CN105656031A - Security risk assessment method of wind-power-included electric power system based on Gaussian mixture distribution characteristics - Google Patents
Security risk assessment method of wind-power-included electric power system based on Gaussian mixture distribution characteristics Download PDFInfo
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- H—ELECTRICITY
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Abstract
The invention relates to a security risk assessment method of a wind-power-included electric power system based on Gaussian mixture distribution characteristics. The security risk assessment method comprises the following steps: counting up the distribution of historical data of output power of a wind power plant; establishing a non-parameter probability distribution model of the output power of the wind power plant; establishing a Gaussian mixture distribution model of the output power of the wind power plant; determining the quantity of Gaussian distribution and initializing parameters of each Gaussian distribution; solving the parameters of each Gaussian distribution and determining the Gaussian mixture distribution characteristics; determining cumulative distribution functions of state variable node voltage and branch power flow; and calculating state variable threshold-crossing probability and severity of generated results, and comprehensively estimating safety risks of the electric power system. According to the security risk assessment method provided by the invention, a semi-invariant solving process of node injection power of the system is greatly simplified, so that the efficiency of semi-invariant calculation of the node injection power and the accuracy of the cumulative distribution functions of state variable node voltage and the branch power flow are improved, and thus effective data supports are provided for security risk assessment of the electric power system.
Description
Technical field
The present invention relates to operation and control of electric power system field, specifically based on Gaussian Mixture distribution characteristics containing wind-powered electricity generation power system security methods of risk assessment.
Background technology
Along with economic fast development and increasingly serious ambient pressure, operation of power networks environment presents the feature made new advances, especially wind-powered electricity generation large-scale grid connection, brings new challenge to the safe operation of power system.
Tidal current analysis is basis and the premise of Power System Security Assessment, adopt probability load flow calculation method, consider the random factors such as wind power output fluctuation, the mathematical model characterizing systematic uncertainty is set up by probability theory, the service condition of power system can be reflected more comprehensively, and find the potential risk in power system and fragility unit.
It is directed to containing security risk assessment problem based on Probabilistic Load Flow in wind-powered electricity generation power system, a kind of typical thinking is had to be exactly: based on the probabilistic model of Power Output for Wind Power Field, each rank moment of the orign of direct solution Power Output for Wind Power Field, then it is translated into cumulant and carries out convolutional calculation, but this calculating process often to expend the plenty of time, and along with the extensive access of wind-powered electricity generation, the uncertain increase of Power Output for Wind Power Field, its probability density non-normality highlights, disobey in any typical probability distribution, solving of moment of the orign becomes more loaded down with trivial details, expend the substantial amounts of time, reduce further the efficiency of conventional probability tidal current computing method and accuracy.
Summary of the invention
For the defect existed in prior art, it is an object of the invention to provide based on Gaussian Mixture distribution characteristics containing wind-powered electricity generation power system security methods of risk assessment, the probability density with the Power Output for Wind Power Field of non-normality is converted into the distribution of typical Gaussian Mixture, it is possible not only to quantify accurately the probability distribution of Power Output for Wind Power Field, enormously simplify the cumulant of system node injecting power and ask for process, make up and conventional probability Load flow calculation solves the defect that the adopted method of cumulant is single, further increase the efficiency of the cumulant calculating of node injecting power and the accuracy of the cumulative distribution function of state variable nodes voltage and Branch Power Flow, out-of-limit for power system voltage, the security risk assessment of Branch Power Flow overload provides effective data supporting.
For reaching object above, the present invention adopts the technical scheme that:
Based on Gaussian Mixture distribution characteristics containing wind-powered electricity generation power system security methods of risk assessment, it is characterised in that comprise the steps:
Step one, statistics Power Output for Wind Power Field historical data distribution, set up the nonparametric probability Distribution Model of Power Output for Wind Power Field;
Step 2, set up the Gaussian Mixture Distribution Model of Power Output for Wind Power Field, determined the number of sub-Gauss distribution by the nonparametric probability Distribution Model of Power Output for Wind Power Field, initialize the parameter of each sub-Gauss distribution;
Step 3, solve the parameter of each sub-Gauss distribution, it is determined that Gaussian Mixture distribution characteristics;
Step 4, Gaussian Mixture distribution characteristics based on Power Output for Wind Power Field, adopt Cumulants method to carry out probabilistic load flow, it is determined that the cumulative distribution function of state variable nodes voltage and Branch Power Flow;
Step 5, cumulative distribution function according to state variable nodes voltage and Branch Power Flow, calculate the out-of-limit probability of state variable and produce severity of consequence, comprehensive assessment power system security risk.
On the basis of technique scheme, in step one, depend on the historical data of Power Output for Wind Power Field, according to non-parametric estmation principle, add up the experienced probability distribution of each node injecting power, set up the nonparametric probability Distribution Model of Power Output for Wind Power Field;
In step 2, Power Output for Wind Power Field is expressed as Gaussian Mixture Distribution Model, and determines the number of sub-Gauss distribution.
On the basis of technique scheme, in step 3, utilize the parameter of each sub-Gauss distribution of cluster algorithm iterative, it is determined that Gaussian Mixture distribution characteristics.
On the basis of technique scheme, in step 4, according to Gaussian Mixture distribution characteristics, using every sub-Gauss distribution scene as Power Output for Wind Power Field, and characterize two rank cumulant before one scene of exerting oneself of wind energy turbine set by the expectation of sub-Gauss distribution and variance, it is expectation and variance, coupling system generator output, load power historical data and power system topological structure and data message, Niu Lafa is adopted to calculate the expected value of Jacobian matrix and state variable, adopt Cumulants method that each scene is carried out probabilistic load flow, integrate and obtain the cumulative distribution function that POWER SYSTEM STATE variable is final.
Of the present invention based on Gaussian Mixture distribution characteristics containing wind-powered electricity generation power system security methods of risk assessment, the probability density with the Power Output for Wind Power Field of non-normality is converted into the distribution of typical Gaussian Mixture, it is possible not only to quantify accurately the probability distribution of Power Output for Wind Power Field, enormously simplify the cumulant of system node injecting power and ask for process, make up and conventional probability Load flow calculation solves the defect that the adopted method of cumulant is single, further increase the efficiency of the cumulant calculating of node injecting power and the accuracy of the cumulative distribution function of state variable nodes voltage and Branch Power Flow, out-of-limit for power system voltage, the security risk assessment of Branch Power Flow overload provides effective data supporting.
Accompanying drawing explanation
The present invention has drawings described below:
The schematic flow sheet of Fig. 1 present invention.
Detailed description of the invention
Below in conjunction with accompanying drawing, the present invention is described in further detail.
Of the present invention based on Gaussian Mixture distribution characteristics containing wind-powered electricity generation power system security methods of risk assessment, it is directed to and solves the problem of difficulty (cumulant solves loaded down with trivial details) based on Probabilistic Load Flow containing Power Output for Wind Power Field probability distribution in security risk assessment in wind-powered electricity generation power system, comprise the steps:
Step one, statistics Power Output for Wind Power Field historical data distribution, set up the nonparametric probability Distribution Model of Power Output for Wind Power Field;
Step 2, set up the Gaussian Mixture Distribution Model of Power Output for Wind Power Field, determined the number of sub-Gauss distribution by the nonparametric probability Distribution Model of Power Output for Wind Power Field, initialize the parameter of each sub-Gauss distribution;
Step 3, solve the parameter of each sub-Gauss distribution, it is determined that Gaussian Mixture distribution characteristics;
Step 4, Gaussian Mixture distribution characteristics based on Power Output for Wind Power Field, adopt Cumulants method to carry out probabilistic load flow, it is determined that the cumulative distribution function of state variable nodes voltage and Branch Power Flow;
Step 5, cumulative distribution function according to state variable nodes voltage and Branch Power Flow, calculate the out-of-limit probability of state variable and produce severity of consequence, comprehensive assessment power system security risk.
On the basis of technique scheme, in step one, depend on the historical data of Power Output for Wind Power Field, according to non-parametric estmation principle, add up the experienced probability distribution of each node injecting power, set up the nonparametric probability Distribution Model of Power Output for Wind Power Field;
In step 2, Power Output for Wind Power Field is expressed as Gaussian Mixture Distribution Model, and determines the number of sub-Gauss distribution.
On the basis of technique scheme, in step 3, utilize the parameter of each sub-Gauss distribution of cluster algorithm iterative, it is determined that Gaussian Mixture distribution characteristics.
On the basis of technique scheme, in step 4, according to Gaussian Mixture distribution characteristics, using every sub-Gauss distribution scene as Power Output for Wind Power Field, and characterize two rank cumulant before one scene of exerting oneself of wind energy turbine set by the expectation of sub-Gauss distribution and variance, it is expectation and variance, coupling system generator output, load power historical data and power system topological structure and data message, Niu Lafa is adopted to calculate the expected value of Jacobian matrix and state variable, adopt Cumulants method that each scene is carried out probabilistic load flow, integrate and obtain the cumulative distribution function that POWER SYSTEM STATE variable is final.
The technical solution adopted in the present invention is: consider following factor:
1, Power Output for Wind Power Field historical data;
2, generator output and load power historical data;
3, power system topological structure and data message.
It it is below a specific embodiment.
Step A. adds up the distribution of Power Output for Wind Power Field historical data, sets up the nonparametric probability Distribution Model of Power Output for Wind Power Field. After improper data screening and wrong data are rejected, obtain Power Output for Wind Power Field sample set, choose suitable siding-to-siding block length, Power Output for Wind Power Field perunit value is carried out interval statistics, obtain the histogram frequency distribution diagram of Power Output for Wind Power Field. By distribution-free regression procedure, utilize kernel function estimation that the probability distribution of Power Output for Wind Power Field is fitted, set up the nonparametric probability Distribution Model of Power Output for Wind Power Field.
Step B. sets up the Gaussian Mixture Distribution Model of Power Output for Wind Power Field, is determined the number of sub-Gauss distribution by the nonparametric probability Distribution Model of Power Output for Wind Power Field, initializes the parameter of each sub-Gauss distribution. The probability density distribution of Power Output for Wind Power Field is approached, the probability density function f of single Gauss distribution by the linear combination of several Gaussian density functionsG(��,��)X () is expressed as follows:
In formula: x is the stochastic variable of Power Output for Wind Power Field; �� is the expected value of Gauss distribution; �� and ��2The respectively standard deviation of Gauss distribution and variance.
The mixing probability density function of n Gauss distribution is expressed as follows:
In formula: ��kFor the weight of mixed distribution neutron Gauss distribution, also referred to as mixed coefficint; ��kAnd ��kThe respectively expected value and standard deviation of sub-Gauss distribution.
Wherein ��kMay also indicate that the prior probability of each blending constituent, it has the property that
Gauss hybrid models neutron gaussian distribution number is more many, and fitting effect is more good, and amount of calculation also can be greatly increased simultaneously, it is therefore desirable to selectes suitable sub-gaussian distribution number n according to the nonparametric probability Distribution Model of Power Output for Wind Power Field.Weights omegakInitial value be set to 1/n, ��kAnd ��kInitial value can take the expected value and standard deviation of node injecting power.
Step C. solves the parameter of each sub-Gauss distribution, it is determined that Gaussian Mixture distribution characteristics. By the Maximum-likelihood estimation principle of expectation maximization (ExpectationMaximization, EM) algorithm, the weights omega of each sub-Gauss distribution of iterativek, it is desirable to value ��kAnd standard deviation sigmak, till being met the solution of iteration convergence.
Step D., based on the Gaussian Mixture distribution characteristics of Power Output for Wind Power Field, adopts Cumulants method to carry out probabilistic load flow, it is determined that the cumulative distribution function of state variable nodes voltage and Branch Power Flow. Owing to the 2 above cumulant in rank of the stochastic variable of Gaussian distributed are 0, using every sub-Gauss distribution as a scene of Power Output for Wind Power Field, therefore it is readily available the front 2 rank cumulant of n group Power Output for Wind Power Field scene, i.e. expectation and variance. By the expected value of Power Output for Wind Power Field, generator output and load power in each scene, obtain n expected value of node injecting power, and at the expected value point of each scene, calculate the expected value obtaining n group Jacobian matrix and state variable nodes voltage, Branch Power Flow.
Utilizing the front 2 rank cumulant of n wind power output scene, each rank cumulant of generator output and load power calculates each rank cumulant obtaining n group node injecting power. A large amount of calculating in order to avoid convolution, adopt the lienarized equation of Load flow calculation, character according to cumulant and the cumulant of node injecting power, carry out n time calculating each rank cumulant of the variable quantity obtaining state variable nodes voltage and Branch Power Flow, then utilize Gram-Charlier series expansion to approach the probability distribution of the variable quantity of state variable, and then obtain the cumulative distribution function of state variable under each scene, this n group cumulative distribution function weight of each sub-Gauss distribution is integrated into the cumulative distribution function that POWER SYSTEM STATE variable is final.
The step E. cumulative distribution function according to state variable, the out-of-limit probability level of solving state variable and severity, comprehensive assessment power system security risk. Cumulative distribution function according to state variable nodes voltage and Branch Power Flow, follow corresponding international and national standard, the out-of-limit probability level of solving state variable node voltage and Branch Power Flow and generation severity of consequence index, be estimated the security risk of power system.
The above; it it is only the preferred embodiments of the present invention; not the present invention being done any pro forma restriction, those skilled in the art utilize the technology contents of the disclosure above to make a little simple modification, equivalent variations or decoration, all fall within protection scope of the present invention.
The content not being described in detail in this specification belongs to the known prior art of professional and technical personnel in the field.
Claims (4)
1. based on Gaussian Mixture distribution characteristics containing wind-powered electricity generation power system security methods of risk assessment, it is characterised in that comprise the steps:
Step one, statistics Power Output for Wind Power Field historical data distribution, set up the nonparametric probability Distribution Model of Power Output for Wind Power Field;
Step 2, set up the Gaussian Mixture Distribution Model of Power Output for Wind Power Field, determined the number of sub-Gauss distribution by the nonparametric probability Distribution Model of Power Output for Wind Power Field, initialize the parameter of each sub-Gauss distribution;
Step 3, solve the parameter of each sub-Gauss distribution, it is determined that Gaussian Mixture distribution characteristics;
Step 4, Gaussian Mixture distribution characteristics based on Power Output for Wind Power Field, adopt Cumulants method to carry out probabilistic load flow, it is determined that the cumulative distribution function of state variable nodes voltage and Branch Power Flow;
Step 5, cumulative distribution function according to state variable nodes voltage and Branch Power Flow, calculate the out-of-limit probability of state variable and produce severity of consequence, comprehensive assessment power system security risk.
2. as claimed in claim 1 based on Gaussian Mixture distribution characteristics containing wind-powered electricity generation power system security methods of risk assessment, it is characterized in that: in step one, depend on the historical data of Power Output for Wind Power Field, according to non-parametric estmation principle, add up the experienced probability distribution of each node injecting power, set up the nonparametric probability Distribution Model of Power Output for Wind Power Field;
In step 2, Power Output for Wind Power Field is expressed as Gaussian Mixture Distribution Model, and determines the number of sub-Gauss distribution.
3. as claimed in claim 1 based on Gaussian Mixture distribution characteristics containing wind-powered electricity generation power system security methods of risk assessment, it is characterised in that: in step 3, utilize the parameter of each sub-Gauss distribution of cluster algorithm iterative, it is determined that Gaussian Mixture distribution characteristics.
4. as claimed in claim 1 based on Gaussian Mixture distribution characteristics containing wind-powered electricity generation power system security methods of risk assessment, it is characterized in that: in step 4, according to Gaussian Mixture distribution characteristics, using every sub-Gauss distribution scene as Power Output for Wind Power Field, and characterize two rank cumulant before one scene of exerting oneself of wind energy turbine set by the expectation of sub-Gauss distribution and variance, it is expectation and variance, coupling system generator output, load power historical data and power system topological structure and data message, Niu Lafa is adopted to calculate the expected value of Jacobian matrix and state variable, adopt Cumulants method that each scene is carried out probabilistic load flow, integrate and obtain the cumulative distribution function that POWER SYSTEM STATE variable is final.
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| CN108173284A (en) * | 2018-01-10 | 2018-06-15 | 中国农业大学 | Active power distribution network method for estimating state and system |
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| CN109389145A (en) * | 2018-08-17 | 2019-02-26 | 国网浙江省电力有限公司宁波供电公司 | Electric energy meter production firm evaluation method based on metering big data Clustering Model |
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| CN112531694A (en) * | 2020-11-27 | 2021-03-19 | 国网重庆市电力公司电力科学研究院 | AC/DC hybrid power grid universe real-time simulation method based on digital twinning technology |
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