CN106250660A - A kind of marine wind electric field harmonic analysis method - Google Patents

Abstract

The modal analysis method of a kind of marine wind electric field resonance, the method includes: 1) according to the most each element of offshore wind farm field system and the annexation of cable, set up system harmonics model；2) setting up the network admittance matrix of system according to described system harmonics model, utilize the mode impedance spectrum of Modal Method solving system, calculate the participation factors of each node, truly there is position in determine resonance；3) sensitivity of system element electric parameter is assessed；4) sensitivity of system design parameters is assessed.This method sets up Equivalent Model according to the parameter of each element of wind energy turbine set, uses the resonance performance of modal analysis method research system under different topology and the parameter such as cable, transformator, can optimize topology design and the Component selection of wind energy turbine set.

Description

Offshore wind power plant resonance analysis method

Technical Field

The invention relates to an offshore wind farm, in particular to a resonance analysis method for the offshore wind farm, which is specifically used for establishing a harmonic model of an offshore wind farm system, and calculating participation degrees of global resonance points and nodes of the system by using a modal method so as to determine the true occurrence position of resonance. And meanwhile, the influence of the change of parameters such as a topological structure, the length of the cable and the like on the resonance degree is evaluated by using sensitivity analysis.

Background

Offshore wind energy resources are abundant, the generated energy is large, land is not occupied, and offshore wind power generation becomes an important development direction in the field of wind power. By 6 months in 2012, the installed capacity of offshore wind power in the world reaches 4620MW, which accounts for about 2% of the total installed capacity of wind power. With the rapid development of offshore wind power, harmonic waves generated by offshore wind power integration can threaten the safety and stability of a power grid system. High-capacity submarine cables are widely applied to offshore wind power transmission systems, and parallel resonance is easy to occur when the cables are connected with inductive elements such as transformers and the like. Once harmonic resonance generated by harmonic waves output by the wind driven generator in a transmission system can cause overvoltage and overcurrent, so that overheating loss of elements can be caused, insulation failure can be caused in serious cases, and even serious electric power accidents can be caused.

A transmission system of a general offshore wind farm comprises a power collection network, an offshore booster station, a high-voltage transmission cable and an onshore converter station. Regarding the topology of the power collection grid, the literature [ Huanglingling, Yinyang, and Guo Ming, and optimization research of the electrical wiring scheme of the large offshore wind farm power grid technology, 2008(08): p.77-81 ] analyzes the investment cost of each element of the offshore wind farm and optimizes the wiring scheme of the power collection grid by combining a genetic algorithm. The document [ Sun Junyo, et al, interior topology optimization design of large offshore alternating current wind farms, grid technology, 2013(07): p.1978-1982 ] and [ Wangjiando, Likingdom, comparison of economy of layout of electrical systems inside offshore wind farms, power system automation, 2009(11): p.99-103 ] compares various current collection grid topologies from an economic point of view. The document [ Liu, X.and S.Islam.reliability issues of offset wind and noise Applied to Power Sys-tems,2008.PMAPS'08.Proceedings of the 10th International Conference on.2008.IEEE ] studied the reliability of wind farm topologies and concluded that the ring topology is superior in reliability to the chain topology. Because a great amount of submarine cables are adopted in the power collection network and are directly connected with the transformer. Besides affecting the economy and reliability of the wind farm, the topological changes of the collection grid can also cause changes of cable lengths, electrical parameters and connection relations of elements, which can have a relatively large influence on resonance. Because the number of system elements related to the power collection network topology is large, the situation is complex, a correct model needs to be established, and the influence of the topology on the resonance can be correctly analyzed by adopting a proper research method.

At present, the offshore wind farm resonance research mainly adopts a frequency spectrum analysis method, but the method has slow detection speed and provides less information. The modal analysis method can obtain information about resonance mechanism and degree by analyzing the property of the characteristic root of the admittance matrix of the system, and provides a new idea for resonance analysis. Sensitivity analysis can determine components that have a greater effect on harmonic resonance, and thus can specifically adjust component parameters. At present, a modal analysis method is not applied to the research of the resonance of a power grid of an offshore wind farm.

Disclosure of Invention

The invention aims to solve the technical problem of providing a method for analyzing the resonance of an offshore wind farm aiming at the defects of the conventional method for analyzing the resonance of the offshore wind farm. In the stage of designing the wind power plant, although the position of the wind turbine is determined according to wind direction, wind power and other factors, the potential risk that resonance may occur needs to be considered in the connection form, the length and the electrical parameters of the cable, so that simulation modeling analysis needs to be performed on the resonance in the stage. According to the method, an equivalent model is established according to parameters of each element of the wind power plant, resonance performance of the system under different topologies and parameters of cables, transformers and the like is researched by using a modal analysis method, and topology design and element selection of the wind power plant can be optimized.

The technical solution of the invention is as follows:

a modal analysis method of offshore wind farm resonance is characterized by comprising the following steps:

1) establishing a system harmonic model according to the connection relation of the offshore wind power plant system, namely each element and the cable;

2) establishing a network admittance matrix of the system according to the system harmonic model, solving a modal impedance frequency spectrum of the system by using a modal method, calculating participation factors of each node, and determining a real occurrence position of resonance;

3) evaluating the sensitivity of the system component electrical parameters;

4) the sensitivity of the system design parameters was evaluated.

The establishing of the system harmonic model comprises the following steps:

1) harmonic model of wind turbine generator:

the single wind turbine generator consists of a wind driven generator, a converter and an LCL filter, is a main harmonic source of a wind power plant, and represents a wind turbine generator harmonic model by an ideal voltage source containing harmonic waves and the LCL filter;

2) harmonic model of the transformer:

the resistance Rs of the wire winding of the transformer and the eddy current loss Rp of the wire winding are calculated according to the following formula: :

$R_s=\frac{X}{tan\mathrm{\φ}}---\left(1\right)$

R_p＝10Xtanφ (2)

wherein X is the leakage reactance of the transformer at 50Hz,h represents the harmonic frequency, and S is the rated power of the transformer;

3) harmonic model of submarine cable:

considering the long-line effect of the submarine cable, a distributed parameter model is adopted, and the calculation formula is shown in (6) to (9):

$Z_c=\sqrt{(R_0+{\mathrm{jhL}}_0)/jh{C}_0}---\left(6\right)$

$\mathrm{\γ}=\sqrt{(R_0+{\mathrm{jhL}}_0){\mathrm{jhC}}_0}---\left(7\right)$

Z＝Z_csinh(γl)＝R+jhL (8)

$Y=\frac{2(\cosh \mathrm{\γ}l-1)}{Z_c\sinh \mathrm{\γ}l}=jhC---\left(9\right).$

the content of the step 2) comprises the following steps:

firstly, all n nodes in the system are labeled, and then a system network admittance matrix Y is established by utilizing the mutual admittance between the node self-admittance and the nodes, wherein an element Y_ii(i ═ 1,2, … n) is the self-admittance of node i, Y_ij(i, j ═ 1,2, … n; i ≠ j) is the inverse number of transadmittance between nodes i, j;

the voltage-current relationship of the n-node system is expressed by the following equation (10):

V＝Y^-1I (10)

y can be decomposed into the following forms:

Y＝LΛT (11)

substitution (10) can give:

TV＝Λ^-1TI (12)

defining U as a modal voltage vector and J as a modal current vector;

at arbitrary frequencies Λ^-1Defined as the modal impedance at that frequency; the voltage at the kth node at this time is:

$v_k={\mathrm{\λ}}_i^{-1}\underset{m=1}{\overset{n}{\mathrm{\Σ}}}{l}_{ki}{t}_{im}{i}_m---\left(13\right)$

where k is the node number, i is the mode number, l_kit_imIs a "participation factor";

and traversing the selected frequency interval to obtain a system modal impedance frequency spectrum in the frequency interval, wherein the amplitude extreme value of the system modal impedance frequency spectrum is a system modal resonance point, the participation factor of each node at the modal resonance point is solved, and the node with the largest participation factor is the true occurrence position of resonance.

The method for evaluating the sensitivity of the electrical parameters of the elements of the system comprises the following steps:

the sensitivity expression of the resonance impedance of the parallel element with admittance Y ═ G + jB is as follows:

$\frac{\∂\left|\mathrm{\λ}\right|}{\∂G}=\frac{d\left|\mathrm{\λ}\right|}{dF}\frac{\∂F}{\∂G}=\frac{S_r{\mathrm{\λ}}_r+S_i{\mathrm{\λ}}_i}{\sqrt{{\mathrm{\λ}}_r^2+{\mathrm{\λ}}_i^2}}---\left(14\right)$

$\frac{\∂\left|\mathrm{\λ}\right|}{\∂B}=\frac{d\left|\mathrm{\λ}\right|}{dF}\frac{\∂F}{\∂B}=\frac{S_r{\mathrm{\λ}}_r-S_i{\mathrm{\λ}}_i}{\sqrt{{\mathrm{\λ}}_r^2+{\mathrm{\λ}}_i^2}}---\left(15\right)$

wherein G represents the real part of the element admittance, B represents the imaginary part of the element admittance, λ_rAnd λ_iRespectively being the k-th eigenvalue lambda_kReal and imaginary parts of, S_rAnd S_iRespectively the node Y of the element of the characteristic value pair_ijSensitivity S of_λ,ijThe real and imaginary parts of (c);

the sensitivity expression for the series element with impedance Z ═ R + jX is as follows:

$\frac{\∂\left|\mathrm{\λ}\right|}{\∂R}=\frac{\mathrm{\μ}(X^2-R^2)+2vRX}{(R^2+X^2)}---\left(16\right)$

$\frac{\∂\left|\mathrm{\λ}\right|}{\∂X}=\frac{v(X^2-R^2)-2\mathrm{\μ}RX}{(R^2+X^2)}---\left(17\right)$

wherein,r represents the real part of the impedance of the series element, and X represents the imaginary part of the impedance of the series element;

let the element parameter be α, define the normalized sensitivity as:

$\frac{\∂\left|\mathrm{\λ}\right|}{\∂\mathrm{\α}}{|}_{norm}=\frac{\frac{\∂\left|\mathrm{\λ}\right|}{\mathrm{\λ}}}{\frac{\∂\mathrm{\α}}{\mathrm{\α}}}=\frac{\∂\left|\mathrm{\λ}\right|}{\∂\mathrm{\α}}\·\frac{\mathrm{\α}}{\mathrm{\λ}}---\left(18\right)$

and the influence of each parameter in the offshore wind power plant on the resonance intensity is quantified by adopting parameter sensitivity analysis.

The electrical parameters of the elements comprise transformer inductance, transformer winding resistance, transformer eddy current loss resistance, and resistance, inductance and capacitance of various types of cables.

The sensitivity of evaluating the design parameter includes:

setting an initial value of a design parameter to α₀The values of the variables of the design parameters are sequentially calculatedEquidistant change to 4 α₀In the process, the system modal resonance impedance and the frequency corresponding to each variable value are drawn into a curve of the system modal resonance impedance and the frequency changing along with the variable value.

The design parameters comprise cable length, cable cross-sectional area and transformer capacity.

Compared with the prior art, the invention has the beneficial effects that:

the traditional impedance spectrum scanning method is simple and feasible, but can only provide the resonance condition of individual nodes, and the resonance condition of the system global is lost. The modal analysis method of the offshore wind farm resonance can conveniently solve the resonance condition of the whole system and can provide more detailed information of resonance positions, participating nodes and the like.

The invention can more clearly reveal the elements most related to resonance based on the parameter sensitivity analysis carried out by a modal method, and provides reliable basis for the topological design of the offshore wind farm and the selection of element parameters.

Drawings

FIG. 1 is a flow chart of an offshore wind farm resonance analysis method based on modal calculation according to the present invention

FIG. 2 is a typical block diagram of an offshore wind farm.

FIG. 3 is a harmonic model diagram of a wind turbine.

Fig. 4 is a diagram of a harmonic model of a transformer.

Fig. 5 is a diagram of a harmonic model of a submarine cable.

FIG. 6 is a diagram of the resonance impedance spectrum of the offshore wind farm mode.

FIG. 7 is a graph of resonant impedance as a function of cable length for different lengths of cable between wind turbines.

FIG. 8 is a graph of resonant frequency versus cable length for different lengths of cable between wind turbines.

Detailed Description

The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

Referring to fig. 1, fig. 1 is a flow chart of the method for analyzing the resonance of the offshore wind farm based on modal calculation, and it can be seen from the flow chart that the method for analyzing the resonance of the offshore wind farm based on modal calculation includes the following steps:

the method comprises the following steps: establishing a harmonic model of each element of the offshore wind farm:

a typical offshore wind farm is constructed as shown in figure 2. The wind turbine is boosted to 35kV through the transformer, then enters the current collection system, is connected to the offshore booster station through the medium-voltage submarine cable and the bus bar, is boosted to 150kV in the offshore booster station, is conveyed to the onshore converter station through the high-voltage cable, and then is merged into the onshore power grid. In order to perform reactive compensation or filter out harmonic waves, a capacitor bank or a filter device is arranged at the corresponding node. In order to accurately evaluate the resonance condition of the system, a correct harmonic model of each element is established, which comprises the following steps:

1) harmonic model of wind turbine generator

A single wind turbine generator set consists of a wind driven generator, a converter and an LCL filter and is a main harmonic source of a wind power plant. Because the invention mainly researches the resonance condition of the transmission system of the wind power plant, the internal structures of the fan and the converter are ignored, and the wind turbine model is represented by an ideal voltage source containing harmonic waves^[13]While leaving the LCL filter as shown in fig. 3.

2) Transformer harmonic model

The offshore wind farm comprises two transformers, namely a 0.69/35kV fan transformer at the outlet end of a fan and an 35/150kV offshore booster transformer at a bus bar. A currently recognized and relatively accurate transformer model is a CIGRE standard harmonic model [ see Wu, x., et al, nodal harmonic interference of AC network in pss/e.in AC and DC Power Transmission,2010. acdc.9iet international conference on.2010.IET ], which approximates the eddy current loss dominating in the winding wire to the square of the frequency and considers the demagnetization effect, which can accurately reflect the actual working condition of the transformer, and the equivalent circuits of the wind turbine transformer and the marine step-up transformer are shown in fig. 4. In the figure, X is the leakage reactance of the transformer at 50Hz, h represents the harmonic frequency, Rs represents the resistance of the wire winding, Rp represents the eddy current loss of the wire winding, and Rs and Rp do not change with the frequency, and the calculation formula is as follows:

R_p＝10Xtanφ (2)

in the formula,and S is the rated power of the transformer.

3) Harmonic model of submarine cable:

in frequency domain equivalence calculations for resonance studies, a submarine cable of unit length can be equated to a lumped parameter pi model. The resistance skin effect is taken into account, and the resistance, inductance and capacitance value of the unit length are calculated by formulas 3-5. However, considering the long-line effect of the submarine cable, a distributed parameter model is required, as shown in fig. 5, and the calculation process is shown in the formula 6-9:

$R_0=\frac{{\mathrm{\ρ}}^{\′}}{r_1^2\mathrm{\π}}(0.187+0.532\sqrt{h})---\left(3\right)$

$L_0=\frac{{\mathrm{\μ}}_0{\mathrm{\μ}}_{dr}}{2\mathrm{\π}}ln\left(\frac{r_2}{r_1}\right)---\left(4\right)$

$C_0={\mathrm{\ϵ}}_0{\mathrm{\ϵ}}_d\·\frac{2\mathrm{\π}}{ln\left(\frac{r_2}{r_1}\right)}---\left(5\right)$

$Z_c=\sqrt{(R_0+{\mathrm{jhL}}_0)/jh{C}_0}---\left(6\right)$

$\mathrm{\γ}=\sqrt{(R_0+{\mathrm{jhL}}_0){\mathrm{jhC}}_0}---\left(7\right)$

Z＝Z_csinh(γl)＝R+jhL (8)

$Y=\frac{2(\cosh \mathrm{\γ}l-1)}{Z_c\sinh \mathrm{\γ}l}=jhC---\left(9\right)$

step two: establishing a network admittance matrix of the system, solving a modal impedance frequency spectrum of the system by using a modal method, calculating participation factors of each node, and determining a real occurrence position of resonance:

a network admittance matrix for an electric power system having n nodes is a linear matrix describing the relationship between voltage and injected current at each node of the electric power network, established based on the equivalent admittance of the system components. Wherein the element Y_ii(i ═ 1,2, … n) is the self-admittance of node i, Y_ijAnd (i, j is 1,2, … n; i ≠ j) is the inverse number of the transadmittance between the node i and the node j, so that a network admittance matrix of the system is established.

For any power system, the system parallel resonance is necessarily generated because the inverse matrix of the network admittance matrix of the system presents elements with large values, and assuming that the admittance matrix of the system is Y, the voltage-current relationship is expressed as follows:

V＝Y^-1I (10)

wherein, V is a node voltage matrix, and I is a node injection current matrix.

The above formula can be broken down into the following forms:

Y＝LΛT (11)

in the formula, Λ is a diagonal eigenvalue matrix, and L, T is a left eigenvector matrix and a right eigenvector matrix respectively, then there is the following modal voltage-current expression:

TV＝Λ^-1TI (12)

defining U-TV as the modal voltage vector and J-TI as the modal current vector.

Suppose when Λ^-1Element λ of (5)_i ^-1Very large, very small modal i current J_iWill result in a large modal i-voltage U_iOther modal voltages will not be affected because there is no coupling between them and the modal i current, Λ is taken^-1The element with the maximum middle value is the modal impedance at the frequency, and the corresponding modal impedance value is calculated by traversing all the frequencies, so that the corresponding modal impedance frequency spectrum can be drawn, and the modal resonance frequency and strength are determined.

The voltage at node k can be expressed as:

$v_k={\mathrm{\λ}}_i^{-1}\underset{m=1}{\overset{n}{\mathrm{\Σ}}}{l}_{ki}{t}_{im}{u}_m---\left(13\right)$

illustrating that the corresponding elements in the key eigenvector describe the relationship between node voltage, node current and eigenvalue, i.e. the influence range of the key resonance, define l_kit_imIs the "participation factor", where k is the node number and i is the mode number. The physical meaning of the participation factor is the degree of contribution of node k to the mode i resonance. The node with larger participation factor is the node greatly influenced by the mode resonance, namely the true resonanceAnd the occurrence position is designed to take resonance suppression measures at the real occurrence position of the resonance, which is a specific node.

Step three: evaluating the influence degree of each element electrical parameter of the system on resonance, namely the sensitivity of the element electrical parameter:

and the influence of each parameter in the offshore wind power plant on the resonance intensity is quantified by adopting parameter sensitivity analysis.

The sensitivity expression of the resonance impedance to the parallel element (admittance Y ═ G + jB) is as follows:

$\frac{\∂\left|\mathrm{\λ}\right|}{\∂G}=\frac{d\left|\mathrm{\λ}\right|}{dF}\frac{\∂F}{\∂G}=\frac{S_r{\mathrm{\λ}}_r+S_i{\mathrm{\λ}}_i}{\sqrt{{\mathrm{\λ}}_r^2+{\mathrm{\λ}}_i^2}}---\left(14\right)$

$\frac{\∂\left|\mathrm{\λ}\right|}{\∂B}=\frac{d\left|\mathrm{\λ}\right|}{dF}\frac{\∂F}{\∂B}=\frac{S_r{\mathrm{\λ}}_r-S_i{\mathrm{\λ}}_i}{\sqrt{{\mathrm{\λ}}_r^2+{\mathrm{\λ}}_i^2}}---\left(15\right)$

wherein G represents the real component admittance and B represents the imaginary component admittance. In the formula of_rAnd λ_iRespectively being the k-th eigenvalue lambda_kReal and imaginary parts of, S_rAnd S_iRespectively the node Y of the element of the characteristic value pair_ijSensitivity S of_λ,ijThe real and imaginary parts of (c).

Since the series element sensitivity expression is conventionally expressed by impedance Z ═ R + jX instead of admittance, it is first calculated as admittance expression Y ═ G + jB, and then definedThe series element sensitivity expression is as follows:

$\frac{\∂\left|\mathrm{\λ}\right|}{\∂R}=\frac{\mathrm{\μ}(X^2-R^2)+2vRX}{(R^2+X^2)}---\left(16\right)$

$\frac{\∂\left|\mathrm{\λ}\right|}{\∂X}=\frac{v(X^2-R^2)-2\mathrm{\μ}RX}{(R^2+X^2)}---\left(17\right)$

wherein R represents the real part of the impedance of the element, and X represents the imaginary part of the impedance of the element.

The sensitivity value reflects the absolute relationship between the actual element and the resonant impedance, but in order to enable a plurality of parameters to be compared with each other and reveal the relative influence degree, the element parameter is set as α, and the normalized sensitivity is defined as follows:

$\frac{\∂\left|\mathrm{\λ}\right|}{\∂\mathrm{\α}}{|}_{norm}=\frac{\frac{\∂\left|\mathrm{\λ}\right|}{\mathrm{\λ}}}{\frac{\∂\mathrm{\α}}{\mathrm{\α}}}=\frac{\∂\left|\mathrm{\λ}\right|}{\∂\mathrm{\α}}\·\frac{\mathrm{\α}}{\mathrm{\λ}}---\left(18\right)$

wherein,andrespectively, representing the relative changes in the resonant impedance values and component parameters.

This index characterizes the percentage of change in the resonant impedance for values of different elements that change by the same percentage, which makes the sensitivity analysis more comparable between elements.

In the transmission system of the offshore wind farm, according to the adopted equivalent harmonic model, the electrical parameters of main elements comprise transformer inductance, transformer winding resistance, transformer eddy current loss resistance, and resistance, inductance and capacitance of various types of cables. These electrical parameters can be fine tuned by adjusting the configuration and materials of the components to change the resonant frequency and impedance of the system. The sensitivity analysis is to measure the influence of each electrical parameter, and provides reliable basis for designers during early element model selection.

Step four: evaluating the sensitivity of the design parameters:

the design parameters of the elements of the wind power plant refer to actual physical parameters such as cable length, cable cross-sectional area, transformer capacity and the like. This type of parameter is characterized by a single parameter value change, which changes multiple electrical parameter values. If the length of the cable is increased, the resistance, inductance and capacitance of the cable are increased. However, the influence of the increase of the resistance, the inductance and the capacitance on the resonance is inconsistent, so that the change of the resonance caused by the increase of the length of the cable cannot be intuitively judged, and the sensitivity analysis of the design parameter is increased.

Setting cable length, transformer capacity and initial value of transformer capacity to α₀Sequentially calculating the variable valuesEquidistant change to 4 α₀In the process, the system modal resonance impedance and frequency corresponding to each variable value are drawn into a curve of the impedance and the frequency changing along with the variable value, so as to explore the influence trend of the design parameters on the system resonance.

The evaluation can provide reference during wind power plant design, determine the cable length and the capacity parameters of each transformer through modeling simulation, and can be used for fine adjustment of parameters when system resonance is reduced.

The invention is further described with reference to the following embodiments, the method for modal analysis of offshore wind farm resonance comprises the following steps:

step one, establishing a harmonic model of each element of an offshore wind farm:

data used for modeling are obtained by an element supplier, and equivalent harmonic models of the wind turbine generator, the transformer and the submarine cable are established.

Step two, the modal analysis can be specifically divided into the following steps:

1) establishing a frequency model of each element of the system, wherein the equivalent resistance, the inductance and the capacitance of the frequency model change along with the frequency;

2) setting an initial frequency f ═ f₀Substituting the value into each element model;

3) writing a network admittance matrix Y at the moment;

4) eigenvalue decomposition of the network admittance matrix Y into Y ═ L Λ T, where Λ is the eigenvalue matrix whose inverse matrix Λ is^-1The diagonal elements of are respectivelyTaking the maximum value as the modal impedance value under the frequency, wherein L and T are respectively a left eigenvector matrix and a right eigenvector matrix;

5) if all the frequencies are traversed, entering the step (6); if not, making f equal to f + Δ f, and selecting the Δ f according to actual needs, and returning to step 3);

6) taking the modal impedance value under each frequency, drawing a continuous frequency modal impedance value curve, judging whether resonance exists according to whether the continuous frequency modal impedance value curve contains a peak, judging the peak with a larger amplitude as resonance, wherein the impedance value of the peak is a resonance impedance value, and the corresponding frequency is modal resonance frequency;

7) and solving participation factors of each node, and determining the participation of each node on resonance contribution:

taking a left eigenvector and a right eigenvector corresponding to the modal state resonant point, and assuming that the eigenvalue corresponding to the resonant node b is lambda_mIf the participation factor of the node b is PF_bm＝L_bmT_mbSelecting a node with a larger participation factor as a main node participating in the resonance;

the determination of the modal resonance impedance and frequency is the basis of the present invention, and the following element electrical parameter sensitivity and design parameter sensitivity analysis are performed based on this.

The sensitivity analysis of the electrical parameters of the elements in the third step can be specifically divided into the following steps:

(1) selecting a resonance k of a certain frequency to be researched and a node ii where an element to be subjected to sensitivity analysis is located;

(2) solving for the participation factor S of node ii at resonance k_λ,ii：

(3) Let λ_k＝λ_r+jλ_i，S_λ,ii＝S_r+jS_iDecomposing two parameters into a real part and an imaginary part;

(4) for any element, its conductance sensitivity is first determinedAnd susceptance sensitivity

(5) For the parallel elements, the electrical parameters of the parallel elements are conductance G and susceptance B, so the conductance sensitivity of the parallel elements is mu, and the susceptance sensitivity is v. (say that lamda requires an inverse number, so the direction of change is reversed)

(6) For the series element, since it is customary to express it by impedance Z ═ R + jX instead of admittance Y ═ G + jB, the transformation expression is required: sensitivity of resistanceReactance sensitivity

(7) In order to compare various parameters with each other and reveal the relative magnitude of the influence degrees, the normalized sensitivity is obtained:i.e. using unnormalised sensitivity valuesAnd the current parameter value and the characteristic value are calculated to obtain the parameter value, and the method is simple and easy to implement.

(8) The impedance value is | lambda due to resonance^-1Therefore, the influence of the electrical parameter of the actual element on the resonance impedance is opposite to the sensitivity, that is, if the sensitivity of the electrical parameter of a certain element is a positive value, the larger the value of the parameter is, the larger the characteristic value is, and the smaller the value of the resonance impedance is; if the sensitivity is negative, the opposite is true, so the final result needs to be changed in sign.

(9) And (4) repeatedly carrying out the sensitivity analysis of the step (1-7) on the electrical parameters of the key elements.

(10) The purpose of analyzing the sensitivity of the design parameters is to provide specific reference for designing the topology of the wind power plant, so that the influence of specific cable length and transformer capacity on resonance needs to be researched. The analysis of the cable length and the transformer capacity comprises the following steps:

(1) selecting a certain parameter to be designed, wherein the parameter is respectively the length of a connecting cable between wind turbines, a wind power plant confluence point connecting cable and the like, the length of a connecting cable with an onshore confluence station and the like, and the parameter is also set as α according to the original value of the parameter₀；

(2) Linearly traversing the parameter values to α ═ 0.25 α₀，Δα＝1/4α₀；

(3) According to the method in the second step, the modal resonance impedance and the frequency when the variable value is alpha are obtained;

(4) if α ═ 4 α₀If not, making α be α + Δ α, and selecting the size of Δ α according to actual needs, and returning to the step (3);

(5) drawing a curve of the resonant impedance and the frequency along with the variation value;

(6) and (4) repeatedly carrying out the sensitivity analysis of the step (1-5) on the key design parameters so as to determine the actual influence of the parameter value change on the resonance.

Example (b):

in order to verify the method for analyzing the offshore wind farm resonance based on modal analysis, which is provided by the invention, the accuracy and feasibility of the method are illustrated by using the analysis result of the offshore wind farm system in Horns Rev2, Denmark.

The wind power plant is in a chain type topological structure. Each wind turbine generator set comprises a squirrel-cage asynchronous motor, a converter, an LCL filter and a box-type outlet step-up transformer (0.69/35 kV). All fans were then connected to a busbar using a chain topology, passed through a step-up transformer (35/150kV), and transported to the onshore grid by long distance cables. All power transmission lines are submarine cables and are buried at 1m of the sea bottom.

1. Solving the system resonance impedance frequency spectrum in the initial state and comparing the performances under different topologies

And respectively solving the resonance impedance frequency spectrum of the system under the chain topology and the bilateral ring topology. As shown in FIG. 6, the values of the resonance impedances are shown in Table 1, and the number of resonance times is shown in Table 2. It can be seen that the resonant impedance of the ring topology is significantly smaller than the chain topology.

TABLE 1 modal resonance impedance of offshore wind farms

TABLE 2 modal resonance times for offshore wind farms

2. Participation factor of key node

Taking the chain topology as an example, the participation factors of all nodes under resonance of each frequency band are obtained, as shown in table 3. It can thus be determined that the resonance is mainly caused by the connection point of the transformer to the cable. Further, taking the node 42 as an example, the participation factor in the low frequency band is much higher than that in the middle frequency band and the high frequency band, which indicates that the node 42 mainly participates in the low frequency resonance and has no direct relation with other resonances. Other nodes can be analyzed in a comparison mode, and therefore the main participating nodes of the frequency resonance are determined.

TABLE 3 participation factor of each node

3. Sensitivity of electrical parameters of each element

The sensitivity of the electrical parameters of each element under resonance of each frequency band is obtained, and the influence degree of each electrical parameter on the resonance can be obtained, as shown in table 4. In the table, Rs1, Rp1 and Lt1 respectively represent the wire winding resistance, the wire winding eddy current loss resistance and the inductance of the fan transformer, Rs2, Rp2 and Lt2 respectively represent the wire winding resistance, the wire winding eddy current loss resistance and the inductance of the offshore step-up transformer, Rcable1-4 respectively represents the resistances of the inter-fan collection cable, the inter-fan chain collection cable, the wind field and bus point collection cable and the high-voltage cable, Lcae 1-4 respectively represents the inductances of the inter-fan collection cable, the inter-fan chain collection cable, the wind field and bus point collection cable and the high-voltage cable, and Ccable1-4 respectively represents the capacitances of the inter-fan collection cable, the inter-fan chain collection cable, the wind field and bus point collection cable and the high-voltage cable.

Taking the high-voltage submarine Cable4 as an example, it is obvious that the main parameters affecting resonance are inductance and capacitance, and the influence degree of resistance is very small. Taking an offshore step-up transformer as an example, the influence degrees of the resistance, the inductance and the capacitance of the transformer can be changed in different frequency bands, and the influence directions are different, so that careful measurement is needed when parameters are adjusted, and an optimal result is achieved.

TABLE 4 sensitivity of the Electrical parameters

4. Sensitivity of each design parameter

And (5) solving the sensitivity of key design parameters under each frequency band. Taking the length of the cable between the wind turbines as an example, the length represents the distance between the wind turbines in the same chain, and needs to be determined at the beginning of the design of the wind power plant. The trend of the impedance and frequency of each frequency band with the variation of the parameter value is shown in fig. 7 and 8. Therefore, the frequency resonance frequency of the medium and high frequency ranges is in a descending trend along with the increase of the length, the medium frequency ranges are influenced more obviously, and the number of times of harmonic resonance of the fan is easily caused by 19, 17, 11 times and the like in the middle of the medium frequency ranges. The resonant frequency of the low frequency band is substantially unaffected. As for the resonant impedance, the low-frequency band impedance tends to decrease first and then increase, and reaches a very high resonant intensity when approaching 3 times of the initial value. The middle and high frequency band resonance impedance basically has a descending trend.

Claims (7)

1. A modal analysis method of offshore wind farm resonance is characterized by comprising the following steps:

1) according to the connection relation of the offshore wind power plant system, namely, each element and the cable, a system harmonic model is established:

2) establishing a network admittance matrix of the system according to the system harmonic model, solving a modal impedance frequency spectrum of the system by using a modal method, calculating participation factors of each node, and determining a real occurrence position of resonance;

3) evaluating the sensitivity of the system component electrical parameters;

4) the sensitivity of the system design parameters was evaluated.

2. A modal analysis method of offshore wind farm resonance as set forth in claim 1, wherein the establishing of the system harmonic model comprises:

1) harmonic model of wind turbine generator:

the single wind turbine generator consists of a wind driven generator, a converter and an LCL filter, is a main harmonic source of a wind power plant, and represents a wind turbine generator harmonic model by an ideal voltage source containing harmonic waves and the LCL filter;

2) harmonic model of the transformer:

the resistance Rs of the wire winding of the transformer and the eddy current loss Rp of the wire winding are calculated according to the following formula: :

$R_s=\frac{X}{tan\mathrm{\φ}}---\left(1\right)$

R_p＝10Xtanφ (2)

wherein X is the leakage reactance of the transformer at 50Hz,h represents the harmonic frequency, and S is the rated power of the transformer;

3) harmonic model of submarine cable:

considering the long-line effect of the submarine cable, a distributed parameter model is adopted, and the calculation formula is shown in (6) to (9):

$Z_c=\sqrt{(R_0+{\mathrm{jhL}}_0)/jh{C}_0}---\left(6\right)$

$\mathrm{\γ}=\sqrt{(R_0+{\mathrm{jhL}}_0){\mathrm{jhC}}_0}---\left(7\right)$

Z＝Z_csinh(γl)＝R+jhL (8)

$Y=\frac{2\left(\cosh \mathrm{\γ}l-1\right)}{Z_c\sinh \mathrm{\γ}l}=jhC---\left(9\right).$

3. a modal analysis method of offshore wind farm resonance as set forth in claim 1, wherein the step 2) comprises:

firstly, all n nodes in the system are labeled, and then a system network admittance matrix Y is established by utilizing the mutual admittance between the node self-admittance and the nodes, wherein an element Y_ii(i ═ 1,2, … n) is the self-admittance of node i, Y_ij(i, j ═ 1,2, … n; i ≠ j) is the inverse number of transadmittance between nodes i, j;

the voltage-current relationship of the n-node system is expressed by the following equation (10):

V＝Y^-1I (10)

y can be decomposed into the following forms:

Y＝LΛT (11)

substitution (10) can give:

TV＝Λ^-1TI (12)

defining U as a modal voltage vector and J as a modal current vector;

Λ -value at arbitrary frequency¹Defined as the modal impedance at that frequency; the voltage at the kth node at this time is:

$v_k={\mathrm{\λ}}_i^{-1}\underset{m=1}{\overset{n}{\Σ}}{l}_{ki}{t}_{im}{i}_m---\left(13\right)$

where k is the node number, i is the mode number, l_kit_imIs a "participation factor”；

And traversing the selected frequency interval to obtain a system modal impedance frequency spectrum in the frequency interval, wherein the amplitude extreme value of the system modal impedance frequency spectrum is a system modal resonance point, the participation factor of each node at the modal resonance point is solved, and the node with the largest participation factor is the true occurrence position of resonance.

4. A method of modal analysis of offshore wind farm resonance as set forth in claim 1, wherein the method of assessing the sensitivity of electrical parameters of the components of the system comprises:

the sensitivity expression of the resonance impedance of the parallel element with admittance Y ═ G + jB is as follows:

$\frac{\∂\left|\mathrm{\λ}\right|}{\∂G}=\frac{d\left|\mathrm{\λ}\right|}{dF}\frac{\∂F}{\∂G}=\frac{S_r{\mathrm{\λ}}_r+S_i{\mathrm{\λ}}_i}{\sqrt{{\mathrm{\λ}}_r^2+{\mathrm{\λ}}_i^2}}---\left(14\right)$

$\frac{\∂\left|\mathrm{\λ}\right|}{\∂B}=\frac{d\left|\mathrm{\λ}\right|}{dF}\frac{\∂F}{\∂B}=\frac{S_r{\mathrm{\λ}}_r-S_i{\mathrm{\λ}}_i}{\sqrt{{\mathrm{\λ}}_r^2+{\mathrm{\λ}}_i^2}}---\left(15\right)$

wherein G represents the real part of the element admittance, B represents the imaginary part of the element admittance, λ_rAnd λ_iRespectively being the k-th eigenvalue lambda_kReal and imaginary parts of, S_rAnd S_iRespectively the node Y of the element of the characteristic value pair_ijSensitivity S of_λ,ijThe real and imaginary parts of (c);

the sensitivity expression for the series element with impedance Z ═ R + jX is as follows:

$\frac{\∂\left|\mathrm{\λ}\right|}{\∂R}=\frac{\mathrm{\μ}(X^2-R^2)+2vRX}{(R^2+X^2)}---\left(16\right)$

$\frac{\∂\left|\mathrm{\λ}\right|}{\∂X}=\frac{v(X^2-R^2)-2\mathrm{\μ}RX}{(R^2+X^2)}---\left(17\right)$

wherein,r represents the real part of the impedance of the series element, and X represents the imaginary part of the impedance of the series element;

let the element parameter be α, define the normalized sensitivity as:

$\frac{\∂\left|\mathrm{\λ}\right|}{\∂\mathrm{\α}}{|}_{norm}=\frac{\frac{\∂\left|\mathrm{\λ}\right|}{\mathrm{\λ}}}{\frac{\∂\mathrm{\α}}{\mathrm{\α}}}=\frac{\∂\left|\mathrm{\λ}\right|}{\∂\mathrm{\α}}\·\frac{\mathrm{\α}}{\mathrm{\λ}}---\left(18\right)$

and the influence of each parameter in the offshore wind power plant on the resonance intensity is quantified by adopting parameter sensitivity analysis.

5. A modal analysis method of offshore wind farm resonance as set forth in claim 1 or 4, wherein said electrical parameters of the components include transformer inductance, transformer winding resistance, transformer eddy current loss resistance, and resistance, inductance, capacitance of each type of cable.

6. A modal analysis method of offshore wind farm resonance as set forth in claim 1, wherein the evaluating the sensitivity of the design parameter comprises:

setting an initial value of a design parameter to α₀The values of the variables of the design parameters are sequentially calculatedEquidistant change to 4 α₀In the process, the system modal resonance impedance and the frequency corresponding to each variable value are drawn into a curve of the system modal resonance impedance and the frequency changing along with the variable value.

7. A modal analysis method of offshore wind farm resonance as set forth in claim 1 or 6, wherein the design parameters include cable length, cable cross-sectional area, transformer capacity.