Vagueness concern in bulk power system reliability assessment methodology 2-3-4

International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –

6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 2, March – April (2013), © IAEME

372

VAGUENESS CONCERN IN BULK POWER SYSTEM

RELIABILITY ASSESSMENT METHODOLOGY

Mr. N.M.G KUMAR1

, Dr.P.SANGAMEWARA RAJU2

1(Research scholar, Department of EEE, S.V.U. College of Engineering.&

Associate Professor, Department of EEE., Sree Vidyanikethan Engineering College) 2(Professor, Department of E.E.E., S.V.U. College of Engineering,

Tirupati, Andhra Pradesh, India)

ABSTRACT

This paper has illustrated the development of a technique for examining the reliability

associated with a generation configuration using an energy based index. The approach is based

upon the Expected Loss of Energy Approach and extends the technique to include the

consideration of energy limitations associated with generation facilities.Safe, secure and

uninterrupted electric power supply plays very important in the operation of the complex electric

power system that provides the efficient electrical infrastructure to supporting all economic,

community progress, social security and to live quality of modern living life. The large utility of

electricity has led to a high vulnerability to power failures. In this way, reliability of power

supply has gained focus and it is important for electric power system planning and operation.This

paper illustrates a method for evaluating the significance of reliability indices for bulk power

systems. The technique utilizes a continuous representation of a generating capacity model for

LOLP (Loss of Load Probability), LOLE (Loss of Load Expectation) and EENS (Expected

Energy Not Supplied) for single area. The objective paper is to describe a load and generation

model for analysis of generation reliability index. This paper illustrates a well known technique

for generating capacity evaluation which includes limited energy sources. The most popular

technique at the present time for assessing the adequacy of an existing or proposed generating

capacity configuration is the Loss of Load Probability or Expectation Method. As an energy

index in bulk power system reliability assessment is EENS (Expected Energy not supplied) is

of great significance for economic analysis and power system planning. This paper mainly

focuses on the following two categories among which one is the establishment of new reliability

index frame work that meets the developing power market and integrates reliability assessment

called Expected Energy Not Supplied (EENS). Here we are considering IEEE-Reliability Test

System (RTS).

INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING

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ISSN 0976 – 6545(Print) ISSN 0976 – 6553(Online) Volume 4, Issue 2, March – April (2013), pp. 372-392

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Total system Generation

Transmission System

Distribution System

Hierarchical Level 1



Keywords: Reliability assessment, power failure, FOR (Forced Outage Rate), EENS

(Expected Energy not Supplied), LOLP (Loss of Load Probability), and LOLE (Loss of Load

Expectation), analytical method, sensitivity analysis, bulk power system reliability, reliability

indices.

I. INTRODUCTION

Reliability is an abstract term meaning endurance, dependability, and good

performance. For engineering systems, however, it is more than an abstract term; it is

something that can be computed, measured, evaluated, planned, and designed into a piece of

equipment or a system. Reliability means the ability of a system to perform the function it is

designed for under the operating conditions encountered during its projected lifetime.

Reliability analysis has a wide range of applications in the engineering field. Many of these

uses can be implemented with either qualitative or quantitative techniques. Qualitative

techniques imply that reliability assessment must depend solely upon engineering experience

and judgment. Quantitative methodologies use statistical approaches to reinforce engineering

judgments. Quantitative techniques describe the historical performance of existing systems

and utilize the historical performance to predict the effects of changing conditions on system

performance [1].

Continuity of electric power supply plays very important in the modern days of

complex electric power system that describes the efficient electrical operation and economic,

community progress, social security and growth of country. The modern days of electric

power system is complex and is always subjected to disturbance around the clock, and is

generally composed of three parts (1) generation, (2) transmission, and (3) distribution

systems, all of which contribute to the production and transportation of electric energy to

customers. The reliability of an electric power system is defined as the probability that the

power system will perform the function of delivering electric energy to customers on a

continuous basis and with acceptable service quality. Power system reliability assessment, the

three power system parts are combined into different system hierarchical levels, as shown in

Figure 1.Hierarchical level 1 (HL1) involves the reliability analysis of only the generation

system, hierarchical level 2 (HL2) includes the reliability evaluation of the composite of both

generation and transmission systems, referred to as the bulk power system or the composite

power system, and hierarchical level 3 (HL3) consists of a reliability study of the entire

power system.

Fig. 1. Hierarchical levels for power system reliability assessment.



374

At the present stage of development, the reliability evaluation of the entire power

system (HL3) is usually not conducted because of the immensity and complexity of the

problem in a practical system. Power system reliability is assessed separately for the

generation system (HL1), the bulk power system (HL2), and the distribution system.

Reliability analysis methods for generation and distribution systems are well developed. Bulk

power system reliability assessment refers to the process of estimating the ability of the

system to simultaneously (a) generate and (b) move energy to load supply points.

Traditionally, it has formed an important element of both power system planning and

operating procedures. The main objective of power system planning is to achieve the least

costly design with acceptable system reliability. For this purpose, long-term reliability

evaluation is usually executed to assist long-range system planning in the following aspects:

[1, 11, 12]

(1)The determination of whether the system has sufficient capacity to meet system load

demands,

(2)The development of a suitable transmission network to transfer generated energy to

customer load points,

(3) A comparative evaluation of expansion plans, and

(4) A review of maintenance schedules for preventive and corrective

Power system operating conditions are subject to changes such as loadability

uncertainty, i.e., the load may be different from that assumed in design studies, and

unplanned component outages. To deliver electricity with acceptable quality and continuity to

customers at minimum cost and to prevent cascading sequences after possible disturbances,

short-term reliability prediction that assists operators in day-to-day operating decisions is

needed. These decisions include determining short-term operating reserves and maintenance

schedules, adding additional control aids and short lead-time equipment, and utilizing special

protection systems.

II. POWER SYSTEM ADEQUACY VERSUS SYSTEM SECURITY

Today’s new operating environment for electrical power system is to supply its

customers with electrical energy as economically as possible and with an acceptable level of

reliability. The prerequisite of reliable electric power supply enhance the significance of

dependence of modern society on electrical energy. Electric power utilities therefore must

provide a reasonable assurance of quality and continuity of service to their customers. In

general, more reliable systems involve more financial investment. It is, however unrealistic to

try to design a power system with a hundred percent reliability and therefore, power system

planners and engineers have always attempted to achieve a reasonable level of reliability at

an affordable cost. It is clear that reliability and related cost/worth evaluation are important

aspects in power system planning and operation reliability of a power system is defined as the

ability of power system to supply consumers' demand continuously with acceptable quality.

The concept of power-system reliability is extremely broad and covers all aspects of the

ability of the power system to satisfy the customer requirements. The perception of power

system reliability may be reasonable involves the security and adequacy and can be

recognized an healthy, Marginal (alert) and emergency (at risk) concerned and designated as

“system reliability”, which is shown in Fig. 2



375

Fig. 2 Subdivision of System Reliability

The Figure 2 represents two basic aspects of power system reliability depends on

system adequacy and System Security. Adequacy relates to the existence of sufficient

facilities within the system to satisfy the consumer load demand or operational constraints.

These include the facilities necessary to generate sufficient energy and the associated

transmission and distribution facilities required to transport the energy to the actual consumer

load points. Adequacy is therefore associated with static conditions which don’t include

system disturbance. Security relates to the ability of the system to respond to disturbances

arising within that system. Security is therefore associated with the response of the system to

perturbations it is subjected to. These include the conditions associated with local and

widespread disturbance of major generation, transmission, services etc. Another aspect of

reliability is system integrity, the ability to maintain interconnected operations. Integration is

violated causes an uncontrolled separation occurs in presence of severe disturbance (Block

out of grid or regional grid).Most of the probabilistic techniques presently available for power

system reliability evaluations are in the domain of adequacy assessment.[1-3]

There are two basically and conceptually different mythologies are present in the

power system reliability studies i.e. the analytical approaches and Monte Carlo simulation

approaches, used in power system reliability evaluation. This is shown is shown in below

Figure 3. An analytical approach represents the system by a mathematical model and

evaluates the reliability indices from this model using analytical solutions. The Monte Carlo

simulation approaches, however, estimates the reliability indices by simulating the actual

process and random behavior of the system and treats the problem as a series of real

experiments.

III. PROBLEM OF STATEMENT FOR BULK POWER SYSTEM RELIABILITY

The bulk power system therefore can be simply represented by a single bus as shown

in Figure 4, at which the total generation and total load demand are connected is normally as

SMLB(single machine connected to load bus) system in power system stability and security

studies. The main objective in HL-I assessment is the evaluation of the system reserve

required to satisfy the system demand and to accommodate the failure and maintenance of the

generating facilities in addition to satisfying any load growth in excess of the forecast. This

area of study can be categorized into two different aspects designated as static and operating

capacity assessment. Static assessment deals with the planning of the capacity required to

Analytical approaches

MCS Approaches

Basic Approaches



376

satisfy the total system load demand and maintain the required level of reliability. Operating

capacity assessment, on the other hand, is mainly focused on the determination of the

required capacity to satisfy the load demand in the short term (usually a few hours) while

maintaining a specified level of reliability. This thesis is focused on static capacity adequacy

evaluation and corresponding cost/worth assessment of generating systems

Fig. 4. System representation at HL-I

There is a wide range of power system reliability assessment techniques are used in

the generating capacity planning and operation [1]. Basically, generating capacity adequacy

evaluation involves the development of a generation model, the development of a load model

and the combination of the two models to produce a risk model as shown in Figure 5. The

system risk is usually expressed by one or more quantitative risk indices. In the direct

analytical method for generating capacity adequacy evaluation, the generation model is

usually in the form of a generating capacity outage probability table, which can be calculated

as a indices in HL-I evaluation simply indicate the overall ability of the generating facilities

to satisfy the total system demand. Generating unit unavailability is an important parameter in

a probabilistic analysis.

Fig..5 Conceptual tasks for HL- I evaluation

IV. RELIABILITY EVALUATION METHODS

Reliability techniques can be divided into the two general categories of probabilistic

and deterministic methods. Both methods are used by electric power utilities at the present

time. Most large power utilities, however, use a probabilistic approach.

Risk model

Generation model Load model

Total

System

Load

Total

generation



377

IV.I. Deterministic Methods Over the years, a range of deterministic methods have been developed by the power

industry for generating capacity planning and operating. These methods evaluate the system

adequacy on the basis of simple and subjective criteria generally termed as “rule of thumb

methods” [1]. Different criteria have been utilized to determine the system reserve capacity.

The following is a brief description of the most commonly used deterministic criteria without

considering energy storage capability.

1. Capacity Reserve Margin (CRM) In this approach, the reserve capacity (RC), which is normally the difference

between the system total installed capacity (IC =Σ Gi, G , is the capacity of Unit i in the

system) and the system peak load (PL), is expressed as a fixed percentage of the total

installed capacity as shown in Equation (1). This method is easy to apply and to understand,

but it does not incorporate any individual generating unit reliability data or load shape

information

%100xIC

PLICRC

−= (1)

2. Loss of the Largest Unit (LLU) In this approach, the required reserve capacity in a system is at least equal to the

capacity of the largest unit (CLU) as expressed in Equation (2). This method is also easy to

apply. Although it incorporates the size of the largest unit in the system, it does not recognize

the system risk due to an outage of one or more generating units. The system reserve

increases with the addition of larger units to the system.

RC ≥ CLU (2)

3. Percentage reserve margin method

In this method the reserve capacity is equal to or greater than the capacity of the

largest unit plus a fixed percentage of either the capacity installed or the peak load as shown

in Equations (3) and (.4). It also incorporates not only the size of the largest unit in the

evaluation but also some measure of load forecast uncertainty. It does not reflect the system

risk as the multiplication factor x (normally in the range of 0-15%) is usually subjectively

determined by the system planner.

RC= CLU + x*IC (.3)

RC= CLU + x*PL (.4)

PL is peak load in MW; IC is Installed capacity in MW

The main disadvantage of deterministic techniques is that they do not consider the

inherent random nature of system component operating failures, of the customer load demand

and of the system behavior. The system risk cannot be determined using deterministic

criteria. Conventional deterministic methods and procedures are severely limited in their

application to modern integrated complex power systems.



378

V. PROBABILISTIC METHODS

The benefits of utilizing probabilistic methods have been recognized since at least

the 1930s and have been applied by utilities in power system reliability analyses since that

time. The unavailability (U) of a generating unit is the basic parameter in building a

probabilistic generation model. This statistic is known as the generating unit forced outage

rate (FOR). It is defined as the probability of finding the unit on forced outage at some distant

time in the future. The unit FOR is obtained using Equation (5).

∑ ∑

∑+

=][][

][

timeuptimedown

timedownFOR (5)

The load model should provide an appropriate representation of the system load over

a specified period of time, which is usually one calendar year in a planning study. The

generation model is normally in the form of an array of capacity levels and their associated

probabilities. This representation is known as a capacity outage probability table (COPT) [1].

Each generating unit in the system is represented by either a two-state or a multi-state model.

Case 1: No Derated State [1] In this case, the generating unit is considered to be either fully available (UP) or

totally out of service (Down) as shown in Figure 6. The availability (A) and the unavailability

(U) of the generating unit are given by Equations (6) and (7) respectively

Fig. 6. Two state model for generating unit

Where λ= unit failure rate and µ = unit repair rate.

µλ

µ

+=A (6)

µλ

λ

+=U (7)

A Recursive Algorithm for Capacity Model Building

The capacity model can be created using a simple algorithm with a multi-state unit,

i.e. a unit which can exist in one or more derated or partial output states as well as in the fully

up and fully down states. The technique is illustrated for a two-state unit addition followed by

the more general case of a multi-state unit. The probability of a capacity outage state of X

MW can be calculated using Equation (8).

C))-(XP'*(U+(X)P'*U)-(I=P(X) (8)

µ

λ

Up 0

Down 1



379

Where the cumulative probabilities of a capacity outage level of X MW before and

after the unit of capacity C is added respectively. Equation (8) is initialized by setting P’(X) =

1.0 for X≤ 0 and P’(X)=0 otherwise.

Case 2: Inclusion of De-rated states

In addition to being in the full capacity and completely failed states, a generating

unit can exist in other states where it operates i.e reduced operating capacity state as shown in

Figure 7. Such states are called derated states. The simplest model that incorporates de-rating

state. This three-state model includes a single derated state in addition to the full capacity and

failed states. The Equation (9) can be used to add multi-state units to a capacity outage

probability table.

Fig. 7. Three state model for generating unit

∑=

−=n

t

i CXPpXP1

' )()( (9)

Where n- the number of unit states, Ci - Capacity outage state i for the unit being added pi -

Probability of existences of the unit state i

Case3: Recursive algorithm for unit removal Generating units are periodically scheduled for unit overhaul and preventive

maintenance. During these scheduled outages, the unit is available neither for service nor for

failure. This situation requires a capacity model which does not include the unit on scheduled

outage. The new model could be created by simply building it from the beginning using

Equation (10).

)1(

)('*)()('

U

CXPUXPXP

−

−−= (10)

In above equation P(X - C) = 1.0 for X < C

Case4: Procedure for Rounding Off Value[1-3] Bulk power generation system having large number of generating units of different

capacities, the table will contain several tens or hundreds possible discrete levels of capacity

outage levels. This outage levels can be reduced by grouping and rounding the capacity

outage into the possible discrete levels. The capacity outage table introduces unnecessary

approximations which can be avoided by the table rounding approach and reduces the

complexity. The capacity rounding increment used depends upon the accuracy desired. The

final rounded table contains capacity outage magnitudes that are multiples of the rounding

increment are calculated by equations (11), and (12). The number of capacity levels decreases

as the rounding increment increases, with a corresponding decrease in accuracy.

Derated 2

Down 1

Up 0



380

For rounding off the values we use the formula

Ck=capacity of higher (kth

) state,

Cj=capacity of lower (jth

) state,

Ci=capacity of variable (ith

) state

)(*)( i

jk

ik

j CPCC

CCCP

−

−=

(11)

)(*)( i

jk

ji

k CPCC

CCCP

−

−=

(12)

For all the states i falling between the required rounding states j and k

The Equation (11) is used for rounding off values for exact state and in between

states and Equation (12) is used for rounding off values for previous state The use of a

rounded table in combination with the load model to calculate the risk level introduces certain

inaccuracies. The error depends upon the rounding increment used and on the slope of the

load characteristic. The error decreases with increasing slope of the load characteristic and for

a given load characteristic the error increases with increased rounding increment. The

rounding increment used should be related to the system size and composition. Also the first

non-zero capacity-on-outage state should not be less than the capacity of the smallest unit.

VI. LOSS OF LOAD .ENERGY INDICES (LOLP, LOLE, EENS) LOSS OF LOAD

PROBABILITY [1]

The generation system model can be convolved with an appropriate load model to

produce a system risk index. The simplest load model that can be used quite extensively, in

which each day is represented by its daily peak load or weekly peak load duration. Prior to

combining the outage probability table it should be realized that there is a difference between

the terms 'capacity outage' and 'loss of load'. The term 'capacity outage' indicates a loss of

generation which may or may not result in a loss of load. This condition depends upon the

generating capacity reserve margin and the system load level. A 'loss of load' will occur only

when the capability of the generating capacity remaining in service is exceeded by the system

load level.

In this approach, the generation system represented by the COPT and the load

characteristic represented by either the DPLVC or the LDC are convolved to calculate the

LOLE index. Figure 8 shows a typical load-capacity relationship where the load model is

represented by the DPLVC or LDC, capacity outage exceeds the reserve, causes a load loss.

Each such outage state contributes to the system LOLE by an amount equal to the product of

the probability and the corresponding time unit. The summation of all such products gives the

system LOLE in a specified period, as expressed mathematically in Equation (13). Capacity

outage less than the reserve do not contribute to the system LOLE The main objective of

power system planning is to achieve the least costly design with acceptable system reliability.

For this purpose, long-term reliability evaluation is usually executed to assist long-range

system planning in the following aspects: (1) the determination of whether the system has



381

Fig. 8 Relationship between load, capacity and reserve

sufficient capacity to meet system load demands, (2) the development of a suitable

transmission network to transfer generated energy to customer load points, (3) a comparative

evaluation of expansion plans, and (4) a review of maintenance schedules [5, 6]. Power

system operating conditions are subject to changes such as load uncertainty, i.e., the load may

be different from that assumed in design studies, and unplanned component outages. To

deliver electricity with acceptable quality to customers at minimum cost and to prevent

cascading sequences after possible disturbances, short-term reliability prediction that assists

operators in day-to-day operating decisions is needed. These decisions include determining

short-term operating reserves and maintenance schedules, adding additional control aids and

short lead-time equipment, and utilizing special protection systems [7, 8].

∑=

=n

K

kk txpLOLE1

(13)

Where n is the number of capacity outage state in excess of the reserve, pk-

probability of the capacity outage Ok ,tk- the time for which load loss will occur, the values in

Equation (13) are the individual probabilities associated with the COPT. The equation can be

modified to use the cumulative probabilities as expressed in Equation (14).

)( 1

1

−

=

−×= ∑ kk

n

k

k ttPLOLE (14)

Where Pk is the cumulative outage probability for capacity outage Ok, tk- the time for

which load loss will occur. The LOLE is expressed as the number of days or number weeks

during the study period if the DPLVC or WPLVC is used. The unit of LOLE is in hours per

period if the LDC is used. If the time tk is the per unit value of the total period considered, the

index calculated by Equation (13) or (14) is called the loss of load probability (LOLP).

VII. LOSS OF ENERGY METHOD (LOEE) [1-3]

The standard LOLE technique uses the daily peak load variation curve or the

individual daily peak loads to calculate the expected number of days in the period that the

daily peak load exceeds the available installed capacity. The area under the load duration

curve represents the energy utilized during the specified period and can be used to calculate

an expected energy not supplied due to insufficient installed capacity. The results of this



382

approach can also be expressed in terms of the probable ratio between the load energy

curtailed due to deficiencies in the generating capacity available and the total load energy

required to serve the requirements of the system. The ratio is generally an extremely small in

figure less than one and can be defined as the ‘Energy Index of Unreliability’. It is more

usual, however, to subtract this quantity from unity and thus obtain the probable ratio

between the load energy that will be supplied and the total load energy required by the

system. This is known as ‘Energy Index of Reliability’ (EIR). The probabilities of having

varying amounts of capacity unavailable are combined with the system load as shown in

Figure 9. Any outage of generating capacity exceeding the reserve will result in a curtailment

of system load energy. In this method the generation system and the load are represented by

the COPT and the LDC respectively. These two models are convolved to produce a range of

energy-based risk indices such as the LOEE, units per million (UPM), system minutes (SM)

and energy index of reliability (EIR) [1]. The area under the LDC, in Figure 9, represents the

total energy demand (E) of the system during the specific period considered. When an outage

with probability occurs, it causes an energy curtailment of, shown as the shaded area in

Figure 9.

Fig. 9. Evaluation of LOEE using LDC

Ok= magnitude of the capacity outage, pk = probability of a capacity outage equal to Ok,,

Ek = energy curtailed by a capacity outage equal to Ok. The total expected energy curtailed or

the LOEE is expressed mathematically in Equation (15). The other indices are expressed in

Equations (16) to (19) respectively. [11]

K

n

k

k EpLOEE ×= ∑=1

(15)

610×=

E

LOEEUPM

(16)

60×=

PL

LOEESM

(17)

60×=

PL

LOEESM

(18)

(19)

∑=

×−=

n

k

kk

E

EpEIR

1

1



383

Algorithm for the Program 1. Read system data table.

2. Find Availability =A , =FOR=U.

3. Find binomial co-efficient = nCr .To find binomial co- efficient create a function factorial

4. Calculate Individual Probability(IP)pk=nCrx(p^(n-r)x(q^ r)

Initialize Cumulative probability Pk =1.0, CP=1-IP

5. Calculation of LOLE

i) Read the peak load data weekly or daily

ii) Read peak load= 2850 MW

iii) Calculate tk = (Ci – 2850) / (slope of the load line)

iv) Calculate LOLE = ∑ pk x tk Calculation of EENS

6. i)Calculation of Energy Available=Capacity available*8760

ii) Calculation of ELC = Total – Energy available

iii) Calculate EENS = ELC * pk

VIII. SYSTEM DATA

The RTS-96 generating system contains 32 units, ranging from 12 MW to 400 MW.

The system contains buses connected by 38 lines or autotransformers at two voltages, 138

and 230 kV shown in figure 10. The total installed generation capacity is 3405MW, The

reserve capacity is 555MW, The peak load of system is 2850MW, The Minimum load of

system is 1981MW, The average load of system is 2336MW, It gives data on weekly peak

loads in per cent of the annual peak load. The annual peak occurs in week 52

Figure 10 IEEE one area RTS-96[7]



384

Table 1 System Generation data for IEEE-RTS System

VIII.I Energy Required From Load Duration Curve The figure 11 to figure 14 shows the LDC and modified LDC.From the weekly load

data for one year the load duration curve is drawn with a peak load of 2850MW. The total

energy required for the corresponding data is calculated by finding out the area of load

duration curve Total energy required = Area of Load Duration Curve = 21154305units

Fig. 11. Original Weekly load duration Characteristics

Fig. 12. Modified weekly load patterns

Size (MW) 12 20 50 76 100 155 197 350 400

No. of Units 5 4 6 4 3 4 3 1 2

Forced

Outage Rate 0.02 0.10 0.01 0.02 0.04 0.04 0.05 0.08 0.12

MTTF (hours) 2940 450 1980 1960 1200 960 950 1150 1100

MTTR (hours) 60 50 20 40 50 40 50 100 150

International Journal of Electrical Engineer

6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 2, March

0

500

1000

1500

2000

2500

3000

1

13

25

37

49

61

73

85

Loa

d D

em

an

d i

n M

W

Modified Dailyload duration curve

Fig. 13.

Fig. 14.

VIII. II. FORMATION OF COPT

The below Table 2- 9 shows the capacity outage probability tables for the 24 bus

system. By using the generation d

calculate

(a) THE CAPACITY OUTAGE PROBABILITY TABLES

Unit-1.(1).No. of units =5 (2).Unit size (MW) =12, (3).Total capacity of system=60MW

International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976

6553(Online) Volume 4, Issue 2, March – April (2013), © IAEME

385

No of Days

85

97

10

9

12

1

13

3

14

5

15

7

16

9

18

1

19

3

20

5

21

7

22

9

24

1

25

3

26

5

27

7

28

9

30

1

31

3

Modified Dailyload duration curve

Fig. 13. Original Daily load patterns

Fig. 14. Modified daily load patterns

OPT 9 shows the capacity outage probability tables for the 24 bus

system. By using the generation data and the failure rate and the repair rates of each unit and

ROBABILITY TABLES

1.(1).No. of units =5 (2).Unit size (MW) =12, (3).Total capacity of system=60MW

ing and Technology (IJEET), ISSN 0976 –

April (2013), © IAEME

31

3

32

5

33

7

34

9

9 shows the capacity outage probability tables for the 24 bus

ata and the failure rate and the repair rates of each unit and

1.(1).No. of units =5 (2).Unit size (MW) =12, (3).Total capacity of system=60MW



386

Table 2 Capacity outage probability for unit- 1

No.of

Units

Capacity (MW) Individual

Probability

Cumulative

Probability Available Unavailable

5 60 0 0.903920 1.000000

4 48 12 0.092236 0.09608

3 36 24 0.003764 0.003844

2 24 36 0.000076 0.00008

1 12 48 0.0000007 0.000003

0 0 60 0 0.000002

Unit-2.(1) .No. of units =4 (2).Unit size (MW)=20, (3).Total capacity of system=80MW

Table 3 Capacity Outage Probability for unit -2

No. of

Units


Probability

Cumulative

Probability Available Unavailable

4 80 0 0.65651 1.00000

3 60 20 0.29160 0.3439

2 40 40 0.048600 0.0523

1 20 60 0.003600 0.0037

0 0 80 0.000100 0.0001

Unit-3 (1).No. of units =3(2).Unit size (MW) =197MW (3).Total capacity of system=591MW

Table 4 Capacity Outage Probability for unit-4

No. of

Units


probability

Cumulative

probability Available unavailable

3 591 0 0.857375 1.000000

2 394 197 0.135375 0.142625

1 197 394 0.007125 0.00725

0 0 591 0.000125 0.000125

Unit-4(1).No. of units = 4(2).Unit size (MW) =76 (3).Total capacity of system=304MW

Table.5 Capacity Outage Probability for unit-4

No. of

Units


probability

Cumulative


4 304 0 0.922368 1.000000

3 228 76 0.075295 0.077632

2 152 152 0.002304 0.002336

1 76 228 0.000031 0.000032

0 0 304 0 0

Unit-5 (1).No. of units =1 (2).Unit size (MW) =350 (3). Total capacity of system=350MW


No. of

Units


probability

Cumulative


1 350 0 0.92 1.00

0 0 350 0.08 0.08

Unit-6 (1).No. of units =3 (2).Unit size (MW) =100 3).Total capacity of system=300 MW



387


No. of

Units


probability

Cumulative

probability Available Unavailable

3 300 0 0.884736 1.000000

2 200 100 0.110592 0.115264

1 100 200 0.004608 0.004672

0 0 300 0.000064 0.000064

Unit-7 (1).No. of units =4MW (2).Unit size =155 MW(3).Total capacity of system=620MW


No.

of

Units


probability

Cumulative


4 620 0 0.849345 1.000000

3 465 155 0.1415577 0.150653

2 310 310 0.0088473 0.009095

1 155 465 0.0002476 0.000248

0 0 620 0.000025 0.000003

Unit-8 (1). No. of units = 6 (2).Unit size (MW) = 50, (3).Total capacity of system=300MW


No. of

Units


probability

Cumulative


6 300 0 0.9414801 1.000000

5 250 50 0.0570594 0.0585199

4 200 100 0.0014409 0.0014605

3 150 150 0.0000194 0.0000196

2 100 200 1.4*E-7 2.1*E-7

1 50 250 5*E-9 7*E-9

0 0 300 1*E-12 1*E-12

Unit-9 (1). No. of units =2 (2).Unit size (MW) =400(3). Total capacity of system=800MW


No. of

Units


probability

Cumulative


2 800 0 0.7744 1.000000

1 400 400 0.2112 0.2256

0 0 800 0.0144 0.0144



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(b)FORMATION OF MERGED TABLE OF TWO UNITS i.e. Table 1 & 2

Table 11 Combination of first two Table Merged data

capacity

unavailability

Individual

probability

0+0=0 0.593606244

0+12=12 0.06051655

0+24=24 0.00247007

0+36=36 0.00005041

0+48=48 0.00000051

0+60=60 0.00005041

20+0=20 0.26358331

20+12=32 0.02689626

20+24=44 0.00109781

20+36=56 0.00002240

20+48=68 0.00000023

20+60=80 0.00009039

40+0=40 0.04393055

40+12=52 0.00448271

40+36=76 0.00000373

40+48=88 0.00000004

40+60=100 0

60+0=60 0

60+12=72 0.00038205

60+24=84 0.00001355

60+36=96 0.00000028

60+48=108 0

60+60=120 0

80+0=80 0

80+12=92 0.00000922

80+24=104 0.00000038

80+36=116 0.00000001

80+48=128 0

80+60=140 0

C) ROUNDING OFF TABLE FOR ENTIRE SYSTEM – 8

Table 12 Rounding OFF

Capacity

unavailability

Individual

probability

0 0.4561740

200 0.22512662

400 0.19669503

600 0.0957801

800 0.02825976

1000 0.00936914

1200 0.00209105

1400 0.00039957

1600 0.00005308

1800 0.00000425

2000 0.00000020

2200 0.00000001



389

Table 13 Calculation of LOLE for the system data

Capacity

in service

Individual

probability tk LOLE

3405 0.4561740 0 -

3205 0.22512662 0 -

3005 0.19669503 0 -

2805 0.02825976 330.88(3.78%) 0.106821892

2605 0.00936914 1801.47(20.56%) 0.192629518

2405 0.00209105 3271.1(37.035%) 0.078100717

2205 0.00039957 4742.6(54.013%) 0.021262872

2005 0.00005308 6213.23(70.92%) 0.003764433

1805 0.00000425 7683.82(87.71%) 0.00001754

1605 0.00000020 - -

1405 0.00000001 - -

Total LOLE 0.40220896

The tables11 shows a merged table one for the first two units and then merge the nine units

we can get the more number of combinations of capacity unavailability and become complex

and get nearly 5000 states. So to reduce the complexity and uncertainty in table and load

duration curve can develop the rounding off the merged tables. After rounding off table with

a nearest discrete level (i.e 100MW, 200 MW…..etc) their probabilities in decrement order as

shown Rounding off tables. The evaluation of individually probability pk by using equations

(11) and (12)

Table 1.14 Summaries of EENS for the given system

Priority Unit capacity

(MW)

EENS

(MU)

Expected energy

output (MU)

1 60 20579.216 577.088

2 80 20147.421 1006.68

3 300 19078.294 2076.01

4 304 17889..2 3265.104

5 300 17045.876 4108.42

6 620 12881.556 8272.7

7 591 11387.849 9766.45

8 350 9880.602 11273.7

9 800 6.6220 21147.68



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(d) EXPECTED ENERGY NOT SUPPLIED

Table 1.15 Calculation of EENS for merged table

Capacity in

service

Individual

probability

ELC Expectation

(ELC*I.P)

0 0.45617401 0 0

0 0.22512662 0 0

0 0.19669503 0 0

24544800 0.07957801 0 0

21067800 0.0282597 0 0

21067800 0.00936914 86505 810.477

19315800 0.00220910 1838505 4061.45

17563800 0.00039957 3590505 1434.65

15811800 0.00005308 5342505 283.58

14059800 0.00000425 7094505 30.15

12307800 0.00000020 8846505 1.769

10555800 0.00000001 10598505 0

Total 6622.076

IX. CONCLUSIONS

As an energy index in bulk power system reliability assessment, EENS (Expected

Energy Not Supplied) is of great significance to reliability and economic analysis, optimal

reliability, power system planning, and so on. Based on the analytical formula, sensitivity

indices can help to identify the system “bottlenecks” effectively and provide essential

information for power system planning and operation. The technique can effectively alleviate

the question of “calculation catastrophe” and provide more detailed valuable information to

planners and designers, as well as important guidance to component maintenance strategies.

Probabilistic methods for the reliability assessment of the composite bulk power generation

and transmission in electric power systems are still under development. It concludes that the

capacity outage Probability tables, process of merging tables, LOLE and EENS for given

IEEE-RTS 24 bus system energy indices and load indices are

LOLP = 0.004022089.

EENS (PU) = 0.000313

UPM = 313.04.

SM = 139.41

EIR = 99.96%

The system peak load is 2850MW with a reserve of 555MW only, but the system risk

level will vary as variations in the units Forced outage rates and peak load variation.

Additional investments in terms of Design, construction, reliability, Maintainability and spare

parts provisioning can results in improved unit’s unavailability levels. The system risk level

can also reduces with good load forecasting techniques such as artificial intelligent

techniques causes reduced reserve level. The loss of load probability approach gives the

reliability of the system adequacy and security accurately. The test system will be a great help

for illustrating power system measures and gaining new insights into their meaning. One area

to explore involves the loss of load probability quantity. The COPT is not easily calculated

without the use of a digital computer and the table will identify the maintenance scheduling

or new unit addition may be started.



391

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392

Theses

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Vagueness concern in bulk power system reliability assessment methodology 2-3-4

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