CN106295231A - A kind of marine wind electric field resonance suppressing method based on modal calculation - Google Patents

Abstract

A kind of marine wind electric field resonance suppressing method based on modal calculation, 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) according to the braking measure of participation factors design resonance.The present invention determines the installation site of wave filter according to participation factors, compared to traditional method only installed at confluence, can preferably suppress the harmonic wave of wind field internal transmission.

Description

A kind of marine wind electric field resonance suppressing method based on modal calculation

Technical field

The present invention relates to marine wind electric field, a kind of marine wind electric field resonance suppressing method based on modal calculation, Specially set up the harmonic-model of offshore wind farm field system, utilize Modal Method to calculate the overall resonance point of system and each node Degree of participation, so that it is determined that resonance truly there is position, and then design resonance braking measure according to participation factors.

Background technology

Offshore wind energy resource enriches, and generated energy is big, and is not take up land soil, and Oversea wind power generation has become as wind-powered electricity generation neck The important development direction in territory.Along 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 certain threat.Offshore wind farm transmission system is widely applied the submarine cable of high capacitive, when cable and transformation When the inductive elements such as device are connected, easily there is parallel resonance.Once the harmonic wave of wind-driven generator output produces in transmission system Harmonic resonance, then can cause overvoltage, overcurrent, cause element over-temperature to be lost, cause time serious insulating unsuccessfully, even cause Serious electric power accident.

The transmission system of general marine wind electric field includes collecting electrical network, offshore boosting station, high-voltage transmission cable and the change of current on the bank Stand.Owing to collection electrical network have employed submarine cable in a large number, and it is directly connected to transformator.The topology of collection electrical network changes except meeting shadow Ring outside the economy of wind energy turbine set, reliability, also result in the change of the annexation of cable length, electric parameter and element Changing, resonance can be caused and compare large effect by this.Because the system element quantity that collection power network topology relates to is many, situation is complicated, Need to set up correct model, use suitable research method, could correctly analyze the topology impact on resonance.

Current marine wind electric field resonance research mainly uses Spectral Analysis Method, but the method detection speed is slow, and provide Information is less.Modal analysis method by analyze system admittance matrix characteristic root character, can obtain relevant resonance mechanism and The information of degree, provides new thinking for harmonic analysis.At present, the most modal analysis method is not applied to marine wind electric field The research of collection electrical network resonance.

Electric harmonic wave 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 more than 97%.And it is to load Wave motion response is fast, can compensate power factor with Dynamic injection electric current to suppress harmonic wave simultaneously.But it is the highest that its shortcoming is cost, and By hardware limitation, cannot use in Large Copacity occasion.

Hybrid filter is to be used in mixed way with active filter by passive filter, and this topology combines passive filtering Device and the Common advantages of active filter, cost is less than pure active filter, and filter effect is better than pure passive filter simultaneously. Shortcoming is that control strategy is more complicated, and be also not lowered to can the degree of large-scale application for cost simultaneously.

The main element of passive filter passive power filter is resistance, inductance, electric capacity, and each element passes through series and parallel In conjunction with mode constitute.Its technology is the most ripe, and has the advantage that capacity is big, be applicable to high-voltage fence, is filtering harmonic wave Reactive-load compensation can be provided simultaneously, low cost and not by hardware limitation, at sea wind energy turbine set is extensively applied.

Summary of the invention

The technical problem to be solved in the present invention is the deficiency for current marine wind electric field harmonic analysis method, proposes one Marine wind electric field resonance suppressing method based on modal calculation.This method sets up equivalent mould according to the parameter of each element of wind energy turbine set Type, uses modal analysis method to study the participation factors for resonator system difference node, and then design resonance braking measure.

The technical solution of the present invention is as follows:

The suppressing method of a kind of marine wind electric field resonance based on modal calculation, its feature is that the method includes following step Rapid:

1) according to the most each element of offshore wind farm field system and the annexation of cable, system harmonics model is set up；

2) set up the network admittance matrix of system according to described system harmonics model, utilize Modal Method solving system Mode impedance spectrum, calculates the participation factors of each node, and determine resonance truly occurs position；

3) for the resonance frequency, based on the key node group that participation factors is maximum, according to system structure, choose and install filtering additional Device node, design wave filter is also installed at this node location；

4) carry out modal resonance analysis, solve the system resonance impedance after installing wave filter additional and frequency, if not up to resonance Suppression requires then to continue Optimal Filter parameter, until meeting the requirements.

Described sets up system harmonics model, including:

1) harmonic-model of Wind turbines:

Single Wind turbines is made up of wind-driven generator, current transformer, LCL filter three part, is the most humorous of wind energy turbine set Wave source, represents Wind turbines harmonic-model with the ideal voltage source containing harmonic wave and LCL filter；

2) harmonic-model of transformator:

The wire winding resistance Rs of transformator and eddy-current loss Rp of wire winding are calculated by following equation::

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

R_p=10X tan φ (2)

In formula, X is the leakage reactance of transformator during 50Hz,H represents overtone order,

S is the rated power of transformator；

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):

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

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

Z=Z_cSinh (γ l)=R+jhL (8)

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

Described step 2) content include:

First, n nodes all in system are carried out label, then utilizes the transadmittance between node self-admittance and node Set up grid admittance matrix Y, wherein, element Y_ii, (i=1,2 ... n) it is the self-admittance of node i, Y_ij, (i, j=1, 2,…n；I ≠ j) it is node i, the opposite number of the transadmittance between j；

The voltage of the system of this n node represents with current relationship such as (10) formula:

V=Y^-1I (10)

Y can be to be decomposed into following form:

Y=L Λ T (11)

Substitute into (10) can obtain:

TV=Λ^-1TI (12)

Definition U=TV is mode voltage vector, and J=TI is mode current vector；

Λ is asked under optional frequency^-1In greatest member, the mode impedance being defined as under this frequency；Now kth node Voltage be:

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

Wherein, k is node number, and i is mode number, l_kit_imFor " participation factors "；

After the selected frequency separation of traversal, obtain the system mode impedance spectrum in this frequency separation, system mode impedance frequency It is system mode resonance point at the amplitude extreme value of spectrum, asks for the participation factors of each node at modal resonance point, possess maximum ginseng Position is truly there is with the node of the factor is resonance.

Described step 3: for the resonance frequency, based on the key node group that participation factors is maximum, according to system structure, choosing Taking and install filter node additional, design wave filter is also installed at this node location.Passive filter group is used to arrange as resonance suppression Execute.Using single tuned filter and high pass filter collaborative work mode, it is humorous that single tuned filter is used for filtering Large Copacity low order Ripple, high pass filter filters low capacity higher hamonic wave.

Step 4: carry out modal resonance analysis, solves the system resonance impedance after installing wave filter additional and frequency, if not up to Resonance suppression requires then to continue Optimal Filter parameter, until meeting the requirements.

Accompanying drawing explanation

Fig. 1 is the FB(flow block) of present invention marine wind electric field based on modal calculation resonance suppressing method

Fig. 2 is the exemplary block diagram of marine wind electric field.

Fig. 3 is the harmonic-model figure of Wind turbines.

Fig. 4 is the harmonic-model figure of transformator.

Fig. 5 is the harmonic-model figure of submarine cable.

Fig. 6 is the modal resonance impedance spectrum figure before and after marine wind electric field adds wave filter.

Detailed description of the invention

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete Describe wholely.

Fig. 1 is the FB(flow block) of present invention marine wind electric field based on modal calculation resonance suppressing method, as seen from the figure, and this Invent marine wind electric field resonance suppressing method based on modal calculation, comprise the following steps:

Step one: set up the harmonic-model of each element of marine wind electric field:

The structure of typical marine wind electric field is as shown in Figure 2.Blower fan to 35kV, enters current collection system through transformer boost afterwards System, is connected to offshore boosting station by middle pressure submarine cable through bus rod, by height after at sea booster stations boost to 150kV Voltage cable is delivered to current conversion station on the bank, then is incorporated to electrical network on the bank.For carrying out reactive-load compensation or filter harmonic wave, at corresponding node Capacitor banks or filter are set.For accurate evaluation system resonance situation, the correct harmonic-model of each element must be set up, bag Include:

1) Wind turbines harmonic-model

Single Wind turbines is made up of wind-driven generator, current transformer, LCL filter three part, is the most humorous of wind energy turbine set Wave source.Because the present invention mainly studies the resonance conditions of wind energy turbine set transmission system, ignore blower fan and current transformer internal structure, With the desired voltage source-representation wind turbine model containing harmonic wave, retain LCL filter, as shown in Figure 3 simultaneously.

2) transformator harmonic-model

Marine wind electric field comprises 0.69/35kV blower fan transformator and the remittance of two kinds of transformators, respectively fan outlet end 35/150kV sea booster transformer at stream bus.Generally acknowledge that transformer model is CIGRE standard harmonic more accurately at present Model [sees 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.], the eddy-current loss accounting for mastery reaction in winding conducting wire is approximated and frequency square by this model It is directly proportional, and considers demagnetizing effect, it is possible to accurately reflect the practical working situation of transformator, blower fan transformator and marine liter The equivalent circuit of pressure transformer is as shown in Figure 4.In figure, X is transformator leakage reactance during 50Hz, and h represents that overtone order, Rs represent to be led Line winding resistance, Rp represents the eddy-current loss of wire winding, and Rs and Rp be not with frequency shift, and its computing formula is as follows:

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

R_p=10X tan φ (2)

In formula,S is the rated power of transformator.

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, the resistance of its unit length, inductance are calculated by formula 3～5 with capacitance.But in view of seabed electricity The long-line effect of cable, needs to use distributed parameter model, as it is shown in figure 5, calculating process is shown in formula 6-9:

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

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

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

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

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

Z=Z_cSinh (γ l)=R+jhL (8)

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

Step 2: set up the network admittance matrix of system, utilizes the mode impedance spectrum of Modal Method solving system, and counts Calculating the participation factors of each node, truly there is position in determine resonance:

The network admittance matrix of one power system with n node, is institute based on the Equivalent admittance of system element Linear matrix that set up, relation between the description each node voltage of electric power networks and injection current.Wherein element Y_ii, (i=1, 2 ... n) it is the self-admittance of node i, Y_ij, (i, j=1,2 ... n；I ≠ j) it is the contrary of transadmittance between node i and node j Number, thus set up the network admittance matrix of system.

For any one power system, the generation of system parallel resonance is necessarily because of the inverse square of its network admittance matrix There is the element that numerical value is the biggest in battle array, it is assumed that the admittance matrix of system is Y, then voltage-current relationship such as following formula represents:

V=Y^-1I (10)

Wherein, V is node voltage matrix, and I is node injection current matrix.

Above formula can be to be decomposed into following form:

Y=L Λ T (11)

In formula, Λ is diagonal angle eigenvalue matrix, and L, T are respectively left eigenvector matrix and right eigenvectors matrix, then have Following formula mode voltage x current expression formula:

TV=Λ^-1TI (12)

Definition U=TV is mode voltage vector, and J=TI is mode current vector.

Assume to work as Λ^-1In elementTime the biggest, the least mode i electric current J_iMay result in the biggest mode i electricity Pressure U_i.And other mode voltage is by unaffected, because not coupling between they and mode i electric current.Take Λ^-1Middle maximum Element is mode impedance under this frequency, travels through all frequencies and calculates corresponding mode resistance 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 be expressed as:

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

Illustrate that the corresponding element in key feature vector describes the pass between node voltage, node current and eigenvalue System, the coverage of i.e. crucial resonance, define l_kit_imFor " participation factors ", wherein k is node number, and i is mode number.Participate in because of The physical significance of son is the node k percentage contribution to mode i resonance.The node that participation factors is bigger is by this modal resonance shadow Truly there is position in that rings bigger node, i.e. resonance, should be targetedly at this specific node during design--resonance true Position is occurred to take resonance braking measure.

Below in conjunction with embodiment, the present invention is further described, the modal analysis method of marine wind electric field resonance, including under Row step:

Step one, sets up the harmonic-model of each element of marine wind electric field:

Modeling data used, all by component supplier gained, set up the equivalence of Wind turbines, transformator and submarine cable Harmonic-model.

Step 2, model analysis specifically can be divided into following steps:

1) setting up the frequency model of each element of system, its equivalent resistance, inductance, electric capacity change with frequency；

2) original frequency f=f is set₀, this value is substituted into each component models；

3) row write out network admittance matrix Y now；

4) network admittance matrix Y carrying out Eigenvalues Decomposition is Y=L Λ T, and wherein Λ is characterized value matrix, its square reciprocal Battle array Λ^-1Diagonal entry be respectivelyTaking the mode resistance value under wherein maximum is this frequency, L and T divides Wei left eigenvector matrix, right eigenvectors matrix；

5) if having traveled through all frequencies, step (6) is entered；If no, then make the big I of f=f+ Δ f, Δ f according to reality Border needs to choose, and returns step 3)；

6) take the mode resistance value under each frequency, plot cline frequency mode resistance value curve, according to cline frequency mode Whether resistance value curve contains crest, it may be judged whether there is resonance, is judged as crest bigger for amplitude resonance, this crest Resistance value be a resonance impedance value, corresponding frequency is modal resonance frequencies；

7) ask for the participation factors of each node, determine the participation that each node is contributed for resonance:

Left eigenvector that delivery state resonance point is corresponding and right characteristic vector, it is assumed that resonance node b characteristic of correspondence value is λ_m, then the participation factors of this node b is PF_bm=L_bmT_mb, choose the node that participation factors is bigger, as the master participating in this resonance Want node；

Step 3, for the resonance frequency, based on the key node group that participation factors is maximum, according to system structure, chooses and adds Dress filter node, design wave filter is also installed at this node location；

Step 4, carries out modal resonance analysis, solves the system resonance impedance after installing wave filter additional and frequency, if not up to Resonance suppression requires 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 correctness and the feasibility of the inventive method.

This wind energy turbine set is chain topology.Each Wind turbines comprises squirrel cage asynchronous motor, current transformer, a LCL Wave filter and box outlet booster transformer (0.69/35kV).Use chain type topology that all blower fans are connected to mother of confluxing afterwards Line, through booster transformer (35/150kV), by the cable transfer of distance ashore electrical network.The most all power transmission lines It is submarine cable, is embedded at the 1m of seabed.

1, solve the system resonance impedance spectrum under original state, and compare the performance under different topology

Solve respectively under the bilateral ring topology of chain topological sum, the resonance impedance frequency spectrum of system.As shown in Figure 6, it is humorous The resistance value that shakes is shown in Table 1, and resonance times is shown in Table 2.Therefrom it will be seen that the resonance impedance of ring topology chain to be significantly less than is opened up Flutter.

The modal resonance impedance of table 1 marine wind electric field

The modal resonance number of times of table 2 marine wind electric field

2, the participation factors of key node

As a example by chain topology, ask under each frequency band resonance, the participation factors of all nodes, as shown in table 3.The most permissible Determining, resonance is mainly caused by the junction point of transformator with cable.And as a example by node 42, it is at the participation factors of low-frequency range Mid Frequency to be far above and high band, illustrate that node 42 has been primarily involved in low-frequency resonant, and there is no direct relation with other resonance. Other nodes can be according to sample relative analysis, and thereby determine that each frequency resonance is primarily involved in node.

The participation factors of each node of table 3

3, for the resonance frequency, based on the key node group that participation factors is maximum, according to system structure, choose and install filtering additional Device node, design wave filter is also installed at this node location.

Coexistence of systems three resonant frequencies, respectively 6.6,17.8 and 20.8 times.Wherein low-frequency resonant 6.6 times is main Participating in node is 42, and the participation node of intermediate frequency and high frequency is more.The major harmonic that wind-driven generator produces is 5,7,11,13,17, 19 times, and be limited in the wind field confluence less than 69kV, voltage distortion rate must not exceed 3%, so the transmission of this wind energy turbine set System has the risk causing harmonic resonance.Participation factors determines the key node exciting resonance, so setting at key node Put the filter effect that wave filter can reach best.At node 42,5,7 times single tuned filters are installed additional for low-frequency resonant.For Medium-high frequency resonance, because node 41 is wind energy turbine set confluence, from the standpoint of filter effect and cost two, installs 17 additional at this node Secondary high pass filter.

4, carry out modal resonance analysis, solve the system resonance impedance after installing wave filter additional and frequency, if not up to resonance Suppression requires then to continue Optimal Filter parameter, until meeting the requirements.

Install the system mode impedance spectrum before and after wave filter additional as shown in Figure 6.It is apparent that have three before filtering Frequency resonance, and after adding wave filter, original three frequency resonance all eliminate.But it is simultaneously introduced new 2.9 time resonance. This is the characteristic of passive filter, i.e. after eliminating primary resonance, may introduce the new resonance frequency.At Practical Project In, can be that Y-Δ connection eliminates 3 subharmonic by arranging transformator.Therefore, this frequency resonance does not results in Harmonics amplification. So, from the point of view of impedance spectrum, add wave filter and serve good resonance inhibition.

Claims (3)

1. a marine wind electric field resonance suppressing method based on modal calculation, it is characterised in that the method comprises the following steps:

1) according to the most each element of offshore wind farm field system and the annexation of cable, system harmonics model is set up:

2) set up the network admittance matrix of system according to described system harmonics model, utilize the mode of Modal Method solving system Impedance spectrum, calculates the participation factors of each node, and determine resonance truly occurs position；

3) for the resonance frequency, based on the key node group that participation factors is maximum, according to system structure, choose and install filter section additional Point, design wave filter is also installed at this node location；

4) carry out modal resonance analysis, solve the system resonance impedance after installing wave filter additional and frequency, if not up to resonance suppression Require then to continue Optimal Filter parameter, until meeting the requirements.

The modal analysis method of marine wind electric field resonance the most according to claim 1, it is characterised in that described foundation system System harmonic-model, including:

1) harmonic-model of Wind turbines:

Single Wind turbines is made up of wind-driven generator, current transformer, LCL filter three part, is the major harmonic source of wind energy turbine set, Wind turbines harmonic-model is represented with the ideal voltage source containing harmonic wave and LCL filter；

2) harmonic-model of transformator:

The wire winding resistance Rs of transformator and eddy-current loss Rp of wire winding are calculated by following equation::

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

R_p=10X tan φ (2)

In formula, X is the leakage reactance of transformator during 50Hz,H represents overtone order, and S is transformator Rated power；

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):

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

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

Z=Z_cSinh (γ l)=R+jhL (8)

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

The modal analysis method of marine wind electric field resonance the most according to claim 1, it is characterised in that described step 2) Content include:

First, n nodes all in system are carried out label, then utilize the transadmittance between node self-admittance and node to set up Grid admittance matrix Y, wherein, element Y_ii, (i=1,2 ... n) it is the self-admittance of node i, Y_ij, (i, j=1,2 ... n；i ≠ j) it is node i, the opposite number of the transadmittance between j；

The voltage of the system of this n node represents with current relationship such as (10) formula:

V=Y^-1I (10)

Y can be to be decomposed into following form:

Y=L Λ T (11)

Substitute into (10) can obtain:

TV=Λ^-1TI (12)

Definition U=TV is mode voltage vector, and J=TI is mode current vector；

Λ is asked under optional frequency^-1In greatest member, the mode impedance being defined as under this frequency；The now electricity of kth node Pressure is:

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

Wherein, k is node number, and i is mode number, l_kit_imFor participation factors；

After the selected frequency separation of traversal, obtain the system mode impedance spectrum in this frequency separation, system mode impedance spectrum Be system mode resonance point at amplitude extreme value, ask for the participation factors of each node at modal resonance point, possess maximum participate in because of Truly there is position in what the node of son was resonance.