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
& TECHNOLOGY (IJEET)
ISSN 0976 – 6545(Print)
ISSN 0976 – 6553(Online)
Volume 4, Issue 2, March – April (2013), pp. 372-392
© IAEME: www.iaeme.com/ijeet.asp
Journal Impact Factor (2013): 5.5028 (Calculated by GISI)
www.jifactor.com
IJEET
© I A E M E

373
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
%100x
IC
PLIC
RC
−
= (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
timedown
FOR (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
Up0 Down1

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 CXPpXP
1
'
)()( (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
CXPUXP
XP
−
−−
= (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.
Derated2 Down1
Up0

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 CP
CC
CC
CP
−
−
= (11)
)(*)( i
jk
ji
k CP
CC
CC
CP
−
−
= (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 txpLOLE
1
(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)
6
10×=
E
LOEE
UPM (16)
60×=
PL
LOEE
SM (17)
60×=
PL
LOEE
SM (18)
(19)
∑=
×
−=
n
k
kk
E
Ep
EIR
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
LoadDemandinMW
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
109
121
133
145
157
169
181
193
205
217
229
241
253
265
277
289
301
313
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
313
325
337
349
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
ProbabilityAvailable 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
ProbabilityAvailable 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
probabilityAvailable 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
probabilityAvailable 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
Capacity (MW)
Individual
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

388
(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

390
(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
REFERENCES
Journal Papers
[1] M. Tanriovena, Q.H. Wub,*, D.R. Turnerb, C. Kocatepea, J. Wangbl, “A new approach to
real-time reliability analysis of transmission system using fuzzy Markov Model”, Electrical
Power and Energy Systems 26, 2004 pp. 821–832
[2] Reliability Test System Task Force of the Application of Probability. Methods Subcommittee,
"IEEE Reliability Test System," on Power Apparatus and Systems, Vol. PAS-98, No.6, pp. 2047-
2054, Nov.lDec. 1979.
[3] Grigg, C ,Billinton, R.; Chen, Q.; et al “The IEEE Reliability Test System-1996. A report
prepared by the Reliability Test System Task Force of the Application of Probability Methods
Subcommittee” on IEEE Transactions on Power Systems,Volume: 14 , Issue: 3 Page(s): 1010-
1020 Aug 1999
[4] Hamoud, G., Billinton, R., “An approximate and practical approach to include uncertainty
concept in generating capacity reliability evaluation” IEEE transaction on power apparatus and
system, vol. PAS-100, no.3, March 1981.
[5] Roy Billinton., P.G.Harrington., “Reliability evaluation in energy limited generating capacity
studies”, IEEE transaction on power apparatus and system, vol.PAS-97,no.6, nov/dec 1978
[6] R. Allan and R. Billinton, “Power System Reliability and its Assessment. Part 1 Background
and Generating Capacity,” Power Engineering Journal, Vol. 6, No. 4, pp. 191-196, July 1992.
[7] R. Allan and R. Billinton,“Power System Reliability and its Assessment. Part 2 Composite
generation and transmission systems,” Power Engineering Journal,Vol. 6, No. 6, pp. 291- 297,
November 1992.
[8] D Devendra Mittal, Om Prakash Mahela and Rohit Jain, “Detection and Analysis of Power
Quality Disturbances under Faulty Conditions in Electrical Power System”, International Journal
of Electrical Engineering & Technology (IJEET), Volume 4, Issue 2, 2013, pp. 25 - 36, ISSN
Print : 0976-6545, ISSN Online: 0976-6553.
[9] Dr C.K.Panigrahi, P.K.Mohanty, A.Nimje, N.Soren, A.Sahu, R.K.Pati, “Enhancing Power
Quality and Reliability in Deregulated Environment”, International Journal of Electrical
Engineering & Technology (IJEET), Volume 2, Issue 2, 2011, pp. 1-11, ISSN Print :
0976-6545, ISSN Online: 0976-6553.
[10] D Devendra Mittal, Om Prakash Mahela and Rohit Jain, “Detection and Analysis of Power
Quality Disturbances under Faulty Conditions in Electrical Power System”, International Journal
of Electrical Engineering & Technology (IJEET), Volume 4, Issue 2, 2013, pp. 25 - 36, ISSN
Print : 0976-6545, ISSN Online: 0976-6553.
[11] Preethi Thekkath and Dr. G. Gurusamy, “Effect of Power Quality on Stand by Power
Systems”, International Journal of Electrical Engineering & Technology (IJEET), Volume 1,
Issue 1, 2010, pp. 118 - 126, ISSN Print : 0976-6545, ISSN Online: 0976-6553.
Books
[8]Billinton, R, and Allan, R.N, “Reliability evaluation of power systems”, New York,
Plenum Press, Second Edition, 1996.
[9]Billinton, R, and Allan, R.N, “Reliability evaluation of engineering systems", New York
Second Edition, 1983.
[10]Endrenyi.J., “Reliability Modeling in Electrical Power Systems", A Wiley –Inter science
Publication, 1978.

392
Theses
[11]Bagen Ph.d. thesis on “Reliability and Cost/Worth Evaluation of Generating Systems
Utilizing Wind and Solar Energy” University of Saskatchewan Saskatoon, Saskatchewan,
Canada pp.15-25. In the year 2005
[12] Fang Yang Ph.d. thesis “ A Comprehensive Approach for bulk Power System Reliability
Assessment” School of Electrical and Computer Engineering Georgia Institute of Tech.
pp.50-90.in the year 2007.
Proceedings Papers
[13] M.Fotuhi, A.Ghafouri, “Uncertainty Consideration in Power System Reliability Indices
Assessment Using Fuzzy Logic Method”, Sharif University of technology, IEEE Conference
on Power Engineering, 2007, Large Engineering Systems, Sharif University of Technology,
Tehran 10-12 Oct. 2007, Page(s): 305 - 309
[14]A Reliability Test System Task Force of the Application of Probability. Methods
Subcommittee, "IEEE Reliability Test System,"on Power Apparatus and Systems, Vol. PAS-
98, No.6, pp. 2047-2054, Nov./Dec. 1979.
[15] Fang Yang, A.P. Sakis Meliopoulos, “A Bulk Power System Reliability Assessment
Methodology”, 8th International Conference on Probabilistic Methods Applied to Power
Systems, IOWA University, Annes, September 16 2004.
[16]X. Zhu, “A New Methodology of Analytical Formula Deduction and Sensitivity Analysis
of EENS in Bulk Power System Reliability Assessment” IEEE Power Systems Conference
and Exposition, IEEEPES2006,(PSCE '06). Page(s): 825 - 831

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

Recomendados

Recomendados

Más contenido relacionado

La actualidad más candente

La actualidad más candente (20)

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

Similar a Vagueness concern in bulk power system reliability assessment methodology 2-3-4 (20)

Más de IAEME Publication

Más de IAEME Publication (20)

Último

Último (20)

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