting into the first equation:

[0334]

[0335] This is an elliptic partial differential equation. Assuming μ is a constant, the equation simplifies to:

[0336]

[0337] This is the Poisson equation, and its solution can be obtained by the Green function method:

[0338]

[0339] where C is the integration constant.

[0340] Know A z Then, we can obtain H x , H y , B x and B y .

[0341] 5. Analytical solution of impedance characteristic equation:

[0342] The impedance characteristic equation is:

[0343]

[0344]

[0345] Assume that R(jω), L(jω) and C(jω) can be expressed as polynomial functions of frequency: R(jω) = R0 + R1ω + R2ω 2

[0346] L(jω)=L0+L1ω+L2ω 2

[0347] C(jω)=C0+C1ω+C2ω 2

[0348] Substituting into the original equation:

[0349]

[0350] Rationalize the complex denominator:

[0351]

[0352] This is the analytical expression of impedance Z(jω).

[0353] 6. Analytical solution of energy conversion equation:

[0354] The energy conversion equation is:

[0355]

[0356] Assume P in (t), P out (t) and P loss (t) can be expressed as a function of time:

[0357] P in (t) = P in0 +P in1 sin(ωt)

[0358] P out (t) = P out0 +P out1 sin(ωt+φ1)

[0359] P loss (t) = P loss0 +P loss1 sin(ωt+φ2)

[0360] Substituting into the original equation:

[0361]

[0362] Expand the sine function on the right:

[0363]

[0364] After finishing, we get:

[0365]

[0366] in:

[0367] A=P in0 -P out0 -P loss0

[0368] B=P in1 -P out1 cos(φ1)-P loss1 cos(φ2)

[0369] C=-P out1 sin(φ1)-P loss1 sin(φ2)

[0370] This is a first-order inhomogeneous differential equation with the general solution:

[0371]

[0372] Where D is the integration constant, which can be obtained by the initial condition E total (0) = E0 Determine:

[0373]

[0374] Therefore, the complete analytical solution to the energy conversion equation is:

[0375]

[0376] 7. Analytical solution of harmonic characteristic equations:

[0377] The harmonic characteristic equation is:

[0378]

[0379] This equation itself is an analytical expression and does not need to be solved further. However, it can be obtained by Fourier transforming it into a frequency domain expression:

[0380]

[0381] where δ(ω) is the Dirac delta function and ω0 is the fundamental angular frequency.

[0382] The calculation formula for total harmonic distortion (THD) is:

[0383]

[0384] 8. Analytical solution of dynamic stability equation:

[0385] The dynamic stability equation is:

[0386]

[0387] in

[0388] Assume a small signal disturbance, that is, δ = δ0 + Δδ, where δ0 is the steady-state operating point and Δδ is a small disturbance. e Taylor expansion at δ0:

[0389]

[0390] Substitute into the original equation and assume that P m is a constant:

[0391]

[0392] make And note that at the steady-state operating point The equation simplifies to:

[0393]

[0394] This is a second-order homogeneous differential equation with constant coefficients, and its characteristic equation is:

[0395]

[0396] Solve for the characteristic roots:

[0397]

[0398] definition (natural frequency) and (damping ratio), the characteristic root can be expressed as:

[0399]

[0400] The analytical solution of the system depends on the value of ζ:

[0401] 1) When ζ>1 (overdamped):

[0402]

[0403] 2) When ζ=1 (critical damping):

[0404]

[0405] 3) When 0<ζ<1 (underdamped):

[0406]

[0407] in is the damped oscillation frequency.

[0408] The constants C1 and C2 can be obtained by the initial conditions Δδ(0) and Sure.

[0409] Here are the multiple analytical solutions obtained:

[0410] 1. Analytical solution of electrical characteristic equation:

[0411]

[0412] in:

[0413]

[0414] 2. Analytical solution of mechanical characteristic equation:

[0415]

[0416] in:

[0417] A=x0-D

[0418]

[0419]

[0420]

[0421] 3. Analytical solution of thermal characteristic equation (one-dimensional simplified case):

[0422]

[0423] in:

[0424]

[0425] 4. Analytical solution of magnetic characteristic equation (one-dimensional simplified case):

[0426]

[0427]

[0428]

[0429] B x =μH x

[0430] B y =μH y

[0431] 5. Analytical solution of impedance characteristic equation:

[0432]

[0433] 6. Analytical solution of energy conversion equation:

[0434]

[0435] in:

[0436] A=P in0 -P out0 -P loss0

[0437] B=P in1 -P out1 cos(φ1)-P loss1 cos(φ2)

[0438] C=-P out1 sin(φ1)-P loss1 sin(φ2)

[0439] 7. Analytical solution of harmonic characteristic equation (frequency domain representation):

[0440]

[0441] 8. Analytical solution of dynamic stability equation:

[0442] For ζ>1 (overdamped):

[0443] For ζ = 1 (critical damping):

[0444] For 0<ζ<1 (underdamped):

[0445] in:

[0446]

[0447]

[0448]

[0449]

[0450] The purpose of this step is to obtain the analytical expression of the dynamic response characteristics of the current limiting and detuning device, providing a theoretical basis for subsequent performance analysis and optimization design.

[0451] The specific implementation of step S60 is: first, select a suitable numerical method. For ordinary differential equations, the Runge-Kutta method or the adaptive step method can be used; for partial differential equations, the finite difference method, the finite element method or the finite volume method can be used; for algebraic equations, the Newton-Raphson method or the quasi-Newton method can be used. Then, determine the computational domain and mesh division. According to the physical characteristics of the problem, determine the size and shape of the computational domain. Mesh the computational domain and use a denser mesh in areas with large gradient changes. Perform mesh independence analysis to ensure that the results are not affected by the size of the mesh. Next, set initial conditions and boundary conditions. The initial conditions can be obtained from experimental data or theoretical analysis. The boundary conditions need to be determined based on the physical model, which may include the first type of boundary conditions (Dirichlet conditions), the second type of boundary conditions (Neumann conditions) or the third type of boundary conditions (Robin conditions). Then, write a solution program or use an existing numerical calculation software package. Perform numerical solution to obtain the distribution of each variable over time and space. During the solution process, monitor the residual and convergence, and adjust the solution parameters or re-mesh if necessary. Post-process the solution results, including data analysis, visualization, etc. Calculate the physical quantities of interest, such as maximum current limiting current, peak temperature, response time, etc. Draw the time history curves and spatial distribution diagrams of each physical quantity. Finally, perform error analysis and result verification. Estimate the errors of the numerical solution, including truncation error and rounding error. Compare the numerical solution with the analytical solution (if any) and experimental data to verify the accuracy of the numerical method. If the results are not ideal, it may be necessary to adjust the numerical method, refine the grid, or improve the physical model. Through multiple calculations, the numerical range solution of the dynamic response characteristics is obtained, including the maximum, minimum and average values ​​of each physical quantity. This step uses various solution techniques in numerical analysis to convert complex differential equations into discrete forms that can be solved by computers. At the same time, the grid division and solution strategies commonly used in computational fluid dynamics and computational electromagnetics are adopted. The purpose of this step is to obtain a numerical solution to the dynamic response characteristics of the current limiting and detuning device to provide a quantitative reference for practical engineering design.

[0452] The specific implementation of step S70 is: first, sort out and analyze the analytical solution and numerical range solution obtained in the previous step. Express the analytical solution as a function expression of each physical quantity over time and space. For example, the current limiting current is expressed as i(t)=I m sin(ωt+φ)e ；t / τ , where I m , ω, φ, and τ are constants related to system parameters. The numerical range solution is expressed as the value interval of each physical quantity, for example, the maximum current limit may be between 5kA and 8kA, and the peak temperature may be between 80℃ and 120℃. Then, the dynamic response characteristic expression is established. The constants in the analytical solution are expressed as system parameters, such as I m =f(Vs ,L,R),τ=g(L,R), where V s is the system voltage, L is the equivalent inductance, and R is the equivalent resistance. This allows us to intuitively see the relationship between each physical quantity and the system parameters. For complex nonlinear relationships, Taylor expansion can be used to approximate and retain the main terms. For example, Next, determine the constraints. Use the numerical range solution as the constraint condition of the dynamic response characteristic expression. For example, 5000≤I m ≤8000, 80≤T max ≤120. These constraints reflect the limitations and requirements of the system in actual work. Then, a complete dynamic response characteristic model is established. The dynamic response characteristic expression and constraints are combined into a complete mathematical model. The model may include a series of equations, inequalities, and parameter ranges. For example:

[0453] i(t)=I m sin(ωt+φ)e ；t / τ

[0454]

[0455] τ=k2L / R

[0456] 5000≤I m ≤8000

[0457] 0.1≤τ≤0.5

[0458] 80≤T max ≤120

[0459] Where k1 and k2 are fitting constants. This model includes both the dynamic characteristics of the system and the constraints of actual operation. Next, verify and optimize the model. Use experimental data to verify the model and check the accuracy of the model prediction. If the prediction results deviate greatly from the experimental data, the model structure or parameters may need to be adjusted. Use sensitivity analysis methods to study the impact of various parameters on system performance. For example, you can calculate and Determine which parameters have the greatest impact on the current limiting effect. Based on the sensitivity analysis results, the model can be further optimized to highlight the key parameters and simplify the minor parameters.

[0460] Finally, the dynamic response characteristic expression of the current limiting and detuning device is established, including:

[0461] 1. Current limiting equation:

[0462] i(t)=I m sin(ωt+φ)e ；t / τ ;

[0463] Where: i(t) is the current limiting current, in A; t is the time, in s; I m is the current limiting current peak value, in A; ω is the system angular frequency, in rad / s; φ is the initial phase angle, in rad; τ is the time constant, in s;

[0464] 2. Current limiting current peak calculation:

[0465]

[0466] Where: k1 is the fitting constant, dimensionless; V s is the system voltage, in V; L is the equivalent inductance, in H; R is the equivalent resistance, in Ω;

[0467] Among them, the time constant is calculated as: τ = k2L / R;

[0468] Where: k2 is the fitting constant, dimensionless;

[0469] 3. Elimination of harmonic voltage equation:

[0470]

[0471] Where: v c (t) is the detuning voltage, in V; V cm is the peak value of the detuning voltage, in V; θ is the initial phase angle of the detuning voltage, in rad; τ v is the detuning voltage time constant, in s;

[0472] 4. Calculation of harmonic elimination voltage peak value:

[0473]

[0474] Where: k3 is the fitting constant, dimensionless; R c is the detuning resistance, in Ω;

[0475] 5. Temperature rise equation:

[0476] Where: ΔT(t) is the temperature rise in K; ΔT max is the maximum temperature rise, in K; τ T is the thermal time constant, in seconds;

[0477] Among them, the maximum temperature rise is calculated as:

[0478] Where: k4 is the fitting constant, dimensionless; h is the thermal conductivity, unit is W / (m 2 ·K); A is the heat dissipation area, unit is m 2 ;

[0479] Among them, the thermal time constant is calculated as: τ T =k5mc p / (hA);

[0480] Where: k5 is the fitting constant, dimensionless; m is the mass of the current limiting and detuning device, in kg; c p is the specific heat capacity, in J / (kg·K);

[0481] 6. Displacement equation:

[0482]

[0483] Where: x(t) is the displacement, in m; X m is the maximum displacement, in m; ω n is the natural angular frequency, in rad / s; ψ is the initial phase angle of displacement, in rad; ζ is the damping ratio, dimensionless;

[0484] Among them, the maximum displacement calculation is: X m =k6F e / k;

[0485] Where: k6 is the fitting constant, dimensionless; F e is the electromagnetic force, in N; k is the spring stiffness, in N / m

[0486] Among them, the electromagnetic force calculation is:

[0487] Where: k7 is the fitting constant, dimensionless; g is the air gap length, unit is m;

[0488] Among them, the natural angular frequency is calculated as:

[0489] Among them, the damping ratio is calculated as:

[0490] Where: c is the damping coefficient, unit is N·s / m;

[0491] 7. Calculation of harmonic content:

[0492]

[0493] Where: THD is the total harmonic distortion, in %; I n is the effective value of the nth harmonic current, in A; I1 is the effective value of the fundamental current, in A;

[0494] Among them, the response time calculation is: t r =k8τln(I i / I f);

[0495] Where: t r is the response time, in seconds; k8 is the fitting constant, dimensionless; I i is the initial current value, in A; I f is the final current value, in A;

[0496] 8. Energy loss calculation:

[0497]

[0498] Where: E loss is energy loss, unit is J; P loss (t) is the instantaneous power loss, in W;

[0499] 9. Calculation of instantaneous power loss:

[0500]

[0501] Where: k9,k 10 is the fitting constant; f is the system frequency, in Hz; B m is the maximum magnetic induction intensity, in T; n is the iron loss coefficient, usually ranging from 1.6 to 2.0;

[0502] The sources or acquisition methods of the variables and parameters in the dynamic response characteristic expression of this model are as follows:

[0503] 1. System parameters (V s ,ω,f): given by the operating conditions of the power system.

[0504] 2. Device parameters (L, R, R c ,m,k,c,g,A): Determined by the equipment design and manufacturing process and can be obtained through experimental measurement.

[0505] 3. Material parameters (c p ,h): Determined by the physical properties of the material used, which can be found in the material manual or measured through experiments.

[0506] 4. Fitting constants (k1 to k 10 ): obtained by regression analysis of a large amount of experimental data. The specific steps are as follows:

[0507] a) Collect experimental data under different working conditions.

[0508] b) Apply the appropriate equation to each set of data.

[0509] c) Use the least squares method or other optimization algorithm to find the constant value that minimizes the sum of squared errors.

[0510] d) Verify the fit results to ensure a good fit over the entire operating range.

[0511] 5. Initial phase angle (φ, θ, ψ): It is determined by the system state at the time of fault occurrence and needs to be obtained through real-time measurement or estimation.

[0512] 6. Time constant (τ, τ v ,τ T ): obtained by experimentally measuring the response curve and fitting the exponential decay function.

[0513] 7. Maximum magnetic induction intensity B m : Obtained through magnetic field simulation or experimental measurement.

[0514] 8. Iron loss coefficient n: obtained by experimentally measuring the loss characteristics of the core material and fitting the loss curve.

[0515] 9. Harmonic current (I n ): obtained by Fourier analysis of the current limiting current. The specific steps are as follows:

[0516] a) Sample the current limiting current i(t) within one cycle.

[0517] b) Apply a Discrete Fourier Transform (DFT) or Fast Fourier Transform (FFT) algorithm to the sampled data.

[0518] c) Calculate the amplitude of each harmonic.

[0519] 10. Initial current value I i And the final current value I f : Obtained through experimental measurement or system simulation.

[0520] This model comprehensively considers the coupling effects of multiple physical fields such as electrical, thermal, mechanical, and magnetic fields, and can more comprehensively describe the dynamic response characteristics of the current limiting and detuning device. In practical applications, it may be necessary to appropriately simplify or expand the model according to specific circumstances.

[0521] This step uses mathematical modeling, optimization theory and system engineering methods, and combines analytical and numerical solutions to establish a dynamic response characteristic model that has both theoretical basis and practical limitations. This model can be directly used for equipment performance evaluation and optimization design, providing strong support for engineering practice.

[0522] Through the above steps, a comprehensive dynamic response characteristic model of the current limiting and detuning device is established. This model not only includes the main physical characteristics of the system, but also takes into account various constraints and requirements in actual engineering. It can be used for equipment performance evaluation, such as predicting key indicators such as current limiting effect, temperature rise, and response time under different working conditions. At the same time, it is also a powerful tool for optimizing design. It can optimize the overall performance of the equipment by adjusting various design parameters such as inductance, resistance, material properties, etc.

[0523] Specifically, the principle of the present invention is to establish a high-precision dynamic response characteristic model based on multi-physics field coupling modeling and data-driven parameter fitting through systematic experimental design and data analysis. This method can effectively solve the problems existing in the prior art, and its principle can be explained from the following aspects:

[0524] 1. Multi-physics coupling modeling: The working process of the current limiting detuning device involves the interaction of multiple physical fields such as electricity, magnetism, heat, and force. This method achieves an accurate description of the coupling effects of these physical fields by establishing a complete set of equations including electrical characteristics, mechanical characteristics, thermal characteristics, magnetic characteristics, etc. For example, the electrical characteristic equation considers the effect of temperature on resistance, the thermal characteristic equation considers Joule heat and eddy current loss, and the magnetic characteristic equation adopts the Jiles-Atherton model that considers the hysteresis effect. This comprehensive modeling method can capture the complex behavior of the device in actual operation and overcome the defect of traditional simplified models that ignore coupling effects.

[0525] 2. Systematic experimental design: This method obtains rich experimental data by designing multiple sets of experiments under initial conditions. These initial conditions include key parameters such as system voltage, frequency, fault type, ambient temperature, etc., covering various working conditions that the device may encounter. The systematic experimental design ensures the comprehensiveness and representativeness of the data, providing a reliable basis for subsequent parameter fitting and model verification.

[0526] 3. Data-driven parameter fitting: Using a large amount of experimental data, this method uses advanced fitting algorithms to fit the parameters in the dynamic response characteristic equations. This data-driven method can effectively overcome the limitations of traditional empirical formulas or theoretical calculations, making the model closer to the performance of the actual device. At the same time, by analyzing the confidence interval and sensitivity of the fitting results, the model structure can be further optimized to improve its accuracy and robustness.

[0527] 4. Numerical-analytical dual solution: This method uses both analytical and numerical solutions to process the fitted equations. The analytical solution provides an accurate mathematical expression of the dynamic response characteristics, which is convenient for theoretical analysis and fast calculation; while the numerical solution gives the range of characteristic parameters, providing more flexible options for practical applications. This dual solution strategy not only ensures the theoretical rigor of the model, but also enhances its applicability in complex situations.

[0528] 5. Closed-loop optimization mechanism: The dynamic response characteristic model established by this method is not only used for performance evaluation, but also can directly guide the optimization design of the device. By analyzing the influence degree and mutual relationship of each parameter in the model, the device structure and materials can be adjusted in a targeted manner to improve its performance. The optimized design can be verified again through experiments and model updates to form a closed-loop optimization process to continuously improve the performance of the device.

[0529] 6. Multi-scale analysis: The modeling process of this method takes into account multiple scales from microscopic to macroscopic. For example, the behavior of magnetic domains is considered in magnetic property modeling, and the influence of material microstructure is considered in thermal property modeling. This multi-scale analysis method enables the model to more accurately describe the response characteristics of the device at different time and space scales.

[0530] 7. Nonlinear effect processing: Current limiting and detuning devices often exhibit strong nonlinear characteristics during operation. This method effectively handles these nonlinear effects by introducing nonlinear terms and piecewise linearization techniques. For example, the Jiles-Atherton model is used in the magnetic characteristic equation to describe the hysteresis phenomenon, and frequency-related equivalent parameters are introduced in the impedance characteristic equation.

[0531] Through the comprehensive application of the above principles, the method proposed by the present invention can accurately and comprehensively determine the dynamic response characteristics of the current limiting and harmonic elimination device, providing a scientific and effective way to solve the problems existing in the prior art.

[0532] In order to better understand and implement the present invention, an embodiment of a specific application scenario of the present invention is provided below: a 220kV substation needs to install a new current limiting and harmonic elimination device due to grid expansion. The substation is located in an industrial park, and the power supply load is mainly large motors and arc furnaces, which have serious harmonic pollution and low power factor problems. At the same time, due to the addition of photovoltaic power generation access, the system short-circuit capacity has increased significantly, which puts higher requirements on the current limiting performance.

[0533] Equipment parameters:

[0534] The current limiting and detuning device to be installed adopts a saturable reactor structure, with a rated voltage of 220kV, a rated current of 2000A, a rated impedance of 5%, and a maximum current limiting multiple of 5 times. The device consists of a main iron core, a control winding, an auxiliary iron core, and a mechanical support structure. The main iron core is made of oriented silicon steel sheets, the control winding uses copper wire, and the auxiliary iron core is made of amorphous alloy material.

[0535] Implementation steps:

[0536] 1. Initial condition setting and experimental testing

[0537] According to the actual situation of the substation and the device parameters, the following initial conditions are set for experimental testing:

[0538] System voltage: 220kV (nominal value) ±10%; System frequency: 50Hz±0.5Hz; Fault type: three-phase short circuit, single-phase grounding, two-phase short circuit grounding; Fault duration: 0.1s, 0.3s, 0.5s; Ambient temperature: -20℃, 25℃, 40℃; Initial magnetic flux: 0%, 50%, 100% rated value;

[0539] The experimental test collected the following data:

[0540] Current limiting: 0-10000A; detuning voltage: 0-300kV; temperature rise: 0-120℃; displacement: 0-10mm; vibration: 0-100m / s 2 ; Harmonic content: 2-13th harmonic, 0-10%; Response time: 0-20ms; Energy loss: 0-1000kJ;

[0541] 2. Collection of multiple experimental data

[0542] By changing the initial conditions, multiple experiments were conducted, and a total of 100 tests were completed. The following are the test results of some typical working conditions:

[0543] Working condition 1. Normal operation status:

[0544] System voltage: 220kV; System frequency: 50Hz; Ambient temperature: 25℃; Initial magnetic flux: 50% rated value; Test results:; Current limiting current: 2000A; Detuning voltage: 11kV; Temperature rise: 35℃; Displacement: 0.5mm; Vibration: 5m / s 2 ; Harmonic content: 3rd harmonic 2%, 5th harmonic 1.5%; Response time: N / A; Energy loss: 50kJ / h;

[0545] Working condition 2: Three-phase short circuit fault:

[0546] System voltage: 242kV (110% rated value); System frequency: 50.2Hz; Fault type: three-phase short circuit; Fault duration: 0.3s; Ambient temperature: 40℃; Initial magnetic flux: 100% rated value; Test results:; Current limiting current: 9500A; Detuning voltage: 55kV; Temperature rise: 80℃; Displacement: 3mm; Vibration: 50m / s 2 ; Harmonic content: N / A; Response time: 5ms; Energy loss: 800kJ;

[0547] Working condition 3, single-phase grounding fault:

[0548] System voltage: 198kV (90% rated value); System frequency: 49.8Hz; Fault type: single-phase grounding; Fault duration: 0.5s; Ambient temperature: -20℃; Initial magnetic flux: 0% rated value; Test results:; Current limiting current: 6000A; Detuning voltage: 35kV; Temperature rise: 50℃; Displacement: 2mm; Vibration: 30m / s 2 ; Harmonic content: 3rd harmonic 5%, 5th harmonic 3%; Response time: 8ms; Energy loss: 500kJ;

[0549] 3. Establishment of dynamic response characteristic equations

[0550] Based on experimental data, a set of equations including electrical characteristics, mechanical characteristics, thermal characteristics, magnetic characteristics, impedance characteristics, energy conversion, harmonic characteristics and dynamic stability is established. The following are some key equations:

[0551] Electrical characteristic equation:

[0552]

[0553] Where L(t) and R(t) are the instantaneous inductance and resistance, respectively, taking into account the effects of temperature and magnetic saturation.

[0554] Thermal characteristic equation:

[0555]

[0556] Among them, Q(x,y,z,t) is the heat source distribution function, which takes into account Joule heating and eddy current losses.

[0557] Magnetic characteristic equation:

[0558] The Jiles-Atherton model is used to describe the hysteresis characteristics, and the effect of temperature on the magnetic properties is considered.

[0559] 4. Parameter fitting

[0560] The nonlinear least squares method is used to fit the parameters in the equation group. The following are the fitting results of some key parameters:

[0561] Initial inductance L0: 0.15H; inductance change ΔL: 0.08H; initial resistance R0: 0.5Ω; temperature coefficient α: 0.004K^(-1); thermal conductivity k: 45W / (m·K); Jiles-Atherton model parameters:; domain wall pinning coefficient k: 2000A / m; domain interaction parameter α: 0.001; hysteresis curve parameter a: 1000A / m; shape parameter c: 0.1;

[0562] 5. Analytical solution

[0563] The fitted equations are solved analytically to obtain the expression of the dynamic response characteristics of the current limiting and detuning device. The following are the analytical solutions of some key characteristics:

[0564] Current limiting current expression:

[0565]

[0566] Among them, C, A and φ are constants related to system parameters.

[0567] Temperature rise expression:

[0568]

[0569] Among them, T ∞ is the ambient temperature, β is the cooling coefficient, Q is the heat generation rate, h is the convection heat transfer coefficient, and S is the heat dissipation area.

[0570] 6. Numerical solution

[0571] The Runge-Kutta method is used to numerically solve the fitted equations and obtain the numerical range of the dynamic response characteristics. The following are the numerical ranges of some key parameters:

[0572] Current limiting multiple: 2.5-5.5; response time: 3-15ms; maximum temperature rise: 60-100℃; harmonic suppression rate: 60%-85%;

[0573] 7. Dynamic response characteristic model establishment

[0574] Based on analytical and numerical solutions, a dynamic response characteristic model of the current limiting and harmonic elimination device is established. The model includes the following main contents:

[0575] (1) Current limiting characteristics: the relationship curve between current limiting multiple and fault current; the relationship curve between current limiting response time and initial magnetic flux; the relationship curve between current limiting impedance and frequency;

[0576] (2) Temperature rise characteristics: the relationship curve between temperature rise and time; the relationship curve between maximum temperature rise and ambient temperature; the relationship curve between thermal time constant and load rate;

[0577] (3) Mechanical properties: relationship curve between displacement and electromagnetic force; relationship curve between vibration frequency and current; mechanical stress distribution diagram;

[0578] (4) Harmonic characteristics: the relationship curve between harmonic suppression rate and frequency; the relationship curve between total harmonic distortion rate and load rate; the distribution diagram of each harmonic content;

[0579] (5) Energy characteristics: curve showing the relationship between energy loss and current; curve showing the relationship between efficiency and load rate; and curve showing the improvement of power factor.

[0580] 8. Model validation and optimization

[0581] Another 10 sets of experimental data were used to verify the established model. The verification results showed that the average error between the model prediction value and the measured value was within 5%, which met the requirements of engineering application.

[0582] Based on the verification results, the model was further optimized:

[0583] The parameters of the Jiles-Atherton model were adjusted to improve the accuracy of the magnetic properties description;

[0584] The second-order temperature correction term for resistivity is introduced to improve the prediction of electrical properties at high temperatures.

[0585] Added an equivalent circuit model that takes eddy current effects into account, improving the accuracy of high-frequency response;

[0586] 9. Application Analysis

[0587] Based on the established dynamic response characteristic model, the application of the current limiting and harmonic elimination device in the 220kV substation was analyzed:

[0588] (1) Current limiting performance analysis: The model predicts that in the most severe three-phase short-circuit fault condition, the device can limit the fault current to within 4.8 times the rated current, and the response time does not exceed 10 ms, meeting the grid protection requirements.

[0589] (2) Temperature rise analysis: Under the most unfavorable high temperature environment (40°C) and continuous overload (120% rated load) conditions, the maximum temperature rise of the device is 85°C, which is lower than the heat resistance level of the insulation material (155°C), ensuring long-term reliable operation.

[0590] (3) Analysis of harmonic suppression effect: In response to the harmonic pollution problem existing in substations, the model prediction device can reduce the total harmonic distortion rate from the original 8% to below 3%, significantly improving the power quality.

[0591] (4) Power factor improvement analysis: By adjusting the operating parameters of the device, the system power factor can be increased from 0.85 to above 0.95, reducing reactive power loss and improving transmission efficiency.

[0592] Conclusion: Through this example, the effectiveness and practicality of the method for determining the dynamic response characteristics of the current limiting and harmonic elimination device are verified. The established model can accurately describe the performance of the device under various working conditions, providing strong support for equipment selection, parameter optimization, and operation and maintenance.

[0593] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for determining the dynamic response characteristics of a current limiting and harmonic elimination device, characterized in that: The following steps are involved: S10, setting initial conditions, conducting experimental tests on the current limiting and harmonic elimination device, and obtaining experimental data, wherein the initial conditions include system voltage, system frequency, fault type, fault duration, ambient temperature, and initial magnetic flux, and the experimental data include current limiting current, harmonic elimination voltage, temperature rise, displacement, vibration, harmonic content, response time, and energy loss; S20, changing the initial conditions multiple times to obtain experimental data of the experimental test of the current limiting and harmonic elimination device, and merging each set of experimental conditions and corresponding experimental data into current limiting and harmonic elimination data; S30, establishing a group of dynamic response characteristic equations of the current limiting and harmonic elimination device including all parameters in the current limiting and harmonic elimination data, including electrical characteristic equations, mechanical characteristic equations, thermal characteristic equations, magnetic characteristic equations, impedance characteristic equations, energy conversion equations, harmonic characteristic equations and dynamic stability equations; S40, fitting the current limiting and harmonic elimination data to the dynamic response characteristic equation group to obtain a fitted equation group; S50, analytically solving the fitted equation group to obtain an analytical solution of the dynamic response characteristics of the current limiting and harmonic elimination device; S60, solving the fitted equation group using a numerical method to obtain a numerical range solution of the dynamic response characteristics; S70, using the analytical solution as a dynamic response characteristic expression of the current limiting and harmonic elimination device, using the numerical range solution as a constraint condition of the dynamic response characteristic expression, and establishing a dynamic response characteristic model of the current limiting and harmonic elimination device for equipment performance evaluation and optimization design.

2. The method for determining the dynamic response characteristics of a current limiting and harmonic elimination device according to claim 1, characterized in that: The electrical characteristic equation is specifically expressed as: Where i(t) is the current limiting current, in A; t is the time, in s; L(t) is the instantaneous inductance of the current limiting and detuning device, in H; V s is the system voltage peak value, in V; ω is the system angular frequency, equal to 2πf, f is the system frequency, in Hz; R(t) is the instantaneous resistance of the current limiting and detuning device, in Ω; V c (t) is the detuning voltage, in V; Among them, the inductance L(t) is calculated using the following formula: Where, L0 is the initial inductance value, in H; ΔL is the inductance change, in H; Φ(t) is the instantaneous magnetic flux, in Wb; Φ sat is the saturation flux, unit is Wb; The resistance R(t) is calculated using the following formula: R(t)=R0[1+α(T(t)-T0)]; Where, R0 is the initial resistance value, unit is Ω; α is the temperature coefficient, unit is 1 / K; T(t) is the instantaneous temperature, unit is K; T0 is the initial temperature, unit is K.

3. The method for determining the dynamic response characteristics of a current limiting and harmonic elimination device according to claim 2, characterized in that: The mechanical characteristic equation is specifically expressed as: Where m is the mass of the movable part, in kg; x(t) is the displacement, in m; c is the damping coefficient, in N·s / m; k is the elastic coefficient, in N / m; F e (t) is the electromagnetic force, unit is N; F m (t) is the external mechanical force, in N; Among them, the electromagnetic force F e (t) is calculated using the following formula:

4. The method for determining the dynamic response characteristics of a current limiting and harmonic elimination device according to claim 3, characterized in that: The thermal characteristic equation is specifically expressed as: Where ρ is the material density, in units of C p is the specific heat capacity, in J / (kg·K); T(x,y,z,t) is the temperature field distribution function, in K; k is the thermal conductivity, in W / (m·K); Q(x,y,z,t) is the heat source distribution function, in is the Hamiltonian operator; Among them, the heat source Q(x,y,z,t) is calculated using the following formula: Q(x,y,z,t)=J 2 (x,y,z,t) / σ(T)? Where J(x,y,z,t) is the current density distribution function, and its unit is σ(T) is the electrical conductivity, which is a function of temperature and its unit is S / m.

5. The method for determining the dynamic response characteristics of a current limiting and harmonic elimination device according to claim 4, characterized in that: The magnetic characteristic equation is specifically expressed as: B = μ0(H+M); Where H is the magnetic field intensity, unit is A / m; J is the current density, unit is D is the electric displacement, in units of B is the magnetic induction intensity, the unit is T; μ0 is the vacuum magnetic permeability, which is equal to 4π×10 -7 H / m; M is the magnetization intensity, the unit is A / m; The magnetization intensity M is calculated using the following formula: Among them, M an is the magnetization curve without hysteresis; k is the domain wall pinning coefficient; δ is the direction parameter, including +1 or -1; α is the interaction parameter between magnetic domains.

6. A method for determining the dynamic response characteristics of a current limiting and harmonic elimination device according to claim 5, characterized in that: The impedance characteristic equation is specifically expressed as: Among them, Z(jω) is the complex impedance, the unit is Ω; R(jω) is the resistance component, the unit is Ω; X(jω) is the reactance component, the unit is Ω; V(jω) is the complex representation of voltage, the unit is V; I(jω) is the complex representation of current, the unit is A; Among them, the calculation formula of the reactance component X(jω) is as follows: Among them, L(jω) is the frequency-dependent equivalent inductance, unit is H; C(jω) is the frequency-dependent equivalent capacitance, unit is F.

7. A method for determining the dynamic response characteristics of a current limiting and harmonic elimination device according to claim 6, characterized in that: The energy conversion equation is specifically expressed as: Among them, E total is the total energy of the system, in J; P in (t) is the input power, in W; P out (t) is the output power, in W; P loss (t) is the power loss, in W; Among them, the power loss P loss The calculation formula of (t) is as follows: P loss (t)=P copper (t)+P core (t)+P mech (t); in: P copper (t) = R(t)i 2 (t) is copper loss, unit is W; is the iron loss, unit is W; is the mechanical loss, unit is W.

8. A method for determining the dynamic response characteristics of a current limiting and harmonic elimination device according to claim 7, characterized in that: The harmonic characteristic equation is specifically expressed as: Among them, I0 is the DC component, the unit is A; I n is the amplitude of the nth harmonic component, in A; φ n is the nth harmonic phase angle, in rad; The calculation formula of total harmonic distortion is as follows:

9. A method for determining the dynamic response characteristics of a current limiting and harmonic elimination device according to claim 8, characterized in that: The dynamic stability equation is specifically expressed as: Among them, δ is the power angle, the unit is rad; M is the moment of inertia, the unit is kg·m 2 ;P m is the mechanical power, in W; P e is the electromagnetic power, in W; D is the damping coefficient, in N·m·s / rad; Electromagnetic power P e Calculation: Where, E is the internal potential of the generator, in V; V is the infinite bus voltage, in V; X is the equivalent reactance, in Ω.

10. A method for determining the dynamic response characteristics of a current limiting and harmonic elimination device according to claim 9, characterized in that: The dynamic response characteristic expression of the current limiting and harmonic elimination device is specifically expressed as: Among them, i(t)=I m sin(ωt+φ)e -t / τ For calculation of current limiting, Used to calculate the peak current limit, v c (t) = V cm sin(ωt+θ)e -t / τv For calculation of detuning voltage, Used for calculation of harmonic elimination voltage peak value, For calculation of temperature change, For calculation of displacement, For the calculation of harmonic content, For calculation of energy loss, Used for calculation of instantaneous power loss; Where i(t) is the current limiting current, in A; t is the time, in s; I m is the current limiting current peak value, in A; ω is the system angular frequency, in rad / s; φ is the initial phase angle, in rad; τ is the time constant, in s; k1 is the fitting constant, dimensionless; V s is the system voltage, in V; L is the equivalent inductance, in H; R is the equivalent resistance, in Ω; v c (t) is the detuning voltage, in V; V cm is the peak value of the detuning voltage, in V; θ is the initial phase angle of the detuning voltage, in rad; τ v is the detuning voltage time constant, in seconds; k3 is the fitting constant, dimensionless; R c is the detuning resistance, in Ω; ΔT(t) is the temperature rise, in K; ΔT max is the maximum temperature rise, in K; τ T is the thermal time constant, in seconds; x(t) is the displacement, in meters; X m is the maximum displacement, in m; ω n is the natural angular frequency, in rad / s; ψ is the initial phase angle of displacement, in rad; ζ is the damping ratio, dimensionless; THD is the total harmonic distortion, in %; I n is the effective value of the nth harmonic current, in A; I1 is the effective value of the fundamental current, in A; E loss is energy loss, unit is J; P loss (t) is the instantaneous power loss, in W; k9, k 10 is the fitting constant; f is the system frequency, in Hz; B m is the maximum magnetic induction intensity, unit is T; n is the iron loss coefficient.

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