CN107301288A - A kind of current transformer electromagnetic transient modeling method based on segmentation generalized state space average - Google Patents

A kind of current transformer electromagnetic transient modeling method based on segmentation generalized state space average Download PDF

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CN107301288A
CN107301288A CN201710470739.2A CN201710470739A CN107301288A CN 107301288 A CN107301288 A CN 107301288A CN 201710470739 A CN201710470739 A CN 201710470739A CN 107301288 A CN107301288 A CN 107301288A
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state variable
current transformer
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CN107301288B (en
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王磊
邓新昌
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Hefei University of Technology
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Abstract

The invention discloses a kind of current transformer electromagnetic transient modeling method based on segmentation generalized state space average, it is characterized in that including:1 system initial value is calculated;2 determine segments and each split time based on amplitude prediction;3 set up current transformer segmentation Generalized State Space Averaging model.The present invention can realize the balance of efficiency and precision to current transformer electromagnetic transient modeling, so that current transformer model is applied to electromagnetic transient modeling and the emulation of extensive serial-parallel power grid.

Description

A kind of current transformer electromagnetic transient modeling method based on segmentation generalized state space average
Technical field
It is specifically a kind of to consider that current transformer is opened the present invention relates to the current transformer electromagnetic transient modeling field of power system Pass action, balance model precision and efficiency, the modeling method applied to electromagnetic transient simulation.
Background technology
The scale access of power system generation of electricity by new energy (such as photovoltaic, blower fan) result in the change of power system operation mode Change, the transient characterisitics through the grid-connected generation of electricity by new energy of current transformer directly affect the power system that contains extensive new-energy grid-connected Dynamic characteristic.Current transformer transient state action situation is complicated, and the current transformer model applied to emulation is closed according to the balance of precision and efficiency There is different application occasion in system, but current current transformer model is not fully applied to the power train of scale new energy power generation grid-connection System electro-magnetic transient efficient emulation.
In current achievement in research, mainly there are Dynamic Phasors, State-space Averaging Principle etc. to the method that current transformer is modeled, But such method can not consider the converter switches action of Microsecond grade, not be suitable for the electromagnetic transient modeling of Microsecond grade.Tradition Grid-connected converter model only carries out basic principle analysis in device level, it is difficult to complete detailed electromagnetic transient analysis.Shape State method of average transient Model is only capable of the fundametal compoment of reflection system, and error ripple, high fdrequency component are needed separately to consider, it is impossible to suitable Answer the continuous simulation of extensive new-energy grid-connected.Not for current transformer frequency change and error in existing achievement in research Direct Analysis, so as to be difficult to the emulation that current transformer precise and high efficiency is realized in the case of compound action.
The content of the invention
The present invention is not enough flat based on segmentation generalized state space there is provided one kind present in above-mentioned prior art to avoid Equal current transformer electromagnetic transient modeling method, to which the balance of efficiency and precision can be realized to new energy power generation grid-connection current transformer, So that grid-connected converter model is applied to electromagnetic transient modeling and the emulation of extensive serial-parallel power grid.
The present invention adopts the following technical scheme that to solve technical problem:
The present invention it is a kind of based on segmentation generalized state space average current transformer electromagnetic transient modeling method the characteristics of be by Following steps are carried out:
Step 1, the initial value of converter system are calculated;
In the built-in vertical shown state variable equations as the formula of the simulation time interval T of converter system:
In formula (1),For the derivative of state variable, f (t, x) is the function on time t and state variable x, and x (0) is shape The initial value of state variable, a is constant, and ε is the dimensionless closed with the interval T-phase of simulation time;
By formula (1) calculate state variable x steady-state value as the electro-magnetic transient of the converter system state variable Initial value;
Step 2, segments n and each split time determined based on amplitude prediction;
Step 2.1, first split time T of note1Initial time be T10;First switch periods T of current transformers1Rise Moment beginning is ts0
Judge first split time T1Initial time T10When whether being the starting of first switch periods Carve ts0, if so, then performing step 2.2;Otherwise, t is mades0=T10+ Δ t so that the initial time T10For described first switch The initial time t in cycles0;Wherein, Δ t is time correct amount;
Step 2.2, given sinusoidal modulation wave, triangular carrier, simulation time interval T and dutycycle variance limit value ε1, calculate and obtain the triangular carrier in each switch periods TsOne antinode t of Triangle ID carrier wave and sinusoidal modulation wavep、tf, And as the switch motion moment in the respective switch cycle, so as to obtain the switch motion moment in all switch periods;
Step 2.3, make segments initial value be n=1,
Step 2.4, the initial value r=2 for making switch periods number;
Step 2.5, utilize formula (2) calculate r-th of switch periods in dutycycle dr, so that r switch periods before obtaining Dutycycle { d1, d2, d3..., dr}:
The dutycycle variances sigma of r switch periods before being calculated according to the dutycycle of the preceding r switch periodsr
Step 2.6, judge σr< ε1Whether set up, such as set up, then make switch periods number r Jia 1 certainly, and return to step 2.5; Otherwise, into step 2.7;
Step 2.7, n-th of split time Tn=(r-1) Ts
Step 2.8, detection are in n-th of split time TnWhether the operating condition of the interior converter system changes, if so, Then perform step 2.9;Otherwise, step 2.11 is performed;
Step 2.9, by n-th of split time TnInterior initial time is designated as Tn0, the operating condition of the converter system The change moment is designated as Tnk, then by initial time Tn0Change moment T to operating conditionnkBetween time interval be adjusted to n-th point Section time Tn
Step 2.10, judge in n-th of split time TnEnd time, whether the converter system resume operation work Condition, if so, then performing step 2.11, otherwise, makes segments n from Jia 1, makes n-th of split time Tn=Ts, and return to step 2.10;
N split time sum ∑ T before step 2.11, calculatingn, and judge ∑ TnWhether < T set up, if so, then represent All time slices are not completed, segments n Jia 1 certainly, and enters step 2.4;Otherwise, represent to complete all time slices, and obtain To segments n and each split time;
Step 3, set up using each split time current transformer segmentation Generalized State Space Averaging model;
Step 3.1, for a current transformer being made up of m group independent switches, set up the horizon state side as shown in formula (3) Journey:
In formula (3), x (t) is the state variable on time t,For the derivative of the state variable on time t, Si (t) it is the switch function on time t of i-th group of independent switch in m group independent switches, AiAnd biFor with i-th group of independent switch phase The coefficient matrix and coefficient vector of pass;A0And b0For constant matrices and constant vector;
Step 3.2, in n-th of split time interval TnOn, ask q ranks Fourier to become the both sides of the horizon state equation Change, so as to set up the current transformer segmentation Generalized State Space Averaging model as shown in formula (4):
In formula (4),<x(t)>qFor the q rank Fourier coefficients of the state variable x (t) on time t, Di(t) to be any one Switch function S in individual switch periodsi(t) average value;
In step 3.3, q rank Fu for obtaining the state variable x (t) by the state variable initial value calculating of the electro-magnetic transient Leaf system number<x(t)>qValue, so as to utilize formula (5) reducing condition variable x (t):
In formula (5), ωqFor q times of fundamental frequency.
It is of the present invention based on segmentation generalized state space average current transformer electromagnetic transient modeling method the characteristics of It is, as follows current transformer segmentation Generalized State Space Averaging model is carried out solving checking and error is determined:
Step 4.1, the reference value ε for determining state variable x relative error ranges2With the limit value q of Fourier expansion exponent numbermax
Step 4.2, the exponent number q=0 for making Fourier space, solve 0 rank Fourier coefficient<x(t)>0It is used as datum quantity;
Step 4.3, the exponent number q for making Fourier space solve q rank Fourier coefficients from Jia 1<x(t)>q, counted using formula (6) Calculate state variable relative error
In formula (6),To reach the q rank Fourier space coefficient sums deployed required for required precision, 0≤q ' ≤q;
Step 4.4, compare relative errorAnd ε2Relation, ifAnd q < qmax, then return to step 4.3;IfAnd q≥qmax, then it represents that the state variable x (t) of institute's current transformer segmentation Generalized State Space Averaging model solves mistake;IfAnd Q < qmax, then it represents that state variable x (t) is solved correctly, and state variable x (t) approximate error is
Compared with the prior art, the present invention has the beneficial effect that:
1st, the present invention combines segmentation method and generalized state space average method, it is proposed that one kind is based on segmentation generalized state The current transformer electromagnetic transient modeling method of space average, changing traditional generalized state space average method needs to be deployed into Fixed-order Several methods, can count and current transformer action situation and electromagnetic transient, to state variable in rational piecewise interval Fourier space only needs to be deployed into suitable exponent number, can just complete modeling, make current transformer electrical-magnetic model more reasonable, so that It more accurately and efficiently can directly reflect the change of quantity of state.
2nd, the present invention predicts the segmentation method for proposing a kind of current transformer transient state modeling based on amplitude, is predicted using amplitude true Determine converter switches action moment, the dutycycle and its variance of each switch periods are calculated by the switch motion moment;Pass through variance ratio Merge, realized on the premise of precision is ensured compared with by the switch periods that multiple dutycycles are similar, acting characteristic is consistent Variable step modeling and simulating, improves the modeling efficiency of electro-magnetic transient.
3rd, the present invention proposes a kind of model checking directly against state variable and error analysis method, using in model The approximate error and relative error of state variable in the coefficient of the Fourier space of state variable, computation model, according to error and The correctness that the exponent number limit value judgment models of Fourier expansion are solved;Compared to other modeling methods, error need not be single Solely analysis checking, so as to improve the efficiency of model.
Brief description of the drawings
Fig. 1 is the schematic flow sheet of the present invention;
Fig. 2 is three-phase PWM converter system figure in the prior art;
Fig. 3 is present invention determine that many split time flow charts;
Fig. 4 is present invention segmentation Generalized State Space Averaging model Establishing process figure;
Fig. 5 is model solution checking of the present invention and error determination module flow chart.
Embodiment
In the present embodiment, a kind of current transformer electromagnetic transient modeling method based on segmentation generalized state space average, by width It is worth and predicts the duty for calculating each switch periods when dutycycle variance, is closed the converter simulation time according to dutycycle variance Reason segmentation.Segmentation method is combined with generalized state space average method, Fourier is carried out to state variable on each split time Series expansion, represents state variable using Fourier expansion coefficient and is averaged, and sets up current transformer segmentation generalized state empty Between averaging model.State variable approximate error is directly calculated according to the Fourier expansion coefficient of each split time state variable And relative error, with implementation model checking and error analysis.Specifically, as shown in figure 1, this method is to enter as follows OK:
Step 1, the initial value of converter system are calculated;
In the built-in vertical shown state variable equations as the formula of the simulation time interval T of converter system:
In formula (1),For the derivative of state variable, f (t, x) is the function on time t and state variable x, and x (0) is shape The initial value of state variable, a is constant, and ε is the dimensionless closed with the interval T-phase of simulation time;
By formula (1) calculate state variable x steady-state value as the electro-magnetic transient of converter system state variable initial value;
By taking the three-phase PWM current transformer shown in Fig. 2 as an example, selection state variable is ig=[ia(t),ib(t),ic(t)]T, ug =[ua(t),ub(t),uc(t)]T, udc=[udc1(t),udc2(t)]T, idc=[idc1(t),idc2(t)]T, state variable ig、ug、 udc、idcIt is all relevant with time t, the solving state variable steady-state value in the simulation time interval T of converter system, into transient state When state variable initial value be stable state finish time value, by taking the magnitude of current as an example, system AC three-phase electricity flow initial value be ig0= [ia0,ib0,ic0]T
Step 2, segments n and each split time determined based on amplitude prediction, as shown in Figure 3;
Step 2.1, first split time T of note1Initial time be T10;First switch periods T of current transformers1Rise Moment beginning is ts0
Judge first split time T1Initial time T10Whether be first switch periods initial time ts0If, It is then to perform step 2.2;Otherwise, t is mades0=T10+ Δ t so that initial time T10For the initial time of first switch periods ts0;Wherein, Δ t is time correct amount;
Step 2.2, given sinusoidal modulation wave, triangular carrier, simulation time interval T and dutycycle variance limit value ε1, meter Calculation obtains triangular carrier in each switch periods TsOne antinode t of Triangle ID carrier wave and sinusoidal modulation wavep、tf, and as corresponding The switch motion moment in switch periods, so as to obtain the switch motion moment in all switch periods;
Step 2.3, make segments initial value be n=1,
Step 2.4, the initial value r=2 for making switch periods number;
Step 2.5, utilize formula (2) calculate r-th of switch periods in dutycycle dr, so that r switch periods before obtaining Dutycycle { d1, d2, d3..., dr}:
The dutycycle variances sigma of r switch periods before being calculated according to the dutycycle of preceding r switch periodsr
Step 2.6, judge σr< ε1Whether set up, such as set up, then make switch periods number r Jia 1 certainly, and return to step 2.5; Otherwise, into step 2.7;
Step 2.7, n-th of split time Tn=(r-1) Ts
Step 2.8, detection are in n-th of split time TnWhether the operating condition of interior converter system changes, if so, then holding Row step 2.9;Otherwise, step 2.11 is performed;
Step 2.9, by n-th of split time TnInterior initial time is designated as Tn0, the operating condition change of converter system Moment is designated as Tnk, then by initial time Tn0Change moment T to operating conditionnkBetween time interval when being adjusted to n-th of segmentation Between Tn
Step 2.10, judge in n-th of split time TnEnd time, whether converter system resume operation operating mode, If so, then performing step 2.11, otherwise, make segments n from Jia 1, make n-th of split time Tn=Ts, and return to step 2.10;
N split time sum ∑ T before step 2.11, calculatingn, and judge ∑ TnWhether < T set up, if so, then represent All time slices are not completed, segments n Jia 1 certainly, and enters step 2.4;Otherwise, represent to complete all time slices, and obtain To segments n and each split time;
Step 3, set up using each split time current transformer segmentation Generalized State Space Averaging model;
Step 3.1, for a current transformer being made up of m group independent switches, set up the horizon state side as shown in formula (3) Journey:
In formula (3), x (t) is the state variable on time t,For the derivative of the state variable on time t, Si (t) it is the switch function on time t of i-th group of independent switch in m group independent switches, AiAnd biFor with i-th group of independent switch phase The coefficient matrix and coefficient vector of pass;A0And b0For constant matrices and constant vector;
Fig. 4 is present invention segmentation Generalized State Space Averaging model Establishing process figure.As shown in figure 4, making segments n first =1, determine model segment time TnFor the 1st split time T1
For different type current transformer or the different operation modes of same current transformer, horizon state equation row WriteMode has Distinguished.In n-th of split time interval TnOn, by taking the three-phase PWM current transformer shown in Fig. 2 as an example, utilize the shape of above-mentioned selection State variable ig、ug、udc、idcSet up horizon state equation as follows:
In formula (4), Si=[S1(t),S2(t),S3(t)]TFor the switch function on time t of three groups of independent switches.
Step 3.2, in n-th of split time interval TnOn, q rank Fourier transformations are asked to the both sides of horizon state equation, So as to set up the current transformer segmentation Generalized State Space Averaging model as shown in formula (5):
In formula (5),<x(t)>qFor the q rank Fourier coefficients of the state variable x (t) on time t, Di(t) to be any one Switch function S in individual switch periodsi(t) average value;
By Fig. 4 flow, q rank Fourier transformations are asked to horizon state equation both sides, state variable x (t) q rank Fu is obtained In leaf system number, by taking the three-phase PWM current transformer shown in Fig. 2 as an example, to horizon state equation in piecewise interval TnOn to above-mentioned selection State variable carry out Fourier expansion, obtain being segmented Generalized State Space Averaging model as follows:
In formula (6), Di=[D1(t),D2(t),D3(t)]TFor three groups of independent switches the switch function on time t it is flat Average.
Step 3.3, calculated by the state variable initial value of electro-magnetic transient and obtain state variable x (t) q rank Fourier coefficients<x (t)>qValue, so as to utilize formula (7) reducing condition variable x (t):
In formula (7), ωqFor q times of fundamental frequency.
By Fig. 4 flow, fragmentation state average vector, solving state variable are determined.Become with the three-phase PWM shown in Fig. 2 Exemplified by stream device, electric current ig=[ia(t),ib(t),ic(t)]T, in n-th of split time interval TnInterior application segmentation generalized state is put down Equal method has
OrderFor ease of solving, exchange is first asked to survey magnitude of current igSegmental averaging vector field be
Simultaneous equations (6) try to achieve i to (10)gEach rank Fourier space coefficient<ig>qValue, then
By Fig. 4 flow, so far complete in n-th of split time interval TnOn segmentation generalized state space average build Mould.If not completing above-mentioned all time slices, n is made from Jia 1, respectively in the 2nd split time interval T2, the 3rd segmentation when Between interval T3, until all completing segmentation generalized state space average modeling on all split times interval, that is, complete using each Split time sets up the process that current transformer is segmented Generalized State Space Averaging model;
Step 4, current transformer segmentation Generalized State Space Averaging model is carried out solving checking and error determined:
Step 4.1, the reference value ε for determining state variable x relative error ranges2With the limit value q of Fourier expansion exponent numbermax
Step 4.2, the exponent number q=0 for making Fourier space, solve 0 rank Fourier coefficient<x(t)>0It is used as datum quantity;
Step 4.3, the exponent number q for making Fourier space solve q rank Fourier coefficients from Jia 1<x(t)>q, utilize formula (11) Calculate state variable relative error
In formula (11),To reach the q rank Fourier space coefficient sums deployed required for required precision, 0≤ q′≤q;
Step 4.4, compare relative errorAnd ε2Relation, ifAnd q < qmax, then return to step 4.3;If And q >=qmax, then it represents that the state variable x (t) of institute's current transformer segmentation Generalized State Space Averaging model solves mistake;IfAnd Q < qmax, then it represents that state variable x (t) is solved correctly, and state variable x (t) approximate error is
Fig. 5 is model solution checking of the present invention and error determination module flow chart.By Fig. 5 flow, with the three-phase shown in Fig. 2 Exemplified by PWM converter, in n-th of split time interval TnInterior a certain moment t, the first Fourier expansion of writ state variable Exponent number q=0, solving state variable fundamental frequency Fourier coefficient<ig>0;Then q is made Jia 1 certainly, state variable ig=[ia(t),ib(t), ic(t)]TExpansion exponent number be q=1, by each rank Fourier space coefficient<ig>qUnderstand:Then Approximate error isRelative error is
By Fig. 5 flow, by relative errorWith relative error range reference value ε2Generalized state space can be carried out to put down Equal model solution checking.Solved in Fig. 5 and meet the conditions of error requirements and beWith the state variable i of above-mentioned selectiongExemplified by, Solve and meet the conditions of error requirements and beIfAnd q < qmax, then q increases by 1, and calculating in Fu of state variable Leaf system number, recalculates relative errorIfAnd q >=qmax, then it represents that current transformer is segmented generalized state space average mould The state variable i of typegSolve mistake;IfAnd q < qmax, then it represents that state variable igSolve correctly, and state variable ig Approximate error be

Claims (2)

1. a kind of current transformer electromagnetic transient modeling method based on segmentation generalized state space average, it is characterized in that as follows Carry out:
Step 1, the initial value of converter system are calculated;
In the built-in vertical shown state variable equations as the formula of the simulation time interval T of converter system:
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mi>&amp;epsiv;</mi> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <mi>t</mi> <mo>,</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mi>a</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
In formula (1),For the derivative of state variable, f (t, x) is the function on time t and state variable x, and x (0) becomes for state The initial value of amount, a is constant, and ε is the dimensionless closed with the interval T-phase of simulation time;
By formula (1) calculate state variable x steady-state value as the electro-magnetic transient of the converter system state variable initial value;
Step 2, segments n and each split time determined based on amplitude prediction;
Step 2.1, first split time T of note1Initial time be T10;First switch periods T of current transformers1Starting when Carve as ts0
Judge first split time T1Initial time T10Whether be first switch periods initial time ts0, If so, then performing step 2.2;Otherwise, t is mades0=T10+ Δ t so that the initial time T10For first switch periods Initial time ts0;Wherein, Δ t is time correct amount;
Step 2.2, given sinusoidal modulation wave, triangular carrier, simulation time interval T and dutycycle variance limit value ε1, calculate The triangular carrier is obtained in each switch periods TsOne antinode t of Triangle ID carrier wave and sinusoidal modulation wavep、tf, and it is used as phase The switch motion moment in the inductive switch cycle, so as to obtain the switch motion moment in all switch periods;
Step 2.3, make segments initial value be n=1,
Step 2.4, the initial value r=2 for making switch periods number;
Step 2.5, utilize formula (2) calculate r-th of switch periods in dutycycle dr, so as to obtain the duty of preceding r switch periods Than { d1, d2, d3..., dr}:
<mrow> <msub> <mi>d</mi> <mi>r</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>t</mi> <mrow> <mi>f</mi> <mi>r</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>t</mi> <mrow> <mi>p</mi> <mi>r</mi> </mrow> </msub> </mrow> <msub> <mi>T</mi> <mrow> <mi>s</mi> <mi>r</mi> </mrow> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
The dutycycle variances sigma of r switch periods before being calculated according to the dutycycle of the preceding r switch periodsr
Step 2.6, judge σr< ε1Whether set up, such as set up, then make switch periods number r Jia 1 certainly, and return to step 2.5;Otherwise, Into step 2.7;
Step 2.7, n-th of split time Tn=(r-1) Ts
Step 2.8, detection are in n-th of split time TnWhether the operating condition of the interior converter system changes, if so, then holding Row step 2.9;Otherwise, step 2.11 is performed;
Step 2.9, by n-th of split time TnInterior initial time is designated as Tn0, the operating condition change of the converter system Moment is designated as Tnk, then by initial time Tn0Change moment T to operating conditionnkBetween time interval when being adjusted to n-th of segmentation Between Tn
Step 2.10, judge in n-th of split time TnEnd time, whether the converter system resume operation operating mode, if It is then to perform step 2.11, otherwise, makes segments n from Jia 1, make n-th of split time Tn=Ts, and return to step 2.10;
N split time sum ∑ T before step 2.11, calculatingn, and judge ∑ TnWhether < T set up, if so, then represent not complete Into all time slices, segments n Jia 1 certainly, and enters step 2.4;Otherwise, represent to complete all time slices, and divided Hop count n and each split time;
Step 3, set up using each split time current transformer segmentation Generalized State Space Averaging model;
Step 3.1, for a current transformer being made up of m group independent switches, set up the horizon state equation as shown in formula (3):
<mrow> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mn>0</mn> </msub> <mi>x</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <msub> <mi>b</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mi>i</mi> </msub> <mi>x</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <msub> <mi>b</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>S</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
In formula (3), x (t) is the state variable on time t,For the derivative of the state variable on time t, Si(t) it is m The switch function on time t of i-th group of independent switch, A in group independent switchiAnd biIt is for related to i-th group of independent switch Matrix number and coefficient vector;A0And b0For constant matrices and constant vector;
Step 3.2, in n-th of split time interval TnOn, q rank Fourier transformations are asked to the both sides of the horizon state equation, from And set up the current transformer segmentation Generalized State Space Averaging model as shown in formula (4):
<mrow> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mn>0</mn> </msub> <mo>&lt;</mo> <mi>x</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <msub> <mo>&gt;</mo> <mi>q</mi> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mi>i</mi> </msub> <mo>&lt;</mo> <mi>x</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <msub> <mo>&gt;</mo> <mi>q</mi> </msub> <mo>+</mo> <msub> <mi>b</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>D</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>t</mi> <mo>&amp;Element;</mo> <msub> <mi>T</mi> <mi>n</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
In formula (4),<x(t)>qFor the q rank Fourier coefficients of the state variable x (t) on time t, Di(t) opened for any one Switch function S in the cycle of passi(t) average value;
Step 3.3, the q ranks Fourier for obtaining the state variable x (t) by the state variable initial value calculating of the electro-magnetic transient are Number<x(t)>qValue, so as to utilize formula (5) reducing condition variable x (t):
<mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>q</mi> <mo>=</mo> <mo>-</mo> <mi>&amp;infin;</mi> </mrow> <mi>&amp;infin;</mi> </munderover> <mo>&lt;</mo> <mi>x</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <msub> <mo>&gt;</mo> <mi>q</mi> </msub> <msup> <mi>e</mi> <mrow> <msub> <mi>j&amp;omega;</mi> <mi>q</mi> </msub> <mi>t</mi> </mrow> </msup> <mo>,</mo> <mi>t</mi> <mo>&amp;Element;</mo> <msub> <mi>T</mi> <mi>n</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
In formula (5), ωqFor q times of fundamental frequency.
2. the current transformer electromagnetic transient modeling method according to claim 1 based on segmentation generalized state space average, its It is characterized in as follows current transformer segmentation Generalized State Space Averaging model to be carried out solving checking and error is determined:
Step 4.1, the reference value ε for determining state variable x relative error ranges2With the limit value q of Fourier expansion exponent numbermax
Step 4.2, the exponent number q=0 for making Fourier space, solve 0 rank Fourier coefficient<x(t)>0It is used as datum quantity;
Step 4.3, the exponent number q for making Fourier space solve q rank Fourier coefficients from Jia 1<x(t)>q, shape is calculated using formula (6) State variable relative error
<mrow> <mover> <mi>o</mi> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <msup> <mi>q</mi> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <mn>0</mn> </mrow> <mi>q</mi> </munderover> <mo>&lt;</mo> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <mo>&gt;</mo> <mi>q</mi> </msub> <mo>-</mo> <mo>&lt;</mo> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <mo>&gt;</mo> <mn>0</mn> </msub> </mrow> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <msup> <mi>q</mi> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <mn>0</mn> </mrow> <mi>q</mi> </munderover> <mo>&lt;</mo> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <mo>&gt;</mo> <mi>q</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
In formula (6),To reach the q rank Fourier space coefficient sums deployed required for required precision, 0≤q '≤q;
Step 4.4, compare relative errorAnd ε2Relation, ifAnd q < qmax, then return to step 4.3;IfAnd q ≥qmax, then it represents that the state variable x (t) of institute's current transformer segmentation Generalized State Space Averaging model solves mistake;IfAnd q < qmax, then it represents that state variable x (t) is solved correctly, and state variable x (t) approximate error is
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