Method for analyzing resonance stability of wind power flexible direct current system by submarine cable parameters

Abstract

The invention discloses a method for analyzing resonance stability of a wind power flexible direct current system by submarine cable parameters, and the method comprises the steps: constructing an admittance model of a current converter and a submarine cable line based on an offshore wind power flexible direct current sending end system, and recognizing a mode resonance condition between a fan subsystem and the flexible direct current system. By establishing a closed-loop interconnection system model, the coupling relation between the fan and the cable flexible direct subsystem is further analyzed, and a characteristic equation is extracted to evaluate the subsynchronous resonance risk and the influence factors thereof. The influence of line parameters on system damping and stability is deeply discussed by analyzing a mapping relation, the resonance intensity can be increased by increasing capacitance, the influence of comprehensive judgment on damping change on a characteristic root and the resonance intensity, and the system damping can be weakened by increasing inductance, so that the overall stability is influenced. Theoretical basis and practical guidance are provided for design and optimization of the offshore wind power flexible direct current system, the resonance risk can be reduced, and the safety and operation efficiency of the system are improved.

Description

Technical Field

[0001] The invention belongs to the field of power systems and renewable energy, and in particular relates to a method for analyzing the resonance stability of a wind power flexible direct current system using submarine cable parameters. Background Art

[0002] Traditional mode resonance is mainly concentrated on land, and onshore overhead lines are generally regarded as inductive when analyzed. However, the capacitance of submarine cable lines is much larger than that of onshore overhead lines. The stability analysis of offshore wind power flexible direct current sending end systems needs to consider the influence of line capacitance. Secondly, offshore flexible direct current converter stations mostly adopt grid-type control, and there is a lack of research on mode resonance between wind turbine subsystems and grid-type flexible direct current converter stations.

[0003] The present invention studies the influence of line parameters on the mode resonance of the offshore wind power flexible direct current sending end system, analyzes the mode resonance between the wind turbine subsystem and the offshore grid-type flexible direct current converter station, and obtains the influence of submarine cable parameters on the mode resonance, establishes an analytical relationship between submarine cable capacitance, inductance and mode resonance, and compares the different effects of capacitance and inductance on mode resonance. Summary of the invention

[0004] The present invention aims to solve the technical problem that the traditional mode resonance existing in the background technology is mainly concentrated in the onshore new energy grid-connected system, and there is a lack of research on the influence of submarine cable parameters on the stability of the offshore wind power flexible direct current sending end system. The purpose is to provide a method for analyzing the resonant stability of wind power flexible direct current systems based on submarine cable parameters, obtain the analytical mapping relationship between capacitor parameters and open-loop modes and their residues, clarify the subsynchronous resonance risk between the flexible direct current side converter and the wind turbine side converter control link; derive the influence law of submarine cable parameters on system damping; and increase the risk consideration factors for subsynchronous oscillations in offshore wind flexible direct current systems.

[0005] In order to solve the technical problem, the technical solution of the present invention is:

[0006] A method for analyzing the resonance stability of a wind power flexible DC system based on submarine cable parameters, the method comprising:

[0007] S1: Based on the offshore wind power flexible DC sending end system, the admittance model of the converter and the submarine cable line based on the synchronous reference coordinate system and the closed-loop characteristic equation of the system are constructed;

[0008] S2: Based on the admittance model and the closed-loop characteristic equation of the system, a closed-loop interconnected system is constructed. The characteristic equation is extracted according to the transfer function model of the closed-loop interconnected system, the subsynchronous resonance risk caused between the control links of the flexible DC converter and the wind turbine converter is determined, and the analytical mapping relationship between the capacitance and the open-loop mode and its residue is derived;

[0009] S3: Based on the analytical mapping relationship, the influence of circuit parameters on system damping and system stability is derived, and the different effects of capacitance and inductance on mode resonance are compared.

[0010] Furthermore, the offshore wind power flexible direct current sending end system model includes: a wind turbine system, a submarine cable line and an offshore flexible direct current converter station system; wherein, the direct-drive wind turbine in the wind turbine system adopts a single-machine aggregation model, the wind turbine system converter adopts a GFL control strategy, the machine-side converter MSC is used to control the output power of the wind turbine, and adopts fixed active power control and fixed generator speed control; the grid-side converter GSC adopts fixed DC voltage control and fixed reactive power control.

[0011] Further, the step S1 specifically includes:

[0012] The polar coordinate system is used to model the direct-drive wind turbine flexible DC grid-connected system to form the grid-side converter GSC and the admittance matrix in polar coordinate form; the admittance matrix is ​​a symmetric matrix, which can be expressed as:

[0013]

[0014] Among them, I t is the grid-side converter current, U 1 is the line start voltage, Y gsc (s) represents the admittance matrix of the grid-side converter, Y g1 and Y g2 is the admittance matrix element, is the grid-side converter current phase angle, θ 1 is the corresponding voltage phase angle;

[0015] The dynamic equation on the grid side takes into account the dynamic characteristics of the line inductance and capacitance, and performs linear processing in the xy coordinate system. When the grid disturbance is zero, the dynamic equation can be expressed as:

[0016]

[0017] Where: Y net (s) = Y L (s)+Y C (s) represents the total line admittance, Y L (s) and Y C (s) is the line admittance matrix, ω 0 is the angular frequency, C l , L g are the equivalent capacitance and inductance of the line respectively, U 2 is the voltage at the end of the transmission line, θ 2 For U 2 Voltage phase angle, I 1 is the current flowing through the filter inductor;

[0018] The admittance model of the voltage source converter of the flexible DC system wind farm is established in polar coordinate form, and its AC port admittance expression is as follows:

[0019]

[0020] Among them, I d , is the current amplitude and phase of the flexible DC converter, θ d is the corresponding voltage phase angle, Y vsc (s) represents the admittance matrix of the flexible DC converter, Y d11 and Y d22 is the element of the admittance matrix;

[0021] By combining equations (1), (2) and (3), we get the closed-loop characteristic equation of the system:

[0022] det(Y gsc (s)+Y net (s)+Y vsc (s))=0 (4)

[0023] The system closed-loop characteristic equation is used to analyze the resonance characteristics of the system, evaluate the risk of subsynchronous resonance, and ensure the stability of the system under different operating conditions.

[0024] Further, the step S2 performs mode analysis based on the closed-loop interconnected system model, specifically including:

[0025] A closed-loop interconnected system model is constructed with the cable flexible direct current system as the feedback subsystem H(s) and the fan subsystem G(s) as the object subsystem. The interconnection interface variable is the filter inductor outlet voltage U 1 and current I 1 , Y gsc (s) is denoted as G(s), and Y net (s)+Y vsc (s) is denoted as H(s);

[0026] The transfer functions G(s) and H(s) of the fan subsystem and the line flexible direct current subsystem in the closed-loop interconnected system model are written as follows:

[0027]

[0028] Where: w is the characteristic root of the fan open-loop state matrix, λ wk is different from λ p ≈λ w The characteristic root of p ≈λ w , p ≈ λw is the characteristic value of the line flexible subsystem; R w and R p are the residues of the corresponding modes of the two subsystems respectively; Substitute equations (5) and (6) into the closed-loop characteristic equation of the interconnected system, and combine the condition λ for the occurrence of the strong coupling mode p ≈λ w Find the degree of deviation when mode resonance occurs

[0029]

[0030] After processing the closed-loop characteristic equation in step S1, the following equation is obtained:

[0031]

[0032] f(C l ) is a constant that only contains line parameters. According to the closed-loop characteristic equation of the system, the change of the characteristic root due to the addition of capacitance is calculated. Substituting the line admittance matrix into the characteristic equation, we can get:

[0033]

[0034] According to Vieta's theorem, we can calculate the numerical solution of s and obtain s 2 The modulus is about 1 / (L g C l ), and under the condition of satisfying the open-loop mode resonance, the characteristic roots between subsystems are approximate. The open-loop characteristic roots are reflected in the s domain as the imaginary part decreases, that is, changes toward the low-frequency end, and the real part of the root may be left or right;

[0035] Substituting the system admittance matrix into the closed-loop characteristic equation, we get: 2 =1 / (L g C l ) into the equation, we get near the mode resonance point:

[0036]

[0037] After adding the line parameters, the open-loop mode resonance intensity is expressed as:

[0038]

[0039] Furthermore, the step S3 of evaluating the influence of line parameters on system damping specifically includes:

[0040] At the open-loop mode resonance point, f(C l ) Find the pair C l With L g Partial derivative of:

[0041]

[0042] According to equations (12) and (13), |f(C l )|To C l With L g The partial derivative of is greater than zero, and it is concluded that as the capacitance and inductance increase, f(C l ) increases, so it can be concluded from formula (11) that the resonance intensity increases, which increases the degree of closed-loop characteristic root deviation;

[0043] According to the movement of the open-loop characteristic roots with line parameters in formula (9), it is found that the increase in capacitance has an impact on the position of the system characteristic roots, causing the open-loop characteristic roots to change; combined with the specific line parameters, the inductance value is larger than the capacitance value, so the inductance has a weak effect on the movement of the characteristic root position and is considered to be negligible, and it can be considered that only the capacitance participates in the movement of the characteristic root; the addition of capacitance has an offset effect on the open-loop mode characteristic roots of the subsystem, which not only changes the characteristic roots under the corresponding mode of the flexible direct subsystem to affect the open-loop mode, but also affects the mode resonance intensity by changing the residue. The two work together to affect the closed-loop characteristic roots of the system; the inductance mainly affects the interaction intensity under the mode resonance and then affects the system damping. The increase in inductance weakens the system damping and reduces the system stability.

[0044] Compared with the prior art, the advantages of the present invention are:

[0045] Comprehensive analysis: This method can comprehensively analyze the dynamic interaction between the wind turbine subsystem and the flexible DC system by constructing the system's admittance model and closed-loop interconnected system, and deeply understand how different factors affect the resonant characteristics of the system.

[0046] Accurately identify resonance conditions: By clearly identifying the modal resonance conditions, the subsynchronous resonance risk can be effectively assessed so that corresponding prevention and control measures can be taken in system design and operation.

[0047] Analytical mapping relationship: Establishing the analytical mapping relationship between capacitance, inductance and system damping enables engineers to intuitively understand and optimize system parameters, and improve system stability and anti-resonance capability.

[0048] Optimization design guidance: The theoretical basis provided by this method can provide guidance for the design and optimization of offshore wind power flexible DC systems, reduce the risks of the system during operation, and improve its safety and economy.

[0049] Wide application: The method is applicable to different types of offshore wind power systems and flexible DC conversion equipment, has good adaptability and flexibility, and can be implemented in multiple engineering applications.

[0050] Improve operating efficiency: Through effective control and optimized design of resonance conditions, the overall operating efficiency of the system can be improved, energy loss can be reduced, and the effective use of renewable energy can be facilitated.

[0051] Combination of theory and practice: The method not only focuses on theoretical analysis, but also pays attention to the feasibility of practical application, making the research results more realistic and helpful for solving problems in actual engineering.

[0052] The above advantages make this method have significant advantages in the resonance analysis of offshore wind power flexible DC systems, and can contribute to improving the reliability and safety of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 , Offshore wind power flexible DC transmission system diagram;

[0054] Figure 2 , closed-loop interconnected system model diagram;

[0055] Figure 3 , characteristic root s domain change diagram;

[0056] Figure 4 , the main flow chart of the method of the present invention;

[0057] Figure 5 , the weakening diagram of line capacitance on mode resonance;

[0058] Figure 6. Changes in wind turbine output and voltage fluctuation when the capacitance increases (a-voltage fluctuation on the flexible DC side, b-active power change). DETAILED DESCRIPTION

[0059] The specific implementation mode of the present invention is described below in conjunction with embodiments:

[0060] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to match the contents disclosed in the specification so that people familiar with this technology can understand and read them, and are not used to limit the conditions under which the present invention can be implemented. Any structural modification, change in proportional relationship or adjustment of size should still fall within the scope of the technical content disclosed in the present invention without affecting the effects and purposes that can be achieved by the present invention.

[0061] At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" cited in this specification are only for the convenience of description and are not used to limit the scope of implementation of the present invention. Changes or adjustments to their relative relationships should be regarded as the scope of implementation of the present invention without substantially changing the technical content.

[0062] Explanation of terms: The offshore wind power flexible DC sending end system consists of three parts: wind turbine system, submarine cable line and flexible DC system. It mainly studies the interaction between the wind turbine grid-side converter GSC and the submarine cable, and between the submarine cable and the flexible DC offshore converter WFVSC.

[0063] Resonance stability refers to the "resonance frequency oscillation of electrical quantities". When the power system suffers a small disturbance, the power network enters an electromagnetic transient oscillation process. The resonance stability is judged by whether the free component of the resonant frequency oscillation in the voltage and current response decays to 0. This belongs to the category of small signal analysis.

[0064] Embodiment 1:

[0065] Establish the admittance model of the sending end system:

[0066] Figure 1 It is a model of the offshore wind power flexible direct current transmission system, including wind turbine system, submarine cable line and offshore flexible direct current converter station system. The direct-drive wind turbine adopts a single-machine aggregation model, the wind turbine system converter adopts the GFL control strategy, the machine-side converter MSC is used to control the output power of the wind turbine, and adopts fixed active power control and fixed generator speed control; the grid-side converter GSC adopts fixed DC voltage control and fixed reactive power control.

[0067] The direct-drive wind turbine flexible grid-connected system is modeled in the polar coordinate system. The admittance matrix of the GSC polar coordinate form is a symmetric matrix:

[0068]

[0069] Among them, I t is the grid-side converter current, U 1 is the line start voltage, Y gsc (s) represents the admittance matrix of the grid-side converter, Y g1 and Y g2 is the admittance matrix element, is the grid-side converter current phase angle, θ 1 is the corresponding voltage phase angle.

[0070] The dynamic equations on the grid side include the dynamic equations of the line inductance and line capacitance, which are linearized in the xy coordinate system. After linearization, the dynamic equation of the grid admittance model containing cable capacitance in polar coordinates is:

[0071]

[0072] Where: Y net (s)=Y L (s)+Y C (s) represents the total line admittance, Y L (s) and Y C (s) is the line admittance matrix, ω 0 is the angular frequency, C l , L g are the equivalent capacitance and inductance of the line respectively, U 2 is the voltage at the end of the transmission line, θ2 For U 2 Voltage phase angle, I 1 is the current flowing through the filter inductor.

[0073] The admittance model of the flexible direct current system WFVSC in polar coordinate form is established, and the expression of its AC port admittance is as follows:

[0074]

[0075] Among them, I d , is the current amplitude and phase of the flexible DC converter, θ d is the corresponding voltage phase angle, Y vsc (s) represents the admittance matrix of the flexible DC converter, Y d11 and Y d22 is the element of the admittance matrix;

[0076] Combining equations (1), (2) and (3), we get the closed-loop characteristic equation of the system:

[0077] det(Y gsc (s)+Y net (s)+Y vsc (s))=0 (4)

[0078] Mode analysis based on closed-loop interconnected system model:

[0079] Figure 2 In this paper, a closed-loop interconnected system model is constructed with the cable flexible direct current system as the feedback subsystem H(s) and the fan subsystem G(s) as the object subsystem. The interconnection interface variable is the filter inductor outlet voltage U 1 and current I 1 , Y gsc (s) is denoted as G(s), and Y net (s)+Y vsc (s) is denoted as H(s).

[0080] The transfer functions G(s) and H(s) of the fan subsystem and the line flexible direct current subsystem in the closed-loop interconnected system model are written as follows:

[0081]

[0082] Where: w is the characteristic root of the fan open-loop state matrix, λ wk is different from λ p ≈λ w The characteristic root of p ≈λ w , p ≈λ w is the characteristic value of the line flexible subsystem; Rw and R p are the residues of the corresponding modes of the two subsystems respectively. Substituting equations (5) and (6) into the closed-loop characteristic equation λ of the interconnected system p ≈λ w , and combined with the condition for the occurrence of strong coupling mode λ p ≈λ w Find the degree of deviation when mode resonance occurs

[0083]

[0084] After processing the closed-loop characteristic equation, the following equation is obtained:

[0085]

[0086] According to the system characteristic equation, the characteristic value is obtained according to the grid admittance matrix, and the corresponding characteristic root is calculated due to the change of capacitance after adding capacitance to the grid side. Substituting the line admittance matrix into the characteristic equation, we can get:

[0087]

[0088] According to Vieta's theorem, we can calculate the numerical solution of s and obtain s 2 The modulus is about 1 / (L g C l ), and the characteristic roots between subsystems are similar under the condition of satisfying the open-loop mode resonance. The open-loop characteristic roots are reflected in the s domain as the imaginary part decreases, that is, changes to the low-frequency end, and the real part of the root may go left or right, such as Figure 3 shown.

[0089] Substituting the system admittance matrix into the closed-loop characteristic equation, we can obtain: The modulus length of the characteristic root derived from the power grid admittance model is s 2 =1 / (L g C l ) is substituted into the equation to get near the mode resonance point:

[0090]

[0091] After adding the line parameters, the open-loop mode resonance intensity is expressed as

[0092]

[0093] Evaluation of the impact of line parameters on system damping:

[0094] At the open-loop mode resonance point, f(C l ) Find the pair C l With L g Partial derivative of:

[0095]

[0096] According to equations (12) and (13), f(C l ) l With L g The partial derivative of is greater than zero, and it is concluded that as the capacitance and inductance increase, f(C l ) increases, so it can be concluded from formula (11) that the resonance intensity increases, which increases the degree of offset of the closed-loop characteristic root; according to the movement of the open-loop characteristic root with the line parameters in formula (9), it is found that the increase of capacitance has an impact on the position of the system characteristic root, causing the open-loop characteristic root to change; and combined with the specific line parameters, the inductance value is larger than the capacitance value, so the inductance has a weak effect on the movement of the characteristic root position and is ignored, and it can be regarded as the movement of the characteristic root only involving the capacitance. The addition of capacitance has an offset effect on the open-loop mode characteristic root of the subsystem, which not only changes the characteristic root under the corresponding mode of the flexible direct subsystem to affect the open-loop mode, but also affects the mode resonance intensity by changing the residue. The two work together to affect the closed-loop characteristic root of the system; the inductance mainly affects the interaction intensity under the mode resonance and then affects the system damping. The increase of inductance weakens the system damping and reduces the system stability.

[0097] The technical solution flow chart of the present invention is as follows Figure 5 As shown:

[0098] Step 1: First, based on the offshore wind power flexible direct current transmission system, construct the admittance model of the converter and the submarine cable line based on the synchronous reference coordinate system, and determine the mode resonance conditions between the wind turbine subsystem and the grid-type flexible direct current system.

[0099] Step 2: Extract the characteristic equation based on the system transfer function model, clarify the subsynchronous resonance risk caused by the control links of the flexible DC converter and the wind turbine converter, and derive the analytical mapping relationship between the capacitor and the open-loop mode and its residue.

[0100] Step 3: Derive the influence of circuit parameters on system damping and system stability based on the analytical mapping relationship, and compare the different effects of capacitance and inductance on mode resonance.

[0101] Embodiment 2:

[0102] This embodiment provides a specific calculation example of a method for analyzing the resonance stability of a wind power flexible DC system using submarine cable parameters:

[0103] Table 1-Main operating parameters of the system

[0104]

[0105] like Figure 5 As shown, three scenarios A, B, and C are set in the example. In scenario A, only the line reactance is considered, and the capacitance is set to 0; scenarios B and C consider the line capacitance and adopt different capacitance values.

[0106] By observing the data in Table 2, it is found that under this operating condition, as the capacitance continues to increase, the open-loop characteristic root of the system will change, and the modal resonance intensity between subsystems will continue to weaken, and the position of the closed-loop characteristic root will gradually move to the left, which will increase the overall stability of the system.

[0107] Table 2 - Impact of capacitors on system characteristic roots

[0108]

[0109] The nonlinear simulation results use the system voltage and power fluctuation amplitude to measure the system damping. Under the working condition in Figure 6, as the line capacitance increases, the fluctuation degree of the DC voltage decreases when disturbed, and the voltage fluctuation recovery also gradually accelerates, indicating that the capacitance has an improving effect on damping at this time.

[0110] By solving the analytical relationship between the submarine cable parameters and the subsystem mode resonance, the interaction between the wind turbine subsystem and the flexible direct current subsystem is analyzed, and the influence of the submarine cable parameters on the system damping is clarified; the research content adds the risk consideration factor of subsynchronous oscillation of the sea breeze flexible direct current system, and the conclusions are as follows:

[0111] 1) The offshore wind power flexible direct current transmission system can be decomposed into a wind turbine subsystem and a line flexible direct current subsystem. Based on the analytical method, it is found that the increase in the reactance of the transmission line leads to an increase in the residues of the wind turbine subsystem and the flexible direct current subsystem in the corresponding open-loop mode, an increase in the degree of deviation of the closed-loop characteristic root, and a weakening of the system damping.

[0112] 2) Based on the numerical analytical relationship, it is clear that the capacitor will change the characteristic roots of the subsystem and the residues in the corresponding mode, and at the same time affect the position of the open-loop mode in the complex frequency domain and the modal resonance intensity. The combined effect of the two on the system damping can be positive or negative.

[0113] 3) Based on the nonlinear simulation results, the influence of fan output on system stability is obtained. Under low power, the open-loop mode positions between subsystems are far apart, and the mode resonance conditions are not met. The system is very stable. Under high power, the system stability decreases due to mode resonance.

[0114] The preferred embodiments of the present invention are described in detail above, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

[0115] Many other changes and modifications may be made without departing from the concept and scope of the present invention.It should be understood that the present invention is not limited to the specific embodiments, and the scope of the present invention is defined by the appended claims.

Claims

1. A method for analyzing the resonance stability of a wind power flexible DC system using submarine cable parameters, characterized in that: The method comprises: S1: Based on the offshore wind power flexible DC sending end system, the admittance model of the converter and the submarine cable line based on the synchronous reference coordinate system and the closed-loop characteristic equation of the system are constructed; S2: Based on the admittance model and the closed-loop characteristic equation of the system, a closed-loop interconnected system is constructed. The characteristic equation is extracted according to the transfer function model of the closed-loop interconnected system, the subsynchronous resonance risk caused between the control links of the flexible DC converter and the wind turbine converter is determined, and the analytical mapping relationship between the capacitance and the open-loop mode and its residue is derived; S3: Based on the analytical mapping relationship, the influence of circuit parameters on system damping and system stability is derived, and the different effects of capacitance and inductance on mode resonance are compared.

2. A method for analyzing the resonance stability of a wind power flexible DC system based on submarine cable parameters according to claim 1, characterized in that: The offshore wind power flexible direct current sending end system model comprises: a wind turbine system, a submarine cable line and an offshore flexible direct current converter station system; wherein the direct-drive wind turbine in the wind turbine system adopts a single-machine aggregation model, the wind turbine system converter adopts a GFL control strategy, the machine-side converter MSC is used to control the output power of the wind turbine, and adopts fixed active power control and fixed generator speed control; the grid-side converter GSC adopts fixed direct current voltage control and fixed reactive power control.

3. The method for analyzing the resonance stability of a wind power flexible DC system based on submarine cable parameters according to claim 1 is characterized in that: The step S1 specifically includes: The polar coordinate system is used to model the direct-drive wind turbine flexible DC grid-connected system to form the grid-side converter GSC and the admittance matrix in polar coordinate form; the admittance matrix is ​​a symmetric matrix, which can be expressed as: Among them, I t is the grid-side converter current, U1 is the line start voltage, Y gsc (s) represents the admittance matrix of the grid-side converter, Y g1 and Y g2 is the admittance matrix element, is the grid-side converter current phase angle, θ1 is the corresponding voltage phase angle; The dynamic equation on the grid side takes into account the dynamic characteristics of the line inductance and capacitance, and performs linear processing in the xy coordinate system. When the grid disturbance is zero, the dynamic equation can be expressed as: Where: Y net (s)=Y L (s)+Y C (s) represents the total line admittance, Y L (s) and Y C (s) is the line admittance matrix, ω0 is the angular frequency, C l , L g are the line equivalent capacitance and line equivalent inductance respectively, U2 is the voltage at the end of the transmission line, θ2 is the U2 voltage phase angle, and I1 is the current flowing through the filter inductor; The admittance model of the voltage source converter of the flexible DC system wind farm is established in polar coordinate form, and its AC port admittance expression is as follows: Among them, I d , is the current amplitude and phase of the flexible DC converter, θ d is the corresponding voltage phase angle, Y vsc (s) represents the admittance matrix of the flexible DC converter, Y d11 and Y d22 is the element of the admittance matrix; By combining equations (1), (2) and (3), we get the closed-loop characteristic equation of the system: det(Y gsc (s)+Y net (s)+Y vsc (s))=0 (4) The system closed-loop characteristic equation is used to analyze the resonance characteristics of the system, evaluate the risk of subsynchronous resonance, and ensure the stability of the system under different operating conditions.

4. The method for analyzing the resonance stability of a wind power flexible DC system based on submarine cable parameters according to claim 1 is characterized in that: The step S2 performs mode analysis based on the closed-loop interconnected system model, specifically including: A closed-loop interconnected system model is constructed with the cable flexible direct current system as the feedback subsystem H(s) and the fan subsystem G(s) as the object subsystem. The interconnected interface variables are the filter inductor outlet voltage U1 and current I1. gsc (s) is denoted as G(s), and Y net (s)+Y vsc (s) is denoted as H(s); The transfer functions G(s) and H(s) of the fan subsystem and the line flexible direct current subsystem in the closed-loop interconnected system model are written as follows: Where: w is the characteristic root of the fan open-loop state matrix, λ wk is different from λ p ≈λ w The characteristic root of p ≈λ w , p ≈λ w is the characteristic value of the line flexible subsystem; R w and R p are the residues of the corresponding modes of the two subsystems respectively; Substitute equations (5) and (6) into the closed-loop characteristic equation of the interconnected system, and combine the condition λ for the occurrence of the strong coupling mode p ≈λ w Find the degree of deviation when mode resonance occurs After processing the closed-loop characteristic equation in step S1, the following equation is obtained: f(C l ) is a constant that only contains line parameters. According to the closed-loop characteristic equation of the system, the change of the characteristic root due to the addition of capacitance is calculated. Substituting the line admittance matrix into the characteristic equation, we can get: According to Vieta's theorem, we can calculate the numerical solution of s and obtain s 2 The modulus is about 1 / (L g C l ), and under the condition of satisfying the open-loop mode resonance, the characteristic roots between subsystems are approximate. The open-loop characteristic roots are reflected in the s domain as the imaginary part decreases, that is, changes toward the low-frequency end, and the real part of the root may be left or right; Substituting the system admittance matrix into the closed-loop characteristic equation, we get: 2 =1 / (L g C l ) into the equation, we get near the mode resonance point: After adding the line parameters, the open-loop mode resonance intensity is expressed as:

5. The method for analyzing the resonance stability of a wind power flexible DC system based on submarine cable parameters according to claim 1 is characterized in that: The step S3 of evaluating the influence of line parameters on system damping specifically includes: At the open-loop mode resonance point, f(C l ) Find the pair C l With L g Partial derivative of: According to equations (12) and (13), |f(C l )|To C l With L g The partial derivative of is greater than zero, and it is concluded that as the capacitance and inductance increase, f(C l ) increases, so it can be concluded from formula (11) that the resonance intensity increases, which increases the degree of closed-loop characteristic root deviation; According to the movement of the open-loop characteristic roots with line parameters in formula (9), it is found that the increase in capacitance has an impact on the position of the system characteristic roots, causing the open-loop characteristic roots to change; combined with the specific line parameters, the inductance value is larger than the capacitance value, so the inductance has a weak effect on the movement of the characteristic root position and is considered to be negligible, and it can be considered that only the capacitance participates in the movement of the characteristic root; the addition of capacitance has an offset effect on the open-loop mode characteristic roots of the subsystem, which not only changes the characteristic roots under the corresponding mode of the flexible direct subsystem to affect the open-loop mode, but also affects the mode resonance intensity by changing the residue. The two work together to affect the closed-loop characteristic roots of the system; the inductance mainly affects the interaction intensity under the mode resonance and then affects the system damping. The increase in inductance weakens the system damping and reduces the system stability.

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