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 PDFInfo
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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
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：
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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}：
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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)：
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</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
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<mo>(</mo>
<mn>3</mn>
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</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)：
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<mi>m</mi>
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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)：
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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
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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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