Research On Probabilistic Load Flow Method Considering Dependence And Its Application

There are many uncertainties in the planning and operation of power systems. The large-scale integration of renewable energy sources and electric vehicles will bring more uncertainties. Probabilistic load flow (PLF) computation can evaluate the impacts of various uncertainties on the load flow operation characteristic of power system and obtain the probability statistics characteristic of node voltage and line flow. It is convenient for operating person to find the weak points and potential risks of system operation. It is a hot topic of current research. PLF has been developed for nearly40years and achieved abundant achievements. However, many issues still need further discussion and improvements, i.e., how to deal with the dependent power injections, how to handle the power injection without known probability distribution function, what are the impacts of dependence factor and integration of electric vehicle charging load (EVCL) and wind power on system load flow operation, etc. Therefore, the PLF method considering dependence and its application are chosen to be the research topics of the dissertation, including the following three aspects:impact of wind speed correlation (WSC) on the operation characteristic of distribution network, PLF method considering dependence among power injections, and analysis on load flow probabilistic characteristic of power system with EVCL and wind power.Impacts of WSC on the operation characteristic of distribution network are comprehensively investigated. The WSC model is established by inverse Nataf transformation. The influence of WSC on the operation of distribution network (including wind power output, node voltage, line flow, and network loss) and maximum installed capacity of wind power is researched by Monte Carlo simulation method (MCSM) based on simple random sampling and chance constrained programming. Simulation results show that WSC greatly impacts both operation characteristic of distribution network and maximum installed capacity of wind power, and considering WSC can guide the planning and operation of distribution network connected with wind power more reasonably.A PLF method based on polynomial normal transformation and Latin hypercube sampling (LHS) is proposed. This method uses the numerical characteristics (including statistical moments and Pearson correlation matrix) of input random variables to establish their probability distribution models by polynomial normal transformation, and then adopts MCSM based on LHS to obtain the numerical characteristics and probability distribution curves of node voltage and line flow. The simulation results show that the proposed method can not only overcome the shortcoming which it is difficult for MCSM to do PLF calculation accurately when the probability distribution functions of input random variables are unknown, but also handle the dependence among input random variables. The proposed method has the advantages of high accuracy, efficient computation and good robustness.A PLF method based on Copula theory and improved LHS is proposed. This method adopts Copula theory to establish the probability distribution model of dependent input random variables. Based on the discrete data of input random variable, a method to obtain its empirical cumulative distribution function and inverse function and an improved LHS are proposed. The proposed PLF method can deal with both linear and nonlinear dependence among input random variables flexibly. It is unconstrained by the marginal distribution type of input random variable. Moreover, this method overcomes the shortcoming that traditional LHS requires the cumulative distribution function of input random variable to be known. The simulation results demonstrate that the proposed method can evaluate the load flow operation characteristic of power system with wind power with high accuracy and efficiency. The proposed method is of some practical engineering value.A PLF method based on cumulant considering the dependence among input random variables using Cholesky decomposition is proposed. Firstly, the dependent input random variables are expressed as the linear combination of uncorrelated random variables based on Cholesky decomposition. Secondly, the cumulants of output random variables are calculated according to the linearized load flow equations and property of cumulants. Thirdly, the cumulative distribution curves of output random variables are obtained by Cornish-Fisher expansion. A method to obtain the cumulants of input random variable based on Monte Carlo sampling is proposed, which calculates the cumulants of input random variable by its samples. The proposed method not only overcomes the shortcoming that traditional PLF method based on cumulant can’t be directly applied to the circumstance in which the input random variables are dependent, but also solves the problem that the cumulants of some input random variables are hard obtained by conventional analytical methods. The influence of wind power penetration on the accuracy of the proposed method is analyzed. The simulation results verify the effectiveness and efficiency of the proposed method.The load flow probabilistic characteristic of power system with EVCL and wind power is researched. The main factors influencing the characteristic of EVCL are analyzed. According to the survey data of vehicles, the driving characteristic of electric vehicle drivers is modeled. Based on the coefficient of variation, the probabilistic models of EVCL, wind power output and system basic load are established. The operating states of line flow and node voltage under five different conditions are analyzed. Simulation results show that EVCL and wind power output have important impacts on load flow of power grid. EVCL curves with different control strategies have different dependence with basic load curve and further have different influence on system load flow.