CN101719184A - Equivalent magnetic-flow difference transient state modeling method of nonlinear magnetic circuit of magnetically controlled shunt reactor - Google Patents

Abstract

The invention provides a practical decoupling electromagnetic transient state modeling method for describing the nonlinear magnetic saturation property of a super/extreme-high voltage magnetically controlled shunt reactor (a high-voltage magnetically controlled shunt reactor), comprising the steps of: describing nonlinear magnetic circuit property with arc hyperbolic functions; decoupling a coupling magnetic circuit equation by providing and utilizing a magnetic-flow substitute algorithm; and establishing an equivalent magnetic-flow difference electromagnetic transient state modeling method. The invention not only accurately reflects the continuously smooth regulation property of a saturated magnetic circuit of the super/extreme-high voltage magnetically controlled shunt reactor and prevents the numerical oscillation of piecewise linearization algorithm, but also can meet the requirements of real-time/faster-than-real-time simulation computation without modifying an admittance matrix and influencing computing speed under the condition of large-range continuous regulation, provides a necessary simulation tool for the real-time electromagnetic transient state computation of the super/extreme-high voltage magnetically controlled shunt reactor and also initiates a new idea for the real-time electromagnetic transient state modeling method of a nuclear element.

Description

The equivalent magnetic-flow difference transient state modeling method of nonlinear magnetic circuit of magnetically controlled shunt reactor

Technical field

The invention belongs to the digital simulation modeling method field, be particularly related to a kind of equivalent magnetic-flow difference transient state modeling method of nonlinear magnetic circuit of magnetically controlled shunt reactor, can be applicable to the digital modeling emulation of the modeling method of saturable magnetic circuit element, particularly magnetic control type paralleling reactor.

Background technology

Along with key water control project power station, Three Gorges, the construction of startup in succession of ten million multikilowatt wind-powered electricity generation base, Jiuquan, Qinghai/Gansu large-scale photovoltaic power station, for solving primary energy and the unbalanced problems of load center distributed pole such as coal, water conservancy, the key rack of China's AC electric power systems should adopt the ultra-high/extra-high voltage compact line to realize remote, jumbo transmission of electricity, gives full play to the vital role that electrical network is optimized the energy resources configuration on a large scale; Promote the efficient intensive development and utilization of primary energy; Help promoting electrical network, power supply coordinated development; Pool utilizes environmental capacity, alleviates the restriction to the national economic development of the energy and environment.

The capacitive charge power of ultra-high/extra-high voltage transmission line of alternation current is huge, trend changes violent and limited insulation margin and suppresses to have caused great challenge for the idle adjusting of system, superpotential.Traditional reactive power compensator as: but (static varcompensator SVC) waits and mostly can't satisfy the needs that idle adjusting and superpotential suppress simultaneously for common high-voltage shunt reactor switching low-voltage shnt capacitor and reactor group, generator leading phase operation and Static Var Compensator.

Controllable parallel reactors can be simplified system's reactive power in the ultra-high/extra-high voltage electrical network, suppresses power-frequency overvoltage and switching overvoltage, elimination generator self-excitation, dynamic compensation line charging power, suppress secondary arc current, damping system resonance etc., can satisfy the many-sided demand of system, thereby have boundless application prospect.

In September, 2007, first cover 500kV high-pressure magnetic formula shunt reactor put into operation successfully at Jiangling, Hubei (Jing Zhou) current conversion station, in system's vital role of having brought into play in service, for development, the operation and maintenance of China's extra-high voltage controlled reactor accumulated invaluable experience.

High-pressure magnetic formula shunt reactor has that capacity can be regulated (all can reach more than 90% to fully loaded regulation rate from zero load), higher hamonic wave on a large scale continuously and active loss is less, reliability is high, use the small electric power electron device, distinguishing feature simple in structure, that integrated cost is low, the technology comparative maturity, the main type that domestic present research and engineering are used.

Theoretical research about the mathematical modeling aspect of high-pressure magnetic formula shunt reactor, has only " a kind of digital simulation modeling method for magnetic control type shunt reactor " (application number: 200810056973) relate to the emulation modelling method of magnetic control type paralleling reactor in the present existing technology, its cardinal principle is to splice the characteristic of simulating magnetic control type paralleling reactor with existing saturation transformer and reactor, further research to high-pressure magnetic formula shunt reactor has important value, but do not set up the accurate mathematical model of the core mechanism of reaction magnetic control type paralleling reactor, and it has adopted penalty method and piecewise-linear techniques, penalty method not only needs to iterate, to in real time/super real-time electromagnetic transient simulation causes obstacle, and the difference of normalized Φ-I magnetization curve and actual excitation property, cause the error of calculation of model very big; Though piecewise-linear techniques calculates simple, but inevitably cause the numerical value concussion between the different segmentations, and the ultra-high/extra-high voltage magnetic control type paralleling reactor is not that general nonlinear element is finely tuned among a small circle, but continuous smooth adjusting on a large scale, high-pressure magnetic formula shunt reactor is as the ingredient of intelligent grid high pressure flexible transmission, if adopt piecewise-linear techniques can not satisfy the computational accuracy that it is regulated on a large scale, can not react the intelligence flexible feature of its continuous smooth adjusting, the plurality of advantages of the body elements of having erased and feature have been damaged the accuracy of mathematical model.And the method for using piece-wise linearization not only can't describe the continuous smooth control characteristic of magnetic control type paralleling reactor, and the simulation accuracy error is very big, can't satisfy the needs of electromagnetic transient in power system emulation.

Because ultra-high/extra-high voltage magnetic control type paralleling reactor range of adjustment is big, regulate frequently, by electro-magnetic transient modeling method in the past, inevitable frequent modification admittance matrix, this will take a large amount of internal memories and time, in real time/and faster than real time simulation calculates and to cause huge difficulty and challenge.Research is in the past regulated this relatively stubborn problem for transient state, does not have literature research to see the work report as yet.

Summary of the invention

At the problems referred to above, the purpose of this invention is to provide a kind of non-linear magnetic circuit saturation characteristic that can accurately describe high-pressure magnetic formula shunt reactor, take into full account the magnetic coupling between each winding of every phase, can react again high-pressure magnetic formula shunt reactor frequent continuously on a large scale transient state control characteristic, satisfy in real time and the electro-magnetic transient modeling method of faster than real time simulation computing velocity and accuracy requirement.For the systematic analysis of ultra-high/extra-high voltage high-pressure magnetic formula shunt reactor provides necessary and effective simulation means.

The present invention proposes a kind of equivalent magnetic-flow difference transient state modeling method of nonlinear magnetic circuit of magnetically controlled shunt reactor, it is characterized in that this method describes the non-linear magnetic circuit characteristic with inverse hyperbolic function, and utilize the magnetic flux alternate algorithm, non-linear magnetic circuit and the decoupling zero of differentiating circuit system of equations, coupling magnetic circuit equation is carried out decoupling zero, thereby set up equivalent magnetic-flow difference electro-magnetic transient model.

Modeling method of the present invention may further comprise the steps:

(1) comprises two windings, U in the main magnetic circuit stem of She Ji high-pressure magnetic formula shunt reactor ₁, U ₂Be AC network side winding voltage, U _D1, U _D2Be the direct current winding voltage, since the magnetic permeability difference of different magnetic circuits, magnetic flux

The magnetic resistance of two main magnetic circuits at place is born excitation mmf main in the total system, resistance is r, electric current is i, and H is a magnetic field intensity, and μ is a magnetic permeability, φ is the alternating voltage initial phase, S is the magnetic circuit equivalent cross-sectional area, and l is the length of magnetic path, and the subscript 1 and 2 of each variable is represented the winding side parameter of left stem and right stem respectively, the subscript 3,4 and 5 of each variable is the parameter of return yoke magnetic circuit, and d represents DC quantity;

(2) can carry out following derivation according to basic magnetic circuit principle, ignore leakage reactance,, have by Faraday's electromagnetic induction law:

$U_1\sin (\mathrm{wt}+{\mathrm{\φ}}_1)=r_1{i}_1+N_1\·S_1\·\frac{{\mathrm{dB}}_1}{\mathrm{dt}}---\left(1\right)$

$U_2\sin (\mathrm{wt}+{\mathrm{\φ}}_2)=r_2{i}_2+N_2\·S_2\frac{{\mathrm{dB}}_2}{\mathrm{dt}}---\left(2\right)$

Ampere circuit law by the magnetic conduction medium has:

H ₁l ₁+H ₃l ₃＝N ₁i ₁+N _d1i _d1 (5)

H ₂l ₂+H ₄l ₄＝N ₂i ₂-N _d2i _d2 (6)

H ₃l ₃＝H ₄l ₄+H ₅l ₅ (7)

Have by the magnetic circuit Kirchhoff's first law:

Saturated magnetization characteristic by the magnetic conduction medium has:

Unsaturated specialization characteristic by the magnetic conduction medium has:

Above-mentioned is the mixed equation group that differential equation group, system of linear equations and Nonlinear System of Equations constitute;

(3) calculate the Nonlinear System of Equations of the magnetic circuit circuit of above-mentioned complexity for decoupling zero, use the magnetic flux alternate algorithm, take into full account the differential concatenation relation of physical symmetry, the electric parallel connection of net side and the field circuit of high-pressure magnetic formula shunt reactor, system of linear equations by Ampere circuit law and magnetic circuit first law, but simultaneous is obtained following formula: subscript m is represented main magnetic circuit in the formula, 0 expression return yoke magnetic circuit

Wherein, each element expression of matrix is as follows:

$\mathrm{\α}=\frac{S_m{l}_0}{{2S}_m{l}_0+{\mathrm{Sl}}_m}---\left(16\right)$

$\mathrm{\β}=\frac{S_m{l}_0+{\mathrm{Sl}}_m}{{2S}_m{l}_0+{\mathrm{Sl}}_m}---\left(17\right)$

In the substitution Ampere circuit law system of equations, and describe non-linear saturable magnetic circuit characteristic with inverse hyperbolic function, arrangement can get:

Its fixed point iterative formula is:

Separating above-mentioned system of equations can get:

Wherein,

(4) because implicit expression trapezoidal integration form is simple, and have suitable precision and good numerical stability, can be suitable for and find the solution the rigidity differential equation group, use the implicit expression trapezoidal integration that the magnetic circuit differential equation group is launched and can be got:

Following formula can be organized into:

$i\left(t\right)=\frac{1}{R_L}u\left(t\right)+I_L(t-\mathrm{\Δt})---\left(28\right)$

Wherein:

$R_L=\frac{2}{r}---\left(29\right)$

Following formula (31) is the decoupling zero equivalent magnetic-flow difference electro-magnetic transient model of deriving with magnetic flux alternate algorithm and implicit expression trapezoidal integration, in an integration step Δ t, Equivalent Model is converted into corresponding difference equation, high-pressure magnetic formula shunt reactor has been described in the t voltage in the moment, electric current and the voltage in the t-Δ t moment, the mutual relationship between the electric current, and t-Δ t voltage and current constantly is the result of calculation of previous step-length, for this step-length is known quantity, like this input and output of model and to the influence of grid each the time step can obtain.

Wherein, according to method of the present invention, the R in the formula (29) _LBe known quantity, above-mentioned model is included into equivalent current source I to the adjusting of reactance value variation _LIn, can carry out Data Update by the real-time calculating of model data and network system, under the frequent situation of regulating of reactor, need not to revise admittance matrix, both guaranteed the precision that transient state is calculated, saved computing time and internal memory again, this modeling method not only can satisfy the types of models and the accuracy requirement of electro-magnetic transient network calculations, and can satisfy the speed needs of real-time calculating.

Wherein, can also use according to method of the present invention to comprise that following continuous function and various forms of combination thereof describe the non-linear magnetic circuit saturation characteristic of high-pressure magnetic formula shunt reactor, thereby carry out simulation modeling:

B＝k ₁·H+k ₂·arctan(H/k ₃)；

B＝k ₁·arctan(H/k ₃)；

$H=\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{a}_{2k+1}\·B^{2k+1};$

$H=\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{a}_{2k+1}\·B^{2k+1}+k_1\·\mathrm{sh}(k_2\·B).$

Wherein, according to method of the present invention, can also use to comprise that following differencing method and various combination thereof come the differential equation of high-pressure magnetic formula shunt reactor is carried out the differencing processing:

Retreat Euler method;

The Taylor expansion method;

The Runge-Kutta method;

The Miline-Hamming method.

Wherein, modeling method of the present invention can also be applied in real time, the simulation modeling of non real-time, electromagnetism, electromechanical transient and calculating, perhaps in the method for designing of control system.

The advantage of technical solution of the present invention is: the present invention with adjustable inverse hyperbolic function describe super the non-linear magnetic circuit saturation characteristic of extra-high voltage magnetic control type paralleling reactor, has the advantage that to lead and not have truncation error continuously, the difficult problem of finding the solution for complex nonlinear system of equations that solve to describe high-pressure magnetic formula shunt reactor saturation characteristic, and take into full account magnetic coupling between each winding of every phase, the present invention proposes the magnetic flux alternate algorithm, non-linear magnetic circuit and the decoupling zero of differentiating circuit system of equations, derive an equivalent magnetic-flow difference electro-magnetic transient modeling method.The adjusting of reactance value variation is included in the equivalent current source, need not to revise admittance matrix, saved computing time and internal memory, can satisfy the demand that real-time/faster than real time simulation is calculated.This has realized the breakthrough in this field 0 at home and abroad in electric analog device/software, for the systematic analysis of ultra-high/extra-high voltage high-pressure magnetic formula shunt reactor provides necessary and effective simulation means, also started new thinking for the real-time electro-magnetic transient modeling method of nonlinear element.

Description of drawings

The present invention is further described below in conjunction with accompanying drawing.

Fig. 1 is the synoptic diagram according to each physical quantity of high-pressure magnetic formula shunt reactor of the present invention, positive dirction and winding connection mode.

Embodiment

The present invention includes the description and the emulation modelling method of magnetic control type paralleling reactor core construction and principle of work thereof.

The basic magnetic circuit circuit theory of 1 high-pressure magnetic formula shunt reactor

High-pressure magnetic formula shunt reactor is to utilize the characteristic of alternating current-direct current composite excitation to change degree of saturation unshakable in one's determination, and its winding connection mode comprises two windings, U as shown in Figure 1 in the main magnetic circuit stem ₁, U ₂Be AC network side winding, U _D1, U _D2Be the direct current winding voltage, since the magnetic permeability difference of different magnetic circuits, magnetic flux

The magnetic resistance of two main magnetic circuits at place is born excitation mmf main in the total system.Resistance is r, and electric current is i, and H is a magnetic field intensity, and μ is a magnetic permeability, and φ is the alternating voltage initial phase, and S is the magnetic circuit equivalent cross-sectional area, and l is the length of magnetic path.Each variable subscript 1,2 is represented left stem and right stem winding side respectively, 3,4,5th, and the return yoke magnetic circuit, d represents DC quantity.

Can carry out following derivation according to basic magnetic circuit principle, ignore leakage reactance,, have by Faraday's electromagnetic induction law:

$U_1\sin (\mathrm{wt}+{\mathrm{\φ}}_1)=r_1{i}_1+N_1\·S_1\·\frac{{\mathrm{dB}}_1}{\mathrm{dt}}---\left(1\right)$

$U_2\sin (\mathrm{wt}+{\mathrm{\φ}}_2)=r_2{i}_2+N_2\·S_2\frac{{\mathrm{dB}}_2}{\mathrm{dt}}---\left(2\right)$

Ampere circuit law by the magnetic conduction medium has:

H ₁l ₁+H ₃l ₃＝N ₁i ₁+N _d1i _d1 (5)

H ₂l ₂+H ₄l ₄＝N ₂i ₂-N _d2i _d2 (6)

H ₃l ₃＝H ₄l ₄+H ₅l ₅ (7)

Have by the magnetic circuit Kirchhoff's first law:

Saturated magnetization characteristic by the magnetic conduction medium has:

Unsaturated specialization characteristic by the magnetic conduction medium has:

Above-mentioned is the mixed equation group that differential equation group, system of linear equations and Nonlinear System of Equations constitute.

2 high-pressure magnetic formula shunt reactor decoupling zero equivalent magnetic-flow difference electro-magnetic transient modeling methods

Calculate the magnetic circuit circuit Nonlinear System of Equations of above-mentioned complexity for decoupling zero, the present invention proposes the magnetic flux alternate algorithm, taken into full account the differential concatenation relation of physical symmetry, the electric parallel connection of net side and the field circuit of high-pressure magnetic formula shunt reactor, system of linear equations by Ampere circuit law and magnetic circuit first law, but simultaneous is obtained following formula: subscript m is represented main magnetic circuit in the formula, 0 expression return yoke magnetic circuit, other mark as previously mentioned.

Wherein, each element expression of matrix is as follows:

$\mathrm{\α}=\frac{S_m{l}_0}{{2S}_m{l}_0+{\mathrm{Sl}}_m}---\left(16\right)$

$\mathrm{\β}=\frac{S_m{l}_0+{\mathrm{Sl}}_m}{{2S}_m{l}_0+{\mathrm{Sl}}_m}---\left(17\right)$

In the substitution Ampere circuit law system of equations, and describe non-linear saturable magnetic circuit characteristic with inverse hyperbolic function, arrangement can get:

Its fixed point iterative formula is:

Separating above-mentioned system of equations can get:

Wherein,

Because implicit expression trapezoidal integration form is simple, and has suitable precision and good numerical stability, can be suitable for and find the solution the rigidity differential equation group, the present invention launches the magnetic circuit differential equation group can get with the implicit expression trapezoidal integration:

Following formula can be organized into:

$i\left(t\right)=\frac{1}{R_L}u\left(t\right)+I_L(t-\mathrm{\Δt})---\left(28\right)$

Wherein:

$R_L=\frac{2}{r}---\left(29\right)$

Following formula is the decoupling zero equivalent magnetic-flow difference electro-magnetic transient model of deriving with magnetic flux alternate algorithm and implicit expression trapezoidal integration, complicated non-linear magnetic circuit circuit differential equation group is derived find the solution into a comparatively succinct equivalent current source model.In an integration step Δ t, Equivalent Model is converted into corresponding difference equation, high-pressure magnetic formula shunt reactor has been described in the t voltage in the moment, electric current and the voltage in the t-Δ t moment, the mutual relationship between the electric current, and t-Δ t voltage and current constantly is the result of calculation of previous step-length, is known quantity for this step-length.Like this input and output of model and to the influence of grid each the time step can obtain.

R in the formula _LBe known quantity, model is included into equivalent current source I to the adjusting of reactance value variation _LIn, can upgrade by the real-time calculating of model data and network system, under the frequent situation of regulating of reactor, need not to revise admittance matrix, both guaranteed the precision that transient state is calculated, saved computing time and internal memory again; This model not only can satisfy the modeling method type and the accuracy requirement of electro-magnetic transient network calculations, and can satisfy the speed needs of real-time calculating.

For example various conversion of the present invention are described below:

1. the present invention is with continuous function-adjustable inverse hyperbolic function; describe super the non-linear magnetic circuit saturation characteristic of extra-high voltage magnetic control type paralleling reactor; have the advantage that can lead and not have truncation error continuously, the non-linear magnetic circuit saturation characteristic of describing high-pressure magnetic formula shunt reactor with other continuous function is carried out similar emulation modelling method and controller algorithm also within protection of the present invention.

2. be the difficult problem of finding the solution of complex nonlinear system of equations that solve to describe high-pressure magnetic formula shunt reactor saturation characteristic; and take into full account magnetic coupling between each winding of every phase; the present invention proposes the magnetic flux alternate algorithm; for example carry out the replacement algorithm of similar thinking with its dependent variable; for example: magnetic flux of the present invention replaced with the equivalence formula of magnetic induction intensity B represent; replace calculating then; non-linear magnetic circuit and the decoupling zero of differentiating circuit system of equations; the magnetic flux alternate algorithm is one of important step of decoupling zero non-linear magnetic circuit circuit equation group; the method according to this invention; amplification is associated and is carried out magnetic circuit circuit variable with other similar fortrans and substitute the method that connects magnetic circuit and circuit equation group, also within protection scope of the present invention.

3. the present invention carries out differencing with the implicit expression trapezoidal integration to the differential equation of high-pressure magnetic formula shunt reactor and handles, and derives an equivalent magnetic-flow difference electro-magnetic transient modeling method.The adjusting of reactance value variation is included in the equivalent current source, need not to revise admittance matrix, saved computing time and internal memory, can satisfy the demand that real-time/faster than real time simulation is calculated.This has realized the breakthrough in this field 0 at home and abroad in electric analog device/software; be easy to according to the present invention to associate and with other differencing method the differential equation of high-pressure magnetic formula shunt reactor carried out differencing and handle, also within protection scope of the present invention.

4. power of the present invention is advocated that the described method of 1-3 carries out analogy and change, reconfigure then, simplify or improve the modeling method of precision and controller algorithm slightly also within protection scope of the present invention.

5. use method of the present invention or modification a little; other non-linear magnetic circuit saturation element are carried out similar electro-magnetic transient modeling method and controller algorithm also within protection of the present invention as (field regulator, nonlinear reactance etc., and other kinds of controlled reactor).

6. the electro-magnetic transient modeling method that the method for method of the present invention or similar derivation used is set up can be applied in real time, in the simulation modeling and calculating of non real-time, electromagnetism, electromechanical transient; and in the method for designing of control system, these are all within protection scope of the present invention.

Invention has been described according to specific exemplary embodiment above.It will be conspicuous carrying out suitable replacement to one skilled in the art or revise under not departing from the scope of the present invention.Exemplary embodiment only is illustrative, rather than to the restriction of scope of the present invention, scope of the present invention is by appended claim definition.

Claims (6)

1. the equivalent magnetic-flow difference transient state modeling method of a nonlinear magnetic circuit of magnetically controlled shunt reactor, it is characterized in that this method describes the non-linear magnetic circuit characteristic with inverse hyperbolic function, and utilize the magnetic flux alternate algorithm, non-linear magnetic circuit and the decoupling zero of differentiating circuit system of equations, coupling magnetic circuit equation is carried out decoupling zero, thereby set up equivalent magnetic-flow difference electro-magnetic transient model.

2. modeling method as claimed in claim 1 is characterized in that may further comprise the steps:

(1) comprises two windings, U in the main magnetic circuit stem of She Ji high-pressure magnetic formula shunt reactor ₁, U ₂Be AC network side winding voltage, U _D1, U _D2Be the direct current winding voltage, since the magnetic permeability difference of different magnetic circuits, magnetic flux

The magnetic resistance of two main magnetic circuits at place is born excitation mmf main in the total system, resistance is r, electric current is i, and H is a magnetic field intensity, and μ is a magnetic permeability, φ is the alternating voltage initial phase, s is the magnetic circuit equivalent cross-sectional area, and l is the length of magnetic path, and the subscript 1 and 2 of each variable is represented the winding side parameter of left stem and right stem respectively, the subscript 3,4 and 5 of each variable is the parameter of return yoke magnetic circuit, and d represents DC quantity;

(2) can carry out following derivation according to basic magnetic circuit principle, ignore leakage reactance,, have by Faraday's electromagnetic induction law:

$U_1\sin (\mathrm{wt}+{\mathrm{\φ}}_1)=r_1{i}_1+N_1\·S_1\·\frac{d{B}_1}{\mathrm{dt}}---\left(1\right)$

$U_2\sin (\mathrm{wt}+{\mathrm{\φ}}_2)=r_2{i}_2+N_2\·S_2\frac{d{B}_2}{\mathrm{dt}}---\left(2\right)$

Ampere circuit law by the magnetic conduction medium has:

H ₁l ₁+H ₃l ₃＝N ₁i ₁+N _d1i _d1(5)

H ₂l ₂+H ₄l ₄＝N ₂i ₂-N _d2i _d2(6)

H ₃l ₃＝H ₄l ₄+H ₅l ₅(7)

Have by the magnetic circuit Kirchhoff's first law:

Saturated magnetization characteristic by the magnetic conduction medium has:

Unsaturated specialization characteristic by the magnetic conduction medium has:

Above-mentioned is the mixed equation group that differential equation group, system of linear equations and Nonlinear System of Equations constitute;

(3) calculate the Nonlinear System of Equations of the magnetic circuit circuit of above-mentioned complexity for decoupling zero, use the magnetic flux alternate algorithm, take into full account the differential concatenation relation of physical symmetry, the electric parallel connection of net side and the field circuit of high-pressure magnetic formula shunt reactor, system of linear equations by Ampere circuit law and magnetic circuit first law, but simultaneous is obtained following formula: subscript m is represented main magnetic circuit in the formula, 0 expression return yoke magnetic circuit

Wherein, each element expression of matrix is as follows:

$\mathrm{\α}=\frac{S_m{l}_0}{2S_m{l}_0+{\mathrm{Sl}}_m}---\left(16\right)$

$\mathrm{\β}=\frac{S_m{l}_0+{\mathrm{Sl}}_m}{2S_m{l}_0+{\mathrm{Sl}}_m}---\left(17\right)$

In the substitution Ampere circuit law system of equations, and describe non-linear saturable magnetic circuit characteristic with inverse hyperbolic function, arrangement can get:

Its fixed point iterative formula is:

Separating above-mentioned system of equations can get:

Wherein,

(4) because implicit expression trapezoidal integration form is simple, and have suitable precision and good numerical stability, can be suitable for and find the solution the rigidity differential equation group, use the implicit expression trapezoidal integration that the magnetic circuit differential equation group is launched and can be got:

Following formula can be organized into:

$i\left(t\right)=\frac{1}{R_L}u\left(t\right)+I_L(t-\mathrm{\Δt})---\left(28\right)$

Wherein:

$R_L=\frac{2}{r}---\left(29\right)$

Following formula (31) is the decoupling zero equivalent magnetic-flow difference electro-magnetic transient model of deriving with magnetic flux alternate algorithm and implicit expression trapezoidal integration, in an integration step Δ t, Equivalent Model is converted into corresponding difference equation, high-pressure magnetic formula shunt reactor has been described in the t voltage in the moment, electric current and the voltage in the t-Δ t moment, the mutual relationship between the electric current, and t-Δ t voltage and current constantly is the result of calculation of previous step-length, for this step-length is known quantity, like this input and output of model and to the influence of grid each the time step can obtain.

3. modeling method as claimed in claim 2 is characterized in that the R in the formula (29) _LBe known quantity, above-mentioned model is included into equivalent current source I to the adjusting of reactance value variation _LIn, can carry out Data Update by the real-time calculating of model data and network system, under the frequent situation of regulating of reactor, need not to revise admittance matrix, both guaranteed the precision that transient state is calculated, saved computing time and internal memory again, this modeling method not only can satisfy the types of models and the accuracy requirement of electro-magnetic transient network calculations, and can satisfy the speed needs of real-time calculating.

4. modeling method as claimed in claim 3 is characterized in that using comprising that following continuous function and various forms of combination thereof describe the non-linear magnetic circuit saturation characteristic of high-pressure magnetic formula shunt reactor, thereby carries out simulation modeling:

B＝k ₁·H+k ₂·arctan(H/k ₃)；

B＝k ₁·arctan(H/k ₃)；

$H=\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{a}_{2k+1}\·B^{2k+1};$

$H=\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{a}_{2k+1}\·B^{2k+1}+k_1\·\mathrm{sh}(k_2\·B).$

5. modeling method as claimed in claim 4 is characterized in that using comprising that following differencing method and various combination thereof come the differential equation of high-pressure magnetic formula shunt reactor is carried out the differencing processing:

Retreat Euler method;

The Taylor expansion method;

The Runge-Kutta method;

The Miline-Hamming method.

6. as the described modeling method of claim 1-5, it is characterized in that this modeling method can being applied in real time, the simulation modeling of non real-time, electromagnetism, electromechanical transient and calculating, perhaps in the method for designing of control system.

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