**3.2 Capacity model**

The capacity model is known as the "Capacity Outage Probability Table (COPT)" that contains all capacity states (available and non-avoidable) in an ascending order of outage magnitude. Each outage (capacity state) is multiplied by its associated probability. If the system contains identical units, the binomial distribution can be used [12].

in the preceding sections are convolved (combined) in the process. The unit of the *LOLE* is in days per year (d/y). The *LOLE* evaluation method is expressed in the

By observing the above equation, the *LOLE* would be applicable if, and only if,

In power system planning another reliability index beside the *LOLE* may be required, so as to determine the size and magnitude of the load that has been lost due to severe outages (i.e., when ), Hence, the *ϵDNS* can be

Since power systems are in fact energy systems, the expected energy not supplied index may be deduced as per **Figure 4**. The *ϵENS* index is used in order to calculate energy sale, which is the real revenue for any electric company.

The ratio of expected energy not supplied ( ) to the system's total energy

*<sup>ϵ</sup>ENSpu* <sup>¼</sup> *<sup>ϵ</sup>ENS*

ð Þ *oi days=year L*½ � *max* . *Reserve* (4)

ð Þ� *DNSi pi MW=year L*½ � *max* . *Reserve* (5)

ð Þ� *ENSi pi MWh=year L*½ � *max* . *Reserve* (6)

*TED* (7)

following mathematical formula:

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

obtained as follows:

*LOLE* ¼ ∑

**3.5 Expected demand not supplied (***ϵDNS***)**

*ϵDNS* ¼ ∑

**3.6 Expected energy not supplied (***ϵENS***)**

*ϵENS* ¼ ∑

**3.7 Energy index of reliability (***EIR***)**

demanded (*TED*) can be found as

*Load duration curve with energy not served.*

**Figure 4.**

**147**

*n i*¼1

*n i*¼1

*n i*¼1 *ti* � *pi*

the maximum load ( ) exceeds the system reserve. Consider now:
