Research On Novel Probabilistic Continuation Power Flow Method For Power Systems Considering Correlation Between Stochastic Variables

There are a large number of random factors in the operation and planning of power system.Wind power as the representative of renewable energy large-scale grid to make it face more uncertainty.In view of the shortcomings of the conventional continuation power flow method in dealing with the stochastic aspect of the system,especially for random load and wind power generation,This paper is based on the continuation power flow algorithm,a probabilistic continuation power flow(P-CPF)model is established based on the semi invariant method for power system considering correlation between stochastic variables.In the case of considering the influence of the correlation stochastic variables of the system,the statistics characteristics of 'cumulant' to describe randomness characteristics,two methods for obtaining the cumulant of random variables are given.That is derived from the characteristic function of the known distribution function or obtained according to the Monte Carlo method.Due to the probabilistic power flow can consider the influence of various uncertain factors on the distribution characteristics of the system.Therefore,the probabilistic power flow with the cumulant method is introduced to the prediction-vertical correction algorithm of CPF.Considering randomness of load growth in predictor step at each load level,the PV curve and voltage distribution characteristics of all load level are obtained.Secondly,the prediction-horizontal correction algorithm of CPF is run to the static voltage stability critical point,in order to be able to take into account the impact of the random variable correlation and the load forecast uncertainty.In this paper,a method for solving the critical point probability distribution based on the cumulant method is proposed.Based on the sensitivity matrix of the critical points on the random parameters,the random parameters variation feature is described by cumulant,according to the properties of homogeneous and additive properties of the cumulant,by calculating the each order cumulant of the stochastic distribution characteristic of the critical point.The probability density function of critical point is obtained by using Gram-Charlier series expansion.Lastly,based on the known distribution characteristics of voltage of partial load level and static voltage stability critical point,constrained least squares method is used to fit the distribution boundary of PV curve,obtain a PV profile that can account for the relevance of random variables.The proposed method is validated in a standard example of the IEEE39.It is concluded that the obtained PV profile is more reasonable.The Monte Carlo simulation method based on Nataf inverse transformation is used as the benchmark.The conclusion is that the method is much more efficient.By using this model,we can not only get the PV distribution domain considering the relevance of random variables,but also the static voltage stability critical point probability distribution characteristics can be obtained.Achieve the static voltage stability probability assessment of the system.