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CN-115688517-B - FD-WENO format-based high-voltage transmission line electromagnetic transient process calculation method

CN115688517BCN 115688517 BCN115688517 BCN 115688517BCN-115688517-B

Abstract

The invention relates to a high-voltage transmission line electromagnetic transient process calculation method based on FD-WENO format, which carries out numerical value flux reconstruction by adopting high-order essentially oscillation-free differential FD-WENO format in space, and carrying out time domain numerical integration calculation on the time domain by adopting a total variation attenuation TVD-RK format, and sequentially solving the change curve of the electric quantity at each point of the power transmission line space along with time step by step. Compared with the prior art, the method can effectively solve the numerical oscillation problem faced by solving the high-voltage transmission line by adopting the traditional time domain finite difference FDTD, and the discrete precision of the high-voltage transmission line in space can reach any precision above 2 steps.

Inventors

  • WANG YONG
  • ZHANG LEI
  • WU XIUHAI

Assignees

  • 国网上海市电力公司
  • 三峡大学

Dates

Publication Date
20260505
Application Date
20221026

Claims (8)

  1. 1. The method for calculating the electromagnetic transient process of the high-voltage transmission line based on the FD-WENO format is characterized by comprising the following steps of: step 1, modeling, namely constructing a multi-conductor transmission line system model by adopting a hyperbolic partial differential equation, namely a telegraph equation, based on distribution parameters and boundary conditions of a high-voltage transmission line, and rewriting the model into a matrix form; Step 2, space domain discretization, namely performing numerical value flux reconstruction by adopting a high-order essentially non-oscillation differential FD-WENO format in space, and performing space discretization on a multi-conductor transmission line system model in a matrix form; The flux value reconstruction is carried out on the boundary of the interval section by adopting a high-order intrinsic oscillation-free differential FD-WENO format, and specifically comprises the following steps: Adopting a third-order WENO-JS3 format, and adopting a boundary of interval to interval Numerical flux at And (3) reconstructing, wherein the expression is as follows: (5) nonlinear combination of two lower order fluxes according to equation (5) to obtain a numerical flux : (6) In the non-linear weight coefficient And a smoothing factor The expression of (2) is as follows: (7) (8) In the formula, , , Is a very small positive number; or adopting a five-order WENO format to make interval-to-interval boundary Numerical flux at And (3) reconstructing, wherein the expression is as follows: (13) nonlinear combining of the three lower order fluxes of formula (13) according to formula (8) to obtain a numerical flux : (14) In the non-linear weight coefficient And a smoothing factor The expression of (2) is as follows: (15) (16) In which the linear weights 、 And , Is a very small positive number; step 3, initializing simulation setting, and detecting and inputting faults or operations of the high-voltage transmission line during electromagnetic transient state numerical calculation; judging whether the high-voltage transmission line system has faults or operation according to the detection result of the moment t, if not, directly transferring to the step 5, otherwise, modifying and updating the multi-conductor transmission line system model after the discrete reconstruction of the space domain; Step 5, time domain discretization, namely carrying out time domain gradual integration on the time domain by adopting a total variation attenuation TVD-RK format; step 6, updating the simulation time ; Step 7, judging whether the numerical integration process is terminated, if so Step 4, continuing to integrate the time domain values of the high-voltage transmission line system at the next time, if so Turning to step 8, wherein, Setting total simulation time; and 8, outputting electromagnetic transient state numerical simulation results of the electric quantity of each point along the high-voltage transmission line.
  2. 2. The method for calculating the electromagnetic transient process of the high-voltage transmission line based on the FD-WENO format according to claim 1, wherein the step 1 is specifically: Step 1.1, establishing a partial differential equation set describing an electromagnetic transient process of a high-voltage transmission line, modeling boundary conditions of the high-voltage transmission line by combining engineering reality, giving boundary equations of the head end and the tail end of the high-voltage transmission line, describing a multi-conductor transmission line system model formed by a three-phase overhead transmission line or a power cable line by adopting a hyperbolic partial differential equation, namely a telegraph equation, wherein the mathematical expression is as follows: (1) wherein: i represents the current traveling wave column vector on the high-voltage transmission line; a distributed parameter resistance matrix representing the high-voltage transmission line; the distributed parameter inductance matrix of the high-voltage transmission line is represented; Representing a distributed parameter capacitance matrix of the high-voltage transmission line; Representing a distribution parameter conductance matrix of the high-voltage transmission line; step 1.2, rewriting formula (1) is the following matrix form: (2) in which the state variables to be solved High voltage transmission line system flux System coefficient matrix System coefficient matrix 。
  3. 3. The method for calculating the electromagnetic transient process of the high-voltage transmission line based on the FD-WENO format according to claim 2, wherein the step 2 is specifically: Step 2.1 defining the length as Along the space arrangement direction, the high-voltage transmission line system of the system Equidistantly divided into Each interval section , Satisfies the following conditions , , For the total length of the high-voltage transmission line, the semi-discretization conservation differential format of formula (2) is: (3) In the formula, Respectively the middle section and the middle section of the high-voltage transmission line system Flux corresponding to the boundary; Is a space discrete step length; step 2.2, adopting a high-order intrinsic oscillation-free differential FD-WENO format to reconstruct flux values of boundaries at interval sections; Step 2.3, adopting Lax-Friedrichs numerical flux to transmit system flux Performing approximate calculation to realize the spatial dispersion of the formula (2); step 2.4, the formula (3) is generalized to be an initial value problem, and the expression is: (4) In the formula, Representing a spatially differential linear operator.
  4. 4. The method for calculating the electromagnetic transient process of the high-voltage transmission line based on the FD-WENO format according to claim 3, wherein the step 2.3 is specifically: Flux is put into Split into positive and negative parts, and the expression is: (9) Wherein, positive flux Satisfying monotonic increment and negative flux Satisfying monotonic decrementability; (10) In the formula, In the formula (2), A is a Jacobian matrix Spectral radius of A, positive flux Negative flux The reconstruction is carried out by adopting the formula (5), and finally the numerical flux is obtained by the formula (6); The WENO differential operator is marked as third-order H WENO3 , if there is (11) Final interval boundary Numerical flux at Represented as (12)
  5. 5. The method for calculating the electromagnetic transient process of the high-voltage transmission line based on the FD-WENO format according to claim 3, wherein the step 2.3 is specifically: Flux is put into Split into positive and negative parts, and the expression is: (17) Wherein, positive flux Satisfying monotonic increment and negative flux Satisfying monotonic decrementability; (18) In the formula, In the formula (2), A is a Jacobian matrix Spectral radius of A, positive flux Negative flux The reconstruction is carried out by adopting a formula (13), and finally the numerical flux is obtained by a formula (14); The WENO differential operator is marked as five-order H WENO5 , and the following steps are: (19) final interval boundary Numerical flux at The method comprises the following steps: (20)
  6. 6. the method for calculating electromagnetic transient process of high voltage transmission line based on FD-WENO format according to claim 3, wherein the initialization simulation setting in step 3 is specifically to set a simulation initial time Integral step number n=0, numerical integral fixed step length h and total time of electromagnetic transient simulation calculation Setting initial values of state variables in the multi-conductor transmission line system model Wherein, the method comprises the steps of, The initial value of the state variable to be solved at the starting endpoint of the high-voltage transmission line.
  7. 7. The method for calculating the electromagnetic transient process of the high-voltage transmission line based on the FD-WENO format according to claim 3, wherein the step 5 is specifically: the dispersion of the formula (3) in the time domain is carried out by adopting a total variation attenuation TVD-RK format to carry out time propulsion, and a 3-order TVD-RK method is adopted, and for the initial value problem formula (4), the calculation expression is as follows: (21) where h represents the step-wise time integration step, The calculation format comprises a 3-time value accumulation process; From the following components State variable of time of day Calculating state variables in Approximation of where 。
  8. 8. The method for calculating the electromagnetic transient process of the high-voltage transmission line based on the FD-WENO format according to claim 3, wherein the step 5 is specifically: the dispersion of the formula (3) in the time domain is carried out by adopting a total variation attenuation TVD-RK format to carry out time propulsion, a 4-level 10-order TVD-RK method is adopted, and for the initial value problem formula (4), the calculation expression is as follows: (22) where h represents the step-wise time integration step, The calculation format comprises a 10-time value accumulation process; From the following components State variable of time of day Calculating state variables in Approximation of where 。

Description

FD-WENO format-based high-voltage transmission line electromagnetic transient process calculation method Technical Field The invention relates to the field of electromagnetic transient processes of power systems, in particular to a high-voltage transmission line electromagnetic transient process calculation method based on an FD-WENO format. Background The electromagnetic transient process of the high-voltage transmission line can be attributed to the transient response solving problem of a more general transmission line system. This problem is an important research content in the field of electromagnetic field numerical computation. When a short circuit fault, overvoltage or other abnormal operation conditions occur in a power system line, the voltage and current on the transmission line can change rapidly in a short time, and damage can be caused to electrical equipment and even the whole power system, and in order to avoid such damage, the voltage and current dynamic change process on the transmission line system needs to be accurately analyzed, so that the transmission line system needs to be accurately solved. The mathematical model of the transmission line system is a typical hyperbolic partial differential equation, and the commonly used numerical method for solving the electromagnetic transient of the system is a time domain finite difference (FDTD) method FINITE DIFFERENCE. However, when there is a discontinuity in the system, the FDTD method generates a non-physical oscillation at the point of the discontinuity, which causes a large error in the calculation result. In order to solve the oscillation phenomenon in the electromagnetic transient calculation process, researchers apply the finite element method to the transient response analysis of the multi-conductor transmission line, and the finite element method can solve the numerical oscillation phenomenon which cannot be solved by the FDTD. Researchers approximate the spatial partial differential by adopting a flux splitting technology and adopting different differential formats according to the positive and negative of the characteristic values, and the problem of non-physical oscillation of the traditional FDTD format and the Lax-Wendroff format at the intermittent solution is solved. Researchers have proposed a variable parameter rational fractional fitting method for suppressing numerical oscillations, which makes the algorithm have L-stability by adjusting parameters, and whose calculation accuracy is 3 rd order. Researchers adopt the Pad approximation of the Taylor series to deduce an explicit and L-stable numerical method, so that the numerical oscillation problem can be avoided, and the intermittent problem can be effectively treated. Researchers apply the improved block method to the time domain simulation of the transmission line, the time domain simulation precision is higher, but the space discrete precision is not high. The above calculation methods can effectively suppress numerical oscillation, but have a problem of low overall accuracy. In particular for spatially discrete accuracy, a central differential format with 2 nd order accuracy is usually employed, in fact a cascaded PI-type equivalent circuit is used to simulate a transmission line of distributed parameters, with spatially 2 nd order discrete accuracy. Most numerical algorithms used for simulating transmission line systems only pursue high precision of time domain simulation, and neglect the influence of space discrete precision on the overall simulation precision. Disclosure of Invention The invention aims to overcome the defects of the prior art and provide the method for calculating the electromagnetic transient process of the high-voltage transmission line based on the FD-WENO format, which can effectively solve the numerical oscillation problem faced by solving the high-voltage transmission line by adopting the traditional FDTD, and the spatial discrete precision of the high-voltage transmission line can reach any precision above 2 steps. The aim of the invention can be achieved by the following technical scheme: The invention provides a method for calculating an electromagnetic transient process of a high-voltage transmission line based on an FD-WENO format, which comprises the following steps: step 1, modeling, namely constructing a multi-conductor transmission line system model by adopting a hyperbolic partial differential equation, namely a telegraph equation, based on distribution parameters and boundary conditions of a high-voltage transmission line, and rewriting the model into a matrix form; step 2, space domain dispersion, namely carrying out numerical value flux reconstruction by adopting a high-order intrinsic oscillation-free differential FD-WENO format in space, and particularly carrying out space dispersion on a multi-conductor transmission line system model in a matrix form; step 3, initializing simulation setting, and detecting and inputting faults o