Research On Key Technologies Of Monte Carlo Simulation For Probabilistic Load Flow Calculation

With the development of Smart Grid and Energy Internet,uncertainties in power systems have greatly increased and the corresponding operation conditions have become more and more complex.Traditional deterministic power flow calculation methods cannot fully depict the states of power systems and stochastic methods have been studied as an effective complementarity of deterministic methods.Probabilistic load flow(PLF)is an efficient tool to analyze the stochastic characteristics of power system steady states.In PLF calculation,various uncertainties are taken into account and probability distributions of node voltages and load flow through lines are obtained which gives more useful information for the planning and operation of power systems.Broadly speaking,PLF calculation methods can be divided into three categories: analytical method,point estimate method and Monte Carlo Simulation(MCS).MCS is studied in this dissertation and the main contributions are summarized as follows:Firstly,three elements of PLF,including probabilistic load flow equations,input random variables and output random variables are analyzed and the PLF calculation model is established.Specifically,a probability distribution function is used to describe each input variable and a correlation matrix is adopted to describe dependences between different input variables.The essence of PLF calculation is solving nonlinear equations with random variables and the key techniques of MCS include sampling of input random variables,correlation control of sample from correlated input random variables,power flow calculation and evaluation of output random variables.Secondly,the sampling techniques of PLF is studied.Based on the concept of effective dimension,the effective dimension in the superposition sense and in the truncation sense of PLF are calculated and the results indicate that PLF is a low-dimensional problem.Therefore in order to improve the efficiency of MCS,QuasiMonte Carlo(QMC)which is based on low discrepancy sequences(LDSs)is used to obtain samples of input random variables.Then the PLF calculation method considering independent input random variables is studied and this method is compared with commonly used MCS methods.Simulation results show that the proposed method is correct and superior among various PLF calculation methods.Thirdly,the correlation control of samples from correlated input random variables is studied.The Genetic Algorithm combined with Local Search(GALS)technique and the multiple linear regression(MLR)technique are proposed to control correlations between samples.These two techniques are compared with popular correlation control techniques and the results show that the proposed techniques are correct and robust in handling correlated non-normal variables.Moreover,by combining sampling techniques and correlation control techniques,the PLF calculation method considering correlated input random variables is designed and the influences of different correlation coefficients,correlation modellings and sampling strategies on PLF results are analyzed.Fourthly,the evaluation method of output random variables is studied.Kernel density estimation(KDE)based on the diffusion partial differential equation is given.A fast KDE algorithm is implemented by means of Discrete Cosine Transform and Inverse Discrete Cosine Transform.Then the Diffusion-based Kernel Density Method(DKDM)is proposed to obtain probability distributions of output random variables and is compared with popular non-parametric methods.The proposed method accounts for both bandwidth calculation and boundary correction of KDE,reflects unimodal or multimodal distributions of data and accurately obtains probability distribution functions of output variables of PLF.Finally,PLF is used in actual power system calculations.The analysis of stochastic static voltage stability and the evaluation of transmission line utilization are studied.Based on traditional voltage stability calculation methods,uncertainties are introduced and the MCS method for stochastic static voltage stability analysis is given.QMC is adopted to improve the calculation efficiency and DKDM is used to obtain probability indices of voltage stability margins.The proposed method is used to analyze the voltage stability of a provincial power grid.With high-level power import,the stability of the system in the valley period of load is studied.Based on PLF the evaluation method of transmission line utilization is established.By studying the influences of variations of loads and failures of equipment on power systems,statistical indices of load flow and probability distributions of utilization rates are obtained.The proposed method is used to analyze the line utilization of a regional power grid which owns ultra-high voltage(UHV)transmission lines.The adaptation of lines with lower voltages to the connection of UHV lines in the early operation period of the UHV grid is studied.