CN115618797A - ST electromagnetic transient model and field-path coupling calculation method based on finite element method - Google Patents

ST electromagnetic transient model and field-path coupling calculation method based on finite element method Download PDF

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CN115618797A
CN115618797A CN202211327425.4A CN202211327425A CN115618797A CN 115618797 A CN115618797 A CN 115618797A CN 202211327425 A CN202211327425 A CN 202211327425A CN 115618797 A CN115618797 A CN 115618797A
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finite element
winding
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杨文英
潘宇航
邱子澜
翟国富
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Harbin Institute of Technology
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Abstract

The invention discloses an ST electromagnetic transient model and field-circuit coupling calculation method based on a finite element method. The invention can jointly solve the ST finite element model and the simulation software of the power system, realize the collaborative simulation of a device level and a system level, accurately reflect the electromagnetic transient characteristics of the ST when the system is short-circuited, injected with harmonic waves and controlled by dynamic power flow, visualize the magnetic field distribution in the ST and simulate the working condition of the ST more truly. The invention can be directly applied to the research and development processes of voltage regulation and tidal current control modules of the electromagnetic unified tidal current controller and test prototypes of ST in simulation software of a power system.

Description

ST electromagnetic transient model and field path coupling calculation method based on finite element method
Technical Field
The invention belongs to the field of smart power grids, relates to a finite element calculation method for the electromagnetic transient characteristics of a Sen Transformer (ST) of an electromagnetic unified power flow controller, and particularly relates to an ST transient electromagnetic field calculation method based on a field-circuit coupling technology.
Background
With the large-scale grid connection of renewable energy sources such as photovoltaic energy, wind power and the like, in a novel power system taking new energy sources as main bodies, problems such as power plant scheduling, power transmission capacity, power flow control and the like become more prominent, and the safety and stability of the power system face severe challenges. Indeed, erecting new high voltage ac or dc transmission lines can meet the growing demand for power transmission. However, the development of a Flexible Alternating Current Transmission System (FACTS) can flexibly, economically and efficiently utilize the existing Transmission and distribution network.
Unified Power Flow Controllers (UPFC) are the FACTS devices with the strongest functions at present, and can effectively solve the problems of voltage regulation and Power Flow control. However, the extremely high construction and operating costs result in their potential for promotion or are limited. The ST based on the phase shifter technology has the four-quadrant power flow control capability similar to that of the UPFC, has the advantages of good economy, high reliability and the like, and can provide an attractive technical route with excellent economy and applicable performance for the consumption of large-scale renewable energy and the development of FACTS devices. However, since the mechanical on-load tap changer is adopted and the tap can only be switched between gears, ST has the disadvantages of slow response speed, incapability of continuous adjustment and the like.
The basic topology of the power flow controller ST is shown in fig. 1, and it comprises two units: the device comprises an excitation unit and a voltage regulating unit. The primary sides of the ST are connected in a star shape and are connected to the transmission end of the transmission line in parallel to form an excitation unit; each secondary side phase is composed of three windings with On-load Tap-changers (OLTC), and a voltage regulating unit is formed. The A phase secondary winding is a 1 、a 2 、a 3 The secondary winding of the B phase is B 1 、b 2 、b 3 The secondary winding of the C phase is C 1 、c 2 、c 3 . Wherein the winding a 1 、b 1 、c 1 Forming a series compensation voltage of phase A, i.e. V ss'A ＝V ss'a1 +V ss'b1 +V ss'c1 Thus, the terminal voltage of the A phaseCan be composed of V sa Adjusted to V s'a . Due to V ss'a1 ,、V ss'b1 、V ss'c1 The phase difference is 120 degrees, and the combination mode of the three voltage phasors can be changed by changing the control of the position of the secondary winding OLTC of the ST, thereby changing V ss'A . Similarly, the series compensation voltage V of the B phase and the C phase can be realized ss'B 、V ss'C Then the voltage at the sending end is changed from V s To V s' Four-quadrant regulation of (i.e. V) s′ ＝V s +V ss′ . In addition, in order to ensure that the A, B and C phases are symmetrical in the voltage regulation process, the a at any time is ensured 1 -b 2 -c 3 (TG 1 ) Equal number of turns of winding put into operation, b 1 -c 2 -a 3 (TG 2 ) Equal number of turns of winding put into operation, and c 1 -a 2 -b 3 (TG 3 ) The number of turns of windings put into operation is equal. But with a tap TG 1 Group, TG 2 Group and TG 3 The number of turns the stack is put into operation may be different from each other.
The traditional electromagnetic transient model of the ST is mainly established based on a magnetic circuit method, and although the analytical model established based on the magnetic circuit method considers the influence of nonlinear characteristics such as eddy current and hysteresis and the like and can be used for quickly calculating the transient characteristic of the ST, the problems of over simplification and serious information loss exist in the modeling process. For example, the magnetic circuit method simplifies the magnetic field by using lumped parameters, and performs modeling solution by equivalent of the magnetic field into a circuit, and in the modeling process, the magnetic field in a certain range is considered to be uniformly distributed, while the actual magnetic field is highly non-uniformly distributed, so the calculation accuracy of the magnetic circuit method is low. Meanwhile, the magnetic circuit method cannot acquire detailed magnetic field distribution inside the ST, and cannot realize accurate calculation of ST multi-physical field coupling. Therefore, accurate electromagnetic field transient calculation has important significance in designing test prototypes of ST, formulating reliable protection schemes, reducing production and operation costs and the like.
Disclosure of Invention
In order to accurately calculate the transient electromagnetic field of the ST under various complex working conditions, the invention provides an ST electromagnetic transient model and field path coupling calculation method based on a finite element method. The invention establishes an ST electromagnetic transient model based on a Finite Element Method (FEM), the model represents the nonlinear characteristics of an iron core material such as saturation, eddy and hysteresis by adopting a J-A hysteresis model according to a Maxwell equation set and a magnetic field control equation, the ST Finite Element model is packaged in a module, field-circuit coupling numerical calculation and electromagnetic transient collaborative simulation are carried out by combining with power system simulation software, a device-level and system-level collaborative simulation task is completed, the ST can complete the power flow control of an external power system, the ST equipment can visualize the internal magnetic field distribution under various working conditions, and an accurate transient electromagnetic field calculation Method is provided for the electromagnetic-thermal-fluid multi-physical field coupling calculation and the development of a test prototype of the ST in the follow-up research. The invention can be directly applied to the voltage regulation and current control module of the electromagnetic unified power flow controller in the simulation software of the power system and the research and development process of the ST test prototype.
The purpose of the invention is realized by the following technical scheme:
a method for constructing an ST electromagnetic transient model based on a finite element method comprises the following steps;
step one, establishing a two-dimensional finite element model according to the geometric dimensions of the iron core and the winding of the ST, and dispersing a solution domain into a finite number of triangular units omega with connected sizes and shapes e Controlling the size and the number of the finite element grids according to the required calculation precision, finally completing the division of the finite element grids, and exporting and analyzing grid information;
step two, establishing a two-dimensional nonlinear magnetic field equation:
set triangular unit omega e The vector magnetic potential of three vertexes K, M and N is A respectively K 、A M 、A N Then triangular unit omega e The unit equation of (a) is shown as follows:
Figure BDA0003912441160000041
after the above formula is time discretized by a backward Euler method, the following algebraic equation is obtained:
Figure BDA0003912441160000042
in the formula, σ e Is the electrical conductivity;
Figure BDA0003912441160000043
is the current density; v is a cell e Is the reluctance ratio; delta of e Is the area of the triangle; q. q of i And r i Is a function related to the vertex coordinates, i = K, M, N; t is time; Δ t is the time step;
for a two-dimensional non-linear magnetic field, magnetic induction B = × a, the relationship of magnetic induction B and vector magnetic position a is defined as follows:
Figure BDA0003912441160000044
in the formula, A e Is the unit omega e The vector magnetic potential of (a);
step three, establishing a J-A hysteresis model:
Figure BDA0003912441160000045
wherein M is magnetization; h e Is the effective magnetic field strength; m is a group of an Has no hysteresis magnetization; delta M Coefficients introduced to prevent non-object understanding during the solution; delta is the direction coefficient when dH/dt>At 0, δ =1, when dH/dt<At 0, δ = -1; k is the pinning coefficient between magnetic domains; alpha is a coupling coefficient reflecting the inside of a magnetic domain; c is the reversible susceptibility; mu.s 0 Is a vacuum magnetic permeability.
A method for performing field-path coupling calculation by using the ST electromagnetic transient model comprises the following steps:
step one, establishing a winding voltage equation of an ST electromagnetic transient model:
Figure BDA0003912441160000051
in the formula, V ST,m Winding voltage for the ST electromagnetic transient model; r is ST,m Is a winding resistance; i is ST,m And i ST,n Are all winding currents; n is a radical of m The number of winding turns; l. the m Is the axial length of the winding; s. the m Is a winding area; delta Sm Is the area of the winding area; m and n both represent winding numbers of the ST electromagnetic transient model;
Figure BDA0003912441160000053
can be determined by dividing Δ i in the following formula ST,n Adding a smaller value and then solving the finite element model to obtain:
Figure BDA0003912441160000052
in the formula i ST,other To remove i ST,n The other winding current;
step two, forming the secondary winding voltage of the ST electromagnetic transient model obtained by numerical calculation into a series compensation voltage V ss′ And injecting the power into an external power system network;
step three, solving the external system network again, and updating the primary winding current i of the ST electromagnetic transient model ST,p And secondary winding current i ST,s And inputting the updated current into the ST finite element model for calculating the next time step, thereby completing the field-circuit coupling numerical calculation of the ST electromagnetic transient model.
Compared with the prior art, the invention has the following advantages:
(1) Compared with the traditional electromagnetic transient model established based on a magnetic circuit method, the calculation method provided by the invention can accurately acquire the magnetic field distribution in the ST and has higher calculation precision.
(2) The invention utilizes the correlation theory of the J-A magnetic hysteresis model to simulate the nonlinear characteristics of the iron core material, such as saturation, eddy current and magnetic hysteresis; and a field-circuit indirect coupling method is adopted to establish connection between the finite element model and an external electric system, so that the electromagnetic transient field-circuit co-simulation of the ST device and the external electric system is realized.
(3) In the calculation process, proper variables are searched according to the working principle and the working characteristic of ST to realize the bidirectional coupling of the finite element module and the external electrical system. The finite element model is packaged in a module mode, so that the finite element model can be flexibly called in power system simulation software and is combined with an external circuit to solve, magnetic field distribution under the conditions of short circuit fault, harmonic injection and the like of an external electrical system can be reflected, the finite element modeling method can be suitable for power flow control of complex and various power systems, the finite element modeling method can be extended to the ST of other different iron core structures, reference is provided for structural optimization design of the ST, and the applicability and the universality of the ST finite element model are improved.
(4) The method can more accurately acquire the change conditions of the electromagnetic parameters such as winding voltage, winding current, winding loss, eddy current loss, hysteresis loss and the like of the ST under different working conditions along with time, and can also accurately extract the field distribution of the ST transient electromagnetic field, and the error is controlled within 5 percent.
(5) The invention can jointly solve the ST finite element model and the simulation software of the power system, realize the collaborative simulation of a device level and a system level, accurately reflect the electromagnetic transient characteristics of the ST when the system is short-circuited, injected with harmonic waves and controlled by dynamic power flow, visualize the magnetic field distribution inside the ST and more truly simulate the working condition of the ST.
Drawings
Fig. 1 is a schematic diagram of the connection of a three-phase three-pole ST to a power transmission network;
FIG. 2 is a two-dimensional finite element model diagram of ST;
FIG. 3 is a diagram of a field-line coupling scheme for ST and external network co-simulation;
FIG. 4 is a detailed pseudo code of field line coupling;
FIG. 5 is a schematic diagram of a power system connection including a ST finite element model used in an embodiment;
FIG. 6 is a diagram of magnetization current and hysteresis loop of a sample triangle unit during the power-on process under working condition 1;
fig. 7 is a comparison diagram of node vector magnetic bits at t =85ms and t =194ms in operating condition 1;
FIG. 8 shows the time domain simulation result of ST under condition 1 and COMSOL
Figure BDA0003912441160000071
A comparative plot of results;
FIG. 9 is a diagram of the frequency domain simulation results of 100ms to 150ms under condition 1;
fig. 10 is the field distribution inside ST at sample points t =85ms and t =194ms in condition 1;
fig. 11 is a comparison graph of node vector magnetic potential at times t =1.27s and t =3.67s in operating condition 2;
fig. 12 shows the active power and reactive power changes of two transmission lines during dynamic power flow control under condition 2;
FIG. 13 is a graph of the variation of the injected series compensation voltage and the ST secondary winding current during dynamic power flow control for condition 2;
fig. 14 shows the field distribution within the ST at sample points t =1.27s and t =3.67s in operating mode 2.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings, but not limited thereto, and any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.
The invention provides a finite element method-based ST electromagnetic transient model and field path coupling numerical calculation method, which aims to solve the following technical problems:
(1) The method aims to simulate the internal electromagnetic characteristics of the ST operation process more accurately and flexibly access an ST finite element model to power system simulation software to realize collaborative simulation, and aims to fill the vacancy of multidisciplinary intersection and field-path coupling numerical calculation for modeling the transient electromagnetic field characteristics of the electromagnetic type unified power flow controller ST.
(2) The field circuit indirect coupling method suitable for the ST device and the external circuit to conduct collaborative simulation is provided, and the provided finite element model can represent electromagnetic field changes inside the ST under different working conditions that an external power system has short circuit faults, harmonic source injection and the like, so that the ST finite element model provided by the invention can be better applied to engineering practice.
(3) The finite element calculation method is used for laying a theoretical foundation for researching the electromagnetic-thermal-fluid multi-physical field coupling calculation and the body structure optimization design of the ST, providing a finite element calculation method for researching the electromagnetic transient characteristics of the ST during the step-by-step adjustment of the dynamic power flow control, and having certain reference significance for researchers dedicated to researching the electromagnetic characteristics of the multi-winding transformer and manufacturers for researching and developing ST test prototypes.
In order to solve the technical problems, firstly, an electromagnetic field finite element model of ST is established, nonlinear characteristics of an iron core material are simulated by using a J-A hysteresis model, bidirectional coupling between the finite element model and an external electric network is realized by adopting a field path indirect coupling technology, and then an electromagnetic finite element model and a power system network coupling calculation platform are established and combined solution is carried out. The specific execution steps are as follows:
step 1, establishing an ST electromagnetic finite element model. The specific modeling process is as follows:
the first step is as follows: using COMSOL
Figure BDA0003912441160000082
And (3) a two-dimensional drawing function of software, namely establishing a two-dimensional finite element model according to the geometric dimensions of the iron core and the winding of the ST, dispersing a solving domain into a limited number of triangular units with connected sizes and shapes, controlling the sizes and the number of the triangular units according to required calculation precision, finally completing the division of a finite element grid, exporting and analyzing grid information, and obtaining the ST two-dimensional finite element model after analysis as shown in figure 2.
The second step is that: when the winding is excited by an external network, the current density in the winding will generate a dynamic magnetic field, which can be described by the vector magnetic bit a. For a two-dimensional plane field, vector magnetic potential A and current density J only have components in the z-axis direction, so the differential equation of the two-dimensional nonlinear magnetic field is as follows:
Figure BDA0003912441160000081
wherein A is the component of vector magnetic potential in the z-axis direction; v is the reluctance ratio; σ is the conductivity; j. the design is a square z Is the component of the current density in the z-axis direction.
According to the Galerkin method, each triangular unit omega e The weighted residual integral over can be written as:
Figure BDA0003912441160000091
in the formula, A e Is unit Ω e Vector magnetic potential of (W) e Is a weighting function. In fig. 2, a triangle unit Ω is provided e The vector magnetic potential of three vertexes K, M and N is A respectively K 、A M 、A N . The whole triangle unit omega e Vector magnetic potential function A of any point in middle e It can be approximated by a linear interpolation function, namely:
A e ＝N K A K +N M A M +N N A N (3)；
in the formula, N K 、N M And N N Is the shape function depicted in fig. 2, as a function of x and y. These shape functions may be defined as:
Figure BDA0003912441160000092
where Δ is the area of the triangle, p i 、q i And r i Is a function related to the vertex coordinates, and the functional relationship thereof is given by equations (5) and (6):
Figure BDA0003912441160000093
Figure BDA0003912441160000094
according to the Karley gold method, A in the formula (2) e Can be replaced by equation (3), weighting function W e Are respectively set as a shape function N K 、N M And N N . After the integral operation is performed on the formula (2), a unit equation of each triangle unit can be obtained, as shown in the formula (7):
Figure BDA0003912441160000095
after the backward euler method is used for time discretization of the formula (7), the following algebraic equation can be obtained:
Figure BDA0003912441160000101
it is noted that the conductivity σ is within one triangular cell e Current density of
Figure BDA0003912441160000102
And reluctance ratio υ e Are all constants. Electrical conductivity sigma e Is given, current density
Figure BDA0003912441160000103
Obtained by inputting currents into primary and secondary windings of ST, magnetic reluctance ratio upsilon e Can be quantitatively expressed by introducing magnetic induction B. For a two-dimensional field, the magnetic induction B = ^ A is also constant inside one triangular unit, depending only on the vertex A K 、A M 、A N . Therefore, only the vector magnetic potential at time t in equation (8) is unknown.
In one unit, the relationship of B and A is defined as follows:
Figure BDA0003912441160000105
further, upsilon e And B 2 The relationship (c) can be obtained from the B-H curve of the core material. An ST model which is more consistent with the practical situation must be provided with an accurate iron core model, and the nonlinear material characteristics of the ST iron core are expressed by the improved J-A hysteresis model.
The third step: to express the hysteresis characteristics of the core material, the J-A hysteresis model decomposes the actual magnetization M into the reversible magnetization M rev And irreversible magnetization M irr Two components, namely:
M＝M rev +M irr (10)；
in the formula, M rev Mainly caused by bending of the domain wall, and M irr Mainly due to the substitution of magnetic domain walls. Irreversible magnetization M irr The ordinary differential equation of (a) is:
Figure BDA0003912441160000111
wherein:
Figure BDA0003912441160000112
H e ＝H+αM (13)；
Figure BDA0003912441160000113
in the formula, H e Is the effective magnetic field strength; m is a group of an For anhysteretic magnetization, it is described by a modified Langevin function; delta M Coefficients introduced to prevent non-object understanding during the solution; delta is the directional coefficient when dH/dt>At 0, δ =1, when dH/dt<At 0, δ = -1; m is a group of s Is the saturation magnetization; k is the pinning coefficient between magnetic domains; alpha is a coupling coefficient reflecting the inside of a magnetic domain; a is a parameter for characterizing the shape of the anhysteretic magnetization curve.
M rev 、M an And M irr The relationship between is defined as follows:
M rev ＝c(M an -M irr ) (15)；
wherein c is a reversible magnetization coefficient.
The energy conservation equation in the magnetization process is as follows:
Figure BDA0003912441160000114
in the formula, mu 0 Is a vacuum magnetic permeability.
The J-A hysteresis model obtained from equation (16) is:
Figure BDA0003912441160000115
from the equation (9), the vector magnetic potential a and the magnetic induction B are associated with each other when the finite element model is solved, so the input quantity of the J-a hysteresis model is the magnetic induction B, and the magnetic field strength H is the output quantity to be solved. Therefore, equation (17) can be rewritten as:
Figure BDA0003912441160000121
2. and calculating a field coupling value. The input parameter of the ST is the current of the primary winding and the secondary winding, and the winding voltage is obtained through finite element model calculation and then forms a series compensation voltage to be injected into an external electric network, so the ST is connected with the external circuit by adopting a field coupling technology.
The field circuit coupling has two methods of direct coupling and indirect coupling to connect the finite element model and the external network. The direct coupling method solves the field equation and the electric network equation simultaneously, which is not suitable for network calculation of a complex electric power system, while the indirect coupling method can solve the field equation and the electric network equation respectively. Therefore, the method is based on the field circuit indirect coupling technology, and can accurately extract the winding voltage considering the multi-winding coupling effect from the finite element model. Because ST has 12 windings in total, the coupling process of the phase windings is complex, and the position of a winding tap can be required to be dynamically adjusted during the compensation of the ST series voltage, so that the operation condition is complex. The exact calculation of the field-line coupling may therefore be directly related to the accuracy of the ST electromagnetic transient solution.
The induced voltage V on the ST winding can be collectively represented by the voltage drop of the winding resistance and the vector magnetic potential according to faraday's law of electromagnetic induction:
Figure BDA0003912441160000122
where r is the winding resistance, I is the winding current, N is the number of winding turns, l is the axial length of the winding, S is the winding area, Δ S Is the area of the winding area.
The vector magnetic potential A is obtained by calculation through a finite element model, and the input variable of the finite element model is primary winding current i of three phases ST ST,p And secondary winding current i ST,s . Therefore, equation (19) can be rewritten as follows according to the chain rule:
Figure BDA0003912441160000123
the 12 windings of ST are arranged according to A, B, C and a 1 、b 1 、c 1 、a 2 、b 2 、c 2 、a 3 、b 3 、c 3 Numbered sequentially from 1 to 12, and the primary and secondary winding voltages of ST are obtained instead of equation (20), namely:
Figure BDA0003912441160000131
in the formula, m and n each represent a winding number of ST. While
Figure BDA0003912441160000132
Can be determined by dividing Δ i in the formula (22) ST,n Solving the finite value by adding a smaller valueObtaining a meta model:
Figure BDA0003912441160000133
in the formula i ST,other To remove i ST,n The other windings are in current. Δ i ST,n Can be determined by the input current i at the present moment ST,n (t) and input current i at historical time ST,n (t- Δ t) are collectively expressed as:
Δi ST,n ＝i ST,n (t)-i ST,n (t-Δt) (23)。
the primary and secondary winding voltages of ST are obtained by the numerical solution formula (21) to form a series compensation voltage V ss' And injecting the finite element model into an external network, thereby realizing the coupling of the finite element model and the external network. Therefore, the field-circuit indirect coupling can be used for realizing the collaborative simulation solution of the ST device and the external power system, and the detailed coupling scheme and pseudo code of the collaborative simulation are respectively shown in FIGS. 3 and 4.
3、COMSOL
Figure BDA0003912441160000134
And establishing an electromagnetic finite element model for comparing with the solving result of the invention. Continuously perfecting commercial finite element software COMSOL on the basis of ST grids in step 1
Figure BDA0003912441160000135
Then, a two-dimensional transient electromagnetic characteristic solving method is utilized, and electromagnetic parameters of ST are combined as follows: winding turns, electrical conductivity of the iron core and the coil, sectional area of a coil wire, material attribute parameters and the like; the network division control parameters are as follows: the type, size, etc. of the grid completes COMSOL
Figure BDA0003912441160000136
Establishing a two-dimensional electromagnetic finite element model. The specific operation process is as follows:
the first step is as follows: setting of boundary conditions and solution domains. In order to be able to make the calculations stable, an infinite box of the electromagnetic structure is established, setting the solving boundary conditions to infinite magnetic anisotropy zeros.
The second step is that: and setting material properties. And finishing the material attribute setting of each component according to the attributes of the ST iron core, the winding and the air domain, and setting the material attribute of the iron core region as a J-A hysteresis model to finally establish a finite element model of the ST.
The third step: coupling of the coil and an external circuit. And setting the number of turns of the coil and the excitation mode of the coil according to the working state of the ST. Setting 12 coils of ST to be in the state of exciting by external current, and then setting COMSOL
Figure BDA0003912441160000141
The model is exported as a module for subsequent co-simulation with the power system software. Thereby completing the whole COMSOL
Figure BDA0003912441160000142
And (4) establishing an ST two-dimensional transient finite element model of the software.
4. And establishing a finite element model and a power system software collaborative simulation platform. The specific operation process is as follows:
the first step is as follows: the finite element model of the invention is packaged with COMSOL in step 3
Figure BDA0003912441160000143
And respectively importing the modules of the model into power system simulation software, such as Matlab/Simulink, PSCAD/EMTDC, PSS/E, DIgSILENT and the like.
The second step is that: and (5) building a system simulation model. The finite element model of the proposed ST is coupled to an external power system, the connection schematic of which is shown in fig. 5. The power system is built in power system simulation software according to the electrical connection relationship shown in fig. 5. The system consists of a finite element model of ST, two voltage sources (G) s1 And G s2 ) And two transmission lines (L) 1 And L 2 ) The power transmission line is modeled by adopting distributed parameters, and the detailed parameters of the system are shown in a table 1.
The third step: and setting system network parameters, the switch state of the circuit breaker and the connection state of the finite element module, and setting simulation time and simulation step length of the system and electric physical quantities to be stored.
The fourth step: and simultaneously solving the system network and the finite element model to complete the collaborative simulation, and performing post-processing after the calculation is completed.
Example (b):
two kinds of condition analysis are carried out on a three-phase three-column ST finite element model, and the geometric shape and mesh subdivision (comprising 1472 units and 758 nodes) are shown in figure 2. The finite element model of the proposed ST is coupled to an external power system, the connection diagram of which is shown in fig. 5. The system consists of a finite element model of ST, two voltage sources (G) s1 And G s2 ) And two transmission lines (L) 1 And L 2 ) The transmission line is modeled by adopting distributed parameters, and ST finite element model parameters and system detailed parameters are respectively shown in a table 1 and a table 2.
Table 1 ST finite element model parameters and settings in the examples
Figure BDA0003912441160000151
Table 2 parameters and settings of major elements of simulation system in embodiment
Figure BDA0003912441160000152
Figure BDA0003912441160000161
In condition 1, the compensation voltage of ST is set to V ss' =0.2p.u., β =120 °, i.e. the secondary tap group TG 3 Operating at 0.2p.u, and tap-group TG 1 And TG 2 Is shorted. The simulation time was set to 250ms and the solving time step for both the finite element model and the external network was set to 10 mus. The following simulations were developed:
1) And (3) electrifying transient state: t =0ms, switch SW 1 Closed, SW 3 Closed to T 1 With the other switches remaining open, ST energized and connected to the Load 1 ；
2) The two-machine double-circuit power transmission line operates: t =50ms, SW 5 Is turned off, SW 3 Closed to T 2 Other switches are closed and configured into a two-machine double-circuit power transmission line system;
3) And (3) harmonic source injection: t =100ms, the switching state of the system remains unchanged, and the generator G is operated s1 Injecting 3 rd and 5 th harmonics;
4) Short-circuit failure: t =150ms, the switch state remains unchanged, and the transmission line L 1 A three-phase short circuit grounding fault occurs at the receiving end;
5) Fault removal: t =200ms, the switch state is kept unchanged, the short-circuit fault is removed, and ST is gradually recovered to the steady-state operation.
In order to study the transient response of the finite element model during ST dynamic power flow control, operating condition 2 dynamically adjusts the active and reactive power of the transmission line by gradually adjusting the on-load tap-changer of ST. Condition 2 also develops in the power system shown in fig. 5 with the switch state set to SW 3 Closed to T 2 ，SW 4 And the other switches are kept closed when the power supply is disconnected, and the single-machine double-circuit power transmission line system is configured. In working condition 2, the simulation time is set to be 4s, and the solving time step length of the finite element model and the external network is set to be 100 mus. The following simulations were carried out:
1) When t is<At 0.5s, V ss' =0, β =0 °; at the moment, ST is short-circuited, and three groups of taps of the secondary winding are not connected.
2) When 0.5s<t<At 2s, V ss' =0.15p.u., β =120 °; in this case, the ST secondary tap group TG 3 It is necessary to adjust the position from 0p.u. to 0.15p.u., step by step, tap pressure adjusting step is set to 0.05p.u./step, and tap operation time is set to 0.5 s/step.
3) When 2s<t<At 4s, V ss' =0.2p.u., β =0 °. In this case, the ST secondary tap group TG 1 The position of 0 p.u.needs to be adjusted to 0.2 p.u.gradually, and TG 3 It is necessary to gradually return from 0.15p.u.to the 0p.u.position.
2. Example simulation analysis
(1) Working condition 1: time domain simulation of field-circuit coupling of the invention
In order to verify the effectiveness of the ST electromagnetic transient finite element model based on field-path coupling, which is provided by the invention, COMSOL (finite element modeling) is adopted in commercial finite element software
Figure BDA0003912441160000172
The same simulation study as the inventive condition 1 was also conducted. COMSOL
Figure BDA0003912441160000171
The geometric parameters and mesh information of the mid-ST model remain consistent with the present invention.
Fig. 6 shows the magnetization current and the hysteresis loops of the sample cells during ST magnetization, from which the hysteresis loss can be calculated. It should be noted that, in the solution at different time steps, the magnetic induction B and the magnetic field strength H of each triangular unit in fig. 2 are updated, which means that each triangular unit corresponds to a hysteresis loop different from each other. Similarly, the transient field distribution information of any specified triangle element and node can be obtained by the finite element model provided by the invention, and the existing commercial finite element software such as COMSOL
Figure BDA0003912441160000181
The field components of these particular cells and nodes cannot be directly obtained.
The variable directly solved by the finite element model is the vector magnetic potential A, and the values of the node vector magnetic potential A at the sampling points t =85ms and t =194ms are given in FIG. 7, and are compared with COMSOL
Figure BDA0003912441160000182
And comparing the solution results.
Other physical quantities of the magnetic field can be obtained through post-processing after the vector magnetic potential A is solved. For example, eddy current loss P ed And hysteresis loss P hy Can be calculated by equation (24) and equation (25), respectively:
Figure BDA0003912441160000183
Figure BDA0003912441160000184
wherein E is the electric field strength, H hy Is a hysteresis field component.
Primary winding current I of ST ST,p Primary winding voltage V ST,p Secondary winding current I ST,s Secondary winding voltage V ST,s Time domain simulation results of winding loss, eddy current loss, hysteresis loss and total loss are shown in fig. 8. In addition, COMSOL
Figure BDA0003912441160000185
The results of the co-simulation of (c) are also plotted in fig. 8, respectively, for comparison with the results obtained from the finite element model proposed by the present invention.
From the node vector magnetic bit in fig. 7 and the time domain simulation result in fig. 8, it can be found that the numerical calculation result of the model proposed by the present invention and COMSOL
Figure BDA0003912441160000186
The solution result goodness of fit is better. In addition, fig. 9 shows the results of the field-line co-simulation of Fast Fourier Transform (FFT) after harmonic injection from 100ms to 150 ms. As can be seen from FIG. 9, the FFT result after harmonic injection is also associated with COMSOL
Figure BDA0003912441160000187
And the validity and the accuracy of the ST finite element model provided by the invention are proved. In addition, at sampling points T =85ms and T =194ms, detailed field distributions such as vector magnetic potential a (Wb/m), magnetic field strength H (a/m), magnetic induction B (T), and eddy current density J (a/m) 2 ) Respectively, are shown in fig. 10.
From the time domain simulation results of FIG. 8, it can be seen that ST is due to core saturation, hysteresis, and magnetic hysteresis during operationThe three-phase waveform is not a standard sine wave due to extremely uneven magnetic field distribution and the like. And after the third and fifth harmonics are injected at t =100ms, the voltage and current waveforms of ST are severely distorted. When t =150ms, because the line L 1 The receiving end of ST has a three-phase short circuit fault, and the secondary winding current flowing into ST increases sharply, so that the maximum value of magnetic induction intensity shown in fig. 10 when T =194ms reaches 2.1T, which is much larger than a normal operating value. The core at this time is heavily saturated, and thus the winding loss and eddy current loss of ST during the three-phase short duration are also increased accordingly. However, the losses generated by the windings and the core may be converted into heat sources that cause the temperature inside the ST device to rise by means of heat conduction, heat convection, and the like. The over-high temperature rise not only can accelerate the insulation aging and induce the accidents of electric breakdown and the like caused by turn-to-turn short circuit of the winding, but also can cause the burning loss or the mechanical deformation damage of the structural component after the long-term overheat operation.
Notably, these detailed transient field distributions help designers develop and optimize test prototypes for ST. For example, designers can optimize the core structure and material parameters of the ST based on these transient field distributions, better selecting ferromagnetic and insulating materials, thereby reducing losses and operating costs, reducing the age degradation of the insulation of the ST, and extending the potential operating life.
(2) Working condition 2: dynamic power flow control of the invention
According to the dynamic power flow control scheme in the working condition 2, the tap position of the secondary winding of the ST is gradually adjusted to change the active power and the reactive power of the power transmission line. FIG. 11 plots the values of the node vector magnetic potential A at sample points t =1.27s and t =3.67s, against COMSOL
Figure BDA0003912441160000191
The solution results are compared to verify the accuracy of the provided ST finite element model in the dynamic power flow regulation process.
The power regulation simulation results of the two transmission lines are shown in fig. 12, and ST is short-circuited and in an uncompensated state at the beginning of the simulation. At this time line L 1 Active power P of L1 And reactive power Q L1 103.97MW and 68.41MVar, respectively; threadRoad L 2 Active power P of L2 And reactive power Q L2 Respectively 88.70MW and 52.65MVar. At t 1 When =0.5s, the compensation voltage of ST is set to 0.15p.u., the angle is 120 °. In this case, ST secondary tap group TG 3 It is necessary to adjust from the position of 0p.u. to 0.15p.u., step by step, tap pressure adjustment step size is set to 0.05p.u./step, and tap operation time is set to 0.5 s/step, which means that it takes 1.5s to complete the adjustment. During this time period, the line L 1 P of L1 Gradually increased to 117.39MW, Q L1 Gradually reduced to 63.67MVar; and the line L 2 P of L2 Gradually reduced to 84.40MW, Q L2 Gradually increased to 63.11MVar. This shows that ST can adjust the power flow distribution of both transmission lines by injecting a compensation voltage. At t 2 When =2s, the compensation voltage of ST is set to 0.2p.u., and the angle is 0 °. In this case, the ST secondary tap group TG 1 It is necessary to adjust the position from 0p.u. to 0.2p.u. step by step, and TG 3 It is necessary to gradually return from 0.15p.u to 0p.u. At t 3 Tap group TG of 3.5s 3 Adjusted back to the 0 p.u.position, and TG 1 The adjustment is continued from the 0.15p.u.position to 0.2p.u.s.. Finally, line L 1 P of L1 Adjusted to 138.87MW, Q L1 Adjusted to 72.73MVar; line L 2 P of L2 Adjusted to 79.32MW, Q L2 Adjusted to 64.38MVar.
The variation process of the injected series compensation voltage and the secondary winding current corresponding to ST during the whole dynamic power flow regulation is shown in fig. 13. The gradual change in current and voltage during tap dynamic adjustment of ST can be seen more clearly in fig. 13. Also, the detailed field distribution at sample points t =1.27s and t =3.67s, st is shown in fig. 14.
As can be seen from the secondary winding current shown in fig. 13 (b), the secondary winding current amplitude of ST does not change much during the dynamic power flow control, which indicates that the maximum magnetic induction intensity of the internal magnetic field of ST does not change much under the normal operating condition, just as the maximum value of magnetic induction intensity at the sampling points T =1.27s and T =3.67s is about 1.6T as shown in fig. 14. The internal loss and the temperature rise are important parameters to be considered when the ST is researched and designed, the size of the iron core loss is closely related to the magnetic induction distribution in the iron core, and a designer can obtain the magnetic induction distribution of the ST under various working conditions according to the finite element model provided by the invention. Therefore, the ST electromagnetic transient finite element model based on field path coupling not only can better represent the current and voltage changes of an internal winding when the ST is adjusted in the dynamic tide, but also can provide detailed transient electromagnetic field distribution when the ST is under different working conditions, thereby being beneficial to research and development of an ST test prototype. The designer can further develop an electromagnetic-thermal-fluid multi-physical field coupling numerical calculation and simulation model of the ST on the basis of the ST electromagnetic transient finite element model provided by the invention, thereby obtaining the real-time interactive change of the ST internal electromagnetic field and the ST internal thermal field.
In addition, the invention can be more flexibly connected with an external network after packaging the provided finite element model into a module, thereby realizing the electromagnetic transient collaborative simulation of the ST equipment and an external power system. For COMSOL
Figure BDA0003912441160000211
And commercial finite element software such as ANSYS and the like, and only support the simulation software and tools which establish a data interaction interface with the commercial finite element software to carry out collaborative simulation, which has certain limitation. The ST model based on the finite element method can be applied to any professional power system simulation software supporting the user-defined function and is not limited by a data interaction interface, so that the applicability of the model and the numerical calculation method provided by the invention in various professional power system simulation software is improved. Meanwhile, the finite element module after function encapsulation can also be applied to the condition that a plurality of ST (test nodes) run simultaneously in a network, so that the model provided by the invention is also suitable when a power system needs to carry out power flow control on a plurality of lines.
3. Calculating the profit
Sen Transformer electromagnetic transient finite element model calculation result and COMSOL based on field-circuit coupling numerical calculation
Figure BDA0003912441160000212
ResultsBasically consistent, and the errors are all within 5 percent. The invention can acquire the distribution of the winding voltage, the winding current and the transient electromagnetic field of the ST under different working conditions of short circuit fault, harmonic injection, dynamic power flow control and the like of an external network, and provides a theoretical basis for researching an electromagnetic-thermal-fluid multi-physical-field coupling simulation model and researching and developing a test prototype of the ST.
The finite element modeling method provided by the invention can be further expanded to the ST of other different iron core structures, such as three-phase four-column type ST, three-phase five-column type ST and ST of a three-dimensional coil transformer structure, so that the universality and potential application value of the ST finite element modeling method provided by the invention are fully demonstrated. In addition, the invention can provide a finite element module of the ST element of the electromagnetic unified power flow controller for power system simulation software during power flow control, and the ST finite element module is conveniently and flexibly called in professional power system simulation software to participate in simulation analysis of power flow control and voltage regulation of a power grid, thereby promoting the future application of the ST device in an actual smart power grid and further highlighting the beneficial effects and application value of the invention.

Claims (4)

1. A method for constructing an ST electromagnetic transient model based on a finite element method is characterized by comprising the following steps:
step one, establishing a two-dimensional finite element model according to the geometric dimensions of the iron core and the winding of the ST, and dispersing a solution domain into a finite number of triangular units omega with connected sizes and shapes e Controlling the size and the number of the finite element grids according to the required calculation precision, finally completing the division of the finite element grids, and exporting and analyzing grid information;
step two, establishing a two-dimensional nonlinear magnetic field equation:
triangular unit omega e The vector magnetic potential of three vertexes K, M and N is A respectively K 、A M 、A N Then triangular unit omega e The unit equation of (a) is shown as follows:
Figure FDA0003912441150000011
after the above formula is subjected to time discretization by a backward Euler method, the following algebraic equation is obtained:
Figure FDA0003912441150000012
in the formula, σ e Is the electrical conductivity;
Figure FDA0003912441150000013
is the current density; v is a cell e Is the magnetoresistance ratio; delta of e Is the area of the triangle; q. q of i And r i Is a function related to the vertex coordinates, i = K, M, N; t is time; Δ t is the time step;
for a two-dimensional non-linear magnetic field, magnetic induction B = × a, the relationship of magnetic induction B and vector magnetic position a is defined as follows:
Figure FDA0003912441150000021
in the formula, A e Is the unit omega e The vector magnetic potential of (1);
step three, establishing a J-A hysteresis model:
Figure FDA0003912441150000022
wherein M is magnetization; h e Is the effective magnetic field strength; m an Has no hysteresis magnetization; delta M Coefficients introduced to prevent non-physical understanding during the solution; delta is the direction coefficient when dH/dt>At 0, δ =1, when dH/dt<At 0, δ = -1; k is the pinning coefficient between magnetic domains; alpha is a coupling coefficient reflecting the inside of a magnetic domain; c is the reversible susceptibility; mu.s 0 Is a vacuum magnetic permeability.
2. The method of claim 1The ST electromagnetic transient model construction method based on the finite element method is characterized in that the M is an 、H e And delta M The calculation formula of (a) is as follows:
Figure FDA0003912441150000023
H e ＝H+αM；
Figure FDA0003912441150000024
wherein H is the magnetic field strength, M s For saturation magnetization, a is a parameter characterizing the shape of the anhysteretic magnetization curve.
3. A method for performing field-path coupling calculations using the ST electromagnetic transient model of any of claims 1-2, the method comprising the steps of:
step one, establishing a winding voltage equation of an ST electromagnetic transient model:
Figure FDA0003912441150000031
in the formula, V ST,m Winding voltage for the ST electromagnetic transient model; r is a radical of hydrogen ST,m Is a winding resistance; I.C. A ST,m And i ST,n Are all winding currents; n is a radical of hydrogen m The number of winding turns; l m Is the axial length of the winding; s m Is a winding area; delta Sm Is the area of the winding area; m and n both represent winding numbers of the ST electromagnetic transient model;
step two, forming the secondary winding voltage of the ST electromagnetic transient model obtained by numerical calculation into a series compensation voltage V ss′ And injecting the power into an external power system network;
step three, solving the external system network again, and updating the primary winding current i of the ST electromagnetic transient model ST,p And secondary windingStream i ST,s And inputting the updated current into the ST finite element model for calculating the next time step, thereby completing the field-circuit coupling numerical calculation of the ST electromagnetic transient model.
4. The method of claim 3, wherein said field-road coupling calculation is performed using an ST electromagnetic transient model
Figure FDA0003912441150000032
The calculation formula of (a) is as follows:
Figure FDA0003912441150000033
in the formula i ST,other To remove i ST,n The rest of the outer winding current.
CN202211327425.4A 2022-10-27 2022-10-27 ST electromagnetic transient model and field-path coupling calculation method based on finite element method Pending CN115618797A (en)

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117077473A (en) * 2023-08-02 2023-11-17 哈尔滨工业大学 Two-dimensional axisymmetric electromagnetic thermal multi-field coupling calculation method based on transmission line method
CN117077473B (en) * 2023-08-02 2024-04-30 哈尔滨工业大学 Two-dimensional axisymmetric electromagnetic thermal multi-field coupling calculation method based on transmission line method

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