A method and system for analyzing the oscillation stability of offshore wind power through a flexible low-frequency transmission system

Abstract

The application discloses a kind of offshore wind power through flexible low-frequency sending system oscillation stability analysis method and system, comprising: based on the mathematical model of M3C main circuit, establish state space model;State space model is expanded into harmonic state space model and is linearized with small signal, and small signal harmonic state space model is obtained;Based on the transfer function matrix between the small signal variables of system obtained by harmonic balance principle, establish M3C low-frequency side multidimensional phase impedance matrix;Multi-dimensional sequence impedance matrix is converted into multidimensional sequence impedance matrix by symmetry transformation, and two-dimensional sequence impedance matrix is extracted from it;Two-dimensional sequence impedance matrix is converted into traditional sequence impedance, and impedance bode chart is used to analyze the oscillation stability of offshore wind power through flexible low-frequency sending system.The internal dynamic characteristics, multi-loop control coupling and complex harmonic characteristics of M3C are fully considered, and the oscillation stability of offshore wind power through flexible low-frequency sending system can be accurately analyzed.

Description

Technical Field

[0001] This invention belongs to the field of power system stability analysis technology, specifically a method and system for analyzing the oscillation stability of offshore wind power transmitted through a flexible low-frequency transmission system. Background Technology

[0002] The circuit structure and control loop technology of the modular multilevel matrix converter (M3C), the core conversion equipment of the flexible low-frequency power transmission system, are highly complex, which poses a great challenge to wideband impedance modeling. Consequently, the oscillation stability analysis of offshore wind power transmitted through the flexible low-frequency power transmission system has become a current research difficulty.

[0003] Existing analytical methods for the oscillation stability of offshore wind power transmitted through flexible low-frequency transmission systems still have the following shortcomings: On the one hand, the refined broadband impedance modeling method for the low-frequency side of the M3C is not yet mature, lacking a refined broadband impedance model that fully considers the harmonic effects of submodules, multi-loop control coupling, and complex harmonic characteristics of ports; on the other hand, low-frequency wind farms will affect the impedance characteristics of the low-frequency side of the M3C, and methods that take into account the influence of interconnection systems in the low-frequency transmission system and thus accurately analyze the oscillation stability of both are still lacking.

[0004] In summary, existing technologies have not yet developed an effective method for analyzing the oscillation stability of offshore wind power transmission systems via flexible low-frequency transmission lines, making it difficult to meet the requirements for broadband oscillation stability analysis of M3C interconnection systems with low-frequency wind farms. Summary of the Invention

[0005] To address the shortcomings of the existing technologies, this invention provides a method and system for analyzing the oscillation stability of offshore wind power transmitted through a flexible low-frequency transmission system. It establishes positive-sequence and negative-sequence impedance models on the low-frequency side of the M3C system, considers the influence of interconnection systems, and utilizes impedance Bode plots to analyze the oscillation stability of offshore wind power transmitted through a flexible low-frequency transmission system, thereby improving the accuracy of the analysis.

[0006] To achieve the above-mentioned objectives, the present invention adopts the following technical solution.

[0007] In a first aspect, the present invention provides a method for analyzing the oscillation stability of an offshore wind power transmission system via a flexible low-frequency transmission system, comprising: Based on the mathematical model of the M3C main circuit, a state-space model is established with low-frequency AC voltage as input variable, low-frequency AC current as output variable, and bridge arm current and bridge arm capacitor voltage as state variables. The state-space model is expanded into a harmonic state-space model and then subjected to small-signal linearization to obtain a small-signal harmonic state-space model. In the small-signal harmonic state-space model, all small-signal quantities are represented as a linear combination of input variable small-signal quantities, output variable small-signal quantities, and state variable small-signal quantities. Based on the harmonic balance principle, the transfer function matrix between small-signal variables of the system is obtained, and the transfer function matrix between small-signal quantities of three-phase current and small-signal quantities of three-phase voltage is established, namely the multi-dimensional phase impedance matrix of the low-frequency side of M3C. The multidimensional phase impedance matrix is ​​transformed into a multidimensional sequence impedance matrix by symmetric transformation, and the two-dimensional sequence impedance matrix of the low-frequency component of M3C is extracted from it. The two-dimensional sequence impedance matrix is ​​transformed into a traditional sequence impedance, and the oscillation stability of the offshore wind power transmission system via flexible low-frequency transmission is analyzed using the impedance Bode plot.

[0008] Furthermore, the mathematical model of the M3C main circuit is based on Kirchhoff's laws, which include Kirchhoff's current law and Kirchhoff's voltage law.

[0009] Furthermore, the harmonic state-space model expands the time-invariant linear elements in the state-space model into a diagonal matrix composed of frequency shifts, and expands the periodic time-varying elements into a Toeplitz matrix. Its fundamental frequency and cutoff order are determined based on the harmonic components in the M3C main circuit.

[0010] Furthermore, based on the control loop, all small-signal quantities in the small-signal harmonic state-space model are represented as a linear combination of input variable small-signal quantities, output variable small-signal quantities, and state variable small-signal quantities; the control loop includes a low-frequency side control loop, a power frequency side control loop, and a circulating current suppression control loop.

[0011] Furthermore, in the step of obtaining the transfer function matrix between small-signal variables of the system based on the harmonic balance principle, in order to avoid solving the small-signal state variables, the transfer function matrix between the small-signal input variables and the small-signal output variables is directly derived, that is, the M3C low-frequency side multidimensional phase impedance matrix.

[0012] Furthermore, the multidimensional phase impedance matrix needs to be rearranged according to each harmonic component, and the symmetric transformation needs to be extended to the harmonic domain, so as to transform the phase impedance under each harmonic component to the sequence impedance under each harmonic component, and extract the two-dimensional sequence impedance matrix under the M3C low-frequency component.

[0013] Furthermore, taking into account the influence of the interconnection system, the two-dimensional sequence impedance matrix under the low-frequency component of M3C is transformed into the traditional sequence impedance of the low-frequency side of M3C. Taking into account the influence of M3C on the interconnection system, the traditional sequence impedance of the interconnection system is obtained. The interconnection system refers to the system in which the low-frequency wind farm is connected to the low-frequency side of M3C via a low-frequency line.

[0014] Furthermore, the source and load of the M3C and the interconnection system are divided at the connection point using impedance analysis, and then the oscillation stability of the offshore wind power transmission system via the flexible low-frequency transmission diagram is analyzed using impedance Bode plots.

[0015] Secondly, the present invention provides an oscillation stability analysis system for offshore wind power transmitted via a flexible low-frequency transmission system, comprising: State-space model building unit: Based on the mathematical model of the M3C main circuit, a state-space model is established with low-frequency side AC voltage as input variable, low-frequency side AC current as output variable, and bridge arm current and bridge arm capacitor voltage as state variables. Harmonic state-space model acquisition unit: expands the state-space model into a harmonic state-space model and performs small-signal linearization processing to obtain a small-signal harmonic state-space model; Small-signal linear combination acquisition unit: Represents all small-signal quantities in the small-signal harmonic state-space model as a linear combination of input variable small-signal quantities, output variable small-signal quantities, and state variable small-signal quantities; Multidimensional phase impedance matrix establishment unit: Based on the harmonic balance principle, the transfer function matrix between small-signal variables of the system is obtained, and the transfer function matrix between small-signal quantities of three-phase current and small-signal quantities of three-phase voltage is established, namely the multidimensional phase impedance matrix of the low-frequency side of M3C. Two-dimensional order impedance matrix extraction unit: Converts the multidimensional phase impedance matrix into a multidimensional order impedance matrix through symmetric transformation, and extracts the two-dimensional order impedance matrix from it; Oscillation Stability Analysis Unit: The two-dimensional sequence impedance matrix is ​​transformed into a traditional sequence impedance, and the oscillation stability of the offshore wind power transmission system via flexible low-frequency transmission is analyzed using the impedance Bode plot.

[0016] The beneficial effects of this invention are as follows: This invention fully considers the internal dynamic characteristics, multi-loop control coupling, and complex harmonic characteristics of the M3C, and establishes positive-sequence and negative-sequence impedance models for the low-frequency side of the M3C. This overcomes the shortcomings of traditional impedance models in terms of internal dynamic characterization, control coupling representation, and harmonic frequency band coverage, enabling a more accurate and comprehensive reflection of the impedance characteristics of the M3C's low-frequency side over a wide frequency range. Furthermore, this invention further considers the influence of the interconnection system on the impedance characteristics and the interaction between the M3C and the interconnection system, enabling a more realistic simulation of the dynamic behavior of offshore wind power transmitted through the flexible low-frequency transmission system in actual operation, avoiding stability analysis biases caused by neglecting the influence and interaction of the interconnection side.

[0017] This invention can accurately analyze the oscillation stability of offshore wind power transmission systems via flexible low-frequency transmission, effectively identify potential oscillation risk frequency bands, and provide a reliable model basis and theoretical foundation for oscillation mechanism analysis, stability assessment, control parameter optimization, and oscillation suppression strategy design.

[0018] This invention can improve the accuracy of oscillation stability analysis and engineering applicability of offshore wind power flexible low-frequency transmission systems under complex operating conditions, enhance the safety and reliability of system operation, and provide technical support for the promotion and application of large-scale, long-distance flexible low-frequency transmission technology for offshore wind power. Attached Figure Description

[0019] Figure 1 This is a flowchart of an oscillation stability analysis method for an offshore wind power transmission system via a flexible low-frequency transmission line, according to the present invention. Figure 2 This is a topology diagram of a low-frequency power transmission system in a specific embodiment of the present invention; Figure 3 This is a schematic diagram of the circuit structure of the M3C system in a specific embodiment of the present invention; Figure 4 This is a schematic diagram of the power frequency side control loop and phase-locked loop of the M3C system in a specific embodiment of the present invention; Figure 5 This is a schematic diagram of the low-frequency control loop of the M3C system in a specific embodiment of the present invention; Figure 6 This is a schematic diagram of the circulating current suppression control loop of the M3C system in a specific embodiment of the present invention; Figure 7 The figure shows the time-domain waveform of the M3C bridge arm capacitor voltage and its FFT analysis results in a specific embodiment of the present invention. Figure 8 This is a frequency sweep verification diagram of the positive sequence impedance and negative sequence impedance of the M3C low-frequency side in a specific embodiment of the present invention; Figure 9 The impedance Bode diagram of the M3C and low-frequency wind farm interconnection system in a specific embodiment of the present invention is shown. Figure 10 This is a time-domain waveform diagram of the low-frequency side power of the low-frequency transmission system in a specific embodiment of the present invention; Figure 11 This is a diagram showing the composition of an oscillation stability analysis system for a flexible low-frequency transmission system for offshore wind power according to the present invention. Detailed Implementation

[0020] The present invention will be described in detail below with reference to embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0021] Example 1

[0022] This embodiment presents a method for analyzing the oscillation stability of offshore wind power transmitted through a flexible low-frequency transmission system. This method fully considers the internal dynamics of the M3C submodule, multi-loop control coupling, and complex harmonic characteristics. It establishes positive-sequence impedance and negative-sequence impedance models on the low-frequency side of the M3C, takes into account the influence of the interconnection system, and uses the impedance Bode plot to analyze the oscillation stability of the offshore wind power transmitted through the flexible low-frequency transmission system.

[0023] like Figure 1 The method for analyzing the oscillation stability of an offshore wind power transmission system via a flexible low-frequency transmission line, as shown below, comprises the following steps: S1. Based on the mathematical model of the M3C main circuit, establish a state-space model with low-frequency AC voltage as input variable, low-frequency AC current as output variable, and bridge arm current and bridge arm capacitor voltage as state variables.

[0024] The mathematical model of the M3C main circuit is based on Kirchhoff's laws.

[0025] S2. Expand the state-space model into a harmonic state-space model and perform small-signal linearization to obtain a small-signal harmonic state-space model.

[0026] The harmonic state-space model incorporates the time-invariant linear element in the state-space model. Expanded into a diagonal matrix formed by frequency shifts : (1) In the formula: The fundamental angular frequency, s This represents the Laplace operator.

[0027] For periodic time-varying elements A Expand it into a Toeplitz matrix A : (2) In the formula: for A The h Second harmonic components.

[0028] Its fundamental frequency and cutoff order h It can be determined based on the harmonic components in the M3C main circuit.

[0029] S3. Based on the control loop, all small-signal quantities in the small-signal harmonic state-space model are represented as a linear combination of input variable small-signal quantities, output variable small-signal quantities, and state variable small-signal quantities.

[0030] The control loop includes a low-frequency side control loop, a power frequency side control loop, and a circulating current suppression control loop.

[0031] S4. Based on the harmonic balance principle, the transfer function matrix between small-signal variables of the system is obtained, and the transfer function matrix between the small-signal quantities of three-phase current and three-phase voltage is established, namely the multi-dimensional phase impedance matrix of the low-frequency side of M3C.

[0032] In the step of obtaining the transfer function matrix between small-signal variables of the system based on the harmonic balance principle, the solution of small-signal state variables can be avoided, and the transfer function matrix between small-signal input variables and small-signal output variables can be directly derived, that is, the multidimensional phase impedance matrix of the low-frequency side of M3C.

[0033] S5. The multidimensional phase impedance matrix is ​​transformed into a multidimensional sequence impedance matrix through symmetric transformation, and the two-dimensional sequence impedance matrix of the low-frequency component of M3C is extracted from it.

[0034] The multidimensional phase impedance matrix is ​​a matrix arranged according to system variables, and needs to be rearranged according to each harmonic component; the symmetric transformation needs to be extended to the harmonic domain, so as to transform the phase impedance under each harmonic component to the sequence impedance under each harmonic component; the multidimensional sequence impedance matrix is ​​the impedance matrix of intra-harmonic and inter-harmonic coupling, and the two-dimensional sequence impedance matrix under the M3C low-frequency component needs to be extracted from it.

[0035] S6. Taking into account the impact of interconnection systems, the two-dimensional sequence impedance matrix is ​​transformed into a traditional sequence impedance, and the impedance Bode plot is used to analyze the oscillation stability of offshore wind power transmitted through a flexible low-frequency transmission system.

[0036] Taking into account the impact of the interconnection system, the two-dimensional sequence impedance matrix under the low-frequency component of M3C is transformed into the traditional sequence impedance of the low-frequency side of M3C. Taking into account the impact of M3C on the interconnection system, the traditional sequence impedance of the interconnection system is obtained. The interconnection system refers to the system in which the low-frequency wind farm is connected to the low-frequency side of M3C via a low-frequency line.

[0037] The source and load of M3C and the interconnection system are divided at the connection point, and then the oscillation stability of the offshore wind power transmission system via the flexible low-frequency transmission system is analyzed by using the impedance Bode plot.

[0038] The following section applies the method of the present invention to analyze the oscillation stability of an offshore wind power transmission system via a flexible low-frequency transmission line.

[0039] by Figure 2 Taking the low-frequency power transmission system shown as an example, the low-frequency wind farm operates at a frequency of 20Hz. After being stepped up by a transformer, it is connected to the low-frequency side of M3C via a low-frequency power transmission line.

[0040] by Figure 3 The circuit structure of the M3C system shown is as follows: Figures 4 to 6 The control structure of the M3C system shown is an example.

[0041] Figure 3middle C arm It is the capacitor of the bridge arm submodule; L arm It is the bridge arm inductor; R arm It is the bridge arm resistance; R is It is the low-frequency side resistor; , , These are the low-frequency side A, B, and C phase currents, respectively. , , These are the voltages of phases A, B, and C on the low-frequency side, respectively. , , These are the currents of phases a, b, and c on the power frequency side; , , These are the voltages of phases a, b, and c on the power frequency side; It is the bridge arm current; It is the voltage across the bridge arm capacitor; It is the bridge arm adjustment system. SM is a submodule.

[0042] According to Kirchhoff's voltage and current laws, taking bridge arm Aa as an example, it satisfies: (3) (4) In the formula: It is the neutral point voltage.

[0043] The voltage loop equations of the nine bridge arms can be superimposed to obtain: .

[0044] As can be seen from the main circuit, (5) In the formula: ; ; .

[0045] The small-signal form of equation (3) is: (6) In the formula: The small signal form representing the variable.

[0046] Similar to the small-signal forms of equations (3) and (4), considering the mathematical model of the main circuit composed of 9 bridge arms, it can be written in matrix form as follows: (7) In the formula, ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; .

[0047] It is a zero matrix; It is the identity matrix; Represents a diagonal matrix; and These are the transfer function matrices between the bridge arm current and the bridge arm capacitor voltage and the modulation index, respectively. and These are the transfer function matrices between the low-frequency side voltage and the power frequency side voltage and the modulation index, respectively.

[0048] From equation (5), we get: (8) In the formula: ; ; . This is the transfer function matrix between the bridge arm current and the power frequency side output current.

[0049] From equations (7) and (8), we can obtain: (9) In the formula: This is the low-frequency side multidimensional phase admittance matrix.

[0050] Figure 4 middle, The three-phase current on the power frequency side (i.e.) , and ), The three-phase voltage on the power frequency side (i.e.) , and ), For the reason The phase angle generated by the phase-locked loop (PLL). for of q Shaft voltage; A PI controller for a phase-locked loop. The initial angular frequency of the PLL; , is the average voltage of the bridge arm capacitors; the variable in the upper right corner Indicates a reference value; and respectively power frequency side d shaft current and q shaft current; and respectively power frequency side d shaft voltage and q Shaft voltage; A PI controller for the DC voltage loop of the power frequency side control loop; A PI controller for the current loop of the power frequency side control loop; and These are the feedforward coefficient and decoupling coefficient of the power frequency side control loop, respectively. The power frequency side angular frequency, This is the equivalent inductance on the power frequency side; This is for power frequency side control delay.

[0051] Figure 5 In the low-frequency side control loop, For low-frequency side three-phase current, This refers to the three-phase voltage on the low-frequency side. and Low frequency side d shaft current and q shaft current; and Low frequency side d shaft voltage and q Shaft voltage; A PI controller for the AC voltage loop of the low-frequency side control loop; A PI controller for the low-frequency side control loop current loop; and These are the feedforward coefficients and decoupling coefficients of the low-frequency control loop, respectively. It is the low-frequency side angle frequency. This is the equivalent inductance on the low-frequency side; This is for low-frequency side control delay.

[0052] Figure 6In the circulating suppression control loop, , , and These represent the first output of the circulating current suppression control loop. α shaft current, first one β shaft current, second one α shaft current and the second β shaft current; , , and These are the first outputs of the circulating current suppression control loop. α Shaft voltage, first one β Shaft voltage, second one α shaft voltage and the second β Axis voltage, the variable in the upper right corner Indicates a reference value.

[0053] by Figure 6 Taking the circulating current suppression control loop in the abc coordinate system as an example, the bridge arm current is transformed to... In coordinate system: (10) In the formula, ; , , , , , , , , for Bridge arm current in coordinate system.

[0054] Further, we can obtain , , and for: (11) From equations (10) and (11), we can obtain: (12) In the formula: .

[0055] From the circulating suppression control loop, we can obtain: (13) In the formula: A PI controller for circulating current suppression control loop; This is the control delay for the circulating current suppression control loop.

[0056] By performing small-signal linearization on equation (13) and combining it with equation (12), we obtain: (14) In the formula: .

[0057] The M3C modulation can be synthesized from the output voltages of each control loop as shown in equation (15).

[0058] (15) In the formula: ; ; ; This is a reference value for the bridge arm capacitor voltage; , , , , These represent the outputs of the power frequency side control loop. α Shaft voltage, power frequency side control loop output β Shaft voltage, low-frequency side control loop output α Shaft voltage, low-frequency side control loop output β Shaft voltage, zero-sequence voltage output from the low-frequency side control loop.

[0059] Equation (15) can then be expressed as a small-signal form of column vectors: (16) In the formula: ; ; .

[0060] From equations (5), (14), and (16), the transfer function matrix between the bridge arm current generated by the low-frequency loop and the modulation index can be obtained. for: (17) Similarly, the transfer function matrix between the bridge arm capacitor voltage and the modulation index can be derived based on the power frequency side control loop and the low frequency side control loop. Transfer function matrix between low-frequency side voltage and modulation index Transfer function matrix between power frequency side voltage and modulation index Transfer function matrix between bridge arm current and modulation index Substituting this into (9) to solve for the transfer function matrix between small-signal quantities in the harmonic state-space model, we obtain... During the solution process, for the time-invariant linear elements in the M3C system... Expand it into Diagonal matrix formed by frequency shift : (18) For periodic time-varying components in the M3C system A It needs to be expanded into a Toeplitz matrix. A : (19) In the formula: for A The h Second harmonic components.

[0061] for It took into consideration h The harmonic balance equation for the second harmonic satisfies: (20) In the formula: taking phase a as an example, we have , for The h Second harmonic components; , for The h Second harmonic components.

[0062] In equation (20) Reorganized into To satisfy: (twenty one) In the formula: , .

[0063] By performing symmetrical component transformation on each of the electric quantities in equation (21), we have: (twenty two) In the formula: This is the low-frequency side multidimensional order admittance matrix; , and The low-frequency side is the first h Secondary positive and negative sequence currents; , and The low-frequency side is the first h Secondary positive and negative sequence voltages.

[0064] From (21) and (22), we can obtain: (twenty three) In the formula: ; ; ; .

[0065] The low-frequency side multidimensional sequence impedance matrix for: (twenty four) It satisfies: (25) from Extract the first k The two-dimensional order impedance matrix of the secondary impedance for: (26) The time-domain waveform of the M3C bridge arm capacitor voltage and its FFT analysis results are as follows: Figure 7 As shown. By Figure 7 It is known that the dynamic characteristics of the M3C submodule are complex. Within the 0-150Hz range, there are a series of harmonic components that are integer multiples of 10Hz in the bridge arm capacitor voltage. Therefore, the fundamental frequency is selected as 10Hz and the cutoff order is determined during impedance modeling. h The value is selected as 15. Therefore, the low-frequency side two-dimensional sequence impedance is... The two-dimensional order impedance matrix of the second impedance is: (27) Combined with the two-dimensional order impedance matrix of the interconnected system The positive sequence impedance Z on the low-frequency side of M3C was obtained. p and negative sequence impedance Z n for: (28) Similarly, the positive-sequence impedance and negative-sequence impedance of the interconnected system can be obtained.

[0066] M3C low-frequency side positive sequence impedance and negative sequence impedance frequency sweep verification, such as... Figure 8 As shown, the established positive-sequence impedance and negative-sequence impedance models of the low-frequency side of the M3C have good consistency with the frequency sweep results.

[0067] This embodiment uses Figure 9 Taking the impedance Bode diagram of the M3C interconnection system with the low-frequency wind farm as an example, we conduct an oscillation stability analysis of the offshore wind power transmission system via a flexible low-frequency transmission system.

[0068] Specifically, when the output of a low-frequency wind farm is 0.5 pu, there is no intersection between the amplitude-frequency curve of the positive-sequence impedance of the low-frequency wind farm and the M3C low-frequency side, and the low-frequency transmission system has no risk of oscillation. When the output of the low-frequency wind farm increases to 0.8 pu, the amplitude-frequency curve of the positive-sequence impedance of the low-frequency wind farm and the M3C low-frequency side intersects at 80 Hz. At this point, the phase of the positive-sequence impedance of the low-frequency wind farm is -120.8°, the phase of the positive-sequence impedance of the M3C low-frequency side is 81.1°, the system phase margin is -21.9°, and the low-frequency transmission system will experience supersynchronous oscillation.

[0069] This embodiment uses Figure 10 Taking the low-frequency side power time-domain waveform of the low-frequency transmission system shown as an example, the accuracy of the oscillation stability analysis method of offshore wind power through the flexible low-frequency transmission system in this invention is verified.

[0070] Specifically, before 4.1s, the output of the low-frequency wind farm was 0.5 pu, and the low-frequency transmission system was operating stably; at 4.1s, the output of the low-frequency wind farm increased to 0.8 pu, and the power on the low-frequency side gradually oscillated and diverged. FFT analysis showed that the oscillation frequency was 60Hz, corresponding to an AC frequency of 80Hz. Figure 9 The analysis of the oscillation stability of the offshore wind power transmitted through the flexible low-frequency transmission system is consistent with the results.

[0071] Example 2 This embodiment is a system for analyzing the oscillation stability of an offshore wind power transmission system via a flexible low-frequency transmission line. Figure 11 As shown, it consists of a state-space model establishment unit, a harmonic state-space model acquisition unit, a small signal linear combination acquisition unit, a multidimensional phase impedance matrix establishment unit, a two-dimensional sequence impedance matrix extraction unit, and an oscillation stability analysis unit.

[0072] State-space model establishment unit: Based on the mathematical model of the M3C main circuit, a state-space model is established with low-frequency side AC voltage as input variable, low-frequency side AC current as output variable, and bridge arm current and bridge arm capacitor voltage as state variables; it is used to implement step S1 in Example 1, which will not be repeated here.

[0073] Harmonic state-space model acquisition unit: expands the state-space model into a harmonic state-space model and performs small-signal linearization processing to obtain a small-signal harmonic state-space model; used to implement step S2 in embodiment 1, which will not be described again here.

[0074] Small-signal linear combination acquisition unit: Represents all small-signal quantities in the small-signal harmonic state-space model as a linear combination of input variable small-signal quantities, output variable small-signal quantities, and state variable small-signal quantities; used to implement step S3 in embodiment 1, which will not be repeated here.

[0075] Multidimensional phase impedance matrix establishment unit: Based on the harmonic balance principle, the transfer function matrix between small-signal variables of the system is obtained, and the transfer function matrix between the small-signal quantities of three-phase current and three-phase voltage is established, that is, the multidimensional phase impedance matrix of the low-frequency side of M3C; it is used to implement step S4 in Example 1, which will not be repeated here.

[0076] Two-dimensional sequence impedance matrix extraction unit: Converts the multidimensional phase impedance matrix into a multidimensional sequence impedance matrix through symmetric transformation, and extracts the two-dimensional sequence impedance matrix from it; used to implement step S5 in embodiment 1, which will not be described again here.

[0077] Oscillation stability analysis unit: Converts the two-dimensional sequence impedance matrix into a traditional sequence impedance and uses the impedance Bode plot to perform oscillation stability analysis of the offshore wind power transmission system via flexible low frequency; used to implement step S6 in Example 1, which will not be described again here.

[0078] It should be noted that each module in the aforementioned oscillation stability analysis system for offshore wind power via a flexible low-frequency transmission system can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module. For specific limitations regarding the oscillation stability analysis system for offshore wind power via a flexible low-frequency transmission system, please refer to the limitations of the oscillation stability analysis method for offshore wind power via a flexible low-frequency transmission system described above; both have the same function and role, and will not be repeated here.

[0079] It should be noted that the order of the above embodiments of the present invention is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. Furthermore, the above description focuses on specific embodiments of this specification. Additionally, the processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired results. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0080] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for analyzing the oscillation stability of an offshore wind power transmission system via a flexible low-frequency transmission line, characterized in that, include: Based on the mathematical model of the M3C main circuit, a state-space model is established with low-frequency AC voltage as input variable, low-frequency AC current as output variable, and bridge arm current and bridge arm capacitor voltage as state variables. The state-space model is expanded into a harmonic state-space model and then subjected to small-signal linearization to obtain a small-signal harmonic state-space model. In the small-signal harmonic state-space model, all small-signal quantities are represented as a linear combination of input variable small-signal quantities, output variable small-signal quantities, and state variable small-signal quantities. Based on the harmonic balance principle, the transfer function matrix between small-signal variables of the system is obtained, and the transfer function matrix between small-signal quantities of three-phase current and small-signal quantities of three-phase voltage is established, namely the multi-dimensional phase impedance matrix of the low-frequency side of M3C. The multidimensional phase impedance matrix is ​​transformed into a multidimensional sequence impedance matrix by symmetric transformation, and the two-dimensional sequence impedance matrix of the low-frequency component of M3C is extracted from it. The two-dimensional sequence impedance matrix is ​​transformed into a traditional sequence impedance, and the oscillation stability of the offshore wind power transmission system via flexible low-frequency transmission is analyzed using the impedance Bode plot.

2. The method for analyzing the oscillation stability of an offshore wind power transmission system via a flexible low-frequency transmission line according to claim 1, characterized in that, The mathematical model of the M3C main circuit is based on Kirchhoff's laws.

3. The method for analyzing the oscillation stability of an offshore wind power transmission system via a flexible low-frequency transmission line according to claim 1, characterized in that, The harmonic state-space model expands the time-invariant linear elements in the state-space model into diagonal matrices formed by frequency shifts, and expands the periodic time-varying elements into Toeplitz matrices. Its fundamental frequency and cutoff order are determined based on the harmonic components in the M3C main circuit.

4. The method for analyzing the oscillation stability of an offshore wind power transmission system via a flexible low-frequency transmission line according to claim 1, characterized in that, Based on the control loop, all small-signal quantities in the small-signal harmonic state-space model are represented as a linear combination of input variable small-signal quantities, output variable small-signal quantities, and state variable small-signal quantities; the control loop includes a low-frequency side control loop, a power frequency side control loop, and a circulating current suppression control loop.

5. The method for analyzing the oscillation stability of an offshore wind power transmission system via a flexible low-frequency transmission line according to claim 1, characterized in that, In the step of obtaining the transfer function matrix between small-signal variables of the system based on the harmonic balance principle, in order to avoid solving the small-signal state variables, the transfer function matrix between the small-signal input variables and the small-signal output variables is directly derived, that is, the M3C low-frequency side multidimensional phase impedance matrix.

6. The method for analyzing the oscillation stability of an offshore wind power transmission system via a flexible low-frequency transmission line according to claim 1, characterized in that, The multidimensional phase impedance matrix needs to be rearranged according to each harmonic component, and the symmetric transformation needs to be extended to the harmonic domain, so as to transform the phase impedance under each harmonic component to the sequence impedance under each harmonic component, and extract the two-dimensional sequence impedance matrix under the M3C low-frequency component.

7. The method for analyzing the oscillation stability of an offshore wind power transmission system via a flexible low-frequency transmission line according to claim 1, characterized in that, Taking into account the impact of the interconnection system, the two-dimensional sequence impedance matrix under the low-frequency component of M3C is transformed into the traditional sequence impedance of the low-frequency side of M3C. Taking into account the impact of M3C on the interconnection system, the traditional sequence impedance of the interconnection system is obtained. The interconnection system refers to the system in which the low-frequency wind farm is connected to the low-frequency side of M3C via a low-frequency line.

8. The method for analyzing the oscillation stability of an offshore wind power transmission system via a flexible low-frequency transmission line according to claim 7, characterized in that, The source and load of M3C and the interconnection system are divided at the connection point by impedance analysis, and then the oscillation stability of offshore wind power transmitted through the flexible low-frequency transmission system is analyzed by impedance Bode plot.

9. A system for analyzing the oscillation stability of offshore wind power transmitted through a flexible low-frequency transmission system, characterized in that, include: State-space model building unit: Based on the mathematical model of the M3C main circuit, a state-space model is established with low-frequency side AC voltage as input variable, low-frequency side AC current as output variable, and bridge arm current and bridge arm capacitor voltage as state variables. Harmonic state-space model acquisition unit: expands the state-space model into a harmonic state-space model and performs small-signal linearization processing to obtain a small-signal harmonic state-space model; Small-signal linear combination acquisition unit: Represents all small-signal quantities in the small-signal harmonic state-space model as a linear combination of input variable small-signal quantities, output variable small-signal quantities, and state variable small-signal quantities; Multidimensional phase impedance matrix establishment unit: Based on the harmonic balance principle, the transfer function matrix between small-signal variables of the system is obtained, and the transfer function matrix between small-signal quantities of three-phase current and small-signal quantities of three-phase voltage is established, namely the multidimensional phase impedance matrix of the low-frequency side of M3C. Two-dimensional order impedance matrix extraction unit: Converts the multidimensional phase impedance matrix into a multidimensional order impedance matrix through symmetric transformation, and extracts the two-dimensional order impedance matrix from it; Oscillation Stability Analysis Unit: The two-dimensional sequence impedance matrix is ​​transformed into a traditional sequence impedance, and the oscillation stability of the offshore wind power transmission system via flexible low-frequency transmission is analyzed using the impedance Bode plot.

10. The oscillation stability analysis system for offshore wind power transmitted via a flexible low-frequency transmission system according to claim 9, characterized in that, In the aforementioned oscillation stability analysis unit, the two-dimensional sequence impedance matrix under the low-frequency component of M3C is transformed into the traditional sequence impedance of the low-frequency side of M3C, taking into account the influence of the interconnection system. The traditional sequence impedance of the interconnection system is obtained by taking into account the influence of M3C on the interconnection system. The interconnection system refers to the system in which the low-frequency wind farm is connected to the low-frequency side of M3C via a low-frequency line.

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