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The paper analyzed time series of fault in four transmission and distribution systems for evidence of self-organized criticality (SOC). The detrended fluctuation analysis (DFA) of the time series shows prominent long-time correlations. Furthermore, the probability distribution of number of faults per day has a power law tail. Thus, the time series of power system fault seem consistent with SOC. Detailed analysis showed that time series of fault in transmission systems derives its SOC from cascading outage within power system and SOC of atmosphere system, while the time series of fault in distribution systems derive its SOC from that of atmosphere system. The roles that cascade outage play in SOC of the time series of fault in distribution systems remain unknown. Since extreme climate will be more intense and frequent with climate variation, the skewed distribution of power systems fault will be intensified as a consequence. Potential application using SOC feature of time series of fault can be developed to facilitate power systems adaptation to climate change in an economical way.