CN104901309B - Electric power system static security assessment method considering wind speed correlation - Google Patents
Electric power system static security assessment method considering wind speed correlation Download PDFInfo
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Abstract
The invention discloses an electric power system static security assessment method considering wind speed correlation. According to wind speed historical data, cut-off pair copula is used to realize wind speed modeling with non-linear correlation; then according to fan power characteristics, electric power system quick static security assessment is realized. The electric power system static security assessment method can be used for processing wind speeds with any probability characteristics in an electric power system and is suitable for quickly assessing the influence of connected wind power plants on the static security of the electric power system in medium-term and long-term plans.
Description
Technical field
The invention belongs to power network safety operation technical field, more particularly to a kind of power train for considering wind speed dependency
System Static security assessment method.
Background technology
The regenerative resource (such as wind-powered electricity generation) of large-scale grid connection, with intermittent, randomness and dependency, produces power system
Raw disturbance.Now need to consider the statistical properties such as the dependency of disturbance, by probabilistic load flow, obtain Operation of Electric Systems special
The statistical information of the amount of levying (such as node voltage amplitude and phase angle, circuit is active and idle etc.), and then find the weakness of system operation
Link, assessment system level of security.
For the modeling problem of dependency wind power, three rank multinomial normal transformations and nine rank multinomial normal transformations are based on
Linearly dependent coefficient is modeled, and is unsuitable for describing nonlinear correlation relation.Rank correlation coefficient is suitable to describe global non-linear dependencies,
But whole correlation properties, such as tail-dependence coefficient etc. cannot be reacted.
Copula models can preferably describe the non-linear, asymmetry between two stochastic variables and tail-dependence coefficient etc.,
It is used widely in power system, such as Probabilistic Load Flow, optimal load flow and available transmission capacity are assessed.Two-dimensional mixing Copula letters
Number can further improve modeling accuracy.But for the model of more higher-dimension, only minority Copula function can use.However, with
Increasing for wind energy turbine set is accessed, the Space correlation of complexity between a large amount of stations, is there is, dependency is often present between any two
Diversity, existing model are difficult to accurately be described by.Thus, being accessed for wind energy turbine set in a large number, wind power level of interpenetration is year by year
The present situation of increase, is needed research with more flexible accurate probabilistic model, and is combined with power of fan characteristic, to improve power train
System Static security assessment level.
The content of the invention
It is an object of the invention to overcome above-mentioned the deficiencies in the prior art, there is provided a kind of power train of consideration wind speed dependency
System Static security assessment method, accesses the impact to power system static safety for assessing wind field.
The technical solution of the present invention is as follows：
A kind of power system static safety evaluation method for considering wind speed dependency, comprises the steps：
Step 1, structure are based on many wind field wind speed (X for blocking pair copula1,…,Xn) pdf model f
(x1,…,xn).F () represents probability-distribution function, and F () can be obtained by experience distribution, is shown below：
Wherein, (x1k,…,xnk) be sample, m is total sample number, and I () is indicative function, when the inequality in bracket into
It is 1 immediately, otherwise is then 0.
Make ui=Fi(xi), it is theoretical according to pair copula, then there is a copula probability-distribution function so that：
F(x1,…,xn)=C (ui,…,un)
There is following relation in copula probability density functions and probability-distribution function C ()：
Pair copula construct copula probability density functions by following formula, and then construct probability-distribution function.
In formula, F (uj+i|u1,…,uj-1) it is in u1,…,uj-1Take with conditions of certain value, uj+iConditional probability point
Cloth.F (uj|u1,…,uj-1) and F (uj+i|u1,…,uj-1) be regarded as stochastic variable, then cj,j+i|1,…,j-1(F(uj|u1,…,
uj-1),F(uj+i|u1,…,uj-1)) be the two stochastic variables two-dimentional copula density functions.Specific dimensional Co pula letter
Number expression formula is referring to document《Pair-copula constructions of multiple dependence》.
For the purpose of simplifying the description, make ej-1,j+i=F (uj+i|u1,…,uj-1), particularly, e0,i=ui(i=1 ..., n).Then need
Pair copula to be built are shown below.
Specifically, build the step of blocking pair copula as follows：
1) historical data of wind speed X is read, u is madei=Fi(xi), obtain U=(U1,…,Un) sample data.
2) j=1 is made, based on (ej-1,j,ej-1,j+i) (i=1 ..., n-j) sample point, respectively using Normal,
Frank, Clayton, t and Gumbel copula is to cj,j+i|1,…,j-1(ej-1,j,ej-1,j+i) be fitted, can adopt
In matlab softwares, copulafit functions are quickly calculated the parameter of corresponding copula functions, and according to foundation Euclidean distance,
Select optimum copula type function.Euclidean distance inspection is as follows：
Wherein, u1i,…,uni(i=1 ... m) it is sample point.
3) e is calculated using following formulaj,j+i
4) j=2 is made, is repeated 2) with 3), is obtained cj,j+i|1,…,j-1(ej-1,j,ej-1,j+i) and ej,j+i(i=1 ..., n-2).
J=3, repeat step is made 2) with 3), to obtain cj,j+i|1,…,j-1(ej-1,j,ej-1,j+i) and ej,j+i(i=1 ..., n-3).Complete
Pair copula are modeled.
Step 2, such as structure probabilistic load flow model, following formula：
In formulaRepresent the net active power injected at power system node i；PijRepresent that node j flows to the circuit of node i
Effective power flow；Represent the net reactive power injected at power system node i；ViRepresent the voltage amplitude of power system node i
Value；VjRepresent the voltage magnitude of power system node j；θijRepresent the phase difference of voltage of power system ij nodes；YijRepresent connection
The line admittance amplitude of ij nodes；Represent the line admittance phase angle of connection ij nodes；GijRepresent power system connection ij nodes
The conductance of circuit；BijRepresent that power system connects the susceptance of ij node lines；N is power system interstitial content；
It is main to consider wind-powered electricity generation and load disturbance, wherein,
In formula, Pw,iWind-power electricity generation for injecting at power system node i is active, PL,iFor all kinds of at power system node i
It is active that load is consumed；Qw,iWind-power electricity generation for injecting at power system node i is idle, QL,iFor each at power system node i
It is idle that type load is consumed；
Power system static security evaluation after step 3, many wind fields accesses of consideration, step are as follows：
1) generate independent and uniform distribution Zj(j=1,2 ..., random number n) can be using the unifrnd of MATLAB softwares
Instruction is generated.
2) to Zj(j=1,2 ..., each sampled point n), according to built probabilistic model, successive iteration solution following formula is obtained
Stochastic variable Uj(j=1,2 ..., n) sampled point.
In formula, F (uj|u1,…,uj-1) it is known u1,…,uj-1When, ujCondition distribution.zj=F (uj|u1,…,uj-1)
Inverse function have analytic expression, refer to document《Pair-copula constructions of multiple dependence》,
Thus solve ujSimply.Based on uj=Fj(xj), obtain the sampling of corresponding wind speed X.
3) the wind speed and wind power characteristic of the blower fan be given for wind field apoplexy machine manufacturer, is converted to wind work(wind speed
Rate, so that obtain the sampling of wind-powered electricity generation.
4) definitiveness Load flow calculation is carried out to wind power samples point respectively, the statistical nature of Probabilistic Load Flow can be obtained, entered
And after may determine that wind energy turbine set is accessed, the static security level of power system.
Compared with prior art, the invention has the beneficial effects as follows：
The random wind speed in power system with any probability nature is coped with, intractability is reduced, and is improve and is built
Mould flexibility ratio and precision, so as to obtain the statistical information of system character, are further obtaining its probability distribution
After the out-of-limit probability of system, i.e. static system can be estimated safely, it is adaptable to assess wind field access after it is quiet to power system
The impact of state safety.
Description of the drawings
Fig. 1 is the structure chart for blocking pair copula.
Fig. 2 is blower fan wind power characteristic.
Specific embodiment
The inventive method is illustrated below in conjunction with accompanying drawing, but should not be limited the scope of the invention with this.
A kind of power system static safety evaluation method for considering dependency, comprises the steps：
Step 1, structure are based on many wind field wind speed (X for blocking pair copula1,…,Xn) pdf model f
(x1,…,xn), Fig. 1 is the structure chart for blocking pair copula.F () represents probability-distribution function.F () can pass through Jing
Test distribution to obtain, be shown below：
Wherein, (x1k,…,xnk) be sample, m is total sample number, and I () is indicative function, when the inequality in bracket into
It is 1 immediately, otherwise is then 0.
Make ui=Fi(xi), it is theoretical according to pair copula, then there is a copula probability-distribution function so that：
F(x1,…,xn)=C (ui,…,un)
There is following relation in copula probability density functions and probability-distribution function C ()：
Pair copula construct copula probability density functions by following formula, and then construct probability-distribution function.
In formula, F (uj+i|u1,…,uj-1) it is in u1,…,uj-1Take with conditions of certain value, uj+iConditional probability point
Cloth.F (uj|u1,…,uj-1) and F (uj+i|u1,…,uj-1) be regarded as stochastic variable, then cj,j+i|1,…,j-1(F(uj|u1,…,
uj-1),F(uj+i|u1,…,uj-1)) be the two stochastic variables two-dimentional copula density functions.Specific dimensional Co pula letter
Number expression formula is referring to document《Pair-copula constructions of multiple dependence》.
For the purpose of simplifying the description, make ej-1,j+i=F (uj+i|u1,…,uj-1), particularly, e0,i=ui(i=1 ..., n).Then need
Pair copula to be built are shown below.
Specifically, build the step of blocking pair copula as follows：
1) historical data of wind speed X is read, u is madei=Fi(xi), obtain U=(U1,…,Un) sample data.
2) j=1 is made, based on (ej-1,j,ej-1,j+i) (i=1 ..., n-j) sample point, respectively using Normal,
Frank, Clayton, t and Gumbel copula is to cj,j+i|1,…,j-1(ej-1,j,ej-1,j+i) be fitted, can adopt
In matlab softwares, copulafit functions are quickly calculated the parameter of corresponding copula functions, and according to foundation Euclidean distance,
Select optimum copula type function.Euclidean distance inspection is as follows：
Wherein, u1i,…,uni(i=1 ... m) it is sample point.
3) e is calculated using following formulaj,j+i
4) j=2 is made, is repeated 2) with 3), is obtained cj,j+i|1,…,j-1(ej-1,j,ej-1,j+i) and ej,j+i(i=1 ..., n-2).
J=3, repeat step is made 2) with 3), to obtain cj,j+i|1,…,j-1(ej-1,j,ej-1,j+i) and ej,j+i(i=1 ..., n-3).Complete
Pair copula are modeled.
Step 2, such as structure probabilistic load flow model, following formula：
In formulaRepresent the net active power injected at power system node i；PijRepresent that node j flows to the circuit of node i
Effective power flow；Represent the net reactive power injected at power system node i；ViRepresent the voltage amplitude of power system node i
Value；VjRepresent the voltage magnitude of power system node j；θijRepresent the phase difference of voltage of power system ij nodes；YijRepresent connection
The line admittance amplitude of ij nodes；Represent the line admittance phase angle of connection ij nodes；GijRepresent power system connection ij nodes
The conductance of circuit；BijRepresent that power system connects the susceptance of ij node lines；N is power system interstitial content；
It is main to consider wind-powered electricity generation and load disturbance, wherein,
In formula, Pw,iWind-power electricity generation for injecting at power system node i is active, PL,iFor all kinds of at power system node i
It is active that load is consumed；Qw,iWind-power electricity generation for injecting at power system node i is idle, QL,iFor each at power system node i
It is idle that type load is consumed；
Power system static security evaluation after step 3, many wind fields accesses of consideration, step are as follows：
3) generate independent and uniform distribution Zj(j=1,2 ..., random number n) can be using the unifrnd of MATLAB softwares
Instruction is generated.
4) to Zj(j=1,2 ..., each sampled point n), according to built probabilistic model, successive iteration solution following formula is obtained
Stochastic variable Uj(j=1,2 ..., n) sampled point.
In formula, F (uj|u1,…,uj-1) it is known u1,…,uj-1When, ujCondition distribution.zj=F (uj|u1,…,uj-1)
Inverse function have analytic expression, refer to document《Pair-copula constructions of multiple dependence》,
Thus solve ujSimply.Based on uj=Fj(xj), obtain the sampling of corresponding wind speed X.
3) the wind speed and wind power characteristic of the blower fan be given for wind field apoplexy machine manufacturer, is converted to wind work(wind speed
Rate, so that obtain the sampling of wind-powered electricity generation.For example, IEC Class II type blower fan wind power characteristics of the Fig. 2 for NREL, expression formula
It is shown below, brings wind speed into and corresponding output wind power is obtained.
In formula, vwFor wind speed, vci、vrAnd vcoThe respectively incision wind speed 3.4m/s of blower fan, rated wind speed 15m/s and cut out
Wind speed 25m/s, PrFor rated power 2MW.
4) definitiveness Load flow calculation is carried out to wind power samples point respectively, the statistical nature of Probabilistic Load Flow can be obtained, entered
And after may determine that wind energy turbine set is accessed, the static security level of power system.
Claims (2)
1. a kind of power system static safety evaluation method for considering wind-force dependency, is characterized in that, the method includes following step
Suddenly：
Step 1, structure are based on many wind field wind speed (X for blocking pair copula1,…,Xn) pdf model f (x1,…,xn)：
Make ui=Fi(xi), wherein, F () represents probability-distribution function；
There is a copula probability-distribution function so that：
F(x1,...,xn)=C (ui,...,un)
The relation of copula probability density functions c () and probability-distribution function C () is as follows：
Pair copula construct copula probability density functions by following formula, and then construct probability-distribution function：
In formula, F (uj+i|u1,…,uj-1) it is in u1,…,uj-1Take with conditions of certain value, uj+iConditional probability distribution；F
(uj|u1,…,uj-1) and F (uj+i|u1,…,uj-1) be regarded as stochastic variable, then cj,j+i|1,…,j-1(F(uj|u1,…,uj-1),F(uj+i
|u1,…,uj-1)) be the two stochastic variables two-dimentional copula density functions；
Step 2, structure Probabilistic Load Flow model, formula are as follows：
In formula,Represent the net active power injected at power system node i；PijRepresent that node j flows to the circuit of node i and has
Work(trend；Represent the net reactive power injected at power system node i；ViRepresent the voltage magnitude of power system node i；
VjRepresent the voltage magnitude of power system node j；θijRepresent the phase difference of voltage of power system ij nodes；YijRepresent connection ij sections
The line admittance amplitude of point；Represent the line admittance phase angle of connection ij nodes；GijRepresent power system connection ij nodal lines
The conductance on road；BijRepresent that power system connects the susceptance of ij node lines；N is power system interstitial content；
Consider wind-powered electricity generation and load disturbance, wherein,
In formula, Pw,iWind-power electricity generation for injecting at power system node i is active, PL,iFor each type load at power system node i
What is consumed is active；Qw,iWind-power electricity generation for injecting at power system node i is idle, QL,iBear for all kinds of at power system node i
It is idle that lotus consumes；
Power system static security evaluation after step 3, many wind fields accesses of consideration, step are as follows：
31) MATLAB Software Create independent and uniform distribution Z are adoptedj(j=1,2 ..., random number n)；
32) to Zj(j=1,2 ..., each sampled point n), according to built probabilistic model, successive iteration solution following formula is obtained at random
Variable Uj(j=1,2 ..., n) sampled point,
33) the wind speed and wind power characteristic of the blower fan be given for wind field apoplexy machine manufacturer, is converted to wind power wind speed, obtains
To the sampling of wind-powered electricity generation；
34) definitiveness Load flow calculation is carried out to wind power samples point respectively, obtains the statistical nature of Probabilistic Load Flow, and then judge wind
After electric field is accessed, the static security level of power system.
2. it is according to claim 1 consider wind-force dependency power system static safety evaluation method, it is characterised in that
Described structure blocks comprising the following steps that for pair copula：
11) historical data of wind speed X is read, u is madei=Fi(xi), obtain U=(U1,…,Un) sample data；
12) make ej-1,j+i=F (uj+i|u1,…,uj-1), wherein, e0,i=ui(i=1 ..., n), the pair copula of structure are such as
Shown in following formula：
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| CN107846039A (en) * | 2017-10-24 | 2018-03-27 | 国网上海市电力公司 | Consider the cluster wind-electricity integration modeling and analysis methods and system of wind speed correlation |
| CN108462180B (en) * | 2018-01-31 | 2020-09-18 | 华中科技大学 | Method for determining probability optimal power flow based on vine copula function |
| CN109242340B (en) * | 2018-09-29 | 2021-08-27 | 国网辽宁省电力有限公司电力科学研究院 | Monitoring data evaluation system and evaluation method for heat storage electric boiler digestion system |
| CN111758198B (en) * | 2019-01-28 | 2023-09-15 | 深圳大学 | Linear asymmetric method for AC power network branch open-type static safety inspection |
| CN111563637B (en) * | 2019-02-13 | 2023-09-12 | 株洲中车时代电气股份有限公司 | Multi-objective probability optimal power flow calculation method and device based on demand response |
| CN110429636B (en) * | 2019-06-25 | 2020-11-13 | 广西电网有限责任公司南宁供电局 | Static voltage stabilization fault screening and sorting method |
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| CN103208798B (en) * | 2013-03-26 | 2014-10-08 | 河海大学 | Method for calculating probability power flow of power system containing wind farm |
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