CN109768550A - A kind of Probabilistic transient stability appraisal procedure considering wind-powered electricity generation correlation - Google Patents
A kind of Probabilistic transient stability appraisal procedure considering wind-powered electricity generation correlation Download PDFInfo
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Abstract
The present invention proposes a kind of simple and effective Probabilistic transient stability evaluation method for the electric system for considering wind power plant uncertainty and correlation in transient stability evaluation in power system field；Using the Dynamic Security Region method of extension, under given fault condition, transient stability evidence is indicated with the linear combination of node injection vector；And three the point estimation methods and the Cornish-Fisher method of development are improved, to handle the correlation between uncertain and different wind power plants；A large amount of simulation calculation has been carried out to improved New England's system, the results showed that, the method for the present invention computational efficiency is apparently higher than the method based on Monte Carlo, and precision is very high.
Description
Technical field
The present invention relates to transient stability evaluation in power system fields, and in particular in the case of considering wind-powered electricity generation correlation, probability
Transient stability appraisal procedure.
Background technique
In recent years, it is gradually penetrated into electric system by the renewable energy of representative of wind-powered electricity generation.It is different from conventional electric generators,
Blower power output is related with wind speed, is affected by weather, and blower node injecting power is caused to have uncertain and correlation.
As extensive blower is connected to the grid, influence of the wind-powered electricity generation to power system transient stability is more significant.From Operation of Electric Systems
For the angle of planning, consider that the Transient Stability Evaluation method of wind-powered electricity generation uncertainty and correlation is more and more important.
Traditional Transient Stability Analysis mostly uses greatly deterministic type method, usually in the component parameters of system, operation item
Part and conflicting mode give in situation, and the conclusion of power system transient stability or unstability is calculated by time-domain-simulation.But this method without
Method fully considers the various uncertain factors including wind-powered electricity generation injection including uncertain, and it is possible to can ignore individual extreme
Situation, so that assessment result is often overly conservative.In response to this, the angle research transient state for having scholar from probability analysis is steady
It is qualitative, propose probabilistic type Transient Stability Analysis method.This method according to influence power system transient stability stochastic variable system
Meter feature determines the probability level of power system transient stability, can fully consider various uncertain factors, so that its analysis knot
Fruit more gears to actual circumstances, and more acurrate, more meaningful information is provided for systems organization and operations staff, to more be able to satisfy electricity
The demand of power enterprise.Therefore, probabilistic type method replenishing in transient stability analysis of power system as deterministic type method
It has been more and more widely used.Probabilistic type method is broadly divided into Monte Carlo method and analytic method at present.
1. Monte Carlo method: largely being taken out with Monte Carlo (Monte-Carlo, MC) emulation mode to uncertain variable
Sample carries out time-domain-simulation for each sampled point and judges its transient stability, according to law of large numbers acquisition probability index to get
To probabilistic transient stability (Transient Stability Probability, TSP).This method can be with flexible design and various
Uncertain factor has very high applicability for complex scene, but its Evaluation accuracy is closely related with number realization,
Think accurately estimation of transient stability, generally requires the calculating time grown very much, therefore this method is used usually as reference method
In the accuracy for examining other methods.Although its computational efficiency can be improved, but still not be suitable for the online of large scale system
Using.
2. analytic method: establishing the analytic expression of power system transient stability probabilistic type index under given failure, and then it is steady to solve transient state
Determine probability.Such as: thering is document to consider the uncertainty of wind-powered electricity generation, derive transient stability margin (Transient Stability
Margin, TSM) expression formula, then using Kalman filtering and Unscented transform estimation TSM distribution.Separately there is document by normalizing
Change transient energy function and dichotomy combine calculate the fault critical mute time (Critical Clearing Time,
CCT), the Transient Instability probability of each given failure is then obtained by the expression formula established between probability of malfunction index and CCT.
But there is no the correlation for considering wind-powered electricity generation output, the assessment energy of this meeting attenuation systems probabilistic transient stability result for these documents
Power.For this purpose, representative sampling policy is proposed in assessment system transient stability, such as point estimations and scene generation side
Method, to handle the correlation between wind-powered electricity generation.Due to the uncertainty of various variables and the randomness of wind power output, transient stability
The derivation of probability resolution formula is complex.In addition, generalling use time-consuming MC emulation obtains probability level, this is but also the party
Method is difficult to realize application on site.
In recent years, security domain (Security Region, SR) method is rapidly developed, the reality with hyperplane form
It is the simplification of quantitative relationship in analytic method with Dynamic Security Region (Practical Dynami Security Region, PDSR)
Provide effective way.Based in the range of engineering is concerned about, the side of the Dynamic Security Region of power system transient stability is described
Boundary can use several hyperplane expression formula approximate representations, can establish the analytical expression of probabilistic transient stability index, will be temporary
The state probability of stability is expressed as the linear combination of node injection vector, so that the speed of analytical Calculation be greatly improved.This method for
The electric system of access double-fed induction blower is equally applicable.It has been obtained in probabilistic type Transient Stability Analysis at present just
Step application, and show its rapidity and accuracy.Such as: thering is document to be based on security domain and propose a discrete and continuous phase knot
The Transient Instability probabilistic model of conjunction, and the Gram-Charlier Series Method based on cumulant is used to calculate truncation normal state
The joint probability distribution of distribution variables, example show that this method has very high computational efficiency.Separately there is document only to consider wind
The uncertainty of electricity studies the probabilistic transient stability of the electric system containing wind-powered electricity generation, establishes based on the temporary of Dynamic Security Region
State probability of stability analytic expression, and combined using cumulant with Gram-Charlier, Cornish-Fisher number of degrees
Method quantizating index, to realize quick, the accurate solution of probabilistic transient stability.
Summary of the invention
In order to overcome the above-mentioned deficiencies of the prior art, the present invention provides establish to consider wind based on effective security domain method
The analytics evaluation method of the Probabilistic transient stability of electric correlation not only guarantees computational accuracy, but also improves calculating speed.
The technical scheme adopted by the invention is that:
Step 1 establishes the probability Distribution Model of each uncertain node injecting power；Generator and load are normal state point
Cloth, blower power output is Weibull distribution, respectively obtains its distribution parameter；
Step 2 obtains the Practical Dynamic Security Region boundary of the electric system containing wind-powered electricity generation；
Step 3 obtains the analytical expression of probabilistic transient stability based on the Practical Dynamic Security Region containing wind-powered electricity generation；
Step 4 calculates 2n+1 estimation point sampling location and weight in independent standard normal space, and building 2n+1 is a
Vector of samples and weight matrix；
Step 5 is calculating the transformed standard of Nataf just according to the correlation matrix ρ of input variable in real space
The linearly dependent coefficient matrix ρ of state distribution variable0；
Step 6 utilizes cholesky decomposition computation ρ0Lower triangular matrix B；
2n+1 vector of samples in the positive state space of step 4 Plays is transformed into original by Nataf inverse transformation by step 7
In beginning space；
Jth (j=1,2 ..., 2n+1) is successively organized and is obtained in the expression formula of former evaluation vector substitution output variable S by step 8
Obtain each rank moment of the orign of S；
Step 9 introduces Cornish-Fisher series expansion and obtains the cumulative distribution function of S, to obtain S less than 0
Probability, as probabilistic transient stability value TSP.
Each rank moment of the orign process of S is obtained in the step 8:
Step 2.1, initial value j=0 is set up；
Step 2.2, j=j+1 is enabled；
Step 2.3, j-th of vector of samples in luv space is substituted into the expression formula of following S variable；
Step 2.4, judge j=2n+1, if meeting condition, export each rank moment of the orign of S in following formula；Otherwise it returns
Step 2.2；
Beneficial effect
Compared with prior art, the beneficial effects of the present invention are: in the case where considering wind-powered electricity generation correlation, efficiently assessment is electric
Force system Probabilistic transient stability.
Detailed description of the invention
Fig. 1 is a kind of flow chart of the Probabilistic transient stability appraisal procedure of consideration wind-powered electricity generation correlation of the invention.
Fig. 2 is method of the invention when related coefficient is 0 and the comparison of monte carlo method solving result.
Fig. 3 is method of the invention when related coefficient is 0.5 and the comparison of monte carlo method solving result.
Fig. 4 is method of the invention when related coefficient is 0.8 and the comparison of monte carlo method solving result.
Specific embodiment
Below with reference to examples of implementation and attached drawing to a kind of Probabilistic transient state of consideration wind-powered electricity generation correlation of the invention
Stability assessment method is described in detail.
A kind of Probabilistic transient stability appraisal procedure of consideration wind-powered electricity generation correlation of the invention, essence are to solve for based on peace
The analytical expression of the probabilistic transient stability of universe proposes so the present invention is directed to the expression formula and improves three point estimations.
As shown in Figure 1, a kind of Probabilistic transient stability appraisal procedure of consideration wind-powered electricity generation correlation of the invention, including it is as follows
Step:
Step 1: establishing the probabilistic model of node injecting power
In electric system, each node injection type is different, to cause each node injecting power distribution difference.This
The electric system that studied system is the blower containing double-fed induction is invented, therefore, node injects there are three types of types, including tradition hair
Motor, load and double-fed induction blower.
Wherein, conventional electric generators and the active power output of load are normal distribution and mutually indepedent, i.e.,Its
In, it, for generator, is generator rating power that μ, which is mean value, for load, from short-term load forecasting, σiFor
Standard deviation is the 5% of its mean value.
The power output of wind power plant depend on wind speed, according to a large amount of actual measurements to data it is found that wind speed meets weber
(Weibull) it is distributed, probability density function is such as shown in (1).
F (v)=(k/c) (v/c)k-1·exp[-(v/c)k] (1)
In formula, k is the form parameter of Weibull distribution, and c is the scale parameter of Weibull distribution.
K, c are obtained by following formula:
K=(σ/μ)-1.086 (2)
C=μ/Γ (1+1/k) (3)
In formula, μ is mean value；σ is standard deviation；Γ is Gamma function.
Functional relation between double-fed induction blower active power of output and wind speed is such as shown in (4):
In formula, PwIt is the active power of blower output；vci, voAnd vrIt is incision, specified and cut-out wind speed respectively；PrFor wind
The rated power of machine.
The probability density function of double-fed induction blower output power can be obtained with formula (1) and formula (4):
f(Pw)=(k'/c') ((Pw-γ')/c')k-1·exp(-((Pw-γ')/c')k)) (5)
C', k' and γ ' it is shown below:
K'=k/3 (7)
In practice, one group of double-fed induction blower is considered as an equivalent blower.The mean value of Power Output for Wind Power Field is pre-
Measured value, standard deviation are the 20% of mean value.
Step 2: obtaining the Practical Dynamic Security Region boundary of the electric system containing wind-powered electricity generation
In the electric system containing wind-powered electricity generation, for a certain particular incident, the structure of system experienced 3 stages, i.e. accident
Before, in accident and after accident, corresponding state equation is such as shown in (9).
In formula, x is state variable；τ is trouble duration；Before i, F, j respectively represent failure, in failure and after failure；f
For system state equation.
DSR is defined on the node power Injection Space before accident, can be expressed as
Ωd(i, j, F)=and y | xd(y)∈A(y)} (10)
In formula, y is the power injection vector of system node；xd(y) be accident remove when etching system state；A (y) be by
Inject the stable region of stable equilibrium point in the post-fault system state space that y is determined.
It is found by a large amount of simulation studies and initial theory analysis, in electric system, in the range of engineering is concerned about, dynamic
It the boundary of security domain (DSR) can be with one or a few hyperplane union approximate description:
In formula, n is system node number；αiAnd βiThe hyperplane equation constant coefficient acquired for node i；PiAnd QiIt is to guarantee system
Critical active and idle injection variable before the accident of transient stability of uniting on system Injection Space.
For high-pressure system, idle injection can be had little effect busbar voltage with in-situ balancing, active injection.Therefore
It can only consider the DSR in active power Injection Space, this is consistent with actual conditions.Therefore, Dynamic Security Region can indicate
Are as follows:
In the case where network topology structure does not change, for set failure, the DSR of injecting power spatially is only
One, not changing with the variation of operating point (injecting), this becomes the transient stability for assessing set failure simply,
The each node active power injection of a system is only needed to substitute into formula (12), if its value, less than 1, active power is infused in dynamic
In security domain boundaries, power system transient stability, conversely, system transient modelling unstability.This obtains the calculating speed of Transient Stability Evaluation
Very big promotion can simplify the quantitative relationship between probabilistic transient stability and node injection based on this, and foundation is injected with node
For the linear representation of the probabilistic transient stability of variable.
Step 3: establishing the analytical expression of the Transient Stability Probability of Power System containing wind-powered electricity generation
Description based on formula (12) to the power system practical Dynamic Security Region boundary of the blower containing double-fed induction, for one
A given failure, system keep the expression formula of the probability of transient stability as follows:
In formula,G (S) is the cumulative distribution function of S；αiOften it is for the hyperplane equation at node i
Number；PiFor the active injection of i-th of node.
As available from the above equation, the solution key of TSP is to obtain G (S), closely related with each node injecting power.Consider wind
The uncertainty and correlation of electricity, the then P at assembling nodeiFor Non-Gaussian Distribution and correlation, therefore solve based on containing wind
The key of the TSP of electro dynamic security domain is to handle the uncertain and correlation of blower node injecting power and solves the tired of S
Product distribution function G (S), to obtain probabilistic transient stability.
Step 4: calculating 2n+1 independent standard normal Evaluation on distribution vector and its respective weights
For the stochastic variable x in each independent standard normal spacei=N (0,1) (i=1,2 ..., n), other changes
In the case where measuring mean value 0, xiThere are three sampled value xi,k(k=1,2,3), the calculating formula of sampled value are as follows:
In formula, i=1,2 ..., n,WithRespectively xiStandard sample value, mean value and variance.
Standard sample valueIt can be obtained by following formula:
In formula,WithRespectively variable xiThe degree of bias and peak value, due to variable xiFor normal distribution, thenWithPoint
It Wei 0 and 3.
Each sampled value xi,kA corresponding weight coefficientAre as follows:
For each sampled value xi,k, it is required to certainty of progress in the case where its dependent variable remains unchanged and comments
Valence needs to carry out from the above 3n evaluation altogether, and evaluation all corresponds to its corresponding weight every time, but as k=3,There is n times evaluation when all stochastic variables take mean value, therefore need to only carry out 2n+1 evaluation,
The weight of the 2n+1 times evaluation is the sum of corresponding weight when all variables take mean value, i.e., total weight number also becomes 2n+ therewith
1。
Wherein each evaluation vector are as follows:
Weight corresponding to each evaluation vector is
Step 5: converting the phase relation that real space correlation matrix is converted to standardized normal distribution using Nataf
Matrix number
Enable Pi(i=1,2 ..., n) indicates that n node injects active power in original correlated variables space, enables zi(i=1,
2 ..., n) indicate n standardized normal distribution stochastic variable in the positive state space of relevant criterion, it is assumed that the linearly dependent coefficient of z and P
Matrix is respectively ρ0And ρ, wherein ρ is it is known that ρ0It is as follows with ρ relational expression:
In formula, μiAnd μjIt is P respectivelyiAnd PjAverage value；σiAnd σjIt is P respectivelyiAnd PjStandard deviation；Φ2(zi,zj,
ρoij) it is ziAnd zjJoint Distribution.To simplify the calculation, it is known that ρ can obtain the correlation matrix of z according to semiempirical formula
ρ0。
Step 6: decomposing ρ using Cholesky0Calculate lower triangular matrix B
ρ0For positive definite symmetric matrices, lower triangular matrix B can be decomposed by Cholesky:
ρ0=BBT (19)
Step 7: obtaining 2n+1 luv space vector of samples using Nataf inverse transformation
By formula (20) by 2n+1 evaluation vector Xi,kIt is converted into evaluation vector Zi,k:
Z=BX (20)
The element such as following formula of each evaluation vector in luv space:
Pi=F-1(Φ(zi)) (21)
In formula, F-1() is the inverse cumulative distribution function of respective nodes active power injection.To by 2n+1 evaluate to
Measure Zi,kIt is transformed into luv space P1,1,P1,2,…,Pn,1,Pn,2,P2n+1。
From Xi,kIt is converted into evaluation vector Pi,kProcess be Nataf inverse transformation.Weight coefficient matrix is not with the change in space
Change and change, still remains unchanged.
Step 8: jth (j=1,2 ..., 2n+1) group evaluation vector successively to be substituted into the origin for acquiring S in the expression formula of S
Square
The expression formula of known S is as follows:
In formula, H is function, PiIndicate the active power injection of N number of node in luv space.
Jth (j=1,2 ..., 2n+1) group evaluation vector is successively substituted into formula (22), 2n+1 evaluation knot can be obtained
Fruit, respectively C1,1,C1,2..., Cn,1,Cn,2,C2n+1, respective weights areThen SlL rank it is former
Point moments estimation value are as follows:
Step 9: obtaining the cumulative distribution function of S based on Cornish-Fisher series expansion, and calculate TSP
The solution throughway of Cornish-Fisher series expansion is the α quantile of unknown variable cumulative distribution function by standard
The α quantile of normal distribution cumulative distribution function is sought, and obtains the cumulative distribution function of unknown variable based on this.If becoming wait ask
The quantile for measuring S is y (α), then can indicate are as follows:
In formula, ξ (α)=Φ-1(α)；gvFor normalized each rank cumulant, can be obtained by formula (25) and (26).
First three rank cumulant of S are as follows:
In formula, E (Sl) be S l rank moment of the orign.
Its normalized each rank cumulant gvAre as follows:
According to formula y (α)=F-1(α), can acquire the cumulative distribution function of stochastic variable S, so that it is general less than 0 to obtain S
Rate value namely probabilistic transient stability value TSP.
The present invention is considered into the result and Monte Carlo that the Probabilistic transient stability appraisal procedure of wind-powered electricity generation correlation is solved
Method acquired results are compared.
The simulation analysis of probabilistic transient stability is carried out by taking 39 node system of IEEE10 machine as an example, which shares 46 transmissions of electricity
Route.The accident set of consideration is the n-1 accident of three phase short circuit fault, that is, considers that disconnection fault occurs respectively for 34 different routes
The case where, faulty line is shown in Table 1, and the fault clearance time is 0.1s.
Example considers that two wind power plants access power grid.33 nodes in system, 34 node originals are respectively 632MW and 508MW
The generator of capacity is substituted with two double-fed induction blowers identical with its capacity respectively now.The incision of blower is cut out and volume
Determine wind speed and is set to 4m/s, 23m/s, 15m/s.The mean value of Power Output for Wind Power Field is predicted value, and 20% as its output
The standard deviation of power.For the mean value of load from short-term load forecasting, standard deviation is set as the 5% of its mean value.Day is negative
Lotus curve, day wind-powered electricity generation power curve and security domain boundaries parameter obtained from document.
1 faulty line of table
Probabilistic transient stability in the case of three kinds of research:
The correlation of example 1:33 node and 34 node wind power plants is 0；
The correlation of example 2:33 node and 34 node wind power plants is 0.5；
The correlation of example 3:33 node and 34 node wind power plants is 0.8；
T=3,33 nodes and 34 node wind power plant weber parameter k are that 5.742, c is respectively 313.26,251.80, γ difference
It is -0.1222, -0.0982.In the case of three kinds, the method and context of methods of the Monte Carlo of 50000 sampling are obtained temporarily
The comparing result of the state probability of stability such as attached drawing 2,3,4.
In the case of three kinds, percentage error maximum of the method for the present invention compared with Monte Carlo method is respectively 2.31899%,
3.77769%, 2.84589%, error is no more than 5%.And context of methods calculating speed obtains compared with monte carlo method
Very big promotion, the calculating time of two methods are shown in Table 2.
The calculating time of 2 two methods of table compares
Corresponding power system transient stability journey under different faults can be compared according to the probabilistic transient stability size being calculated
Degree, and then help operational planner to be ranked up failure, and screen effective failure.
The method of the present invention consider output of wind electric field uncertainty and its between correlation, be based on power train containing wind-powered electricity generation
The research achievement of system Practical Dynamic Security Region establishes the analytical expression of probabilistic transient stability, and combines and be based on Nataf inversion
Three point estimations changed assess Probabilistic transient stability.This method is demonstrated by the comparison with monte carlo method to comment
Estimate the accuracy and rapidity when the Probabilistic transient stability for considering wind-powered electricity generation correlation.
Claims (2)
1. a kind of Probabilistic transient stability appraisal procedure for considering wind-powered electricity generation correlation, it is characterised in that: the following steps are included:
Step 1 establishes the probability Distribution Model of each uncertain node injecting power；Generator and load are normal distribution, wind
Machine power output is Weibull distribution, respectively obtains its distribution parameter；
Step 2 obtains the Practical Dynamic Security Region boundary of the electric system containing wind-powered electricity generation；
Step 3 obtains the analytical expression of probabilistic transient stability based on the Practical Dynamic Security Region containing wind-powered electricity generation；
Step 4 calculates 2n+1 estimation point sampling location and weight in independent standard normal space, constructs 2n+1 sampling
Vector sum weight matrix；
Step 5 calculates the transformed standard normal of Nataf point according to the correlation matrix ρ of input variable in real space
The linearly dependent coefficient matrix ρ of cloth variable0；
Step 6 utilizes cholesky decomposition computation ρ0Lower triangular matrix B；
2n+1 vector of samples in the positive state space of step 4 Plays is transformed into original sky by Nataf inverse transformation by step 7
Between in；
Jth (j=1,2 ..., 2n+1) is successively organized in the expression formula of former evaluation vector substitution output variable S and is obtained S by step 8
Each rank moment of the orign；
Step 9 introduces Cornish-Fisher series expansion and obtains the cumulative distribution function of S, so that it is general less than 0 to obtain S
Rate, as probabilistic transient stability value TSP.
2. a kind of Probabilistic transient stability appraisal procedure for considering wind-powered electricity generation correlation according to claim 1, it is characterised in that:
Each rank moment of the orign process of S is obtained in the step 8:
Step 2.1, initial value j=0 is set up；
Step 2.2, j=j+1 is enabled；
Step 2.3, j-th of vector of samples in luv space is substituted into the expression formula of following S variable；
Step 2.4, judge j=2n+1, if meeting condition, export each rank moment of the orign of S in following formula；Otherwise return step
2.2；
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