CN117195801A - Modeling method for converter - Google Patents
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Abstract
The invention discloses a modeling method of a converter, which comprises the following steps: step S1, respectively establishing corresponding models for a main circuit and a control circuit of the converter according to a linear period time-varying system theory; and S2, combining the main circuit and the control circuit model through the relation between the input variables and the output variables, and establishing a complete harmonic state space model. According to the invention, on the basis of the traditional time domain state space model of the converter, the model is transformed from the time domain to the frequency domain, the converter multi-input multi-output model capable of reflecting the harmonic influence among different frequencies is built, the harmonic coupling condition among different frequencies can be considered, the harmonic analysis of low, medium and high frequency bands is realized, more accurate consideration is provided for harmonic analysis and stability evaluation, and meanwhile, the potential harmonic exceeding standard and resonance influence when large-scale power electronic equipment is accessed into a distribution network can be further analyzed, so that the method is also suitable for a multi-converter system.
Description
Technical Field
The invention belongs to the technical field of power electronics, and particularly relates to a modeling method of a converter.
Background
At present, with the gradual deepening of the power electronization degree of a power system, more power electronic switching devices mainly based on nonlinearity are connected into the power system on the power transmission, distribution and power utilization sides, so that the power quality problems of oscillation, resonance, overtaking harmonic waves and the like can be caused. Meanwhile, the number of converters injected into the power grid is increased continuously at the power distribution side, so that the harmonic wave influence among different converters or among the power grid and the converters is more complex, and a new challenge is provided for the stable operation of the power grid. Two-level converters are the most popular and widely used objects, and modeling and analysis thereof are very necessary.
The method is characterized in that the analysis of AC-DC side frequency coupling is carried out on the converter, and a corresponding converter model is established. The traditional modeling method for the converter is mainly small-signal modeling, is one of the current research hotspots, and has the advantages that a mathematical model can be converted into a dq domain so as to realize linearization of the model, but the obtained model can only analyze harmonic coupling between the same frequency based on the traditional frequency domain analysis method, and cannot pay attention to the coupling condition between different frequencies. The harmonic linearization-based descriptive function method can improve modeling accuracy in a high frequency band, but is still a single-input single-output model in essence, and cannot analyze interaction of multiple converters in the high frequency band.
Disclosure of Invention
The technical problem to be solved by the embodiment of the invention is to provide a modeling method for a converter, which is used for analyzing harmonic coupling among different frequencies, and is suitable for a single converter system and a multi-converter system.
In order to solve the technical problems, the invention provides a modeling method of a converter, comprising the following steps:
step S1, respectively establishing corresponding models for a main circuit and a control circuit of the converter according to a linear period time-varying system theory;
and S2, combining the main circuit and the control circuit model through the relation between the input variables and the output variables, and establishing a complete harmonic state space model.
Further, in the step S1, the establishing a main circuit model of the converter specifically includes:
converting a time domain state space equation of the main circuit into a frequency domain state space equation;
when the system is in a steady state, a harmonic state space equation is obtained;
a harmonic transfer function of the main circuit state space model is obtained.
Further, the frequency domain state space equation of the main circuit is:
wherein,
wherein i is a 、i b 、i c U is three-phase grid current dc The ∈A is the direct current voltage which is output after rectification, and the ∈A represents the disturbance quantity of the signal;is composed of->The dimension of the complex Fourier coefficient of the time domain signal after the exponential form Fourier decomposition is determined by the size of the considered harmonic frequency h; definition A T And B is connected with T In the matrix, I is 2h+1 order identity matrix, Z m The matrix is a zero matrix, and the size is 2h+1 order matrix; n (N) k A block diagonal matrix consisting of k N matrices, wherein N matrices are 2h+1 order diagonal matrices,>toeplitz matrix representing corresponding element, toeplitz matrix Γ [ C ] corresponding to constant C]＝c×I 2h+1 。
Further, the harmonic state space equation is:
(A T -N 4 )X+B T U＝0。
further, the harmonic transfer function matrix of the main circuit state space model is:
H T ＝-(A T -N 4 ) -1 B T 。
further, in the step S1, the establishing a control circuit model of the converter specifically includes:
carrying out small signal linearization on a state equation of a control circuit under a dq coordinate system; the control circuit adopts constant direct current voltage control and current inner loop control;
converting the formula after linearization of the small signal into a formula adapting to a harmonic state space model;
and acquiring a harmonic state space equation of the control circuit.
Further, the formula after linearization of the small signal is as follows:
wherein x is 1 、x 2 Constant direct current voltage control state variables x of the outer ring and the inner ring of the rectifier respectively 3 To determine the q-axis DC current control state variable, k vp 、k ip Respectively the proportional coefficient and integral coefficient, k of the outer loop control of the constant direct voltage ip 、k ii The proportional coefficient and the integral coefficient of the constant q-axis direct current control are respectively; let k 1 ＝k vp ，k 2 ＝k vi ，k 3 ＝k ip ，k 4 ＝k ii 。
Further, the formula for adapting the harmonic state space model is:
wherein:
Γ[cosθ]＝Γ[…,0.5,0,0.5,…]
Γ[sinθ]＝Γ[…,0.5j,0,-0.5j,…,]
further, for signalsAnd->And (3) changing the Park inverse transformation to an abc coordinate system to obtain a harmonic state space equation of the control circuit as follows:
Y c ＝C c X c +D c U c
wherein,
further, the step S2 specifically includes:
the state space model of the main circuit and the control circuit is partitioned:
eliminating the intermediate variable Y to obtain:
set U c1 ＝X T The model is reduced to:
order the
Then there are:
wherein,
the corresponding harmonic transfer function matrix is as follows:
H f ＝-A f -1 B f
will H f The tiles are a matrix as follows:
wherein H is 1 Is H f Upper left hand sub-matrix in matrix, H 2 Is H f The upper right hand sub-matrix in the matrix, results in the following relationship:
X T ＝H 1 U T1 +H 2 X T
the method comprises the following steps:
the implementation of the invention has the following beneficial effects: according to the invention, on the basis of the traditional time domain state space model of the converter, the model is transformed from the time domain to the frequency domain, the converter multi-input multi-output model capable of reflecting the harmonic influence among different frequencies is built, the harmonic coupling condition among different frequencies can be considered, the harmonic analysis of low, medium and high frequency bands is realized, more accurate consideration is provided for harmonic analysis and stability evaluation, and meanwhile, the potential harmonic exceeding standard and resonance influence when large-scale power electronic equipment is accessed into a distribution network can be further analyzed, so that the method is also suitable for a multi-converter system.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic flow chart of a modeling method of a current transformer according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of a PWM rectifier main circuit in an embodiment of the present invention.
FIG. 3 is a schematic diagram of the input/output variable relationship of the master HSS model in an embodiment of the present invention.
Fig. 4 is a schematic diagram of a control circuit according to an embodiment of the invention.
FIG. 5 is a schematic diagram showing the combination of the master and control circuits HSS model in accordance with an embodiment of the present invention.
Fig. 6a and fig. 6b are schematic diagrams of comparison between calculated values of a simulation model and an HSS model in the embodiment of the invention under the working condition 1, wherein fig. 6a is a schematic diagram of comparison between amplitude values of each subharmonic of the dc voltage, and fig. 6b is a schematic diagram of comparison between amplitude values of each subharmonic of the harmonic current.
Fig. 7a and fig. 7b are schematic diagrams of comparison between calculated values of the simulation model and the HSS model in the embodiment of the invention under the working condition 2, wherein fig. 7a is a schematic diagram of comparison between amplitude values of each subharmonic of the dc voltage, and fig. 7b is a schematic diagram of comparison between amplitude values of each subharmonic of the harmonic current.
Fig. 8a and 8b are schematic diagrams of comparison between calculated values of a simulation model and an HSS model in the embodiment of the invention under the working condition 3, wherein fig. 8a is a schematic diagram of comparison between amplitude values of each subharmonic of the dc voltage, and fig. 8b is a schematic diagram of comparison between amplitude values of each subharmonic of the harmonic current.
Fig. 9a and 9b are schematic diagrams of comparison between calculated values of a simulation model and an HSS model in the embodiment of the invention under the working condition 4, wherein fig. 9a is a schematic diagram of comparison between amplitude values of each subharmonic of the dc voltage, and fig. 9b is a schematic diagram of comparison between amplitude values of each subharmonic of the harmonic current.
FIG. 10 is a graph of a-phase current waveforms of HSS model and simulation model under working condition 1 in accordance with an embodiment of the present invention.
Detailed Description
The following description of embodiments refers to the accompanying drawings, which illustrate specific embodiments in which the invention may be practiced.
Referring to fig. 1, an embodiment of the present invention provides a method for modeling a converter, including:
step S1, respectively establishing corresponding models for a main circuit and a control circuit of the converter according to a linear period time-varying system theory;
and S2, combining the main circuit and the control circuit model through the relation between the input variables and the output variables, and establishing a complete harmonic state space model.
Specifically, first, the concept of the harmonic state space HSS (Harmonic State Space) is introduced, which converts the time domain variable into the frequency domain by utilizing the characteristic that the amplitude value and the phase angle of the periodic signal in the frequency domain do not change with time, so as to realize the normalization of the time-varying model.
Defining a linear time period system as:
wherein A (t), B (t), C (t), D (t) are continuous periodic function matrices.
Any periodic signal can be represented by a fourier transform as:
wherein omega 0 Fundamental angular velocity of x (t), x k Is the kth complex fourier coefficient of x (t).
To describe the dynamics of a signal, an Exponential Modulation Period (EMP) signal is used as a general form of x (t):
further developing to obtain a harmonic state space equation containing all harmonic components, wherein the equation is as follows:
expressed as a matrix:
wherein n=diag (…, -j2ω) 0 ,-jω 0 ,0,jω 0 ,j2ω 0 …); A. b, C, D is a Toeplitz matrix of complex Fourier coefficients of A (t), B (t), C (t), D (t), shaped as:
where h is the harmonic order under consideration.
The solution X, which is solved by the HSS model, can be reconverted into the time domain by the following equation:
x(t)＝Γ(t)X (7)
wherein,X＝[X -h ,…,X -1 ,X 0 ,X 1 ,…,X h ] T 。
in this embodiment, step S1 establishes mathematical models of the main circuit and the control circuit, respectively.
The main circuit of the two-level PWM rectifier is shown in fig. 2, and according to the circuit relationship, the following time domain state space equation can be expressed:
wherein,
after linearization of the small signal, equation (8) can be converted into
Wherein i is a 、i b 、i c U is three-phase grid current dc The "≡" indicates the disturbance of the signal for the rectified DC voltage.
The HSS equation for transferring the main circuit small signal state space equation to the frequency domain is shown as a formula (10):
wherein,
by X T For example the first matrix of elements of (c),is composed of->The dimension of the complex Fourier coefficient of the time domain signal after the exponential Fourier decomposition is determined by the harmonic frequency. For example, study of the interaction relationship between the h harmonics, +.>Is a column matrix of (2h+1) and the remaining matrix elements are similar. Definition A T And B is connected with T In the matrix of the matrix,i is (2h+1) order identity matrix, Z m The size of the matrix is a zero matrix, and the size of the matrix is a (2h+1) order square matrix. N (N) k A block diagonal matrix consisting of k N matrices, wherein N matrices are (2h+1) order diagonal matrices, h is the harmonic order considered, +.>Toeplitz matrix Γ [ C ] representing the corresponding element for a constant C]＝c×I 2h+1 。
When the system is in steady state, the s variable will approach 0, i.e. sx=0, at which time the harmonic state space equation can be written as:
(A T -N 4 )X+B T U＝0 (13)
the harmonic transfer function HTF (Harmonic Transfer Function) matrix of the master circuit HSS model is then obtained as follows:
H T ＝-(A T -N 4 ) -1 B T (14)
thus, as shown in FIG. 3, FIG. 3 shows the relationship of state variables to input variables.
In the control circuit, constant DC voltage control and current inner loop control are adopted, the structure is as shown in figure 4, and x is defined by assuming that the angle obtained by the phase-locked loop is theta 1 、x 2 Constant direct current voltage control state variables x of the outer ring and the inner ring of the rectifier respectively 3 For determining a q-axis DC current control state variable, where k vp 、k ip Respectively the proportional coefficient and integral coefficient, k of the outer loop control of the constant direct voltage ip 、k ii The proportional coefficient and the integral coefficient of the constant q-axis direct current control are respectively.
According to fig. 4, the column writes the state equation under the dq coordinate system as follows:
let k 1 ＝k vp ，k 2 ＝k vi ，k 3 ＝k ip ，k 4 ＝k ii Through small signal linearityThe model obtained after the conversion is as follows:
to adapt to HSS theory, the PI controller is transformed into a formula that adapts to the harmonic state space model:
in the circuit topology derivation process, i a 、i b 、i c The time domain is converted into the frequency domain and written as a Toeplitz matrix consisting of Fourier coefficients. Meanwhile, the Park transformation and the anti-Park transformation are converted into the formulas adapting to the harmonic state space model, as follows:
wherein:
Γ[cosθ]＝Γ[…,0.5,0,0.5,…] (19)
Γ[sinθ]＝Γ[…,0.5j,0,-0.5j,…,] (20)
/>
for signalsAnd->The harmonic state space equation of the control circuit can be obtained by changing Park inverse transformation to be under an abc coordinate system as follows:
wherein,
/>
similarly, at X c Matrix elements in (e.g.)Is composed of->The time domain signal of (2) is composed of complex Fourier coefficients after exponential Fourier decomposition, and the matrix order is determined by the number of considered harmonics. For example, consider the h-order harmonic, then +.>Column matrix with matrix size of 2h+1, other matrix elements are similar, U c And X is c Similarly.
At A c 、B c 、C c 、D c The sub-matrix size of each matrix is a square matrix of (2h+1) order, and is a toeplitz matrix, similar to the HSS model matrix elements deduced by the main circuit.
To study the effect of the ac side harmonic voltage on the current and the effect of the output side dc ripple on the ac side current, it is necessary to reduce the harmonic state space equation to the harmonic transfer function.
For equations (10) and (25), the complete HSS model of the PWM rectifier can be obtained after combining and simplifying by eliminating intermediate variables in the manner shown in fig. 5.
The HSS model of the master and control circuits is partitioned as follows:
eliminating the intermediate variable Y to obtain
If U is c1 ＝X T The model can be reduced to:
from the formula (33), let
Then there are:
wherein,
the corresponding harmonic transfer function matrix is as follows:
H f ＝-A f -1 B f (37)
due to H f Is a matrix of (7, 7) × (2h+1), for which a state variable of X is desired T The input variable is U T1 For H f Partitioning it into matrices as follows:
wherein H is 1 Is H f The upper left corner submatrix in the matrix has the size of (4, 3) x (2h+1); h 2 Is H f The upper right hand sub-matrix in the matrix has a size of (4, 4) × (2h+1), whereby the following relationship is obtained:
X T ＝H 1 U T1 +H 2 X T (39)
the method can obtain:
in order to verify the correctness of the model established in the embodiment of the present invention, simulation analysis and verification are performed as follows.
Firstly, building a corresponding PWM rectifier simulation model, wherein system parameters are shown in table 1.
Table 1 three-phase VIENNA rectifier parameters
To verify the validity of the HSS model, four network side harmonic voltage conditions as shown in table 2 were set.
Table 2 network side harmonic voltage conditions
In the above-mentioned established HSS model, the harmonic wave is analyzed by taking h as 21, and the theoretical and simulation result pair obtained under the working condition 1 is shown in fig. 6a-6 b. As can be seen from the graph, when a disturbance voltage with a magnitude of 20V is applied to the grid side, a harmonic current mainly 5 times is generated at the PCC, and a 4-time harmonic voltage disturbance is generated at the dc side along with 3 and 7-time harmonic currents with smaller magnitudes.
The results of the working conditions 2-4 are shown in fig. 7a-7b, 8a-8b and 9a-9b, wherein the rules shown in fig. 7a-7b and 8a-8b are consistent with those shown in fig. 6a-6b, respectively, and the application of the disturbance voltage to the ac side for h times can generate the same-frequency ac current, and the disturbance voltage has an effect on h + -1 times but does not take the dominant effect, wherein the amplitude of h-1 times can be higher. And at the same time, a voltage disturbance of h-1 times is generated on the direct current side. When 5 and 7 harmonic voltage mixed disturbance is applied, corresponding 5 and 7 harmonic current disturbance is generated on the alternating current side, and meanwhile lower 3 and 9 harmonic current disturbance is generated, wherein under the condition that the amplitude of the applied disturbance is the same, the lower the harmonic frequency is, the larger the amplitude of the corresponding disturbance is generated. Meanwhile, corresponding 4-time and 6-time voltage disturbance can be generated on the direct current side, and the amplitude is reduced along with the increase of the applied harmonic frequency.
In order to further verify the accuracy of the model, after obtaining the frequency domain value of the corresponding output variable through the HSS model, the frequency domain value may be converted to the corresponding time domain expression through the formula (7), taking the phase a as an example, so as to obtain waveforms of the HSS model and the simulation model under the working condition 1 as shown in fig. 10, the coupling relationship can be reflected on the whole, and in consideration of factors such as calculation errors, influence of simulation, spectrum leakage and the like, the HSS model established in the embodiment of the invention can be reflected to be basically correct.
As can be seen from the above description, compared with the prior art, the invention has the following beneficial effects: according to the invention, on the basis of the traditional time domain state space model of the converter, the model is transformed from the time domain to the frequency domain, the converter multi-input multi-output model capable of reflecting the harmonic influence among different frequencies is built, the harmonic coupling condition among different frequencies can be considered, the harmonic analysis of low, medium and high frequency bands is realized, more accurate consideration is provided for harmonic analysis and stability evaluation, and meanwhile, the potential harmonic exceeding standard and resonance influence when large-scale power electronic equipment is accessed into a distribution network can be further analyzed, so that the method is also suitable for a multi-converter system.
The foregoing disclosure is illustrative of the present invention and is not to be construed as limiting the scope of the invention, which is defined by the appended claims.
Claims (10)
1. A method of modeling a current transformer, comprising:
step S1, respectively establishing corresponding models for a main circuit and a control circuit of the converter according to a linear period time-varying system theory;
and S2, combining the main circuit and the control circuit model through the relation between the input variables and the output variables, and establishing a complete harmonic state space model.
2. The method for modeling a current transformer according to claim 1, wherein in the step S1, the step of establishing a main circuit model of the current transformer specifically includes:
converting a time domain state space equation of the main circuit into a frequency domain state space equation;
when the system is in a steady state, a harmonic state space equation is obtained;
a harmonic transfer function of the main circuit state space model is obtained.
3. The method of modeling a current transformer of claim 2, wherein the frequency domain state space equation of the main circuit is:
wherein,
wherein i is a 、i b 、i c U is three-phase grid current dc The ∈A is the direct current voltage which is output after rectification, and the ∈A represents the disturbance quantity of the signal;is composed of->The dimension of the complex Fourier coefficient of the time domain signal after the exponential form Fourier decomposition is determined by the size of the considered harmonic frequency h; definition A T And B is connected with T In the matrix, I is 2h+1 order identity matrix, Z m The matrix is a zero matrix, and the size is 2h+1 order matrix; n (N) k A block diagonal matrix composed of k N matrices, wherein N matrix is 2h+1 order diagonal matrix, Γ [ -]Toeplitz matrix representing corresponding element, toeplitz matrix Γ [ C ] corresponding to constant C]＝c×I 2h+1 。
4. A current transformer modeling method according to claim 3, wherein the harmonic state space equation is:
(A T -N 4 )X+B T U＝0。
5. the method of modeling a current transformer of claim 4, wherein the harmonic transfer function matrix of the main circuit state space model is:
H T ＝-(A T -N 4 ) -1 B T 。
6. the method for modeling a current transformer according to claim 1, wherein in the step S1, the step of modeling a control circuit of the current transformer specifically includes:
carrying out small signal linearization on a state equation of a control circuit under a dq coordinate system; the control circuit adopts constant direct current voltage control and current inner loop control;
converting the formula after linearization of the small signal into a formula adapting to a harmonic state space model;
and acquiring a harmonic state space equation of the control circuit.
7. The method of modeling a current transformer of claim 6, wherein the small signal linearized formula is:
wherein x is 1 、x 2 Constant direct current voltage control state variables x of the outer ring and the inner ring of the rectifier respectively 3 To determine the q-axis DC current control state variable, k vp 、k ip Respectively the proportional coefficient and integral coefficient, k of the outer loop control of the constant direct voltage ip 、k ii The proportional coefficient and the integral coefficient of the constant q-axis direct current control are respectively; let k 1 ＝k vp ，k 2 ＝k vi ，k 3 ＝k ip ，k 4 ＝k ii 。
8. The method of modeling a converter according to claim 7, wherein the formula for adapting the harmonic state space model is:
wherein:
Γ[cosθ]＝Γ[…,0.5,0,0.5,…]
Γ[sinθ]＝Γ[…,0.5j,0,-0.5j,…,]
9. the current transformer modeling method of claim 8, wherein the current transformer modeling method is specific to a signalAnd->And (3) changing the Park inverse transformation to an abc coordinate system to obtain a harmonic state space equation of the control circuit as follows:
Y c ＝C c X c +D c U c
wherein,
10. the current transformer modeling method according to claim 9, wherein the step S2 specifically comprises:
the state space model of the main circuit and the control circuit is partitioned:
eliminating the intermediate variable Y to obtain:
set U c1 ＝X T The model is reduced to:
order the
Then there are:
wherein,
the corresponding harmonic transfer function matrix is as follows:
H f ＝-A f -1 B f
will H f Partitioning into blocks, e.gThe matrix shown below:
wherein H is 1 Is H f Upper left hand sub-matrix in matrix, H 2 Is H f The upper right hand sub-matrix in the matrix, results in the following relationship:
X T ＝H 1 U T1 +H 2 X T
the method comprises the following steps:
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