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

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 obtained as follows:

$$
\epsilon \text{DNS} = \sum\_{i=1}^{n} (\text{DNS}\_i) \cdot p\_i \text{MW/year} \qquad \qquad \left[ L\_{\text{max}} \ge \text{Reserve} \right] \tag{5}
$$

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

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.

$$
\epsilon \text{ENS} = \sum\_{i=1}^{n} (\text{ENS}\_i) \cdot p\_i \text{ MW} / \text{year} \ [L\_{\text{max}} > \text{Reserve}] \tag{6}
$$

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

The ratio of expected energy not supplied ( ) to the system's total energy demanded (*TED*) can be found as

$$
\epsilon \text{ENS}\_{pu} = \frac{\epsilon \text{ENS}}{TED} \tag{7}
$$

**Figure 4.** *Load duration curve with energy not served.*

This ratio, in fact, is so small because of the small nature of the and the large nature of the *TED*, so, one can deduce another important reliability index called the *EIR*, which can be expressed as follows

$$EIR = \mathbf{1} - \epsilon E \text{NS}\_{pu} \tag{8}$$

• When the first unit ( ) is loaded according to the priority loading level #1, it will occupy the area (0 ) and shifts the new expected energy not supplied upward (i.e., above ). Therefore, the expected energy supplied by

• When the second unit (C2) is loaded according to the priority loading level #2, it will occupy the area ( ) and then shift the new expected energy not supplied upward above . Therefore, the expected energy supplied by

• When the third unit ( ) is operated according to the priority loading level #3, it will occupy the area and then shift expected energy not supplied above , and then the process ends, and the remaining expected energy not supplied will be above . As such, the expected energy supplied by

The following example shows an industrial compound case having two generating units, namely, 80 MW and 60 MW, which are assigned with a loading priority of "1" and "2," respectively. The expected energy supplied and the energy index of reliability are both to be determined, so as to optimize its energy

**Capacity (MW) FOR Loading priority** 80 0.06 1 60 0.03 2

The LDC is to be considered as a straight line connecting a maximum load of 160 MW and a minimum load of 80 MW (**Figure 6**). If the total operating time is

The solution hereto is to, first, calculate the expected energy not supplied before

a. The expected energy supplied (*ϵES*)by each unit in the system

any unit in the system is being loaded , i.e., at 0 MW, which is

b.The energy index of reliability (*EIR*) of the system

unit will be = .

*Load duration curve displaying units loading priority.*

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

unit will be = .

production with least possible operating cost.

**Example:** A power plant has the following data:

unit will be

**Figure 5.**

100 hours, evaluate the following:

**149**
