Interval Power Flow Analysis Based On Relative Distance Measure

Viewing power system from the angle of node injection power,uncertainties have been flooding into power system with a high penetration rate.Renewable energies generation such as wind and solar power have inherent volatility and intermittentness.Meanwhile,power users are increasingly active and diversified in power supply quality.which severely challenges the planning,operation and control of the power system.However,traditional methods always need impractical assumptions,and the results tend to be single-dimensional homogenization.To this end,this paper focus on the most accessible and most interpretable interval,and takes the interval acquisition,interval mathematics representation to interval power flow analysis as the research content and provide a multidimensional perspective.The research process is organized as follows:Firstly,the background and research significance of power system uncertainty are described in detail,and the current research fields are discussed from the perspectives of uncertainty modeling theory and power system power flow analysis considering uncertainty.The status quo of scientific research highlights the innovation and main work of this paper.Furthermore,the interval transformation strategy of data with different uncertainty characteristics is summarized and analyzed.For the data with insignificant data characteristics,a fuzzy c-means(FCM clustering)method with adaptive clustering number is proposed to preprocess the data.If the interval model is directly generated by data,the extreme value is proposed or The interval modeling method based on the mean value;if the probability distribution acquisition interval is adopted,the interval modeling method based on the two intervals formed by the distribution endpoints or the α-cut multi-interval is proposed;if the probability distribution is used to obtain the interval A method using kernel density estimation and then using confidence interval approximation is proposed.At the same time,from the perspectives of operation mode and equation form,the interval conservation problem of classical Moore interval analysis algebra is deeply analyzed,and the suppression effect of affine and interval subdivision under the classical Moore interval framework is explored.The interval analysis method based on RDM(relative distance measure)and the uncertainty index such as interval span,interval distribution and interval center of gravity are introduced.Aiming at the problems of basic algebraic operations,linear and nonlinear models,considering the dimensions of characterization,information and interval expansion,the advantages and characteristics of RDM interval algebra in uncertainty characterization are compared.The research shows that the interval conservation problem of Moore interval theory starts from the four arithmetic levels and is affected by the equation form;affine algebra and interval subdivision can alleviate the problem to some extent;the results of RDM interval are not affected by the equation form.And can reflect uncertainty from a multidimensional level.Finally,the interval model of node injection power and the RDM interval algebra representation theory are integrated into the interval DC power flow model and the interval AC power flow model,and the interval distribution of voltage and power are analyzed,and compared with those obtained with the classical Moore interval theory The research shows that RDM-based interval power flow analysis can give a narrower range than the trend analysis based on classical Moore interval theory,and reflect the distribution of uncertainty from multiple dimensions;the voltage phase of the interval DC power flow of RDM is interval element The linear superposition of the variables,the branch flow can be either superimposed or canceled,and the whole is trapezoidal or triangular.The result of the interval AC trend is the nonlinear superposition of the interval original variables,and the overall result is approximately trapezoidal or triangular.The trapezoidal distribution shows that the two interval meta-variables contribute differently to the power flow results,and the triangular distribution shows that the contributions of the two are comparable.For the offset state,if the correlation of the interval variables is considered,the uncertainty can be reduced.