# Power System Reliability

The Power System Reliability is the ability of a power system network to perform its function for a given time period under certain conditions. The main areas of an electric power system are generation, transmission, and distribution and the basic function of a modern electric power system is supplying its customers the cost-effective electric energy with a high degree of reliability. In the context of an electric power system, reliability may simply be expressed as concern regarding the system’s ability for providing a satisfactory amount of electrical power [I].

The history of power system reliability goes back to the early years of 1930s when probability concepts were applied to electric power system-associated problems [2,3]. Over the years, a large number of publications on the subject have appeared. Most of these publications are listed in Refs. [4-7].

This chapter presents various important aspects of power system reliability.

## Power System Reliability-Related Terms and Definitions

There are many terms and definitions used in the area of power system reliability. Some of these are as follows [8-11]: ^{•}

Forced outage. This is when a unit or a piece of equipment has to be taken out of sendee because of damage or a component failure.

- • Forced outage rate. This is (for equipment) expressed by the total number of forced outage hours times 100 over the total number of service hours plus the total number of forced outage hours.
- • Power system reliability. This is the degree to which the performance of the elements in a bulk system results in electrical energy being delivered to customers within the framework of stated standards and in the amount needed.
- • Scheduled outage. This is the shutdown of a generating unit, transmission line, or other facility, for inspection or maintenance, as per an advance schedule.
- • Forced outage hours. These are the total number of hours a unit or a piece of equipment spends in the forced outage condition.

- •
**Forced derating.**This is when a unit or a piece of equipment is operated at a forced derated or lowered capacity because of a component failure or damage. - •
**Mean time to forced outage.**This is analogous to mean time to failure (MTTF) and is expressed by the total of service hours over the total number of forced outages. - •
**Mean forced outage duration.**This is analogous to mean time to repair (MTTR) and is expressed by the total number of forced outage hours over the total number of forced outages.

## Power System Service Performance Indices

In the electric power system area, generally various service performance-related indices are calculated for the total system, a specific region or voltage level, designated feeders or different groups of customers, etc. [1]. Six of these indices are as follows [1,12].

**8.3.1 Index I**

This index is known as average service availability index and is defined by where

is the average service availability.

ct] is the customer hours of available sendee.

*Yi* is the customer hours demanded. These hours are expressed by the 12- month average number of customers serviced times 8760 hours.

**8.3.2 Index II**

This index is known as system average interruption duration index and is defined by where

*в _{2}* is the system average interruption duration.

*a _{2}* is the sum of customer interruption durations per year.

*Y**2* is the total number of customers.

**8.3.3 Index III**

This index is known as customer average interruption duration index and is defined by where

*0 _{i}* is the customer average interruption duration.

*y _{}}* is the total number of customer interruptions per year.

«з is the sum of customer interruption durations per year.

**8.3.4 Index IV**

This index is known as customer average interruption frequency index and is expressed by

where

*в _{4}* is the customer average interruption frequency.

*a*is the total number of customer interruptions per year.

_{4}*У л* is the total number of customers affected. It is to be noted that the customers affected should only be counted once, irrespective of the number of interruptions they may have experienced throughout the year.

**8.3.5 Index V**

This index is known as system average interruption frequency index and is expressed by

where

*в _{5}* is the system average interruption frequency.

*a _{5}* is the total number of customer interruptions per year.

*Уs* is the total number of customers.

**8.3.6 Index VI**

This index is concerned with measuring service quality (i.e., measuring the continuity of electricity supply to the customer) and is defined by [5,12]

where

*в _{6}* is the mean number of annual down hours (i.e., service outage hours) per customer.

(8760) is the total number of hours in one year.

*MTEI* is the mean time of electricity interruption.

*MTTFis* the mean time to failure (i.e., the average time between electricity interruptions).

**Example 8.1**

Assume that the annual failure rate of the electricity supply is 0.8 and the mean time of electricity interruption is 5 hours. Calculate the mean number of annual down hours (i.e., service outage hours) per customer.

In this case, mean time to failure (i.e., the average time between electricity interruptions) is

By substituting the calculated value and the specified values into Equation

(8.6), we get

Thus, the mean number of annual down hours (i.e., service outage hours) per customer is 3.998 hours.