CN109217287A - The method for solving of ac and dc systems Transient Voltage Stability security domain - Google Patents
The method for solving of ac and dc systems Transient Voltage Stability security domain Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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- G—PHYSICS
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/26—Arrangements for eliminating or reducing asymmetry in polyphase networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
- Y02E40/50—Arrangements for eliminating or reducing asymmetry in polyphase networks
Abstract
The invention discloses a kind of method for solving of ac and dc systems Transient Voltage Stability security domain, this method is utilized respectively energy function method and strangeness suppression theory analysis ac and dc systems Enhancement of Transient Voltage Stability.Based on ac and dc systems dynamic element transient potential energy variation characteristic, the crucial dynamic element parameter space for describing security domain is had found.Further construct the Transient Voltage Stability security domain boundaries determined jointly by the stable manifold and singular surface of transient voltage unstability related primary unstable equilibrium point.Then it is utilized respectively Q linear approximation method and finds out the security domain boundaries determined by the stable manifold of transient voltage unstability related primary unstable equilibrium point, and find out the security domain boundaries determined by singular surface using the second Taylor series technology.The present invention, to the influence of Transient Voltage Stability, is chosen key parameter and constitutes dynamic security domain space, be conducive to the rapid effective monitoring system of operations staff by multiple dynamic elements in analysis multi-computer system.
Description
Technical field
The present invention relates to Transient Voltage Stability in Electric Power System Journal of Sex Research field, in particular to a kind of ac and dc systems transient state electricity
Press the method for solving for stablizing security domain.
Background technique
It is big power supply to pursue scale and benefit to concentrate exploitation since non-renewable energy is distributed in remote districts more, and in load
The heart is often big city, so that the ac and dc systems of long-distance and large-capacity power transmission become the typical mould of current power industry operation
Formula.Since load increasingly increases, the extension of circuit network needs the long period, so that system running pressure is increasing, when tight
After weight failure occurs, the risk of the numerous safety and stability of systems face.In the middle, ac and dc systems transient voltage destabilization problems are planning
The field that operations staff extremely pays close attention to.
By studying the mechanism of system transient modelling Voltage Instability, the condition of Transient Voltage Stability is calculated, system operation is conducive to
Personnel's reasonable arrangement system operation mode, guarantee system have suitable safety margin as far as possible, cope be difficult to avoid that all kinds of and disturb
Dynamic, failure.Transient voltage unstability may be caused by following practical factors: since generator excited system ability is limited after failure
System, the power consumption of load are difficult to meet as induction-motor load dynamic reactive value of demand increases outside or All other routes network element
Ability of supplying electric power deficiency etc..In multi-computer system, each equipment is different to transient voltage buckling effects, needs detailed analysis.
It is common based on individual system mode growth process time-domain-simulation method or based on stable region to carry out Transient stability analysis
Method.Method advantage based on stable region has quick discrimination stability and obtains the stability margin etc. of system.Based on the temporary of domain
State Voltage Stability Analysis method is a kind of promising method.In order to further operations staff is convenient for control using Transient Stability Regions
System operation, quicklook monitoring system safety margin, academia and industry propose and used dynamic security domain theory and
The relevant technologies.
Excitation system can be improved the transient stability of electric system, have become the common recognition of electric power circle.AC system event
Direct current recovery characteristics after barrier have an impact transient stability, if direct current transmits too fast, the thyristor commutation of active recovery
It is a large amount of idle that type direct current system needs AC system to provide, and has an adverse effect to Transient Voltage Stability, if direct current system
Voltage restores too fast, and by the constraint of hvdc control mode, direct current, which transmits active recovery, to be slowed down, to affect receiving-end system
Active balance and transient rotor angle stability.After failure in the power recovery process of direct current, current limiting low-voltage controlling unit plays pole
Its important role, relevant recovery voltage parameter setting need to be furtherd investigate and optimize.In addition, using motor as the dynamic of representative
The recovery of load after a failure equally causes stress system transient modelling voltage stabilization.Motor after a failure Voltage Drop the case where
The deceleration of lower generation and with voltage fluctuation and the behaviors such as irregular operating, will lead to still online motor and generate than normal
The bigger reactive requirement of situation exacerbates the imbalance of system dynamic reactive-load and the risk of transient voltage unstability.The nothing of motor
Function demand is based on its output power, and when output power variation, the system safety requirements of generation also changes.
It is short that existing data describes the Dynamic Security Region to the constraint of pure AC system transient rotor angle stability, ac and dc systems
The method for solving of phase voltage stabilization Practical Dynamic Security Region, the security domain mentioned is in node injecting power spatial description.But do not see
It refers to the method for solving of the Dynamic Security Region of ac and dc systems transient voltage stability constraint, is suitable for Computation of Dynamic Security Region in the middle
The feature modeling in Transient Voltage Stability domain, system dynamic element analysis that Transient Voltage Stability is had a major impact and its crucial
Parameter selects also to have not been reported as important step.
In conclusion in multi-computer system, suitable method is needed to find from the above-mentioned numerous dynamic elements referred to pair
The key element that system transient modelling voltage stability has an important influence on, and its key parameter is further found out, construct transient voltage
Stablize safe domain space.
Summary of the invention
The purpose of the present invention is to overcome the shortcomings of the existing technology and deficiency, and it is steady to provide a kind of ac and dc systems transient voltage
The method for solving of Dingan County's universe, this method are made by influence of multiple dynamic elements to Transient Voltage Stability in analysis multi-computer system
With selection key parameter constitutes dynamic security domain space, is conducive to the rapid effective monitoring system of operations staff.
The purpose of the present invention is realized by the following technical solution: the solution of ac and dc systems Transient Voltage Stability security domain
Method, comprising steps of
1) ac and dc systems Transient stability analysis model is established；
2) energy function method and strangeness suppression theory analysis ac and dc systems Enhancement of Transient Voltage Stability are utilized respectively；
3) stable manifold and surprise of ac and dc systems transient voltage unstability related primary unstable equilibrium point are constructed respectively
The mathematic(al) representation of antarafacial；
4) it is based on ac and dc systems dynamic element transient potential energy variation characteristic, constructs the crucial dynamic for describing security domain
Element parameter space；
5) security domain boundaries determined by the stable manifold of transient voltage unstability related primary unstable equilibrium point are found out
And the security domain boundaries determined by singular surface, the intersection of the two are Transient Voltage Stability security domain boundaries.
Preferably, in the step 4), the step of constructing the crucial dynamic element parameter space for describing security domain, is:
(4-1) is based on complete mathematical models of power system, constructs corresponding energy function formula, extracts wherein and dynamic
The potential energy component function of each dynamic element is established in the relevant part of force device；
Before period where (4-2) reaches maximum value according to potential energy after each dynamic element failure in half of cycle, potential energy
The ratio of voltage magnitude and potential variation amount, filters out to the event when ratio and potential energy peak value of variable quantity and idle work variable quantity
Hindering lower Enhancement of Transient Voltage Stability influences several relatively large dynamic elements as crucial dynamic element, selects above-mentioned pass respectively
The corresponding control parameter of key dynamic element constructs the crucial dynamic element parameter space for describing security domain.
Preferably, before seeking security domain boundaries, electric system can be described by following differential-algebraic equation group:
0=G (x, y, α) (1)
Wherein, F defines the dynamic of generator and its excitation system, HVDC transmission system (HVDC), induction machine
Characteristic；G is the power flow equation of network；X is system state variables；Y is system algebraic variable；α is adjustable parameter；
Assuming that electric system is by single failure, dynamic process be divided into failure before, in failure, three phases after failure,
It is assumed that failure removal fore-aft adjustable parameter alpha remains unchanged；
Before failure: stable equilibrium point (x of the Operation of Electric Systems in following equation0,y0):
0=G1(x, y, α) t < 0 (2)
In failure: it is operating point (x before failure that the dynamic of system, which can be expressed as following initial value,0,y0) the differential equation:
Wherein t=0 is time of failure, t=tFFor fault clearing time,For lopcus function in failure.
After failure: the dynamic of system can be expressed as system mode when following initial value is failure removalThe differential equation:
So, the security domain determined by the stable manifold of transient voltage unstability related primary unstable equilibrium point is defined as
The set of following adjustable parameter:
In formulaThe original state of system, A (x after expression failure removalsep(α)) indicate failure after meet service condition
Asymptotic Stability equalization point xsepThe stable region of (α)；The local boundary of further security domain can be expressed as follows
Wherein h is the stable manifold of transient voltage unstability related primary unstable equilibrium point.
Preferably, it in the step 5), is found out using Q linear approximation method and is allocated by transient voltage unstability related primary shakiness
Weigh security domain boundaries determined by the stable manifold of point.
Further, described to be found out using Q linear approximation method by transient voltage unstability related primary unstable equilibrium point
Stable manifold determined by security domain boundariesThe step of be:
Wherein, α0To make original state after failure fall in the steady of transient voltage unstability related primary unstable equilibrium point just
Parameter value in constant current shape；C0ForIn α0The functional value at place, C1ForIn α0The gradient at place, Δ α
=α-α0Indicate α in α0The increment at place.Δα:C0+C1Δ α refers to that Δ α meets subsequent equation C0+C1Δ α=0 is constrained.
Preferably, in the step 5), the security domain side determined by singular surface is found out using the second Taylor series technology
Boundary.
Further, the step that the security domain boundaries determined by singular surface are found out using the second Taylor series technology
Suddenly it is:
The singular surface of system are as follows:
S=(x, y) | F (x, y, α)=0, G (x, y, α)=0, det [Gy(x, y, α)]=0 (10)
WhereinPoint in S is strangeness suppression (SIB) point, in parameter
Within the SIB neighborhood of a point that a certain parameter determines in space, it is full for certainly existing the every bit on smooth curved surface a S, S all
The absorbing boundary equation of the SIB point of sufficient equation (10), S indicates are as follows:
ψ (α)=0 (11)
The second Taylor series form of ψ (α) is derived below by boundary condition:
Defined function Φ=[det (Gy)]2, then have
That is the absorbing boundary equation ψ (α) of S=Φ (α).It defines the security domain boundaries determined by singular surface and is expressed as { SIBs },
{ SIBs }=and α | Φ (α)=0 }.
Assuming that αsIt is the parameter value for making system that strangeness suppression occur, it is right according to compound function partial differential computing rule
It carries out secondary Taylor expansion, ignores higher-order expansion item more than two times, then has the approximate description as follows about S:
In formula: M is the number of controllable parameter, αiAnd αjThe ith and jth component of respectively α；
In order to solve the approximate expression of the security domain boundaries determined by singular surface, be given below it is refined in power flow equation can
Than the calculation method of matrix character sensitivity and Method For Calculating Eigenvector Sensitivity:
According to matrix determinant calculation formula, have
Wherein λiFor GyThe ith feature value of (x, y, α).
With αiFor, first derivative of the Φ to parameter are as follows:
Φ is to parameter alphatAnd αrSecond dervative are as follows:
Wherein αtAnd αrThe respectively t of α and r-th of component.
Φ is sought to the single order and second dervative of parameter, needs to calculate sensitivity of the characteristic value about parameter, first calculates
Single order Feature Sensitivity has by taking ith feature value, to the sensitivity of t-th of parameter as an example
In formula: yjFor j-th of component of y,For the corresponding sub-block of Hessian matrix of power flow equation；ωtAnd vtPoint
It Wei not λiLeft and right feature vector after normalization；
Then second order Feature Sensitivity can be obtained by following formula
Single order Feature Sensitivity and second order Feature Sensitivity are substituted into formula (14) respectively and formula (15) obtains function phi to ginseng
Each rank partial derivative of the Φ to parameter is substituted into formula (12), can get the two of function phi by several first-order partial derivatives and second-order partial differential coefficient
Rank Taylor expansion.Enable α=αs+ Δ α, then have
{ SIBs }=and α | Φ (α)=0 }.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1, the present invention mentions accordingly according to energy function method and strangeness suppression theory analysis transient voltage instability Mechanism
The method for solving for having gone out a kind of ac and dc systems Transient Voltage Stability security domain constructs on dynamic element key parameter space
By the Transient Voltage Stability security domain boundaries of the higher-dimension representation of a surface.Transient Voltage Stability security domain proposed by the present invention not only considers
Pass through transient voltage unstability caused by the stable manifold of transient voltage unstability related primary unstable equilibrium point, it is also contemplated that by
The transient voltage unstability caused by strangeness suppression, the relatively perfect building of Transient Voltage Stability security domain, to transient state
Voltage stability theory analysis and ac and dc systems, which expand application, certain directive significance.
2, thus the present invention can analyze multiple dynamic elements in multi-computer system to Transient Voltage Stability influence and
Choose key parameter constitute dynamic security domain space, can help operations staff solve ac and dc systems by transient voltage unstability about
The safety problem of beam, reasonable disposition dynamic element key parameter, the flexible arrangement method of operation effectively monitor operational safety nargin,
Transient voltage is guided to control complex optimum.
Detailed description of the invention
Fig. 1 is the flow chart of the present embodiment method.
Fig. 2 is tri- machine of IEEE, nine node system figure in the present embodiment.
Fig. 3 is dynamic element key parameter (K0-Tm-VL) transient voltage security domain local boundary spatially.
Fig. 4 is the present embodiment K0-VLStable manifold in space by transient voltage unstability related primary unstable equilibrium point is true
Fixed security domain local boundary sectional view, wherein K0Indicate field regulator gain coefficient, VLIndicate that VDCOL controls voltage lower bound
Parameter.
Fig. 5 is K0-VLThe security domain local boundary determined in space by singular surface, wherein C1Indicate real border curve；
C2Indicate second approximation boundary.
Specific embodiment
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art
Every other embodiment obtained without creative efforts, shall fall within the protection scope of the present invention.
Embodiment
Referring to Fig. 1, the method for solving of the present embodiment ac and dc systems Transient Voltage Stability security domain, comprising the following steps:
Step 1: establishing ac and dc systems Transient stability analysis model
Using three machines, nine node system figure shown in Fig. 2 in the present embodiment, building includes generator third-order model, excitation system
First order modeling, induction conductivity third-order model and the HVDC transmission system utility model for calculating dynamic response.
Wherein generator third-order model equation is described as follows:
Excitation system first order modeling equation is described as follows:
Induction conductivity third-order model equation is described as follows:
HVDC transmission system mesolow Current limited Control link (VDCOL) governing equation is described as follows:
In above formula, subscript i represents network bus nodal scheme, in the present embodiment, when i=1,2,3, that is, has accessed generator
Bus, when i=6, that is, accessed induction motor load bus.When i=1,2,3, ωiFor generator speed, δiFor power generation
Machine rotor angle, MiFor generator inertia time constant, PmiFor generator mechanical power, DiFor damped coefficient, E 'qiIt is temporary for q axis
State potential, XdiFor the transient state reactance of generator, X 'diFor the subtranient reactance of generator, T 'doiFor d axis time constant,
EfdiFor excitation potential, PeiFor generator electromagnetic power, K0For field regulator gain coefficient, TviFor excitation con-trol time constant,
kiFor in excitation voltage first-order mathematic model, the relevant linear coefficient of accessed busbar voltage, liMake to generate electricity for access bus i
The control constant that machine excitation is positive；VdRFor rectification side voltage magnitude, VHAnd VLRespectively VDCOL controls voltage limits parameter, VdR0
For bus rectification side reference voltage, KIFor by VH, VL, Idrefmax, IdrefminThe control coefrficient of decision, IdrefFor DC control feedback
Electric current；As i=6, T 'doiFor stator open circuit time constant, MiFor induction conductivity inertia time constant, E 'LiFor built-in potential width
Value, XrFor rotor windings equivalence leakage reactance, XmAnti-, the X for rotor mutual inductancesFor stator winding leakage reactance, X 'iFor transient state reactance, XiIt is same
Walk reactance, δiFor induction conductivity generator rotor angle, siFor induction conductivity slippage, TmiFor induction conductivity machine torque, TmTurn for machinery
Square constant component, TmsFor part relevant to slippage in machine torque, TeiFor electromagnetic torque；
Step 2: being utilized respectively energy function method and strangeness suppression theory analysis ac and dc systems Transient Voltage Stability
Property
In the present embodiment, bus 5 is in the 1s moment and three phase short circuit fault is arranged, and the 1.18s moment removes, PSAT software into
It is interrupted when row time-domain-simulation, under the failure, transient state running track encounters singular surface after failure, leads to subordination principle
(DAE) time-domain-simulation under model can not operation, at this time after fault clearance moment energy value be 0.36, allocated less than leading shakiness
The obtained transition energy of weighing apparatus point, but transient state running track encounters singular surface under the failure, after failure, causes under DAE model
Time-domain-simulation can not operation, since unusual bifurcation and transient voltage unstability are closely related, the present embodiment is also considered as
Transient voltage unstability occurs.
Step 3: constructing the stable manifold of ac and dc systems transient voltage unstability related primary unstable equilibrium point respectively
With the mathematic(al) representation of singular surface.
Step 4: being based on ac and dc systems dynamic element transient potential energy variation characteristic, the pass for describing security domain is constructed
Key dynamic element parameter space.
(1) be based on complete mathematical models of power system, construct corresponding energy function formula, extract wherein with dynamic electric
The potential energy component function of each dynamic element is established in the relevant part of power element, wherein dynamic element includes but is not limited to generate electricity
Machine, HVDC transmission system, induction conductivity.
(2) during failure, electric system injects big energy to power grid, and generator speed increase causes kinetic energy to increase, therefore
After barrier is removed, total terpene lactones, kinetic energy is gradually converted into the potential energy of each element and transmission line of electricity along electric power networks.With dynamic
The change in oscillation of energy, the potential energy of each dynamic element are gradually increased and also along with certain oscillations.Born potential energy amplification is most
Local energy overshoot by bigger energy impact, will be also more readily formed accordingly in big dynamic element, and then causes herein
It more easily collapses, therefore after utilization failure, first half of potential energy oscillating curve where each dynamic element potential energy maximum value
The potential energy increment of period wave carrys out simple analysis power grid weak section.
(3) before the period where reaching maximum value according to potential energy after each dynamic element failure in half of cycle, potential energy becomes
The ratio of voltage magnitude and potential variation amount, filters out to the failure when ratio and potential energy peak value of change amount and idle work variable quantity
Lower Enhancement of Transient Voltage Stability influences several relatively large dynamic elements, and selects corresponding control parameter as this hair respectively
The parameter space of bright security domain.
Based on Fig. 2 system, and be in the 1s moment in bus 5 and three phase short circuit fault be set, and respectively at 1.05s, 1.1s,
1.14s, 1.178s remove failure.
It is inscribed when comparing same fault clearance, potential energy oscillation amplification is apparent that after failure: direct current system, No. 2 hairs
Motor is maximum by the oscillation amplitude of minimum to maximum value in this period for reaching potential energy maximum value, is secondly induced electricity
Engine load is finally No. 1 generator and No. 3 generators.
Where potential energy reaches maximum value after each dynamic element failure in preceding half of cycle in period, the potential energy of direct current system
The ratio of variable quantity and idle work variable quantity is much higher than other equipment, followed by No. 2 generators and induction motor load, and away from event
No. 3 farthest generators of barrier point electrical distance are then minimum.Illustrate under the recovery characteristics effect of each electrical equipment, direct current receiving end
The variation of commutation system dynamic reactive causes when being impacted by ceiling capacity, direct current system potential energy oscillation amplitude and amplification speed
It is easier to become larger, i.e., is easier in this pendulum so that local energy is excessive, generating system stability beyond ability to bear at this
It destroys, and then acceleration system transient voltage collapses.Meanwhile the gesture of No. 2 generators, high-voltage direct current and induction motor load
Can peak value when voltage magnitude and potential variation amount ratio well below No. 1 generator and No. 3 generators, therefore No. 2 generators,
Direct current system, induction motor load form the weak section of the electric system, are also the crucial dynamic member in the present embodiment
Part.In conclusion being based on transient voltage instability Mechanism, the field regulator gain coefficient K of No. 2 generators is chosen0, high voltage direct current
Transmission system VDCOL controls voltage lower bound parameter VLWith induction conductivity machine torque constant component TmBuilding is for describing safety
The crucial dynamic element parameter space in domain.
Step 5: solving ac and dc systems Transient Voltage Stability security domain, that is, solve Transient Voltage Stability security domain boundaries.
It is found out using Q linear approximation method by the stabilization of transient voltage unstability related primary unstable equilibrium point in the present embodiment
Security domain boundaries determined by manifoldThe security domain side determined by singular surface is found out with using the second Taylor series technology
Boundary { SIBs }, but it is not limited to this kind of method.Then Transient Voltage Stability security domain boundaries are
Original state is fallen in except stable region after failure or system occurs strangeness suppression and all may cause transient voltage
Unstability, in order to construct comprehensive Transient Voltage Stability security domain boundaries, present invention needs are found out by transient voltage unstability correlation master
Security domain boundaries and the security domain boundaries determined by singular surface determined by the stable manifold of unstable equilibrium point are led, then complete
Whole Transient Voltage Stability security domain is made of above-mentioned two parts boundary.
Electric system can be described by following differential-algebraic equation group:
0=G (x, y, α) (1)
Wherein, F defines the dynamic of generator and its excitation system, HVDC transmission system (HVDC), induction machine etc.
Step response；G is the power flow equation of network；X is system state variables；Y is system algebraic variable；α is adjustable parameter.
(5.1) the security domain side determined by the stable manifold of transient voltage unstability related primary unstable equilibrium point is sought
Boundary
Assuming that electric system is by single failure, dynamic process be divided into failure before, in failure, three phases after failure
(it is assumed that failure removal fore-aft adjustable parameter alpha remains unchanged).
Before failure: stable equilibrium point (x of the Operation of Electric Systems in following equation0, y0):
0=G1(x, y, α) t < 0 (2)
In failure: it is operating point (x before failure that the dynamic of system, which can be expressed as following initial value,0, y0) the differential equation:
Wherein t=0 is time of failure, t=tFFor fault clearing time, φ is lopcus function in failure.
After failure: the dynamic of system can be expressed as system mode when following initial value is failure removalThe differential equation:
So, the security domain determined by the stable manifold of transient voltage unstability related primary unstable equilibrium point is defined as
The set of following adjustable parameter:
In formulaThe original state of system, A (x after expression failure removalsep(α)) indicate failure after meet service condition
Asymptotic Stability equalization point xsepThe stable region of (α)；The local boundary of further security domain can be expressed as follows
Wherein h is the stable manifold of transient voltage unstability related primary unstable equilibrium point.
The second approximation and sensitivity of stable manifold based on transient voltage unstability related primary unstable equilibrium point calculate
The method of Transient Voltage Stability security domain local boundary has quasi- quadratic approximation, Q linear approximation method etc..COMPREHENSIVE CALCULATING precision and meter
Effect of both speed is calculated, the present invention takes Q linear approximation method to seek being allocated by transient voltage unstability related primary shakiness
Weigh security domain boundaries determined by the stable manifold of point.
The local Q linear approximation of Transient Voltage Stability security domain boundaries
Wherein, α0To make original state after failure fall in the steady of transient voltage unstability related primary unstable equilibrium point just
Parameter value in constant current shape；C0ForIn α0The functional value at place, C1ForIn α0The gradient at place, Δ α
=α-α0, indicate α in α0The increment at place.
(5.2) security domain boundaries determined by singular surface are sought
Strangeness suppression (the Singularity Induced proposed with venkatasubramanian
Bifurcation, SIB) mathematical definition for, the singular surface of system is
S=(x, y) | F (x, y, α)=0, G (x, y, α)=0, det [Gy(x, y, α)]=0 (10)
WhereinPoint in S is strangeness suppression point, when system motion arrives
Strangeness suppression occurs at the point.At strangeness suppression point, differential-algebraic equation failure.In strangeness suppression
Near point, the minor change of state variable x can result in algebraic variable y and great variety occur, this meets transient voltage collapse
Feature.The Transient Voltage Stability security domain that the present invention constructs contains the constraint that strangeness suppression occurs for system, it is believed that transient state
A part security domain boundaries determined by singular surface of voltage stabilization security domain boundaries are constituted.
Within the SIB neighborhood of a point that a certain parameter determines in parameter space, certainly exist on smooth curved surface a S, S
Every bit be all the SIB point for meeting equation group (10), the absorbing boundary equation of S can indicate are as follows:
ψ (α)=0 (11)
The second Taylor series form of ψ (α) is derived below by boundary condition.
Defined function Φ=[det (Gy)]2, then have
That is the absorbing boundary equation ψ (α) of S=Φ (α)；It defines the security domain boundaries determined by singular surface and is expressed as { SIBs },
{ SIBs }=and α | Φ (α)=0 }；
Assuming that αsIt is the parameter value for making system that strangeness suppression occur, it is right according to compound function partial differential computing rule
It carries out secondary Taylor expansion, ignores higher-order expansion item more than two times, then has the approximate description as follows about S:
In formula: M is the number of controllable parameter, αiAnd αjThe ith and jth component of respectively α；
In order to solve the approximate expression of the security domain boundaries determined by singular surface, be given below it is refined in power flow equation can
Than the calculation method of matrix exgenvalue sensitivity and Method For Calculating Eigenvector Sensitivity:
According to matrix determinant calculation formula, have
Wherein λiFor GyThe ith feature value of (x, y, α).
With αiFor, first derivative of the Φ to parameter are as follows:
Second dervative of the Φ to parameter are as follows:
Wherein αtAnd αrThe respectively t of α and r-th of component.
Φ is sought to the single order and second dervative of parameter, needs to calculate sensitivity of the characteristic value about parameter, first calculates
Single order Eigenvalue Sensitivity has by taking ith feature value, to the sensitivity of t-th of parameter as an example
In formula: yjFor j-th of component of y,For the corresponding sub-block of Hessian matrix of power flow equation；ωtAnd vtPoint
It Wei not λiLeft and right feature vector after normalization；
Then second order Eigenvalue Sensitivity can be obtained by following formula
Single order Eigenvalue Sensitivity and second order Eigenvalue Sensitivity are substituted into formula (14) respectively and formula (15) obtains function phi
To the first-order partial derivative and second-order partial differential coefficient of parameter, each rank partial derivative of the Φ to parameter is substituted into formula (12), can get function phi
The second Taylor series.Enable α=αs+ Δ α, then have
{ SIBs }=and α | Φ (α)=0 }.
Specific to example shown in Fig. 2, be in the 1s moment in bus 5 and three phase short circuit fault be set, remove in 1.178s therefore
Barrier.
(1) it is found out using Q linear approximation method by the stable manifold institute of transient voltage unstability related primary unstable equilibrium point
Determining security domain boundaries are shown in Fig. 3, Fig. 4, calculated result are as follows:
hQL={ α0+ Δ α: C0+C1Δ α=0 }
Wherein,
C0+C1Δ α=0.139+3.6689 × 10-4ΔK0+0.2788ΔVL-2.9187ΔTm=0
C0=0.139
C1=[3.6689 × 10-4 0.2788 -2.9187]
(2) approximation of the security domain local boundary determined by singular surface is found out using the second Taylor series technology, in (K0-
VL) space expression formula be (it is assumed that TmIt is fixed) are as follows:
Φ=24.0256V2 L-31.2209VL-K0+ 9.5793=0
Referring to Fig. 5, C1Indicate real border curve；C2Indicate second approximation boundary.Compared with real border, side of the present invention
Method curve error is smaller, it was demonstrated that the validity of this method.
To sum up (1) and (2), in (K0-VL) in space, by hQLAnd Φ, available Transient Voltage Stability security domain side
Boundary, compared with existing method, the resulting boundary of this patent is more complete.
The above embodiment is a preferred embodiment of the present invention, but embodiments of the present invention are not by above-described embodiment
Limitation, other any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present invention,
It should be equivalent substitute mode, be included within the scope of the present invention.
Claims (7)
1. the method for solving of ac and dc systems Transient Voltage Stability security domain, which is characterized in that comprising steps of
1) ac and dc systems Transient stability analysis model is established；
2) energy function method and strangeness suppression theory analysis ac and dc systems Enhancement of Transient Voltage Stability are utilized respectively；
3) stable manifold and singular surface of ac and dc systems transient voltage unstability related primary unstable equilibrium point are constructed respectively
Mathematic(al) representation；
4) it is based on ac and dc systems dynamic element transient potential energy variation characteristic, constructs the crucial dynamic element for describing security domain
Parameter space；
5) find out the security domain boundaries determined by the stable manifold of transient voltage unstability related primary unstable equilibrium point and
The security domain boundaries determined by singular surface, the intersection of the two are Transient Voltage Stability security domain boundaries.
2. the method for solving of ac and dc systems Transient Voltage Stability security domain according to claim 1, which is characterized in that institute
The step of stating in step 4), constructing the crucial dynamic element parameter space for describing security domain is:
(4-1) is based on complete mathematical models of power system, constructs corresponding energy function formula, extract wherein with dynamic power
The potential energy component function of each dynamic element is established in the relevant part of element；
Before period where (4-2) reaches maximum value according to potential energy after each dynamic element failure in half of cycle, potential variation
The ratio of voltage magnitude and potential variation amount, filters out under the failure when amount and the ratio and potential energy peak value of idle work variable quantity
Enhancement of Transient Voltage Stability influences several relatively large dynamic elements as crucial dynamic element, selects respectively above-mentioned crucial dynamic
The corresponding control parameter of state element constructs the crucial dynamic element parameter space for describing security domain.
3. the method for solving of ac and dc systems Transient Voltage Stability security domain according to claim 1, which is characterized in that ask
Before taking security domain boundaries, electric system is described by following differential-algebraic equation group:
0=G (x, y, α) (1)
Wherein, F defines the dynamic characteristic of generator and its excitation system, HVDC transmission system, induction machine；G is net
The power flow equation of network；X is system state variables；Y is system algebraic variable；α is adjustable parameter；
Assuming that electric system is by single failure, dynamic process be divided into failure before, in failure, three phases after failure, it is assumed that
Failure removal fore-aft adjustable parameter alpha remains unchanged；
Before failure: stable equilibrium point (x of the Operation of Electric Systems in following equation0, y0):
0=G1(x, y, α) t < 0 (2)
In failure: it is operating point (x before failure that the dynamic of system, which can be expressed as following initial value,0, y0) the differential equation:
Wherein t=0 is time of failure, t=tFFor fault clearing time,For lopcus function in failure；
After failure: the dynamic of system can be expressed as system mode when following initial value is failure removalThe differential equation:
So, the security domain determined by the stable manifold of transient voltage unstability related primary unstable equilibrium point is defined as
The set of adjustable parameter:
In formulaThe original state of system, A (x after expression failure removalsep(α)) indicate failure after meet service condition gradually
Nearly stable equilibrium point xsepThe stable region of (α)；The local boundary of further security domain can be expressed as follows
Wherein h is the stable manifold of transient voltage unstability related primary unstable equilibrium point.
4. the method for solving of ac and dc systems Transient Voltage Stability security domain according to claim 3, which is characterized in that institute
It states in step 5), is found out using Q linear approximation method by the stable manifold institute of transient voltage unstability related primary unstable equilibrium point
Determining security domain boundaries.
5. the method for solving of ac and dc systems Transient Voltage Stability security domain according to claim 4, which is characterized in that institute
It states and finds out the safety determined by the stable manifold of transient voltage unstability related primary unstable equilibrium point using Q linear approximation method
Domain boundaryThe step of be:
Wherein, α0To make original state after failure fall in the stationary flow of transient voltage unstability related primary unstable equilibrium point just
Parameter value in shape；C0ForIn α0The functional value at place, C1ForIn α0The gradient at place, Δ α=α-
α0, indicate α in α0The increment at place.
6. the method for solving of ac and dc systems Transient Voltage Stability security domain according to claim 3, which is characterized in that institute
It states in step 5), finds out the security domain boundaries determined by singular surface using the second Taylor series technology.
7. the method for solving of ac and dc systems Transient Voltage Stability security domain according to claim 6, which is characterized in that institute
Stating the step of finding out the security domain boundaries determined by singular surface using the second Taylor series technology is:
The singular surface of system are as follows:
S=(x, y) | F (x, y, α)=0, G (x, y, α)=0, det [Gy(x, y, α)]=0 (10)
WhereinIt is SIB point, that is, strangeness suppression point in S, in parameter space
Within the SIB neighborhood of a point that a certain parameter determines, the every bit certainly existed on smooth curved surface a S, S is all to meet equation
(10) absorbing boundary equation of SIB point, S indicates are as follows:
ψ (α)=0 (11)
The second Taylor series form of ψ (α) is derived below by boundary condition:
Defined function Φ=[det (Gy)]2, then have
That is the absorbing boundary equation ψ (α) of S=Φ (α)；It defines the security domain boundaries determined by singular surface and is expressed as { SIBs },
{ SIBs }=and α | Φ (α)=0 }；
Assuming that αsIt is that the parameter value for making system that strangeness suppression occur carries out it according to compound function partial differential computing rule
Secondary Taylor expansion, ignores higher-order expansion item more than two times, then has the approximate description as follows about S:
In formula: M is the number of controllable parameter, αiAnd αjThe ith and jth component of respectively α；
In order to solve the approximate expression of the security domain boundaries determined by singular surface, Jacobean matrix in power flow equation is given below
The calculation method of battle array Eigenvalue Sensitivity and Method For Calculating Eigenvector Sensitivity:
According to matrix determinant calculation formula, have
Wherein λiFor GyThe ith feature value of (x, y, α)；
With αiFor, Φ is to parameter alphaiFirst derivative are as follows:
Φ is to parameter alphat、αrSecond dervative are as follows:
Wherein αtAnd αrThe respectively t of α and r-th of component；
Φ is sought to the single order and second dervative of parameter, needs to calculate sensitivity of the characteristic value about parameter, first calculates single order
Eigenvalue Sensitivity has by taking ith feature value, to the sensitivity of t-th of parameter as an example
In formula: yjFor j-th of component of y,For the corresponding sub-block of Hessian matrix of power flow equation；ωtAnd vtRespectively λi
Left and right feature vector after normalization；
Then second order Eigenvalue Sensitivity can be obtained by following formula:
Single order Eigenvalue Sensitivity and second order Eigenvalue Sensitivity are substituted into formula (14) respectively and formula (15) obtains function phi to ginseng
Each rank partial derivative of the Φ to parameter is substituted into formula (12), can get the two of function phi by several first-order partial derivatives and second-order partial differential coefficient
Rank Taylor expansion, enables α=αs+ Δ α, then have
{ SIBs }=and α | Φ (α)=0 }.
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| CN113555891A (en) * | 2021-05-28 | 2021-10-26 | 华南理工大学 | Method for estimating stability region of alternating current-direct current system containing uncertain parameters based on sum of squares |
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