Power transmission line overvoltage analysis method and device, electronic equipment and storage medium

Abstract

The application discloses a power transmission line overvoltage analysis method and device, electronic equipment and storage medium. The power transmission line overvoltage analysis method comprises the following steps: obtaining a first ordinary differential equation group with 2nd order accuracy and a second ordinary differential equation group with 3rd order accuracy based on a one-dimensional hyperbolic conservation law equation; establishing a telegraph equation of voltage traveling wave and current traveling wave of a current power transmission line with time and space, and obtaining a flux reconstruction mathematical model of the current power transmission line according to the first ordinary differential equation group, the second ordinary differential equation group and the telegraph equation; obtaining a line end boundary condition of the current power transmission line based on the flux reconstruction mathematical model, and obtaining an end overvoltage of the current power transmission line according to the line end boundary condition. The application realizes accurate and efficient power transmission line overvoltage calculation, and saves power transmission line overvoltage calculation time.

Description

Technical Field

[0001] This invention relates to the field of power transmission line technology, and in particular to a method, apparatus, electronic device, and storage medium for analyzing overvoltage in power transmission lines. Background Technology

[0002] Due to the vast mountainous terrain, complex and diverse geographical environment, and distinct micro-meteorological characteristics, high-voltage overhead transmission lines often pass through high mountains, hills, and valleys. This makes the transmission lines in this region much more susceptible to lightning strikes than other electrical equipment in the power system. Under conditions such as switching operations and lightning strikes, overvoltage waves will be generated inside the transmission lines, which places high demands on the insulation of the lines. The insulation level of transmission lines is mainly determined by the number of insulator discs in the insulator string and the air gap of the line insulation. Obtaining these parameters requires overvoltage calculations of the transmission lines.

[0003] Due to the widespread use of commercial electromagnetic transient software such as PSCAD / EMTDC, the calculation of overvoltage in transmission lines has become very convenient. Although the model library in commercial software contains a wealth of line models, PSCAD software still uses the classic implicit trapezoidal integral method for numerical algorithms, and there are still some problems to be solved in terms of numerical accuracy and computational efficiency. Summary of the Invention

[0004] This invention provides a method, apparatus, electronic device, and storage medium for analyzing overvoltage in transmission lines, in order to solve the problems of low accuracy and low efficiency in current overvoltage calculations for transmission lines.

[0005] According to one aspect of the present invention, a method for analyzing overvoltage in transmission lines is provided, the method comprising:

[0006] Based on the one-dimensional hyperbolic conservation law equation, we obtain a first set of ordinary differential equations with second-order accuracy and a second set of ordinary differential equations with third-order accuracy.

[0007] Establish the telegraph equations for the voltage traveling wave and current traveling wave of the current transmission line in terms of time and space, and obtain the flux reconstruction mathematical model of the current transmission line based on the first set of ordinary differential equations, the second set of ordinary differential equations and the telegraph equations;

[0008] Based on the flux reconstruction mathematical model, the boundary conditions at both ends of the current transmission line are determined, and the overvoltage at the end of the current transmission line is obtained according to the boundary conditions at both ends of the line.

[0009] Optionally, the one-dimensional hyperbolic conservation law equation is given by the following formula:

[0010]

[0011] Where u is a function of spatial distance x and time t; f(u) is called flux; u0(x) represents the initial condition;

[0012] Based on the one-dimensional hyperbolic conservation law equations, we obtain a first set of ordinary differential equations with second-order accuracy and a second set of ordinary differential equations with third-order accuracy, including:

[0013] Divide the interval [xa, xb] into N equal parts at equal intervals, with x... 1 / Starting from x N+1 / 2 The endpoint is [x]. The i-th interval segment is [x]. i-1 / 2 ,x i+1 / 2 ], i∈[1,N], in any interval I i =[x i-1 / 2 ,x i+1 / 2 Inside, let x i+1 / 2 -x i-1 / 2 =Δx i ,u(x i ,t)=u i Based on the one-dimensional hyperbolic conservation law equation, the following polynomial is obtained:

[0014]

[0015] in, Let u(x,t) be in the integration interval I i Mean value of the integral over;

[0016] Based on the polynomials, determine the first set of ordinary differential equations with second-order accuracy and the second set of ordinary differential equations with third-order accuracy, respectively.

[0017] Optionally, determining the first set of ordinary differential equations with second-order accuracy and the second set of ordinary differential equations with third-order accuracy based on the polynomials includes:

[0018] If t remains constant Let x i-1 / 2 =0, x i+1 / 2 =1 and x i+3 / 2 =2, then we can get:

[0019]

[0020] Again according to The first set of ordinary differential equations with second-order accuracy determined by polynomials is:

[0021]

[0022] If t remains constant Then we can obtain:

[0023]

[0024] The second set of ordinary differential equations with third-order accuracy determined based on polynomials is as follows:

[0025]

[0026] Optionally, establish the telegraphic equations for the voltage and current traveling waves of the current transmission line as a function of time and space, specifically:

[0027]

[0028] Where ν represents the voltage traveling wave column vector on the current transmission line; i represents the current traveling wave column vector on the current transmission line; R represents the distributed parameter resistance matrix of the current transmission line; L represents the distributed parameter inductance matrix of the current transmission line; C represents the distributed parameter capacitance matrix of the current transmission line; and G represents the distributed parameter conductance matrix of the current transmission line.

[0029] Optionally, obtaining the flux reconfiguration mathematical model of the current transmission line based on the first set of ordinary differential equations, the second set of ordinary differential equations, and the telegraph equations includes:

[0030] Substituting the first and second sets of ordinary differential equations into the telegraph equations and solving numerically yields the following:

[0031]

[0032] in, coefficient matrix coefficient matrix

[0033] Definition I i =[x i-1 / 2 ,x i+1 / 2 The mean value of the integral over u(x,t) is:

[0034]

[0035] Accordingly, the mathematical model for flux reconfiguration of the current transmission line is obtained, specifically as follows:

[0036]

[0037] Where X = u1, u2, ..., u N ];

[0038]

[0039]

[0040] Where Δx is the discrete step length of the transmission line in space; N is the number of grid cells in space.

[0041] Optionally, the boundary conditions at both ends of the current transmission line based on the flux reconstruction mathematical model include:

[0042] Based on the aforementioned flux reconstruction mathematical model, the boundary conditions at both ends of the current transmission line are as follows:

[0043]

[0044] Where, r s This represents the load resistance of the current transmission line.

[0045] Optionally, the overvoltage at the end of the current transmission line is obtained based on the boundary conditions at both ends of the line, including:

[0046] If the current transmission line is closed under no-load conditions, the overvoltage at the end of the current transmission line gradually decreases with the transient component.

[0047] If a lightning surge wave intrudes into the beginning of the current transmission line, the traveling wave of the lightning will be repeatedly refracted and reflected at the end of the current transmission line, resulting in severe attenuation and deformation of the waveform of the overvoltage at the end of the current transmission line.

[0048] According to another aspect of the present invention, a transmission line overvoltage analysis device is provided, the transmission line overvoltage analysis device comprising:

[0049] The ordinary differential equation system determination module is used to execute the first ordinary differential equation system with second-order accuracy and the second ordinary differential equation system with third-order accuracy based on the one-dimensional hyperbolic conservation law equation;

[0050] The mathematical model construction module is used to execute the telegraph equations for establishing the voltage traveling wave and current traveling wave of the current transmission line in terms of time and space, and to obtain the flux reconstruction mathematical model of the current transmission line based on the first set of ordinary differential equations, the second set of ordinary differential equations and the telegraph equations.

[0051] The overvoltage analysis module is used to perform the boundary conditions at both ends of the current transmission line based on the flux reconstruction mathematical model, and to obtain the terminal overvoltage of the current transmission line according to the boundary conditions at both ends of the line.

[0052] According to another aspect of the present invention, an electronic device is provided, the electronic device comprising:

[0053] At least one processor; and

[0054] A memory communicatively connected to the at least one processor; wherein,

[0055] The memory stores a computer program that can be executed by the at least one processor, which enables the at least one processor to perform the transmission line overvoltage analysis method according to any embodiment of the present invention.

[0056] According to another aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium storing computer instructions for causing a processor to execute and implement the transmission line overvoltage analysis method according to any embodiment of the present invention.

[0057] The technical solution of this invention obtains a first set of ordinary differential equations with second-order accuracy and a second set of ordinary differential equations with third-order accuracy based on the one-dimensional hyperbolic conservation law equation; establishes telegraphic equations for the voltage and current traveling waves of the current transmission line as a function of time and space; and obtains a flux reconstruction mathematical model of the current transmission line based on the first set of ordinary differential equations, the second set of ordinary differential equations, and the telegraphic equations; based on the flux reconstruction mathematical model, the boundary conditions at both ends of the current transmission line are determined, and the terminal overvoltage of the current transmission line is obtained based on the boundary conditions at both ends. This invention solves the problem of low accuracy and low efficiency in current transmission line overvoltage calculations, achieving accurate and efficient transmission line overvoltage calculations while saving calculation time.

[0058] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of the present invention, nor is it intended to limit the scope of the invention. Other features of the invention will become readily apparent from the following description. Attached Figure Description

[0059] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0060] Figure 1 This is a flowchart of a transmission line overvoltage analysis method provided in Embodiment 1 of the present invention;

[0061] Figure 2 This is a schematic diagram of the arrangement of sampling template points for numerical flux reconstruction according to Embodiment 1 of the present invention;

[0062] Figure 3 This is a schematic diagram of the circuit breaker closing during no-load charging of a transmission line according to Embodiment 1 of the present invention;

[0063] Figure 4This is a comparison chart of simulation results of the voltage at the end of a transmission line applicable to Embodiment 1 of the present invention;

[0064] Figure 5 This is a waveform diagram of lightning overvoltage at the end of a transmission line applicable to Embodiment 1 of the present invention;

[0065] Figure 6 This is a waveform diagram of lightning overcurrent near the end of a transmission line applicable to Embodiment 1 of the present invention;

[0066] Figure 7 This is a schematic diagram of the structure of a transmission line overvoltage analysis device according to Embodiment 2 of the present invention;

[0067] Figure 8 This is a schematic diagram of the structure of an electronic device that implements the overvoltage analysis method for power transmission lines according to embodiments of the present invention. Detailed Implementation

[0068] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0069] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0070] Example 1

[0071] Figure 1This is a flowchart of a transmission line overvoltage analysis method provided in Embodiment 1 of the present invention. This embodiment is applicable to the case of transmission line overvoltage analysis using a time-domain explicit method based on flux reconstruction. This transmission line overvoltage analysis method can be executed by a transmission line overvoltage analysis device, which can be implemented in hardware and / or software and can be configured in electronic equipment within the transmission line. Figure 1 As shown, the overvoltage analysis method for this transmission line includes:

[0072] S110. Based on the one-dimensional hyperbolic conservation law equation, a first set of ordinary differential equations with second-order accuracy and a second set of ordinary differential equations with third-order accuracy are obtained.

[0073] In this embodiment, the initial value problem of the one-dimensional hyperbolic conservation law equation is analyzed, and the one-dimensional hyperbolic conservation law equation is established as follows (1):

[0074]

[0075] Here, u is a function of spatial distance x and time t, f(u) is called flux, and u0(x) represents the initial condition.

[0076] Furthermore, the interval [xa, xb] is divided into N equal parts at equal intervals, with x... 1 / 2 Starting from x N+1 / 2 The endpoint is [x]. The i-th interval segment is [x]. i-1 / 2 ,x i+1 / 2 ], i∈[1,N];

[0077] It is understandable that in any interval I i =[x i-1 / 2 ,x i+1 / 2 Within this equation, assuming f(u) = au, a > 0, we can obtain the following by taking the definite integral over both sides of equation (1):

[0078]

[0079] Let x i+1 / 2 -x i-1 / 2 =Δx i ,u(x i ,t)=u i Divide both sides of equation (2) by Δx i And by the mean value theorem for integrals, we can obtain the following polynomial (3):

[0080]

[0081] in, Let u(x,t) be in the integration interval I i The mean value of the integral over .

[0082] Furthermore, u(x,t) is numerically approximated using polynomial (3), such as... Figure 2 The sampled template points are S = {I} i ,I i+1}for u i+1 / 2 Refactor.

[0083] Based on the polynomials, determine the first set of ordinary differential equations with second-order accuracy and the second set of ordinary differential equations with third-order accuracy, respectively.

[0084] If t remains constant Let x i-1 / 2 =0, x i+1 / 2 =1 and x i+3 / 2 =2, then we can get:

[0085]

[0086] Again according to The first set of ordinary differential equations with second-order accuracy determined by polynomials is:

[0087]

[0088] If t remains constant If the sampled template point is S = S1, then we can obtain:

[0089]

[0090] If the sampled template point is S = S0, then:

[0091]

[0092] If the sampled template points are S = S2, then:

[0093]

[0094] The second set of ordinary differential equations with third-order accuracy in the time domain, based on polynomial (3), is as follows:

[0095]

[0096] The present invention can complete the numerical flux reconstruction through the above steps, and then use the first set of ordinary differential equations with second-order accuracy shown in Equation (5) and the second set of ordinary differential equations with third-order accuracy shown in Equation (9) to perform electromagnetic transient numerical calculations on the telegraph equations of high-voltage transmission lines.

[0097] S120. Establish the telegraph equations for the voltage traveling wave and current traveling wave of the current transmission line in terms of time and space, and obtain the flux reconstruction mathematical model of the current transmission line based on the first set of ordinary differential equations, the second set of ordinary differential equations and the telegraph equations.

[0098] Specifically, mathematical equations for the voltage and current traveling waves of the transmission line with time and space are established, i.e., the telegraphic equations for the voltage and current traveling waves of the current transmission line with time and space, as shown below:

[0099]

[0100] Where ν represents the voltage traveling wave column vector on the current transmission line; i represents the current traveling wave column vector on the current transmission line; R represents the distributed parameter resistance matrix of the current transmission line; L represents the distributed parameter inductance matrix of the current transmission line; C represents the distributed parameter capacitance matrix of the current transmission line; and G represents the distributed parameter conductance matrix of the current transmission line.

[0101] Substituting the first set of ordinary differential equations with second-order precision shown in equation (5) and the second set of ordinary differential equations with third-order precision shown in equation (9) into the telegraph equation in equation (10) for numerical solution, we can obtain equation (11):

[0102]

[0103] in, coefficient matrix coefficient matrix

[0104] Definition I i =[x i-1 / 2 ,x i+1 / 2 The mean value of the integral over u(x,t) is:

[0105]

[0106] Furthermore, along the horizontal direction of the current transmission line, the current transmission line is divided into a series of equally spaced intervals I. i =[x i-1 / 2 ,x i+1 / 2 Similarly, by taking the definite integral of both sides of equation (11) in the x-direction, we obtain:

[0107]

[0108] Substituting the first set of ordinary differential equations with second-order accuracy shown in equation (5) into equation (13) yields:

[0109]

[0110] Furthermore, by rewriting equation (14) in matrix form, we obtain the mathematical model for flux reconfiguration of the current transmission line, which is as follows:

[0111]

[0112] In the formula: X = [u1, u2, ..., u N ];

[0113]

[0114]

[0115] Where Δx is the discrete step length of the transmission line in space; N is the number of grid cells in space.

[0116] In this embodiment, the third-order TVD-RK method is used for the numerical integration in the time domain of equation (15). For the initial value problem, let u t =L(u), and the flux reconstruction mathematical model of the current transmission line telegraph equation can be obtained:

[0117]

[0118] In the formula, h represents the step size of the stepwise integration in the time domain.

[0119] Thus, the flux reconstruction process of the current transmission line telegraph equations can be completed through the above steps.

[0120] S130. Based on the flux reconstruction mathematical model, determine the boundary conditions at both ends of the current transmission line, and obtain the overvoltage at the end of the current transmission line according to the boundary conditions at both ends.

[0121] Specifically, solving for overvoltage at the end of a transmission line using the above formula (15) requires considering the boundary conditions at both ends of the line, that is, the boundary conditions at both ends of the current transmission line based on the flux reconstruction mathematical model are as follows:

[0122]

[0123] Where, r s This represents the load resistance of the current transmission line.

[0124] In this application, if the current transmission line is in a no-load closing state, the overvoltage at the end of the current transmission line gradually decreases with the transient component. It is understood that, considering the no-load closing problem of a single transmission line, to better reflect the level of overvoltage experienced by the line, the level of overvoltage at the end of the transmission line when the closing phase is 90° is considered, such as... Figure 3As shown, the distributed parameters of the transmission line are: R = 0.2568 Ω / km, L = 0.2568 H / km, C = 8.60 × 10⁻⁶. -9 F / km.

[0125] For example, a simulation model of a transmission line under no-load charging is established in PSCAD simulation software, ensuring that the integration step size is 1μs in time and the number of interval grids is N=30 in space. The simulation results of the voltage at the end of the line are compared as shown in the figure. Figure 4 As shown. From Figure 4 As can be seen, the simulation results of PSCAD simulation and the overvoltage analysis method of transmission lines provided in this embodiment are basically consistent. As the transient component gradually decays, the simulation results of the two methods almost completely overlap, which confirms the effectiveness of the overvoltage analysis of the transmission line's end.

[0126] In another embodiment, if a lightning shock wave intrudes into the head end of the current transmission line, the lightning traveling wave is repeatedly refracted and reflected at the end of the current transmission line, resulting in severe attenuation and deformation of the waveform of the overvoltage at the end of the current transmission line.

[0127] For example, when a lightning surge intrudes into the head end of a 120km transmission line, the voltage at the end of the 120km transmission line is simulated and calculated. Using 12 π-type chains instead of a long line with distributed parameters will introduce significant errors. When the end of the transmission line is unloaded, the capacitance per unit length C = 8.30 × 10⁻⁹ F / km, the inductance L = 1.33 × 10⁻⁴ H / km, the parallel path of the lightning current surge R = 1kΩ, and the lightning current surge i adopts a double exponential impulse current, with its maximum value i m =10kA, the time-domain expression is:

[0128]

[0129] In the formula, A = 1.037; τ1 = 0.4074 μs, which represents the time required for the current to rise from zero to the peak value, called the wavefront action time; and τ2 = 68.22 μs, which represents the time required for the current to fall from the peak value to half the peak value, called the apparent half-peak time.

[0130] In this invention, the number of spatial interval grids is N=30, and the simulation waveform is shown below. Figure 5 and 6 As shown. From Figure 5 and 6As can be seen, the lightning traveling wave undergoes repeated refraction and reflection at the end of the current transmission line. During this process, the waveform is severely attenuated and deformed, with the instantaneous maximum voltage approaching 800kV and the maximum current reaching 15kA. This poses a serious threat to the insulation of the current transmission line. Therefore, it is advisable to consider installing surge arresters at the end of the current transmission line to suppress the damage of the surge wave to the insulation performance of the current transmission line.

[0131] It should be noted that the electromagnetic transient simulation of transmission lines proposed in this invention is an explicit algorithm, possessing second- or third-order accuracy in spatial dimensions and fourth- or third-order accuracy in temporal dimensions. Compared to most existing implicit numerical algorithms, it exhibits higher computational efficiency. Furthermore, comparison with simulation results from PSCAD software verifies the effectiveness of the proposed method for analyzing end-point overvoltages in current transmission lines.

[0132] The technical solution of this invention obtains a first set of ordinary differential equations with second-order accuracy and a second set of ordinary differential equations with third-order accuracy based on the one-dimensional hyperbolic conservation law equation; establishes telegraphic equations for the voltage and current traveling waves of the current transmission line as a function of time and space; and obtains a flux reconstruction mathematical model of the current transmission line based on the first set of ordinary differential equations, the second set of ordinary differential equations, and the telegraphic equations; based on the flux reconstruction mathematical model, the boundary conditions at both ends of the current transmission line are determined, and the terminal overvoltage of the current transmission line is obtained based on the boundary conditions at both ends. This invention solves the problem of low accuracy and low efficiency in current transmission line overvoltage calculations, achieving accurate and efficient transmission line overvoltage calculations while saving calculation time.

[0133] Example 2

[0134] Figure 7 This is a schematic diagram of the structure of a power transmission line overvoltage analysis device provided in Embodiment 3 of the present invention. Figure 7 As shown, the overvoltage analysis device for the transmission line includes:

[0135] The ordinary differential equation system determination module 710 is used to execute the first ordinary differential equation system with second-order accuracy and the second ordinary differential equation system with third-order accuracy based on the one-dimensional hyperbolic conservation law equation;

[0136] The mathematical model construction module 720 is used to execute the telegraph equations for establishing the voltage traveling wave and current traveling wave of the current transmission line in terms of time and space, and to obtain the flux reconstruction mathematical model of the current transmission line based on the first set of ordinary differential equations, the second set of ordinary differential equations and the telegraph equations.

[0137] The overvoltage analysis module 730 is used to perform the boundary conditions at both ends of the current transmission line based on the flux reconstruction mathematical model, and to obtain the end overvoltage of the current transmission line according to the boundary conditions at both ends of the line.

[0138] Optionally, the one-dimensional hyperbolic conservation law equation is given by the following formula:

[0139]

[0140] Where u is a function of spatial distance x and time t; f(u) is called flux; u0(x) represents the initial condition;

[0141] The ordinary differential equation system determination module 710 is specifically used for:

[0142] Divide the interval [xa, xb] into N equal parts at equal intervals, with x... 1 / Starting from x N+1 / 2 The endpoint is [x]. The i-th interval segment is [x]. i-1 / 2 ,x i+1 / 2 ], i∈[1,N], in any interval I i =[x i-1 / 2 ,x i+1 / 2 Inside, let x i+1 / 2 -x i-1 / 2 =Δx i ,u(x i ,t)=u i Based on the one-dimensional hyperbolic conservation law equation, the following polynomial is obtained:

[0143]

[0144] in, Let u(x,t) be in the integration interval I i Mean value of the integral over;

[0145] Based on the polynomials, determine the first set of ordinary differential equations with second-order accuracy and the second set of ordinary differential equations with third-order accuracy, respectively.

[0146] Optionally, determining the first set of ordinary differential equations with second-order accuracy and the second set of ordinary differential equations with third-order accuracy based on the polynomials includes:

[0147] If t remains constant Let x i-1 / 2 =0, x i+1 / 2 =1 and x i+3 / 2 =2, then we can get:

[0148]

[0149] Again according to The first set of ordinary differential equations with second-order accuracy determined by polynomials is:

[0150]

[0151] If t remains constant Then we can obtain:

[0152]

[0153] The second set of ordinary differential equations with third-order accuracy determined based on polynomials is as follows:

[0154]

[0155] Optionally, establish the telegraphic equations for the voltage and current traveling waves of the current transmission line as a function of time and space, specifically:

[0156]

[0157] Where ν represents the voltage traveling wave column vector on the current transmission line; i represents the current traveling wave column vector on the current transmission line; R represents the distributed parameter resistance matrix of the current transmission line; L represents the distributed parameter inductance matrix of the current transmission line; C represents the distributed parameter capacitance matrix of the current transmission line; and G represents the distributed parameter conductance matrix of the current transmission line.

[0158] Optionally, obtaining the flux reconfiguration mathematical model of the current transmission line based on the first set of ordinary differential equations, the second set of ordinary differential equations, and the telegraph equations includes:

[0159] Substituting the first and second sets of ordinary differential equations into the telegraph equations and solving numerically yields the following:

[0160]

[0161] in, coefficient matrix coefficient matrix

[0162] Definition I i =[x i-1 / 2 ,x i+1 / 2 The mean value of the integral over u(x,t) is:

[0163]

[0164] Accordingly, the mathematical model for flux reconfiguration of the current transmission line is obtained, specifically as follows:

[0165]

[0166] Where X = [u1, u2, ..., u N ];

[0167]

[0168]

[0169] Where Δx is the discrete step length of the transmission line in space; N is the number of grid cells in space.

[0170] Optionally, the boundary conditions at both ends of the current transmission line based on the flux reconstruction mathematical model include:

[0171] Based on the aforementioned flux reconstruction mathematical model, the boundary conditions at both ends of the current transmission line are as follows:

[0172]

[0173] Where, r s This represents the load resistance of the current transmission line.

[0174] Optionally, the overvoltage at the end of the current transmission line is obtained based on the boundary conditions at both ends of the line, including:

[0175] If the current transmission line is closed under no-load conditions, the overvoltage at the end of the current transmission line gradually decreases with the transient component.

[0176] If a lightning surge wave intrudes into the beginning of the current transmission line, the traveling wave of the lightning will be repeatedly refracted and reflected at the end of the current transmission line, resulting in severe attenuation and deformation of the waveform of the overvoltage at the end of the current transmission line.

[0177] The transmission line overvoltage analysis device provided in this embodiment of the invention can execute the transmission line overvoltage analysis method provided in any embodiment of the invention, and has the corresponding functional modules and beneficial effects for executing the transmission line overvoltage analysis method.

[0178] Example 3

[0179] Figure 8A schematic diagram of an electronic device 810 that can be used to implement embodiments of the present invention is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices (e.g., helmets, glasses, watches, etc.), and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the invention described and / or claimed herein.

[0180] like Figure 8 As shown, the electronic device 810 includes at least one processor 811 and a memory, such as a read-only memory (ROM) 812 or a random access memory (RAM) 813, communicatively connected to the at least one processor 811. The memory stores computer programs executable by the at least one processor. The processor 811 can perform various appropriate actions and processes based on the computer program stored in the ROM 812 or loaded from storage unit 818 into the RAM 813. The RAM 813 can also store various programs and data required for the operation of the electronic device 810. The processor 811, ROM 812, and RAM 813 are interconnected via a bus 814. An input / output (I / O) interface 815 is also connected to the bus 814.

[0181] Multiple components in electronic device 810 are connected to I / O interface 815, including: input unit 816, such as keyboard, mouse, etc.; output unit 817, such as various types of displays, speakers, etc.; storage unit 818, such as disk, optical disk, etc.; and communication unit 819, such as network card, modem, wireless transceiver, etc. Communication unit 819 allows electronic device 810 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0182] Processor 811 can be a variety of general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of processor 811 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various special-purpose artificial intelligence (AI) computing chips, various processors running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. Processor 811 performs the various methods and processes described above, such as the overvoltage analysis method for transmission lines.

[0183] In some embodiments, the transmission line overvoltage analysis method may be implemented as a computer program tangibly contained in a computer-readable storage medium, such as storage unit 818. In some embodiments, part or all of the computer program may be loaded and / or installed on electronic device 810 via ROM 812 and / or communication unit 819. When the computer program is loaded into RAM 813 and executed by processor 811, one or more steps of the transmission line overvoltage analysis method described above may be performed. Alternatively, in other embodiments, processor 811 may be configured to perform the transmission line overvoltage analysis method by any other suitable means (e.g., by means of firmware).

[0184] Various embodiments of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), systems-on-a-chip (SoCs), payload-programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments may include implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0185] Computer programs used to implement the methods of the present invention may be written in any combination of one or more programming languages. These computer programs may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the processor, the computer programs cause the functions / operations specified in the flowcharts and / or block diagrams to be performed. The computer programs may be executed entirely on a machine, partially on a machine, or as a standalone software package, partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0186] In the context of this invention, a computer-readable storage medium can be a tangible medium that may contain or store a computer program for use by or in conjunction with an instruction execution system, apparatus, or device. A computer-readable storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination thereof. Alternatively, a computer-readable storage medium may be a machine-readable signal medium. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0187] To provide interaction with a user, the systems and techniques described herein can be implemented on an electronic device having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the electronic device. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0188] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as data servers), or computing systems that include middleware components (e.g., application servers), or computing systems that include frontend components (e.g., user computers with graphical user interfaces or web browsers through which users can interact with implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., communication networks). Examples of communication networks include local area networks (LANs), wide area networks (WANs), blockchain networks, and the Internet.

[0189] A computing system can include clients and servers. Clients and servers are generally located far apart and typically interact through communication networks. The client-server relationship is created by computer programs running on the respective computers and having a client-server relationship with each other. The server can be a cloud server, also known as a cloud computing server or cloud host, which is a hosting product within the cloud computing service system to address the shortcomings of traditional physical hosts and VPS services, such as high management difficulty and weak business scalability.

[0190] It should be understood that the various forms of processes shown above can be used, with steps reordered, added, or deleted. For example, the steps described in this invention can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution of this invention can be achieved, and this is not limited herein.

[0191] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A power transmission line overvoltage analysis method characterized by, include: Based on the one-dimensional hyperbolic conservation law equation, we obtain a first set of ordinary differential equations with second-order accuracy and a second set of ordinary differential equations with third-order accuracy. Establish the telegraph equations for the voltage traveling wave and current traveling wave of the current transmission line in terms of time and space, and obtain the flux reconstruction mathematical model of the current transmission line based on the first set of ordinary differential equations, the second set of ordinary differential equations and the telegraph equations; Based on the flux reconstruction mathematical model, the boundary conditions at both ends of the current transmission line are determined, and the overvoltage at the end of the current transmission line is obtained according to the boundary conditions at both ends of the line. The one-dimensional hyperbolic conservation law equation is shown in the following equation: where u is a function of the spatial distance x and time t; called flux; denotes the initial value condition; Based on the one-dimensional hyperbolic conservation law equations, we obtain a first set of ordinary differential equations with second-order accuracy and a second set of ordinary differential equations with third-order accuracy, including: Divide the interval [x a ,x b ] into N equal parts, take x as the starting point and x as the end point, the i-th interval is , in any interval , let , , based on the one-dimensional hyperbolic conservation law equation, the following polynomial is obtained: wherein is the integral of over the interval Based on the polynomials, determine the first set of ordinary differential equations with second-order accuracy and the second set of ordinary differential equations with third-order accuracy respectively; The step of determining the first set of ordinary differential equations with second-order accuracy and the second set of ordinary differential equations with third-order accuracy based on the polynomials includes: If t remains constant, , set , and , we obtain: Rein , according to Then, the first-order ordinary differential equation group with 2-order accuracy is determined based on the polynomial: If t remains constant, then we obtain: The second set of ordinary differential equations with third-order accuracy determined based on polynomials is as follows: ； The telegraphic equations for the voltage and current traveling waves of the current transmission line are established as follows: wherein, represents a voltage traveling wave train vector on the current transmission line; represents a current traveling wave train vector on the current transmission line; represents a distributed parameter resistance matrix of the current transmission line; represents a distributed parameter inductance matrix of the current transmission line; represents a distributed parameter capacitance matrix of the current transmission line; represents a distributed parameter conductance matrix of the current transmission line; The process of obtaining the flux reconfiguration mathematical model of the current transmission line based on the first set of ordinary differential equations, the second set of ordinary differential equations, and the telegraph equations includes: Substituting the first and second sets of ordinary differential equations into the telegraph equations and solving numerically yields the following results. in, Coefficient matrix Coefficient matrix ; definition superior The integral value is: Accordingly, the mathematical model for flux reconfiguration of the current transmission line is obtained, specifically as follows: in, ; ； in, For the distance of the transmission line in space.

2. The overvoltage analysis method for transmission lines according to claim 1, characterized in that, The boundary conditions at both ends of the current transmission line based on the flux reconstruction mathematical model include: Based on the aforementioned flux reconstruction mathematical model, the boundary conditions at both ends of the current transmission line are as follows: in, This represents the load resistance of the current transmission line.

3. The overvoltage analysis method for transmission lines according to claim 2, characterized in that, The overvoltage at the end of the current transmission line is obtained based on the boundary conditions at both ends of the line, including: If the current transmission line is closed under no-load conditions, the overvoltage at the end of the current transmission line gradually decreases with the transient component. If a lightning surge wave intrudes into the beginning of the current transmission line, the traveling wave of the lightning will be repeatedly refracted and reflected at the end of the current transmission line, resulting in severe attenuation and deformation of the waveform of the overvoltage at the end of the current transmission line.

4. A transmission line overvoltage analysis device, characterized in that, include: The ordinary differential equation system determination module is used to execute the first ordinary differential equation system with second-order accuracy and the second ordinary differential equation system with third-order accuracy based on the one-dimensional hyperbolic conservation law equation; The mathematical model construction module is used to execute the telegraph equations for establishing the voltage traveling wave and current traveling wave of the current transmission line in terms of time and space, and to obtain the flux reconstruction mathematical model of the current transmission line based on the first set of ordinary differential equations, the second set of ordinary differential equations and the telegraph equations. The overvoltage analysis module is used to perform the boundary conditions at both ends of the current transmission line based on the flux reconstruction mathematical model, and to obtain the terminal overvoltage of the current transmission line according to the boundary conditions at both ends of the line. The one-dimensional hyperbolic conservation law equation is shown in the following equation: Where u is a function of spatial distance x and time t; This is called flux; Indicate the initial value condition; Based on the one-dimensional hyperbolic conservation law equations, we obtain a first set of ordinary differential equations with second-order accuracy and a second set of ordinary differential equations with third-order accuracy, including: The interval [x a ,x b Divide into N equal parts at equal intervals, with Starting from, The endpoint is the i-th segment. In any interval Inside, order , Based on the one-dimensional hyperbolic conservation law equation, the following polynomial is obtained: in, for In the integration interval Mean value of the integral over; Based on the polynomials, determine the first set of ordinary differential equations with second-order accuracy and the second set of ordinary differential equations with third-order accuracy respectively; The step of determining the first set of ordinary differential equations with second-order accuracy and the second set of ordinary differential equations with third-order accuracy based on the polynomials includes: If t remains constant ,set up , and That is, we get: Again ,according to Then, the first set of ordinary differential equations with second-order accuracy determined based on polynomials is: If t remains constant Then we get: The second set of ordinary differential equations with third-order accuracy determined based on polynomials is as follows: ； The telegraphic equations for the voltage and current traveling waves of the current transmission line are established as follows: in, This represents the column vector of the voltage traveling wave on the current transmission line; This represents the current traveling wave column vector on the current transmission line. This represents the distributed parameter resistance matrix of the current transmission line; This represents the distributed parameter inductance matrix of the current transmission line; This represents the distributed parameter capacitance matrix of the current transmission line; This represents the distributed parameter conductance matrix of the current transmission line; The process of obtaining the flux reconfiguration mathematical model of the current transmission line based on the first set of ordinary differential equations, the second set of ordinary differential equations, and the telegraph equations includes: Substituting the first and second sets of ordinary differential equations into the telegraph equations and solving numerically yields the following results. in, Coefficient matrix Coefficient matrix ; definition superior The integral value is: Accordingly, the mathematical model for flux reconfiguration of the current transmission line is obtained, specifically as follows: in, ; ； in, For the distance of the transmission line in space.

5. An electronic device, characterized in that, The electronic device includes: At least one processor; and A memory communicatively connected to the at least one processor; wherein, The memory stores a computer program that can be executed by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to perform the transmission line overvoltage analysis method according to any one of claims 1-3.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that, when executed by a processor, implement the transmission line overvoltage analysis method according to any one of claims 1-3.

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