CN105488315B - The grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator - Google Patents
The grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator Download PDFInfo
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Abstract
The present invention provides a kind of grid-connected analysis methods for generating sub-synchronous oscillation of wind-driven generator comprising following steps：It establishes wind-driven generator and is concatenated the linearized system model that compensating electric capacity accesses infinite large power system；Seek the steady stability point of linearized system model；The characteristic root of the coefficient matrix of linearized system model and left and right feature vector are sought according to steady stability point；Each secondary frequency of oscillation of the linearized system model is sought according to characteristic root, and the state variable in linearized system model with the Oscillatory mode shape strong correlation of each secondary frequency of oscillation is sought according to left and right feature vector；Change the parameter value of state variable, obtains each secondary frequency of oscillation with the variable condition under the parameter value variation of its corresponding states variable.The present invention is realized carries out quantitative analysis to the sub-synchronous oscillation of the grid-connected generation of wind-driven generator, to be conducive to the sub-synchronous oscillation progress to the grid-connected generation of wind-driven generator effectively monitoring and reply.
Description
Technical field
The present invention relates to the grid-connected analysis and research for generating sub-synchronous oscillation of wind-driven generator, are sent out more particularly, to a kind of wind-force
The grid-connected analysis method for generating sub-synchronous oscillation of motor.
Background technology
Large-scale wind generator generally hands in stream Transmission Mode retroactively by string and is connected to the grid, and can improve conveying energy in this way
Power, but sub-synchronous oscillation problem may be brought simultaneously, to easily cause wind-driven generator off-grid.Wind-driven generator it is subsynchronous
Oscillation includes mainly influence generator effect (IGE), subsynchronous control interaction (SSCI), the effect of subsynchronous shafting torsional oscillation
(SSTI).According to current research, due to the use of the controller of power electronic equipment in wind generator system, subsynchronous control phase
Interaction (SSCI) is that it generates the principal element of sub-synchronous oscillation.However, being there is no at present for the grid-connected generation of wind-driven generator
Sub-synchronous oscillation reason carries out determining quantifier elimination, thus cannot be had in face of the sub-synchronous oscillation of the grid-connected generation of wind-driven generator
The monitoring and reply of effect.
Invention content
The purpose of the present invention is to provide a kind of grid-connected analysis methods for generating sub-synchronous oscillation of wind-driven generator, to realize
Quantitative analysis is carried out to the sub-synchronous oscillation of the grid-connected generation of wind-driven generator, to be conducive to the grid-connected generation of wind-driven generator
Sub-synchronous oscillation effectively monitor and cope with.
In order to achieve the above objectives, the present invention provides a kind of grid-connected analysis sides for generating sub-synchronous oscillation of wind-driven generator
Method includes the following steps：
It establishes wind-driven generator and is concatenated the linearized system model that compensating electric capacity accesses infinite large power system；
Seek the steady stability point of the linearized system model；
The characteristic root of the coefficient matrix of the linearized system model and left and right feature are sought according to the steady stability point
Vector；
Each secondary frequency of oscillation of the linearized system model is sought according to the characteristic root, and according to the left and right spy
Sign vector seeks the state variable in the linearized system model with the Oscillatory mode shape strong correlation of each secondary frequency of oscillation；
Change the parameter value of the state variable, obtains parameter value of each secondary frequency of oscillation with its corresponding states variable
Variable condition under variation.
The grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator of the present invention, the linearized system model include
Linearisation：
The blade of wind-driven generator, three mass block shafting models of gear-box and rotor；
Five rank transient Models of wind-driven generator；
The frequency converter rotor-side control system model of wind-driven generator；
The DC voltage model of wind-driven generator；
The frequency converter stator side control system model of wind-driven generator；
The electrical-magnetic model of smoothing reactor and transformer；
The electrical-magnetic model of RLC transmission lines of electricity containing series compensation capacitance；
Infinitely great electric network model.
The grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator of the present invention, the blade of the wind-driven generator,
Three mass block shafting models of gear-box and rotor are：
In formula,For three mass block Axial Status equations of generator, XMBecome for the state of three mass block shafting equations
Amount, and XM=[Δ θ1 Δθ2 Δθ3 Δω1 Δω2 Δω3], wherein Δ θ1 Δθ2 Δθ3Respectively blade, gear-box
With the mechanical rotation angle amount of being slightly variable of rotor, Δ ω1 Δω2 Δω3The respectively mechanical angular speed of blade, gear-box and rotor
The amount of being slightly variable；
uM=[Δ Tw ΔTe]T；
Wherein, AMFor XMCoefficient matrix, uMFor the input quantity of three mass block shafting equations, BMFor uMCoefficient matrix, M1,
M2,M3The respectively rotary inertia of blade, gear-box and rotor, D1,D2,D3The respectively self-damping of blade, gear-box and rotor
Coefficient, D12,D23Mutual damping coefficient respectively between blade and gear-box, between gear-box and rotor, Δ Tw,ΔTeRespectively
The wind disturbance torque amount of being slightly variable, the electromagnetic torque amount of being slightly variable of rotor of blade, H1,H2,H3Respectively blade, gear-box and rotor
Inertia constant, k12,k23The perunit value of axis rigidity respectively between blade and gear-box, between gear-box and rotor, ωb
For a reference value of system rotating speed.
The grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator of the present invention, five ranks of the wind-driven generator are temporary
States model is：
In formula,For five rank transient state state equations of generator, XGFor the state variable of five rank transient state, AGFor XGBe
Matrix number, uGFor the input quantity of five rank transient state, BGFor uGCoefficient matrix,
Also, XG=[Δ ψqs Δψds Δψqr Δψdr]T
uG=[Δ uqs Δuds Δuqr Δudr Δωr]T
Wherein, Δ uqs、ΔudsRespectively stator voltage q, d axis component variable quantity, Δ uqr、ΔudrRespectively rotor voltage
Q, d axis components variable quantity, Δ ψqs、ΔψdsRespectively stator magnetic linkage q, d axis components variable quantity, Δ ψqr、ΔψdrRespectively rotor magnetic
Chain q, d axis component variable quantity, ωsFor stator field speed, ωbFor a reference value of system rotating speed, Δ ωrFor the increasing of rotor speed
Amount, Rs、RrRespectively stator resistance and rotor resistance, Xs、XrRespectively Stator and rotor leakage reactance, XmFor excitation electricity
Anti-, s is motor slip ratio, ψqr0、ψdr0To be respectively the initial value of stator magnetic linkage q, d axis component, s0For the first of motor slip ratio
Initial value, D are damped coefficient, D=XsXr+(Xs+Xr)/Xm, XrrFor rotor windings equivalent reactance, and Xrr=Xr+Xm, XssFor stator
Winding equivalent reactance, and Xss=Xs+Xm。
The grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator of the present invention, the frequency converter of the wind-driven generator
Rotor-side control system model：
In formula,Respectively the 1st to the 4th intermediate state variable change amount, Δ Ps、ΔQsRespectively
For stator active and reactive power variable quantity, Δ Ps_ref, Δ Qs_refThe respectively reference value variation of stator active and reactive power
Amount, Kp1、Kp2、Kp3Respectively the 1st to the 3rd power contorl parameters, Ki1、Ki2、Ki3Respectively the 1st to the 3rd current control parameter,Respectively d, q axis component variable quantity of rotor voltage,Respectively d, q axis of stator voltage point
Variable quantity is measured,The respectively initial value of d, q axis component of rotor voltage,Respectively stator voltage
D, q axis component initial value,Respectively d, q axis component variable quantity of rotor current,Respectively
For d, q axis component variable quantity of stator current,The respectively initial value of d, q axis component of rotor current,The respectively initial value of d, q axis component of stator current, XmFor excitation reactance, Δ s is motor slip ratio variable quantity,
XrrFor rotor windings equivalent reactance, and Xrr=Xr+Xm, XrFor rotor leakage reactance.
The grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator of the present invention, the DC side of the wind-driven generator
Voltage model is：
ΔPg=idg0Δudg+udg0Δidg+iqg0Δuqg+uqg0Δiqg
ΔPr=idr0Δudr+udr0Δidr+iqr0Δuqr+uqr0Δiqr
Wherein,For the voltage variety on DC capacitor, Δ udg、ΔuqgRespectively grid side frequency converter d, q axis
Component of voltage variable quantity, Δ idg、ΔiqgRespectively grid side frequency converter d, q shaft currents component variation amount, C are DC link electricity
Capacitance, udg0、uqg0The respectively initial value of grid side frequency converter d, q shaft voltage components, idg0、iqg0Respectively grid side frequency converter
D, the initial value of q shaft currents component, Δ Pg、ΔPrRespectively stator side and stator side active power variable quantity, ωbTurn for system
The a reference value of speed,Initial Voltage Value on DC capacitor.
The grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator of the present invention, the frequency converter of the wind-driven generator
Stator side control system model is：
Δidg_ref=Kpdg(ΔVDC_ref-ΔVDC)+KidgΔx5
Δudg=Kpg[Kpdg(ΔVDC_ref-ΔVDC)+KidgΔx5-idg]+KigΔx6
Δuqg=Kpg(Δiqg_ref-Δiqg)+KigΔx7
Wherein,It is the 5th to the 7th intermediate state variable, KpdgFor net side current transformer Voltage loop ratio
Coefficient, KidgFor net side current transformer Voltage loop integral coefficient, KpgFor net side current transformer electric current loop Proportional coefficient KigFor net side unsteady flow
Device electric current loop integral coefficient, Δ VDCFor the variable quantity of DC voltage, Δ VDC_refFor the variable quantity of the reference value of DC voltage, Δ
idg、ΔiqgThe respectively variable quantity of grid side electric current d, q axis components, Δ idg_ref、Δiqg_refRespectively grid side electric current d, q
The variable quantity of the reference value of axis component.
The grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator of the present invention, the smoothing reactor and transformer
Electrical-magnetic model be：
In formula, XRL=[Δ idg Δiqg]T, URL=[Δ uds Δuqs]T
WhereinFor smoothing reactor and the state equation of the electro-magnetic transient of transformer, XRLFor smoothing reactor and transformation
The state variable of the electro-magnetic transient of device, uRLFor the input quantity of smoothing reactor and the electro-magnetic transient of transformer, ARLFor XRLCoefficient
Matrix, BRLFor uRLCoefficient matrix, X1、R1Reactance for smoothing reactor and transformer and resistance, Δ uds,ΔuqsRespectively
Set end voltage d, q axis component variable quantity, Δ idg,ΔiqgFor the variable quantity of d, q axis component of grid side current transformer electric current, Δ uds、
ΔuqsRespectively d, q axis component variable quantity of stator voltage, ωbFor a reference value of system rotating speed.
The grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator of the present invention, it is described containing series compensation capacitance
The electrical-magnetic model of RLC transmission lines of electricity is：
In formula, XRLC=[Δ id Δiq Δucd Δucq]T
YRLC=[Δ id Δiq]T
uRLC=[Δ uds Δuqs Δudg Δuqg]T
Wherein,For the state equation of the electro-magnetic transient of the RLC transmission lines of electricity of series compensation capacitance, XRLCIt is mended for series connection
Repay the state variable of the electro-magnetic transient of the RLC transmission lines of electricity of capacitance, uRLCFor the electromagnetism of the RLC transmission lines of electricity of series compensation capacitance
The input quantity of transient state, ARLCFor XRLCCoefficient matrix, BRLCFor uRLCCoefficient matrix, Δ id,ΔiqFor series circuit electric current d, q
The variable quantity of axis component, Δ ucd,ΔucqFor the variable quantity of series capacitance both end voltage d, q axis component, Δ udg、ΔuqgRespectively
The variable quantity of infinitely great supply voltage d, q axis component, and Δ udg=Δ uqg=0, R2,X2Resistance for series circuit and reactance,
xcFor the reactance of series capacitance, ωbFor a reference value of system rotating speed, YRLCFor the RLC transmission line of electricity output quantities of series compensation capacitance.
The grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator of the present invention, the infinity electric network model is it
The constant voltage source that internal impedance is zero.
The present invention wind-driven generator it is grid-connected generate sub-synchronous oscillation analysis method, further include：
When rotor-side converter and stator side current transformer use different control strategies, the two is coordinately transformed, with
Uniform coordinate eliminates existing differential seat angle between electrical quantity.
The grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator of the present invention, it is described to seek the linearized system
The steady stability point of model, specially：
The simulation model that the linearized system model is built by simulation software carries out the simulation model initial
Change, to seek the quiescent operation point of simulation model.
The grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator of the present invention, it is described according to the steady stability point
The characteristic root of the coefficient matrix of the linearized system model and left and right feature vector are sought, specially：
Initial parameter and initialization parameters obtained are substituted into the linearized system model, to calculate coefficient matrix
Characteristic root, left eigenvector, right feature vector.
The grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator of the present invention, it is described to be sought according to the characteristic root
Each secondary frequency of oscillation of the linearized system model, specially：
If characteristic root is λ=σ+j ω, frequency of oscillation is
Then indicate that the damping ratio of the Oscillatory mode shape rate of decay is
According to the relationship between features described above root and frequency of oscillation, the corresponding frequency of oscillation of different characteristic root is acquired；
Wherein, σ is characterized the real part of root, and ω is characterized the imaginary part of root.
The grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator of the present invention, it is described according to the left and right feature
Vector seeks the state variable with the Oscillatory mode shape strong correlation of each secondary frequency of oscillation in the linearized system model, specifically
For：
Wherein, PiFor the participation matrix of i-th of mode, PiElement PniIndicate n-th of state variable in i-th of mode
Degree of participation, Uni,VniRespectively coefficient matrix is about eigenvalue λiLeft and right feature vector.
In the grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator of the present invention, wind-driven generator is being established through string
Connection compensating electric capacity accesses on the basis of the linearized system model of infinite large power system, first seeks the coefficient of linearized system model
The characteristic root of matrix and left and right feature vector；Then each secondary frequency of oscillation of linearized system model is taken according to Evaluating Eigenvalues, and
It seeks becoming with the state of the Oscillatory mode shape strong correlation of each secondary frequency of oscillation in linearized system model according to left and right feature vector
Amount；The parameter value for finally changing state variable obtains under parameter value variation of each secondary frequency of oscillation with its corresponding states variable
Variable condition realizes and carries out quantitative analysis to the sub-synchronous oscillation of the grid-connected generation of wind-driven generator, to be conducive to wind-force
The sub-synchronous oscillation that generator connecting in parallel with system generates effectively monitor and cope with.
Description of the drawings
Attached drawing described herein is used to provide further understanding of the present invention, and is constituted part of this application, not
Constitute limitation of the invention.In the accompanying drawings：
Fig. 1 is the flow of the grid-connected analysis method for generating sub-synchronous oscillation of the wind-driven generator of one embodiment of the invention
Figure；
Fig. 2 is three mass block shafting moulds of the blade of the wind-driven generator of one embodiment of the invention, gear-box and rotor
The schematic diagram of type；
Fig. 3 is the schematic diagram of the DC voltage model of the wind-driven generator of one embodiment of the invention；
Fig. 4 is the controller chassis of the frequency converter rotor-side control system model of the wind-driven generator of one embodiment of the invention
Figure；
Fig. 5 is the current transformer control of the frequency converter stator side control system model of the wind-driven generator of one embodiment of the invention
Block diagram processed；
Fig. 6 is when rotor-side converter and grid side current transformer are using different control strategies in one embodiment of the invention
Coordinate transform schematic diagram.
Specific implementation mode
To make the objectives, technical solutions, and advantages of the present invention clearer, with reference to embodiment and attached drawing, to this
Invention is described in further details.Here, the illustrative embodiments of the present invention and their descriptions are used to explain the present invention, but do not make
For limitation of the invention.
Below in conjunction with the accompanying drawings, the specific implementation mode of the present invention is described in further detail.
Refering to what is shown in Fig. 1, the grid-connected analysis method for generating sub-synchronous oscillation of the wind-driven generator of the embodiment of the present invention, including
Following steps：
Step S101, establish wind-driven generator (such as double-fed induction wind driven generator) be concatenated compensating electric capacity access it is infinite
The linearized system model of large power system.The linearized system model includes the blade, gear-box and rotor of wind-driven generator
Three mass block shafting models, wind-driven generator five rank transient Models, the frequency converter rotor-side control system of wind-driven generator
Model, the DC voltage model of wind-driven generator, the frequency converter stator side control system model of wind-driven generator, flat wave reactance
The electrical-magnetic model and infinity of the electrical-magnetic model of device and transformer, RLC transmission lines of electricity containing series compensation capacitance
Electric network model.Each model part is illustrated one by one below：
One, three mass block shafting models of the blade of wind-driven generator, gear-box and rotor
In order to find the influence of sub-synchronous oscillation shaft, the blade, gear-box, generator amature of wind-driven generator are established
Three mass block models write the shafting equation of motion by the relationship row of rotating speed and windup-degree between each mass block；Copy steamer
The shafting of the shafting torsional oscillation model of generating set, wind-driven generator can also indicate with mass block spring model, i.e. blade-tooth
Roller box-generator amature is expressed as 1,2 and No. 3 mass block, as shown in Figure 2.The portion can be obtained using small interference analytic approach
Shown in the lienarized equation of sub-model such as formula (1).Wherein all amounts are famous value of the conversion to high-speed side.
It is obtained after Axial Status spatial model is converted to perunit value and linearisation shown in state equation such as formula (2), the state
Equation such as formula (2) is three mass block shafting models of the blade of the wind-driven generator linearized, gear-box and rotor.
Wherein, XM=[Δ θ1 Δθ2 Δθ3 Δω1 Δω2 Δω3]
uM=[Δ Tw ΔTe]T
Wherein, AMFor XMCoefficient matrix, uMFor the input quantity of three mass block shafting equations, BMFor uMCoefficient matrix, M1,
M2,M3The respectively rotary inertia of blade, gear-box and rotor, D1,D2,D3The respectively self-damping of blade, gear-box and rotor
Coefficient, D12,D23Mutual damping coefficient respectively between blade and gear-box, between gear-box and rotor, Δ Tw,ΔTeRespectively
The wind disturbance torque amount of being slightly variable, the electromagnetic torque amount of being slightly variable of rotor of blade, H1,H2,H3Respectively blade, gear-box and rotor
Inertia constant, k12,k23The perunit value of axis rigidity respectively between blade and gear-box, between gear-box and rotor, ωb
For the synchronous angular velocity of electrical system, a reference value as system rotating speed.
Two, five rank transient Models of wind-driven generator
Assuming that selected synchronous rotating frame is reference frame, it is contemplated that aerogenerator stator transient process is built
Vertical equation of the influence generator in d, q coordinate system.The influence generator voltage equation such as formula (3) indicated with perunit value is shown.
Shown in relationship such as formula (4) between magnetic linkage and electric current：
Shown in the electromagnetic torque of generator such as formula (5)
Shown in state equation such as formula (6) after linearisation, which is five rank transient state of the wind-driven generator linearized
Model.
Wherein, XG=[Δ ψqs Δψds Δψqr Δψdr]T
uG=[Δ uqs Δuds Δuqr Δudr Δωr]T
Wherein, Δ uqs、ΔudsRespectively stator voltage q, d axis component variable quantity, Δ uqr、ΔudrRespectively rotor voltage
Q, d axis components variable quantity, Δ ψqs、ΔψdsRespectively stator magnetic linkage q, d axis components variable quantity, Δ ψqr、ΔψdrRespectively rotor magnetic
Chain q, d axis component variable quantity, ωsFor stator field speed, ωbFor the synchronous angular velocity of electrical system, as system rotating speed
A reference value, Δ ωrFor rotor speed increment, Rs、RrRespectively stator resistance and rotor resistance, Xs、XrRespectively Stator
With rotor leakage reactance, XmFor excitation reactance, s is motor slip ratio, ψqr0、ψdr0For be respectively stator magnetic linkage q, d axis component just
Initial value, s0For the initial value of motor slip ratio, D is damped coefficient, D=XsXr+(Xs+Xr)/Xm, XrrFor the equivalent resistance of rotor windings
It is anti-, and Xrr=Xr+Xm, XssFor stator winding equiva lent impedance, and Xss=Xs+Xm。
Three, the frequency converter rotor-side control system model of wind-driven generator
Rotor-side Frequency Converter Control is used based on stator magnetic linkage oriented vector controlled, i.e. d axis and stator magnetic linkage direction weight
It closes, with symbol subscriptIt indicates, main control targe is the active power and set end voltage of wind-driven generator, wherein active and electric
Pressure passes through respectivelyWithIt controls, control block diagram is as shown in Figure 4.Specifically：
In small-signal model, formula (7-14) analysis by Linearization there is into relational expression during linearisation：
Equation such as formula (15-20) is obtained after then linearizing, formula 15-20 is the frequency converter rotor of the wind-driven generator linearized
Shown in the control system model of side：
In formula,Respectively the 1st to the 4th intermediate state variable change amount, Δ Ps、ΔQsRespectively
For stator active and reactive power variable quantity, Δ Ps_ref, Δ Qs_refThe respectively reference value variation of stator active and reactive power
Amount, Kp1、Kp2、Kp3Respectively the 1st to the 3rd power contorl parameters, Ki1、Ki2、Ki3Respectively the 1st to the 3rd current control parameter,Respectively d, q axis component variable quantity of rotor voltage,Respectively d, q axis of stator voltage point
Variable quantity is measured,The respectively initial value of d, q axis component of rotor voltage,Respectively stator voltage
D, q axis component initial value,Respectively d, q axis component variable quantity of rotor current,Respectively
D, q axis component variable quantity of stator current,The respectively initial value of d, q axis component of rotor current,
The respectively initial value of d, q axis component of stator current, XmFor excitation reactance, Δ s is motor slip ratio variable quantity, XrrFor rotor
Winding equiva lent impedance, and Xrr=Xr+Xm, XrFor rotor leakage reactance.
Four, the DC voltage model of wind-driven generator
It is illustrated in figure 3 the DC voltage model of wind-driven generator, according to electric current positive direction as defined in Fig. 3, DC side
Active loss PDCEqual to current transformer stator side active-power PgWith current transformer rotor-side active-power PrDifference, i.e.,
PDC=Pg-Pr (21)
Rotor active power, DC side active power can be expressed as:
Pr=udridr+uqriqr (22)
Pg=udgidg+uqgiqg (23)
Formula (22-24) is substituted into formula (21), then shown in the model of current transformer DC side such as formula (25).
Linearisation formula (25) obtains the equation of perunit value expression, as shown in formula (26).
Wherein Δ PgWith Δ PrExpression formula is
ΔPg=idg0Δudg+udg0Δidg+iqg0Δuqg+uqg0Δiqg
ΔPr=idr0Δudr+udr0Δidr+iqr0Δuqr+uqr0Δiqr
Wherein,For the voltage variety on DC capacitor, Δ udg、ΔuqgRespectively grid side frequency converter d, q axis
Component of voltage variable quantity, Δ idg、ΔiqgRespectively grid side frequency converter d, q shaft currents component variation amount, C are DC link electricity
Capacitance, udg0、uqg0The respectively initial value of grid side frequency converter d, q shaft voltage components, idg0、iqg0Respectively grid side frequency converter
D, the initial value of q shaft currents component, Δ Pg、ΔPrRespectively stator side and stator side active power variable quantity, ωbTo be electrically
The synchronous angular velocity of system, as a reference value of system rotating speed,Initial Voltage Value on DC capacitor.
Five, the frequency converter stator side control system model of wind-driven generator
The control of the frequency converter stator side of wind-driven generator uses the rotating coordinate system based on stator voltage vector oriented, i.e. d axis
With stator voltage direction, main control targe is that stable DC side voltage and control generator generator terminal are idle, is become respectively by net side
Flow the current component i of devicedgAnd iqgIt is controlled, control block diagram is as shown in Figure 5.Its concrete model is as follows：
Δidg_ref=Kpdg(ΔVDC_ref-ΔVDC)+KidgΔx5 (28)
Δudg=Kpg[Kpdg(ΔVDC_ref-ΔVDC)+KidgΔx5-idg]+KigΔx6 (31)
Δuqg=Kpg(Δiqg_ref-Δiqg)+KigΔx7 (32)
Wherein,It is the 5th to the 7th intermediate state variable, KpdgFor net side current transformer Voltage loop ratio system
Number, KidgFor net side current transformer Voltage loop integral coefficient, KpgFor net side current transformer electric current loop Proportional coefficient KigFor net side current transformer
Electric current loop integral coefficient, Δ VDCFor the variable quantity of DC voltage, Δ VDC_refFor the variable quantity of the reference value of DC voltage, value
It is zero, Δ idg、ΔiqgThe respectively variable quantity of grid side electric current d, q axis components, Δ idg_ref、Δiqg_refRespectively grid side
The variable quantity of the reference value of electric current d, q axis component, value zero.
Six, the electrical-magnetic model of smoothing reactor and transformer
When carrying out subsynchronous oscillation of electrical power system analysis, transmission line of electricity needs to use electrical-magnetic model, and differential is used in combination
Equation is described.Circuit, transformer and infinitely great power supply can be equivalent to RL circuits and lumped parameter model.In abc three-phases
Under coordinate system, shown in the RL circuit a phases differential equation such as formula (33).
ua=Ladia/dt+iaRa (33)
Wherein, uaFor the voltage at RL circuits both ends, iaTo flow through the electric current of circuit, Ra, LaFor a phase resistances, inductance, b phases and
C phases are similarly understood.
Shown in the circuit abc three-phases differential equation such as formula (34)
For with generator model interface, circuit model need to also convert by three phase coordinate systems to synchronous rotating frame.Conversion
Shown in matrix such as formula (35).
In formula, Kabc→dqIndicate that transition matrix, θ indicate the angle of a phases and d axis.Above-mentioned derivation is summarized, RL circuits
It linearizes shown in perunit value state-space model such as formula (36), formula (36) is the smoothing reactor linearized and the electricity of transformer
Magnetic transient Model.
Wherein, XRL=[Δ idg Δiqg]T, URL=[Δ uds Δuqs]T
WhereinFor smoothing reactor and the state equation of the electro-magnetic transient of transformer, XRLFor smoothing reactor and transformation
The state variable of the electro-magnetic transient of device, uRLFor the input quantity of smoothing reactor and the electro-magnetic transient of transformer, ARLFor XRLCoefficient
Matrix, BRLFor uRLCoefficient matrix, X1、R1Reactance for smoothing reactor and transformer and resistance, Δ uds,ΔuqsRespectively
Set end voltage d, q axis component variable quantity, Δ idg,ΔiqgFor the variable quantity of d, q axis component of grid side current transformer electric current, Δ uds、
ΔuqsRespectively d, q axis component variable quantity of stator voltage, ωbFor the synchronous angular velocity of electrical system, it is used as system rotating speed
A reference value.
Seven, the electrical-magnetic model of the RLC transmission lines of electricity containing series compensation capacitance
For RLC series circuits, state-space model it is required input be circuit both ends voltage difference, i.e., four
Voltage value.The appearance of capacitance is so that model needs the voltage for increasing capacitance both ends as state variable simultaneously.RLC series circuits are micro-
Divide shown in equation such as formula (37), formula (37) is the electro-magnetic transient of the RLC transmission lines of electricity containing series compensation capacitance linearized
Model.
Wherein, XRLC=[Δ id Δiq Δucd Δucq]T
YRLC=[Δ id Δiq]T
uRLC=[Δ uds Δuqs Δudg Δuqg]T
Wherein,For the state equation of the electro-magnetic transient of the RLC transmission lines of electricity of series compensation capacitance, XRLCIt is mended for series connection
Repay the state variable of the electro-magnetic transient of the RLC transmission lines of electricity of capacitance, uRLCFor the electromagnetism of the RLC transmission lines of electricity of series compensation capacitance
The input quantity of transient state, ARLCFor XRLCCoefficient matrix, BRLCFor uRLCCoefficient matrix, Δ id,ΔiqFor series circuit electric current d, q
The variable quantity of axis component, Δ ucd,ΔucqFor the variable quantity of series capacitance both end voltage d, q axis component, Δ udg、ΔuqgRespectively
The variable quantity of infinitely great supply voltage d, q axis component, and Δ udg=Δ uqg=0, R2,X2Resistance for series circuit and reactance,
xcFor the reactance of series capacitance, ωbFor the synchronous angular velocity of electrical system, as a reference value of system rotating speed, YRLCFor series connection
The RLC transmission line of electricity output quantities of compensating electric capacity.
Eight, infinitely great electric network model
Infinitely great electric network model is the constant voltage source that its internal impedance is zero.
The frequency converter stator side control of the frequency converter rotor-side control system model and wind-driven generator of above-mentioned wind-driven generator
In system model processed, rotor-side converter uses Stator flux oriented control, stator side current transformer to use stator voltage vector oriented control
System, there are differential seat angle between electrical quantity, needs to carry out dq coordinate systems to xy coordinates since the two uses different control strategies
Conversion, rotor current transformer electrical quantity is transformed under unified coordinate system xy coordinate systems (as shown in Figure 6), in favor of processing.Wherein,
Shown in conversion formula such as formula (38-39).
Wherein, α is the angle of x-axis and d axis.
Step S102 seeks the steady stability point of the linearized system model.Specifically, building line by simulation software
The simulation model of property system model, initializes simulation model, to seek the quiescent operation point of simulation model.So as to
To determine that wind-driven generator single machine passes through by known total active power and total reactive power, set end voltage, generator amature slippage
Series compensation capacitance access Infinite bus system the active power for being assigned to stator and rotor, stator current and rotor current and
The amplitude and phase angle of rotor voltage.Wherein, in power grid or prime mover small sample perturbations occur for the synchronous generator being connected in parallel on power grid
When, operating status will change, and after disturbing disappearance, stable operation in the state that power generation function is returned to originally is known as
Generator is steady stability, otherwise is exactly unstable, and this steady stability state is exactly steady stability point.
Step S103, sought according to the steady stability point coefficient matrix of the linearized system model characteristic root and
Left and right feature vector.Specifically, initial parameter and initialization parameters obtained are substituted into the linearized system model, in terms of
Calculate the characteristic root, left eigenvector, right feature vector of coefficient matrix.
Step S104 seeks each secondary frequency of oscillation of the linearized system model according to the characteristic root, and according to institute
It states left and right feature vector and seeks shape in the linearized system model with the Oscillatory mode shape strong correlation of each secondary frequency of oscillation
State variable.Specifically：
If characteristic root is λ=σ+j ω, frequency of oscillation is
Then indicate that the damping ratio of the Oscillatory mode shape rate of decay is
According to the relationship between features described above root and frequency of oscillation, the corresponding frequency of oscillation of different characteristic root is acquired；
Wherein, σ is characterized the real part of root, and ω is characterized the imaginary part of root.
Wherein, PiFor the participation matrix of i-th of mode, PiElement PniIndicate n-th of state variable in i-th of mode
Degree of participation, also reflect the influence degree of i-th of mode pair, n-th of quantity of state, Uni,VniRespectively coefficient matrix about
Eigenvalue λiLeft and right feature vector.
Step S105 changes the parameter value of the state variable, obtains each secondary frequency of oscillation and becomes with its corresponding states
Variable condition under the parameter value variation of amount.Such as keep other parameters constant, only change a certain with state variable strong correlation
The size of a parameter value, observation characteristic root and the situation of change for participating in the factor, obtain system stability and those relating to parameters
Conclusion, to it is quantitative find out influence wind-driven generator single machine be concatenated compensating electric capacity access Infinite bus system stability because
Element.
The embodiment of the present invention is being concatenated the small interference of compensating electric capacity access Infinite bus system progress to wind-driven generator single machine
It is each to seek by the characteristic value and left and right feature vector of the coefficient matrix of solving model on the basis of the model for linearizing gained
The participation factor of state variable, you can judge system sub-synchronous oscillation and shafting torsional oscillation stability, obtain and damped with shafting torsional oscillation
Characteristic is found out and the mass block of feature torsional mode strong correlation and the change of relevant system in the relevant information of which state variable
Amount, to be monitored and take effective precautionary measures.
Those skilled in the art will also be appreciated that various illustrative components, blocks, unit and the step that the embodiment of the present invention is listed
Suddenly it can be realized by the combination of hardware, software or both.It is realized to hardware or software is then passed through depending on specific
Application and whole system design requirement.Those skilled in the art can use various each specific application
Method realizes the function, but this realization is understood not to the range beyond protection of the embodiment of the present invention.
Various illustrative logical blocks or unit described in the embodiment of the present invention can by general processor,
Digital signal processor, application-specific integrated circuit (ASIC), field programmable gate array or other programmable logic devices, discrete gate
Or described function is realized or is operated in transistor logic, the design of discrete hardware components or any of the above described combination.General place
It can be microprocessor to manage device, and optionally, which may be any traditional processor, controller, microcontroller
Device or state machine.Processor can also be realized by the combination of computing device, such as digital signal processor and microprocessor,
Multi-microprocessor, one or more microprocessors combine a digital signal processor core or any other like configuration
To realize.
The step of method described in the embodiment of the present invention or algorithm can be directly embedded into hardware, processor execute it is soft
The combination of part module or the two.Software module can be stored in RAM memory, flash memory, ROM memory, EPROM storages
Other any form of storaging mediums in device, eeprom memory, register, hard disk, moveable magnetic disc, CD-ROM or this field
In.Illustratively, storaging medium can be connect with processor, so that processor can read information from storaging medium, and
It can be to storaging medium stored and written information.Optionally, storaging medium can also be integrated into processor.Processor and storaging medium can
To be set in ASIC, ASIC can be set in user terminal.Optionally, processor and storaging medium can also be set to use
In different components in the terminal of family.
In one or more illustrative designs, above-mentioned function described in the embodiment of the present invention can be in hardware, soft
Part, firmware or the arbitrary of this three combine to realize.If realized in software, these functions can store and computer-readable
On medium, or with one or more instruction or code form be transmitted on the medium of computer-readable.Computer readable medium includes electricity
Brain storaging medium and convenient for allow computer program to be transferred to from a place telecommunication media in other places.Storaging medium can be with
It is that any general or special computer can be with the useable medium of access.For example, such computer readable media may include but
It is not limited to RAM, ROM, EEPROM, CD-ROM or other optical disc storage, disk storage or other magnetic storage devices or other
What can be used for carry or store with instruct or data structure and it is other can be by general or special computer or general or specially treated
The medium of the program code of device reading form.In addition, any connection can be properly termed computer readable medium, example
Such as, if software is to pass through a coaxial cable, fiber optic cables, double from a web-site, server or other remote resources
Twisted wire, Digital Subscriber Line (DSL) are defined with being also contained in for the wireless way for transmitting such as example infrared, wireless and microwave
In computer readable medium.The disk (disk) and disk (disc) includes compress disk, radium-shine disk, CD, DVD, floppy disk
And Blu-ray Disc, disk is usually with magnetic duplication data, and disk usually carries out optical reproduction data with laser.Combinations of the above
It can also be included in computer readable medium.
Particular embodiments described above has carried out further in detail the purpose of the present invention, technical solution and advantageous effect
Describe in detail it is bright, it should be understood that the above is only a specific embodiment of the present invention, the guarantor being not intended to limit the present invention
Range is protected, all within the spirits and principles of the present invention, any modification, equivalent substitution, improvement and etc. done should be included in this
Within the protection domain of invention.
Claims (5)
1. a kind of grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator, which is characterized in that include the following steps：
It establishes wind-driven generator and is concatenated the linearized system model that compensating electric capacity accesses infinite large power system；
Seek the steady stability point of the linearized system model；
Sought according to the steady stability point coefficient matrix of the linearized system model characteristic root and left and right feature to
Amount；
Seek each secondary frequency of oscillation of the linearized system model according to the characteristic root, and according to the left and right feature to
Amount seeks the state variable in the linearized system model with the Oscillatory mode shape strong correlation of each secondary frequency of oscillation；
Change the parameter value of the state variable, obtains parameter value variation of each secondary frequency of oscillation with its corresponding states variable
Under variable condition；Wherein,
The linearized system model includes linearisation：
The blade of wind-driven generator, three mass block shafting models of gear-box and rotor；
Five rank transient Models of wind-driven generator；
The frequency converter rotor-side control system model of wind-driven generator；
The DC voltage model of wind-driven generator；
The frequency converter stator side control system model of wind-driven generator；
The electrical-magnetic model of smoothing reactor and transformer；
The electrical-magnetic model of RLC transmission lines of electricity containing series compensation capacitance；
Infinitely great electric network model；Wherein,
Three mass block shafting models of the blade of the wind-driven generator, gear-box and rotor are：
In formula,For three mass block Axial Status equations of generator, XMFor the state variable of three mass block shafting equations, and XM
=[Δ θ1 Δθ2 Δθ3 Δω1 Δω2 Δω3], wherein Δ θ1 Δθ2 Δθ3Respectively blade, gear-box and rotor
The mechanical rotation angle amount of being slightly variable, Δ ω1 Δω2 Δω3The respectively mechanical angular speed amount of being slightly variable of blade, gear-box and rotor；
uM=[Δ Tw ΔTe]T；
Wherein, AMFor XMCoefficient matrix, uMFor the input quantity of three mass block shafting equations, BMFor uMCoefficient matrix, M1,M2,M3
The respectively rotary inertia of blade, gear-box and rotor, D1,D2,D3The respectively self-damping coefficient of blade, gear-box and rotor,
D12,D23Mutual damping coefficient respectively between blade and gear-box, between gear-box and rotor, Δ Tw,ΔTeRespectively blade
The wind disturbance torque amount of being slightly variable, the electromagnetic torque amount of being slightly variable of rotor, H1,H2,H3Respectively blade, gear-box and rotor is used
Property constant, k12,k23The perunit value of axis rigidity respectively between blade and gear-box, between gear-box and rotor, ωbTo be
The a reference value of system rotating speed；
Five rank transient Models of the wind-driven generator are：
In formula,For five rank transient state state equations of generator, XGFor the state variable of five rank transient state, AGFor XGCoefficient square
Battle array, uGFor the input quantity of five rank transient state, BGFor uGCoefficient matrix,
Also, XG=[Δ ψqs Δψds Δψqr Δψdr]T
uG=[Δ uqs Δuds Δuqr Δudr Δωr]T
Wherein, Δ uqs、ΔudsRespectively stator voltage q, d axis component variable quantity, Δ uqr、ΔudrRespectively rotor voltage q, d axis
Component variation amount, Δ ψqs、ΔψdsRespectively stator magnetic linkage q, d axis components variable quantity, Δ ψqr、ΔψdrRespectively rotor flux q, d
Axis component variable quantity, ωsFor stator field speed, ωbFor a reference value of system rotating speed, Δ ωrFor rotor speed increment, Rs、Rr
Respectively stator resistance and rotor resistance, Xs、XrRespectively Stator and rotor leakage reactance, XmFor excitation reactance, s is electricity
Machine revolutional slip, ψqr0、ψdr0To be respectively the initial value of stator magnetic linkage q, d axis component, s0For the initial value of motor slip ratio, D is
Damped coefficient, D=XsXr+(Xs+Xr)/Xm, XrrFor rotor windings equivalent reactance, and Xrr=Xr+Xm, XssIt is equivalent for stator winding
Reactance, and Xss=Xs+Xm；
The frequency converter rotor-side control system model of the wind-driven generator：
In formula,Respectively the 1st to the 4th intermediate state variable change amount, Δ Ps、ΔQsIt is respectively fixed
Sub- active and reactive power variable quantity, Δ Ps_ref, Δ Qs_refThe respectively reference value variable quantity of stator active and reactive power, Kp1、
Kp2、Kp3Respectively the 1st to the 3rd power contorl parameters, Ki1、Ki2、Ki3Respectively the 1st to the 3rd current control parameter,Respectively d, q axis component variable quantity of rotor voltage,Respectively d, q axis component of stator voltage
Variable quantity,The respectively initial value of d, q axis component of rotor voltage,The respectively d of stator voltage,
The initial value of q axis components,Respectively d, q axis component variable quantity of rotor current,Respectively stator
D, q axis component variable quantity of electric current,The respectively initial value of d, q axis component of rotor current,Respectively
For the initial value of d, q axis component of stator current, XmFor excitation reactance, Δ s is motor slip ratio variable quantity, XrrFor rotor windings
Equivalent reactance, and Xrr=Xr+Xm, XrFor rotor leakage reactance；
The DC voltage model of the wind-driven generator is：
In formula, Δ PgWith Δ PrExpression formula is
ΔPg=idg0Δudg+udg0Δidg+iqg0Δuqg+uqg0Δiqg
ΔPr=idr0Δudr+udr0Δidr+iqr0Δuqr+uqr0Δiqr
Wherein,For the voltage variety on DC capacitor, Δ udg、ΔuqgRespectively grid side frequency converter d, q shaft voltages point
Measure variable quantity, Δ idg、ΔiqgRespectively grid side frequency converter d, q shaft currents component variation amount, C are DC link capacitance,
udg0、uqg0The respectively initial value of grid side frequency converter d, q shaft voltage components, idg0、iqg0Respectively grid side frequency converter d, q axis
The initial value of current component, Δ Pg、ΔPrRespectively stator side and stator side active power variable quantity, ωbFor the base of system rotating speed
Quasi- value,Initial Voltage Value on DC capacitor；
The frequency converter stator side control system model of the wind-driven generator is：
Δudg=Kpg[Kpdg(ΔVDC_ref-ΔVDC)+KidgΔx5-idg]+KigΔx6
Δuqg=Kpg(Δiqg_ref-Δiqg)+KigΔx7
Wherein,It is the 5th to the 7th intermediate state variable, KpdgFor net side current transformer Voltage loop proportionality coefficient,
KidgFor net side current transformer Voltage loop integral coefficient, KpgFor net side current transformer electric current loop Proportional coefficient KigFor net side current transformer electric current
Ring integral coefficient, Δ VDCFor the variable quantity of DC voltage, Δ VDC_refFor the variable quantity of the reference value of DC voltage, Δ idg、Δ
iqgThe respectively variable quantity of grid side electric current d, q axis components, Δ idg_ref、Δiqg_refRespectively grid side electric current d, q axis components
Reference value variable quantity；
The electrical-magnetic model of the smoothing reactor and transformer is：
In formula, XRL=[Δ idg Δiqg]T, URL=[Δ uds Δuqs]T
WhereinFor smoothing reactor and the state equation of the electro-magnetic transient of transformer, XRLFor smoothing reactor and transformer
The state variable of electro-magnetic transient, uRLFor the input quantity of smoothing reactor and the electro-magnetic transient of transformer, ARLFor XRLCoefficient square
Battle array, BRLFor uRLCoefficient matrix, X1、R1Reactance for smoothing reactor and transformer and resistance, Δ uds,ΔuqsRespectively machine
Terminal voltage d, q axis component variable quantity, Δ idg,ΔiqgFor the variable quantity of d, q axis component of grid side current transformer electric current, Δ uds、Δ
uqsRespectively d, q axis component variable quantity of stator voltage, ωbFor a reference value of system rotating speed；
The electrical-magnetic model of the RLC transmission lines of electricity containing series compensation capacitance is：
In formula, XRLC=[Δ id Δiq Δucd Δucq]T
YRLC=[Δ id Δiq]T
uRLC=[Δ uds Δuqs Δudg Δuqg]T
Wherein,For the state equation of the electro-magnetic transient of the RLC transmission lines of electricity of series compensation capacitance, XRLCFor series compensation electricity
The state variable of the electro-magnetic transient of the RLC transmission lines of electricity of appearance, uRLCFor the electro-magnetic transient of the RLC transmission lines of electricity of series compensation capacitance
Input quantity, ARLCFor XRLCCoefficient matrix, BRLCFor uRLCCoefficient matrix, Δ id,ΔiqFor series circuit electric current d, q axis point
The variable quantity of amount, Δ ucd,ΔucqFor the variable quantity of series capacitance both end voltage d, q axis component, Δ udg、ΔuqgIt is respectively infinite
The variable quantity of big supply voltage d, q axis component, and Δ udg=Δ uqg=0, R2,X2Resistance for series circuit and reactance, xcFor
The reactance of series capacitance, ωbFor a reference value of system rotating speed, YRLCFor the output quantity of the RLC transmission lines of electricity of series compensation capacitance；
Each secondary frequency of oscillation that the linearized system model is sought according to the characteristic root, specially：
If characteristic root is λ=σ+j ω, frequency of oscillation is
Then indicate that the damping ratio of the Oscillatory mode shape rate of decay is
According to the relationship between features described above root and frequency of oscillation, the corresponding frequency of oscillation of different characteristic root is acquired；
Wherein, σ is characterized the real part of root, and ω is characterized the imaginary part of root；
The oscillation sought according to the left and right feature vector in the linearized system model with each secondary frequency of oscillation
The state variable of mode strong correlation, specially：
According to formulaCalculating seek in the linearized system model with each secondary frequency of oscillation
Oscillatory mode shape strong correlation state variable；
Wherein, PiFor the participation matrix of i-th of mode, PiElement PniIndicate the ginseng of n-th of state variable in i-th of mode
With degree, Uni,VniRespectively coefficient matrix is about eigenvalue λiLeft and right feature vector.
2. the grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator according to claim 1, which is characterized in that institute
It is the constant voltage source that its internal impedance is zero to state infinitely great electric network model.
3. the grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator according to claim 1, which is characterized in that also
Including：
When rotor-side converter and stator side current transformer use different control strategies, the two is coordinately transformed, with unified
Coordinate eliminates existing differential seat angle between electrical quantity.
4. the grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator according to claim 1, which is characterized in that institute
The steady stability point for seeking the linearized system model is stated, specially：
The simulation model that the linearized system model is built by simulation software initializes the simulation model, with
Seek the quiescent operation point of simulation model.
5. the grid-connected analysis method for generating sub-synchronous oscillation of wind-driven generator according to claim 4, which is characterized in that institute
State according to the steady stability point seek the linearized system model coefficient matrix characteristic root and left and right feature vector,
Specially：
Initial parameter and initialization parameters obtained are substituted into the linearized system model, to calculate the feature of coefficient matrix
Root, left eigenvector, right feature vector.
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| CN106599526B (en) * | 2017-02-17 | 2020-02-11 | 华北电力大学（保定） | Impedance analysis method for sub-synchronous oscillation of thermal power generating unit |
| CN107359626B (en) * | 2017-09-12 | 2020-05-15 | 国电南瑞科技股份有限公司 | Subsynchronous oscillation control method for large-scale new energy base power grid |
| CN109193699B (en) * | 2018-09-28 | 2020-09-04 | 上海交通大学 | Wind turbine converter PI parameter optimization method for subsynchronous oscillation suppression |
| CN109301842B (en) * | 2018-10-23 | 2022-04-22 | 国网吉林省电力有限公司 | Wind power plant subsynchronous oscillation cutting method based on negative damping contribution |
| CN111931351B (en) * | 2020-07-16 | 2022-02-15 | 广东电网有限责任公司电力科学研究院 | Method, system and equipment for calculating external overvoltage of wind turbine generator |
| CN114123232B (en) * | 2021-08-20 | 2024-04-26 | 华北电力大学（保定） | Subsynchronous oscillation suppression method for doubly-fed wind turbine based on linear active disturbance rejection control |
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