The impact energy decay in a step-up chain containing two sections is numerically studied.There is a marked biphasic behavior of energy decay in the first section.Two sections close to the interface are in compression...The impact energy decay in a step-up chain containing two sections is numerically studied.There is a marked biphasic behavior of energy decay in the first section.Two sections close to the interface are in compression state.The degree of compression of the first section first decreases and becomes weakest at ＂crossing＂ time of biphasic behavior of energy,then increases.The further calculations provide the dependence of the character time on mass ratio（m1/m2）,where m1 and m2are the particle mass in the first and second section respectively.The bigger the α（α = [（？ m1-m2）/（？ m1＋ m2）]2 with？ = 1.345）,the bigger the energy ratio is.The multipulse structure restricts the transport of energy.展开更多
Studying the propagation of cascading failures through the transmission network is key to asses and mitigate the risk faced the energy system. As complex systems the power grid failure is often studied using some prob...Studying the propagation of cascading failures through the transmission network is key to asses and mitigate the risk faced the energy system. As complex systems the power grid failure is often studied using some probability distributions. We apply 4 well-known probabilistic models, Poisson model, Power Law model, Generalized Poisson Branching process model and Borel-Tanner Branching process model, to a 14-year utility historical outage data from a regional power grid in China, computing probabilities of cascading line outages. For this data, the empirical distribution of the total number of line outages is well approximated by the initial line outages propagating according to a Borel-Tanner branching process. Also for this data, Power law model overestimates, while Generalized Possion branching process and Possion model underestimate, the probability of larger outages. Especially, the probability distribution generated by the Poisson model deviates heavily from the observed data, underestimating the probability of large events (total no. of outages over 5) by roughly a factor of 10-2 to 10-5. The observation is confirmed by a statistical test of model fitness. The results of this work indicate that further testing of Borel-Tanner branching process models of cascading failure is appropriate, and should be further discussed as it outperforms other more traditional models.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61174007 and 61307041)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2013AL014)
文摘The impact energy decay in a step-up chain containing two sections is numerically studied.There is a marked biphasic behavior of energy decay in the first section.Two sections close to the interface are in compression state.The degree of compression of the first section first decreases and becomes weakest at ＂crossing＂ time of biphasic behavior of energy,then increases.The further calculations provide the dependence of the character time on mass ratio（m1/m2）,where m1 and m2are the particle mass in the first and second section respectively.The bigger the α（α = [（？ m1-m2）/（？ m1＋ m2）]2 with？ = 1.345）,the bigger the energy ratio is.The multipulse structure restricts the transport of energy.
文摘Studying the propagation of cascading failures through the transmission network is key to asses and mitigate the risk faced the energy system. As complex systems the power grid failure is often studied using some probability distributions. We apply 4 well-known probabilistic models, Poisson model, Power Law model, Generalized Poisson Branching process model and Borel-Tanner Branching process model, to a 14-year utility historical outage data from a regional power grid in China, computing probabilities of cascading line outages. For this data, the empirical distribution of the total number of line outages is well approximated by the initial line outages propagating according to a Borel-Tanner branching process. Also for this data, Power law model overestimates, while Generalized Possion branching process and Possion model underestimate, the probability of larger outages. Especially, the probability distribution generated by the Poisson model deviates heavily from the observed data, underestimating the probability of large events (total no. of outages over 5) by roughly a factor of 10-2 to 10-5. The observation is confirmed by a statistical test of model fitness. The results of this work indicate that further testing of Borel-Tanner branching process models of cascading failure is appropriate, and should be further discussed as it outperforms other more traditional models.
