CN107301288B - Converter electromagnetic transient modeling method based on segmented generalized state space average - Google Patents

Converter electromagnetic transient modeling method based on segmented generalized state space average Download PDF

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CN107301288B
CN107301288B CN201710470739.2A CN201710470739A CN107301288B CN 107301288 B CN107301288 B CN 107301288B CN 201710470739 A CN201710470739 A CN 201710470739A CN 107301288 B CN107301288 B CN 107301288B
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converter
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CN107301288A (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 current transformer electromagnetic transient modeling method based on segmented generalized state space average, which is characterized by comprising the following steps of: 1, calculating a system initial value; 2, determining the number of segments and each segment time based on the amplitude prediction; and 3, establishing a segmented generalized state space average model of the current transformer. The invention can realize the balance of efficiency and precision for the electromagnetic transient modeling of the converter, thereby ensuring that the converter model is suitable for the electromagnetic transient modeling and simulation of a large-scale series-parallel power grid.

Description

Converter electromagnetic transient modeling method based on segmented generalized state space average
Technical Field
The invention relates to the field of electromagnetic transient modeling of a converter of a power system, in particular to a modeling method which considers the switching action of the converter, the precision and the efficiency of a balance model and is applied to electromagnetic transient simulation.
Background
The large-scale access of new energy power generation (such as photovoltaic and fan) of the power system causes the change of the operation mode of the power system, and the transient characteristic of the new energy power generation which is connected by the converter directly influences the dynamic characteristic of the power system containing large-scale new energy grid connection. The transient state action condition of the converter is complex, the converter model applied to simulation has different application occasions according to the balance relation between precision and efficiency, but the current converter model is not completely suitable for electromagnetic transient state high-efficiency simulation of a large-scale new energy power generation grid-connected power system.
In the current research results, the methods for modeling the converter mainly include a dynamic phasor method, a state space averaging method and the like, but the methods cannot consider microsecond-level converter switching actions and are not suitable for microsecond-level electromagnetic transient modeling. The traditional grid-connected converter model only performs basic principle analysis at a device level, and is difficult to complete detailed electromagnetic transient process analysis. The transient model of the state averaging method can only reflect fundamental wave components of the system, error ripples and high-frequency components need to be additionally considered, and the method cannot adapt to continuous simulation of large-scale new energy grid connection. In the existing research results, the frequency change and the error of the converter are not directly analyzed, so that the converter is difficult to accurately and efficiently simulate under the condition of complex actions.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a converter electromagnetic transient modeling method based on segmented generalized state space average, so that the balance of efficiency and precision of a new energy power generation grid-connected converter can be realized, and the grid-connected converter model is suitable for electromagnetic transient modeling and simulation of a large-scale parallel-serial power grid.
The invention adopts the following technical scheme for solving the technical problems:
the invention relates to a converter electromagnetic transient modeling method based on segmented generalized state space average, which is characterized by comprising the following steps of:
step 1, calculating an initial value of a converter system;
establishing a state variable equation shown as a formula (1) in a simulation time interval T of the converter system:
Figure BDA0001327030360000011
in the formula (1), the reaction mixture is,
Figure BDA0001327030360000012
is the derivative of the state variable, f (T, x) is a function with respect to time T and the state variable x, x (0) is the initial value of the state variable, a is a constant, and ε is the infinitesimal quantity associated with the simulation time interval T;
taking the steady state value of the state variable x calculated by the formula (1) as a state variable initial value of the electromagnetic transient of the converter system;
step 2, determining the number n of segments and each segment time based on amplitude prediction;
step 2.1, recording the first segment time T1Is at a starting time T10(ii) a First switching period T of the converters1Is at a starting time ts0；
Judging the first segment time T1At a starting time T10Whether it is the starting time t of the first switching periods0If yes, executing step 2.2; otherwise, let ts0＝T10+ Δ T, such that said starting instant T10Is the first oneStarting time t of a switching cycles0(ii) a Wherein, Δ t is the time correction amount;
step 2.2, a sine modulation wave, a triangular carrier wave, the simulation time interval T and a duty ratio variance limit value epsilon are given1And calculating to obtain the triangular carrier wave in each switching period TsA pair of intersections t of the inner triangular carrier wave and the sine modulated wavep、tfAnd as the switching action time in the corresponding switching period, thereby obtaining the switching action time in all switching periods;
step 2.3, the initial value of the segment number is made to be n-1,
step 2.4, setting the initial value r of the switching period number to be 2;
step 2.5, calculating the duty ratio d in the r-th switching period by using the formula (2)rTo obtain the duty ratio { d ] of the first r switching periods1，d2，d3，…，dr}：
Figure BDA0001327030360000021
Calculating the variance sigma of the duty ratio of the first r switching periods according to the duty ratio of the first r switching periodsr；
Step 2.6, judge sigmar＜ε1If yes, the switching period number r is added with 1 by itself, and the step 2.5 is returned; otherwise, go to step 2.7;
step 2.7, nth segment time Tn＝(r-1)Ts；
Step 2.8, detecting the segment time T at the nthnWhether the operation condition of the converter system is changed or not is judged, and if yes, the step 2.9 is executed; otherwise, executing step 2.11;
step 2.9, segmenting the nth time TnThe initial time is denoted as Tn0And the time when the operation condition of the converter system changes is recorded as TnkThen the initial time Tn0To the moment T of change of the operating conditionsnkThe time interval between the segments is adjusted to the nth segment time Tn；
Step 2.10, judge in the nth segment time TnIf yes, executing step 2.11, otherwise, adding the number n of the segments to 1 by itself, and enabling the nth segment time Tn＝TsAnd returning to the step 2.10;
step 2.11, calculating the sum sigma T of the first n segmentation timenAnd determines sigma TnIf the T is less than the preset threshold, indicating that all time segments are not finished, adding 1 to the number n of the segments, and entering a step 2.4; otherwise, all time segmentation is finished, and the number n of segments and each segmentation time are obtained;
step 3, establishing a current transformer segmented generalized state space average model by utilizing each segmented time;
step 3.1, establishing a time domain state equation shown in the formula (3) for a current transformer formed by m groups of independent switches:
Figure BDA0001327030360000031
in the formula (3), x (t) is a state variable with respect to time t,
Figure BDA0001327030360000032
is a derivative of a state variable with respect to time t, Si(t) is the switching function over time t of the i-th group of individual switches of the m groups of individual switches, AiAnd biIs a coefficient matrix and a coefficient vector related to the ith group of independent switches; a. the0And b0Constant matrix and constant vector;
step 3.2, in the nth subsection time interval TnAnd solving q-order Fourier transform on two sides of the time domain state equation, thereby establishing a segmented generalized state space average model of the converter as shown in the formula (4):
Figure BDA0001327030360000033
in the formula (4), the reaction mixture is,<x(t)>qfourier coefficients of order q of a state variable x (t) with respect to time t，Di(t) is a switching function S in any switching cyclei(t) average value;
step 3.3, calculating the q-order Fourier coefficient of the state variable x (t) according to the initial value of the state variable of the electromagnetic transient<x(t)>qTo reduce the state variable x (t) using equation (5):
Figure BDA0001327030360000034
in the formula (5), ωqQ times the fundamental frequency.
The invention also discloses a current transformer electromagnetic transient modeling method based on the segmented generalized state space average, which is characterized in that the current transformer segmented generalized state space average model is solved, verified and error determined according to the following method:
step 4.1, determining the reference value epsilon of the relative error range of the state variable x2And a limit value q of the Fourier expansion ordermax；
Step 4.2, making the order q of the Fourier series equal to 0, and solving the Fourier coefficient of 0 order<x(t)>0As a reference amount;
4.3, adding 1 to the order q of the Fourier series, and solving the Fourier coefficient of q order<x(t)>qCalculating the relative error of the state variables by using equation (6)
Figure BDA0001327030360000035
Figure BDA0001327030360000041
In the formula (6), the reaction mixture is,
Figure BDA0001327030360000042
q-order Fourier series coefficients needed to be expanded to meet the precision requirement are added, and q' is more than or equal to 0 and less than or equal to q;
step 4.4, comparing the relative error
Figure BDA0001327030360000043
And ε2In a relation of (1), if
Figure BDA0001327030360000044
And q is more than qmaxReturning to the step 4.3; if it is
Figure BDA0001327030360000045
And q is not less than qmaxThen, the state variable x (t) of the segmented generalized state space average model of the converter is represented as a solving error; if it is
Figure BDA0001327030360000046
And q is more than qmaxIt means that the state variable x (t) is solved correctly, and the approximate error of the state variable x (t) is
Figure BDA0001327030360000047
Compared with the prior art, the invention has the beneficial effects that:
1. the invention combines a segmentation method and a generalized state space averaging method, provides a converter electromagnetic transient modeling method based on segmented generalized state space averaging, changes the method that the traditional generalized state space averaging method needs to be expanded to a fixed order, can take into account the action condition and the electromagnetic transient process of a converter, can complete modeling only by expanding the Fourier series of a state variable to a proper order in a reasonable segmentation interval, and enables the electromagnetic transient model of the converter to be more reasonable, thereby being capable of directly reflecting the change of the state quantity more accurately and efficiently.
2. The invention provides a segmentation method of transient modeling of a converter based on amplitude prediction, which determines the switching action time of the converter by using the amplitude prediction, and calculates the duty ratio and the variance of each switching period according to the switching action time; a plurality of switching cycles with similar duty ratios and consistent action characteristics are combined together through variance comparison, variable step modeling simulation is achieved on the premise that accuracy is guaranteed, and modeling efficiency of electromagnetic transient is improved.
3. The invention provides a model verification and error analysis method directly aiming at state variables, which utilizes the Fourier series coefficients of the state variables in a model to calculate the approximate error and the relative error of the state variables in the model, and judges the correctness of model solution according to the error and the order limit value expanded by the Fourier series; compared with other modeling methods, errors do not need to be analyzed and verified independently, and therefore the efficiency of the model is improved.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a prior art three-phase PWM converter system diagram;
FIG. 3 is a flow chart of the present invention for determining a multi-segment time;
FIG. 4 is a flow chart of the present invention for building a piecewise generalized state space average model;
FIG. 5 is a flow diagram of a model solution verification and error determination module of the present invention.
Detailed Description
In the embodiment, the converter electromagnetic transient modeling method based on the segmented generalized state space average calculates the duty ratio and the duty ratio variance of each switching period through amplitude prediction, and reasonably segments the converter simulation time according to the duty ratio variance. Combining the segmentation method with the generalized state space averaging method, performing Fourier series expansion on the state variables in each segmentation time, averaging by using Fourier series expansion coefficients to represent the state variables, and establishing a segmented generalized state space averaging model of the converter. And directly calculating the approximate error and the relative error of the state variable according to the Fourier series expansion coefficient of the state variable of each section time so as to realize model verification and error analysis. Specifically, as shown in fig. 1, the method is performed as follows:
step 1, calculating an initial value of a converter system;
establishing a state variable equation shown as a formula (1) in a simulation time interval T of the converter system:
Figure BDA0001327030360000051
in the formula (1), the reaction mixture is,
Figure BDA0001327030360000052
is the derivative of the state variable, f (T, x) is a function with respect to time T and the state variable x, x (0) is the initial value of the state variable, a is a constant, and ε is the infinitesimal quantity associated with the simulation time interval T;
taking the steady state value of the state variable x calculated by the formula (1) as an initial state variable value of the electromagnetic transient of the converter system;
taking the three-phase PWM converter shown in FIG. 2 as an example, the state variable is selected as 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)]TState variable ig、ug、udc、idcAll are related to time T, a steady state value of a state variable is solved in a simulation time interval T of the converter system, an initial value of the state variable when the converter system enters a transient state is a steady state ending time value, and taking current magnitude as an example, an initial value of three-phase current magnitude on the alternating current side of the system is ig0＝[ia0,ib0,ic0]T；
Step 2, determining the number n of segments and each segment time based on the amplitude prediction, as shown in fig. 3;
step 2.1, recording the first segment time T1Is at a starting time T10(ii) a First switching period T of the converters1Is at a starting time ts0；
Judging the first segment time T1At a starting time T10Whether it is the starting time t of the first switching cycles0If yes, executing step 2.2; otherwise, let ts0＝T10+ Δ T, such that the starting time T10For the start time t of the first switching cycles0(ii) a Wherein, Δ t is the time correction amount;
step 2.2, a sine modulation wave, a triangular carrier wave, a simulation time interval T and a duty ratio variance limit value epsilon are given1And calculating to obtain a triangular carrier waveEach switching period TsA pair of intersections t of the inner triangular carrier wave and the sine modulated wavep、tfAnd as the switching action time in the corresponding switching period, thereby obtaining the switching action time in all switching periods;
step 2.3, the initial value of the segment number is made to be n-1,
step 2.4, setting the initial value r of the switching period number to be 2;
step 2.5, calculating the duty ratio d in the r-th switching period by using the formula (2)rTo obtain the duty ratio { d ] of the first r switching periods1，d2，d3，…，dr}：
Figure BDA0001327030360000061
Calculating the variance sigma of the duty ratio of the first r switching periods according to the duty ratio of the first r switching periodsr；
Step 2.6, judge sigmar＜ε1If yes, the switching period number r is added with 1 by itself, and the step 2.5 is returned; otherwise, go to step 2.7;
step 2.7, nth segment time Tn＝(r-1)Ts；
Step 2.8, detecting the segment time T at the nthnWhether the operation condition of the inner converter system is changed or not is judged, if yes, the step 2.9 is executed; otherwise, executing step 2.11;
step 2.9, segmenting the nth time TnThe initial time is denoted as Tn0And the time when the operation condition of the converter system changes is recorded as TnkThen the initial time Tn0To the moment T of change of the operating conditionsnkThe time interval between the segments is adjusted to the nth segment time Tn；
Step 2.10, judge in the nth segment time TnIf so, executing the step 2.11, otherwise, adding 1 to the number n of the segments and enabling the nth segment time Tn＝TsAnd returning to the step 2.10;
step 2.11, calculating the sum sigma T of the first n segmentation timenAnd determines sigma TnIf the T is less than the preset threshold, indicating that all time segments are not finished, adding 1 to the number n of the segments, and entering a step 2.4; otherwise, all time segmentation is finished, and the number n of segments and each segmentation time are obtained;
step 3, establishing a current transformer segmented generalized state space average model by utilizing each segmented time;
step 3.1, establishing a time domain state equation shown in the formula (3) for a current transformer formed by m groups of independent switches:
Figure BDA0001327030360000062
in the formula (3), x (t) is a state variable with respect to time t,
Figure BDA0001327030360000063
is a derivative of a state variable with respect to time t, Si(t) is the switching function over time t of the i-th group of individual switches of the m groups of individual switches, AiAnd biIs a coefficient matrix and a coefficient vector related to the ith group of independent switches; a. the0And b0Constant matrix and constant vector;
FIG. 4 is a flow chart of the method for building a segmented generalized state space average model. As shown in fig. 4, first, let the number of segments n be 1, and determine the model segment time TnFor the 1 st segment time T1。
For different types of converters or different working modes of the same converter, the column writing modes of the time domain state equation are different. In the nth segment time interval TnIn the above, taking the three-phase PWM converter shown in fig. 2 as an example, the selected state variable i is utilizedg、ug、udc、idcThe time domain state equation is established as follows:
Figure BDA0001327030360000071
in the formula (4), Si＝[S1(t),S2(t),S3(t)]TSwitching function with respect to time t for three groups of independent switches.
Step 3.2, in the nth subsection time interval TnAnd in the above step, solving q-order Fourier transform on two sides of a time domain state equation, thereby establishing a segmented generalized state space average model of the converter as shown in formula (5):
Figure BDA0001327030360000072
in the formula (5), the reaction mixture is,<x(t)>qfourier coefficient of order q of a state variable x (t) with respect to time t, Di(t) is a switching function S in any switching cyclei(t) average value;
according to the flow of fig. 4, q-order fourier transform is solved for both sides of the time domain state equation to obtain q-order fourier coefficients of the state variables x (T), and the three-phase PWM converter shown in fig. 2 is taken as an example, and the time domain state equation is divided into the segment intervals TnPerforming Fourier series expansion on the selected state variables to obtain a segmented generalized state space average model as follows:
Figure BDA0001327030360000073
in the formula (6), Di＝[D1(t),D2(t),D3(t)]TIs the average of the switching function over time t for three groups of individual switches.
Step 3.3, calculating a q-order Fourier coefficient of the state variable x (t) according to the initial value of the state variable of the electromagnetic transient<x(t)>qTo reduce the state variable x (t) using equation (7):
Figure BDA0001327030360000074
in the formula (7), ωqQ times the fundamental frequency.
According to the flow of fig. 4, a segmented state average vector field is determined, and the state variables are solved. As shown in FIG. 2Three-phase PWM converter shown as an example, current ig＝[ia(t),ib(t),ic(t)]TIn the nth segment time interval TnThe method for averaging the generalized states of the internal application segments comprises
Figure BDA0001327030360000081
Order to
Figure BDA0001327030360000082
To facilitate the solution, the AC measured current i is firstly solvedgIs a piecewise average vector field of
Figure BDA0001327030360000083
Figure BDA0001327030360000084
Simultaneous equations (6) to (10) to find igEach order Fourier series coefficient<ig>qA value of (1), then
Figure BDA0001327030360000085
According to the flow of FIG. 4, the nth segment time interval T is completednThe above piecewise generalized state space average is modeled. If all the time segments are not completed, let n add 1 by itself, and respectively in the 2 nd segment time interval T2The 3 rd segmented time interval T3Until the segmented generalized state space average modeling is completed in all the segmented time intervals, namely the process of building a segmented generalized state space average model of the converter by utilizing each segmented time is completed;
step 4, solving and verifying the space average model of the segmented generalized state of the converter and determining errors:
step 4.1, determining the reference value epsilon of the relative error range of the state variable x2And a limit value q of the Fourier expansion ordermax；
Step 4.2, making the order q of the Fourier series equal to 0, and solving the Fourier coefficient of 0 order<x(t)>0As a reference amount;
4.3, adding 1 to the order q of the Fourier series, and solving the Fourier coefficient of q order<x(t)>qCalculating the relative error of the state variables by using equation (11)
Figure BDA0001327030360000086
Figure BDA0001327030360000087
In the formula (11), the reaction mixture is,
Figure BDA0001327030360000088
q-order Fourier series coefficients needed to be expanded to meet the precision requirement are added, and q' is more than or equal to 0 and less than or equal to q;
step 4.4, comparing the relative error
Figure BDA0001327030360000091
And ε2In a relation of (1), if
Figure BDA0001327030360000092
And q is more than qmaxReturning to the step 4.3; if it is
Figure BDA0001327030360000093
And q is not less than qmaxThen, the state variable x (t) of the segmented generalized state space average model of the converter is represented as a solving error; if it is
Figure BDA0001327030360000094
And q is more than qmaxIt means that the state variable x (t) is solved correctly, and the approximate error of the state variable x (t) is
Figure BDA0001327030360000095
FIG. 5 is a flow diagram of a model solution verification and error determination module of the present invention. According to the flow of FIG. 5, the three-phase PWM converter shown in FIG. 2 is used asFor example, in the nth segment time interval TnAt a certain time t, firstly, the expansion order q of the Fourier series of the state variable is equal to 0, and the fundamental frequency Fourier coefficient of the state variable is solved<ig>0(ii) a Then let q add 1, state variable ig＝[ia(t),ib(t),ic(t)]TThe expansion order of (1) is q, and each order of Fourier series coefficient<ig>qTherefore, the following steps are carried out:
Figure BDA0001327030360000096
the approximation error is
Figure BDA0001327030360000097
Relative error of
Figure BDA0001327030360000098
According to the scheme of FIG. 5, the relative error is calculated
Figure BDA0001327030360000099
And a relative error range reference value epsilon2Generalized state space average model solution verification can be performed. In FIG. 5, the condition for solving the error requirement is
Figure BDA00013270303600000910
With the above selected state variable igFor example, the condition for solving the error requirement is
Figure BDA00013270303600000911
If it is
Figure BDA00013270303600000912
And q is more than qmaxQ is increased by 1 and the fourier coefficients of the state variables are calculated, the relative error is recalculated
Figure BDA00013270303600000913
If it is
Figure BDA00013270303600000914
And q is not less than qmaxThen, the state variable i of the segmented generalized state space average model of the current transformer is representedgSolving errors; if it is
Figure BDA00013270303600000915
And q is more than qmaxThen, it represents the state variable igCorrect solution and state variable igHas an approximation error of
Figure BDA00013270303600000916

Claims (2)

1. A current transformer electromagnetic transient modeling method based on segmented generalized state space average is characterized by comprising the following steps:
step 1, calculating an initial value of a converter system;
establishing a state variable equation shown as a formula (1) in a simulation time interval T of the converter system:
Figure FDA0001327030350000011
in the formula (1), the reaction mixture is,
Figure FDA0001327030350000012
is the derivative of the state variable, f (T, x) is a function with respect to time T and the state variable x, x (0) is the initial value of the state variable, a is a constant, and ε is the infinitesimal quantity associated with the simulation time interval T;
taking the steady state value of the state variable x calculated by the formula (1) as a state variable initial value of the electromagnetic transient of the converter system;
step 2, determining the number n of segments and each segment time based on amplitude prediction;
step 2.1, recording the first segment time T1Is at a starting time T10(ii) a First switching period T of the converters1Is at a starting time ts0；
Judging the first segment time T1At a starting time T10Whether it is the starting time t of the first switching periods0If yes, executing step 2.2; otherwise, let ts0＝T10+ Δ T, such that said starting instant T10Is the starting time t of the first switching periods0(ii) a Wherein, Δ t is the time correction amount;
step 2.2, a sine modulation wave, a triangular carrier wave, the simulation time interval T and a duty ratio variance limit value epsilon are given1And calculating to obtain the triangular carrier wave in each switching period TsA pair of intersections t of the inner triangular carrier wave and the sine modulated wavep、tfAnd as the switching action time in the corresponding switching period, thereby obtaining the switching action time in all switching periods;
step 2.3, the initial value of the segment number is made to be n-1,
step 2.4, setting the initial value r of the switching period number to be 2;
step 2.5, calculating the duty ratio d in the r-th switching period by using the formula (2)rTo obtain the duty ratio { d ] of the first r switching periods1，d2，d3，…，dr}：
Figure FDA0001327030350000013
Calculating the variance sigma of the duty ratio of the first r switching periods according to the duty ratio of the first r switching periodsr；
Step 2.6, judge sigmar＜ε1If yes, the switching period number r is added with 1 by itself, and the step 2.5 is returned; otherwise, go to step 2.7;
step 2.7, nth segment time Tn＝(r-1)Ts；
Step 2.8, detecting the segment time T at the nthnWhether the operation condition of the converter system is changed or not is judged, and if yes, the step 2.9 is executed; otherwise, executing step 2.11;
step 2.9, segmenting the nth time TnThe initial time is denoted as Tn0Operation condition change of the converter systemThe time is recorded as TnkThen the initial time Tn0To the moment T of change of the operating conditionsnkThe time interval between the segments is adjusted to the nth segment time Tn；
Step 2.10, judge in the nth segment time TnIf yes, executing step 2.11, otherwise, adding the number n of the segments to 1 by itself, and enabling the nth segment time Tn＝TsAnd returning to the step 2.10;
step 2.11, calculating the sum sigma T of the first n segmentation timenAnd determines sigma TnIf the T is less than the preset threshold, indicating that all time segments are not finished, adding 1 to the number n of the segments, and entering a step 2.4; otherwise, all time segmentation is finished, and the number n of segments and each segmentation time are obtained;
step 3, establishing a current transformer segmented generalized state space average model by utilizing each segmented time;
step 3.1, establishing a time domain state equation shown in the formula (3) for a current transformer formed by m groups of independent switches:
Figure FDA0001327030350000021
in the formula (3), x (t) is a state variable with respect to time t,
Figure FDA0001327030350000022
is a derivative of a state variable with respect to time t, Si(t) is the switching function over time t of the i-th group of individual switches of the m groups of individual switches, AiAnd biIs a coefficient matrix and a coefficient vector related to the ith group of independent switches; a. the0And b0Constant matrix and constant vector;
step 3.2, in the nth subsection time interval TnAnd solving q-order Fourier transform on two sides of the time domain state equation, thereby establishing a segmented generalized state space average model of the converter as shown in the formula (4):
Figure FDA0001327030350000023
in the formula (4), the reaction mixture is,<x(t)>qfourier coefficient of order q of a state variable x (t) with respect to time t, Di(t) is a switching function S in any switching cyclei(t) average value;
step 3.3, calculating the q-order Fourier coefficient of the state variable x (t) according to the initial value of the state variable of the electromagnetic transient<x(t)>qTo reduce the state variable x (t) using equation (5):
Figure FDA0001327030350000024
in the formula (5), ωqQ times the fundamental frequency.
2. The method for modeling the electromagnetic transient of the current transformer based on the segmented generalized state space average of claim 1, wherein the segmented generalized state space average model of the current transformer is subjected to solution verification and error determination according to the following method:
step 4.1, determining the reference value epsilon of the relative error range of the state variable x2And a limit value q of the Fourier expansion ordermax；
Step 4.2, making the order q of the Fourier series equal to 0, and solving the Fourier coefficient of 0 order<x(t)>0As a reference amount;
4.3, adding 1 to the order q of the Fourier series, and solving the Fourier coefficient of q order<x(t)>qCalculating the relative error of the state variables by using equation (6)
Figure FDA0001327030350000031
Figure FDA0001327030350000032
In the formula (6), the reaction mixture is,
Figure FDA0001327030350000033
q-order Fourier series coefficients needed to be expanded to meet the precision requirement are added, and q' is more than or equal to 0 and less than or equal to q;
step 4.4, comparing the relative error
Figure FDA0001327030350000034
And ε2In a relation of (1), if
Figure FDA0001327030350000035
And q is more than qmaxReturning to the step 4.3; if it is
Figure FDA0001327030350000036
And q is not less than qmaxThen, the state variable x (t) of the segmented generalized state space average model of the converter is represented as a solving error; if it is
Figure FDA0001327030350000037
And q is more than qmaxIt means that the state variable x (t) is solved correctly, and the approximate error of the state variable x (t) is
Figure FDA0001327030350000038
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