Low-frequency offshore wind power system stability analysis method and device

Abstract

The invention discloses a low-frequency offshore wind power system stability analysis method and device, and relates to the field of power system stability analysis, and the method comprises the steps: obtaining an MMC power frequency side voltage and a DRU low frequency side current of a DRU-MMC converter, a grid connection point current and a grid connection point voltage of a wind power plant, and a grid connection point voltage of a machine side converter; constructing a fan system model, a direct current network line model and an MMC converter station model; performing linearization processing on the stable working point of each model to obtain a whole-system small-signal model of the low-frequency offshore wind power system; solving the whole-system small signal model to obtain a state matrix; and determining the stability of the low-frequency offshore wind power system according to the state matrix. By implementing the method, the problem that a traditional time domain simulation linearization model is large in error can be solved, and accurate evaluation of the dynamic stability of the low-frequency offshore wind power system containing a large number of nonlinear links is achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of power system stability analysis, in particular to a low-frequency offshore wind power system stability analysis method and device. BACKGROUND

[0002] In recent years, with the increasing demand for renewable energy worldwide, offshore wind power, as a green, efficient and sustainable clean energy form, is rapidly developing worldwide. Compared with onshore wind power, offshore wind power has the advantages of more stable wind resources, larger available area, less noise and visual impact away from load centers, etc. Especially in the deep sea area, it has broad prospects for large-capacity centralized development. However, with the increase of single-machine capacity of offshore wind turbines, the total installed capacity of wind farms is rapidly expanding, and the transmission distance between the land grid and the offshore wind farm is also greatly extended. The traditional power frequency transmission method gradually exposes the problems of large capacitance effect, obvious power attenuation, and high voltage control difficulty. Under this background, low-frequency transmission technology emerges as the times require and becomes a new transmission method connecting large-capacity offshore wind farms and land grids. Low-frequency transmission has the advantages of reduced capacitive current, increased transmission distance, and reduced loss of converter equipment, which has obvious advantages in improving system stability and economy.

[0003] For low-frequency transmission technology, a high-efficiency access scheme that has gradually emerged in recent years is the "DRU-MMC" structure, that is, the offshore side uses uncontrollable diode rectifier units (DRU) for rectification, and the onshore side uses modular multilevel converters (MMC) for inversion. Compared with the traditional VSC-VSC system, this structure has higher reliability and economy, but it also brings new control challenges, especially at the wind farm end, as the DRU cannot actively regulate voltage and reactive power, resulting in weak support for system transient and dynamic performance, especially in low-frequency systems, which is prone to oscillation mode coupling and poor power angle stability.

[0004] In order to enhance the network construction capability and operation stability of the system, in recent years, it is proposed to use virtual synchronous generator (VSG) control strategy in the wind farm grid-side converter, which can simulate the rotational inertia and damping behavior of traditional synchronous machines to improve the dynamic response performance and fault ride-through capability of the wind farm. At the same time, combined with virtual impedance technology, droop control strategy and auxiliary converter access, the frequency response and reactive power support capability of the wind farm can be further adjusted.

[0005] However, traditional time-domain simulation approximates the system as a linear model, and calculates whether oscillation will occur through mathematical formulas. But this method requires that the system is close to steady state and the disturbance is small. However, the DRU-MMC+VSG system has a large number of nonlinear links, and the linearization model error is very large. Therefore, it is difficult to systematically evaluate the dynamic stability characteristics of the entire low-frequency offshore wind power system by relying only on time-domain simulation analysis. Summary of the Invention

[0006] This invention provides a method and apparatus for stability analysis of low-frequency offshore wind power systems, which can solve the problem of large errors in traditional time-domain simulation linearization models and achieve accurate assessment of the dynamic stability of low-frequency offshore wind power systems containing a large number of nonlinear elements.

[0007] An embodiment of the present invention provides a method for stability analysis of a low-frequency offshore wind power system, comprising:

[0008] Obtain the MMC power frequency side voltage and DRU low frequency side current of the DRU-MMC converter, as well as the grid connection point current, grid connection point voltage and turbine-side converter grid connection point voltage of the wind farm;

[0009] Based on the MMC power frequency side voltage and DRU low frequency side current of the DRU-MMC converter, as well as the grid connection point current, grid connection point voltage, and turbine-side converter grid connection point voltage of the wind farm, a wind turbine system model, a DC network line model, and an MMC converter station model are constructed. The wind turbine system model includes: a dynamic model of the wind turbine grid-side converter, a dynamic model of the wind turbine converter DC link, and a dynamic model of the wind turbine side converter. The DC network line model includes: a dynamic model of the low frequency line and a dynamic model of the DRU. The MMC converter station model includes: a dynamic model of the MMC, a dynamic model of the MMC DC link, and a dynamic model of the MMC power frequency phase-locked loop.

[0010] Linearization is performed on the stable operating points of the wind turbine system model, DC network line model, and MMC converter station model to obtain the whole system small-signal model of the low-frequency offshore wind power system.

[0011] Solving the small-signal model of the entire system yields the state matrix of the low-frequency offshore wind power system;

[0012] The stability of low-frequency offshore wind power systems is determined based on the state matrix.

[0013] Furthermore, based on the state matrix, the stability of the low-frequency offshore wind power system is determined, including:

[0014] Determine whether all eigenvalues ​​in the state matrix are less than 0;

[0015] If so, the low-frequency offshore wind power system is determined to be stable;

[0016] Otherwise, the low-frequency offshore wind power system is considered unstable.

[0017] Furthermore, after determining the stability of the low-frequency offshore wind power system based on the state matrix, the following steps are also included:

[0018] Under unstable conditions of low-frequency offshore wind power systems, the oscillation modes of low-frequency offshore wind power systems are determined based on the state matrix.

[0019] Participation factor analysis was performed on each oscillation mode to determine the corresponding oscillation participation variables;

[0020] The low-frequency offshore wind power system is regulated based on the oscillation participation variables.

[0021] Furthermore, the dynamic model of the wind turbine grid-side converter includes:

[0022]

[0023] The dynamic model of the DC link in the wind turbine converter includes:

[0024]

[0025] Where Δx1 represents the small-signal disturbance component of the d-axis intermediate state variable x1 of the wind turbine grid-side converter voltage control loop, Δx2 represents the small-signal disturbance component of the q-axis intermediate state variable x2 of the wind turbine grid-side converter voltage control loop, Δx3 represents the small-signal disturbance component of the d-axis intermediate state variable x3 of the wind turbine grid-side converter current control loop, Δx4 represents the small-signal disturbance component of the q-axis intermediate state variable x4 of the wind turbine grid-side converter current control loop, A1 represents the coefficient matrix of the wind farm state variables, B1 represents the coefficient matrix of the wind farm input variables, and i d This represents the d-axis current of the grid-side converter of the wind turbine. Indicates the d-axis current reference value of the wind turbine grid-side converter, i q This represents the q-axis current of the grid-side converter of the wind turbine. This indicates the reference value of the q-axis current of the wind turbine grid-side converter, u. d This represents the d-axis voltage of the grid-side converter of the wind turbine. This indicates the reference value of the d-axis voltage of the wind turbine grid-side converter, u. q This represents the q-axis voltage of the grid-side converter of the wind turbine. This indicates the reference value of the q-axis voltage of the wind turbine grid-side converter, V. d This indicates the reference value of the d-axis voltage of the wind turbine grid-side converter, V. q This represents the reference value of the q-axis voltage of the wind turbine grid-side converter, Δi. d Indicates the d-axis current i of the wind turbine grid-side converter d Small signal disturbance component, Δi q i represents the q-axis current i of the grid-side converter of the wind turbine. q The small-signal disturbance component, R1 represents the equivalent resistance of the wind turbine converter connecting reactance, L1 represents the equivalent inductance of the wind turbine converter connecting reactance, ω represents the angular frequency, ΔV dThis indicates the reference value V of the d-axis voltage of the wind turbine grid-side converter. d Small signal disturbance component, ΔV q V represents the reference value of the q-axis voltage of the wind turbine grid-side converter. q Small signal disturbance component, Δu d The voltage u of the grid-side converter of the wind turbine represents the d-axis voltage. d Small signal disturbance component, Δu q U represents the q-axis voltage u of the wind turbine grid-side converter. q Small signal disturbance components.

[0026] Furthermore, the low-frequency line dynamic model includes:

[0027]

[0028] The DRU dynamic model includes:

[0029]

[0030] Among them, u d1 This represents the d-axis voltage on the low-frequency submarine cable machine side, Δu. d1 Indicates the d-axis voltage u on the low-frequency submarine cable machine side. d1 Small signal perturbation component, u q1 This represents the q-axis voltage on the low-frequency submarine cable machine side, Δu q1 Indicates the q-axis voltage u on the low-frequency submarine cable machine side. q1 Small signal disturbance component, Δu md Indicates the d-axis voltage u on the low-frequency submarine cable network side. md Small signal disturbance component, Δu mq Indicates the q-axis voltage u on the low-frequency submarine cable network side. mq Small signal disturbance component, Δi ld Indicates the d-axis inductor current i on the low-frequency submarine cable machine side. ld Small signal disturbance component, Δi lq Indicates the q-axis inductor current i on the low-frequency submarine cable machine side. lq The small signal disturbance component, A2 represents the coefficient matrix of the low-frequency submarine cable state variables, and B2 and C2 both represent the coefficient matrices of the low-frequency submarine cable input variables, i d1 Δi represents the d-axis current at the grid connection point of the wind farm. d1 The d-axis current i at the grid connection point of the wind farm is represented by... d1 The small signal perturbation component, i q1 Δi represents the q-axis current at the grid connection point of the wind farm. q1 i represents the q-axis current at the grid connection point of the wind farm. q1 Small signal disturbance component, Δi md Indicates the d-axis current i on the low-frequency side of the DRU md Small signal disturbance component, Δi mqIndicates the q-axis current i on the low-frequency side of the DRU mq The small-signal perturbation component, Δω represents the small-signal perturbation component with angular frequency ω, i dc Δi represents the DC current of the DRU converter transformer. dc i represents the DC current of the DRU converter transformer. dc Small signal disturbance component, L dc Indicates smoothing inductance, ΔU dc U represents the DC voltage of the DRU converter transformer. dc Small signal disturbance components.

[0031] Furthermore, the MMC dynamic model includes:

[0032]

[0033] The dynamic model of the MMC DC link includes:

[0034]

[0035] The dynamic model of the MMC power frequency phase-locked loop includes:

[0036]

[0037] Where Δx5 represents the small-signal disturbance component of the d-axis intermediate state variable x5 of the MMC converter power outer loop, Δx6 represents the small-signal disturbance component of the q-axis intermediate state variable x6 of the MMC converter power outer loop, Δx7 represents the small-signal disturbance component of the d-axis intermediate state variable x7 of the MMC converter current inner loop, Δx8 represents the small-signal disturbance component of the q-axis intermediate state variable x8 of the MMC converter current inner loop, A3 represents the coefficient matrix of the MMC converter state variables, B3 represents the coefficient matrix of the MMC converter input variables, and U dc U represents the constant DC voltage, i.e., the DC voltage of the DRU converter transformer. dcref Indicates the conventional DC voltage U dc The voltage reference value, Q ref The power reference value represents the instantaneous reactive power of a low-frequency wind farm, where Q represents the instantaneous reactive power of the low-frequency wind farm, and i represents the instantaneous reactive power of the low-frequency wind farm. sd This represents the d-axis current on the grid side of the MMC converter. Indicates the reference value of the d-axis current on the grid side of the MMC converter, i sq This represents the q-axis current on the grid side of the MMC converter. U represents the reference value of the grid-side q-axis current of the MMC converter. sd U represents the grid-side d-axis voltage of the MMC converter. sq This represents the grid-side q-axis voltage of the MMC converter, V. sdThis represents the d-axis reference voltage on the grid side of the MMC converter, V. sq C represents the grid-side q-axis reference voltage of the MMC converter. eq U represents the equivalent capacitance of the MMC converter, N represents the number of bridge arm submodules of the MMC converter, and U represents the number of submodules of the bridge arm of the MMC converter. dc0 x represents the steady-state DC voltage value of the MMC converter. PLL u represents the intermediate state variable of the phase-locked loop. sq θ represents the grid-side q-axis voltage of the MMC converter. PLL This represents the phase output of the phase-locked loop, ω represents the angular frequency, and K... iPLL K represents the integral gain coefficient of the phase-locked loop. pPLL This represents the proportional gain coefficient of the phase-locked loop.

[0038] Furthermore, the dynamic model of the wind farm turbine-side converter includes:

[0039]

[0040] Where x9 represents the intermediate state variable of the DC capacitor voltage of the machine-side converter, x 10 x represents the intermediate state variable of the AC voltage of the machine-side converter. 11 The x represents the intermediate state variable on the d-axis of the inner loop of the converter current on the machine side. 12 u represents the intermediate state variable on the q-axis of the inner loop of the converter current on the machine side. dc This indicates the DC capacitor voltage of the machine-side converter. U represents the reference value of the DC capacitor voltage of the machine-side converter. ac_M This indicates the AC voltage of the machine-side converter. Q represents the reference value of the AC voltage of the machine-side converter. M Indicates the reactive power of the machine-side converter. Indicates the reference value of reactive power of the machine-side converter, i d_M This indicates the d-axis current of the machine-side converter. Indicates the reference value of the d-axis current of the machine-side converter, i q_M This indicates the q-axis current of the machine-side converter. This indicates the reference value for the q-axis current of the machine-side converter.

[0041] Furthermore, the whole-system small-signal model includes:

[0042]

[0043]

[0044] Where Δx represents the state variables of the low-frequency offshore wind power system, A represents the state matrix of the low-frequency offshore wind power system, B represents the input matrix of the low-frequency offshore wind power system, and Δu represents the input variables of the low-frequency offshore wind power system. pll_G Δθ represents the small-signal disturbance component of the intermediate state variable of the wind farm turbine-side phase-locked loop. pll_G Δi represents the small-signal disturbance component of the phase output of the wind farm turbine-side phase-locked loop. d Δi represents the small-signal disturbance component of the d-axis current of the wind farm converter. q Δu represents the small-signal disturbance component of the q-axis current of the wind farm converter. dc Δω2 represents the small-signal disturbance component of the bridge arm submodule capacitor voltage of the MMC converter, Δω2 represents the small-signal disturbance component of the angular frequency control of the wind farm grid-side converter, Δθ represents the small-signal disturbance component of the angular frequency output reference angle in the active-frequency outer loop control loop, and Δi represents the small-signal disturbance component of the angular frequency output reference angle in the active-frequency outer loop control loop. d_M Δi represents the small-signal disturbance component of the d-axis current of the wind farm turbine-side converter. q_M Δx represents the small-signal disturbance component of the q-axis current of the wind farm generator-side converter. PLL Δθ represents the small-signal perturbation component of the intermediate state variable of the phase loop. PLL Δi represents the small-signal perturbation component of the phase output of the phase-locked loop. sd Indicates the d-axis current i on the grid side of the MMC converter. sd Small signal disturbance component, Δi sq Indicates the grid-side q-axis current i of the MMC converter. sq Small signal disturbance component, ΔU d_M ΔU represents the small-signal disturbance component of the d-axis voltage at the grid connection point of the wind farm's turbine-side converter. q_M ΔV represents the small-signal disturbance component of the q-axis voltage at the grid connection point of the wind farm's turbine-side converter. d_M ΔV represents the small-signal disturbance component of the d-axis reference voltage at the grid connection point of the wind farm's converter. q_M Δu represents the small-signal disturbance component of the q-axis reference voltage at the grid connection point of the wind farm's converter. sd Δu represents the small-signal disturbance component of the d-axis voltage at the grid connection point of the wind farm. sq Δv represents the small-signal disturbance component of the q-axis voltage at the grid connection point of the wind farm. sd Δv represents the small-signal disturbance component of the d-axis reference voltage at the grid connection point of the wind farm. sq ΔU represents the small-signal disturbance component of the q-axis reference voltage at the grid connection point of the wind farm. sd ΔU represents the small-signal disturbance component of the d-axis voltage on the MMC power frequency side. sq ΔV represents the small-signal disturbance component of the q-axis voltage on the MMC power frequency side. sdΔV represents the small-signal disturbance component of the d-axis reference voltage on the MMC power frequency side. sq This represents the small-signal disturbance component of the q-axis reference voltage on the MMC power frequency side.

[0045] Based on the above method embodiments, the present invention provides corresponding device embodiments, including: an electrical data acquisition module, a dynamic model construction module, a dynamic model integration module, a model solving module, and a system stability analysis module;

[0046] The electrical data acquisition module is used to acquire the MMC power frequency side voltage and DRU low frequency side current of the DRU-MMC converter, as well as the grid connection point current, grid connection point voltage and turbine-side converter grid connection point voltage of the wind farm.

[0047] The dynamic model building module is used to construct wind turbine system models, DC network line models, and MMC converter station models based on the MMC power frequency side voltage and DRU low frequency side current of the DRU-MMC converter, as well as the grid connection point current, grid connection point voltage, and turbine-side converter grid connection point voltage of the wind farm. The wind turbine system model includes: dynamic models of the wind turbine grid-side converter, dynamic models of the wind turbine converter DC link, and dynamic models of the wind turbine side converter. The DC network line model includes: dynamic models of the low frequency line and the DRU. The MMC converter station model includes: dynamic models of the MMC, dynamic models of the MMC DC link, and dynamic models of the MMC power frequency phase-locked loop.

[0048] The dynamic model integration module is used to linearize the stable operating points of the wind turbine system model, DC network line model, and MMC converter station model to obtain the whole system small-signal model of the low-frequency offshore wind power system.

[0049] The model solving module is used to solve the small-signal model of the entire system to obtain the state matrix of the low-frequency offshore wind power system.

[0050] The system stability analysis module is used to determine the stability of low-frequency offshore wind power systems based on the state matrix.

[0051] Furthermore, the stability analysis device for low-frequency offshore wind power systems also includes: an analysis and control module;

[0052] The analysis and control module includes: an oscillation mode analysis unit, a participating variable analysis unit, and a system control unit;

[0053] The oscillation mode analysis unit is used to determine the oscillation modes of a low-frequency offshore wind power system based on the state matrix under unstable conditions.

[0054] The participation variable analysis unit is used to perform participation factor analysis on each oscillation mode to determine the corresponding oscillation participation variables;

[0055] The system control unit is used to regulate the low-frequency offshore wind power system based on the oscillation participation variables.

[0056] Compared with the prior art, the beneficial effects of this embodiment are as follows:

[0057] This invention obtains the MMC power frequency side voltage and DRU low frequency side current of the DRU-MMC converter, as well as the grid connection point current, grid connection point voltage, and turbine-side converter grid connection point voltage of the wind farm. Based on these, a wind turbine system model, a DC network line model, and an MMC converter station model are constructed. The wind turbine system model includes: a dynamic model of the wind turbine grid-side converter, a dynamic model of the wind turbine converter DC link, and a dynamic model of the wind turbine-side converter. The DC network line model includes: a low-frequency line dynamic model and a DRU dynamic model. The MMC converter station model includes: an MMC dynamic model, an MMC DC link dynamic model, and an MMC power frequency phase-locked loop dynamic model. These nonlinear models realistically reflect the behavior of the low-frequency offshore wind power system. Next, the stable operating points of the wind turbine system model, DC network line model, and MMC converter station model are linearized, thereby connecting them through their input-output relationships to form a complete system model, namely, the full-system small-signal model of the low-frequency offshore wind power system. The state matrix is ​​obtained by solving the small-signal model, and then the stability of the low-frequency offshore wind power system is determined based on the state matrix.

[0058] In summary, this invention constructs a sub-model containing various nonlinear elements and linearizes it at the stable operating point to obtain a small-signal model. This not only accurately captures the nonlinear nature of the system but also achieves precise linearization analysis, thereby solving the problem of large errors in traditional time-domain simulation linearization models. It enables accurate assessment of the dynamic stability of low-frequency offshore wind power systems containing a large number of nonlinear elements. Attached Figure Description

[0059] Figure 1 This is a flowchart illustrating a method for stability analysis of low-frequency offshore wind power systems according to an embodiment of the present invention;

[0060] Figure 2 This is an equivalent topology diagram of a low-frequency submarine cable π-type equivalent circuit model provided in an embodiment of the present invention;

[0061] Figure 3 This is an equivalent topology diagram of the DRU dynamic model provided in an embodiment of the present invention;

[0062] Figure 4 This is an equivalent topology diagram of the equivalent model of the DC link of an MMC converter provided in an embodiment of the present invention;

[0063] Figure 5 This is an equivalent topology diagram of the dynamic characteristic closed-loop structure of the MMC power frequency side phase-locked loop provided in an embodiment of the present invention;

[0064] Figure 6 This is a schematic diagram of the structure of a low-frequency offshore wind power system stability analysis device provided in an embodiment of the present invention. Detailed Implementation

[0065] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0066] In the description of this invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated.

[0067] like Figure 1 As shown, in order to solve the problem of large errors in traditional time-domain simulation linearization models, an embodiment of the present invention provides a stability analysis method for low-frequency offshore wind power systems, which includes at least the following steps:

[0068] Step S1: Obtain the MMC power frequency side voltage and DRU low frequency side current of the DRU-MMC converter, as well as the grid connection point current, grid connection point voltage and turbine-side converter grid connection point voltage of the wind farm;

[0069] For step S1, the MMC power frequency side voltage and DRU low frequency side current of the DRU-MMC converter, as well as the grid connection point current, grid connection point voltage and turbine-side converter grid connection point voltage of the wind farm are obtained through various electrical sensors.

[0070] The aforementioned MMC power frequency side voltage includes the MMC power frequency side d-axis voltage U. sd MMC power frequency side q-axis voltage U sq MMC power frequency side d-axis reference voltage V sd and MMC power frequency side q-axis reference voltage V sq ;

[0071] The low-frequency side current of the DRU includes the d-axis current i of the low-frequency side of the DRU. md and the low-frequency side q-axis current i of the DRU mq ;

[0072] The grid connection point current of a wind farm includes the d-axis current i at the wind farm's grid connection point. d1 And the q-axis current i at the grid connection point of the wind farm q1 ;

[0073] The grid connection point voltage of a wind farm includes the d-axis voltage u at the wind farm's grid connection point.sd q-axis voltage u at the grid connection point of the wind farm sq d-axis reference voltage v at the grid connection point of the wind farm sd And the q-axis reference voltage v at the grid connection point of the wind farm sq ;

[0074] The grid connection point voltage of the wind farm's generator-side converter includes the d-axis voltage U of the wind farm's generator-side converter at the grid connection point. d_M q-axis voltage U at the grid connection point of the wind farm's turbine-side converter q_M d-axis reference voltage V at the grid connection point of the wind farm's turbine-side converter d_M And the q-axis reference voltage V at the grid connection point of the wind farm generator-side converter q_M .

[0075] The values ​​of each electrical quantity of the system during steady-state operation are obtained through simulation or actual measurement. The deviation of each electrical quantity from its steady-state value is calculated. This deviation is regarded as the small-signal disturbance component of the corresponding electrical quantity and is used as the input variable for subsequent system stability analysis, as shown in Table 1.

[0076] Table 1 Input variables of the system small-signal model

[0077]

[0078] Step S2: Based on the MMC power frequency side voltage and DRU low frequency side current of the DRU-MMC converter, as well as the grid connection point current, grid connection point voltage, and turbine-side converter grid connection point voltage of the wind farm, construct the wind turbine system model, DC network line model, and MMC converter station model; the wind turbine system model includes: the dynamic model of the wind turbine grid-side converter, the dynamic model of the wind turbine converter DC link, and the dynamic model of the wind turbine side converter; the DC network line model includes: the low frequency line dynamic model and the DRU dynamic model; the MMC converter station model includes: the MMC dynamic model, the MMC DC link dynamic model, and the MMC power frequency phase-locked loop dynamic model;

[0079] For step S2, based on the MMC power frequency side voltage and DRU low frequency side current of the DRU-MMC converter obtained in step S1, as well as the grid connection point current, grid connection point voltage and turbine-side converter grid connection point voltage of the wind farm, a wind turbine system model, a DC network line model and an MMC converter station model are constructed. The wind turbine system model includes a dynamic model of the wind turbine grid-side converter, a dynamic model of the wind turbine converter DC link, and a dynamic model of the wind turbine side converter; the DC network line model includes a low frequency line dynamic model and a DRU dynamic model; and the MMC converter station model includes an MMC dynamic model, an MMC DC link dynamic model and an MMC power frequency phase-locked loop dynamic model.

[0080] The following sections will provide a detailed explanation of the construction process for each of the following dynamic models: wind turbine grid-side converter dynamic model, wind turbine converter DC link dynamic model, wind turbine-side converter dynamic model, low-frequency line dynamic model, DRU dynamic model, MMC dynamic model, MMC DC link dynamic model, and MMC power frequency phase-locked loop dynamic model.

[0081] 1) Regarding the dynamic model of the wind turbine grid-side converter:

[0082] First, a dynamic model of the wind farm on the low-frequency side is derived to obtain a small-signal model for power calculation. The small-signal model can reflect the dynamic characteristics of the wind farm under small disturbances. On this basis, the outer loop control of the virtual synchronous generator and the dual inner loop control of voltage and current are derived to obtain the dynamic model of the grid-side converter. At the same time, the generator-side converter and the aerodynamic part of the wind turbine are equivalent to controlled current sources to simulate the wind speed change and power change of the wind farm, and the dynamic model of the generator-side converter and the aerodynamic part is derived.

[0083] Specifically, the instantaneous power calculation module for low-frequency wind farms is constructed using the following expression:

[0084]

[0085] Where P represents the instantaneous active power of the low-frequency wind farm, Q represents the instantaneous reactive power of the low-frequency wind farm, and i d i represents the d-axis current of the grid-side converter of the wind turbine. q U represents the q-axis current of the grid-side converter of the wind turbine. d U represents the d-axis voltage of the grid-side converter of the wind turbine. q This represents the q-axis voltage of the grid-side converter of the wind turbine.

[0086] Further small-signal perturbation analysis yields the following small-signal model for instantaneous power calculation:

[0087]

[0088] Where ΔP represents the small-signal disturbance component of the instantaneous active power of the low-frequency wind farm, ΔQ represents the small-signal disturbance component of the instantaneous reactive power of the low-frequency wind farm, and Δu d The voltage u of the grid-side converter of the wind turbine represents the d-axis voltage. d Small signal disturbance component, Δu q U represents the q-axis voltage u of the wind turbine grid-side converter. q Small signal disturbance component, Δi d Indicates the d-axis current i of the wind turbine grid-side converter d Small signal disturbance component, Δi q i represents the q-axis current i of the grid-side converter of the wind turbine. q Small signal disturbance components.

[0089] For the virtual synchronous generator control loop in the power outer loop, the grid-side network construction control dynamic model is constructed as follows:

[0090]

[0091] Small-signal perturbation analysis was performed on it, and its small-signal model is as follows:

[0092]

[0093] Where J represents the virtual inertia in the network control loop, ω represents the angular frequency, and P m The mechanical power of the wind turbine is represented by ω0, which, in this invention, is assumed to be lossless and equal to the power of the wind turbine converter on the machine side. ω0 represents the rated angular frequency. e Let represent the electromagnetic power of the wind turbine, D represent the virtual damping in the grid control loop, θ represent the reference angle of the angular frequency output in the active-frequency outer loop control loop, Δω represent the small disturbance of the angular frequency in the grid control loop with a steady-state value of 0, ΔP represent the small disturbance of the active power in the grid control loop with a steady-state value of 0, ΔP is an intermediate variable that needs to be substituted into the dynamic equation of the power calculation module for simplification, and Δθ represent the small disturbance of the reference angle of the angular frequency output in the active-frequency outer loop control loop.

[0094] The mathematical equation for the reactive voltage excitation control loop can be described as follows:

[0095] E=E0+∫k v (Q ref -Q e )dt; (5)

[0096] Where E represents the outer loop electromotive force of the converter virtual synchronous generator control, E0 represents the rated value of the outer loop electromotive force of the converter virtual synchronous generator control, and k v This represents the voltage droop factor in the reactive voltage excitation circuit. In this embodiment, k v =1, Q ref Q represents the converter's reactive power reference value. e This indicates the reactive power measurement value of the converter.

[0097] Based on the mathematical equations for reactive voltage excitation control described above, a small-signal linearization process is performed on them. The linearized small-signal model is as follows:

[0098] ΔE=k q ΔQ+k v ΔU; (6)

[0099] Where ΔE represents the small-signal disturbance component of the outer loop electromotive force of the converter virtual synchronous generator control, kq ΔQ represents the droop coefficient of reactive power in the reactive voltage excitation circuit, ΔQ represents the small-signal disturbance component of the reactive power of the converter, and ΔU represents the small-signal disturbance component of the converter terminal voltage.

[0100] Based on the aforementioned small-signal model of reactive voltage excitation control, further analysis is conducted by incorporating the voltage and current dual inner-loop control loop. To reduce the order of the control, the virtual impedance control loop is ignored when establishing the small-signal model of the grid-connected wind farm. It is assumed that the E∠θ output from the grid-connected power outer loop control, after dq transformation, is directly output as the dq-axis voltage reference value of the voltage control loop. and The specific relationships are as follows:

[0101]

[0102] in, Indicates the d-axis voltage reference value of the voltage control loop. Small signal disturbance components, Indicates the q-axis voltage reference value of the voltage control loop. Small signal disturbance components.

[0103] For the voltage and current dual inner loop control loop, for ease of analysis, the intermediate state variables of the voltage loop control are defined as x1 and x2, and the intermediate state variables of the current loop control are defined as x3 and x4, respectively, to describe the dynamic process of the voltage control loop and the current control loop. The specific relationships are as follows:

[0104]

[0105] Where x1 represents the intermediate state variable of the voltage control loop along the d-axis, x2 represents the intermediate state variable of the voltage control loop along the q-axis, x3 represents the intermediate state variable of the current control loop along the d-axis, and x4 represents the intermediate state variable of the current control loop along the q-axis.

[0106] Furthermore, combining the proposed voltage loop control strategy and substituting the intermediate state variables, the voltage loop equation is obtained as follows:

[0107]

[0108] in, This indicates the reference value of the d-axis current in the current control loop. k represents the reference value of the q-axis current in the current control loop. p1 and k i1 These represent the d-axis proportional and integral parameters of the current control loop, respectively, k p2 and k i2 These represent the q-axis proportional and integral parameters of the current control loop, respectively. This indicates the reference value of the d-axis voltage of the voltage control loop. This indicates the reference value for the q-axis voltage of the voltage control loop.

[0109] For the current loop, the output of the voltage loop control equation and and the actual measured value of current i d and i q The difference is used as the PI input, introducing a decoupling component, and finally outputting the voltage reference value V of the grid-side converter. d and V q The specific formula is as follows:

[0110]

[0111] Among them, V d This represents the d-axis voltage reference value of the grid-side converter, V. q This represents the reference value of the q-axis voltage of the grid-side converter, k. p3 and k i3 These represent the d-axis proportional and integral parameters of the voltage control loop, respectively, k p4 and k i4 These represent the q-axis proportional and integral parameters of the voltage control loop, respectively, and L represents the converter inductance.

[0112] Further integrating the dynamic relationships between the voltage control loop and the current control loop yields a dynamic model of the wind turbine grid-side converter. In a preferred embodiment, the dynamic model of the wind turbine grid-side converter includes:

[0113]

[0114] Where Δx1 represents the small-signal disturbance component of the d-axis intermediate state variable x1 of the voltage control loop, Δx2 represents the small-signal disturbance component of the q-axis intermediate state variable x2 of the voltage control loop, Δx3 represents the small-signal disturbance component of the d-axis intermediate state variable x3 of the current control loop, Δx4 represents the small-signal disturbance component of the q-axis intermediate state variable x4 of the current control loop, A1 represents the coefficient matrix of the wind farm state variables, B1 represents the coefficient matrix of the wind farm input variables, and i d i represents the d-axis current of the grid-side converter of the wind turbine. q U represents the q-axis current of the grid-side converter of the wind turbine. d U represents the d-axis voltage of the grid-side converter of the wind turbine. q This represents the q-axis voltage of the grid-side converter of the wind turbine, V. d This indicates the reference value of the d-axis voltage of the wind turbine grid-side converter, V. q This indicates the reference value of the q-axis voltage of the grid-side converter of the wind turbine.

[0115] Specifically, the coefficient matrix A1 of the wind farm state variables is as follows:

[0116]

[0117] The coefficient matrix B1 of the wind farm input variables is as follows:

[0118]

[0119] 2) Regarding the dynamic model of the DC link in the wind turbine converter:

[0120] To simplify the analysis and achieve order reduction, the turbine-side converter and aerodynamic components of the wind farm are equated as controlled current sources to simulate the characteristics of wind speed variations and power fluctuations in the wind farm. The dynamic equations for the turbine-side converter and aerodynamic components are as follows:

[0121]

[0122] Among them, u dc P represents the DC capacitor voltage of the grid-side converter of the wind turbine. m P represents the power output of the wind turbine converter on the machine side. s C represents the grid-side power of the wind turbine converter. dc U represents the DC capacitance value of the grid-side converter of the wind turbine. wdc0 This indicates the rated DC capacitor voltage of the grid-side converter of the wind turbine.

[0123] Furthermore, small-signal disturbance analysis was performed on it to obtain the dynamic equation of the DC link of the wind turbine converter:

[0124]

[0125] Where, Δu dc Indicates the DC capacitor voltage u of the wind turbine grid-side converter. dc Small signal disturbance component, ΔP m Indicates the power P of the wind turbine converter on the machine side. m Small signal disturbance component, Δu d The voltage u of the grid-side converter of the wind turbine represents the d-axis voltage. d Small signal disturbance component, Δu q U represents the q-axis voltage u of the wind turbine grid-side converter. q Small signal disturbance component, Δi d Indicates the d-axis current i of the wind turbine grid-side converter d Small signal disturbance component, Δi q i represents the q-axis current i of the grid-side converter of the wind turbine. q Small signal disturbance components.

[0126] Meanwhile, the voltage and current relationship at the grid connection interface of the wind farm is analyzed. The specific voltage and current relationship is as follows:

[0127]

[0128] Where R1 represents the equivalent resistance of the wind turbine converter connecting reactor, and L1 represents the equivalent inductance of the wind turbine converter connecting reactor.

[0129] Furthermore, by integrating the dynamic characteristics of the DC link and the AC interface, a dynamic model of the DC link of the wind turbine converter is obtained. In a preferred embodiment, the dynamic model of the DC link of the wind turbine converter includes:

[0130]

[0131] Where, Δi d Indicates the d-axis current i of the wind turbine grid-side converter d Small signal disturbance component, Δi q i represents the q-axis current i of the grid-side converter of the wind turbine. q Small signal disturbance component, ω represents angular frequency, ΔV d This indicates the reference value V of the d-axis voltage of the wind turbine grid-side converter. d Small signal disturbance component, ΔV q V represents the reference value of the q-axis voltage of the wind turbine grid-side converter. q Small signal disturbance component, Δu d The voltage u of the grid-side converter of the wind turbine represents the d-axis voltage. d Small signal disturbance component, Δu q U represents the q-axis voltage u of the wind turbine grid-side converter. q Small signal disturbance components.

[0132] 3) Regarding the dynamic model of low-frequency lines:

[0133] In this embodiment, the low-frequency submarine cable adopts a π-type equivalent circuit model, and the equivalent topology is as follows: Figure 2 As shown. Based on the equivalent topology diagram, and through Kirchhoff's Voltage Law (KVL) and Current Law (KCL), the mathematical model of the equivalent circuit of the low-frequency submarine cable is derived as follows:

[0134]

[0135] Among them, u 1a u 1b and u 1c R represents the a-phase voltage, b-phase voltage, and c-phase voltage at the receiving end of the equivalent low-frequency submarine cable. line i represents the equivalent resistance of the equivalent circuit of a low-frequency submarine cable. 1a i 1b and i 1c Let i represent the a-phase current, b-phase current, and c-phase current at the receiving end of the equivalent low-frequency submarine cable. la i lb and i lcL represents the a-phase current, b-phase current, and c-phase current at the equivalent line sending end of the low-frequency submarine cable after passing through the grounding node. line i represents the equivalent inductance of the equivalent circuit of a low-frequency submarine cable. ma i mb and i mc These represent the phase a, phase b, and phase c currents at the equivalent line sending end of the low-frequency submarine cable, respectively. ma u mb and u mc These represent the phase a, phase b, and phase c voltages at the equivalent line sending end of the low-frequency submarine cable, respectively. line This represents the equivalent capacitance of the equivalent circuit of a low-frequency submarine cable.

[0136] Its corresponding dynamic equation is:

[0137]

[0138] Among them, u d1 This represents the d-axis voltage on the low-frequency submarine cable machine side, u q1 Indicates the q-axis voltage on the low-frequency submarine cable machine side, i d1 This represents the d-axis current on the low-frequency submarine cable machine side, i.e., the d-axis current at the wind farm grid connection point. q1 This represents the q-axis current on the low-frequency submarine cable machine side, i.e., the q-axis current at the wind farm grid connection point. ld i represents the d-axis inductance current on the low-frequency submarine cable machine side. lq This represents the q-axis inductor current on the low-frequency submarine cable machine side, ω1 represents the angular frequency of the low-frequency submarine cable, and u md U represents the d-axis voltage on the low-frequency submarine cable network side. mq Indicates the q-axis voltage on the low-frequency submarine cable network side, i md This represents the d-axis current on the low-frequency submarine cable network side, i.e., the d-axis current on the low-frequency side of the DRU. mq This represents the q-axis current on the low-frequency submarine cable network side, i.e., the q-axis current on the low-frequency side of the DRU.

[0139] After processing, small-signal disturbance analysis is performed to obtain a low-frequency line dynamic model. In a preferred embodiment, the low-frequency line dynamic model includes:

[0140]

[0141] Among them, u d1 This represents the d-axis voltage on the low-frequency submarine cable machine side, Δu. d1 Indicates the d-axis voltage u on the low-frequency submarine cable machine side. d1 Small signal perturbation component, u q1 This represents the q-axis voltage on the low-frequency submarine cable machine side, Δu q1 Indicates the q-axis voltage u on the low-frequency submarine cable machine side. q1 Small signal disturbance component, Δu mdIndicates the d-axis voltage u on the low-frequency submarine cable network side. md Small signal disturbance component, Δu mq Indicates the q-axis voltage u on the low-frequency submarine cable network side. mq Small signal disturbance component, Δi ld Indicates the d-axis inductor current i on the low-frequency submarine cable machine side. ld Small signal disturbance component, Δi lq Indicates the q-axis inductor current i on the low-frequency submarine cable machine side. lq The small signal disturbance component, A2 represents the coefficient matrix of the low-frequency submarine cable state variables, and B2 and C2 both represent the coefficient matrices of the low-frequency submarine cable input variables, i d1 Δi represents the d-axis current at the grid connection point of the wind farm. d1 The d-axis current i at the grid connection point of the wind farm is represented by... d1 The small signal perturbation component, i q1 Δi represents the q-axis current at the grid connection point of the wind farm. q1 i represents the q-axis current at the grid connection point of the wind farm. q1 Small signal disturbance component, Δi md Indicates the d-axis current i on the low-frequency side of the DRU md Small signal disturbance component, Δi mq Indicates the q-axis current i on the low-frequency side of the DRU mq The small-signal perturbation component, Δω represents the small-signal perturbation component with angular frequency ω.

[0142] Specifically, the coefficient matrix A2 of the low-frequency submarine cable state variables is as follows:

[0143]

[0144] The coefficient matrices B2 and C2 of the low-frequency submarine cable input variables are as follows:

[0145]

[0146] 4) Regarding the DRU dynamic model:

[0147] Ignoring power transmission losses and considering only the DC component on the DC side and the fundamental frequency component on the low-frequency side, its mathematical model can be equivalent to a combination of a low-frequency current source and a controlled voltage source on the DC side. This equivalent method simplifies the complex power electronic topology of the DRU and facilitates dynamic characteristic analysis. The corresponding equivalent topology diagram is shown below. Figure 3 As shown.

[0148] At this point, the magnitude of the equivalent current source on the low-frequency side is determined by the output power and bus voltage on the wind farm side, while the magnitude of the equivalent controlled voltage source on the DC side is determined by the bus voltage on the low-frequency side and the DC current on the DC side.

[0149]

[0150] Among them, V dru U represents the DC side voltage of the DRU converter valve. AC L represents the effective value of the line voltage on the valve side of the converter transformer of the DRU converter valve. B I represents the leakage inductance of the converter transformer. dc L represents direct current. dc This represents the DC inductance of the DRU converter transformer, k represents the commutation ratio, and i dc This represents the DC current of the DRU converter transformer.

[0151] Furthermore, small-signal perturbation analysis is performed on it to obtain the DRU dynamic model. In a preferred embodiment, the DRU dynamic model includes:

[0152]

[0153] Among them, i dc Δi represents the DC current of the DRU converter transformer. dc i represents the DC current of the DRU converter transformer. dc Small signal disturbance component, L dc Indicates smoothing inductance, ΔU dc U represents the DC voltage of the DRU converter transformer. dc Small signal disturbance components.

[0154] 5) Regarding the MMC dynamic model:

[0155] The power frequency side MMC uses a standard DC voltage (i.e., the DC voltage U of the DRU converter transformer). dc To facilitate the analysis and differentiation of the state variables of the wind farm, intermediate state variables x5 and x6 of the power outer loop and intermediate state variables x7 and x8 of the current inner loop are introduced to describe the dynamic characteristics of the voltage control loop and the current control loop. The dynamic equations of the power outer loop and the current inner loop are as follows:

[0156]

[0157] Where x5 represents the intermediate state variable of the d-axis of the power outer loop, x6 represents the intermediate state variable of the q-axis of the power outer loop, x7 represents the intermediate state variable of the d-axis of the current inner loop, and x8 represents the intermediate state variable of the q-axis of the current inner loop. dcref Indicates the conventional DC voltage U dc The voltage reference value, Q ref The power reference value represents the instantaneous reactive power of a low-frequency wind farm, where Q represents the instantaneous reactive power of the low-frequency wind farm, and i represents the instantaneous reactive power of the low-frequency wind farm. sd This represents the d-axis current on the grid side of the MMC converter. This represents the current reference value for the d-axis current on the grid side of the MMC converter, i. sq This represents the q-axis current on the grid side of the MMC converter. This represents the reference value for the q-axis current on the grid side of the MMC converter.

[0158] Combining the control strategy and substituting the intermediate state variables, the voltage loop equation is obtained as follows:

[0159]

[0160] Where, k p5 and k i5 These represent the d-axis proportional and integral parameters of the MMC DC voltage control loop, respectively, k p6 and k i6 These represent the proportional and integral parameters of the q-axis of the reactive power control loop, respectively.

[0161] The current loop equation is the output of the voltage loop equation. and and actual measured current i sd and i sq The difference is the PI input, and the final output voltage reference value V sd and V sq for:

[0162]

[0163] Among them, V sd This indicates the reference value of the d-axis voltage on the grid side of the MMC converter, V. sq This represents the reference value of the grid-side q-axis voltage of the MMC converter, k. p7 and k i7 Let k represent the d-axis proportional and integral parameters of the MMC current inner loop, respectively. p8 and k i8 U represents the q-axis proportional and integral parameters of the MMC current inner loop, respectively. sd U represents the grid-side d-axis voltage of the MMC converter. sq This represents the grid-side q-axis voltage of the MMC converter.

[0164] Combining the above formula, the MMC dynamic model is obtained. In a preferred embodiment, the MMC dynamic model includes:

[0165]

[0166] Where Δx5 represents the small-signal disturbance component of the d-axis intermediate state variable x5 of the power outer loop, Δx6 represents the small-signal disturbance component of the q-axis intermediate state variable x6 of the power outer loop, Δx7 represents the small-signal disturbance component of the d-axis intermediate state variable x7 of the current inner loop, Δx8 represents the small-signal disturbance component of the q-axis intermediate state variable x8 of the current inner loop, A3 represents the coefficient matrix of the MMC converter state variables, B3 represents the coefficient matrix of the MMC converter input variables, and i sd i represents the d-axis current on the grid side of the MMC converter. sq U represents the grid-side q-axis current of the MMC converter. sd U represents the grid-side d-axis voltage of the MMC converter. sq This represents the grid-side q-axis voltage of the MMC converter, V. sd This indicates the reference value of the d-axis voltage on the grid side of the MMC converter, V. sq This indicates the reference value of the grid-side q-axis voltage of the MMC converter.

[0167] Specifically, the coefficient matrix A3 of the MMC converter state variables is as follows:

[0168]

[0169] The coefficient matrix B3 of the MMC converter input variables is as follows:

[0170]

[0171] Similarly, the voltage and current relationship on the power frequency side of the MMC valve is analyzed, and the specific voltage and current relationship is as follows:

[0172]

[0173] After simplification, the voltage-current relationship is obtained in matrix form:

[0174]

[0175] It should be noted that the DC link of an MMC converter originally involves complex arm dynamics, interphase circulating currents, and multi-component interactions. To reduce the order of these interactions and simplify the analysis of the dynamic characteristics between MMC converter arms, the interphase circulating current characteristics are ignored in the derivation. This means that the DC characteristics of each phase arm are assumed to be consistent, with no interphase circulating current interference. Simultaneously, the influence of differential-mode and common-mode components on the control system is ignored; only the fundamental frequency dynamics on the DC side are considered, simplifying the multi-component coupling analysis. For example... Figure 4 The diagram shows the equivalent topology of the DC link of an MMC converter. A controlled current source simulates the power interaction between the AC and DC sides of the MMC, with its current magnitude determined by the power control characteristics of the AC side. The equivalent capacitance C... eq It incorporates the equivalent characteristics of the MMC bridge arm capacitances to describe the DC voltage u.DC The dynamic changes.

[0176] 6) Regarding the dynamic model of the MMC DC link:

[0177] In an MMC converter, each bridge arm consists of N sub-modules connected in series, and each sub-module contains a capacitor. Under ideal operating conditions, it is assumed that the capacitor voltages of all sub-modules are balanced, i.e., the capacitor voltage of each sub-module is u. dc Since the N sub-modules of the bridge arm are connected in series, according to the property that the total voltage of a series circuit is equal to the sum of the voltages of each part, the total voltage of a single bridge arm is Nu. dc The DC voltage u of MMC DC The relationship can be derived from the voltages of both the upper and lower bridge arms:

[0178] u DC =Nu dc (34)

[0179] Among them, u DC This represents the DC voltage of the MMC converter, N represents the number of bridge arm submodules of the MMC converter, and u dc This represents the average capacitor voltage of the bridge arm submodule.

[0180] During the analysis, it was assumed that the MMC converter arms were symmetrical, meaning that the parameter settings and configurations of each submodule were identical. Based on the power balance principle, the following can be derived:

[0181]

[0182] Among them, C sm This indicates the capacitance value of the bridge arm submodule of the MMC converter.

[0183] Substituting equation (34) into equation (35), we obtain the equivalent capacitance C of the six arms of the MMC converter. eq :

[0184]

[0185] When the energy is balanced among the arms of the MMC converter, according to the law of power conservation, the MMC converter has the following power relationship:

[0186]

[0187] Wherein, ΔP MMC (t) represents the power difference of the MMC converter, P dc (t) represents the DC-side power of the MMC converter, P ac (t) represents the AC side power of the MMC converter, U dc0 i represents the steady-state value of the DC voltage of the MMC converter. DCThis represents the DC current of the MMC converter, and C represents the equivalent DC capacitance of the MMC converter.

[0188] Combining the above equations, we obtain the dynamic model of the MMC DC link. In a preferred embodiment, the dynamic model of the MMC DC link includes:

[0189]

[0190] Among them, C eq U represents the equivalent capacitance of the MMC converter, N represents the number of bridge arm submodules of the MMC converter, and U represents the number of submodules of the bridge arm of the MMC converter. dc0 This represents the steady-state DC voltage value of the MMC converter.

[0191] 7) Regarding the dynamic model of the MMC power frequency phase-locked loop:

[0192] like Figure 5 The diagram shows the equivalent topology of the closed-loop structure of the MMC power frequency side phase-locked loop. In actual operation, the system will utilize the phase angle θ output by the phase-locked loop. PLL Then, at this angle, the required voltage is decomposed into dq components to obtain the required dq-axis components; further, the calculated q-axis voltage components are... Input to PI control loop H PI_s In this case, maintain the reference value for setting the q-axis voltage component. The angular velocity ω of the phase-locked loop output can then be calculated. e Analysis shows that when ω e When constant, the q-axis voltage component When the value is always 0, the d-axis voltage component will be realized. and grid voltage v s The overlap of phase-locked loops (PLLs) enables the control system to synchronously track the specified grid voltage.

[0193] according to Figure 5 Based on the above analysis, the dynamic model of the MMC power frequency phase-locked loop is obtained. In a preferred embodiment, the dynamic model of the MMC power frequency phase-locked loop includes:

[0194]

[0195] Where, x PLL u represents the intermediate state variable of the phase-locked loop. sq θ represents the grid-side q-axis voltage of the MMC converter. PLL This represents the phase output of the phase-locked loop, ω represents the angular frequency, and K... iPLL K represents the integral gain coefficient of the phase-locked loop. pPLL This represents the proportional gain coefficient of the phase-locked loop.

[0196] 8) Regarding the dynamic model of the wind farm generator-side converter:

[0197] When establishing the dynamic model of the wind farm's generator-side converter, the dq-axis inner and outer loop control equations for constant DC voltage / reactive power control are involved. Since these equations contain integral terms, intermediate state variables x9 and x are introduced into the generator-side converter voltage outer loop to better handle these integral terms. 10 And the intermediate state variable x of the inner loop of the converter current on the machine side. 11 and x 12 .

[0198] In a preferred embodiment, the dynamic model of the wind farm turbine-side converter includes:

[0199]

[0200] Where x9 represents the intermediate state variable of the DC capacitor voltage of the machine-side converter, x 10 x represents the intermediate state variable of the AC voltage of the machine-side converter. 11 The x represents the intermediate state variable on the d-axis of the inner loop of the converter current on the machine side. 12 u represents the intermediate state variable on the q-axis of the inner loop of the converter current on the machine side. dc This indicates the DC capacitor voltage of the machine-side converter. U represents the reference value of the DC capacitor voltage of the machine-side converter. ac_M This indicates the AC voltage of the machine-side converter. Q represents the reference value of the AC voltage of the machine-side converter. M Indicates the reactive power of the machine-side converter. Indicates the reference value of reactive power of the machine-side converter, i d_M This indicates the d-axis current of the machine-side converter. Indicates the reference value of the d-axis current of the machine-side converter, i q_M This indicates the q-axis current of the machine-side converter. This indicates the reference value for the q-axis current of the machine-side converter.

[0201] Traditional linearization models often directly linearize the entire system when dealing with highly nonlinear components in power electronic systems, leading to significant approximation errors. This invention addresses this by constructing dynamic models for wind turbine grid-side converters, wind turbine converter DC links, wind farm generator-side converters, low-frequency lines, DRUs, MMCs, MMC DC links, and MMC power frequency phase-locked loops. First, it performs mechanistic-level nonlinear modeling of each key system component. Then, it processes each component individually using small-signal linearization, significantly reducing the errors caused by linearization approximation. This fundamentally improves the fitting accuracy of the linearization model to the actual system and effectively solves the problem of large errors caused by oversimplification of system component characteristics or coarse linearization processes in traditional time-domain simulation linearization models.

[0202] Step S3: Linearize the stable operating points of the wind turbine system model, DC network line model, and MMC converter station model to obtain the whole system small-signal model of the low-frequency offshore wind power system;

[0203] For step S3, based on the wind turbine system model, DC network line model and MMC converter station model constructed in step S2, the steady operating point (i.e., the steady-state condition of the system during normal operation) of these models is linearized. The state variables and input variables in each module model are decomposed into steady-state values ​​and small disturbance components. The nonlinear equations are then Taylor expanded at the steady operating point, and higher-order small terms are ignored, thus obtaining the linearized differential equations.

[0204] In a preferred embodiment, the system-wide small-signal model includes:

[0205]

[0206] Where Δx represents the state variables of the low-frequency offshore wind power system, A represents the state matrix of the low-frequency offshore wind power system, B represents the input matrix of the low-frequency offshore wind power system, and Δu represents the input variables of the low-frequency offshore wind power system. pll_G Δθ represents the small-signal disturbance component of the intermediate state variable of the wind farm turbine-side phase-locked loop. pll_G Δi represents the small-signal disturbance component of the phase output of the wind farm turbine-side phase-locked loop. d Δi represents the small-signal disturbance component of the d-axis current of the wind farm converter. q Δu represents the small-signal disturbance component of the q-axis current of the wind farm converter. dc Δω2 represents the small-signal disturbance component of the capacitor voltage of the bridge arm submodule of the MMC converter, Δω2 represents the small-signal disturbance component of the angular frequency of the converter grid control on the wind farm grid side, Δθ represents the small-signal disturbance component of the reference angle of the angular frequency output in the active-frequency outer loop control loop, and Δi represents the small-signal disturbance component of the reference angle of the angular frequency output in the active-frequency outer loop control loop. d_MΔi represents the small-signal disturbance component of the d-axis current of the wind farm turbine-side converter. q_M Δx represents the small-signal disturbance component of the q-axis current of the wind farm generator-side converter. PLL Δθ represents the small-signal perturbation component of the intermediate state variable of the phase loop. PLL Δi represents the small-signal perturbation component of the phase output of the phase-locked loop. sd Δi represents the small-signal disturbance component of the grid-side d-axis current of the MMC converter. sq Indicates the grid-side q-axis current i of the MMC converter. sq Small signal disturbance component, ΔU d_M ΔU represents the small-signal disturbance component of the d-axis voltage at the grid connection point of the wind farm's turbine-side converter. q_M ΔV represents the small-signal disturbance component of the q-axis voltage at the grid connection point of the wind farm's turbine-side converter. d_M ΔV represents the small-signal disturbance component of the d-axis reference voltage at the grid connection point of the wind farm's converter. q_M Δu represents the small-signal disturbance component of the q-axis reference voltage at the grid connection point of the wind farm's converter. sd Δu represents the small-signal disturbance component of the d-axis voltage at the grid connection point of the wind farm. sq Δv represents the small-signal disturbance component of the q-axis voltage at the grid connection point of the wind farm. sd Δv represents the small-signal disturbance component of the d-axis reference voltage at the grid connection point of the wind farm. sq ΔU represents the small-signal disturbance component of the q-axis reference voltage at the grid connection point of the wind farm. sd ΔU represents the small-signal disturbance component of the d-axis voltage on the MMC power frequency side. sq ΔV represents the small-signal disturbance component of the q-axis voltage on the MMC power frequency side. sd ΔV represents the small-signal disturbance component of the d-axis reference voltage on the MMC power frequency side. sq This represents the small-signal disturbance component of the q-axis reference voltage on the MMC power frequency side.

[0207] In this embodiment, the state matrix A of the low-frequency offshore wind power system is a 33*33 order state matrix, specifically as follows:

[0208]

[0209] The input matrix B of the low-frequency offshore wind power system is a 33*16 order input matrix, specifically as follows:

[0210]

[0211] Among them, the matrix element a in the state matrix A of the low-frequency offshore wind power system ijThe coupling coefficients between system state variables are represented by i = 1, 2, 3, ..., 33, j = 1, 2, 3, ..., 33. The values ​​reflect the dynamic interaction strength of the two state variables under small disturbances. The b in the input matrix B of the low-frequency offshore wind power system... uv The coefficients represent the influence of system input variables on state variables, u = 1, 2, 3, ..., 33, v = 1, 2, 3, ..., 16, and their values ​​reflect the strength of the effect of a certain input disturbance on a specific state variable.

[0212] The state variables of the small-signal model of the whole system are shown in Table 2 below.

[0213] Table 2 State variables of the small-signal model of the whole system

[0214]

[0215] Step S4: Solve the small-signal model of the entire system to obtain the state matrix of the low-frequency offshore wind power system;

[0216] For step S4, based on the whole system small-signal model of the low-frequency offshore wind power system constructed in step S3, combined with the input variables in Table 2 and the system parameters shown in Table 3, the eigenvalues ​​of the state matrix of the low-frequency offshore wind power system are obtained by using MATLAB function tools. These eigenvalues ​​can reflect the dynamic characteristics of the system under small disturbances, and provide a quantitative basis for the stability assessment and control strategy optimization of the low-frequency offshore wind power system.

[0217] Table 3 System parameters of low-frequency offshore wind power system

[0218]

[0219] Step S5: Determine the stability of the low-frequency offshore wind power system based on the state matrix.

[0220] In a preferred embodiment, determining the stability of a low-frequency offshore wind power system based on a state matrix includes:

[0221] Determine whether all eigenvalues ​​in the state matrix are less than 0;

[0222] If so, the low-frequency offshore wind power system is determined to be stable;

[0223] Otherwise, the low-frequency offshore wind power system is considered unstable.

[0224] It should be noted that in the small-signal model of the entire system In this model, Δx represents a small perturbation of the state variable. When there is no external input, i.e., Δu = 0, the small-signal model of the entire system becomes... The form of the solution is determined by the eigenvalues ​​of the state matrix A.

[0225] Suppose λ is an eigenvalue of A, and its corresponding eigenvector is r. Then the solution to the equation contains e. λt The components of r. If the real part of the eigenvalue λ is less than 0, then e λt The disturbance component will gradually disappear as time t increases, and the system can return to a steady state, i.e., the system is stable; if there exists an eigenvalue λ whose real part is greater than or equal to 0, then e λt The disturbance may increase or remain unchanged over time, and the disturbance may continue to amplify or persist. The system cannot return to a steady state, which means the system is unstable.

[0226] For step S5, the stability of the low-frequency offshore wind power system is determined by analyzing its eigenvalues ​​based on the state matrix of the low-frequency offshore wind power system obtained in step S4. Specifically, the stability is determined by checking whether all eigenvalues ​​of the state matrix are less than 0. If all eigenvalues ​​are less than 0, it indicates that the disturbance of the state variables will decay over time under small disturbances and eventually return to a steady state, thus the low-frequency offshore wind power system is determined to be stable. Conversely, if there are eigenvalues ​​not less than 0, it means that the disturbance will increase over time or continue to oscillate, and the system cannot maintain a steady state, thus the low-frequency offshore wind power system is determined to be unstable.

[0227] In a preferred embodiment, after determining the stability of the low-frequency offshore wind power system based on the state matrix, the method further includes:

[0228] Under unstable conditions of low-frequency offshore wind power systems, the oscillation modes of low-frequency offshore wind power systems are determined based on the state matrix.

[0229] Participation factor analysis was performed on each oscillation mode to determine the corresponding oscillation participation variables;

[0230] The low-frequency offshore wind power system is regulated based on the oscillation participation variables.

[0231] In one embodiment of the present invention, if the low-frequency offshore wind power system is determined to be unstable through step S5, further decompose all eigenvalues ​​of the state matrix, extract the imaginary part of each eigenvalue to calculate the oscillation frequency, and finally, classify the dynamic modes corresponding to all eigenvalues ​​by combining the numerical range of the oscillation frequency, so as to determine all the oscillation modes existing in the system. Taking the low-frequency offshore wind power system based on the DRU-MMC converter of the present invention as an example, as shown in Table 4, the above process analysis shows that it contains 8 oscillation modes, of which 2 belong to high-frequency oscillation modes and 6 belong to subsynchronous oscillation modes.

[0232] Table 4 Oscillation Modes of Low-Frequency Offshore Wind Power Systems Based on DRU-MMC Converters

[0233]

[0234]

[0235] Furthermore, after determining the oscillation modes of the system, the damping ratio can be used to further analyze the decay characteristics of the oscillations. Since the damping ratio reflects the decay rate of the oscillations, the larger the damping ratio, the faster the oscillation decays, and the less likely it is to affect the stability of the entire system. By combining the damping ratio data for each oscillation mode in Table 4, the potential impact of different oscillation modes on the system stability can be intuitively determined.

[0236] Based on the eigenvalues ​​corresponding to each oscillation mode, participation factor analysis is performed on the oscillation modes of the system to determine the oscillation participation variables of each oscillation mode, as shown in Table 5. These oscillation participation variables have a direct correspondence with the oscillation participation modules of the low-frequency offshore wind power system. Finally, based on the correspondence between the oscillation participation variables and the oscillation participation modules, the oscillation participation modules of the low-frequency offshore wind power system are targeted for regulation, such as optimizing the control strategy of the wind farm, adjusting the operating parameters of the DRU, or improving the modulation method of the MMC, in order to optimize the system oscillation characteristics and improve the overall stability.

[0237] Table 5 Oscillation modes and oscillation participants of the system

[0238]

[0239]

[0240] like Figure 6 As shown, based on the above method embodiments, corresponding apparatus embodiments are provided;

[0241] One embodiment of the present invention provides a stability analysis device for a low-frequency offshore wind power system, comprising: an electrical data acquisition module, a dynamic model construction module, a dynamic model integration module, a model solving module, and a system stability analysis module;

[0242] The electrical data acquisition module is used to acquire the MMC power frequency side voltage and DRU low frequency side current of the DRU-MMC converter, as well as the grid connection point current, grid connection point voltage and turbine-side converter grid connection point voltage of the wind farm.

[0243] The dynamic model building module is used to construct wind turbine system models, DC network line models, and MMC converter station models based on the MMC power frequency side voltage and DRU low frequency side current of the DRU-MMC converter, as well as the grid connection point current, grid connection point voltage, and turbine-side converter grid connection point voltage of the wind farm. The wind turbine system model includes: dynamic models of the wind turbine grid-side converter, dynamic models of the wind turbine converter DC link, and dynamic models of the wind turbine side converter. The DC network line model includes: dynamic models of the low frequency line and the DRU. The MMC converter station model includes: dynamic models of the MMC, dynamic models of the MMC DC link, and dynamic models of the MMC power frequency phase-locked loop.

[0244] The dynamic model integration module is used to linearize the stable operating points of the wind turbine system model, DC network line model, and MMC converter station model to obtain the whole system small-signal model of the low-frequency offshore wind power system.

[0245] The model solving module is used to solve the small-signal model of the entire system to obtain the state matrix of the low-frequency offshore wind power system.

[0246] The system stability analysis module is used to determine the stability of low-frequency offshore wind power systems based on the state matrix.

[0247] In a preferred embodiment, the low-frequency offshore wind power system stability analysis device further includes: an analysis and control module;

[0248] The analysis and control module includes: an oscillation mode analysis unit, a participating variable analysis unit, and a system control unit;

[0249] The oscillation mode analysis unit is used to determine the oscillation modes of a low-frequency offshore wind power system based on the state matrix under unstable conditions.

[0250] The participation variable analysis unit is used to perform participation factor analysis on each oscillation mode to determine the corresponding oscillation participation variables;

[0251] The system control unit is used to regulate the low-frequency offshore wind power system based on the oscillation participation variables.

[0252] It is understood that the above-described device embodiments correspond to the method embodiments of the present invention, and can implement the low-frequency offshore wind power system stability analysis method provided by any of the above-described method embodiments of the present invention.

[0253] It should be noted that the device embodiments described above are merely illustrative, and some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Furthermore, in the accompanying drawings of the device embodiments provided by this invention, the connection relationships between modules indicate that they have communication connections, which can specifically be implemented as one or more communication buses or signal lines. Those skilled in the art can understand and implement this without any creative effort.

[0254] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A stability analysis method for low-frequency offshore wind power systems, characterized in that, include: Obtain the MMC power frequency side voltage and DRU low frequency side current of the DRU-MMC converter, as well as the grid connection point current, grid connection point voltage and turbine-side converter grid connection point voltage of the wind farm; Based on the MMC power frequency side voltage and DRU low frequency side current of the DRU-MMC converter, as well as the grid connection point current, grid connection point voltage and the generator-side converter grid connection point voltage of the wind farm, a wind turbine system model, a DC network line model and an MMC converter station model are constructed. The wind turbine system model includes: a dynamic model of the wind turbine grid-side converter, a dynamic model of the wind turbine converter DC link, and a dynamic model of the wind turbine-side converter; the DC network line model includes: a dynamic model of the low-frequency line and a dynamic model of the DRU; the MMC converter station model includes: an MMC dynamic model, a dynamic model of the MMC DC link, and a dynamic model of the MMC power frequency phase-locked loop. Linearization is performed on the stable operating points of the wind turbine system model, DC network line model, and MMC converter station model to obtain the whole system small-signal model of the low-frequency offshore wind power system. Solving the small-signal model of the entire system yields the state matrix of the low-frequency offshore wind power system; The stability of low-frequency offshore wind power systems is determined based on the state matrix.

2. The stability analysis method for low-frequency offshore wind power systems according to claim 1, characterized in that, Based on the state matrix, the stability of the low-frequency offshore wind power system is determined, including: Determine whether all eigenvalues ​​in the state matrix are less than 0; If so, the low-frequency offshore wind power system is determined to be stable; Otherwise, the low-frequency offshore wind power system is considered unstable.

3. The stability analysis method for low-frequency offshore wind power systems according to claim 1, characterized in that, After determining the stability of the low-frequency offshore wind power system based on the state matrix, the following steps are also included: Under unstable conditions of low-frequency offshore wind power systems, the oscillation modes of low-frequency offshore wind power systems are determined based on the state matrix. Participation factor analysis was performed on each oscillation mode to determine the corresponding oscillation participation variables; The low-frequency offshore wind power system is regulated based on the oscillation participation variables.

4. The stability analysis method for low-frequency offshore wind power systems according to claim 1, characterized in that, The dynamic model of the wind turbine grid-side converter includes: The dynamic model of the DC link of the wind turbine converter includes: Where Δx1 represents the small-signal disturbance component of the d-axis intermediate state variable x1 of the wind turbine grid-side converter voltage control loop, Δx2 represents the small-signal disturbance component of the q-axis intermediate state variable x2 of the wind turbine grid-side converter voltage control loop, Δx3 represents the small-signal disturbance component of the d-axis intermediate state variable x3 of the wind turbine grid-side converter current control loop, Δx4 represents the small-signal disturbance component of the q-axis intermediate state variable x4 of the wind turbine grid-side converter current control loop, A1 represents the coefficient matrix of the wind farm state variables, B1 represents the coefficient matrix of the wind farm input variables, and i d This represents the d-axis current of the grid-side converter of the wind turbine. Indicates the d-axis current reference value of the wind turbine grid-side converter, i q This represents the q-axis current of the grid-side converter of the wind turbine. This indicates the reference value of the q-axis current of the wind turbine grid-side converter, u. d This represents the d-axis voltage of the grid-side converter of the wind turbine. This indicates the reference value of the d-axis voltage of the wind turbine grid-side converter, u. q This represents the q-axis voltage of the grid-side converter of the wind turbine. This indicates the reference value of the q-axis voltage of the wind turbine grid-side converter, V. d This indicates the reference value of the d-axis voltage of the wind turbine grid-side converter, V. q This represents the reference value of the q-axis voltage of the wind turbine grid-side converter, Δi. d Indicates the d-axis current i of the wind turbine grid-side converter d Small signal disturbance component, Δi q i represents the q-axis current i of the grid-side converter of the wind turbine. q The small-signal disturbance component, R1 represents the equivalent resistance of the wind turbine converter connecting reactance, L1 represents the equivalent inductance of the wind turbine converter connecting reactance, ω represents the angular frequency, ΔV d This indicates the reference value V of the d-axis voltage of the wind turbine grid-side converter. d Small signal disturbance component, ΔV q V represents the reference value of the q-axis voltage of the wind turbine grid-side converter. q Small signal disturbance component, Δu d The voltage u of the grid-side converter of the wind turbine represents the d-axis voltage. d Small signal disturbance component, Δu q U represents the q-axis voltage u of the wind turbine grid-side converter. q Small signal disturbance components.

5. The stability analysis method for low-frequency offshore wind power systems according to claim 4, characterized in that, The low-frequency line dynamic model includes: The DRU dynamic model includes: Among them, u d1 This represents the d-axis voltage on the low-frequency submarine cable machine side, Δu. d1 Indicates the d-axis voltage u on the low-frequency submarine cable machine side. d1 Small signal perturbation component, u q1 This represents the q-axis voltage on the low-frequency submarine cable machine side, Δu q1 Indicates the q-axis voltage u on the low-frequency submarine cable machine side. q1 Small signal disturbance component, Δu md Indicates the d-axis voltage u on the low-frequency submarine cable network side. md Small signal disturbance component, Δu mq Indicates the q-axis voltage u on the low-frequency submarine cable network side. mq Small signal disturbance component, Δi ld Indicates the d-axis inductor current i on the low-frequency submarine cable machine side. ld Small signal disturbance component, Δi lq Indicates the q-axis inductor current i on the low-frequency submarine cable machine side. lq The small signal disturbance component, A2 represents the coefficient matrix of the low-frequency submarine cable state variables, and B2 and C2 both represent the coefficient matrices of the low-frequency submarine cable input variables, i d1 Δi represents the d-axis current at the grid connection point of the wind farm. d1 The d-axis current i at the grid connection point of the wind farm is represented by... d1 The small signal perturbation component, i q1 Δi represents the q-axis current at the grid connection point of the wind farm. q1 i represents the q-axis current at the grid connection point of the wind farm. q1 Small signal disturbance component, Δi md Indicates the d-axis current i on the low-frequency side of the DRU md Small signal disturbance component, Δi mq Indicates the q-axis current i on the low-frequency side of the DRU mq The small-signal perturbation component, Δω represents the small-signal perturbation component with angular frequency ω, i dc Δi represents the DC current of the DRU converter transformer. dc i represents the DC current of the DRU converter transformer. dc Small signal perturbation component, L dc Indicates smoothing inductance, ΔU dc U represents the DC voltage of the DRU converter transformer. dc Small signal disturbance components.

6. The stability analysis method for low-frequency offshore wind power systems according to claim 5, characterized in that, The MMC dynamic model includes: The dynamic model of the MMC DC link includes: The MMC power frequency phase-locked loop dynamic model includes: Where Δx5 represents the small-signal disturbance component of the d-axis intermediate state variable x5 of the MMC converter power outer loop, Δx6 represents the small-signal disturbance component of the q-axis intermediate state variable x6 of the MMC converter power outer loop, Δx7 represents the small-signal disturbance component of the d-axis intermediate state variable x7 of the MMC converter current inner loop, Δx8 represents the small-signal disturbance component of the q-axis intermediate state variable x8 of the MMC converter current inner loop, A3 represents the coefficient matrix of the MMC converter state variables, B3 represents the coefficient matrix of the MMC converter input variables, and U dc U represents the constant DC voltage, i.e., the DC voltage of the DRU converter transformer. dcref Indicates the conventional DC voltage U dc The voltage reference value, Q ref The power reference value represents the instantaneous reactive power of a low-frequency wind farm, where Q represents the instantaneous reactive power of the low-frequency wind farm, and i represents the instantaneous reactive power of the low-frequency wind farm. sd This represents the d-axis current on the grid side of the MMC converter. Indicates the reference value of the d-axis current on the grid side of the MMC converter, i sq This represents the q-axis current on the grid side of the MMC converter. U represents the reference value of the grid-side q-axis current of the MMC converter. sd U represents the grid-side d-axis voltage of the MMC converter. sq This represents the grid-side q-axis voltage of the MMC converter, V. sd This represents the d-axis reference voltage on the grid side of the MMC converter, V. sq C represents the grid-side q-axis reference voltage of the MMC converter. eq U represents the equivalent capacitance of the MMC converter, N represents the number of bridge arm submodules of the MMC converter, and U represents the number of submodules of the bridge arm of the MMC converter. dc0 x represents the steady-state DC voltage value of the MMC converter. PLL u represents the intermediate state variable of the phase-locked loop. sq θ represents the grid-side q-axis voltage of the MMC converter. PLL This represents the phase output of the phase-locked loop, ω represents the angular frequency, and K... iPLL K represents the integral gain coefficient of the phase-locked loop. pPLL This represents the proportional gain coefficient of the phase-locked loop.

7. The stability analysis method for low-frequency offshore wind power systems according to claim 6, characterized in that, The dynamic model of the wind farm turbine-side converter includes: Where x9 represents the intermediate state variable of the DC capacitor voltage of the machine-side converter, x 10 x represents the intermediate state variable of the AC voltage of the machine-side converter. 11 The x represents the intermediate state variable on the d-axis of the inner loop of the converter current on the machine side. 12 u represents the intermediate state variable on the q-axis of the inner loop of the converter current on the machine side. dc This indicates the DC capacitor voltage of the machine-side converter. U represents the reference value of the DC capacitor voltage of the machine-side converter. ac_M This indicates the AC voltage of the machine-side converter. Q represents the reference value of the AC voltage of the machine-side converter. M Indicates the reactive power of the machine-side converter. Indicates the reference value of reactive power of the machine-side converter, i d_M This indicates the d-axis current of the machine-side converter. Indicates the reference value of the d-axis current of the machine-side converter, i q_M This indicates the q-axis current of the machine-side converter. This indicates the reference value for the q-axis current of the machine-side converter.

8. The stability analysis method for low-frequency offshore wind power systems according to claim 7, characterized in that, The system-wide small-signal model includes: Where Δx represents the state variables of the low-frequency offshore wind power system, A represents the state matrix of the low-frequency offshore wind power system, B represents the input matrix of the low-frequency offshore wind power system, and Δu represents the input variables of the low-frequency offshore wind power system. pll_G Δθ represents the small-signal disturbance component of the intermediate state variable of the wind farm turbine-side phase-locked loop. pll_G Δi represents the small-signal disturbance component of the phase output of the wind farm turbine-side phase-locked loop. d Δi represents the small-signal disturbance component of the d-axis current of the wind farm converter. q Δu represents the small-signal disturbance component of the q-axis current of the wind farm converter. dc Δω2 represents the small-signal disturbance component of the bridge arm submodule capacitor voltage of the MMC converter, Δω2 represents the small-signal disturbance component of the angular frequency control of the wind farm grid-side converter, Δθ represents the small-signal disturbance component of the angular frequency output reference angle in the active-frequency outer loop control loop, and Δi represents the small-signal disturbance component of the angular frequency output reference angle in the active-frequency outer loop control loop. d_M Δi represents the small-signal disturbance component of the d-axis current of the wind farm turbine-side converter. q_M Δx represents the small-signal disturbance component of the q-axis current of the wind farm turbine-side converter. PLL Δθ represents the small-signal perturbation component of the intermediate state variable of the phase loop. PLL Δi represents the small-signal perturbation component of the phase output of the phase-locked loop. sd Indicates the d-axis current i on the grid side of the MMC converter. sd Small signal disturbance component, Δi sq Indicates the grid-side q-axis current i of the MMC converter. sq Small signal disturbance component, ΔU d_M ΔU represents the small-signal disturbance component of the d-axis voltage at the grid connection point of the wind farm's turbine-side converter. q_M ΔV represents the small-signal disturbance component of the q-axis voltage at the grid connection point of the wind farm's turbine-side converter. d_M ΔV represents the small-signal disturbance component of the d-axis reference voltage at the grid connection point of the wind farm's converter. q_M Δu represents the small-signal disturbance component of the q-axis reference voltage at the grid connection point of the wind farm's converter. sd Δu represents the small-signal disturbance component of the d-axis voltage at the grid connection point of the wind farm. sq Δv represents the small-signal disturbance component of the q-axis voltage at the grid connection point of the wind farm. sd Δv represents the small-signal disturbance component of the d-axis reference voltage at the grid connection point of the wind farm. sq ΔU represents the small-signal disturbance component of the q-axis reference voltage at the grid connection point of the wind farm. sd ΔU represents the small-signal disturbance component of the d-axis voltage on the MMC power frequency side. sq ΔV represents the small-signal disturbance component of the q-axis voltage on the MMC power frequency side. sd ΔV represents the small-signal disturbance component of the d-axis reference voltage on the MMC power frequency side. sq This represents the small-signal disturbance component of the q-axis reference voltage on the MMC power frequency side.

9. A stability analysis device for a low-frequency offshore wind power system, characterized in that, include: The system includes an electrical data acquisition module, a dynamic model construction module, a dynamic model integration module, a model solving module, and a system stability analysis module. The electrical data acquisition module is used to acquire the MMC power frequency side voltage and DRU low frequency side current of the DRU-MMC converter, as well as the grid connection point current, grid connection point voltage and turbine-side converter grid connection point voltage of the wind farm. The dynamic model building module is used to build a wind turbine system model, a DC network line model, and an MMC converter station model based on the MMC power frequency side voltage and DRU low frequency side current of the DRU-MMC converter, as well as the grid connection point current, grid connection point voltage, and generator-side converter grid connection point voltage of the wind farm. The wind turbine system model includes: a dynamic model of the wind turbine grid-side converter, a dynamic model of the wind turbine converter DC link, and a dynamic model of the wind turbine-side converter; the DC network line model includes: a dynamic model of the low-frequency line and a dynamic model of the DRU; the MMC converter station model includes: an MMC dynamic model, a dynamic model of the MMC DC link, and a dynamic model of the MMC power frequency phase-locked loop. The dynamic model integration module is used to linearize the stable operating points of the wind turbine system model, DC network line model, and MMC converter station model to obtain the whole system small-signal model of the low-frequency offshore wind power system. The model solving module is used to solve the small-signal model of the entire system to obtain the state matrix of the low-frequency offshore wind power system. The system stability analysis module is used to determine the stability of the low-frequency offshore wind power system based on the state matrix.

10. The low-frequency offshore wind power system stability analysis device according to claim 9, characterized in that, Also includes: Analysis and control module; The analysis and control module includes: an oscillation mode analysis unit, a participating variable analysis unit, and a system control unit; The oscillation mode analysis unit is used to determine the oscillation mode of the low-frequency offshore wind power system based on the state matrix under unstable conditions. The participating variable analysis unit is used to perform participation factor analysis on each oscillation mode and determine the corresponding oscillation participating variables. The system control unit is used to control the low-frequency offshore wind power system according to the oscillation participation variables.

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