METHOD FOR EVALUATING RESONANCE STABILITY OF FLEXIBLE DIRECT CURRENT (DC) TRANSMISSION SYSTEM IN OFFSHORE WIND FARM

Abstract

A method for evaluating resonance stability of a flexible direct current (DC) transmission system in an offshore wind farm includes: establishing an s-domain equivalent circuit of a flexible DC transmission system in an offshore wind farm, constructing an s-domain node admittance matrix of the flexible DC transmission system in the offshore wind farm, determining a resonant mode of the system based on a zero root of a determinant of the node admittance matrix, and determining stability of the system. In the method, an s-domain impedance model is used to describe dynamic characteristics of a wind turbine, a flexible DC converter, and other power devices, avoiding coupling between device modeling and an operation mode of the system. In addition, the node admittance matrix is used for analysis so as to fully consider a plurality of power electronic devices and a grid structure of the offshore wind farm, realizing comprehensive analysis.

Claims

1. A method for evaluating resonance stability of a flexible direct current (DC) transmission system in an offshore wind farm, wherein the transmission system comprises the offshore wind farm and a flexible DC converter, the offshore wind farm converts wind energy into a DC and transmits the DC to the flexible DC converter, the converter further converts the DC into an alternating current (AC) to supply power to an onshore power grid system, and the method comprises the following steps: (1) establishing s-domain impedance models of power devices comprising a wind turbine, a step-up transformer, and a medium-voltage collecting submarine cable in the offshore wind farm; (2) establishing an s-domain impedance model of the flexible DC converter; (3) constructing an s-domain impedance equivalent circuit of the system based on the above established s-domain impedance models; (4) establishing an s-domain node admittance matrix Y(s) of the system based on the s-domain impedance equivalent circuit; (5) calculating a zero root s.sub.0 of a determinant of the s-domain node admittance matrix Y(s) of the system in a frequency range of 1 Hz to 1000 Hz, in other words, solving an equation |Y(s.sub.0)=0; and (6) using above calculated zero roots s.sub.0 of all determinants as all resonant modes of the system in the frequency range of 1 Hz to 1000 Hz, describing the resonant modes in a complex form and presenting them in a complex plane coordinate system; and if the zero roots so of all the determinants are located on a left-half plane of the complex plane coordinate system, determining that all the resonant modes are stable and the system has no risk of resonance instability; or if a zero root s.sub.0 of any determinant is located on a right-half plane of the complex plane coordinate system, which indicates that a resonant mode corresponding to the determinant is unstable, determining that the system has a risk of resonant instability.

2. The method according to claim 1, wherein the establishing s-domain impedance models of a wind turbine, a step-up transformer, and a medium-voltage collecting submarine cable in step (1) specifically comprises: analyzing transmission of a voltage perturbation component of a certain frequency of an AC system of the offshore wind farm in each power device and a quantitative correspondence between perturbation components based on a principle of frequency component balance, to determine a corresponding current perturbation component, and converting a frequency characteristic of port impedance of each power device into an s-domain impedance model of the power device based on a correspondence between a frequency domain and an s domain, wherein a ratio of the voltage perturbation component to the current perturbation component is port impedance of each power device at the frequency, and the power devices comprise the wind turbine, the step-up transformer, and the medium-voltage collecting submarine cable.

3. The method according to claim 1, wherein there are two types of wind turbines in the offshore wind farm: a doubly-fed wind turbine and a direct-drive wind turbine.

4. The method according to claim 3, wherein the doubly-fed wind turbine is composed of a fan, a rotor-side converter, and a grid-side converter, and its s-domain impedance model is as follows: $Z_{\mathrm{DFIG}}\left(s\right)=\frac{\left[\frac{\left\{\frac{s}{s-j{\omega }_m}\left[R_r+Z_{\mathrm{RSC}}\left(s-j{\omega }_m\right)\right]+s\left(L_r-M\right)\right\}\times \mathrm{sM}}{\left\{\frac{s}{s-j{\omega }_m}\left[R_r+Z_{\mathrm{RSC}}\left(s-j{\omega }_m\right)\right]+s\left(L_r-M\right)\right\}+\mathrm{sM}}+R_s+s\left(L_s-M\right)\right]\times \left[Z_{\mathrm{GSC}}\left(s\right)+{\mathrm{sL}}_g\right]}{\left[\frac{\left\{\frac{s}{s-j{\omega }_m}\left[R_r+Z_{\mathrm{RSC}}\left(s-j{\omega }_m\right)\right]+s\left(L_r-M\right)\right\}\times \mathrm{sM}}{\left\{\frac{s}{s-j{\omega }_m}\left[R_r+Z_{\mathrm{RSC}}\left(s-j{\omega }_m\right)\right]+s\left(L_r-M\right)\right\}+\mathrm{sM}}+R_s+s\left(L_s-M\right)\right]+\left[Z_{\mathrm{GSC}}\left(s\right)+{\mathrm{sL}}_g\right]}$ $\{\begin{array}{c}{Z}_{\mathrm{RSC}}\left(s\right)=\frac{R_{\mathrm{RL},\mathrm{RSC}}+{\mathrm{sL}}_{\mathrm{RL},\mathrm{RSC}}+K_{m,\mathrm{RSC}}{U}_{\mathrm{dc},\mathrm{RSC}}\left(H_{\mathrm{In},\mathrm{RSC}}\left(s-j{\omega }_1\right)-{\mathrm{jK}}_{i,\mathrm{RSC}}\right)G_{i,\mathrm{RSC}}}{1-K_{m,\mathrm{RSC}}{U}_{\mathrm{dc},\mathrm{RSC}}{K}_{v,\mathrm{RSC}}{G}_{v,\mathrm{RSC}}}\\ Z_{\mathrm{GSC}}\left(s\right)=\frac{R_{\mathrm{RL},\mathrm{GSC}}+{\mathrm{sL}}_{\mathrm{RL},\mathrm{GSC}}+K_{m,\mathrm{GSC}}{U}_{\mathrm{dc},\mathrm{GSC}}\left(H_{\mathrm{In},\mathrm{GSC}}\left(s-j{\omega }_1\right)-{\mathrm{jK}}_{i,\mathrm{GSC}}\right)G_{i,\mathrm{GSC}}}{1-K_{m,\mathrm{GSC}}{U}_{\mathrm{dc},\mathrm{GSC}}{K}_{v,\mathrm{GSC}}{G}_{v,\mathrm{GSC}}}\end{array}$ wherein Z.sub.DFIG(s) represents impedance of the doubly-fed wind turbine at a frequency s, ω.sub.m represents an angular velocity of a rotor of the fan, R.sub.r represents resistance of the rotor of the fan, L.sub.r represents inductance of the rotor of the fan, R.sub.s represents resistance of a stator of the fan, L.sub.s represents inductance of the stator of the fan, M represents mutual inductance of the rotor and the stator of the fan, L.sub.g represents filter inductance of the grid-side converter, Z.sub.RSC(s) and Z.sub.RSC(s−jω.sub.m) represent impedance of the rotor-side converter at frequencies s and s−jω.sub.m respectively, Z.sub.GSC(s) represents impedance of the grid-side converter at the frequency s, s represents a Laplace operator, j represents a imaginary unit, R.sub.RL,RSC and L.sub.RL,RSC represent resistance and inductance of an egress circuit of the rotor-side converter respectively, K.sub.m,RSC represents a voltage modulation coefficient of the rotor-side converter, K.sub.m,GSC represents a voltage modulation coefficient of the grid-side converter, U.sub.dc,RSC represents a DC-side voltage of the rotor-side converter, U.sub.dc,GSC represents a DC-side voltage of the grid-side converter, H.sub.In, RSC(s−jω.sub.1) represents a transfer function for PI of inner-loop control of the rotor-side converter at a frequency s−jω.sub.1, H.sub.In,GSC(s−jω.sub.1) represents a transfer function for PI of inner-loop control of the grid-side converter at the frequency s−jω.sub.1, K.sub.i,RSC represents a current decoupling coefficient of inner-loop control of the rotor-side converter, K.sub.i,GSC represents a current decoupling coefficient of inner-loop control of the grid-side converter, G.sub.i,RSC represents a per-unit coefficient of current measurement of the rotor-side converter, G.sub.i,GSC represents a per-unit coefficient of current measurement of the grid-side converter, G.sub.v,RSC represents a per-unit coefficient of voltage measurement of the rotor-side converter, G.sub.v,GSC represents a per-unit coefficient of voltage measurement of the grid-side converter, K.sub.v,RSC represents a voltage compensation coefficient of inner-loop control of the rotor-side converter, K.sub.v,GSC represents a voltage compensation coefficient of inner-loop control of the grid-side converter, ω.sub.1 represents an angular frequency of the power grid system, and R.sub.RL,GSC and L.sub.RL,GSC represent resistance and inductance of an egress circuit of the grid-side converter respectively.

5. The method according to claim 3, wherein the direct-drive wind turbine is composed of a fan and a grid-tied converter, and its s-domain impedance model is as follows: $\begin{array}{c}{Z}_{\mathrm{PMSG}}\left(s\right)=Z_{\mathrm{VSC}}\left(s\right)+{\mathrm{sL}}_{g,\mathrm{VSC}}\\ \{Z_{\mathrm{VSC}}\left(s\right)=\frac{R_{\mathrm{RL},\mathrm{VSC}}+{\mathrm{sL}}_{\mathrm{RL},\mathrm{VSC}}+K_{m,\mathrm{VSC}}{U}_{\mathrm{dc},\mathrm{VSC}}\left(H_{\mathrm{In},\mathrm{VSC}}\left(s-j{\omega }_1\right)-{\mathrm{jK}}_{i,\mathrm{VSC}}\right)G_{i,\mathrm{VSC}}}{1-K_{m,\mathrm{VSC}}{U}_{\mathrm{dc},\mathrm{VSC}}{K}_{v,\mathrm{VSC}}{G}_{v,\mathrm{VSC}}}\end{array}$ wherein, Z.sub.PMSG(s) represents impedance of the direct-drive wind turbine at a frequency s, Z.sub.VSC(s) represents impedance of the grid-tied converter at the frequency s, L.sub.g,VSC represents filter inductance of the grid-tied converter, R.sub.RL,VSC and L.sub.RL,VSC represent resistance and inductance of an egress circuit of the grid-tied converter respectively, K.sub.m,VSC represents a voltage modulation coefficient of the grid-tied converter, U.sub.dc,VSC represents a DC-side voltage of the grid-tied converter, H.sub.In,VSC(s−jω.sub.1) represents a transfer function for PI of inner-loop control of the grid-tied converter at a frequency s−jω.sub.1, K.sub.i,VSC represents a current decoupling coefficient of inner-loop control of the grid-tied converter, G.sub.i,VSC represents a per-unit coefficient of current measurement of the grid-tied converter, G.sub.v,VSC represents a per-unit coefficient of voltage measurement of the grid-tied converter, K.sub.v,VSC represents a voltage compensation coefficient of inner-loop control of the grid-tied converter, s represents a Laplace operator, j represents a imaginary unit, and ω.sub.1 represents an angular frequency of the power grid system.

6. The method according to claim 1, wherein a specific implementation of step (2) is as follows: building a simulation model of the flexible DC converter in electromagnetic transient-state simulation software, injecting a current perturbation component of a certain frequency into an AC side of the flexible DC converter to measure a corresponding voltage perturbation component, obtaining a ratio of the current perturbation component to the voltage perturbation component, namely, AC-side impedance of the flexible DC converter, and traversing each frequency to obtain a frequency characteristic curve of the AC-side impedance of the flexible DC converter; and finally obtaining the s-domain impedance model of the flexible DC converter by fitting points of the characteristic curve, wherein the s-domain impedance model is as follows: $Z_{\mathrm{MMC}}\left(s\right)=\frac{a_n{s}^n+a_{n-1}{s}^{n-1}+.Math.+a_{1}s+a_0}{b_m{s}^m+b_{m-1}{s}^{m-1}+.Math.+b_{1}s+b_0}$ wherein Z.sub.MMC(s) represents impedance of the flexible DC converter at a frequency s, a.sub.0 to a.sub.n represent coefficients of a to-be-fitted numerator polynomial, b.sub.0 to b.sub.m represent coefficients of a to-be-fitted denominator polynomial, s represents a Laplace operator, and n and m represent specified orders of the numerator polynomial and the denominator polynomial respectively.

7. The method according to claim 1, wherein in step (5), the zero roots s.sub.0 of all the determinants are obtained by solving the equation |Y(s.sub.0)|=0 by a Jacobi iterative method or a Newton iterative method.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0022] FIG. 1 is a schematic flowchart of steps of a method for analyzing resonance stability of a flexible DC transmission system in an offshore wind farm according to the present disclosure;

[0023] FIG. 2 is a schematic structural diagram of a flexible DC transmission system in an offshore wind farm;

[0024] FIG. 3 is an equivalent schematic diagram of an s-domain impedance model of a doubly-fed wind turbine;

[0025] FIG. 4 is an equivalent schematic diagram of an s-domain impedance model of a direct-drive wind turbine;

[0026] FIG. 5(a) is a schematic diagram of a frequency characteristic of AC-side impedance (including an amplitude and a phase angle) of a flexible DC converter in a V/F control mode in a frequency range of 1 Hz to 100 Hz;

[0027] FIG. 5(b) is a schematic diagram of a frequency characteristic of AC-side impedance (including an amplitude and a phase angle) of a flexible DC converter in a V/F control mode in a frequency range of 100 Hz to 1000 Hz;

[0028] FIG. 6 is a schematic diagram of an example s-domain equivalent circuit of a flexible DC transmission system in an offshore wind farm; and

[0029] FIG. 7 is a schematic diagram of an example resonant mode of a flexible DC transmission system in an offshore wind farm.

DETAILED DESCRIPTION

[0030] In order to more specifically describe the present disclosure, the technical solution of the present disclosure is described in detail below with reference to the accompanying drawings and specific implementations.

[0031] As shown in FIG. 1, a method for evaluating resonance stability of a flexible DC transmission system in an offshore wind farm in the present disclosure specifically includes the following steps:

[0032] (1) Establish s-domain impedance models of a wind turbine, a step-up transformer, a medium-voltage collecting submarine cable, and other power devices in an offshore wind farm, where this step specifically includes: analyzing transmission of a voltage perturbation component of a certain frequency of an AC system of the offshore wind farm in each power device and a quantitative correspondence between perturbation components based on a principle of frequency component balance, to determine a corresponding current perturbation component, and converting a frequency characteristic of port impedance of each power device into an s-domain impedance model of the power device based on a correspondence between a frequency domain and an s domain, where a ratio of the voltage perturbation component to the current perturbation component is port impedance of each power device at the frequency.

[0033] There are two types of wind turbines: a doubly-fed wind turbine and a direct-drive wind turbine. An s-domain impedance model of the doubly-fed power turbine is expressed as follows:

[00004]$Z_{\mathrm{DFIG}}\left(s\right)=\frac{\left[\frac{\left\{\frac{s}{s-j{\omega }_m}\left[R_r+Z_{\mathrm{RSC}}\left(s-j{\omega }_m\right)\right]+s\left(L_r-M\right)\right\}\times \mathrm{sM}}{\left\{\frac{s}{s-j{\omega }_m}\left[R_r+Z_{\mathrm{RSC}}\left(s-j{\omega }_m\right)\right]+s\left(L_r-M\right)\right\}+\mathrm{sM}}+R_s+s\left(L_s-M\right)\right]\times \left[Z_{\mathrm{GSC}}\left(s\right)+{\mathrm{sL}}_g\right]}{\left[\frac{\left\{\frac{s}{s-j{\omega }_m}\left[R_r+Z_{\mathrm{RSC}}\left(s-j{\omega }_m\right)\right]+s\left(L_r-M\right)\right\}\times \mathrm{sM}}{\left\{\frac{s}{s-j{\omega }_m}\left[R_r+Z_{\mathrm{RSC}}\left(s-j{\omega }_m\right)\right]+s\left(L_r-M\right)\right\}+\mathrm{sM}}+R_s+s\left(L_s-M\right)\right]+\left[Z_{\mathrm{GSC}}\left(s\right)+{\mathrm{sL}}_g\right]}$$\{\begin{array}{c}{Z}_{\mathrm{RSC}}\left(s\right)=\frac{R_{\mathrm{RL},\mathrm{RSC}}+{\mathrm{sL}}_{\mathrm{RL},\mathrm{RSC}}+K_m{U}_{\mathrm{dc}}\left(H_{\mathrm{In},\mathrm{RSC}}\left(s-j{\omega }_1\right)-{\mathrm{jK}}_{i,\mathrm{RSC}}\right)G_i}{1-K_m{U}_{\mathrm{dc}}{K}_v{G}_v}\\ Z_{\mathrm{GSC}}\left(s\right)=\frac{R_{\mathrm{RL},\mathrm{GSC}}+{\mathrm{sL}}_{\mathrm{RL},\mathrm{GSC}}+K_m{U}_{\mathrm{dc}}\left(H_{\mathrm{In},\mathrm{GSC}}\left(s-j{\omega }_1\right)-{\mathrm{jK}}_{i,\mathrm{GSC}}\right)G_i}{1-K_m{U}_{\mathrm{dc}}{K}_v{G}_v}\end{array}$

where Z.sub.DFIG(s) represents s-domain impedance of a doubly-fed fan system, Z.sub.RSC(s) represents s-domain impedance of a rotor-side converter in the doubly-fed fan system, Z.sub.GSC(s) represents s-domain impedance of a grid-side converter in the doubly-fed fan system, ω.sub.m represents a speed of a rotor of a fan, R.sub.r represents resistance of the rotor of the fan, L.sub.r represents inductance of the rotor of the fan, R.sub.s represents resistance of a stator of the fan, L.sub.s represents inductance of the stator of the fan, M represents mutual inductance of the rotor and the stator of the fan, L.sub.g represents filter inductance of the converter, R.sub.RL,RSC and L.sub.RL,RSC represent resistance and inductance of an egress circuit of the rotor-side converter in the doubly-fed fan system respectively, K.sub.m represents a voltage modulation coefficient of the converter, U.sub.dc represents a DC-side voltage of the converter, H.sub.In,RSC(s) represents a transfer function for PI of an inner-loop control of the rotor-side converter in the doubly-fed fan system, K.sub.i,RSC represents a current decoupling coefficient of the inner-loop control of the rotor-side converter in the doubly-fed fan system, G.sub.i represents a per-unit coefficient of current measurement of the converter, G.sub.v represents a per-unit coefficient of voltage measurement of the converter, K.sub.v represents a voltage compensation coefficient of the inner-loop control of the converter, R.sub.RL,GSC and L.sub.RL,GSC represent resistance and inductance of an egress circuit the grid-side converter in the doubly-fed fan system respectively, H.sub.In,GSC(s) represents a transfer function for PI of an inner-loop control of the grid-side converter in the doubly-fed fan system, and K.sub.i,GSC represents a current decoupling coefficient of the inner-loop control of the grid-side converter in the doubly-fed fan system.

[0034] An s-domain impedance model of the direct-drive wind turbine is expressed as follows:

[00005]$\begin{array}{c}{Z}_{\mathrm{PMSG}}\left(s\right)=Z_{\mathrm{VSC}}\left(s\right)+{\mathrm{sL}}_g\\ \{Z_{\mathrm{VSC}}\left(s\right)=\frac{R_{\mathrm{RL},\mathrm{VSC}}+{\mathrm{sL}}_{\mathrm{RL},\mathrm{VSC}}+K_m{U}_{\mathrm{dc}}\left(H_{\mathrm{In},\mathrm{VSC}}\left(s-j{\omega }_1\right)-{\mathrm{jK}}_{i,\mathrm{VSC}}\right)G_i}{1-K_m{U}_{\mathrm{dc}}{K}_v{G}_v}\end{array}$

where Z.sub.PMSG(s) represents s-domain impedance of a direct-drive fan system, Z.sub.VSC(s) represents s-domain impedance of a grid-tied converter in the direct-drive fan system, R.sub.RL,VSC and L.sub.RL,VSC represent resistance and inductance of an egress circuit of the grid-tied converter in the direct-drive fan system respectively, H.sub.In,VSC(s) represents a transfer function for PI of an inner-loop control of the grid-tied converter in the direct-drive fan system, and K.sub.i,VSC represents a current decoupling coefficient of the inner-loop control of the grid-tied converter in the direct-drive fan system.

[0035] (2) Establish an s-domain impedance model of a flexible DC converter in an offshore converter station, where this step specifically includes: building a simulation model of the flexible DC converter (in a V/F control mode) in the offshore converter station in electromagnetic transient-state simulation software, injecting a current perturbation component of a certain frequency into an AC side of the flexible DC converter to measure a corresponding voltage perturbation component, obtaining a ratio of the current perturbation component to the voltage perturbation component, namely, AC-side impedance of the flexible DC converter, fitting a frequency characteristic of the AC-side impedance of the flexible DC converter based on results obtained at different frequencies, and converting the frequency characteristic of the AC-side impedance of the flexible DC converter into the s-domain impedance model of the flexible DC converter based on a correspondence between a frequency domain and an s domain.

[0036] The s-domain impedance model of the flexible DC converter is expressed as follows:

[00006]$Z_{\mathrm{MMC}}\left(s\right)=\frac{a_n{s}^n+.Math.+a_k{s}^k+.Math.+a_0}{b_m{s}^m+.Math.+b_k{s}^k+.Math.+b_0}$

where Z.sub.MMC(s) represents s-domain impedance of the flexible DC converter, a.sub.0, . . . a.sub.k, . . . a.sub.n represent coefficients of numerator terms of a fractional polynomial, b.sub.0, . . . b.sub.k , . . . b.sub.m represent coefficients of denominator terms of the fractional polynomial, and n and m represent orders of the numerator terms and the denominator terms of the fractional polynomial respectively.

[0037] (3) Construct an s-domain equivalent circuit of a flexible DC transmission system in the offshore wind farm based on steps (1) and (2).

[0038] (4) Construct an s-domain node admittance matrix Y(s) of the flexible DC transmission system in the offshore wind farm based on step (3), where

[00007]$Y\left(s\right)=\left[\begin{array}{ccccc}{y}_{11}& .Math.& y_{1j}& .Math.& y_{1n}\\ .Math.& \ddots & .Math.& \ddots & .Math.\\ y_{j1}& .Math.& y_{\mathrm{jj}}& .Math.& y_{\mathrm{jn}}\\ .Math.& \ddots & .Math.& \ddots & .Math.\\ y_{n1}& .Math.& y_{\mathrm{nj}}& .Math.& y_{\mathrm{nn}}\end{array}\right].$

[0039] (5) Calculate a zero root s.sub.0 of a determinant of the node admittance matrix Y(s) of the flexible DC transmission in the offshore wind farm in a frequency range of 1 Hz to 1000 Hz, in other words, solve an equation |Y(s.sub.0)|=0, based on step (4).

[0040] (6) Use above calculated zero roots s.sub.0 of all determinants in step (5) as all resonant modes of the flexible DC transmission system in the offshore wind farm in the frequency range of 1 Hz to 1000 Hz, and determine resonance stability of the system based on distribution of the resonant modes on a complex plane; and if all the resonant modes are located on a left-half part of the complex plane, determine that all the resonant modes are stable and the system has no risk of resonance instability; or if a resonant mode is located on a right-half part of the complex plane, which indicates that the resonant mode is unstable, determine that the system has a risk of resonant instability.

[0041] Next, a flexible DC transmission system in an offshore wind farm is used as an example, as shown in FIG. 2. Resonance stability of the flexible DC transmission system in the offshore wind farm is analyzed.

[0042] Step 1: Establish s-domain impedance models of a doubly-fed wind turbine and a direct-drive wind turbine in the offshore wind farm. A DC-side voltage of a converter generally remains constant. Therefore, the doubly-fed wind turbine and the direct-drive wind turbine each can be decomposed into grid-tied units dominated by a two-level voltage source converter. Based on a principle of frequency component balance, an s-domain impedance model of the two-level voltage source converter can be established. Then, based on the decomposition of the doubly-fed wind turbine and the direct-drive wind turbine, the s-domain impedance models of the doubly-fed wind turbine and the direct-drive wind turbine can be obtained, as shown in FIG. 3 and FIG. 4 respectively.

[0043] Step 2: Establish an s-domain impedance model of a flexible DC converter in an offshore converter station. A simulation model of the flexible DC converter (in a V/F control mode) in the offshore converter station is built in electromagnetic transient-state simulation software, a current perturbation component of a certain frequency is injected into an AC side of the flexible DC converter to measure a corresponding voltage perturbation component, a ratio of the current perturbation component to the voltage perturbation component, namely, AC-side impedance of the flexible DC converter, is obtained, a frequency characteristic of the AC-side impedance of the flexible DC converter can be fitted based on results obtained at different frequencies, and the frequency characteristic of the AC-side impedance of the flexible DC converter is converted into the s-domain impedance model of the flexible DC converter based on a correspondence between a frequency domain and an s domain. The frequency characteristic of the AC-side impedance of the flexible DC converter in the V/F control mode is shown in FIG. 5(a) and FIG. 5(b).

[0044] Step 3: Construct an examples-domain equivalent circuit of the flexible DC transmission system in the offshore wind farm. Based on the established s-domain impedance models of the doubly-fed wind turbine and the direct-drive wind turbine in the offshore wind farm, the s-domain impedance model of the flexible DC converter in the offshore converter station, and an example grid structure of the flexible DC transmission system in the offshore wind farm, the example s-domain equivalent circuit of the flexible DC transmission system in the offshore wind farm is constructed, as shown in FIG. 6.

[0045] Step 4: Establish an example s-domain node admittance matrix of the flexible DC transmission system in the offshore wind farm. Based on the constructed example s-domain equivalent circuit of the flexible DC transmission system in the offshore wind farm, all nodes can be numbered first, and then self admittance y.sub.ii and mutual admittance y.sub.ij of the nodes can be filled in according to a numbering sequence. After all the nodes in the system are traversed, the node admittance matrix Y(s) of the system is formed.

[0046] Step 5: Determine an example resonant mode of the flexible DC transmission system in the offshore wind farm and resonance stability of the flexible DC transmission system. The example resonant mode of the flexible DC transmission system in the offshore wind farm is determined, in other words, a zero root of a determinant of the node admittance matrix of the system is obtained. Firstly, a frequency characteristic of the determinant of the node admittance matrix of the system in a frequency range of 1 Hz to 1000 Hz is determined through frequency scanning, and an abnormal frequency point of the system is determined. Then, the abnormal frequency point is used as an initial value of a Newton-Raphson iterative method to obtain a solution iteratively. All resonant modes are obtained and presented in a complex plane coordinate system, and the resonance stability of the flexible DC transmission system in the offshore wind farm is determined based on distribution of the resonant modes. If all the resonant modes are located on a left-half complex plane, it is determined that all the resonant modes are stable and the system has no risk of resonance instability; or if a resonant mode is located on a right-half complex plane, it indicates that the resonant mode corresponding to the determinant is unstable, and it is determined that the system has a risk of resonant instability.

[0047] The example distribution of the resonant modes of the flexible DC transmission system in the offshore wind farm in this implementation is shown in FIG. 7. As shown in FIG. 7, the system mainly has three resonant modes with resonant frequencies being 76 Hz, 113 Hz, and 125 Hz respectively in the frequency range of 1 Hz to 1000 Hz, and the three resonant modes are all located on the left-half complex plane. Therefore, the three resonant modes are stable, and the system has no risk of resonant instability.

[0048] The above description of the embodiments is intended to facilitate a person of ordinary skill in the art to understand and use the present disclosure. Obviously, a person skilled in the art can easily make various modifications to these embodiments, and apply a general principle described herein to other embodiments without creative efforts. Therefore, the present disclosure is not limited to the embodiments herein. All improvements and modifications made by a person skilled in the art according to the disclosure of the present disclosure should fall within the protection scope of the present disclosure. CLAIMS: