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

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 system planning and operation and can be defined as

$$\text{Foreed outage rate} \ (\text{FOR}) = \frac{\text{sum of time unit is being out of service}}{\text{Total time considered for unit service}} \tag{1}$$

$$\text{FOR} = \frac{t\_1 + t\_2 + t\_3}{\text{Total time}} \tag{2}$$

Also, availability can be defined as

$$\text{Availability } (\text{AV}) = \frac{\text{Time unit is being in service}}{\text{Total time considered for unit service}} \tag{3}$$

and AV þ FOR = 1.

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

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

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 sections.

**Figure 2.** *Unit being available and unavailable.*
