Three-phase converter impedance modeling method for specific subharmonic elimination pulse width modulation

Abstract

The invention provides a three-phase converter impedance modeling method for specific subharmonic elimination pulse width modulation. The method comprises the following steps: S1, determining switching angle distribution of a three-phase converter; s2, generating a specific sub-harmonic elimination pulse width modulation waveform based on the switch angle distribution, and analyzing the specific sub-harmonic elimination pulse width modulation waveform to obtain a modulation ratio and a corresponding table of amplitude and phase of each sub-harmonic; and S3, determining a space state equation of the three-phase converter, determining an impedance model of the three-phase converter based on the space state equation, and constructing a harmonic state space equation considering specific sub-harmonics to eliminate the influence of the pulse width modulation dominant harmonics based on the mapping relation between the modulation ratio and the dominant harmonics in different switching angle numbers through the method. And then an impedance model of the three-phase converter is constructed, so that the alternating current impedance of the three-phase converter can be represented when pulse width modulation is eliminated by using specific subharmonic waves under different modulation ratios.

Description

Technical Field

[0001] The invention relates to an impedance modeling method, in particular to an impedance modeling method for a three-phase converter oriented to specific subharmonic elimination pulse width modulation. Background Art

[0002] Power electronic converters have developed rapidly in the past decade due to their flexible control and rapid response, and have been widely used in power systems, transportation, mining and metallurgy. With the requirements of these related applications for converter voltage and power, the series and parallel use of converters and the construction of microgrids have become important needs. However, due to the harmonic coupling of modulation and control involved in converters, broadband oscillation occurs when multiple converters are connected in series and parallel to form a network, which has a significant impact on the converter and the power supply system, and even collapses.

[0003] In the prior art, impedance modeling is performed for three-phase converters or thyristor rectifiers. These topologies use carrier modulation technology or phase-shift control strategies, such as averaging the switching function of the converter, approximating the dual Fourier transform and Bessel function based on carrier modulation technology, etc. These processing methods are only applied to high switching frequency modulation scenarios. However, in order to effectively reduce the power loss of the converter and improve the overall efficiency of the converter, the converter often needs to adopt specific subharmonic elimination pulse width modulation technology. The impedance modeling method in the prior art is not suitable for this scenario, resulting in the lack of an impedance model for the three-phase converter in this scenario, which in turn affects the oscillation risk analysis and stability assessment of the entire system.

[0004] Therefore, in order to solve the above technical problems, it is urgent to propose a new technical means. Summary of the invention

[0005] In view of this, the purpose of the present invention is to provide an impedance modeling method for a three-phase converter for specific subharmonic elimination pulse width modulation. Based on the mapping relationship between the modulation ratio and the dominant harmonic under different numbers of switching angles, a harmonic state space equation taking into account the influence of the dominant harmonic of the specific subharmonic elimination pulse width modulation is constructed, and then an impedance model of the three-phase converter is constructed, so that the AC impedance of the three-phase converter when the specific subharmonic elimination pulse width modulation is used under different modulation ratios can be characterized, and accurate data support can be provided for the subsequent broadband oscillation risk and stability analysis of the entire system.

[0006] The present invention provides a three-phase converter impedance modeling method for specific subharmonic elimination pulse width modulation, comprising the following steps:

[0007] S1. Determine the switching angle distribution of the three-phase converter;

[0008] S2. Generate a specific harmonic elimination pulse width modulation waveform based on the switch angle distribution, and analyze the specific harmonic elimination pulse width modulation waveform to obtain a corresponding table of the modulation ratio and the amplitude and phase of each harmonic;

[0009] S3. Determine the spatial state equation of the three-phase converter, and determine the impedance model of the three-phase converter based on the spatial state equation.

[0010] Further, determining the switch angle distribution specifically includes:

[0011] The constraint equation of the special subharmonic elimination pulse width modulation of the three-phase converter is constructed, wherein the constraint equation includes a two-level special subharmonic elimination pulse width modulation constraint equation and a three-level special subharmonic elimination pulse width modulation constraint equation:

[0012] The constraint equation of two-level specific subharmonic elimination pulse width modulation is:

[0013]

[0014] The constraint equation for eliminating the three-level specific subharmonics and modulating the pulse width is:

[0015]

[0016] in:

[0017] N is the number of switching angles contained in a specific subharmonic elimination pulse width modulation waveform within a quarter cycle, α i is the phase corresponding to the i-th switching angle, m is the output modulation ratio of the three-phase converter, m = V ref (2V dc / π), V ref and V dc are the fundamental voltage and DC bus voltage expected to be output by the converter respectively;

[0018] The constraint equations of the pulse width modulation with specific subharmonic elimination are solved by the Levenberg-Marquardt method to obtain the switching angle distribution.

[0019] Further, step S3 specifically includes:

[0020] Constructing a three-phase converter time domain model:

[0021]

[0022] Where: v a 、v b and v c are the AC side voltage of the three-phase converter, R s is the AC side line resistance of the three-phase converter, Ls is the AC side inductance of the three-phase converter, C dc is the DC side capacitance of the three-phase converter, R dc is the DC side resistance of the three-phase converter, i a 、i b and i c are the AC side current of the three-phase converter, e dc is the DC side power supply voltage of the three-phase converter;

[0023] Convert the time domain model into state space equations:

[0024]

[0025] in:

[0026]

[0027] The matrices C and D are determined by the output vector y;

[0028] Convert the time domain signal x in the state space equation into the matrix form of the frequency domain signal X:

[0029] x(t)=Γ(t)X

[0030]

[0031] And transform the matrices A, B, C and D into Toeplitz matrices, denoted as Г(A), Г(B), Г(C) and Г(D) respectively;

[0032] The frequency domain expression of formula (4) is:

[0033]

[0034] Where: N is equal to diag(…,-jnω1I,…,-jω1I,j0I,jω1I,…,jnω1I,…);

[0035] In the field of steady-state operation trajectory, equation (4) is linearized to obtain:

[0036]

[0037] Based on formula (7), the harmonic state space of the three-phase converter is determined as follows:

[0038]

[0039] Where: Г(A p ), Г(B p )、Г(C p ) and Г(D p) are equal to Г(A), Г(B), Г(C) and Г(D) respectively;

[0040] The impedance model of the three-phase converter is:

[0041] G p = Г(C p )[sI-(Г(A p )-N p )] -1 Г(B p )+Г(D p ), where s represents the complex frequency.

[0042] Beneficial effects of the present invention: Through the present invention, based on the mapping relationship between the modulation ratio and the dominant harmonic under different numbers of switching angles, a harmonic state space equation taking into account the influence of the dominant harmonic of the pulse width modulation with specific subharmonic elimination is constructed, and then an impedance model of the three-phase converter is constructed, so that the AC impedance of the three-phase converter when the pulse width modulation with specific subharmonic elimination is used under different modulation ratios can be characterized, providing accurate data support for the subsequent broadband oscillation risk and stability analysis of the entire system. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0044] Figure 1 It is a flow chart of the present invention.

[0045] Figure 2 This is the switch angle distribution diagram of the present invention.

[0046] Figure 3 This is a diagram of the unified SHEPWM waveform restoration algorithm of the present invention. DETAILED DESCRIPTION

[0047] The present invention is further described in detail below:

[0048] The present invention provides a three-phase converter impedance modeling method for specific subharmonic elimination pulse width modulation, comprising the following steps:

[0049] S1. Determine the switching angle distribution of the three-phase converter;

[0050] S2. Generate a specific harmonic elimination pulse width modulation waveform based on the switch angle distribution, and analyze the specific harmonic elimination pulse width modulation waveform to obtain a corresponding table of the modulation ratio and the amplitude and phase of each harmonic;

[0051] S3. Determine the spatial state equation of the three-phase converter, and determine the impedance model of the three-phase converter based on the spatial state equation. Through the above method, based on the mapping relationship between the modulation ratio and the dominant harmonic under different numbers of switching angles, construct the harmonic state space equation that takes into account the influence of the dominant harmonic of the special subharmonic elimination pulse width modulation, and then construct the impedance model of the three-phase converter, so as to characterize the AC impedance of the three-phase converter when using the special subharmonic elimination pulse width modulation under different modulation ratios, and provide accurate data support for the subsequent broadband oscillation risk and stability analysis of the entire system. Among them, the special subharmonic elimination pulse width modulation is abbreviated as SHEPWM in English.

[0052] In this embodiment, determining the switch angle distribution specifically includes:

[0053] The constraint equation of the special subharmonic elimination pulse width modulation of the three-phase converter is constructed, wherein the constraint equation includes a two-level special subharmonic elimination pulse width modulation constraint equation and a three-level special subharmonic elimination pulse width modulation constraint equation:

[0054] The constraint equation of two-level specific subharmonic elimination pulse width modulation is:

[0055]

[0056] The three-level specific subharmonic,elimination, pulse,width,modulation,constraint equation is:

[0057]

[0058] in:

[0059] N is the number of switching angles contained in a specific subharmonic elimination pulse width modulation waveform within a quarter cycle, α i is the phase corresponding to the i-th switching angle, m is the output modulation ratio of the three-phase converter, m = V ref (2V dc / π), V ref and V dc are the fundamental voltage and DC bus voltage expected to be output by the converter respectively;

[0060] The constraint equation of the specific subharmonic elimination pulse width modulation is solved by the Levenberg-Marquardt method to obtain the switch angle distribution. The Levenberg-Marquardt method is a prior art and will not be described in detail here. In addition, the corresponding waveform is generated based on the switch angle distribution and the level jump rule of the SHEPWM waveform. The waveform process is as follows: Figure 3 As shown, this is a prior art and will not be described in detail here.

[0061] Further, step S3 specifically includes:

[0062] Constructing a three-phase converter time domain model:

[0063]

[0064] Where: v a 、v b and v c are the AC side voltage of the three-phase converter, R s is the AC side line resistance of the three-phase converter, L s is the AC side inductance of the three-phase converter, C dc is the DC side capacitance of the three-phase converter, R dc is the DC side resistance of the three-phase converter, i a 、i b and i c are the AC side current of the three-phase converter, e dc is the DC side power supply voltage of the three-phase converter; s a 、s b 、s c Respectively represent the switching state of the three-phase converter; s a 、s b 、s c Respectively represent the switching state of the three-phase converter; s a 、s b 、s c The switching state is represented by 0 and 1, 0 means that the electronic switch of the three-phase converter is off, and 1 means it is on. The state is determined by the corresponding table of the modulation ratio and the amplitude and phase of each harmonic, such as Figure 2 , the current switch state can be determined by the modulation ratio;

[0065] Convert the time domain model into state space equations:

[0066]

[0067] in:

[0068]

[0069] The matrices C and D are determined by the output vector y. The determination process can be carried out using the existing technology and will not be described in detail here.

[0070] Convert the time domain signal x in the state space equation into the matrix form of the frequency domain signal X:

[0071] x(t)=Γ(t)X

[0072]

[0073] And convert matrices A, B, C and D into Toeplitz matrix form, denoted as Г(A), Г(B), Г(C) and Г(D) respectively; take Г(A) as an example:

[0074]

[0075] Where: Z m is an m-dimensional zero matrix, A0 represents the DC component of the time domain signal x, A1...A n Represents the positive frequency component of the time domain signal x, A-1...A- n Represents the negative frequency component of the time domain signal x;

[0076] The frequency domain expression of formula (4) is:

[0077]

[0078] Where: N is equal to diag(…,-jnω1I,…,-jω1I,j0I,jω1I,…,jnω1I,…);

[0079] In the field of steady-state operation trajectory, equation (4) is linearized to obtain:

[0080]

[0081] Based on formula (7), the harmonic state space of the three-phase converter is determined as follows:

[0082]

[0083] Where: Г(A p ), Г(B p )、Г(C p ) and Г(D p ) are equal to Г(A), Г(B), Г(C) and Г(D) respectively;

[0084] The impedance model of the three-phase converter is:

[0085] G p = Г(C p )[sI-(Г(A p )-N p )] -1 Г(B p )+Г(D p ), where s represents the complex frequency.

[0086] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. A three-phase converter impedance modeling method for specific subharmonic elimination pulse width modulation, characterized in that: The following steps are involved: S1. Determine the switching angle distribution of the three-phase converter; S2. Generate a specific harmonic elimination pulse width modulation waveform based on the switch angle distribution, and analyze the specific harmonic elimination pulse width modulation waveform to obtain a corresponding table of the modulation ratio and the amplitude and phase of each harmonic; S3. Determine the spatial state equation of the three-phase converter, and determine the impedance model of the three-phase converter based on the spatial state equation.

2. The impedance modeling method of a three-phase converter for pulse width modulation with specific subharmonic elimination according to claim 1 is characterized in that: Determining the switch angle distribution specifically includes: The constraint equation of the special subharmonic elimination pulse width modulation of the three-phase converter is constructed, wherein the constraint equation includes a two-level special subharmonic elimination pulse width modulation constraint equation and a three-level special subharmonic elimination pulse width modulation constraint equation: The constraint equation of two-level specific subharmonic elimination pulse width modulation is: The constraint equation for eliminating the three-level specific subharmonics and modulating the pulse width is: in: N is the number of switching angles contained in a specific subharmonic elimination pulse width modulation waveform within a quarter cycle, α i is the phase corresponding to the i-th switching angle, m is the output modulation ratio of the three-phase converter, m = V ref (2V dc / π), V ref and V dc are the fundamental voltage and DC bus voltage expected to be output by the converter respectively; The constraint equations of the specific subharmonic elimination pulse width modulation are solved using the Levenberg-Marquardt method to obtain the switching angle distribution.

3. The impedance modeling method for a three-phase converter with pulse width modulation for specific subharmonic elimination according to claim 2 is characterized in that: Step S3 specifically includes: Constructing a three-phase converter time domain model: Where: v a 、v b and v c are the AC side voltage of the three-phase converter, R s is the AC side line resistance of the three-phase converter, L s is the AC side inductance of the three-phase converter, C dc is the DC side capacitance of the three-phase converter, R dc is the DC side resistance of the three-phase converter, i a 、i b and i c are the AC side current of the three-phase converter, e dc is the DC side power supply voltage of the three-phase converter; Convert the time domain model into state space equations: in: The matrices C and D are determined by the output vector y; Convert the time domain signal x in the state space equation into the matrix form of the frequency domain signal X: x(t)=Γ(t)X And transform the matrices A, B, C and D into Toeplitz matrices, denoted as Г(A), Г(B), Г(C) and Г(D) respectively; The frequency domain expression of formula (4) is: Where: N is equal to diag(…,-jnω1I,…,-jω1I,j0I,jω1I,…,jnω1I,…); In the field of steady-state operation trajectory, equation (4) is linearized to obtain: Based on formula (7), the harmonic state space of the three-phase converter is determined as follows: Where: Г(A p ), Г(B p )、Г(C p ) and Г(D p ) are equal to Г(A), Г(B), Г(C) and Г(D) respectively; The impedance model of the three-phase converter is: G p = Г(C p )[sI-(Г(A p )-N p )] -1 Г(B p )+Г(D p ), where s represents the complex frequency.

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