**1. Introduction**

Reliability is one of the most important criteria, which must be taken into consideration during all phases of power system planning, design, and operation. A reliability criterion is required to establish target reliability levels and to consistently analyze and compare the future reliability levels with feasible alternative expansion plans. This need has resulted in the development of comprehensive reliability evaluation and modeling techniques [1–6]. As a measure of power system reliability evaluation in generation expansion planning and energy production, three fundamental indices are widely adopted and used.

The first reliability index is the loss of load expectation (*LOLE*) which denotes the expected average number of days per year during which the system is being on outages, i.e., load exceeds the available generating capacity.

The second index is the expected demand not supplied (*ϵDNS*) which measures the size of load that has been lost due to the severe outages occurrence.

The third index is the expected energy not supplied (*ϵENS*), which is defined as the expected size of energy not being supplied by the generating unit(s) residing in the system during the period considered due to capacity deficit or unexpected severe power outages [7, 8].

The status of a generating unit is described as morphing into one of the several

To investigate the effect of a unit on system generation reliability, it is impera-

Experience has shown that no machine is so reliable and dependable that it is

available in successful operating condition all the time. That means that the machine needs to be off service (out of service) for maintenance or it may be off due to some other problems affecting its operation (see **Figure 1**). As such, an off-service status includes planned outages and forced outages. Planned outages (scheduled outages) are the ones when (a) unit(s) is purposely shutdown or taken out of service for maintenance or replacement. Forced outages are defined as the ones when (a) unit(s) is out of service due to failure (also called unscheduled or unplanned outage). The last one is the most severe and important factor in power

Forced outage rate FOR ð Þ¼ sum of time unit is being out of service

*<sup>A</sup>*vailability AV ð Þ¼ Time unit is being in service

The two terms "availability and forced outage rate" represent the probability of successful and failure event occurrence. According to the probability theory, it is known that the product AV1 � AV2 represents the probability that both unit 1 and unit 2 are simultaneously in operation during a specified interval of time, and, also, AV1 � AV2 � AV3 means 1 and 2 and 3 are in operation at the same time, and FOR1 � FOR2 � FOR3 means that units 1, 2, and 3 are out of service in the same time. Also, AV1 � FOR2 means the probability that unit 1 is available (in service) and

For system generation reliability evaluation (including system expansion planning and/or systems interconnection), two models, namely, capacity model and load model, are needed; these are demonstrated and elaborated in the next two

FOR <sup>¼</sup> *<sup>t</sup>*<sup>1</sup> <sup>þ</sup> *<sup>t</sup>*<sup>2</sup> <sup>þ</sup> *<sup>t</sup>*<sup>3</sup>

Total time considered for unit service (1)

Total time considered for unit service (3)

Total time (2)

tive to know its probability of residing in each state as in **Figure 1**. Hence, the

following section introduces some basic probability concepts.

**3. Introduction to power system reliability evaluation**

**3.1 Availability (AV) and forced outage rate (FOR)**

system planning and operation and can be defined as

Also, availability can be defined as

and AV þ FOR = 1.

unit 2 is unavailable (out of service) in the same time.

sections.

**Figure 2.**

**145**

*Unit being available and unavailable.*

This can be seen in **Figure 2** as follows

possible states, as shown in **Figure 1**.

*Reliability Evaluation of Power Systems DOI: http://dx.doi.org/10.5772/intechopen.85571*

The implementations of these indices are now increasing since they are significant in physical and economic terms. Compared with generation reliability evaluation, there are also reliability indices related and pertinent to network (transmission and distribution) reliability evaluation.

There are two basic concepts usually considered in network reliability, namely, violation of quality and violation of continuity.

The first criterion considers violation of voltage limits and violation of line rating or carrying capacity, and the second criterion assumes that lines are of infinite capacity.

The transmission and distribution networks can be analyzed in a similar manner to that used in generation reliability evaluation, that is, the probability of not satisfying power continuity. This would give frequency and duration in network evaluation a simplification that is necessary. Provided the appropriate component reliability indices are known, it is relatively simple to calculate the expected failure rate (*λ*) of the system, the average duration of the outage (*r*), and the unavailability (*U*). To do this, the values of *λ*, *r* and *U* are required for each component of the system [9–11].
