CN111400954A - Finite element oil paper insulation space charge calculation method and system based on time-step transient upstream - Google Patents
Finite element oil paper insulation space charge calculation method and system based on time-step transient upstream Download PDFInfo
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Abstract
The invention relates to the field of insulation design and optimization calculation in a high-voltage direct-current converter transformer, and particularly discloses a method and a system for calculating oil paper insulation space charge based on a time-step transient upstream finite element, wherein the method comprises the following steps: (1) establishing an oil paper insulation space charge two-dimensional calculation domain (2), and solving a Poisson equation by using a finite element method to obtain the electric field intensity; (3) discretizing a current continuous equation to construct a finite element form; (4) the effect of the addition of a temperature gradient on the carrier mobility; (5) solving a current continuous equation based on a time-step transient upstream finite element method; (6) continuously iterating, and solving the solution of an equation formed by coupling the Poisson equation and the current continuous equation in each instantaneous value; the method introduces the time-stepping method into the transient finite element calculation, so that the space charge numerical value calculation is more accurate, the convergence is better, and the method can be applied to the internal insulation calculation and the optimized design of the high-voltage direct-current converter transformer.
Description
Technical Field
The invention relates to the field of insulation design and optimization calculation in a high-voltage direct-current converter transformer, in particular to a method and a system for calculating oil paper insulation space charge based on a time-step transient upstream finite element.
Background
The converter transformer is a core device of a high-voltage direct-current transmission system, and the working state of the converter transformer is directly related to the safe and stable operation of a power grid. The oil paper insulation is used as a main insulation medium of a converter transformer and generally works under a direct current electric field, so that space charges in an insulation material can migrate and accumulate, the space charges in an oil paper insulation system can cause the degradation of an insulator and the distortion of the electric field, and the insulation system can be broken down due to the excessively high charge accumulation and the local field intensity. The conditions of the electric field in the insulating material and the transport and accumulation of space charge can be understood by means of a numerical simulation method. The accumulation and migration of space charge in the interior of the insulating material increase the field strength value of local areas in the interior of the insulating material and cause the occurrence of breakdown, so that it is necessary to study the dynamic characteristics of space charge to optimize the design of the oil paper insulating material.
Under the action of a direct current electric field, partial space charges can be accumulated in the oil paper insulating material, due to physical and chemical defects, charge traps are formed, partial free charges and partial free holes are captured, and the accumulation condition of the space charges is intensified, so that the simulation calculation of the oil paper insulating space charges needs to consider the processes that free electrons and free holes are captured by the traps to stay in a medium, and trapped electrons and holes escape from the traps. In addition, recombination occurs when electrons and holes meet, and the recombination also has a great influence on charge dissipation. Space charge plays a crucial role in weakening or enhancing the electric field. Therefore, it is necessary to simulate the space charge dynamic characteristics to understand the oil paper insulation electric field and the charge distribution.
Disclosure of Invention
The invention aims to provide a method and a system for calculating oil paper insulation space charge based on a time-step transient upstream finite element, which are used for analyzing the working environment and condition of an actual converter transformer, adding an oil paper insulation dynamic process model, and obtaining the distribution of space charge and the distribution of electric field intensity by using a deduced time-step transient upstream finite element method, thereby having a guiding function on the oil paper insulation design of the converter transformer.
In order to achieve the purpose, the invention provides a method for calculating the charge of an oil paper insulation space based on time-step transient upstream finite element, which comprises the following steps:
s1, collecting structural parameters and material attributes of the converter transformer oil paper insulation system, and establishing a two-dimensional calculation domain according to the actual operation environment of the converter transformer, wherein the two-dimensional calculation domain specifically comprises the following steps: a Schottky emission model and a carrier trap, trap and recombination model;
s2, dividing the two-dimensional calculation domain into a plurality of triangular units according to the shape and the parameters of the two-dimensional calculation domain to obtain the serial number and the node coordinates of each triangular unit;
s3, setting and calculating the material attribute value and the boundary condition of the oiled paper insulating material, and setting initial values of the electric field intensity and the charge density of the oiled paper insulating material;
s4, obtaining current density of injected polar plate charges by adopting a Schottky emission model for the polar plate, discretizing a current continuous equation according to a bipolar charge transport model and a space charge trap theory to obtain a vectorized finite element equation on each unit, assembling a unit rigidity matrix for the charge density, adding a temperature gradient condition, solving a transient upstream finite element equation based on a time-step method to obtain the charge density, and substituting the charge density into a Poisson equation to solve the node electric field intensity;
and S5, solving the equation system coupling the Poisson equation and the current continuous equation at each moment to obtain the instantaneous values of the electric field intensity and the charge density at different moments.
Preferably, in the foregoing technical solution, the two-dimensional calculation domain in S1 specifically includes: a Schottky emission model and a carrier trap, trap and recombination model.
Preferably, in the above technical solution, in S4, the bipolar charge transport model is described as follows: poisson equation:
current continuity equation:
net density of charge:
ρ0＝ρht+ρhμ-ρeμ-ρet(4)
wherein, the dielectric constant of the insulating dielectric material is shown; ρ is the space charge density; j is the current density resulting from carrier transport,
is the electric field strength; t represents time; m is four charge carriers; smFour carrier source terms; rhoeu，ρet，ρhu，ρhtCharge density for free electrons, trapped electrons, free holes, trapped holes; μ is the carrier mobility.
Preferably, in the above technical solution, the schottky emission model is described as follows:
1) applying a voltage to the positive plate
The negative plate is grounded
2) Expression for the schottky model:
Je(t) and Jh(t) is the charge current density of electrons and holes injected by the positive and negative plates, EeAnd EhThe electric field intensity at the positive and negative plates is shown, A is Richardson constant, and 1.2 × 10 is obtained in calculation6A/(m2K2)，ωeAnd ωhIs the injection barrier of electrons and holes, k is the boltzmann constant;
3) source term of carrier
The trap, trap and recombination processes of four carriers are expressed by the formula seμ、shμ、set、shtRespectively representing the source terms of free electrons, free holes, trapped electrons, trapped holes, S0-S3Coefficient of recombination between charges, BeAnd BhCoefficient for representing free electron/hole trapping by trap, DeAnd DhCoefficient for escape of trapped electrons/holes from traps, pet0And ρet0Is the density of electron and hole traps;
where v is the escape frequency of carriers escaping the trap, Δ UtreAnd Δ UtrhRepresenting the energy levels of the electron and hole traps.
Preferably, in the above technical solution, the description of solving the transient upstream finite element equation and the cell stiffness matrix of the charge density by the time-step method in S4 is as follows:
wherein m represents four carrier types, and formula (13) is discretized to obtain a finite element calculation formula at a certain point i in the region:
the carrier velocity vector is:
the charge density can be obtained by linear interpolation of finite element nodes:
ρ(x,y)＝Naρa+Nbρb+Ncρc(16)
where Ni (i ═ a, b, c) denotes coefficients associated with finite element node coordinates;
and (3) carrying out unit rigidity matrix assembly on the charge density, and according to a time step method and an up-flow finite element method, deducing a current continuous equation containing a time step delta t:
where M and K are coefficient matrices derived from equation (14), and f is the source term S in equation (14);
the step length Δ t needs to be chosen appropriately, set fsThe truncation error is obtained by the Crank-Nicolson method as the source term of the function:
can obtain the product
As can be seen from equation (19), the truncation error is proportional to the square of the step size. Thus, predicting the next step
The step length is:
etolerancetolerance value representing error, ekDenotes the magnitude of the error in the K-th step, KSFThe safety factor can be 0.8, and the step length is ensured not to be too large or too small. When e isk+1>etoleranceWhen the step length error value is too large, the step length of the (k + 1) th step needs to be recalculated;
in the formula (I), the compound is shown in the specification,
and
the step length and the error obtained in the previous step of calculation are adopted, the safety factor can be slightly larger at this time, namely 0.9 is needed, and the value formula of p is described as follows:
preferably, in the above technical solution, the temperature gradient in S4 is described as follows:
carrier mobility versus temperature expression:
wherein, WμActivation energy of mobility, μ0Are the coefficients of the function. The charge density distribution under different temperature gradients is observed by changing different temperatures and then influencing the mobility of space charges.
Corresponding to the method, the invention also discloses a finite element oiled paper insulation space charge calculation system based on the time-step transient upstream, which comprises the following steps:
the first module is used for collecting structural parameters and material attributes of the converter transformer oil paper insulation system, and establishing a two-dimensional calculation domain according to the actual operation environment of the converter transformer, wherein the two-dimensional calculation domain specifically comprises the following components: a Schottky emission model and a carrier trap, trap and recombination model;
the second module is used for dividing the two-dimensional calculation domain into a plurality of triangular units according to the shape and the parameters of the two-dimensional calculation domain to obtain the serial number and the node coordinates of each triangular unit;
the third module is used for setting and calculating the material attribute value and the boundary condition of the oil paper insulating material, and setting initial values of the electric field intensity and the charge density of the oil paper insulating material;
the fourth module is used for obtaining the current density of the injected polar plate charges by adopting a Schottky emission model for the polar plate, discretizing a current continuous equation according to a bipolar charge transport model and a space charge trap theory to obtain a vectorized finite element equation on each unit, carrying out unit rigidity matrix assembly on the charge density, adding a temperature gradient condition, solving a transient upstream finite element equation based on a time-step method to obtain the charge density, and substituting the charge density into a Poisson equation to solve the node electric field intensity;
and the fifth module is used for solving an equation set coupling the Poisson equation and the current continuous equation at each moment to obtain the instantaneous values of the electric field intensity and the charge density at different moments.
Compared with the prior art, the invention has the following beneficial effects:
1. the method and the system for calculating the oil paper insulation space charge based on the time-step transient upstream finite element adopt a method of calculating domain meshing, divide the calculation region into a plurality of triangular units according to the shape and the parameters of the calculation region, obtain the serial number and the node coordinates of each triangular unit, and are convenient for the finite element method to calculate.
2. The method for solving the current continuous equation has the advantages that the current continuous equation is solved, the unit stiffness matrix is assembled, the current continuous equation is solved by using the time-step transient upstream finite method, the time-step transient upstream finite method has the characteristics of flexibility, applicability, strong adaptability and the like, the charge density is solved by using the time-step transient upstream finite method, the solved problem can be normalized, the equation can be flexibly processed and solved, and the result numerical value of the charge density is more accurately calculated and has better convergence.
3. The invention also adds the influence of the temperature gradient on the carrier mobility, so that the calculation result of the charge density is more accurate.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a system flow chart of a finite element oilpaper insulation space charge calculation method and system based on time-step transient upstream.
FIG. 2 is a method flow diagram of a finite element oilpaper insulation space charge calculation method and system based on time-step transient upstream.
FIG. 3 is a graphical representation of a curved oilpaper insulated computing unit grid of the present invention.
Fig. 4 is a diagram of trap theory and the process of trapping, detrapping and recombination of four space charges in the oiled paper insulation material according to the invention.
FIG. 5 is a schematic diagram of the present invention for determining upstream finite elements.
Detailed Description
The following detailed description of the preferred embodiments of the present invention is provided in conjunction with the accompanying drawings, although it will be understood that the scope of the invention is not limited to the specific embodiments.
The embodiment of the invention discloses a method for calculating the charge of an oil paper insulation space based on time-step transient upstream finite element, as shown in figure 1, comprising the following steps:
s1, collecting structural parameters and material attributes of the converter transformer oil paper insulation system, and establishing a two-dimensional calculation domain according to the actual operation environment of the converter transformer, wherein the two-dimensional calculation domain specifically comprises the following steps: a Schottky emission model and a carrier trap, trap and recombination model;
step S2, dividing the two-dimensional calculation domain into a plurality of triangular units according to the shape and the parameters of the two-dimensional calculation domain to obtain the serial number and the node coordinates of each triangular unit;
step S3, setting and calculating the material attribute value and the boundary condition of the oiled paper insulating material, and setting initial values of the parameters of the electric field intensity and the charge density of the oiled paper insulating material;
s4, obtaining current density of charges injected into the polar plate by adopting a Schottky emission model for the polar plate, discretizing a current continuous equation according to a bipolar charge transport model and a space charge trap theory to obtain a vectorized finite element equation on each unit, assembling a unit rigidity matrix of the charge density, adding a temperature gradient condition, solving a transient upstream finite element equation based on a time-step method to obtain the charge density, and substituting the charge density into a Poisson equation to solve the electric field intensity of a node;
and step S5, solving an equation system coupling the Poisson equation and the current continuous equation at each moment to obtain the instantaneous values of the electric field intensity and the charge density at different moments.
According to the calculation method, the change rules of the electric fields and the space charges of different oil paper insulating materials under different operating conditions are calculated, and the efficiency and the precision of the provided calculation method are compared and analyzed by utilizing the existing simulation tool so as to verify the effectiveness of the provided method.
The bipolar charge transport model in the above step S4 is described as follows:
poisson equation:
current continuity equation:
net density of charge:
ρ0＝ρht+ρhμ-ρeμ-ρet(4)
is the dielectric constant of the insulating dielectric material; ρ is the space charge density; j is the current density resulting from carrier transport,
is the electric field strength; t represents time; m is four charge carriers; smFour carrier source terms; rhoeu，ρet，ρhu，ρhtCharge density for free electrons, trapped electrons, free holes, trapped holes; μ is the carrier mobility.
The schottky emission model in step S1 or step S4 is described as follows:
according to the forced boundary condition, the trap-in, trap-out and recombination processes of the Schottky emission model are as follows:
1) applying a voltage to the positive plate
The negative plate is grounded
2) Expression of schottky model
Je(t) and Jh(t) is the charge current density of electrons and holes injected by the positive and negative plates, EeAnd EhThe electric field intensity at the positive and negative plates is shown, A is Richardson constant, and 1.2 × 10 is obtained in calculation6A/(m2K2)，ωeAnd ωhIs the injection barrier of electrons and holes, k is the boltzmann constant;
3) source term of carrier
The trap, trap and recombination processes of four carriers are expressed by the formula seμ、shμ、set、shtRespectively representing the source terms of free electrons, free holes, trapped electrons, trapped holes, S0-S3Coefficient of recombination between charges, BeAnd BhCoefficient for representing free electron/hole trapping by trap, DeAnd DhCoefficient for escape of trapped electrons/holes from traps, pet0And ρet0The process of carrier trap/trap and recombination is shown in fig. 3, which is the density of electron and hole traps;
where v is the escape frequency of carriers escaping the trap, Δ UtreAnd Δ UtrhRepresenting the energy levels of the electron and hole traps;
the description of solving the transient upstream finite element equation and the cell stiffness matrix of the charge density by the time-stepping method in the step S4 is as follows:
wherein m represents four carrier types, and formula (13) is discretized to obtain a finite element calculation formula at a certain point i in the region:
the charge density is obtained by linear interpolation of finite element nodes:
ρ(x,y)＝Naρa+Nbρb+Ncρc(15)
where Ni (i ═ a, b, c) denotes coefficients associated with finite element node coordinates;
the carrier velocity vector is:
the change in carrier mobility with temperature is shown below
Wherein WμActivation energy of mobility, μ0The coefficient of the function is used for observing the charge density distribution under different temperature gradients by changing different temperatures and further influencing the mobility of space charges.
And (3) carrying out unit rigidity matrix assembly on the charge density, and deducing a current continuity equation containing a time step delta t according to a time step method and an up-flow finite element method:
where M and K are coefficient matrices derived from equation (14), and f is the source term S in equation (14);
the charge density value ρ at the next time can be obtained by L U decomposition or Gaussian elimination as shown in FIG. 4n+1；
The step length delta t needs to be properly selected, an excessively large step length can cause that the judgment condition of convergence cannot be achieved, the program is not converged, an excessively small step length can increase the iteration times, the operation time is too long, and the occupied computing resources are excessive, so that a variable step length algorithm can be used in the program, a proper step length is selected in each iteration, the program is converged, the computing speed is accelerated, and f is setsFor the source term of the function, we can derive the truncation error as:
the following can be obtained:
as can be seen from equation (20), the truncation error is proportional to the square of the step size, so the step size of the next step
Comprises the following steps:
etolerancetolerance value representing error, ekDenotes the magnitude of the error in the K-th step, KSFThe safety factor can be 0.8, the step length is ensured not to be too large or too small, when ek+1>etoleranceTime, explain the step errorIf the difference is too large, the step length of the (k + 1) th step needs to be recalculated:
in the formula (I), the compound is shown in the specification,
and
the step length and the error obtained in the previous step of calculation are adopted, the safety factor can be slightly larger than 0.9, and the value of p is as follows:
corresponding to the embodiment of the method, the embodiment also discloses a system for calculating the charge of the oil paper insulation space based on the time-step transient upstream finite element, which comprises the following first to fifth modules:
the first module is used for collecting structural parameters and material attributes of the converter transformer oil paper insulation system, and establishing a two-dimensional calculation domain according to the actual operation environment of the converter transformer, wherein the two-dimensional calculation domain specifically comprises the following components: a Schottky emission model and a carrier trap, trap and recombination model;
the second module is used for dividing the two-dimensional calculation domain into a plurality of triangular units according to the shape and the parameters of the two-dimensional calculation domain to obtain the serial number and the node coordinates of each triangular unit;
the third module is used for setting and calculating the material attribute value and the boundary condition of the oil paper insulating material, and setting initial values of the electric field intensity and the charge density of the oil paper insulating material;
the fourth module is used for obtaining the current density of the injected polar plate charges by adopting a Schottky emission model for the polar plate, discretizing a current continuous equation according to a bipolar charge transport model and a space charge trap theory to obtain a vectorized finite element equation on each unit, carrying out unit rigidity matrix assembly on the charge density, adding a temperature gradient condition, solving a transient upstream finite element equation based on a time-step method to obtain the charge density, and substituting the charge density into a Poisson equation to solve the node electric field intensity;
and the fifth module is used for solving an equation set coupling the Poisson equation and the current continuous equation at each moment to obtain the instantaneous values of the electric field intensity and the charge density at different moments.
Referring to fig. 1, firstly, collecting structural parameters and material attributes of an oil paper insulation system of a converter transformer, establishing a two-dimensional calculation domain according to the actual operation environment of the converter transformer, secondly, dividing the two-dimensional calculation domain into a plurality of triangular units, and setting initial values for parameters of electric field intensity and charge density of the oil paper insulation material and time parameters; solving the electric field intensity according to the Poisson equation, solving the transient upstream finite element current continuous equation by a time-step method, solving an equation set coupling the Poisson equation and the current continuous equation at each moment, and obtaining the instantaneous values of the electric field intensity and the charge density at different moments
Referring to fig. 2, parameters of electric field intensity and charge density of the oiled paper insulation material and initial parameter values of time parameters are determined, initial electric field intensity is solved through a poisson equation, a schottky emission model is adopted for a polar plate to obtain current density of charges injected into the polar plate, a current continuous equation is discretized according to a bipolar charge transport model and a space charge trap theory to obtain a vectorized finite element current continuous equation on each unit, the charge density is subjected to unit rigidity matrix assembly, a temperature gradient condition is added, a transient upstream finite element current continuous equation is solved through dynamic step length adjustment based on a time-step method to obtain charge density, and the charge density is substituted into the poisson equation to solve node electric field intensity.
Referring to fig. 3, the two-dimensional calculation domain is divided into a plurality of triangle units according to the shape and parameters of the two-dimensional calculation domain, and the number and node coordinates of each triangle unit are obtained. The inner boundary is the anode, voltage V is applied, the outer boundary is the cathode, and zero potential is applied. The carriers move between the two plates.
Referring to fig. 4, in the process of charge migration under the action of a dc electric field, a part of free charges and free holes are captured by a charge trap to cause trapping and detrapping of space charges, and recombination occurs when electrons and holes meet each other.
Referring to fig. 5, for each node, the upstream cell is defined as a triangular cell facing the carrier mobility direction vector of the node, i.e., the upstream cell ensures that the space charge density of the upstream region of the mobility direction vector is always greater than that of the downstream region. In the finite element algorithm, the updating of the upstream elements is realized by gradually updating each element in the program, and the updating is started from the boundary of the anode and gradually updated to the cathode.
The foregoing descriptions of specific exemplary embodiments of the present invention have been presented for purposes of illustration and description. It is not intended to limit the invention to the precise form disclosed, and obviously many modifications and variations are possible in light of the above teaching. The exemplary embodiments were chosen and described in order to explain certain principles of the invention and its practical application to enable one skilled in the art to make and use various exemplary embodiments of the invention and various alternatives and modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims and their equivalents.
Claims (10)
1. A method for calculating the charge of an oil paper insulation space based on time-step transient upstream finite element is characterized by comprising the following steps:
s1, collecting structural parameters and material attributes of the converter transformer oil paper insulation system, and establishing a two-dimensional calculation domain according to the actual operation environment of the converter transformer, wherein the two-dimensional calculation domain specifically comprises the following steps: a Schottky emission model and a carrier trap, trap and recombination model;
s2, dividing the two-dimensional calculation domain into a plurality of triangular units according to the shape and the parameters of the two-dimensional calculation domain to obtain the serial number and the node coordinates of each triangular unit;
s3, setting and calculating the material attribute value and the boundary condition of the oiled paper insulating material, and setting initial values of the electric field intensity and the charge density of the oiled paper insulating material;
s4, obtaining current density of injected polar plate charges by adopting a Schottky emission model for the polar plate, discretizing a current continuous equation according to a bipolar charge transport model and a space charge trap theory to obtain a vectorized finite element equation on each unit, assembling a unit rigidity matrix for the charge density, adding a temperature gradient condition, solving a transient upstream finite element equation based on a time-step method to obtain the charge density, and substituting the charge density into a Poisson equation to solve the node electric field intensity;
and S5, solving the equation system coupling the Poisson equation and the current continuous equation at each moment to obtain the instantaneous values of the electric field intensity and the charge density at different moments.
2. The method for calculating the charge of the oil paper insulation space based on the finite element flowing up in the transient time step according to claim 1, wherein the method comprises the following steps: in S4, the bipolar charge transport model is described as follows:
poisson equation:
current continuity equation:
net density of charge:
ρ0＝ρht+ρhμ-ρeμ-ρet(4)
wherein, the dielectric constant of the insulating dielectric material is shown; ρ is the space charge density; j is the current density resulting from carrier transport,
is the electric field strength; t represents time; m is fourA seed carrier; smFour carrier source terms; rhoeu，ρet，ρhu，ρhtCharge density for free electrons, trapped electrons, free holes, trapped holes; μ is the carrier mobility.
3. The method for calculating the insulation space charge of the finite element oilpaper based on the time-step transient upflow, according to claim 1, wherein the schottky emission model and the carrier trap, trap and recombination model in S1 are described as follows:
1) applying a voltage to the positive plate
The negative plate is grounded
2) Expression for the schottky model:
Je(t) and Jh(t) is the charge density of electrons and holes injected by the positive and negative plates, EeAnd EhThe electric field intensity at the positive and negative plates is shown, A is Richardson constant, and 1.2 × 10 is obtained in calculation6A/(m2K2)，ωeAnd ωhIs the injection barrier of electrons and holes, k is the boltzmann constant;
3) model of carrier trap, trap and recombination:
the trap, trap and recombination processes of four carriers are expressed by the formula seμ、shμ、set、shtRespectively representing the source terms of free electrons, free holes, trapped electrons, trapped holes, S0-S3Coefficient of recombination between charges, BeAnd BhCoefficient for representing free electron/hole trapping by trap, DeAnd DhCoefficient for escape of trapped electrons/holes from traps, pet0And ρet0Is the density of electron and hole traps;
where v is the escape frequency of carriers escaping the trap, Δ UtreAnd Δ UtrhRepresenting the energy levels of the electron and hole traps.
4. The method for calculating the insulation space charge of the oilpaper based on the time-stepping transient upstream finite element according to claim 1, wherein the description of solving the transient upstream finite element equation and the cell stiffness matrix of the charge density by the time-stepping method in the step S4 is as follows:
wherein m represents four carrier types, and formula (13) is discretized to obtain a finite element equation at a certain point i in the two-dimensional calculation domain:
the carrier velocity vector is:
the charge density is obtained by linear interpolation of finite element nodes:
ρ(x,y)＝Naρa+Nbρb+Ncρc(16)
where Ni (i ═ a, b, c) denotes coefficients associated with finite element node coordinates;
and (3) carrying out unit rigidity matrix assembly on the charge density, and according to a time step method and an up-flow finite element method, deducing a current continuous equation containing a time step delta t:
where M and K are coefficient matrices derived from equation (14), and f is the source term S in equation (14);
the step length Δ t needs to be chosen appropriately, set fsThe truncation error is obtained by the Crank-Nicolson method as the source term of the function:
can obtain the product
As can be seen from equation (20), the truncation error is proportional to the square of the step size, and therefore the next step size is:
etolerancetolerance value representing error, ekDenotes the magnitude of the error in the K-th step, KSFThe safety factor is 0.8, when ek +1>etoleranceWhen the step length error value is too large, the step length of the (k + 1) th step needs to be recalculated:
in the formula (I), the compound is shown in the specification,
and
the step length and the error obtained in the previous step of calculation are obtained, the value of the safety factor is 0.9, and the value formula of p is described as follows:
5. the method for calculating the insulation space charge based on the time-step transient upstream finite element oilpaper according to claim 1, wherein the temperature gradient in S4 is described as follows:
carrier mobility versus temperature expression:
wherein, WμActivation energy of mobility, μ0Is a coefficient of function, and the charge density distribution under different temperature gradients is observed by changing different temperatures to further influence the mobility of space charge.
6. A finite element oil paper insulation space charge calculation system based on time step transient upstream is characterized by comprising:
the first module is used for collecting structural parameters and material attributes of the converter transformer oil paper insulation system, and establishing a two-dimensional calculation domain according to the actual operation environment of the converter transformer, wherein the two-dimensional calculation domain specifically comprises the following components: a Schottky emission model and a carrier trap, trap and recombination model;
the second module is used for dividing the two-dimensional calculation domain into a plurality of triangular units according to the shape and the parameters of the two-dimensional calculation domain to obtain the serial number and the node coordinates of each triangular unit;
the third module is used for setting and calculating the material attribute value and the boundary condition of the oil paper insulating material, and setting initial values of the electric field intensity and the charge density of the oil paper insulating material;
the fourth module is used for obtaining the current density of the injected polar plate charges by adopting a Schottky emission model for the polar plate, discretizing a current continuous equation according to a bipolar charge transport model and a space charge trap theory to obtain a vectorized finite element equation on each unit, carrying out unit rigidity matrix assembly on the charge density, adding a temperature gradient condition, solving a transient upstream finite element equation based on a time-step method to obtain the charge density, and substituting the charge density into a Poisson equation to solve the node electric field intensity;
and the fifth module is used for solving an equation set coupling the Poisson equation and the current continuous equation at each moment to obtain the instantaneous values of the electric field intensity and the charge density at different moments.
7. The time-step transient upflow finite element oilpaper insulation space charge based computing system of claim 6, wherein: the description of the bipolar charge transport model in the fourth module is as follows:
poisson equation:
current continuity equation:
net density of charge:
ρ0＝ρht+ρhμ-ρeμ-ρet(27)
wherein, the dielectric constant of the insulating dielectric material is shown; ρ is the space charge density; j is the current density resulting from carrier transport,
is the electric field strength; t represents time; m is four charge carriers; smFour carrier source terms; rhoeu，ρet，ρhu，ρhtCharge density for free electrons, trapped electrons, free holes, trapped holes; μ is the carrier mobility.
8. The time-step transient upflow finite element oilpaper insulation space charge based computing system of claim 6, wherein the schottky emission model and the carrier trap, recombination model in the first module are described as follows:
1) applying a voltage to the positive plate
The negative plate is grounded
2) Expression for the schottky model:
Je(t) and Jh(t) is the charge density of electrons and holes injected by the positive and negative plates, EeAnd EhThe electric field intensity at the positive and negative plates is shown, A is Richardson constant, and 1.2 × 10 is obtained in calculation6A/(m2K2)，ωeAnd ωhIs the injection barrier of electrons and holes, k is the boltzmann constant;
3) model of carrier trap, trap and recombination:
the trap, trap and recombination processes of four carriers are expressed by the formula seμ、shμ、set、shtRespectively representing the source terms of free electrons, free holes, trapped electrons, trapped holes, S0-S3Coefficient of recombination between charges, BeAnd BhCoefficient for representing free electron/hole trapping by trap, DeAnd DhCoefficient for escape of trapped electrons/holes from traps, pet0And ρet0Is the density of electron and hole traps;
where v is the escape frequency of carriers escaping the trap, Δ UtreAnd Δ UtrhRepresenting the energy levels of the electron and hole traps.
9. The system of claim 6, wherein the fourth module describes the cell stiffness matrix for solving transient upstream finite element equations and charge densities by a time-stepping method as follows:
wherein m represents four carrier types, and formula (13) is discretized to obtain a finite element equation at a certain point i in the two-dimensional calculation domain:
the carrier velocity vector is:
the charge density is obtained by linear interpolation of finite element nodes:
ρ(x,y)＝Naρa+Nbρb+Ncρc(39)
where Ni (i ═ a, b, c) denotes coefficients associated with finite element node coordinates;
and (3) carrying out unit rigidity matrix assembly on the charge density, and according to a time step method and an up-flow finite element method, deducing a current continuous equation containing a time step delta t:
where M and K are coefficient matrices derived from equation (14), and f is the source term S in equation (14);
the step length Δ t needs to be chosen appropriately, set fsThe truncation error is obtained by the Crank-Nicolson method as the source term of the function:
can obtain the product
As can be seen from equation (20), the truncation error is proportional to the square of the step size, and therefore the next step size is:
etolerancetolerance value representing error, ekDenotes the magnitude of the error in the K-th step, KSFThe safety factor is 0.8, when ek +1>etoleranceWhen the step length error value is too large, the step length of the (k + 1) th step needs to be recalculated:
in the formula (I), the compound is shown in the specification,
and
the step length and the error obtained in the previous step of calculation are obtained, the value of the safety factor is 0.9, and the value formula of p is described as follows:
10. the time-step transient upflow finite element oilpaper insulation space charge based computing system of claim 6, in which the fourth module, the temperature gradient is described as follows:
carrier mobility versus temperature expression:
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112182920A (en) * | 2020-08-24 | 2021-01-05 | 中国电力科学研究院有限公司 | Iterative method for determining field intensity value of direct current transmission line synthetic electric field |
| CN113063706A (en) * | 2021-03-30 | 2021-07-02 | 重庆大学 | Device and method for measuring average mobility of liquid dielectric medium carriers |
| CN116680965A (en) * | 2023-08-04 | 2023-09-01 | 矿冶科技集团有限公司 | FDEM acceleration method based on self-adaptive time step excavation supporting simulation |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104866683A (en) * | 2015-06-03 | 2015-08-26 | 武汉大学 | Transient upper element-based oil paper insulation internal space charge transport simulation method |
| CN109783855A (en) * | 2018-12-11 | 2019-05-21 | 重庆大学 | A kind of change of current based on upper non-mesh method becomes the calculation method of space charge |
-
2020
- 2020-03-26 CN CN202010222354.6A patent/CN111400954A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104866683A (en) * | 2015-06-03 | 2015-08-26 | 武汉大学 | Transient upper element-based oil paper insulation internal space charge transport simulation method |
| CN109783855A (en) * | 2018-12-11 | 2019-05-21 | 重庆大学 | A kind of change of current based on upper non-mesh method becomes the calculation method of space charge |
Non-Patent Citations (2)
| Title |
|---|
| 连启祥: "油纸绝缘内部合成电场数值模拟方法", 《电工技术学报》 * |
| 连启祥: "采用瞬态上流元法的油纸绝缘瞬态电场研究", 《浙江大学学报》 * |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112182920A (en) * | 2020-08-24 | 2021-01-05 | 中国电力科学研究院有限公司 | Iterative method for determining field intensity value of direct current transmission line synthetic electric field |
| CN112182920B (en) * | 2020-08-24 | 2024-05-10 | 中国电力科学研究院有限公司 | Iterative method for determining field intensity value of DC transmission line composite electric field |
| CN113063706A (en) * | 2021-03-30 | 2021-07-02 | 重庆大学 | Device and method for measuring average mobility of liquid dielectric medium carriers |
| CN116680965A (en) * | 2023-08-04 | 2023-09-01 | 矿冶科技集团有限公司 | FDEM acceleration method based on self-adaptive time step excavation supporting simulation |
| CN116680965B (en) * | 2023-08-04 | 2023-09-29 | 矿冶科技集团有限公司 | FDEM acceleration method based on self-adaptive time step excavation supporting simulation |
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