| The traction load of high-speed railway is a special electric load with a strong rules of train operation but still with a certain degree of uncertainty.The traction load has obvious characteristics such as asymmetry,nonlinearity,impact and random fluctuation.The geographical environment of high-speed railways on our national territory is changeable,and the network of high-speed railway connections between cities has gradually formed.The single-phase,high-power and asymmetric traction load that moves with space and time is bound to have a profound impact on the regional power grid when it is connected to.The train on the railway is affected by uncertain factors such as switching of working conditions(traction,inertia,regenerative braking),line conditions(gradient,bridge,tunnel),operation organization(speed limit,delay)and other uncertain factors during operation.With the rapid development of the new power system,the randomness of the power system is enhanced,and the asynchronous networking makes the grid capacity smaller.The reduction of regional grid capacity,the enhancement of the randomness of the power system and the increase of uncertain traction load of high-speed railways all bring new challenges to the interaction between the traction power supply system and the grid.Therefore,there are very important theoretical significance and application value for studying the probabilistic model establishment method of traction load considering uncertainty,as well as studying the probabilistic analysis method of the interaction between traction load and regional power grid in space and time.This paper considers the uncertainty of traction load with space and time in the process of train operation.Aiming at the probabilistic modeling methods of traction load considering the uncertainty and its application,some fundamental issues are conducted in-depth research by using probability theory and statistical analysis methods,such as the non-parametric probabilistic modeling methods for traction load,as well as the calculation methods of threephase probabilistic power flow for power grids with the asymmetric traction load.And they are applied to the probability analysis of the interaction between the asymmetric traction load and regional power grid in space and time.The main research work includes:(1)To study the discrete non-parametric probability model of traction load,this paper proposed a probability density estimation method based on the histogram of optimal bin width.Poisson point events were used to construct a histogram.The value function was defined by mean integrated squared error(MISE),and the optimal bin width was calculated from the minimum value of the value function by combing the Sturges rule and the average shift histogram(ASH)idea.This method realized that the optimal smooth bin width is a compromise between variance and deviation.Through the high-speed railway traction load test data,the accuracy and effectiveness of the method proposed in this paper were verified,as well as the adaptability of the probability distribution characteristics of the traction load under different sampling intervals and different working conditions.The proposed method improved the accuracy of the probability density histogram as a reference benchmark.(2)To study the continuous non-parametric probability model of traction load,this paper proposed a non-parametric probability modeling method of traction load based on Diffusionbased kernel density estimator(DKDE).The unique solution of the diffusion partial differential equation(Diffusion-PDE)based on the finite field can get the general form of the kernel density estimation calculation formula.The boundary conditions of Diffusion-PDE can solve the boundary deviation problem of the traditional kernel density estimation method.The optimal bandwidth of DKDE was calculated by cyclic progressive method.The test data of feeder current,active and reactive power of a certain traction station were taken as the analysis examples.By comparing the probability density function(PDF)curve and the goodness of fit test index,the accuracy and adaptability of DKDE applied to establish the non-parametric probability distributions traction load were verified.(3)To study the correlation between traction load sequences,the correlation analysis method based on optimal extension method is proposed.According to the spatiotemporal characteristics of the traction load,the idea of curve alignment or curve registration is used.Taking the maximum value of the Pearson/Spearman/Kendall correlation coefficient among the traction load sequences as the objective function,and taking the extension time range and the monotonicity of the sequence occurrence time as the constraints,the optimal delay mathematical model of the correlation between the traction load sequences is established.Combined with the normalized root mean square error(NRMSE)index,a generalized EM algorithm is proposed to solve the optimal delay model.The case studies are carried out on the traction load sequence of one train and two trains at any time of the four traction substations of the high-speed railway.Furthermore,the effects of no-load removal processing and different test intervals are considered.The correctness and effectiveness of the method proposed in this paper are verified.The proposed method can mine the potential correlation between the traction load data and prevent the misjudgment of the traction load correlation.(4)To study the operation analysis of the high-speed railway multi-traction load connected to the power grid considering the spatial correlation,a three-phase probabilistic power flow calculation method for power grids with traction loads based on an improved Latin hypercube sampling(LHS)was proposed in this paper.Firstly,the three-phase probabilistic power flow calculation model for the power grid with the asymmetry and multiple traction load was established.The improved LHS method was proposed by combining the equal probability conversion principle and the rank correlation Cholesky decomposition technology,and random sampling was performed on the non-parametric probability model based on DKDE of traction load considering the spatial correlation.The median Latin hypercube sampling method was introduced in the sampling process to improve calculation efficiency.The effectiveness of the proposed method was verified by the example analysis based on the modified IEEE-14 and IEEE-30 bus three-phase system and the measured data of a high-speed railway traction station.It also analyzes the probabilistic influence of traction load on grid voltage amplitude,voltage unbalance and grid loss rate under different correlation levels.(5)To study the probabilistic analysis of the impact of high-speed railway traction load on the power grid considering the time series and correlation,the DKDE method was used to establish the time series probability model of the traction load in different spatial locations.A time-series three-phase probabilistic power flow calculation method of high-speed railway traction loads connected to the power grid based on a three-point estimate method considering the correlation is proposed.This method effectively improves the efficiency of the time-series three-phase probabilistic power flow calculation.This method can not only consider the randomness and spatial correlation of the traction load at different locations,but also fully consider the time sequence of the traction load at different times.Through the modified IEEE-14 node three-phase system and the measured data of a high-speed railway traction station,the calculation cases analyzed,and the probability density curve of voltage amplitude and voltage unbalance were obtained.The results obtained verified the effectiveness and adaptability of the proposed method.And considering factors such as the number of traction stations and the connection mode,correlation,load level and other factors,the probability analysis of the influence of the traction load connected to the power grid on the voltage were carried out. |
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