CN115618797B - 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 PDFInfo
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Abstract
The invention discloses an ST electromagnetic transient model and a field path coupling calculation method based on a finite element method. The invention can solve the ST finite element model and the simulation software of the electric power system in a combined way, realizes the collaborative simulation of the device level and the system level, can accurately reflect the electromagnetic transient characteristics of the ST when the system is short-circuited, harmonic wave injection and dynamic power flow control, and enables the magnetic field distribution inside the ST to be visualized, thereby more truly simulating the working condition of the ST. The invention can be directly applied to the voltage regulation and power flow 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 test prototype of ST.
Description
Technical Field
The invention belongs to the field of smart grids, relates to a finite element calculation method for electromagnetic transient characteristics of an electromagnetic unified power flow controller (Sen transducer) (ST), and particularly relates to a ST transient electromagnetic field calculation method based on a field coupling technology.
Background
With the large-scale grid connection of renewable energy sources such as photovoltaic and wind power, the problems of power plant scheduling, transmission capacity, power flow control and the like are more prominent in a novel power system taking new energy sources as main bodies, and the safety and stability of the power system face serious challenges. Indeed, the erection of new high voltage ac or dc transmission lines can meet the growing power transmission demands. But further developments in flexible ac transmission systems (Flexible Alternate Current Transmission System, FACTS) allow flexible, economical, efficient use of existing transmission and distribution networks.
The unified power flow controller (Unified Power Flow Controllers, UPFC) is the most powerful FACTS device at present, and can effectively solve the problems of voltage regulation and power flow control. However, extremely high manufacturing and operating costs result in their popularization potential or are limited. The ST based on the phase shifter technology has four-quadrant power flow control capability similar to UPFC, has the advantages of good economy, high reliability and the like, and can provide a very attractive technical route with good economy and applicable performance for the digestion of large-scale renewable energy and the development of a FACTS device. However, the mechanical on-load tap changer is adopted, and the tap can only be switched between gear positions, so that the ST has the defects of low 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: an excitation unit and a voltage regulating unit. ST primary sides are star-shaped connected and connected in parallel to a transmission line transmitting end to form an excitation unit; each secondary side is composed of three windings with On-load Tap-changer (OLTC) to form a voltage regulating unit. The A phase secondary winding is a 1、a2、a3, the B phase secondary winding is B 1、b2、b3, and the C phase secondary winding is C 1、c2、c3. the winding a 1、b1、c1 forms a phase a series compensation voltage, i.e. V ss'A＝Vss'a1+Vss'b1+Vss'c1, so that the voltage at the transmitting end of the phase a can be adjusted from V sa to V s'a. Because of the 120 degree phase difference between V ss'a1,、Vss'b1、Vss'c1, the combination mode of the three voltage phasors can be changed by changing the control of the ST secondary winding OLTC position, thereby changing V ss'A. Similarly, the compensation voltage V ss'B、Vss'C of the B phase and the C phase in series connection can be realized, and then the four-quadrant adjustment of the voltage of the transmitting end from V s to V s', namely V s′＝Vs+Vss′, can be realized. In addition, in order to ensure that A, B, C three phases remain symmetrical during voltage regulation, the number of turns of the winding that is put into operation at any time a 1-b2-c3(TG1) is equal, the number of turns of the winding that is put into operation b 1-c2-a3(TG2) is equal, and the number of turns of the winding that is put into operation c 1-a2-b3(TG3) is equal. The number of turns put into operation for the tap TG 1 group, TG 2 group, and TG 3 group may be different from one another.
The electromagnetic transient model of the traditional ST is mainly established based on a magnetic circuit method, and although the analysis model established based on the magnetic circuit method considers the influence of nonlinear characteristics such as eddy current, hysteresis and the like, the electromagnetic transient model can be used for rapid calculation of ST transient characteristics, and the problems of excessive simplification and serious information deletion exist in the modeling process. For example, the magnetic circuit method adopts lumped parameters to simplify the magnetic field, equivalent magnetic field is converted into a circuit to carry out modeling solution, and the magnetic field in a certain range is considered to be uniformly distributed in the modeling process, and the actual magnetic field is highly unevenly distributed, so the calculation accuracy of the magnetic circuit method is lower. Meanwhile, the magnetic circuit method cannot acquire detailed magnetic field distribution in the ST, and accurate calculation of ST multi-physical field coupling cannot be realized. Therefore, accurate electromagnetic field transient calculation has important significance in the aspects of designing test prototypes of ST, making reliable protection schemes, reducing production and operation costs and the like.
Disclosure of Invention
In order to accurately calculate the transient electromagnetic field of ST under various complex working conditions, the invention provides a ST electromagnetic transient model and a field path coupling calculation method based on a finite element method. The invention establishes an electromagnetic transient model of the ST based on a finite element Method (FINITE ELEMENT Method, FEM), the model adopts a J-A hysteresis model to represent nonlinear characteristics of iron core materials, such as saturation, vortex and hysteresis, the finite element model of the ST is subjected to module encapsulation, field coupling numerical calculation and electromagnetic transient collaborative simulation are carried out by combining electric power system simulation software, and the collaborative simulation task of a device level and a system level is completed, so that the ST can complete the tide control of an external electric power system, and the internal magnetic field distribution of ST equipment under various working conditions can be visualized, thereby providing an accurate transient electromagnetic field calculation Method for the electromagnetic-thermal-fluid multi-physical field coupling calculation and development test prototype of the ST for subsequent research. The invention can be directly applied to the voltage regulation and power flow 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 test prototype of ST.
The invention aims at realizing the following technical scheme:
a construction method of ST electromagnetic transient model based on finite element method comprises the following steps;
Step one, a two-dimensional finite element model is established according to the geometric dimensions of an iron core and windings of the ST, a solving domain is discretized into triangle units omega e with limited size and shape connection, the size and the number of the triangle units omega e are controlled according to required calculation precision, finally, the division of finite element grids is completed, and grid information is exported and analyzed;
step two, establishing a two-dimensional nonlinear magnetic field equation:
Assuming that the vector magnetic bits of the three vertices K, M, N of the triangle unit Ω e are a K、AM、AN, respectively, the unit equation of the triangle unit Ω e is as follows:
After the above formula is subjected to time discretization by using a backward Euler method, the following algebraic equation is obtained:
wherein σ e is the conductivity; Is the current density; v e is the magnetic reluctance rate; Δ e is the area of the triangle; q i and r i are functions related to vertex coordinates, i= K, M, N; t is time; Δt is the time step;
for a two-dimensional nonlinear magnetic field, the magnetic induction intensity The relationship between the magnetic induction B and the vector magnetic potential A is defined as follows:
Wherein A e is the vector magnetic position of the unit omega e;
Step three, establishing a J-A hysteresis model:
Wherein M is magnetization; h e is the effective magnetic field strength; m an is the hysteresis free magnetization; delta M is a coefficient introduced to prevent non-physical solutions from occurring during the solution process; delta is the direction coefficient, delta=1 when dH/dt >0, delta= -1 when dH/dt < 0; k is a pinning coefficient between magnetic domains; alpha is a coupling coefficient reflecting the inside of the magnetic domain; c is the reversible susceptibility; mu 0 is vacuum 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:
Wherein V ST,m is the winding voltage of the ST electromagnetic transient model; r ST,m is the winding resistance; i ST,m and I ST,n are both winding currents; n m is the number of winding turns; l m is the axial length of the winding; s m is a winding area; Δ Sm is the area of the winding area; m and n each represent a winding number of the ST electromagnetic transient model; It can be obtained by solving the finite element model by adding a smaller value to Δi ST,n in the following equation:
where i ST,other is the remaining winding current except i ST,n;
Step two, forming a series compensation voltage V ss′ by using the secondary winding voltage of the ST electromagnetic transient model obtained by numerical calculation, and injecting the series compensation voltage V ss′ into an external power system network;
And thirdly, re-solving an external system network, updating the primary winding current i ST,p and the secondary winding current i ST,s of the ST electromagnetic transient model, inputting the updated currents into the ST finite element model for the calculation of the next time step, and thus completing the field path coupling numerical calculation of the ST electromagnetic transient model.
Compared with the prior art, the invention has the following advantages:
(1) From the field point of view, the invention establishes the electromagnetic transient finite element model of the ST based on Maxwell's equations, and 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 related theory of J-A hysteresis model to simulate the nonlinear characteristics of iron core materials, such as saturation, vortex and hysteresis; and a field path indirect coupling method is adopted to enable the finite element model to be connected with an external electric system, so that the electromagnetic transient field path collaborative simulation of the ST device and the external electric system is realized.
(3) In the calculation process, the invention needs to find suitable variables according to the working principle and the working characteristics of ST to realize the bidirectional coupling of the finite element module and an external electrical system. The finite element model is packaged in a module, so that the finite element model can be flexibly called in power system simulation software and can be combined with an external circuit to solve, meanwhile, the magnetic field distribution under the conditions of short circuit faults, harmonic injection and the like of an external electric system can be reflected, the finite element model can be suitable for flow control of a complex and various power system, the finite element modeling method can be expanded to ST of other different iron core structures, references are provided for structural optimization design of the finite element model, and the applicability and the universality of the finite element model are improved.
(4) The invention can more accurately acquire the change condition of electromagnetic parameters such as winding voltage, winding current, winding loss, eddy current loss, hysteresis loss and the like of ST under different working conditions along with time, and can accurately extract the field distribution of ST transient electromagnetic field, and the error is controlled within 5%.
(5) The invention can solve the ST finite element model and the simulation software of the electric power system in a joint way, realizes the collaborative simulation of the device level and the system level, can accurately reflect the electromagnetic transient characteristics of the ST when the system is short-circuited, harmonic wave injection and dynamic power flow control, and enables the magnetic field distribution inside the ST to be visualized, thereby more truly simulating the working condition of the ST.
Drawings
FIG. 1 is a schematic diagram of a connection of a three-phase three-column ST to a power transmission network;
FIG. 2 is a two-dimensional finite element model diagram of ST;
FIG. 3 is a schematic diagram of a field coupling scheme for co-simulation of ST and external networks;
FIG. 4 is a detailed pseudocode of field coupling;
FIG. 5 is a schematic diagram of a power system connection including an ST finite element model used in the embodiments;
FIG. 6 is a graph of magnetizing current and hysteresis loops of a sample delta unit during condition 1 power-on;
FIG. 7 is a graph of node vector magnetic potential comparisons at times t=85 ms and t=194 ms for condition 1;
FIG. 8 is a graph comparing ST time domain simulation results with COMSOLMultiphysics results in condition 1;
FIG. 9 is a graph of frequency domain simulation results of 100ms to 150ms in condition 1;
fig. 10 is a field distribution inside ST at sampling points t=85 ms and t=194 ms in the condition 1;
FIG. 11 is a graph of node vector magnetic potential comparisons at times t=1.27 s and t=3.67 s for condition 2;
FIG. 12 shows the active power and reactive power variation of two transmission lines during dynamic power flow control under condition 2;
FIG. 13 is a graph showing the variation of the injected series compensation voltage and ST secondary winding current during dynamic power flow control for condition 2;
Fig. 14 shows the field distribution inside ST at sampling points t=1.27 s and t=3.67 s in the working condition 2.
Detailed Description
The following description of the present invention is provided with reference to the accompanying drawings, but is not limited to the following description, and any modifications or equivalent substitutions of the present invention should be included in the scope of the present invention without departing from the spirit and 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 at accurately simulating the internal electromagnetic characteristics of the ST operation process, can flexibly access the ST finite element model into the simulation software of the power system to realize collaborative simulation, and aims at filling the gap of multi-disciplinary intersection and field path coupling numerical calculation of transient electromagnetic field characteristic modeling of the electromagnetic unified power flow controller ST.
(2) The invention provides a field path indirect coupling method suitable for collaborative simulation of an ST device and an external circuit, and the provided finite element model can represent the electromagnetic field change inside ST under different working conditions such as short circuit fault, active harmonic source injection and the like of an external power system, so that the ST finite element model provided by the invention can be better applied to engineering practice.
(3) The method lays a theoretical foundation for researching electromagnetic-thermal-fluid multi-physical field coupling calculation and body structure optimization design of the ST, provides a finite element calculation method for researching electromagnetic transient characteristics of the ST during dynamic power flow control step-by-step adjustment, and has a certain reference significance for scientific researchers and factories for researching the electromagnetic characteristics of the multi-winding transformer and research and development of ST test prototypes.
In order to solve the technical problems, the invention firstly establishes an electromagnetic field finite element model of ST, utilizes a J-A hysteresis model to simulate the nonlinear characteristic of an iron core material, adopts a field indirect coupling technology to realize the bidirectional coupling of the finite element model and an external electric network, and then establishes an electromagnetic finite element model and an electric power system network coupling calculation platform to carry out joint solution. The specific implementation steps are as follows:
and 1, building an ST electromagnetic finite element model. The specific modeling process is as follows:
The first step: and utilizing the two-dimensional drawing function of COMSOL Multiphysics software, 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 triangle units with limited size and shape, controlling the size and the number of the triangle units according to the required calculation precision, finally completing the division of finite element grids, deriving and analyzing grid information, and enabling the analyzed ST two-dimensional finite element model to be shown in figure 2.
And a second step of: when the windings are energized by an external network, the current density in the windings will generate a dynamic magnetic field, which can be described by the vector magnetic potential a. For a two-dimensional planar field, the vector magnetic potential A and the current density J only have z-axis direction components, so the differential equation of the two-dimensional nonlinear magnetic field is:
wherein A is a component of the vector magnetic potential in the z-axis direction; v is the magnetic resistance; sigma is conductivity; j z is the component of the current density in the z-axis direction.
According to galerkin's method, the weighted residual integral on each triangle element Ω e can be written as:
Where A e is the vector magnetic position of element Ω e and W e is the weighting function. In fig. 2, the vector magnetic bits of three vertexes K, M, N of a triangle unit Ω e are set to a K、AM、AN, respectively. The vector magnetic potential function a e at any point in the entire triangle element Ω e can be approximated by a linear interpolation function, namely:
Ae＝NKAK+NMAM+NNAN (3)；
Where N K、NM and N N are shape functions described in FIG. 2, and are functions of x and y. These shape functions can be defined as:
Where Δ is the area of the triangle, p i、qi and r i are functions related to the vertex coordinates, the functional relationship of which is given by equations (5) and (6):
According to galkin's method, a e in equation (2) can be replaced by equation (3), and the weighting function W e is set as the shape functions N K、NM and N N, respectively. The integral operation is carried out on the formula (2) to obtain a unit equation of each triangle unit, as shown in the formula (7):
After time discretization of formula (7) using the backward euler method, the following algebraic equation can be obtained:
Notably, the conductivity σ e, the current density in a triangular cell And the magnetic reluctance ratio v e are constant. The distribution of conductivity σ e is given, current densityThe magnetic reluctance rate v e can be quantitatively expressed by introducing the magnetic induction intensity B, which can be obtained by inputting the current of the primary and secondary windings of ST. For two-dimensional fields, magnetic inductionIs also constant inside a triangle unit, depending only on vertex a K、AM、AN. Therefore, only the vector magnetic potential at the time point t in the expression (8) is unknown.
In one unit, the relationship of B and A is defined as follows:
In addition, the relationship of v e to B 2 can be obtained from the B-H curve of the core material. An ST model which is more compatible with practical situations must be provided with an accurate core model, and the nonlinear material characteristics of the ST core are represented by an improved J-a hysteresis model in the present invention.
And a third step of: to express the hysteresis characteristics of the core material, the J-a hysteresis model decomposes the actual magnetization M into two components, reversible magnetization M rev and irreversible magnetization M irr, namely:
M＝Mrev+Mirr (10)；
Where M rev is primarily caused by bending of the domain wall, and M irr is primarily derived from substitution of the domain wall. The ordinary differential equation for the irreversible magnetization M irr is:
Wherein:
He＝H+αM (13)；
Wherein H e is the effective magnetic field strength; m an is the hysteresis free magnetization, described by the modified Langevin function; delta M is a coefficient introduced to prevent non-physical solutions from occurring during the solution process; delta is the direction coefficient, delta=1 when dH/dt >0, delta= -1 when dH/dt < 0; m s is saturation magnetization; k is a pinning coefficient between magnetic domains; alpha is a coupling coefficient reflecting the inside of the magnetic domain; a is a parameter characterizing the shape of the hysteresis free magnetization curve.
The relationship between M rev、Man and M irr is defined as follows:
Mrev＝c(Man-Mirr) (15)；
wherein c is a reversible magnetization coefficient.
The energy conservation equation in the magnetization process is:
wherein mu 0 is vacuum permeability.
The J-A hysteresis model can be obtained according to equation (16) as:
As can be seen from the equation (9), the vector magnetic potential a and the magnetic induction intensity B are correlated when the finite element model is solved, so that the input quantity of the J-a hysteresis model is the magnetic induction intensity B, and the magnetic field intensity H is the output quantity to be solved. Therefore, formula (17) can be rewritten as:
2. And (5) calculating a field path coupling numerical value. The input parameters of ST are the current of primary and secondary windings, the winding voltage is calculated by a finite element model, and then the series compensation voltage is formed and injected into an external electric network, so that the connection of ST and an external circuit is realized by adopting a field coupling technology.
The field 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, and the indirect coupling method can solve the field equation and the electric network equation respectively. Therefore, the invention is based on the field path indirect coupling technology, and can accurately extract the winding voltage considering the multi-winding coupling effect from the finite element model. Since ST has 12 windings in total, the coupling process of the interphase windings is complex, and the position of the winding tap may need to be dynamically adjusted during ST series voltage compensation, so that the operation condition is complex. The exact computation of the field coupling may therefore directly relate to the accuracy of the ST electromagnetic transient solution.
The induced voltage V on the ST winding can be represented jointly by the voltage drop of the winding resistance and the vector magnetic potential according to faraday's law of electromagnetic induction:
wherein r is the winding resistance, I is the winding current, N is the winding number of turns, l is the axial length of the winding, S is the winding area, and delta S is the area of the winding area.
Since the vector magnetic potential A is calculated by a finite element model, the input variables of the finite element model are the primary winding current i ST,p and the secondary winding current i ST,s of the ST three phases. Therefore, the chain law formula (19) can be rewritten as:
The 12 windings of ST are numbered from 1 to 12 in sequence A、B、C、a1、b1、c1、a2、b2、c2、a3、b3、c3 and substituted into (20) to obtain primary and secondary winding voltages of ST, namely:
where m and n each represent a winding number of ST. While It can be obtained by solving the finite element model by adding a smaller value to Δi ST,n in equation (22):
Where i ST,other is the remaining winding current except i ST,n. Δi ST,n can be collectively represented by the input current at the present time i ST,n (t) and the input current at the historical time i ST,n (t- Δt), namely:
ΔiST,n＝iST,n(t)-iST,n(t-Δt) (23)。
after the primary side winding voltage and the secondary side winding voltage of ST are obtained through the numerical solution formula (21), a series compensation voltage V ss' is formed and is injected into an external network, and therefore coupling between the finite element model and the external network is achieved. Therefore, based on the field path indirect coupling, the co-simulation solution of the ST device and an external power system can be realized, and the detailed coupling scheme and the pseudo code of the co-simulation are respectively shown in fig. 3 and 4.
3. COMSOL Multiphysics building an electromagnetic finite element model for comparison with the solving result of the invention. The model establishment of commercial finite element software COMSOLMultiphysics is continuously perfected on the basis of the ST grid in the step 1, and then a two-dimensional transient electromagnetic characteristic solving method is utilized, and the electromagnetic parameters of ST are combined as follows: winding turns, iron core and coil conductivity, coil wire sectional area, material attribute parameters and the like; the network separation control parameters are as follows: the type, the size and the like of the grid complete COMSOL Multiphysics two-dimensional electromagnetic finite element model establishment. The specific operation process is as follows:
The first step: boundary conditions and setting of solving domains. In order to enable stable calculation, an infinite box of the electromagnetic structure is established, and a solving boundary condition is set to be an infinite magnetic anisotropy zero point.
And a second step of: material property settings. According to the properties of the ST iron core, the windings and the air domain, the material property setting of each part is completed, the material property of the iron core area is set to be J-A hysteresis model, and finally, the finite element model of ST is established.
And a third step of: coupling of the coil and the external circuit. The number of turns of the coil and the coil excitation mode are set according to the working state of ST. And setting the 12 coils of the ST to be in a state of exciting by external current, and then deriving a COMSOL Multiphysics model as a module for the follow-up co-simulation with the power system software. Thus, the building of the ST two-dimensional transient finite element model of the whole COMSOLMultiphysics software is completed.
4. And constructing a finite element model and a power system software collaborative simulation platform. The specific operation process is as follows:
the first step: the finite element model is packaged, and the finite element model and the COMSOL Multiphysics model module in the step 3 are respectively led into power system simulation software, such as Matlab/Simulink, PSCAD/EMTDC, PSS/E, DIgSILENT and the like.
And a second step of: and (5) constructing a system simulation model. The finite element model of the ST is coupled to an external power system, the connection schematic of which is shown in fig. 5. The power system is built in the power system simulation software according to the electrical connection relation shown in fig. 5. The system consists of a finite element model of ST, two voltage sources (G s1 and G s2) and two power transmission lines (L 1 and L 2), wherein the power transmission lines are modeled by adopting distributed parameters, and the detailed parameters of the system are shown in Table 1.
And a third step of: setting system network parameters, the switching state of a circuit breaker and the connection state of a finite element module, and setting simulation time and simulation step length of the system and the electric physical quantity to be stored.
Fourth step: and simultaneously solving a system network and the finite element model, completing collaborative simulation, and performing post-processing after calculation is completed.
Examples:
Two working condition analyses were performed for a three-phase three-column ST finite element model, the geometry and mesh division (comprising 1472 cells and 758 nodes in total) of which are shown in fig. 2. The finite element model of the ST is coupled to an external power system, the connection schematic 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 power transmission lines (L 1 and L 2), wherein the power transmission lines are modeled by adopting distributed parameters, and the parameters of the ST finite element model and the detailed parameters of the system are respectively shown in tables 1 and 2.
Table 1 ST finite element model parameters and settings in the examples
Table 2 main element parameters and settings of the simulation system in the embodiment
In condition 1, the offset voltage for ST is set to V ss' = 0.2p.u., β = 120 °, i.e., the secondary tap group TG 3 operates at a 0.2p.u., while tap groups TG 1 and TG 2 are shorted. The simulation time was set to 250ms and the solution time step for both the finite element model and the external network was set to 10 mus. The following simulations were performed:
1) Power-on transients: t=0 ms, switch SW 1 is closed, SW 3 is closed to T 1, the other switches remain open, ST is powered on and connected to Load 1;
2) The two-machine double-circuit transmission line operates: t=50 ms, SW 5 is open, SW 3 is closed to T 2, and the other switches are all closed, so as to configure a two-machine double-circuit transmission line system;
3) Harmonic source injection: t=100 ms, the switching state of the system remains unchanged, and the generator G s1 injects 3 and 5 harmonics;
4) Short circuit fault: t=150ms, the switch state remains unchanged, and a three-phase short circuit ground fault occurs at the receiving end of the power transmission line L 1;
5) Fault removal: t=200 ms, the switching state remains unchanged, the short-circuit fault is removed, and ST gradually returns to steady-state operation.
In order to study the transient response of the finite element model during ST dynamic power flow control, condition 2 dynamically adjusts the active and reactive power of the transmission line by gradually adjusting the on-load tap changer of ST. Operating mode 2 is also deployed in the power system shown in fig. 5, with switch state set SW 3 closed to T 2,SW4 open and the other switches kept closed, configured as a single-machine double-circuit power transmission line system. In the working condition 2, the simulation time is set to 4s, and the solution time step of the finite element model and the external network is set to 100 μs. The following simulations were performed:
1) When t <0.5s, V ss' = 0, β = 0 °; at this time, ST is short-circuited, and none of the three sets of taps of the secondary winding is connected.
2) When 0.5s < t <2s, V ss' = 0.15p.u., β = 120 °; at this time, the ST secondary tap group TG 3 needs to be adjusted stepwise from a position of 0p.u. to 0.15p.u., the tap voltage step size is set to 0.05 p.u./speed, and the tap actuation time is set to 0.5 s/speed.
3) When 2s < t <4s, V ss' = 0.2p.u., β = 0 °. At this time, the ST secondary tap group TG 1 needs to be gradually adjusted from a position of 0p.u. to 0.2p.u., and TG 3 needs to be gradually adjusted from a position of 0.15p.u. back to 0p.u.
2. Example simulation analysis
(1) Working condition 1: time domain simulation of field coupling of the invention
In order to verify the effectiveness of the ST electromagnetic transient finite element model based on field coupling, the simulation research same as the working condition 1 of the invention is also carried out on commercial finite element software COMSOL Multiphysics. The geometric parameters and mesh information of the ST model in COMSOL Multiphysics remain consistent with the invention.
Fig. 6 shows the magnetizing current and hysteresis loop of the sample cell during ST magnetization, from which hysteresis loss can be calculated. It is noted that in the solution of different time steps, the magnetic induction B and the magnetic field H of each triangle in fig. 2 are updated, which means that each triangle corresponds to a hysteresis loop different from each other. Likewise, transient field distribution information for any given triangular cell and node can be obtained by the finite element model proposed by the present invention, whereas existing commercial finite element software such as COMSOL Multiphysics cannot directly obtain the field components for those particular cells and nodes.
The variables directly solved by the finite element model are vector magnetic bits a, and the values of node vector magnetic bits a at sampling points t=85 ms and t=194 ms are given in fig. 7 and compared with the result of the solution of COMSOL Multiphysics.
Other physical quantities of the magnetic field can be obtained by post-processing after solving the vector magnetic potential a. For example, the eddy current loss P ed and the hysteresis loss P hy can be calculated by the formula (24) and the formula (25), respectively:
Where E is the electric field strength and H hy is the hysteresis field component.
The results of the time domain simulation of the primary winding current I ST,p, primary winding voltage V ST,p, secondary winding current I ST,s, secondary winding voltage V ST,s, winding losses, eddy current losses, hysteresis losses and total losses of ST are shown in fig. 8. In addition, the co-simulation results of COMSOL Multiphysics are also plotted in fig. 8, respectively, for comparison with the results obtained by the finite element model of the present invention.
From the node vector magnetic potential in fig. 7 and the time domain simulation result in fig. 8, it can be found that the numerical calculation result of the model provided by the invention has better matching degree with the solution result COMSOL Multiphysics. In addition, fig. 9 shows the field path co-simulation results of the fast fourier transform (Fast Fourier Transform, FFT) after the harmonic injection from 100ms to 150 ms. As can be seen from fig. 9, the FFT result after the harmonic injection is also consistent with COMSOL Multiphysics, thereby proving the validity and accuracy of the ST finite element model proposed by the present invention. In addition, at sampling points t=85 ms and t=194 ms, detailed field distributions such as vector magnetic bit a (Wb/m), magnetic field strength H (a/m), magnetic induction strength B (T), and eddy current density J (a/m 2) are shown in fig. 10, respectively.
As can be seen from the time domain simulation results of fig. 8, ST is not a standard sine wave during operation due to core saturation, hysteresis, and extremely uneven magnetic field distribution. While after three and five harmonics of t=100 ms are injected, the voltage and current waveforms of ST are severely distorted. When t=150ms, because of the three-phase short-circuit fault at the receiving end of the line L 1, the secondary winding current flowing into ST increases sharply, so that the maximum magnetic induction intensity shown at t=194 ms in fig. 10 reaches 2.1T, which is far greater than the normal operating value. The core is severely saturated at this time, and thus the winding loss and eddy current loss of ST during the three-phase short-circuit duration also increase accordingly. However, losses generated by the windings and the core are converted into heat sources, which cause the temperature inside the ST device to rise by means of heat conduction and convection. The insulation aging can be accelerated due to the excessively high temperature rise, accidents such as electric breakdown and the like caused by winding turn-to-turn short circuit are induced, and structural members can be burnt or mechanically deformed and damaged due to long-term overheat operation.
Notably, these detailed transient field distributions help designers develop and optimize experimental prototypes of ST. For example, designers may optimize ST core structure and material parameters based on these transient field distributions to better select ferromagnetic and insulating materials, thereby reducing losses and operating costs, reducing age degradation of ST insulation, and extending potential operating life.
(2) Working condition 2: dynamic power flow control of the present invention
According to the dynamic power flow control scheme in the working condition 2, the tap positions of the ST secondary windings are 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 sampling points t=1.27 s and t=3.67 s and compares them with the solution results of COMSOLMultiphysics to verify the accuracy of the proposed ST finite element model during dynamic power flow regulation.
The power adjustment simulation results of the two power transmission lines are shown in fig. 12, and ST is shorted at the start of simulation and in an uncompensated state. At this time, the active power P L1 and the reactive power Q L1 of the line L 1 are 103.97MW and 68.41MVar, respectively; the active power P L2 and the reactive power Q L2 of line L 2 are 88.70MW and 52.65MVar, respectively. At t 1 =0.5 s, the compensation voltage of ST is set to 0.15p.u., and the angle is 120 °. At this time, the ST secondary tap group TG 3 needs to be adjusted stepwise from a position of 0p.u. to 0.15p.u., the tap voltage adjustment step size is set to 0.05 p.u./speed, and the tap operation time is set to 0.5 s/speed, which means that it takes 1.5s to complete the adjustment. During this time period, P L1 of line L 1 gradually increased to 117.39mw and q L1 gradually decreased to 63.67MVar; while P L2 of line L 2 gradually decreases to 84.40mw and q L2 gradually increases to 63.11MVar. This shows that ST can adjust the power flow distribution of the two transmission lines by injecting a compensation voltage. At t 2 =2s, the compensation voltage of ST is set to 0.2p.u., and the angle is 0 °. At this time, the ST secondary tap group TG 1 needs to be gradually adjusted from a position of 0p.u. to 0.2p.u., and TG 3 needs to be gradually adjusted from a position of 0.15p.u. back to 0p.u. At t 3 = 3.5s, tap set TG 3 has been adjusted back to the 0p.u. position, while TG 1 needs to be adjusted further from the 0.15p.u. position to 0.2p.u.. Finally, P L1 of line L 1 was adjusted to 138.87mw and q L1 was adjusted to 72.73MVar; p L2 on line L 2 was adjusted to 79.32MW and Q L2 was adjusted to 64.38MVar.
The series compensation voltage injected and the secondary winding current corresponding to ST are varied throughout the dynamic power flow regulation period as shown in fig. 13. The stepwise changes in current and voltage of ST during tap dynamics adjustment can be seen more clearly from fig. 13. Similarly, at sampling points t=1.27 s and t=3.67 s, the st detailed field distribution 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 dynamic power flow control, which means that the amplitude of the maximum magnetic induction intensity of the internal magnetic field of ST also does not change much under normal operation, as shown in fig. 14, the maximum magnetic induction intensity at the sampling points t=1.27 s and t=3.67 s are both about 1.6T. 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 intensity distribution inside the iron core, and a designer can obtain the magnetic induction intensity 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 can not only better represent the current and voltage change of the internal winding of ST during dynamic power flow adjustment, but also provide detailed transient electromagnetic field distribution of ST under different working conditions, which is beneficial to the research and development of ST test prototypes. The designer can further develop the 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, so as to obtain real-time interactive changes of the electromagnetic field and the thermal field inside the ST.
In addition, the finite element model can be flexibly connected with an external network after being packaged into a module, so that the electromagnetic transient collaborative simulation of ST equipment and an external power system is realized. For commercial finite element software such as COMSOLMultiphysics and ANSYS, only simulation software and tools establishing a data interaction interface with the commercial finite element software are supported for co-simulation, and the method 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, is not limited by a data interaction interface, and therefore the applicability of the model and the numerical calculation method in various professional power system simulation software is improved. Meanwhile, the finite element module after function encapsulation can be applied to the condition that a plurality of STs run simultaneously in a network, so that the model provided by the invention is also applicable when the power system needs to carry out the power flow control of a plurality of lines.
3. Calculating profits
The calculation result of the Sen transducer electromagnetic transient finite element model based on the field path coupling numerical calculation is basically consistent with the COMSOL Multiphysics result, and the error is within 5%. According to the invention, winding voltage, winding current and transient electromagnetic field distribution of the ST can be obtained under different working conditions such as short-circuit fault, harmonic injection, dynamic power flow control and the like of an external network, and theoretical basis is provided for researching an electromagnetic-thermal-fluid multi-physical field coupling simulation model and a research and development test prototype of the ST.
The finite element modeling method provided by the invention can be further extended to ST of other different iron core structures, such as three-phase four-column ST, three-phase five-column ST and ST of a three-dimensional roll transformer structure, which fully explains the universality and potential application value of the ST finite element modeling method provided by the invention. In addition, the invention can provide the finite element module of the ST element of the electromagnetic unified power flow controller for the power system simulation software when the power flow control is carried out, and the finite element module of the ST is conveniently and flexibly called in the professional power system simulation software to participate in the simulation analysis of the power flow control and the voltage regulation of the power grid, thereby promoting the future application of the ST device in the actual smart power grid and further highlighting the beneficial effect and the application value of the invention.
Claims (4)
1. The construction method of the ST electromagnetic transient model based on the finite element method is characterized by comprising the following steps:
Step one, a two-dimensional finite element model is established according to the geometric dimensions of an iron core and windings of the ST, a solving domain is discretized into triangle units omega e with limited size and shape connection, the size and the number of the triangle units omega e are controlled according to required calculation precision, finally, the division of finite element grids is completed, and grid information is exported and analyzed;
step two, establishing a two-dimensional nonlinear magnetic field equation:
Assuming that the vector magnetic bits of the three vertices K, M, N of the triangle unit Ω e are a K、AM、AN, respectively, the unit equation of the triangle unit Ω e is as follows:
After the above formula is subjected to time discretization by using a backward Euler method, the following algebraic equation is obtained:
wherein σ e is the conductivity; Is the current density; v e is the magnetic reluctance rate; Δ e is the area of the triangle; q i and r i are functions related to vertex coordinates, i= K, M, N; t is time; Δt is the time step;
For a two-dimensional nonlinear magnetic field, the relationship between the magnetic induction b= v x a and the vector magnetic bit a is defined as follows:
Wherein A e is the vector magnetic position of the unit omega e;
Step three, establishing a J-A hysteresis model:
Wherein M is magnetization; h e is the effective magnetic field strength; m an is the hysteresis free magnetization; delta M is a coefficient introduced to prevent non-physical solutions from occurring during the solution process; delta is the direction coefficient, delta=1 when dH/dt >0, delta= -1 when dH/dt < 0; k is a pinning coefficient between magnetic domains; alpha is a coupling coefficient reflecting the inside of the magnetic domain; c is the reversible susceptibility; mu 0 is vacuum permeability.
2. The method for constructing an ST electromagnetic transient model based on the finite element method according to claim 1, wherein the calculation formulas of M an、He and δ M are as follows:
He＝H+αM；
wherein H is the magnetic field intensity, M s is the saturation magnetization, and a is a parameter for representing the shape of the hysteresis-free magnetization curve.
3. A method for performing field path coupling calculation using the ST electromagnetic transient model constructed by the method of any one of claims 1-2, said method comprising the steps of:
Step one, establishing a winding voltage equation of an ST electromagnetic transient model:
Wherein V ST,m is the winding voltage of the ST electromagnetic transient model; r ST,m is the winding resistance; i ST,m and I ST,n are both winding currents; n m is the number of winding turns; l m is the axial length of the winding; s m is a winding area; Δ Sm is the area of the winding area; m and n each represent a winding number of the ST electromagnetic transient model;
Step two, forming a series compensation voltage V ss′ by using the secondary winding voltage of the ST electromagnetic transient model obtained by numerical calculation, and injecting the series compensation voltage V ss′ into an external power system network;
And thirdly, re-solving an external system network, updating the primary winding current i ST,p and the secondary winding current i ST,s of the ST electromagnetic transient model, inputting the updated currents into the ST finite element model for the calculation of the next time step, and thus completing the field path coupling numerical calculation of the ST electromagnetic transient model.
4. The method for performing field path coupling calculation using ST electromagnetic transient model according to claim 3, characterized in that said method comprises the steps ofThe calculation formula of (2) is as follows:
where i ST,other is the remaining winding current except i ST,n.
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