The intermittency and variability of permeated distributed generators (DGs) could cause many critical security and economy risks to distribution systems. This paper applied a certain mathematical distribution to imitate the output variability and uncertainty of DGs. Then, four risk indices—EENS (expected energy not supplied), PLC (probability of load curtailment), EFLC (expected frequency of load curtailment), and SI (severity index)—were established to reflect the system risk level of the distribution system. For the certain mathematical distribution of the DGs’ output power, an improved PEM (point estimate method)-based method was proposed to calculate these four system risk indices. In this improved PEM-based method, an enumeration method was used to list the states of distribution systems, and an improved PEM was developed to deal with the uncertainties of DGs, and the value of load curtailment in distribution systems was calculated by an optimal power flow algorithm. Finally, the effectiveness and advantages of this proposed PEM-based method for distribution system assessment were verified by testing a modified IEEE 30-bus system. Simulation results have shown that this proposed PEM-based method has a high computational accuracy and highly reduced computational costs compared with other risk assessment methods and is very effective for risk assessments.
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