Analytical Calculation Of Probability Density Distribution Of Power Grid Reliability Index Considering Cut Sets Overlaping

In recent years, with the continuous enhancement of power grid structure, the normal operation mode of a single component failure, in general, it will not cause a greater impact on the power grid. However, in some special circumstances, multiple faults occur. For example, because of the bad weather(storms, snow, ice, etc.) caused by broken wires, towers collapsed, insulator flashover etc. that parts of a plurality of high voltage transmission line trip in succession. As large distribution system, it have many components, the structure is complex, especially the poor reliability of the system, it is very possible for component failure overlapping. These faults cause serious damage to the structure of power grid, causing large area power outages, and pose a serious threat to the safe and stable operation of the power grid. However, at present, the analytical method is used to calculate the probability distribution of reliability indices of power system. Therefore, considering the minimum cut set event occurrence, the power system reliability index random function is modeled, and the probability density distribution curve is obtained, which to give more scientific and accurate decision-making basis for the planning and operation personnel, has a very important significance.From the perspective of the reliability index of the probability density distribution, Based on the minimum cut set method and the network block theory, Considering the overlapping of cut set, In view of the analytical model of the reliability index of the large power grid and the distribution network, the analytical model of the reliability index and the reliability of the components is studied deeply.The main research contents of this paper include:Existing research for distribution network mainly based on single fault. In this paper, we consider the multi order fault, based on radial distribution network blocking, combined with the engineering practical a block may not appear two component failure,each sub block is equivalent to a first-order minimal cut sets. Consider the case of multiple minimal cut sets, under the assumption of the element life time and repair time are exponentially distributed, the number of failures in the time of [0,t] is poisson distribution.The frequency of the occurrence of the multiple minimal cut sets is derived from the poisson distribution. In view of the effect of the n cut sets on the n-1 cut sets, the frequency distribution of the independent occurrence of only n-1 minimal cut sets can be obtained if the effect is removed. Finally, through a series of rigorous mathematical derivation and theoretical analysis, the probability density distribution of the system outage frequency is obtained. Through the example analysis results show that for poor reliability or larger scale systems, consider the cut set overlap after assessment of closer to the practical engineering, avoiding the use of existing reliability analytical model underestimates the reliability of the system.Based on the assumption that the component failure time is subject to exponential distribution, The probability distribution of random occurrence time of each minimal cut set is derived by considering the order of the equivalent minimum cut sets. thus to determine the occurrence time and disappearance time of each minimal cut event, and then to form the system state time series. For each time period, the outage load point and the type of power cut are analyzed, and the analytical expression of the reliability index of distribution network is derived. By using the non parametric kernel density estimation method, the probability distribution of the reliability index is calculated by the expression of random function. By selecting with comparative method of evaluating proves consider cut sets overlap and order, the end result will be more to reflect the system actual operation risk situation, that can help planning and operation personnel quickly and intuitively grasp the overall characteristics of the system reliability level.Application of the cut set theory to the large power system with poor reliability and large number of components, and the phenomenon of cut set overlapping is reflected in the system fault component, find out all the non repeating components contained in the cut sets. Based on the assumption that the number of component failures follows the Poisson distribution, the parameters of the first order to the multiple order cut sets are derived. The number of occurrences of a single minimum cut set, which is obtained from the sample of this parameter, contains the number of times of occurrence of the minimum cut set and other minimal cut sets. In order to avoid the high evaluation result, this paper derives the probability distribution of the number of the actual occurrence times according to the occurrence of the failure event within one year, Finally obtain the frequency of occurrence of each failure event within one year, as well as the frequency of the system failure load. In the end, a numerical example shows the feasibility and effectiveness of the proposed method, which makes up for the shortcomings of the existing analytical method to solve the probability density distribution of reliability index.Since the minimal cut sets of the large power networks are mostly of multiple orders, this paper no longer assume that the minimum cut set event dwell time is subject to the sum of all the components in the minimal cut set and the exponential distribution of the parameters, But based on the cut set overlapping thought, combined with the theory, with elements as the research object, considering the fault components in order, the probability distribution of the time of failure of each component is derived, and the state time series of the large power system are formed. To derive the first minimum cut sets appear time and finally a minimal cut sets disappearance time, the dwell time of the cut sets can be obtained, and the analytic expression of the random function of the reliability index of the large power system is formed. Finally, reliability evaluation of RBTS reliability test system is carried out, and the comparison of the results from the analytical model and sequential Monte Carlo simulation verifies the validity of this proposed method.