Distribution System Reliability Indices

$($a$)$ What are distribution system reliability indices and why are they used? List $5$ distribution reliability indices.

$($b$)$ Calculate the SAIDI and SAIFI for a distribution system serving $10,000$ customers and in which there were total of $5$ outages during the year, with relevant details of the outages provided in the table below.

# Customers Interrupted

Outage Duration $[$min$]$

$50$

$90$

$1000$

$90$

$2$

$175$

$2$

$120$

$1$

$30$