**3.4 Loss of load expectation (***LOLE***)**

The *LOLE* risk index is the most widely accepted and utilized probabilistic method in power generation reliability evaluation for purposes of system expansion and interconnection. The two models, namely, the COPT and the LDC, mentioned

#### **Figure 3.**

*System load duration curve, where Oi is the ith outage(s) state in the COPT, ti is the number of times unit(s) is unavailable, Pi is the probability of this ith unavailable, and is the energy not supplied due to severe outage (s) occurrence.*

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

**3.2 Capacity model**

*Reliability and Maintenance - An Overview of Cases*

bution can be used [12].

**3.3 Load model**

magnitude.

(consumed).

system planning and operation.

pertinent captions related to it.

**Figure 3.**

**146**

*(s) occurrence.*

**3.4 Loss of load expectation (***LOLE***)**

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 distri-

The load model is known as the "load duration curve (LDC)" which is the most favorable one to be used instead of the regular load variation curve. There are some facts about the LDC that should be realized and can be summarized as follows:

a. The LDC is an arrangement of all load levels in a descending order of

b.The area under the LDC represents the energy demanded by the system

c. LDC can be used in economic dispatching, reliability evaluation, and power

d.It is more convenient to deal with than the regular timely load variation curve.

The above discussion for the load duration curve is depicted in **Figure 3** with all

The *LOLE* risk index is the most widely accepted and utilized probabilistic method in power generation reliability evaluation for purposes of system expansion and interconnection. The two models, namely, the COPT and the LDC, mentioned

*System load duration curve, where Oi is the ith outage(s) state in the COPT, ti is the number of times unit(s) is unavailable, Pi is the probability of this ith unavailable, and is the energy not supplied due to severe outage* 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 following mathematical formula:

$$\text{LOLE} = \sum\_{i=1}^{n} t\_i \cdot p\_i(o\_i) \, days / year \, [L\_{\text{max}} \ge Reserve] \tag{4}$$

By observing the above equation, the *LOLE* would be applicable if, and only if, the maximum load ( ) exceeds the system reserve. Consider now:
