Modelling Of Wind Speed Correlation Based On Non-parametric Copula And Its Application In Probabilistic Optimal Power Flow

With the carbon peaking and carbon neutrality goals proposed,the proportion of wind power in the energy structure is increasing substantially in the whole world.The randomness and volatility of wind power generation have an increasingly significant impact on the security and economic operation of the power system.Due to the uncertainty of wind power outputs,the traditional deterministic power flow analysis methods are no longer appropriate.Therefore,a method that can consider the randomness of power injection is needed to solve the power flow.Probabilistic optimal power flow(POPF)is an effective tool to analyze the influence of the randomness of wind power generation on the uncertainty of the system operation state.Since there is a definite functional relationship between wind power output and wind speed,it is very important to build an accurate wind speed probability model for the accuracy of POPF.With the substantial increase in the installed capacity of wind power,wind farms are always collected in areas with abundant wind sources,so the wind speed correlation between adjacent wind farms cannot be ignored.Since the correlation between wind speeds has a strong tail effect rather than a simple linear relationship,it is of great significance to establish a probability model that can accurately describe the complex correlation between wind speeds.In addition,the correlation of wind farms in different regions are individual.It is difficult to establish a universal parameterized probability model to formulate the correlation of wind farms.Therefore,a non-parametric probability model driven by data is an urgent need,which can capture the correlation of random variables more accurately.The main research content of this paper is to propose an accurate non-parametric proba-bilistic model considering the wind speed correlation of adjacent wind farms as well as a multi-objective POPF model considering both system cost and risk,and apply the wind speed corre-lation modeling to improve the accuracy of POPF.In terms of correlation modeling,we firstly proposes a bivariate non-parametric Copula function based on the kernel density estimation via the diffusion process,short for BDK Copula,and performs density correction which makes it a Copula function in the true sense? On the basis of BDK Copula,a multivariate non-parametric Copula,PBDK Copula(Pair Bivariate Diffusive Kernel Copula)is constructed by Pair-Copula theory,which can accurately describe the wind speed correlation of multiple wind farms.The proposed wind speed correlation modeling method is applied to the wind power output sampling of POPF model.In order to improve the efficiency of the algorithm,a Sobol sequence sampling method based on the PBDK Copula is proposed,which is applied to the quasi-Monte Carlo algorithm for solving the POPF.Finally,we propose a multi-objective POPF model,which considers the system cost and the losses incurred in response to extreme wind power output conditions.The model reflects the fuel cost and conditional value at risk under a certain degree of confidence.Afterwards,the PBDK Copula is verifed by the Goodness-of-Fit tests on wind speed data sets from three regions in Northwest China.Besides,POPF simulations are executed on a mod-ified IEEE-57 bus system with wind farms integrated to verify the effectiveness of the proposed method in POPF.The simulation results show that the PBDK Copula has a superior performance in modelling the wind speed correlations,which conduces to improve the accuracy of the POPF results.In addition,the proposed sampling method can also improve the efficiency of solving the POPF model.