**4.2 Method of evaluation of the expected energy supplied**

The expected energy supplied ) by each unit available and being operated in the system can be evaluated by using the above concept of the expected energy not supplied ( ), as shown below:

$$
\epsilon \text{ES}\_{i} = \epsilon \text{ENS}\_{i-1} - \epsilon \text{ENS}\_{i} \text{ MWh/year} \tag{9}
$$

This method adopts a priority loading order, i.e., the generating units are loaded according to their least operating costs. The procedure applied is described above (see **Figure 5**).

The process of the above figure can be interpreted in the following steps:


## **Figure 5.**

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

The expected energy supplied (*ϵES*) by the generating units (existing in the system) can be evaluated by using the concept of the expected energy not supplied (*ϵENS*) described previously. In this method, several factors are taken into consid-

• Capacity-Availability Table (CAT): a table that contains all the capacity states of the units in the system arranged according to their ascending order of

The expected energy supplied ) by each unit available and being operated in the system can be evaluated by using the above concept of the expected energy not

This method adopts a priority loading order, i.e., the generating units are loaded according to their least operating costs. The procedure applied is described above

• The load duration curve is implemented, as it is the type of curve that is widely used in power system reliability evaluation and planning for its convenience and flexibility. It is derived from the ordinary load curve and hence can be defined as "the arrangement of all load levels in a descending order of

• The expected energy not supplied before any unit is operated is the

The process of the above figure can be interpreted in the following steps:

*ϵESi* ¼ *ϵENSi*�<sup>1</sup> � *ϵENSi* MWh*=*year (9)

• Loading priority levels: implies loading units in accordance to their least operating cost, i.e., operating, first, the most efficient and economical operating units (called the base units), then the more cost operating units (called the intermediate units), followed by the costliest operating units (called the peaker units), and so on. This means that the least cost operating units occupy the lower levels in the LDC, and the most expensive operating units

*EIR* ¼ 1 � *ϵENSpu* (8)

called the *EIR*, which can be expressed as follows

*Reliability and Maintenance - An Overview of Cases*

**4. Energy production evaluation methodology**

• Unit forced outage rate (FOR).

occupy the upper levels in the LDC.

supplied ( ), as shown below:

(see **Figure 5**).

magnitude."

**148**

total area under the LDC.

**4.2 Method of evaluation of the expected energy supplied**

• Load duration curve (LDC).

availabilities.

**4.1 Basic concept**

eration:

*Load duration curve displaying units loading priority.*


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 production with least possible operating cost.


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

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 100 hours, evaluate the following:

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

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

The solution hereto is to, first, calculate the expected energy not supplied before any unit in the system is being loaded , i.e., at 0 MW, which is

**Figure 6.** *Load duration curve for the given example.*

Therefore, the expected total energy not supplied after the second unit is being

**System capacity (MW) Availability** 0.06 0.03 = 0.0018 0.06 0.97 = 0.0582 0.94 0.03 = 0.0282 0.94 0.97 = 0.9118

**System capacity (MW) Availability** 0 0.06 80 0.94

As such, the expected energy supplied by the unit 80 MW can be

Hence, unit no. 1 (80 MW) will serve , and unit no. 2 (60 MW) will

Now, the final remaining expected total energy not supplied MWh for this system is 711.55 MWh, and the system energy index of reliability ( ) can be

**5. Applications of reliability indices in power system planning**

Optimal reliability evaluation is an essential step in power system planning processes in order to ensure dependable and continuous energy flow at reasonable costs. Therefore, the reliability index, namely, the loss of load expectation (*LOLE*), discussed in Section 3.4 along with the other complementary indices discussed in Sections 3.5–3.7 can be quite useful. Indeed, in order to substantiate and verify the applicability thereof, these indices have been applied to a real power system case study situated in the northern part of the Kingdom of Saudi Arabia. This power system is supposed to serve a major populated community with a potential future commercial and industrial load growth acknowledging the Kingdom's "Vision

added will be

*System CAT at priority order level no. 2.*

*System CAT at priority order level no. 1.*

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

serve .

evaluated as

**Table 2.**

**Table 1.**

evaluated as

2030."

**151**

Now start loading the units starting with the first unit (i.e., 80 MW as unit no. 1 for the priority order no. 1). This is shown in **Table 1**.

$$\begin{aligned} \epsilon ENS\_1 \, [0 \,\text{MW}] &= 12000 \cdot 0.06 = 720 \text{ MWh} \\\\ \epsilon ENS\_1 \, [80 \,\text{MW}] &= \left[ \frac{1}{2} \cdot 100 \cdot (160 - 80) \right] \text{(\$0 \,\text{-}94)} = 3760 \text{ MWh} \end{aligned}$$

Therefore, the expected total energy not supplied after the first unit is being added will be

Therefore, the expected energy supplied by the unit 80 MW can be evaluated as

$$
\epsilon \epsilon E S\_1 = \epsilon \text{MW} S\_0 - \epsilon T E N S\_1 = 12000 \text{ - MWh = 7520} \text{ } \text{MWh}
$$

Now, loading the second unit (i.e., unit of 60 MW as unit no. 2 for the priority order no. 2), the new CAT in **Table 2** will be

$$
\epsilon ENS\_2 \text{[10 MW]} \quad = 1200 \times 0.0018 = 21.6 \qquad \text{MWh}
$$

$$
\epsilon ENS\_2 \text{[160 MW]} \quad = 6000 \times 0.0592 = 349.2 \quad \text{MWh}
$$

$$
\epsilon ENS\_2 \text{[80 MW]} \quad = 4000 \times 0.0282 = 112.8 \quad \text{MWh}
$$

$$
\epsilon ENS\_2 \text{[140 MW]} = 250 \times 0.9118 = 227.95 \quad \text{MWh}
$$


#### **Table 1.**

*System CAT at priority order level no. 1.*


#### **Table 2.**

Now start loading the units starting with the first unit (i.e., 80 MW as unit no. 1

Therefore, the expected total energy not supplied after the first unit is being

Therefore, the expected energy supplied by the unit 80 MW can be

Now, loading the second unit (i.e., unit of 60 MW as unit no. 2 for the priority

for the priority order no. 1). This is shown in **Table 1**.

order no. 2), the new CAT in **Table 2** will be

added will be

evaluated as

**150**

**Figure 6.**

*Load duration curve for the given example.*

*Reliability and Maintenance - An Overview of Cases*

*System CAT at priority order level no. 2.*

Therefore, the expected total energy not supplied after the second unit is being added will be

$$
\epsilon \epsilon TENS\_7 = 21.6 + 349.2 + 112.8 + 227.95 = 711.55 \text{ MWh}
$$

As such, the expected energy supplied by the unit 80 MW can be evaluated as

$$
\epsilon ES\_2 = \epsilon TENS\_1 - \epsilon TENS\_2 = 4480 - 711.55 = 3608.45 \text{ MWb}
$$

Hence, unit no. 1 (80 MW) will serve , and unit no. 2 (60 MW) will serve .

Now, the final remaining expected total energy not supplied MWh for this system is 711.55 MWh, and the system energy index of reliability ( ) can be evaluated as

$$EIR = 1 - \frac{\epsilon THNS\_2}{\epsilon TENS\_0} = 1 - \frac{711.55}{12000} = 0.94$$
