CN113917550A - Magnetic storm induced ground electric field calculation method and device considering coastal effect - Google Patents
Magnetic storm induced ground electric field calculation method and device considering coastal effect Download PDFInfo
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Abstract
The application relates to the technical field of magnetic storm induced ground electric fields, in particular to a method and a device for calculating a magnetic storm induced ground electric field considering a coastal effect. The method for calculating the magnetic storm induced geoelectric field considering the coastal effect comprises the following steps: determining a ground conductivity model, collecting original magnetic storm data, and determining a ground electric field base value according to the ground conductivity model and the original magnetic storm data; determining transmission line characteristic parameters of the ground conductivity model, and determining the negative potential gradient of the distorted electric field according to the ground electric field basic value and the transmission line characteristic parameters based on the ground conductivity model; and determining the magnetic storm induction ground electric field according to the ground electric field base value and the negative potential gradient of the distorted electric field. By adopting the scheme, the calculation efficiency is effectively improved by avoiding using a numerical solution, the distribution condition of the magnetic storm induction ground field along the direction vertical to the sea-land boundary surface can be given, and meanwhile, the method can be used for evaluating the influence of transverse conductivity change on the ground field and GIC in the long conductor during the magnetic storm.
Description
Technical Field
The application relates to the technical field of magnetic storm induced ground electric fields, in particular to a method and a device for calculating a magnetic storm induced ground electric field considering a coastal effect.
Background
In a space weather event, the interaction between the solar wind and the earth's magnetic field causes geomagnetic disturbances. According to faraday's law of electromagnetic induction, the varying earth magnetic field generates a ground electric field, inducing a current in the grounded conductor loop at a frequency of 0.0001-0.01Hz, called a Geomagnetic Induction Current (GIC). The collimated flow flows in the foundation system, which affects the normal operation of the system and makes the system face security threat. In an electric power system, the GIC flows into the transformer through the transformer neutral point, and can saturate the transformer half-waves, resulting in transformer overheating, increased harmonics, and increased reactive losses. Under the action of the GIC, misoperation of the relay can be caused, and serious power grid power failure accidents are caused. The magnetic storm damages a pipe network system, generates GIC and pipe-to-ground potential, aggravates pipeline corrosion, shortens the service life of the pipeline and even has the consequences of leakage and explosion. For railway systems, especially high-speed rail electrical systems, GIC paths exist in traction networks, track circuits and locomotive systems, and the railway running safety is threatened.
With the rapid development of social economy, the production and life quality of people increasingly depend on the safe and stable operation of a power grid. Therefore, it is very important to accurately evaluate the damage of the GIC event to the normal operation of the power system and improve the capability of the power grid in resisting extreme space weather disasters. Determining whether a power system is susceptible to a magnetic storm generally includes two stages: 1) in the geophysical stage, a horizontal electric field on the surface of the ground, called a magnetic storm induction ground field, is determined according to the data of the geomagnetic field disturbed by the magnetic storm and the electrical structure of the ground; 2) and in the engineering stage, calculating the power grid GIC driven by the induction ground electric field based on the power grid topological structure and the direct current parameters. Under the condition of known earth electric field, the calculation of the step is converted into a simple circuit problem. It can be seen that the study of induced earth electric fields plays a crucial role in the evaluation of the effects of magnetic storms on ground based systems.
When the induced earth electric field distribution is calculated, a plane wave method is widely used at present, namely, the earth electric conductivity is assumed to be only related to the depth, and a one-dimensional layered electric conductivity model is generally adopted to calculate the induced earth electric field according to the ground magnetic field observation data. In the frequency range of magnetic storm induction, the penetration depth of the electromagnetic field reaches hundreds of kilometers, and at the depth, the transverse change of the earth conductivity in a small range is not large, and the precision requirement of engineering calculation can be met by adopting a one-dimensional simplified model. However, with the development of economy and the need of long-distance power transmission in China, the scale of the power grid is continuously enlarged, and the large-ground conductivity structure of the region spanned by the power grid is inevitably diversified and complicated. The distribution of the ground electric field varies in different ground structures, and especially, different degrees of distortion are generated near the interface of the medium. When the target substation is located near a coastline, as the conductivity of seawater is far greater than that of adjacent land, when a magnetic storm occurs, the difference of induced currents in two media is large, the current density difference on two sides of a sea-land interface causes the induced electric field of the land to be remarkably enhanced in the direction perpendicular to the coast, and the grid GIC is increased along with the increase of the grid GIC, which is also called as the coast effect of the GIC. At this time, the one-dimensional earth model cannot reflect the difference, and a large error is caused by neglecting the earth electric field distortion caused by the transverse sudden change of the conductivity, and even a wrong conclusion can be obtained. Therefore, the research on the influence of the coastal effect on the magnetic storm induced ground electric field is of great significance.
Disclosure of Invention
The present application is directed to solving, at least to some extent, one of the technical problems in the related art.
Therefore, a first objective of the present application is to provide a method for calculating a magnetic storm induced ground field considering a coastal effect, so as to solve the technical problem that the calculation process of the magnetic storm induced ground field considering the coastal effect is complex at present.
A second object of the present application is to provide a magnetic storm induced ground electric field calculation apparatus considering the coast effect.
In order to achieve the above object, a method for calculating a magnetic storm induced ground field considering a coast effect according to an embodiment of the present application includes:
determining a ground conductivity model, collecting original magnetic storm data, and determining a ground electric field base value according to the ground conductivity model and the original magnetic storm data;
determining transmission line characteristic parameters of a ground conductivity model, and determining the negative potential gradient of a distorted electric field according to the ground electric field basic value and the transmission line characteristic parameters on the basis of the ground conductivity model;
and determining the magnetic storm induction ground electric field according to the ground electric field base value and the negative potential gradient of the distorted electric field.
Optionally, in an embodiment of the present application, the determining a ground electric field base value according to the ground conductivity model and the raw magnetic storm data includes:
determining frequency domain magnetic field components according to the original magnetic storm data;
the earth conductivity model is a one-dimensional layered model, and earth surface wave impedance is determined according to the earth conductivity model;
and determining the ground electric field base value based on Maxwell equation according to the frequency domain magnetic field component and the earth surface wave impedance.
Optionally, in an embodiment of the present application, the earth conductivity model is a one-dimensional layered model, and the earth-surface wave impedance is determined according to the earth conductivity model; determining the ground electric field base value based on Maxwell equation according to the frequency domain magnetic field component and the surface wave impedance, including:
determining the bottom-layer wave impedance according to:
wherein S isNIs the bottom wave impedance, mu, in a model of earth conductivity0Is the value of magnetic permeability in vacuum, kNFor the propagation constant of the underlayer in the model of the earth conductivity, σNConductivity of the underlying infinite half space;
determining the earth surface wave impedance based on the following formula by utilizing a recurrence relation according to the bottom layer wave impedance:
wherein Sn is the wave impedance of the nth layer in the earth conductivity model, k0The magnetic permeability value in vacuum is shown, kn isThe propagation constant of the n-th layer in the model of the earth conductivity, hn is the thickness of the n-th layer in the model of the earth conductivity, rnThe reflection coefficient of the nth layer in the earth conductivity model; σ is the conductivity.
Determining the frequency domain electric field component based on Maxwell's equations according to:
wherein the content of the first and second substances,
is a frequency domain electric field component, mu0Is the value of the magnetic permeability in a vacuum,
as a component of the magnetic field in the frequency domain, S0Is the earth surface wave impedance;
and determining the ground electric field base value according to the frequency domain electric field component.
Optionally, in an embodiment of the present application, the determining the transmission line characteristic parameter of the ground conductivity model, and determining the distortion electric field negative potential gradient according to the ground electric field base value and the transmission line characteristic parameter based on the ground conductivity model, includes:
the transmission line characteristic parameters are the resistance of the conducting layer, the cross sectional area and the conductance of the ground shell layer;
determining boundary conditions, and determining the distorted electric field negative potential gradient of the simple earth structure and the complex earth structure in the earth conductivity model according to the earth electric field basic value and the transmission line characteristic parameters based on the boundary conditions;
the simple ground structure is a land structure or a seawater structure with only one electrical distribution;
the complex earth structure is a complex earth structure comprising a plurality of electrical distributions.
Optionally, in an embodiment of the application, the boundary condition is determined from a Thevenin equivalent circuit.
Optionally, in an embodiment of the present application, the determining, based on the boundary condition, a distorted electric field negative potential gradient of a simple earth structure and a complex earth structure in the earth conductivity model according to the earth electric field basic value and the transmission line characteristic parameter includes:
dividing the earth conductivity model into a plurality of earth unit cells;
determining the distorted electric field voltage of the earth unit cell according to the transmission line characteristic parameters and the earth electric field basic value based on boundary conditions;
and determining the negative potential gradient of the distorted electric field of the land structure and the seawater structure according to the distorted electric field voltage of the earth unit cell.
Optionally, in an embodiment of the present application, the determining a magnetic storm induced ground electric field according to the ground electric field base value and a distorted electric field negative potential gradient includes:
determining the magnetic storm induced ground electric field of the land structure and the sea water structure according to the following formula:
wherein E is1(x) Magnetic storm induced ground electric field for land structure, E2(x) The magnetic storm induction ground electric field is of a seawater structure, x is the distance from a coastline, 0 is the position of the coastline, E1Ground electric field base value of land structure, E2Is the basic value of the ground electric field of the seawater structure, U is the distortion electric field voltage of the ground unit cell, sigmaslIs the conductivity, σ, of the land-side conductive layersrIs sea water conductivity, gamma1Is the propagation constant of the land structure, gamma2For sea water structuresA broadcast constant.
Optionally, in an embodiment of the present application, the determining, based on the boundary condition, a distorted electric field negative potential gradient of a simple earth structure and a complex earth structure in the earth conductivity model according to the earth electric field basic value and the transmission line characteristic parameter includes:
dividing the earth conductivity model into a plurality of earth unit cells, and determining a pi-type equivalent circuit formed by the earth unit cells and equivalent circuit parameters;
determining a node admittance network according to the pi-type equivalent circuit;
determining a distortion electric field voltage at each node in the node admittance network according to an admittance matrix and a current source matrix based on the boundary condition;
and determining the negative potential gradient of the distorted electric field of the complex earth structure according to the distorted electric field voltage at each node in the node admittance network.
Optionally, in an embodiment of the present application, the determining a magnetic storm induced ground field according to the ground field base value and a distortion electric field voltage includes:
determining the magnetostorm induced ground field of the complex earth structure according to the following formula:
wherein E (x) is a magnetostorm induced ground field of complex earth structure, EiThe ground electric field basic value of the complex earth structure is shown, x is the distance from the coastline, 0 is the position of the coastline, U is the distorted electric field voltage at each node in the node admittance network, and U is the distorted electric field voltagek、UiThe distortion electric field voltages of the node k and the node i are respectively, gamma is a propagation constant of a complex earth structure, and L is a unit length.
In summary, in the method for calculating the magnetic storm induced ground electric field according to the embodiment of the first aspect of the present application, a ground electric field base value is determined according to a ground electric conductivity model and original magnetic storm data by determining the ground electric conductivity model and collecting the original magnetic storm data; determining transmission line characteristic parameters of a ground conductivity model, and determining the negative potential gradient of a distorted electric field according to the ground electric field basic value and the transmission line characteristic parameters on the basis of the ground conductivity model; and determining the magnetic storm induction ground electric field according to the ground electric field base value and the negative potential gradient of the distorted electric field. According to the method, the calculation efficiency is effectively improved by avoiding the use of a numerical solution, the distribution condition of the magnetic storm induction ground electric field along the direction perpendicular to the sea-land boundary surface can be given, meanwhile, the power grid operation personnel can be helped to fully know the risk of GIC, the situation that the danger points in the power grid are ignored due to the fact that the transverse conductivity difference is not considered in the traditional method is avoided, and references are provided for establishing reasonable magnetic storm disaster prevention measures for different geographic positions.
In order to achieve the above object, a magnetic storm induced ground electric field computing device considering a coast effect according to an embodiment of the present application includes:
the base value determining module is used for determining a ground conductivity model, collecting original magnetic storm data and determining a ground electric field base value according to the ground conductivity model and the original magnetic storm data;
the gradient determining module is used for determining transmission line characteristic parameters of a ground conductivity model and determining the negative potential gradient of the distorted electric field according to the ground electric field basic value and the transmission line characteristic parameters on the basis of the ground conductivity model;
and the electric field determining module is used for determining the magnetic storm induction ground electric field according to the ground electric field base value and the negative potential gradient of the distorted electric field.
In summary, the magnetic storm induced ground electric field calculation apparatus provided in the embodiment of the second aspect of the present application determines a ground conductivity model and collects original magnetic storm data through a base value determination module, and determines a ground electric field base value according to the ground conductivity model and the original magnetic storm data; the gradient determining module determines transmission line characteristic parameters of a ground conductivity model, and determines the negative potential gradient of the distorted electric field according to the ground electric field basic value and the transmission line characteristic parameters on the basis of the ground conductivity model; and the electric field determining module determines the magnetic storm induction ground electric field according to the ground electric field base value and the negative potential gradient of the distorted electric field. According to the method, the calculation efficiency is effectively improved by avoiding the use of a numerical solution, the distribution condition of the magnetic storm induction ground electric field along the direction perpendicular to the sea-land boundary surface can be given, meanwhile, the power grid operation personnel can be helped to fully know the risk of GIC, the situation that the danger points in the power grid are ignored due to the fact that the transverse conductivity difference is not considered in the traditional method is avoided, and references are provided for establishing reasonable magnetic storm disaster prevention measures for different geographic positions.
Additional aspects and advantages of the present application will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the present application.
Drawings
The foregoing and/or additional aspects and advantages of the present application will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
fig. 1 is a flowchart of a method for calculating a magnetic storm induced ground electric field considering a coast effect according to an embodiment of the present application;
FIG. 2 is a schematic structural diagram of a three-segment model provided in an embodiment of the present application;
FIG. 3 is a schematic diagram illustrating a calculation result of a magnetic storm induced ground field of a three-segment model according to an embodiment of the present application;
fig. 4 is a schematic structural diagram of a magnetic storm induced ground electric field computing device considering a coast effect according to an embodiment of the present application.
Detailed Description
Reference will now be made in detail to embodiments of the present application, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are exemplary only for the purpose of explaining the present application and are not to be construed as limiting the present application. On the contrary, the embodiments of the application include all changes, modifications and equivalents coming within the spirit and terms of the claims appended hereto.
At present, an analytic method, an integral equation method, a finite difference method, a finite element method, and a boundary element method are mainly used for calculating the magnetostorm induced ground electric field considering the coast effect. The analytic method has high calculation precision, but the calculation process is complex. The integral equation method is based on an integral form of Maxwell's equation, and only the source region of the electromagnetic field is discrete. The calculations of numerical calculation methods such as the finite difference method, the finite element method, and the boundary element method have strong dependency on the grid and have high requirements for calculation power.
Example 1
Fig. 1 is a flowchart of a method for calculating a magnetic storm induced ground field in consideration of a coast effect according to an embodiment of the present application.
As shown in fig. 1, an embodiment of the present application provides a method for calculating a magnetic storm induced ground field considering a coastal effect, including the following steps:
and step 130, determining the magnetic storm induction ground electric field according to the ground electric field basic value and the negative potential gradient of the distorted electric field.
It should be noted that the magnetostorm induced ground electric field considering the coast effect includes a ground electric field base value and a distorted electric field.
Specifically, the ground electric field base value is the ground surface electric field horizontal component, determined by the varying magnetic field and the ground conductivity model. The earth conductivity model is a one-dimensional layered model, and in each region far from the boundary, the conductivity has no transverse change.
Further, the earth conductivity model satisfies a generalized thin sheet model.
Specifically, the distorted electric field is an electric field which is near the interface and causes the magnetic storm induced ground electric field to generate local distortion due to the existence of the conductivity difference.
Further, a generalized thin sheet model representing a ground electric conductivity structure is compared with a conductor model based on a distributed power supply transmission line theory, and the electric conductivity is set to be constant in a direction parallel to an interface.
In the embodiment of the application, the ground electric field base value is determined according to the ground electric conductivity model and the original magnetic storm data, and the method comprises the following steps:
determining frequency domain magnetic field components according to the original magnetic storm data;
the earth conductivity model is a one-dimensional layered model, and earth surface wave impedance is determined according to the earth conductivity model;
and determining the ground electric field base value based on Maxwell equation according to the frequency domain magnetic field component and the earth surface wave impedance.
In particular, the horizontal variation component of the electric field and also of the magnetic field is much smaller than the vertical variation component. And determining the horizontal component of the time domain magnetic field according to the original magnetic storm data, and performing Fourier transform on the horizontal component of the time domain magnetic field to obtain the horizontal component of the frequency domain magnetic field.
In the embodiment of the application, the earth conductivity model is a one-dimensional layered model, and earth wave impedance is determined according to the earth conductivity model; determining a ground electric field base value based on Maxwell equation according to the frequency domain magnetic field component and the earth surface wave impedance, comprising the following steps:
determining the bottom-layer wave impedance according to:
wherein S isNIs the bottom wave impedance, mu, in a model of earth conductivity0Is the value of magnetic permeability in vacuum, kNFor the propagation constant of the underlayer in the model of the earth conductivity, σNConductivity of the underlying infinite half space;
determining the earth surface wave impedance based on the following formula by utilizing a recurrence relation according to the bottom layer wave impedance:
wherein Sn is the wave impedance of the nth layer in the earth conductivity model, mu0The permeability value in vacuum is shown, kn is the propagation constant of the n-th layer in the earth conductivity model, hn is the thickness of the n-th layer in the earth conductivity model, and rnThe reflection coefficient of the nth layer in the earth conductivity model; σ is the conductivity.
Determining the frequency domain electric field component according to the following formula based on Maxwell equation:
wherein the content of the first and second substances,
is a frequency domain electric field component, mu0Is the value of the magnetic permeability in a vacuum,
as a component of the magnetic field in the frequency domain, S0Is the earth surface wave impedance;
and determining the ground electric field base value according to the frequency domain electric field component.
Specifically, the frequency domain electric field component is subjected to inverse fourier transform to obtain a time domain electric field component, i.e., a ground electric field base value.
In the embodiment of the present application, determining the transmission line characteristic parameter of the ground conductivity model, and determining the distortion electric field negative potential gradient according to the ground electric field base value and the transmission line characteristic parameter based on the ground conductivity model, includes:
the transmission line characteristic parameters are the resistance of the conducting layer, the cross sectional area and the conductance of the ground shell layer;
determining boundary conditions, and determining the distorted electric field negative potential gradient of the simple earth structure and the complex earth structure in the earth conductivity model according to the earth electric field basic value and the transmission line characteristic parameters based on the boundary conditions;
the simple ground structure is a land structure or a seawater structure with only one electrical distribution;
a complex earth structure is one that includes multiple electrical distributions.
It should be noted that the earth conductivity model is divided into a plurality of earth unit cells, and each earth unit cell is configured to be composed of a uniform voltage source, a series impedance and a parallel admittance. Wherein the pressure drop of the earth unit cell is determined according to:
wherein dx is a ground unit cell, γ is a propagation constant, Y is a parallel admittance,
is a uniform voltage source, and E is a ground electric field base value.
Specifically, the electrical parameters of the transmission line are determined by the series impedance Z ═ R + j ω L and the parallel admittance Y ═ G + j ω C per unit length. Thus, the transmission line characteristic parameters of the earth conductivity model are the resistance of the conductive layer, i.e., the resistance of the deposited layer, the cross-sectional area, and the conductance of the crust layer.
Further, the conductive layer resistance is determined according to:
wherein Z is the resistance of the conductive layer, σsIs the conductivity of the conductive layer, dsIs the conductive layer thickness and w is the conductive layer width.
The electrical conductance of the crust layer is determined according to the following formula:
wherein Y is the electrical conductance of the crust layer, σcIs the electrical conductivity of the crust of the earth, dcIs the thickness of the crust layer and w is the width of the crust layer.
Further, a propagation constant and a characteristic impedance are determined from the series impedance and the parallel admittance.
The propagation constant is determined according to the following equation:
wherein, gamma is a propagation constant, Z is a series impedance, and Y is a parallel admittance.
The characteristic impedance is determined according to:
wherein Z is0For characteristic impedance, Z is the series impedance and Y is the parallel admittance.
In an embodiment of the application, the boundary condition is determined from the Thevenin equivalent circuit.
In the embodiment of the application, based on the boundary condition, the distortion electric field negative potential gradient of the simple earth structure and the complex earth structure in the earth conductivity model is determined according to the earth electric field basic value and the transmission line characteristic parameter, and the distortion electric field negative potential gradient comprises the following steps:
dividing the earth conductivity model into a plurality of earth unit cells;
determining the distorted electric field voltage of the earth unit cell according to the transmission line characteristic parameters and the earth electric field basic value based on the boundary condition;
and determining the negative potential gradient of the distorted electric field of the land structure and the seawater structure according to the distorted electric field voltage of the earth unit cell.
In particular, the earth conductivity model is divided into an infinite number of earth unit cells, then the earth field base value in each earth unit cell is considered to be a constant, and thus the uniform voltage source in each earth unit cell is zero. Based on the Thevenin equivalent circuit, the distorted electric field voltage of the earth unit cell extending from x1 to x2 is determined according to the following equation:
wherein, U is the distortion electric field voltage of the earth unit cell, A, B is the terminal voltage constant of the earth conductivity model, E is the earth electric field base value in the earth unit cell, gamma is the propagation constant, and A 'and B' are Thevenin equivalent circuit parameters.
Further, thevenin equivalent circuit parameters are determined according to the following formula:
wherein A 'and B' are Thevenin equivalent circuit parameters, E1Ground electric field base value of land structure, E2Base value of ground electric field, gamma, for sea water structure1Is the propagation constant of the land structure, gamma2Is the propagation constant of the seawater structure, U1Is a first terminal voltage, U2Is the second terminal voltage, Z1Is a first impedance, Z2Is the second impedance.
Further, the first termination voltage and the first impedance are termination voltage and impedance of the Thevenin equivalent circuit from right to left, i.e. from the sea structure to the land structure, and
Z1＝Z01；
the second terminal voltage and the second impedance are the terminal voltage and the impedance of the Thevenin equivalent circuit from left to right, i.e. from the land structure to the sea structure, and
Z2＝Z02。
in particular, in a transmission line termination of simple earth structure, with determination
In the embodiment of the present application, determining the magnetic storm induced ground electric field according to the ground electric field base value and the negative potential gradient of the distorted electric field comprises:
determining the magnetic storm induced ground electric field of the land structure and the sea water structure according to the following formula:
wherein E is1(x) Magnetic storm induced ground electric field for land structure, E2(x) The magnetic storm induction ground electric field is of a seawater structure, x is the distance from a coastline, 0 is the position of the coastline, E1Ground electric field base value of land structure, E2Is the basic value of the ground electric field of the seawater structure, U is the distortion electric field voltage of the ground unit cell, sigmaslIs the conductivity, σ, of the land-side conductive layersrIs sea water conductivity, gamma1Is the propagation constant of the land structure, gamma2Is the propagation constant of the seawater structure.
In particular, when the geodetic structure is known as a simple geodetic structure, the magnetostorm induced ground field is a function of frequency and position.
In the embodiment of the application, based on the boundary condition, the distortion electric field negative potential gradient of the simple earth structure and the complex earth structure in the earth conductivity model is determined according to the earth electric field basic value and the transmission line characteristic parameter, and the distortion electric field negative potential gradient comprises the following steps:
dividing the earth conductivity model into a plurality of earth unit cells, and determining a pi-type equivalent circuit formed by the earth unit cells and equivalent circuit parameters;
determining a node admittance network according to the pi-type equivalent circuit;
determining a distortion electric field voltage at each node in the node admittance network according to the admittance matrix and the current source matrix based on the boundary condition;
and determining the negative potential gradient of the distorted electric field of the complex earth structure according to the distorted electric field voltage at each node in the node admittance network.
Specifically, a node admittance network formed by combining pi-type equivalent circuits calculates the earth surface electric field of a complex earth structure, and the size of the solution depends on the earth surface electric field basic value and the geometric characteristics and the electromagnetic properties of an earth conductivity model.
Specifically, the equivalent circuit parameters are determined according to the following equation:
wherein Z is0For characteristic impedance, γ is the propagation constant of a complex earth structure, L is the cell length, YEIs the newly added series impedance in the pi-type equivalent circuit,
is a newly added parallel admittance, I, in a pi-type equivalent circuitEThe current source is newly added in the pi-type equivalent circuit, Z is series impedance, and E is the base value of the ground electric field.
Specifically, the line current of each earth unit cell is determined by the current source, the earth unit cell head-end node voltage difference, and the earth unit cell admittance, and thus, the respective electrical quantities satisfy the following equations:
the terminal voltage at each node in the node admittance network can be given by a modified admittance matrix and a current source matrix, the matrix form being U ═ Y-1J, wherein U is the terminal voltage at each node in the node admittance network, Y is the modified admittance matrix, and J is the current source matrix.
Further, the total ground admittance at each node in the node admittance network is the sum of the parallel ground admittances of adjacent earth unit cells, the diagonal element Y of the admittance matrixiiEqual to the sum of all admittances connected to node i, including the ground admittance, the off-diagonal element YkiEqual to the negative admittance between nodes k and i, i.e.:
Yki＝-ykik＝i
specifically, the distorted electric field voltage at each node in the node admittance network is determined according to:
wherein, U is the distortion electric field voltage at each node in the node admittance network, gamma is the propagation constant of the complex ground structure, and L is the unit length.
Further, since the target earth structure does not exist in isolation, reasonable boundary conditions need to be set in order to ensure the physical effectiveness of the model. And setting an active terminal of a ground structure in the non-solution area as a boundary condition at the tail end of the ground conductivity model, and representing the active terminal by using a Thevenin equivalent circuit, wherein a voltage source and series impedance are respectively represented by open-circuit voltage and short-circuit current, and then determining the voltage and impedance of the Thevenin equivalent circuit according to the following formula:
Zth＝Z0
wherein, UthIs the voltage of Thevenin equivalent circuit, gamma is the propagation constant, E is the ground electric field base value, ZthIs the impedance of the Thevenin equivalent circuit, Z0Is the characteristic impedance.
Further, to facilitate integration with the nodal admittance network, the thevenin equivalent circuit is converted to a norton equivalent circuit according to:
wherein, JnoIs a Norton current, YnoIs the norton impedance.
Further, elements in the admittance matrix and the current source matrix of the first node in the node admittance network are determined according to the following formula:
determining the elements in the admittance matrix and the current source matrix of the last node in the node admittance network according to the following formula:
in this embodiment of the present application, determining the magnetic storm induced ground field according to the ground field base value and the distorted electric field voltage includes:
determining the magnetostorm induced ground field of the complex earth structure according to the following formula:
wherein E (x) is a magnetostorm induced ground field of complex earth structure, EiThe ground electric field basic value of the complex earth structure is shown, x is the distance from the coastline, 0 is the position of the coastline, U is the distorted electric field voltage at each node in the node admittance network, and U is the distorted electric field voltagek、UiThe distortion electric field voltages of the node k and the node i are respectively, gamma is a propagation constant of a complex earth structure, and L is a unit length.
By taking a scene as an example, the magnetic storm induced ground electric field calculation method provided by the embodiment of the application is applied to a three-segment model, the three-segment model consists of three earth structures with different conductivity distributions, each region in the three-segment model can be represented by a thin sheet model, each layer of each region has the same thickness, the resistivity of a crust layer and the conductivity of a mantle layer are also the same, but the conductivity of a first layer of each region has obvious difference, as shown in fig. 2.
Fig. 3 is a calculation result of the magnetostorm induced ground field of the three-segment model, where x is 1000km and x is 2000km respectively represent two interfaces of different electrical structures of the earth, a dotted line is a calculation result of the magnetostorm induced ground field calculation method provided in the embodiment of the present application, a solid line is a calculation result of the finite element method, and results of the two methods tend to be consistent, which shows that the magnetostorm induced ground field calculation method provided in the embodiment of the present application is effective.
In summary, the method for calculating the magnetostorm induced ground electric field provided by the embodiment of the application determines a ground electric field base value according to a ground electric conductivity model and original magnetic storm data by determining the ground electric conductivity model and collecting the original magnetic storm data; determining transmission line characteristic parameters of the ground conductivity model, and determining the negative potential gradient of the distorted electric field according to the ground electric field basic value and the transmission line characteristic parameters based on the ground conductivity model; and determining the magnetic storm induction ground electric field according to the ground electric field base value and the negative potential gradient of the distorted electric field. According to the method, the calculation efficiency is effectively improved by avoiding the use of a numerical solution, the distribution condition of the magnetic storm induction ground electric field along the direction perpendicular to the sea-land boundary surface can be given, meanwhile, the power grid operation personnel can be helped to fully know the risk of GIC, the situation that the danger points in the power grid are ignored due to the fact that the transverse conductivity difference is not considered in the traditional method is avoided, and references are provided for establishing reasonable magnetic storm disaster prevention measures for different geographic positions.
In order to implement the above embodiments, the present application also proposes a magnetic storm induced ground electric field calculation apparatus considering a coast effect.
Fig. 4 is a schematic structural diagram of a magnetic storm induced ground electric field computing device considering a coast effect according to an embodiment of the present application.
As shown in fig. 4, a magnetic storm induced ground electric field calculation apparatus considering a coast effect, includes:
the base value determining module 410 is used for determining a ground conductivity model, collecting original magnetic storm data, and determining a ground electric field base value according to the ground conductivity model and the original magnetic storm data;
the gradient determining module 420 is used for determining the transmission line characteristic parameters of the ground conductivity model, and determining the negative potential gradient of the distorted electric field according to the ground electric field basic value and the transmission line characteristic parameters based on the ground conductivity model;
and an electric field determining module 430 for determining the magnetostorm induced ground electric field according to the ground electric field base value and the negative potential gradient of the distorted electric field.
In summary, the magnetic storm induced ground electric field calculation apparatus provided in the embodiment of the present application determines a ground conductivity model and collects original magnetic storm data through the base value determination module, and determines a ground electric field base value according to the ground conductivity model and the original magnetic storm data; the gradient determining module determines transmission line characteristic parameters of the ground conductivity model, and determines the negative potential gradient of the distorted electric field according to the ground electric field basic value and the transmission line characteristic parameters on the basis of the ground conductivity model; the electric field determining module determines the magnetic storm induction ground electric field according to the ground electric field basic value and the negative potential gradient of the distorted electric field. According to the method, the calculation efficiency is effectively improved by avoiding the use of a numerical solution, the distribution condition of the magnetic storm induction ground electric field along the direction perpendicular to the sea-land boundary surface can be given, meanwhile, the power grid operation personnel can be helped to fully know the risk of GIC, the situation that the danger points in the power grid are ignored due to the fact that the transverse conductivity difference is not considered in the traditional method is avoided, and references are provided for establishing reasonable magnetic storm disaster prevention measures for different geographic positions.
It should be noted that, in the description of the present application, the terms "first", "second", etc. are used for descriptive purposes only and are not to be construed as indicating or implying relative importance. In addition, in the description of the present application, "a plurality" means two or more unless otherwise specified.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and the scope of the preferred embodiments of the present application includes other implementations in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present application.
It should be understood that portions of the present application may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.
It will be understood by those skilled in the art that all or part of the steps carried by the method for implementing the above embodiments may be implemented by hardware related to instructions of a program, which may be stored in a computer readable storage medium, and when the program is executed, the program includes one or a combination of the steps of the method embodiments.
In addition, functional units in the embodiments of the present application may be integrated into one processing module, or each unit may exist alone physically, or two or more units are integrated into one module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode. The integrated module, if implemented in the form of a software functional module and sold or used as a stand-alone product, may also be stored in a computer readable storage medium.
The storage medium mentioned above may be a read-only memory, a magnetic or optical disk, etc.
In the description herein, reference to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the application. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Although embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present application, and that variations, modifications, substitutions and alterations may be made to the above embodiments by those of ordinary skill in the art within the scope of the present application.
Claims (10)
1. A magnetic storm induced telluric field calculation method considering a coast effect, comprising:
determining a ground conductivity model, collecting original magnetic storm data, and determining a ground electric field base value according to the ground conductivity model and the original magnetic storm data;
determining transmission line characteristic parameters of a ground conductivity model, and determining the negative potential gradient of a distorted electric field according to the ground electric field basic value and the transmission line characteristic parameters on the basis of the ground conductivity model;
and determining the magnetic storm induction ground electric field according to the ground electric field base value and the negative potential gradient of the distorted electric field.
2. The method of magnetostorm induced ground field calculation as claimed in claim 1 wherein said determining a ground field contribution from said earth conductivity model and said raw magnetostorm data comprises:
determining frequency domain magnetic field components according to the original magnetic storm data;
the earth conductivity model is a one-dimensional layered model, and earth surface wave impedance is determined according to the earth conductivity model;
and determining the ground electric field base value based on Maxwell equation according to the frequency domain magnetic field component and the earth surface wave impedance.
3. The method of calculating a magnetostorm induced ground field according to claim 2, wherein the earth conductivity model is a one-dimensional layered model, and the earth wave impedance is determined from the earth conductivity model; determining the ground electric field base value based on Maxwell equation according to the frequency domain magnetic field component and the surface wave impedance, including:
determining the bottom-layer wave impedance according to:
wherein S isNIs the bottom wave impedance, mu, in a model of earth conductivity0Is the value of magnetic permeability in vacuum, kNFor the propagation constant of the underlayer in the model of the earth conductivity, σNConductivity of the underlying infinite half space;
determining the earth surface wave impedance based on the following formula by utilizing a recurrence relation according to the bottom layer wave impedance:
wherein Sn is the wave impedance of the nth layer in the earth conductivity model, mu0The permeability value in vacuum is shown, kn is the propagation constant of the n-th layer in the earth conductivity model, hn is the thickness of the n-th layer in the earth conductivity model, and rnThe reflection coefficient of the nth layer in the earth conductivity model; σ is the conductivity.
Determining the frequency domain electric field component based on Maxwell's equations according to:
wherein the content of the first and second substances,
is a frequency domain electric field component, mu0Is the value of the magnetic permeability in a vacuum,
as a component of the magnetic field in the frequency domain, S0Is the earth surface wave impedance;
and determining the ground electric field base value according to the frequency domain electric field component.
4. The method of calculating the magnetostorm induced telluric field according to claim 1, wherein the determining the transmission line characteristic parameters of the ground conductivity model, and the determining the distortion electric field negative potential gradient based on the ground conductivity model and the transmission line characteristic parameters, comprises:
the transmission line characteristic parameters are the resistance of the conducting layer, the cross sectional area and the conductance of the ground shell layer;
determining boundary conditions, and determining the distorted electric field negative potential gradient of the simple earth structure and the complex earth structure in the earth conductivity model according to the earth electric field basic value and the transmission line characteristic parameters based on the boundary conditions;
the simple ground structure is a land structure or a seawater structure with only one electrical distribution;
the complex earth structure is a complex earth structure comprising a plurality of electrical distributions.
5. The method of calculating a magnetostorm induced ground field according to claim 4, wherein the boundary condition is determined according to Thevenin equivalent circuit.
6. The magnetostorm induced telluric field calculation method of claim 4, wherein said determining distorted electric field negative potential gradients of simple and complex earth structures in the earth conductivity model from the telluric field fundamental values and transmission line characteristic parameters based on the boundary conditions comprises:
dividing the earth conductivity model into a plurality of earth unit cells;
determining the distorted electric field voltage of the earth unit cell according to the transmission line characteristic parameters and the earth electric field basic value based on boundary conditions;
and determining the negative potential gradient of the distorted electric field of the land structure and the seawater structure according to the distorted electric field voltage of the earth unit cell.
7. The method of calculating a magnetostorm induced ground field according to claim 6, wherein the determining a magnetostorm induced ground field according to the ground field base value and a distorted electric field negative potential gradient comprises:
determining the magnetic storm induced ground electric field of the land structure and the sea water structure according to the following formula:
wherein E is1(x) Magnetic storm induced ground electric field for land structure, E2(x) The magnetic storm induction ground electric field is of a seawater structure, x is the distance from a coastline, 0 is the position of the coastline, E1Ground electric field base value of land structure, E2Is the basic value of the ground electric field of the seawater structure, U is the distortion electric field voltage of the ground unit cell, sigmaslIs the conductivity, σ, of the land-side conductive layersrIs sea water conductivity, gamma1Is the propagation constant of the land structure, gamma2Is the propagation constant of the seawater structure.
8. The magnetostorm induced telluric field calculation method of claim 4, wherein said determining distorted electric field negative potential gradients of simple and complex earth structures in the earth conductivity model from the telluric field fundamental values and transmission line characteristic parameters based on the boundary conditions comprises:
dividing the earth conductivity model into a plurality of earth unit cells, and determining a pi-type equivalent circuit formed by the earth unit cells and equivalent circuit parameters;
determining a node admittance network according to the pi-type equivalent circuit;
determining a distortion electric field voltage at each node in the node admittance network according to an admittance matrix and a current source matrix based on the boundary condition;
and determining the negative potential gradient of the distorted electric field of the complex earth structure according to the distorted electric field voltage at each node in the node admittance network.
9. The method of calculating the magnetostorm induced telluric field according to claim 8, wherein the determining the magnetostorm induced telluric field according to the telluric field base value and the distorted electric field voltage comprises:
determining the magnetostorm induced ground field of the complex earth structure according to the following formula:
wherein E (x) is a magnetostorm induced ground field of complex earth structure, EiThe ground electric field basic value of the complex earth structure is shown, x is the distance from the coastline, 0 is the position of the coastline, U is the distorted electric field voltage at each node in the node admittance network, and U is the distorted electric field voltagek、UiThe distortion electric field voltages of the node k and the node i are respectively, gamma is a propagation constant of a complex earth structure, and L is a unit length.
10. A magnetic storm induced telluric field computing device considering coastal effect, the magnetic storm induced telluric field computing device comprising:
the base value determining module is used for determining a ground conductivity model, collecting original magnetic storm data and determining a ground electric field base value according to the ground conductivity model and the original magnetic storm data;
the gradient determining module is used for determining transmission line characteristic parameters of a ground conductivity model and determining the negative potential gradient of the distorted electric field according to the ground electric field basic value and the transmission line characteristic parameters on the basis of the ground conductivity model;
and the electric field determining module is used for determining the magnetic storm induction ground electric field according to the ground electric field base value and the negative potential gradient of the distorted electric field.
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