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This work studies the power quality impacts of electric transportation charging including electric buses (EBs) and electric vehicles (EVs) on distribution systems. The stochastic harmonic models for EBs and EVs and the stochastic models for their usage scenarios are built utilising the measured charging data. Based on these models, a power quality analysis method considering the charging uncertainties of EBs and EVs is proposed in this study and then their impacts on distribution systems are investigated. The Monte Carlo simulation is integrated into the proposed method to study the under voltage, overcurrent, voltage unbalance, transformer overload, harmonic current, voltage etc. caused by the stochastic charging of EBs and EVs. An actual distribution system acquired from Taiwan Power Company is taken as an example to validate the practicability of the proposed method. The test results of the proposed stochastic model are compared with those of the conservative model. [ABSTRACT FROM AUTHOR]