CN106295231B - A kind of marine wind electric field resonance suppressing method based on modal calculation - Google Patents
A kind of marine wind electric field resonance suppressing method based on modal calculation Download PDFInfo
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Abstract
A kind of marine wind electric field resonance suppressing method based on modal calculation, this method comprises: 1) establishing system harmonics model according to offshore wind farm field system, that is, each element and cable connection relationship；2) the participation factor of each node is calculated using the mode impedance spectrum of Modal Method solving system according to the network admittance matrix of the system harmonics model foundation system, determines the true generation position of resonance；3) according to the braking measure for participating in factor design resonance.The present invention determines the installation site of filter according to the factor is participated in, and compared to traditional method only installed at confluence, can preferably inhibit the harmonic wave of wind field internal transmission.
Description
Technical field
The present invention relates to marine wind electric field, especially a kind of marine wind electric field resonance suppressing method based on modal calculation,
The harmonic-model for specially establishing offshore wind farm field system calculates the global resonance point and each node of system using Modal Method
Degree of participation, so that it is determined that the true generation position of resonance, and then according to participating in the braking measure of factor design resonance.
Background technique
Offshore wind energy resource is abundant, and generated energy is big, and is not take up land soil, and Oversea wind power generation has become wind-powered electricity generation neck
The important development direction in domain.With the fast development of offshore wind farm, the harmonic wave of the grid-connected generation of offshore wind farm can be to network system
Safety and stability causes centainly to threaten.The submarine cable that high capacitive is widely applied in offshore wind farm Transmission system, when cable and transformation
When the inductive elements such as device are connected, parallel resonance easily occurs.Once the harmonic wave of wind-driven generator output generates in Transmission system
Harmonic resonance, then can cause overvoltage, overcurrent, element over-temperature is caused to be lost, cause when serious insulation fail, or even cause
Serious electric power accident.
The Transmission system of general marine wind electric field includes collection power grid, offshore boosting station, high-voltage transmission cable and the change of current on the bank
It stands.Due to largely using submarine cable in collection power grid, and it is directly connected to transformer.The topology for collecting power grid changes in addition to meeting shadow
It rings except the economy of wind power plant, reliability, also results in the change of the connection relationship of cable length, electric parameter and element
Change, this can cause bigger influence to resonance.Because the system element quantity that collection power network topology is related to is more, situation is complicated,
It needs to establish correct model, using suitable research method, could correctly analyze influence of the topology to resonance.
Current marine wind electric field resonance research mainly uses Spectral Analysis Method, but this method detection speed is slow, and provide
Information is less.Modal analysis method by the property of analysis system admittance matrix characteristic root, it is available in relation to resonance mechanism and
The information of degree provides new thinking for harmonic analysis.Currently, modal analysis method is applied to marine wind electric field not yet
Collect the research of power grid resonance.
Electric harmonic filter is divided into passive power filter, Active Power Filter-APF and hybrid filter.
The filtering accuracy of Active Power Filter-APF is high, and harmonic current rejection rate may be up to 97% or more.And it is to load
Wave motion response is fast, can be with Dynamic injection electric current to inhibit harmonic wave, while compensating power factor.But the disadvantage is that cost is too high, and
By hardware limitation, it is not available in large capacity occasion.
Hybrid filter is to be used in mixed way passive filter and active filter, and this topology combines passive filtering
The Common advantages of device and active filter, cost is lower than pure active filter, while filter effect is better than pure passive filter.
The disadvantage is that control strategy is more complex, at the same cost be also not lowered to can large-scale application degree.
The main element of passive filter passive power filter is resistance, inductance, capacitor, and each element passes through series and parallel
In conjunction with mode constitute.Its technology is more mature, and has the advantages that capacity is big, is suitable for high-voltage fence, is filtering out harmonic wave
It is capable of providing reactive compensation simultaneously, it is at low cost and not by hardware limitation, at sea it is widely applied in wind power plant.
Summary of the invention
The technical problem to be solved by the present invention is to be directed to the deficiency of current marine wind electric field harmonic analysis method, one kind is proposed
Marine wind electric field resonance suppressing method based on modal calculation.This method establishes equivalent mould according to the parameter of each element of wind power plant
Type, the participation factor of resonator system difference node is directed to modal analysis method research, and then designs resonance braking measure.
Technical solution of the invention is as follows:
A kind of suppressing method of the marine wind electric field resonance based on modal calculation, it is characterized in that this method includes following step
It is rapid:
1) according to offshore wind farm field system, that is, each element and cable connection relationship, system harmonics model is established；
2) according to the network admittance matrix of the system harmonics model foundation system, Modal Method solving system is utilized
Mode impedance spectrum calculates the participation factor of each node, determines the true generation position of resonance；
3) it is directed to the resonance frequency, based on the maximum key node group of the factor is participated in, according to system structure, chooses and installs filtering additional
Device node designs filter and installs in the node location；
4) modal resonance analysis is carried out, system resonance impedance and frequency after installing filter additional are solved, if not up to resonance
Inhibit to require then to continue Optimal Filter parameter, until meeting the requirements.
Described establishes system harmonics model, comprising:
1) harmonic-model of Wind turbines:
Single Wind turbines are made of wind-driven generator, current transformer, LCL filter three parts, are the main humorous of wind power plant
Wave source indicates Wind turbines harmonic-model with the ideal voltage source containing harmonic wave and LCL filter；
2) harmonic-model of transformer:
The wire winding resistance Rs of transformer and the eddy-current loss Rp of wire winding are calculated according to the following formula::
Rp=10X tan φ (2)
In formula, the leakage reactance of transformer when X is 50Hz,H indicates overtone order,
S is the rated power of transformer；
3) harmonic-model of submarine cable:
In view of the long-line effect of submarine cable, using distributed parameter model, calculating formula is shown in (6)~(9):
Z=ZcSinh (γ l)=R+jhL (8)
The content of the step 2) includes:
Firstly, carrying out label to n nodes all in system, the transadmittance between node self-admittance and node is then utilized
Establish grid admittance matrix Y, wherein element Yii, (i=1,2 ... n) be node i self-admittance, Yij, (i, j=1,
2,…n；I ≠ j) it is node i, the opposite number of the transadmittance between j；
The voltage and current relationship of the system of the n node such as (10) formula indicate:
V=Y-1I (10)
Y can be decomposed into following form:
Y=L Λ T (11)
Substituting into (10) can obtain:
TV=Λ-1TI (12)
Definition U=TV is mode voltage vector, and J=TI is mode current vector；
Λ is sought at any frequency-1In greatest member, the mode impedance being defined as under the frequency；Kth node at this time
Voltage are as follows:
Wherein, k is node number, and i is mode number, lkitimFor " participating in the factor "；
After traversing selected frequency separation, the system mode impedance spectrum in the frequency separation, system mode impedance frequency are obtained
It is system mode resonance point at the amplitude extreme value of spectrum, seeks the participation factor of each node at modal resonance point, have maximum ginseng
Node with the factor is the true generation position of resonance.
The step 3: being directed to the resonance frequency, based on the maximum key node group of the factor is participated in, according to system structure, choosing
Installation filter node is taken, filter is designed and is installed in the node location.It is arranged using passive filter group as resonance inhibition
It applies.Using single tuned filter and high-pass filter collaborative work mode, single tuned filter is humorous for filtering out large capacity low order
Wave, high-pass filter filter out low capacity higher hamonic wave.
Step 4: carrying out modal resonance analysis, solve system resonance impedance and frequency after installing filter additional, if not up to
Resonance inhibits to require then to continue Optimal Filter parameter, until meeting the requirements.
Detailed description of the invention
Fig. 1 is that the present invention is based on the flow diagrams of the marine wind electric field resonance suppressing method of modal calculation
Fig. 2 is the typical structure diagram of marine wind electric field.
Fig. 3 is the harmonic-model figure of Wind turbines.
Fig. 4 is the harmonic-model figure of transformer.
Fig. 5 is the harmonic-model figure of submarine cable.
Fig. 6 is the modal resonance impedance spectrum figure that marine wind electric field is added before and after filter.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description.
Fig. 1 is that the present invention is based on the flow diagrams of the marine wind electric field resonance suppressing method of modal calculation, as seen from the figure, this
Marine wind electric field resonance suppressing method of the invention based on modal calculation, including the following steps:
Step 1: the harmonic-model of each element of marine wind electric field is established:
The structure of typical marine wind electric field is as shown in Figure 2.Blower boosts to 35kV through transformer, enters current collection system later
System, is connected to offshore boosting station through bus rod by middle pressure submarine cable, at sea booster stations pass through height after boosting to 150kV
Voltage cable is delivered to converter station on the bank, then is incorporated to onshore power grid.To carry out reactive compensation or filtering out harmonic wave, at corresponding node
Capacitor group or filter are set.For accurate evaluation system resonance situation, the correct harmonic-model of each element must be established, is wrapped
It includes:
1) Wind turbines harmonic-model
Single Wind turbines are made of wind-driven generator, current transformer, LCL filter three parts, are the main humorous of wind power plant
Wave source.Because the present invention mainly studies the resonance conditions of wind power plant Transmission system, ignore blower and current transformer internal structure,
With the desired voltage source-representation wind turbine model containing harmonic wave, while retaining LCL filter, as shown in Figure 3.
2) transformer harmonic-model
It include two kinds of transformers, respectively the 0.69/35kV blower transformer at fan outlet end and remittance in marine wind electric field
Flow the sea the 35/150kV step-up transformer at bus.Generally acknowledge that more accurately transformer model is CIGRE standard harmonic at present
Model is [referring to Wu, X., et al.Nodal harmonic impedance derivation of AC network in
PSS/E.in AC and DC Power Transmission,2010.ACDC.9th IET International
Conference on.2010.IET.], which will account for the eddy-current loss approximation and frequency square of leading role in winding conducting wire
It is directly proportional, and demagnetizing effect is considered, it can accurately reflect the practical working situation of transformer, blower transformer and marine liter
The equivalent circuit of pressure transformer is as shown in Figure 4.In figure, X be 50Hz when transformer leakage reactance, h indicate overtone order, Rs expression lead
Line winding group resistance, Rp indicates the eddy-current loss of wire winding, and Rs and Rp, not with frequency shift, calculation formula is as follows:
Rp=10X tan φ (2)
In formula,S is the rated power of transformer.
3) harmonic-model of submarine cable:
In the frequency domain equivalent calculation of resonance research, the submarine cable of unit length can be equivalent to lumped parameter π model.
Meter and resistance kelvin effect, resistance, inductance and the capacitance of unit length are calculated by formula 3~5.But in view of seabed electricity
The long-line effect of cable needs to use distributed parameter model, as shown in figure 5, calculating process is shown in formula 6-9:
Z=ZcSinh (γ l)=R+jhL (8)
Step 2: establishing the network admittance matrix of system, using the mode impedance spectrum of Modal Method solving system, and counts
The participation factor for calculating each node determines the true generation position of resonance:
The network admittance matrix of one electric system with n node, is the institute based on the Equivalent admittance of system element
The linear matrix of relationship between establish, each node voltage of description electric power networks and Injection Current.Wherein element Yii, (i=1,
2 ... n) be node i self-admittance, Yij, (i, j=1,2 ... n；I ≠ j) transadmittance between node i and node j it is opposite
Number, to set up the network admittance matrix of system.
For any one electric system, the generation of system parallel resonance is necessarily because of the inverse square of its network admittance matrix
There is the very big element of numerical value in battle array, it is assumed that the admittance matrix of system is Y, then voltage-current relationship such as following formula indicates:
V=Y-1I (10)
Wherein, V is node voltage matrix, and I is node injection current matrix.
Above formula can be decomposed into following form:
Y=L Λ T (11)
In formula, Λ is diagonal eigenvalue matrix, and L, T are respectively left eigenvector matrix and right eigenvectors matrix, then have
Following formula mode voltage and current expresses formula:
TV=Λ-1TI (12)
Definition U=TV is mode voltage vector, and J=TI is mode current vector.
Assuming that working as Λ-1In elementWhen very big, then the mode i electric current J of very littleiIt will lead to very big mode i electricity
Press Ui.And other mode voltages will be unaffected, because they are not coupled between mode i electric current.Take Λ-1In it is maximum
Element is mode impedance under the frequency, traverses all frequencies and calculates corresponding mode impedance value, can draw out corresponding mode
Impedance spectrum, so that it is determined that modal resonance frequencies and intensity.
The voltage of node k can indicate are as follows:
Illustrate that the corresponding element in key feature vector describes the pass between node voltage, node current and characteristic value
System, i.e., the coverage of crucial resonance, defines lkitimFor " participating in the factor ", wherein k is node number, and i is mode number.Participate in because
The physical significance of son is percentage contribution of the node k to mode i resonance.Participating in the biggish node of the factor is by the modal resonance shadow
Ring biggish node, the i.e. true generation position of resonance, when design should be targetedly in the specific node -- resonance it is true
Position occurs and takes resonance braking measure.
Below with reference to embodiment, the present invention is further described, the modal analysis method of marine wind electric field resonance, including under
Column step:
Step 1 establishes the harmonic-model of each element of marine wind electric field:
It models data used all to be obtained by component supplier, establishes the equivalent of Wind turbines, transformer and submarine cable
Harmonic-model.
Step 2, model analysis can specifically be divided into following steps:
1) frequency model of each element of system is established, equivalent resistance, inductance, capacitor change with frequency；
2) original frequency f=f is set0, this value is substituted into each component models；
3) column write out network admittance matrix Y at this time；
4) carrying out Eigenvalues Decomposition to network admittance matrix Y is Y=L Λ T, and wherein Λ is characterized value matrix, square reciprocal
Battle array Λ-1Diagonal entry be respectivelyTaking wherein maximum value is the mode impedance value under the frequency, L and T points
It Wei not left eigenvector matrix, right eigenvectors matrix；
If 5) traversed all frequencies, (6) are entered step；If no, enabling f=f+ Δ f, Δ f size can be according to reality
Border needs to choose, and return step 3)；
6) the mode impedance value under each frequency is taken, cline frequency mode impedance value curve is drawn in, according to cline frequency mode
Whether impedance value curve contains wave crest, judges whether there is resonance, the biggish wave crest of amplitude is judged as generation resonance, the wave crest
Impedance value be a resonance impedance value, corresponding frequency is modal resonance frequencies；
7) the participation factor for seeking each node determines the participation that each node contributes resonance:
The corresponding left eigenvector of modulus state resonance point and right feature vector, it is assumed that the corresponding characteristic value of resonance node b is
λm, then the participation factor of node b is PFbm=LbmTmb, choose and participate in the biggish node of the factor, as the master for participating in the resonance
Want node；
Step 3, according to system structure, is chosen and is added based on the maximum key node group of the factor is participated in for the resonance frequency
Filter node is filled, filter is designed and is installed in the node location；
Step 4 carries out modal resonance analysis, solves system resonance impedance and frequency after installing filter additional, if not up to
Resonance inhibits to require then to continue Optimal Filter parameter, until meeting the requirements.
Embodiment:
In order to verify the analysis method of the marine wind electric field resonance based on model analysis proposed in the present invention, below with
The analysis result of Denmark's Horns Rev2 offshore wind farm field system illustrates the correctness and feasibility of the method for the present invention.
The wind power plant is chain topology.Each Wind turbines include squirrel cage asynchronous motor, current transformer, a LCL
Filter and box outlet step-up transformer (0.69/35kV).It is female that all blowers are connected to by confluence using chain type topology later
Line passes through the cable transfer of long range ashore power grid by step-up transformer (35/150kV).Wherein all power transmission lines
It is submarine cable, is embedded at the 1m of seabed.
1, the system resonance impedance spectrum under original state is solved, and compares the performance under different topology
It is solved under chain topology and bilateral ring topology respectively, the resonance impedance frequency spectrum of system.As shown in fig. 6, its is humorous
Vibration impedance value is shown in Table 1, and resonance times are shown in Table 2.Therefrom it can be seen that, the resonance impedance of ring topology will be significantly less than chain and open up
It flutters.
The modal resonance impedance of 1 marine wind electric field of table
The modal resonance number of 2 marine wind electric field of table
2, the participation factor of key node
By taking chain topology as an example, seek under each frequency band resonance, the participation factor of all nodes, as shown in table 3.It is possible thereby to
It determines, resonance is mainly caused by the tie point of transformer and cable.And by taking node 42 as an example, in the participation factor of low-frequency range
To be much higher than Mid Frequency and high band, illustrate that node 42 has been primarily involved in low-frequency resonant, and have no direct relation with other resonance.
Other nodes can be according to sample comparative analysis, and thereby determine that each frequency resonance is primarily involved in node.
The participation factor of each node of table 3
3, it is directed to the resonance frequency, based on the maximum key node group of the factor is participated in, according to system structure, chooses and installs filtering additional
Device node designs filter and installs in the node location.
Coexistence of systems is in three resonance frequencies, and respectively 6.6,17.8 and 20.8 times.Wherein low-frequency resonant 6.6 times main
Participating in node is 42, and the participation node of intermediate frequency and high frequency is more.Wind-driven generator generate major harmonic be 5,7,11,13,17,
19 times, and be limited in the wind field confluence lower than 69kV, voltage distortion rate must not exceed 3%, so the transmission of the wind power plant
System has the risk for causing harmonic resonance.It participates in the factor and the key node of excitation resonance has been determined, so being set at key node
Set the filter effect that filter can reach best.Install 5,7 single tuned filters additional at node 42 for low-frequency resonant.For
Medium-high frequency resonance from the aspect of filter effect and cost two, installs 17 additional in this node because node 41 is wind power plant confluence
Secondary high-pass filter.
4, modal resonance analysis is carried out, system resonance impedance and frequency after installing filter additional are solved, if not up to resonance
Inhibit to require then to continue Optimal Filter parameter, until meeting the requirements.
System mode impedance spectrum before and after installation filter is as shown in Figure 6., it is apparent that before filtering, there are three
Frequency resonance, and after filter is added, original three frequencys resonance is all eliminated.But 2.9 times new resonance are introduced simultaneously.
This is the characteristic of passive filter, i.e., after eliminating primary resonance, may introduce the new resonance frequency.In Practical Project
In, it can be Y- Δ connection by setting transformer to eliminate 3 subharmonic.Therefore, which not will cause Harmonics amplification.
So filter is added and plays good resonance inhibitory effect from the point of view of impedance spectrum.
Claims (2)
1. a kind of marine wind electric field resonance suppressing method based on modal calculation, it is characterised in that this method includes the following steps:
1) according to the connection relationship of offshore wind farm field system each element and cable, system harmonics model is established:
2) according to the network admittance matrix of the system harmonics model foundation system, the mode of Modal Method solving system is utilized
Impedance spectrum calculates the participation factor of each node, determines the true generation position of resonance；
Firstly, carrying out label to n nodes all in system, then established using the transadmittance between node self-admittance and node
Grid admittance matrix Y, wherein element YiiFor the self-admittance of node i, wherein i=1,2 ... n, YijFor node i, between j
Transadmittance opposite number, wherein i, j=1,2 ... n；i≠j；
The voltage and current relationship of the system of the n node such as (10) formula indicate:
V=Y-1I (10)
Y is decomposed into following form:
Y=L Λ T (11)
Substituting into (10) can obtain:
TV=Λ-1TI (12)
Definition U=TV is mode voltage vector, and J=TI is mode current vector；
Λ is sought at any frequency-1In greatest member, the mode impedance being defined as under the frequency；The electricity of kth node at this time
Pressure are as follows:
Wherein, k is node number, and i is mode number, lkitimTo participate in the factor；
After traversing selected frequency separation, the system mode impedance spectrum in the frequency separation is obtained, system mode impedance spectrum
Be system mode resonance point at amplitude extreme value, seek the participation factor of each node at modal resonance point, have it is maximum participate in because
The node of son is the true generation position of resonance；
3) it is directed to the resonance frequency, based on the maximum key node group of the factor is participated in, according to system structure, chooses and installs filter section additional
Point designs filter and installs in the node location；
4) modal resonance analysis is carried out, system resonance impedance and frequency after installing filter additional are solved, if not up to resonance inhibits
It is required that then continuing Optimal Filter parameter, until meeting the requirements.
2. the marine wind electric field resonance suppressing method according to claim 1 based on modal calculation, it is characterised in that described
Establish system harmonics model, comprising:
1) harmonic-model of Wind turbines:
Single Wind turbines are made of wind-driven generator, current transformer, LCL filter three parts, are the major harmonic sources of wind power plant,
Wind turbines harmonic-model is indicated with the ideal voltage source containing harmonic wave and LCL filter；
2) harmonic-model of transformer:
The wire winding resistance Rs of transformer and the eddy-current loss Rp of wire winding are calculated according to the following formula:
Rp=10Xtan φ (2)
In formula, the leakage reactance of transformer when X is 50Hz,S is the rated power of transformer；
3) harmonic-model of submarine cable:
In view of the long-line effect of submarine cable, using distributed parameter model, calculating formula is shown in (6)~(9):
Z=ZcSinh (γ l)=R+jhL (8)
H indicates overtone order.
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| CN106896267B (en) * | 2017-02-07 | 2019-05-10 | 中国石油化工股份有限公司 | A kind of Distribution Network Harmonics resonance improvement modal analysis method |
| CN108879723B (en) * | 2018-06-28 | 2021-02-02 | 中国电建集团华东勘测设计研究院有限公司 | Method for determining type and main participation area of internal resonance of offshore wind power plant |
| CN109869286B (en) * | 2019-02-12 | 2020-09-18 | 苏州热工研究院有限公司 | Vibration state monitoring method for wind generating set |
| CN110718917B (en) * | 2019-11-18 | 2022-03-25 | 国网青海省电力公司 | Implementation method for constructing generation of power electronic harmonic resonance source |
| CN112701689B (en) * | 2020-12-16 | 2023-01-20 | 深圳供电局有限公司 | Wide-area resonance evaluation and early warning method based on limited distribution points |
| CN114389282A (en) * | 2022-01-21 | 2022-04-22 | 福州大学 | Affine-based uncertainty modal analysis method |
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