Reliability modeling and evaluation of sulaimani erbil electrical power system

1

Abstract-The work presented in this paper deals with the reliability
evaluation of Sulaimani-Erbil electrical Power System by two
different techniques, minimal cut set and disjoint technique.
Computer program is written in Basic language in order to
implement tie set and cut set algorithms for the evaluation of the
unreliability index of the power network.

Keywords-Reliability Modeling, Reliability indices, Graph Theory,
Disjoint Technique.

I. INTRODUCTION
ower system is always consists of a large number of
components which are interconnected in some
purposeful way. The reliability of a power system
depends on the reliability of its components as well as its
configuration. In system reliability studies, the goal is to
predict suitable reliability indices for the system based on the
component failure data and system design [1]. A complete and
accurate reliability model should be able to represent the
variation characteristics of the system interested for all aspects
of performance. Selection of the actual form and the type of the
reliability model depends upon a large number of factors which
should be carefully examined during the formulation process of
the reliability analysts. The first factor which influences the
selection of the reliability model is the system functional
arrangement and the second factor arises from the types of
variation which may take place in the performance aspects of
the various elements of the system [2].In general, the system is
of two types (depending on the structure of the system), a

simple structure system and a complex structure system.
The purpose of investigating the reliability for the area of
Sulaimani-Erbil electrical power system is that: i) This system
has been operated for more than 10 years as a split network due
to the political and economical sanction against the last regime
of Iraq in the Kurdistan region. ii) UN agencies were
responsible to develop the network due to 986 UN resolution of
oil for food program, and the agency UNDP was in charge of a
large number of rehabilitation program and iii) It was necessary
to identify the system maintenance requirements and to specify
the weak points of the network and to list their priorities.

II. DESCRIPTION OF SULAIMANI-ERBIL ELECTRICAL
POWER SYSTEM
Prior to about 1990, there were twelve 132 kV tie lines to the
region from the other Governorates of Iraq. Now, there are
only two 132 kV circuits which connect Dohuk Governorate to
Mosul region. At present, there is no any connection to Erbil


and Sulaimany Governorates from the national grid [3]. The
energy supply to all three Governorates is restricted due to the
shortages of power supply and even the available supply is not
reliable due to the present network situation. The power
network of Governorates Erbil and Sulaimani had been cut off
from the national grid. The power supply of the two
Governorates had to rely on the two hydropower stations at
Derbandikhan and Dukan, located in the Sulaimani region with
the only one 132 kV line connecting Dohuk with the original
national grid. However, the electrical power supply of this line

was also limited, infrequent and unreliable. The capacities of
the power stations installed in Dokan and Derbandikhan are (5
x 80 MW) and (3 x 83 MW) respectively, which are
insufficient to meet the power demand [4]. To improve the
condition of power supply for these three governorates, a 29
MW Diesel power plant was installed in each governorate
(Sulaimany, Erbil and Dohuk) [5].
The Sulaimani-Erbil 132 kV transmission system consists of 8
lines whose length varies between 25 and 99 km.

III. TIE SET AND CUT SET METHOD

A tie set of a network is a subset of edges (representing
components) that constitutes a path from input to output. If all
the components of the tie set operate, the overall system
operates properly. If no node is passed through by more than
one time when tracing the tie set, such a tie set is called the
minimal tie set. In other words, if any one of the components of
a given minimal tie set is removed, the remaining set is no
longer a tie set. A cut set is a subset of system components
which, when failed, causes failure of a system. In terms of a
reliability network, the definition can be interpreted as a set of
components which must fail in order to disrupt all paths
between the input and output of the reliability network. The
system reliability can be determined from the tie set and the cut
set but the cut set method is more powerful than the tie set
method in evaluating the reliability of a system for the
following two reasons [6-7]:
1) It can be easily programmed with digital computer for the
fast and efficient solution of any general network.

2) The cut set is directly related to the modes of system failure
and therefore it is easy to identify the distinct and discrete
ways in which a system may fail.
The minimum subset of any given set of components which
can cause system failure is known as a minimal cut set. A
minimal cut set is a set of system components which, when
failed, cause failure of the system but when none of the
component of the set fails, the system will not be failure [7].
Asso R. Majeed,

Ghamgeen Izat Rashed, S.J.Cheng, Senior Member, IEEE
Reliability Modeling and Evaluation of
Sulaimani – Erbil Electrical Power System
P
1-4244-0493-2/06/$20.00 ©2006 IEEE.
2
Table 1 Networks information
No. of cut
sets
No.
Network
No .of nodes
No. of braches
No .of Paths
No .of minimal paths
1
st
order
2
nd

order
3
rd
order
Reliability
Unreliability
1 Fig.2 6 9 13 13 0 2 17 0.999797 0.000203
2 Fig.3 8 12 26 26 0 3 35 0.999695 0.000305
3 Fig.4 12 20 164 150 0 2 39 0.999797 0.000203

The following definition of minimal cut set is also appropriate:
If {A} is a cut set and no subset of {A} forms a cut set, then
{A} is a minimal cut set [8].

IV. APPLICATION OF MINIMAL CUT SET

The following example is used to illustrate the algorithm
which can be used to obtain the minimal cut sets.
Considering the bridge type network shown in Fig.(1-a)[7],the
minimal tie set is made up of
components:
3524514231
X and ,, XXXXXXXXX
, as
shown in Fig.(1-b), which means that the minimal tie set can be
represented by Eqn.1:
) 1 .() ()()()(
3524514231
XXXXXXXXXXS ∩∩∪∩∩∪∩∪∩=
Similarly, the minimal cut set is made up of components,

3524514321
X and ,, XXXXXXXXX
, as shown in
Fig.(1-C). Thus, it can be represented by Eqn.2
) 2 () ()()()(
3524514321
XXXXXXXXXXS
′
∩
′
∩
′
∪
′
∩
′
∩
′
∪
′
∩
′
∪
′
∩
′
=

Therefore, employing the minimum-cut-set method, the
unreliability of the system is represented by Eqn,3:

)()(
)()()()()(
3121
43214321
EEPEEP
EPEPEPEPEEEEPQ
∩−∩−
+++=∪∪∪=
)()()()(
43423241
EEPEEPEEPEEP
∩−∩−∩−∩−
)()()(
431421321
EEEPEEEPEEEP
∩∩+∩∩+∩∩+
)3) (()(
4321432
EEEEPEEEP
∩∩∩−∩∩+

where
211
)( XXEP
′
∩
′
=

432

)( XXEP
′
∩
′
=

4513
)( XXXEP
′
∩
′
∩
′
=

3524
)( XXXEP
′
∩
′
∩
′
=

542143213524514321
XXXXXXXXXXXXXXXXXXQ
′′′′
−
′′′′
−

′′′
+
′′′
+
′′
+
′′
=

)4 ( 2
54321435243515321
XXXXXXXXXXXXXXXXX
′′′′′
+
′′′′
−
′′′′
−
′′′′
−
From this example, it is able to describe the algorithm used to
form the minimal cut set as follows:
1) Deduce all minimal paths.
2) Construct an incidence matrix that identifies all component
in each path.
3) If all elements of any column of the incidence matrix is
non-zero, the component associated with that column
forms a first order cut.
4) Combine two columns to form a second order cut.
Elimination any cut containing first order cuts to give the

second order minimal cuts.
5) Repeat step (4) with three columns at a time to give third
order cuts and to eliminate any cuts containing first and
second order cuts; and
6) Continue this procedure until maximum order of cut has
been reached.
Only the first, the second and the third order cut sets are
considered in the current investigation.
Two basic approximations are used to deal with the
evaluation of power system reliability by the minimal cut set:
1) The first approximation is that Eqn.3 is a precise
representation of the minimal cut set. However, as this is a very
complicated equation, it is approximated by the following
simplified form:
)5) (()()()(
4321
EPEPEPEPQ +++≅

For this particular case the following representation can be
obtained:
)6 (
3524514321
QQQQQQQQQQQ +++=

If the terms in the right hand side of Eqn.6 are identical, the
system unreliability becomes:
)7( 22
32
QQQ
sys

+=

2) The cut sets of high orders are neglected because the
probability of their occurrence becomes relatively very small.
Different networks shown in Fig.2-4 are solved using the
above mentioned method. The results are given in table 1.
1 3
2 4
5


(a)

1 3
2 4
1 45
2
5 3



(b)

1
2
3
4
1
4
5

2
3
5


E1 E2 E3 E4
(c)
Fig.(1) Reliability block diagrams showing bridge arrangement and its
equivalents: a) bridge-type network; b) equivalent minimum-tie set
diagram; c) equivalent minimum-cut set diagram


3

Read Input Data :
1-Number of Nodes
2 -Number o f Branches
3-Incidence an d
Connectio n Ma trix
Subroutine Pr ogram f or
find ing all pa ths in th e system
Subroutine Pr ogram f or
finding minim al paths in the
system
Subroutine Pr ogram f or
constructing incide nce matrix
and from it minimal cutsets
finding for the system
Subroutine Pr ogram f or
finding reliability of the

system by using
approxima tion metho d
Printin g Resul ts


Fig.5 Program Flowchart for Reliability
Evaluation by using cut set method

V.
CONNECTION AND INCIDENCE MATRIX

The connection matrix is defined as an analytic
correspondence of the system configuration and has a size
of
kk ×
.
The incidence matrix identifies all components between any
two nodes.
VI. SOFTWARE DEVELOPMENT

For the purpose of reliability evaluation, a software package
programmed in BASIC language is developed. The flowchart
of the program is shown in Fig.5.
The program consists of two parts. The first part makes the
qualitative evaluation and second part makes the quantitative
evaluation.
In the first part the software package, the following steps are
included:
1-Enter the number of nodes and the number of branches of the
system.

2-Enter the connection matrix and the incidence matrix which
can be used to identify each element between two nodes.
3-Establish the subprogram for finding all paths in the network.
4-Establish the subprogram for finding all minimal paths of the
network from the paths obtained in step 3 by removing all
paths that have a path sub set.
5-Construct the incidence matrix which can be used to identify
all components in each path.
6-Form the minimal cut set from the incidence matrix obtained
in step 5.
In the second part of the software package, the quantitative
steps are performed for reliability evaluation of the system
from the minimal cut set by use of the approximation method
mentioned above.


VII. Disjoint Technique
In a generalized network, the terminal pair reliability
expression is usually derived from the logic diagram of the
system by the following two steps [9]:
1) All minimal paths or cut sets are determined.
2) The system success / failure function is changed into
reliability expression using probability theory, Boolean algebra
and graph theory.

VIII. EXCLUSIVE OPERATOR

Exclusive operator
E
is a kind of operation of Boolean

expression which is defined as follows:
)8 ()(
ii
XXE
≡

) 9 ) (( )()() (
12121121
mmm
FEFFFFEFFEFFFE
−
∪∪∪≡

)10) (() ()() (
2121 mm
FEFEFEFFFE ≡∪∪∪

For a particular case, if
ii
XF
=
, for all
i
, the above
relationship can be simplified to the following form:
)( )()() (
12121121 mmm
XEXXXXEXXEXXXE
−
∪∪∪=

)11 (
121211 mm
XXXXXXX
−
∪∪∪=

)() ()() (
2121 mm
XEXEXEXXXE =∪∪∪

)12 (
21 m
XXX=

It can be seen from Eqn.11 that all conjunctive terms are
mutually disjoint.

IX. Reliability Evaluation
This method makes use of some of the elementary operators
of Boolean algebra. The starting point can be either the system
–success function or the system-failure function. The choice
between of these two depends on the number of paths or cut
set. The method consists in applying exclusive operator
on
)( functionsucesssystemS −−
, which results in all its
terms being mutually disjoint [9].
The following assumptions are used in this method [9]:

4n2
n3
n1
1
2
3
5
6
7
n5
n4

n6
8
9
4

Fig.2 Network No.1


n2
n5
n1
n3
n6
n4
n7
n8
1
2
68
12
11
97
3
510
4

Fig.3 Network No.2


n12

n9 n4
n11
n2
n1
n3
n7
n6
n5
n8
n10
20
12
11
2
1
3
5
6
7
8
16
15
14
13
19
17
10
9

Fig.4 Network No.3

4
n1
n2
n3
n4
n5
X4
X3X1
X2
X5
X7
X6

Fig.6 A general non series parallel network
X1
x4
X3
x2
x5


Fig.7 bridge-type network
1- All nodes are perfectly reliable.
2- Each branch of the overall network takes either of the
following two states: good or bad.
3-The network is free from self-loops and directed cycles.
Steps used for the calculation of the terminal pair reliability
are given below:
1) The system success function is written as:
)13 (

21 m
TTTS ∪∪∪=

where
i
T
represent the minimal paths of the network.
Eq.13 is directly obtained by processing of determining
paths.
2) For each
i
T
,
mi ≤<
1
,
i
F
is defined to be the union of
all predecessor terms
121
, ,,
−i
TTT
in which any literal
that is presented in both
i
T
and any of the predecessor
terms is deleted from those predecessor terms, i.e.

121

−
∪∪∪=
ii
TTTF
for each literal
of
)14 (1
→
i
T

In fact, the literals of
i
T
are assigned the Boolean value of 1
and this value is substituted in any predecessor term in which
they occur. The resulting function
i
F
can be simplified by
using standard Boolean reduction identities as shown in
Appendix (A).
3) Using Exclusive operator
E
, to obtain:
)15 () (int)(
2
1 i

m
i
i
FETTdisjoS
U
=
=

4) All logical variables are changed into their analogue
probability variables to get the reliability expression (all
terms are mutually exclusive).
)16 (,int)(
iiii
qXpXdisjoSR →
′
→=

If source –terminal cut set is used instead of the paths in a
particular system, the system failure function is obtained and
can be processed similarly to derive system unreliability
expression.

X. Application of Disjoint Technique

Application One:

Consider the general non series parallel network shown in
Fig.6 [9]:
1- The cut set for the above network
is

753265314326547621
,,,,, XXXXXXXXXXXXXXXXXX
,thus the system
unreliability function is give by Eqn. 17:
) 17 (
753265314326547621
XXXXXXXXXXXXXXXXXXS
′′′′
∪
′′′′
∪
′′′
∪
′′′
∪
′′
∪
′′
=
′

By applying Eqn.14, the definition of exclusive operator and
Eqn.15,
i
F
,
)(
i
FE
and

int)(disjoS
can be calculated as
follows:
The representation of the unreliability is given as follows:
++++++=
61432127176542117621
()()( ppqqqqppppqqqpqpqqqqQ

)18) (()
641753274265316751
pppqqqqpppqqqqqPPP ++

Application Two:

To use system success function for finding the reliability
expression of a system, consider the bridge shown in Fig.7:
The minimal paths for this bridge are:
3525414231
,,, XXXXXXXXXX
and the system reliability
can be expressed as:
3525414231
XXXXXXXXXXS ∪∪∪=

By applying Eqn.14, the definition of exclusive operator and
Eqn.15,
i
F
,
)(

i
FE
and
int)(disjoS
are found as follows:
The reliability expression is as follows:
41352235413113131
)()( qqpppqqpppqpqppppS ++++=

If all components are assumed to be identical, the reliability
expression is given by the followings:
2323322
qpqpqpqppS ++++=

Assuming the component reliability 0.99 and applying the two
methods mentioned above, the system reliability for the solved
two examples is obtained and given in table 2.

i
F

)(
i
FE

)(
ii
FET

212

XXF
′′
=

211
XXX
′
∪

)(
21176
XXXXX
′
∪
′′

7213
XXXF
′
∪
′′
=

)(
2117
XXXX
′
∪

))((

2117654
XXXXXXX
′
∪
′′′

)(
57614
XXXXF
′
∪
′′
∪
′
=

675161
XXXXXX
′
∪

)(
675161432
XXXXXXXXX
′
∪
′′′

7425
XXXF

′
∪
′
∪
′
=

742
XXX

)(
7426531
XXXXXXX
′′′′

4616
XXXF
′
∪
′
∪
′
=

641
XXX

)(
6417532
XXXXXXX

′′′′

i
F

)(
i
FE

)(
ii
FET

312
XXF =

311
XXX
′
∪
′

)(
31131
XXXXX
′
∪
′

233

XXF ∪=

23
XX
′′

)(
23541
XXXXX
′′

414
XXF ∪=

41
XX
′′

)(
41352
XXXXX
′′

5
It can be seen from table 2 that the approximation method
gives the upper bound value of the reliability since the
probability of the intersected events is ignored, while the
disjointed reliability expression gives more accurate value. The
error is included in the original starting set of cut set but not in
the quantitative evaluation of the symbolic reliability

expression.

Table 2 System reliability for the two solved examples

No.
Network
Approximation
Method
Disjoint
Method
1 Fig.6 0.99979798 0.99979801
2 Fig.7 0.99879900 0.99979805

XI. Sulaimani-Erbil Electrical Power System Reliability
Evaluation

Fig.8 shows the single line diagram of the 132 kV systems
for Sulaimani-Erbil electrical power system.
For the purpose of reliability assessment, data were collected
for each transmission line for the period of 6 years [10]. With
the relevant data, the reliability indices were found and the
reliability of each 132 kV transmission line is calculated for
two cases:
1-Only forced outages of the line are taken into account
2-Both the forced and scheduled outages of the line are taken
into account.
The following assumptions are made:
1.
Reliability values are assumed for those lines without available
data.

2. The reliability of Dokan-Tasluja 132 kV transmission line
during the period 1996 to 2001 is evaluated in two parts:
 from 1996 to 1998 the line is operated with double circuit
 and from 1999 to 2001 the line is operated with single circuit
because one of the circuits is energized by 33 KV.
3. Reliability of Dokan and Derbandikhan H/P are considered
to be 0.98 and 0.95 respectively [11].
4. Reliability of the 29 MW Diesel power station is assumed to
be 0.9.
5. Reliabilities of the 33 kV and 11 kV transmission lines are
assumed to be 0.9.
The reliability of each line is given in table 3 and table 4 for
the period 1996-2001

XII. Reliability Modeling of the System

A simplified reliability model for regional power system is
shown in Fig.9, in which the following assumptions are made:
1. The line components are modeled as a single block also the
sending and the receiving ends are assumed fully reliable.
2. The regional power stations are considered as a separate
blocks.
3. All components are unidirectional except the components
that construct ring in the system.
The detail of the coding for the component numbers is given in
table 5.
XIII. Representation of nodes

To represent nodes (branches) in the reliability network

model, a general Terminal Numbering Convention (TNC) is
used in this paper [12]. In this convention the numbering of
nodes (branches) begins at the source and continues in such
away that the output terminal of each branch (node) is assigned
a number greater than the number assigned for its input
terminal, taking further care that each node (branch) is
assigned a specific number. Using TNC, the first vertex
1
n

represents the source and the last vertex
k
n
represents the sink
where
k
is total number of the nodes.
XIV. Case Study and Results

From the reliability block diagram of regional power system
fourteen case studies are investigated. The reliability of each
case study is evaluated for the period of 1996-2001 for the
following two states:
In state one, only the forced outages of the line are take into
account and in state two, both the scheduled and forced outages
of the line are take into account.
1. Case 1 to case 8 reliability of regional power system
evaluated by evaluating minimal paths and cuts of the
system from the network modeling and by using the
program that is established for this purpose. For each case

study different S/S assumed to be the output of the system
as:
a. in case study no.1 Rizgary S/S is take as a sink node
because this S/S is the main S/S in Sulaimani governorate
and the main tie lines for Sulaimani region connected to
this S/S.
b. in case study no.3 Tasluja S/S is take as a sink node
because this S/S supplying Tasluja cement factory and it is
considered an important substation for reconnection of
the regional system to the national grid.
c. in case study no.5 Dokan S/S is take as a sink node
because it supplies Dokan water pumping station.
d. in case study no.6 Derbandikhan S/S is take as a sink node
because it supplies some factories in this area.
e. in case study no.7 and 8 Azadi and N.E. S/S are taken as a
sink node respectively. These two S/S are the main
substations in Erbil governorate and main tie lines for
Erbil governorate connected with these two S/S.
2. Case study 9 and 10 reliability of the regional power system
evaluated, with 29 MW Diesel power station are taken into
account for both Sulaimani and Erbil governorate.
3. Case study 11 and 12 reliability of the regional power system
evaluated by disjoint technique and compared with the
previous case studies.
4. Case study 13 and 14 investigate the indices Annual Average
Interruption Rate (AAIR), this indices indicated the
expected number of days in a year that the specified outage
for a given load point will happen and it’s evaluated from
the following relation:

AAIR = Q * 365 = (1-R) * 365

6
XV. Results of case Studies
Table 6 shows the reliability for case 1 to 8 that is studied during the
period of 1996-2001 with different types of outages taken into account.
Table 7 shows the system reliability for cases 9 and 10 when the 29 MW
Diesel power stations is take into account for both Sulaimani and Erbil
region in the year 2001.
Table 8 shows the unreliability for cases 11 and 12 obtained by
deriving a symbolic equation using disjoint technique.
Table 9 and table 10 show the results of AAIR evaluation for cases 13
and 14.
XVI. Conclusions
This paper investigates the reliability of power system. In the reliability
evaluation, power system is modeled by the (RBD) and two techniques,
cut sets and disjoint, are used.
The investigation results show that both the cut sets and the disjoint
techniques can be used to evaluate the reliability of power system. The
disjoint technique gives more efficient and accurate solution. However,
it is more complex and consequently more time consuming. As to the
Sulaimani-Erbil power system, following conclusions are obtained:
1-It is found that the 132 kV transmission line power system that
energized by 33 kV system reduces the reliability of the system.
Therefore, in order to improve the reliability of the 132 kV power
systems, these lines must be restored to 132 kV level.
2-The Reliability of the system will be increased if the 29 MW diesel
power station is taken into account for Sulaimani-Erbil region.
3-As the outage of power plant greatly reduces the reliability of the
power system, it must be carefully programmed

4-The T tied line greatly effects on the reliability of the overall power
system.

Table 4 regional 132 kV transmission line reliability data during the period 1996-2001
forced and scheduled outages are take into account
Reliability Data (Forced and planning Outages Take into
Account)
Calculated
Name of the line
1996 1997 1998 1999
Dokan-asluja
0.99853075 0.99993133 0.999996942 0.994440639
Tasluja-Rizgari
Dokan-Azadi
0.918537492 0.965886606 0.976601979 0.965865677
Dokan-N.E.
0.917067016 0.912359209 0.962621766 0.944446347
Azadi-N.E.
Tasluja-Azmer
Azmer-Rizgari
Derbandikhan-Rizgar
i
0.970818154 0.968302892 0.976721842 0.945987443
Derbandikhan-Azmer
0.96340126 0.778076484 0.88245624 0.961244292

Table (4) Continue
Reliability Data (Forced and planning
Outages Take into Account)
Calculated

Name of the line
2000 2001

Assumed
Dokan-asluja 0.999089253 0.997644597
Tasluja-Rizgari 0.95
Dokan-Azadi 0.984105571 0.985761035
Dokan-N.E. 0.971745978 0.913671994
Azadi-N.E. 0.95
Tasluja-Azmer 0.95
Azmer-Rizgari 0.95
Derbandikhan-Rizgari 0.981360049 0.983837519
Derbandikhan-Azmer 0.948315118 0.963759513

Table (5) Component Coding of the system RBD
Component
Number
Component Type
1 Dokan H/P
2 Dokan S/S
3 Dokan-Tasluja 132 KV Transmission line
4 Tasluja S/S
5 Tasluja-Rizgari 132 KV Transmission line
6 Rizgari S/S
7 Dokan-Azadi 132 KV Transmission line
8 Dokan-North Erbil 132 KV Transmission line
9 Tasluja-Azmar 132 KV Transmission line
10 Azmar-Rizgari 132 KV Transmission line
11 Azadi S/S
12 Azadi- North Erbil 132 KV Transmission line
13 North Erbil S/S
14 Azmar S/S
15 Derbandikhan-Azmar 132 KV Transmission line

16 Derbandikhan H/P
17 Derbandikhan S/S
18
Derbandikhan –Rizgari 132 KV Transmission line
19 29 MW Diesel Power Station
20 11 KV Transmission Line
21 29 MW Diesel Power Station
22 Industrial S/S
23 33 KV Transmission Line

Table 3 regional 132 kV transmission line reliability data during the period
1996-2001 only forced outages are take into account
Calculated Reliability index for all 132 kV Transmission lines
Calculated
Name of the line
1996 1997 1998 1999
Dokan-asluja
0.998776941 0.999999536 0.999999965 0.997707382
Tasluja-Rizgari
Dokan-Azadi
0.959333257 0.98684551 0.993571157
0.99865106
5
Dokan-N.E.
0.955166591 0.995681126 0.996767504 0.99434551
Azadi-N.E.
Tasluja-Azmer
Azmer-Rizgari
Derbandikhan-Rizgar
i

0.976193458 0.982597032 0.992646499 0.999733638
Derbandikhan-Azmer
0.978348892 0.965863775 0.987840563 0.991093988

Table 3 Continue
Calculated Reliability index for all
132 kV Transmission lines
Calculated

Name of the line
2000 2001
Assumed
Dokan-asluja 0.999905131 0.999743151
Tasluja-Rizgari 0.95
Dokan-Azadi 0.993825896 0.992802511
Dokan-N.E. 0.995197708 0.979861111
Azadi-N.E. 0.95
Tasluja-Azmer 0.95
Azmer-Rizgari 0.95
Derbandikhan-Rizgari 0.994573467 0.990711568
Derbandikhan-Azmer 0.991442775 0.98391172
7

Table 6 reliability results for case study 1-8 during the period 1996-2001
Reliability Results for each case study obtained from the
program ( Only Forced Outages Take into Account)
Years
Case
Study
Numbers
1996 1997 1998
1 0.99874341 0.99881959 0.99885482
2 0.99768347 0.99803263 0.99860013
3 0.99887484 0.99893808 0.99894822
4 0.99890494 0.99895394 0.99898607
5 0.94564784 0.94677657 0.94736171
6 0.97564787 0.97677660 0.97736174
7 0.99505866 0.99822354 0.99860597

8 0.99485034 0.99866533 0.99876583
Case
Study
Numbers
Reliability Results for each case study obtained from the
program ( Scheduled and Forced Outages Take into
Account)
1 0.99870563 0.99865115 0.99876189
2 0.99735302 0.99671572 0.99748737
3 0.99884993 0.99880522 0.99889511
4 0.99886429 0.99863273 0.99882758
5 0.94479823 0.93976295 0.94440871
6 0.97479832 0.96976298 0.97440875
7 0.98807019 0.99411255 0.99685073
8 0.98799670 0.99143618 0.99615175

Table 8 Unreliability and Reliability Results for case study 11 and 12
Case Study
Numbers
Years

Reliability
results from
disjoint method


Reliability results
from
approximation
method

Only Forced Outages Taken into
Account
1996 0.998748062 0.99874341
1997 0.998822864 0.99881959
1998 0.998857484 0.99885482
1999 0.998764729 0.99875963
2000 0.99885846 0.99885577
11
2001 0.998838939 0.99883592
1996 0.994950121 0.99485034
1997 0.998671602 0.99866533
1998 0.998769628 0.99876583
1999 0.998619351 0.99861377
2000 0.998681822 0.99867743
12
2001 0.997801362 0.99778998

Table 8 Continue
Case Study
Numbers
Years

Reliability
results from
disjoint method


Reliability

results from
approximation
method


Scheduled and Forced Outages
Taken into Account
1996 0.998711296 0.99870563
1997 0.998661428 0.99865115
1998 0.998767499 0.99876189
1999 0.998420777 0.99840850
2000 0.998767479 0.99876273
11
2001 0.998709733 0.99870372
1996 0.98835124 0.98799670
1997 0.991604149 0.99143618
1998 0.996203793 0.99615175
1999 0.994234003 0.99412298
2000 0.997079661 0.99705076
12
2001 0.993418684 0.99334556

Table ( 6)Continue
Reliability Results for each case study obtained from the
program ( Only Forced Outages Take into Account)
Years

Case Study
Numbers
1999 2000 2001

1 0.99875963 0.99885577 0.99883592
2 0.99884975 0.99870163 0.99847949
3 0.9988296 0.99894410 0.99893349
4 0.99887538 0.99894452 0.9988609
5 0.94518203 0.94732368 0.94703025
6 0.97518206 0.97732371 0.97703028
7 0.99882901 0.99860883 0.99843705
8 0.99861377 0.99867743 0.99778998
Case Study
Numbers
Reliability Results for each case study obtained from the
program ( Scheduled and Forced Outages Take into Account)
1 0.99840850 0.99876273 0.99870372
2 0.99587101 099787313 0.9979704
3 0.99860466 0.99888206 0.99881327
4 0.99861902 0.99888027 0.99882865
5 0.93961537 0.94545001 0.94442785
6 0.96961540 0.97545004 0.97442788
7 0.99519396 0.99766874 0.99695003
8 0.99412298 0.99705076 0.99334556

Table 7 Reliability Results For Case Study 9 and 10
Case Study Numbers
Reliability Results (Only Forced Outage
Taken into Account)
9 0.99979740
10 0.99935985
Case Study Numbers
Reliability Results (Scheduled and Forced
Outage Taken into Account)

9 0.99977642
10 0.99878043

8

Dokan H/P
5*8 0 M W
1
Dokan S/S
2
Tasluja S/S
34
Chamchamal
S/S
To Kirkuk
Rizgary S/S
5
Azmar S/S
6
Old Kirkuk
7

8 Derbandikhan H/P
3*8 3 M W
9
10
Kifri S/S
Hamrin H/P
Azadi S/S
11
17
12
N.E S/S
13
18
19
Erbil Park S/S
To Karkosh
Salahadeen S/S
14
Khalifan S/S
Soran S /S
15
Kalar S/S
To Dibs G/P

Fig.8 Single Line Diagram of 132 kV Power System For Sulaimani-Erbil Region
Table 9 AAIR evaluation for case study 13
Q
S
AAIR (Days /Year)
Years

Only Forced Outages Taken into Account
1996 0.00125661 0.45866265
1997 0.00118041 0.43084965
1998 0.00114517 0.41798705
1999 0.00124035 0.45272775
2000 0.00114424 0.4176476
2001 0.00116409 0.42489285

Scheduled and Forced Outages Taken into
Account
1996 0.00129435 0.47243775
1997 0.00134884 0.4923266
1998 0.00123808 0.4518992
1999 0.0015915 0.5808975
2000 0.00123728 0.4516072
2001 0.00129627 0.47313855

Table 10 AAIR evaluation for case study 14
Q
S
AAIR (Days /Year)
Years
Only Forced Outages Taken into Account
1996 0.00514967 1.87962955
1997 0.00133465 0.48714725
1998 0.00123419 0.45047935
1999 0.00138625 0.50598125
2000 0.00132259 0.48274535
2001 0.00221002 0.8066573

Scheduled and Forced Outages Taken into
Account
1996 0.01200333 4.38121545
1997 0.00856382 3.1257943
1998 0.00384827 1.40461855
1999 0.00587702 2.1451123
2000 0.00294927 1.07648355
2001 0.00665445 2.42887425

21 22
23
12 3 4
6
7
8
11 12
13
19
20
16
17
15
14
9
10
18
5


Fig.9 Reliability Block Diagram for Sulaimani-Erbil Electrical Power System

9

Appendix A
BOOLEAN ALGEBRA
1- Commutative Laws:
a)
abba +=+
b)
abba ×=×

2-Distributive Laws:
a)
)()()( cabacba +×+=×+

b)
)()()( cabacba ×+×=+×

3-Identity Laws:
a)
aa =+ 0
b)
aa =×1

4-Complement Laws:
a)
1=
′
+ aa
b)
0=

′
× aa

5-Idempotent Laws:
a)
aaa =+
b)
aaa =×

6-Boundedness Laws:
a)
11
=+a
b)
00
=×a

7-Absorption Laws:
a)
abaa =×+
)(
b)
abaa =+×
)(

8-Associative Laws:
a)
)()( cbacba ++=++
b)
)()( cbacba ××=××

9-Involution Law:
aa =
′′
)(

10-DeMorgan’s Laws:
a)
baba
′
×
′
=
′
+
)(
b)
baba
′
+
′
=
′
×
)(

11-Disjoint set:
baaba
′
+=+

REFERENCES

[1] J. Endrenyi, “Reliability Modeling in Electrical Power
Systems”, John Wiley and Sons, Newyork, Ny,1978
[2] A.E.Green and A.J.Bourne “ Reliability Technology”, John
Wiley & Sons Ltd., 1972.
[3] Feasibility study on the options for the addition of
generation capacity in the northern governorates of Iraq.
Final report, prepared by SMEC Nov. 1999
[4] Distribution Construction Manual, Revesion 2:February
2002, Distribution sector UNDP –ENRP.
[5] Electricity Network Development plan Sulaimany
governorate. Revesion 1: February 2002,UNDP-ENRP,
Distribution sector.
[6] T. Gönen “ Electric Power Transmission System
Engineering Analysis and Design”, John Wiley and Sons,
1988.
[7] R. Billinton and R. N.Allan “ Reliability Evaluation of
Engineering Systems”, Pitman Advanced Publishing
Program, 1983.
[8] G.B.Jasmon and K.W. Foong “ A method for evaluating all
the minimal cuts of a graph”, IEEE Transactions on
Reliability, Vol.R-36, No.5, December 1987.
[9] S. Rai and K.K. Aggarwal “ An efficient method for
reliability evaluation of a general network”, IEEE
Transactions on reliability, Vol.R-27, No.3, August 1978.
[10] G.I.Rashed, A.R.Majeed and S. J.cheng “ Determination
of Data for Reliability Analysis of a Transmission System

in Sulaimani-Erbil Network”, Asian network for scientific
information, Information Technologu Journal, Vol.(4),
No.2, pp.106-113, Jan. 2005.
[11] T.M.Tahir ”Load forecasting and power system reliability
evaluation”, MSC.,Thesis, University of Technology,
Electrical Engineering Dept., Nov. 1994.
[12] S.S.Yau, Y.S. Tang “ An efficient algorithm for generating
complete test sets for combinational logic circuit”, IEEE
Trans. Computers, Vol.C-20, pp 1245-1251, Nov. 1971.







Asso R. Majeed,(E-mail: )
received his Ph.D. in electrical engineering from Baghdad
university, Iraq. Recently he is head of electrical engineering
department in Sulaimani university. His area is power system
reliability.


Ghamgeen I. Rashed,(E-mail:)
received his bachelor degree in electrical engineering from
Salahaadin University- Iraq, in 1995, and his M.sc. in
University of Sulaimani-Iraq in 2003. Recently he is Ph.D
student in Huazhong University of Science and Technology,
China.

Shijie Cheng, senior member
IEEE,(E-mail:). Got his ph.D. degree
in Canada in 1988. He is a life professor of the Huazhong
University of Science and Technology, China. In recent years
he has been engaged in the areas of power line communication,
intelligent control, stabilization control of power system and
superconducting power technology.