(Redirected from Reliability)

NOTE: All names, factors, equations, definitions, and applications discussed in this guide were taken from the IEEE Std 1366 2003 Edition.

# Introduction

This documentation provides the definitions for the 12 indices used in the reliability analysis of a distribution system. This guide also identifies the factors that go into the calculations for each reliability index. It is important to note that these indices are used to analyze distribution systems only. Generation and transmission systems are not looked at in this type of study.

# Definitions

This section provides definitions to assist the user in understanding the factors that affect index calculations.

1. Customer: A metered electrical service point for which an active bill account is established. Within GridLAB-D the customer list is generated by looking for all the meter and triplex_meter objects written in the .glm file.

2. Momentary Interruption: A single operation of an interrupting device that results in a voltage of zero at the node. Take one operation of a recloser for example. The single operation of a recloser opening then closing would be considered one momentary interruption if the operation resulted in interrupting one or more customers.

3. Momentary Interruption Event: An interruption lasting five minutes or less. For example, if a circuit breaker operates five times then holds within five minutes of the first operation, then those five momentary interruptions are considered one momentary interruption event.

4. Sustained Interruption: An interruption that last more than five minutes.

# Reliability Indices

## Index Factors

The factors listed below indicate the data needed to calculate the indices. All factors are collected over a single reporting period of one year.

• ${\displaystyle r_{i}}$ = restoration time, in minutes, for interruption event ${\displaystyle i}$
• ${\displaystyle N_{i}}$ = number of interrupted customers for each sustained interruption event
• ${\displaystyle N_{mi}}$ = number of interrupted customers for each momentary interruption event
• ${\displaystyle N_{T}}$ = number of customers for distribution area of interest
• ${\displaystyle L_{i}}$ = the total connected kVA load interrupted for the each sustained interruption event
• ${\displaystyle L_{T}}$ = the total connected kVA load served
• ${\displaystyle IM_{i}}$ = the number of momentary interruption operations for each momentary interruption event
• ${\displaystyle IM_{E}}$ = number of momentary interruption events
• ${\displaystyle CN}$ = total number of customers who have experienced a least one sustained interruption
• ${\displaystyle CNT_{(k>n)}}$ = total number of customers who have experienced more than n interruption events
• ${\displaystyle k}$ = number of interruption events experienced by an individual customer

## Sustained Interruption Indices

### SAIFI

SAIFI, the system average interruption frequency index, shows how often the average customer experiences a sustained interruption over a period of time. In GridLAB-D that period of time is a year. The equation below is used to calculate SAIFI.

${\displaystyle SAIFI={\frac {\sum N_{i}}{N_{T}}}}$

### SAIDI

SAIDI, the system average interruption duration index, shows the average duration of a sustained interruption for a customer during the reporting period. In GridLAB-D this index is given in minutes. The equation below is used to calculate SAIDI.

${\displaystyle SAIDI={\frac {\sum r_{i}N_{i}}{N_{T}}}}$

### CAIDI

CAIDI, the customer average interruption duration index, shows average time needed to restore service. This index is given in minutes in GridLAB-D. The equation below is used to calculate CAIDI.

${\displaystyle CAIDI={\frac {SAIDI}{SAIFI}}}$

### CTAIDI

CTAIDI, the customer total average interruption duration index, shows the total average time that customers who experienced an interruption were without power. This index is given in minutes in GridLAB-D. The equation below is used to calculate CTAIDI.

${\displaystyle CTAIDI={\frac {\sum r_{i}N_{i}}{CN}}}$

### CAIFI

CAIFI, the customer average interruption frequency index, shows average frequency of sustained interruptions experienced for customers who actually experienced a sustained interruption. The equation below is used to calculate CAIFI.

${\displaystyle CAIFI={\frac {\sum N_{i}}{CN}}}$

### ASAI

ASAI, the average service availability index, shows the fraction of time that a customer has received power during the reporting period. This index is given as a percentage within GridLAB-D. The equation below is used to calculate ASAI

${\displaystyle ASAI={\frac {N_{T}*(Numberofhours/year)-\sum r_{i}N_{i}}{N_{T}*(Numberofhours/year)}}}$

NOTE: There is no specification between regular years and leap years when calculating this index in GridLAB-D. The regular 8760 hours/year is used when calculated this index.

### CEMI${\displaystyle _{n}}$

CEMI${\displaystyle _{n}}$, the customers experiencing multiple interruptions index, shows the fraction of individual customers experiencing more than ${\displaystyle n}$ sustained interruptions over the total number of customers served. The equation below is used to calculate the index.

${\displaystyle CEMI_{n}={\frac {\sum CN_{(k>n)}}{N_{T}}}}$

### ASIFI

ASIFI, the average system interruption frequency index, is based on load instead of number of customers interrupted. This index is useful analyzing distribution systems made up primarily of industrial and commercial customers. If the system being analyzed had a homogeneous load distribution, then ASIFI would be the same as SAIFI. Also this index includes only interrupted load from sustained interruption events. The equation below is used to calculate the index.

${\displaystyle ASIFI={\frac {\sum L_{i}}{L_{T}}}}$

### ASIDI

ASIDI, the average system interruption duration index, is based on load instead of number of customers interrupted. Its use is the same a previously discussed in the section above. The equation below is used to calculate the index.

${\displaystyle ASIFI={\frac {\sum r_{i}L_{i}}{L_{T}}}}$

## Momentary Interruption Indices

### MAIFI

MAIFI, the momentary average interruption frequency index, shows the average frequency of momentary interruption. The equation below is used to calculate the index.

${\displaystyle MAIFI={\frac {\sum IM_{i}N_{mi}}{N_{T}}}}$

### MAIFI${\displaystyle _{E}}$

MAIFI${\displaystyle _{E}}$, the momentary average interruption event frequency index, shows the average frequency of momentary interruption events. The equation below is used to calculate the index.

${\displaystyle MAIFI_{E}={\frac {\sum IM_{E}N_{mi}}{N_{T}}}}$

### CEMSMI${\displaystyle _{n}}$

CEMSMI${\displaystyle _{n}}$, customers experiencing multiple sustained interruption and momentary interruption events, shows the fraction of individual customers who experienced more than ${\displaystyle n}$ interruption events of any kind over the total customers served. This index looks a how many events a customer experienced, regardless of whether they are sustained or momentary. The equation below is used to calculate the index.

${\displaystyle CEMSMI_{n}={\frac {\sum CNT_{(k>n)}}{N_{T}}}}$

# References

IEEE Std 1366-2003. IEEE Guide for Electric Power Distribution Reliability Indices. Available online at: www.ieee.org