Energy and Power En gi neering, 2011, 3, 499-507
doi:10.4236/epe.2011.34060 Published Online September 2011 (http://www.SciRP.org/journal/epe)
A Practical Framework for Reliability and Quality
Assessment of Power Systems
Mohamed A. El-Kady, Badr M. Alshammari
Power System Reliability and Security, King Saud University, Riyadh, Saud Arabia
Received August 2, 2011; revised September 5, 2011; accepted September 20, 2011
Abstract
This paper presents a new practical framework for evaluating reliability levels associated with power system
supply-demand balance. The framework has been developed as part of a recent major industry-supported
research and development study. The novel framework is based on three metaphors (dimensions) represent-
ing the relationship between available generation capacities and required demand levels. The first metaphor
defines whether or not the capacity exists, the second metaphor defines whether or not the capacity is needed,
and the last metaphor defines whether or not the capacity can reach (delivered to) the demand. The eight
possible combinations associated with the 0/1 (Yes/No) values of the three metaphors would, in turn, define
a set of powerful system-wide performance quality measures relating to generation deficiency, redundancy,
bottling, etc. Practical applications to a portion of the Saudi power grid are also presented for demonstration
purposes. The work of the paper constitutes a new line of research in system reliability assessment where the
derived system-wide performance quality indices are capable of addressing and revealing areas of deficien-
cies and bottlenecks as well as redundancies in the composite generation-demand structure of large-scale
power grids. In addition, the sensitivities of the performance quality indices with respect to variations in the
system operating parameters represent powerful information, which can be used to assess the level of degra-
dation in the reliability measure or the performance quality index under consideration.
Keywords: Power Systems, Reliability, Quality Assessment, Linear Programming
1. Introduction
Electric power utilities have a key mandate to maintain a
continuous and sufficient power supply to the customers
at a reasonable cost. Power system cost-effectiveness,
security, adequacy and reliability analyses have evolved
over the years from mere theoretical topics of limited
interest, during the era of generous economy and abun-
dant supply and facilities, to a vital branch in today’s
highly-competitive business environment of power utility
planning and operations [1-4]. In response to the growing
interest in system security and reliability by power utili-
ties, several schools of thought have evolved with the
associated pioneering research aimed at conducting the
security and reliability assessment in an efficient, accu-
rate manner and with as much realization of the business
nature and practical circumstances of the power utility as
possible. As has happened with many power system dis-
ciplines, the prime interest in system security, adequacy
and reliability has gradually shifted from completing and
refining the theoretical basis, through developing suitable
computational tools for demonstrating the capability and
practicality of the methodologies, to upgrading the com-
putational tools to handle the large-scale nature of pre-
sent power systems and, finally, to relate various security,
quality and reliability indices to the practical concerns of
utility engineers and executives regarding supply and/or
transmission deficiencies as well as the risk associated
with ignoring such deficiencies [5,6].
This paper summarizes the results of a recent major
industry-supported research and development study in
which a novel framework was developed for evaluating
performance quality indices associated with power sys-
tem generation-demand balance. The novel technique
utilizes a basic linear programming formulation, which
offers a general and comprehensive framework to assess
the harmony and compatibility of generation and demand
in a power system. Using the method proposed in this
paper, integrated system reliability evaluation and quality
assessment can be performed globally on the whole sys-
tem or locally on portions in the power grid. It can be
applied to the system under normal operation or subject

M. A. EL-KADY ET AL. 500
to contingencies with certain or random occurrences
[7-10]. The methodology presented in this paper has
been implemented in an efficient computerized algorithm
which analyzes the network structure, generation and
load balance and evaluates various composite system
performance quality indices. Practical application to a
portion of the Saudi power grid is also presented in the
paper for demonstration purposes.
2. Problem Formulation
2.1. Network Model
Let number of buses in the power network, where
B
n
B
LG
, nnn
L
n and G number of load and gen-
erator buses, respectively. Also, in the network model
used, nT = number of transmission branches (lines and
transformers). In order to facilitate subsequent formula-
tion, it is assumed, without loss of generality, that the
load buses are numbered as
n
1, 2,,
L
n followed by ge-
nerator buses as 1, ,
L
LG
, where nnn
L
GB
.
For example, the sample power system shown in Figure
1 has , nG = 2, nL = 2 and nT = 5.
nn n
4
B
n
Now, let

B
T be the bus incidence matrix
representing the connectivity pattern between buses and
lines. The entries of A are either 0, 1 or –1. Therefore, an
element Abt = 1 if bus b is feeding a transmission branch t;
Abt = –1 if bus b is fed from a branch t, otherwise Abt = 0.
In the current analysis, the A-Matrix is partitioned
row-wise into AL and AG associated, respectively, with
load and generator buses. The rows of A (or columns of
AT) represent groups of buses while the columns of A (or
rows of AT) represent groups of transmission links. We
also note that for practical large-scale networks, the ma-
trix A is extremely sparse.
nnA
2.2. Performance Quality Assessment
Although the basic definitions pertaining to system per-
formance quality are simple to state and often seem
5
4
1
3
5
~
~
Bus 3
Bus 4
Bus 2
Bus 1
Figure 1. A sample power system.
intuitive at first glance, a great deal of care should be
exercised in order to recognize some subtle differences
in the definition and formulation of the composite per-
formance quality indices. Let,
T
P = vector of nT elements representing transmission
branch capacities
L
P = vector of nL elements of peak bus loads
G P = vector of nG elements representing generator
capacities
g
P
For simplicity of notation, we shall use t
P to denote
a general element t of the vector T
P (rather than the
more strict notation of Tt P). Similarly, we shall use l
P
and
g
P to denote general elements of L
P and G P
respectively. However, when confusion may occur, we
will use the strict notation of Ti
P, Li P and Gi P. Now
consider the schematic configurations of Figure 2 which
depicts the transfer connectivity between generation
through transmission to load.
If, for example the local generation capacity
g
P at
bus g exceeds the corresponding transmission capability
g
t
t T
P


in Figure 2(b), where Tg denotes the set of
transmission branches connected to generator bus g, then
using the terminology introduced in the previous section,
we may say that a positive amount of
g
g
t
tT
PP


 


 of
generation beyond bus g has been bottled (blocked from
usage). We should note that such a definition applies to a
specific scenario of system configuration (the A-matrix)
and loading conditions. For example, in the above dis-
cussion, we assumed that the set Tg does not represent
any of pre-defined contingency scenarios. That is, Tg
represents the full transmission capacity at bus g.
In addition to the above definitions, we also define –
using similar notation—the following vector for later use
G
P = Vector of generation site capacities, which repre-
sents the maximum future expanded generation capacity
that could be available at the same generation site.
2.3. Master Linear Program
In the proposed scheme, the integrated system quality
~
T
G
L
(a)
(c) (b)
Figure 2. G-T-L transfer connectivity.

M. A. EL-KADY ET AL.501
assessment is performed via solving a master linear pro-
gramming problem [11] in which a feasible power flow
is established which minimizes the total system non-
served load subject to capacity limits and flow equations.
The master linear program, which utilizes the network
bus incidence matrix A, is formulated as

L
n
l = 1
LG T
L
T
G
LL
L
GG
G
TT
TT
Minimize f =
with respect to , and
such that =
,
,
,
l
p








PP P
P
APP
0
PP
P0
PP
P
PP
PP
(1)
In the master linear program, PL, PG, and PT are nL, nG
and nT column vectors representing the actual load bus
powers (measured outward), generator bus powers (mea-
sured inwards) and transmission line powers (measured
as per the network bus incidence matrix A), respectively.
The solution of the above linear program provides a
more realistic (less conservative) flow pattern in view of
the fact that when load curtailments are anticipated, all
system generation resources would be re-dispatched in
such a way which minimizes such load cuts. The feasible
flow pattern established from the Master Linear Program
is then used to evaluate various integrated system quality
indices through a set of closely related sub-problems. For
example, a sub-problem may be defined to evaluate the
total system loss of load subject to a given contingency
scenario. In this case, the sum of all elements of the PL
vector is subtracted from the total nominal system load.
The resulting amount, if positive, would constitute the
total system loss of load (Load Not-Served).
3. Quality Metaphors
3.1. Conceptual Framework
As was indicated before, the novel framework presented
in this paper is based on three metaphors (dimensions)
representing the relationship between certain system
generation capacity and the demand. These metaphors
are illustrated in Table 1, and relate to the following de-
mand fulfillment issues:
1) Need of capacity for demand fulfillment.
2) Existence of capacity (availability for demand ful-
fillment).
3) Ability of capacity to reach the demand.
The first metaphor defines whether or not the capacity
is needed, the second metaphor defines whether or not
the capacity exists, and the last metaphor defines whether
Table 1. Illustration of quality assessment metaphors.
Quality
State Quality Metaphor of a Capacity
#Quality
Measure NER (N)
Needed? (E) Exists? (R) Can Reach?
1Utilized 111Yes Yes Yes
2Bottled 110Yes Yes No
3Shortfall 101Yes No Yes
4Deficit
100Yes No No
5Surplus 011No Yes Yes
6 Redundant 010No Yes No
7Spared 001No No Yes
8Saved 000No No No
or not the capacity can reach (delivered to) the demand.
The eight possible combinations associated with the 0/1
(Yes/No) values of the three metaphors would, in turn,
define a set of powerful system-wide performance qual-
ity measures, namely:
1) Utilized: A given capacity is said to be utilized if it
is needed (for demand fulfillment), exists, and can reach
the demand.
2) Bottled: A given capacity is said to be bottled if it
is needed (for demand fulfillment) and exists, but cannot
reach the demand.
3) Shortfall: A given capacity is said to be shortfall if
it is needed (for demand fulfillment) and, anyhow, does
not exist and can reach the demand.
4) Deficit: A given capacity is said to be deficit if it is
needed (for demand fulfillment) but, however, does not
exist and cannot reach the demand.
5) Surplus: A given capacity is said to be surplus if it
is not needed (for demand fulfillment) although exists
and can reach the demand.
6) Redundant: A given capacity is said to be redun-
dant if it is not needed (for Demand fulfillment) al-
though exists but, anyhow, cannot reach the demand.
7) Spared: A given capacity is said to be spared if it
is not needed (for demand fulfillment) and, anyhow, does
not exist although can reach the demand.
8) Saved: A given capacity is said to be saved if it is
no needed (for demand fulfillment) and, anyhow, does
not exist and cannot reach the demand.
We note here that the above performance quality
measures are associated with different combinations
(topples) of the three quality metaphors, namely, “exis-
tence”, “need” and “ability to reach the demand”. The
corresponding quality state of a given capacity can be
represented, as demonstrated in Table 1, by a three-value
expression of either a “Yes/No” or “1/0” type indicating

M. A. EL-KADY ET AL. 502
the true/false value associated with each quality meta-
phor.
As will be demonstrated later, the evaluation of the
above quality indices requires the knowledge of the fol-
lowing data types for the demand and various system
facilities:
1) The value of demand required to be supplied.
2) The value of generation capacity as well as the
maximum site capacity (the limit of potential increase in
existing generation capacity).
3) The value of transmission capacity.
3.2. Illustrative Example of Quality Metaphors
As a simple illustrative example, consider the sample
2-bus system of Figure 3, where a demand (load) of 50
(per-unit) is supplied by a generating facility having an
available capacity of 70 (per-unit) and a site capacity of
90 (per-unit). The load is supplied through a transmission
facility having an available capacity of 40 (per-unit) and
a route capacity of 100 (per-unit). For this simple system,
the quality indices can be easily evaluated by inspection
as shown in Table 2. In order to facilitate understanding
of the meaning of the different quality indices and ensure
correct interpretation of their definitions, Appendix I
contains a complete list of the quality indices for many
case scenarios involving different values of required load
supply level as well as generation and generation capaci-
ties.
3.3. Large-Scale Implementation
For real life power systems with practical sizes, the qual-
ity indices cannot be evaluated by inspection as was done
in the previous illustrative example. An appropriate
computerized scheme is needed in order to properly
evaluate various quality indices according to their stated
definitions. The master linear program presented before
Capacity =
G
P
= 70
Site Capacity =
G P
= 90
Demand =
L
P
= 50
L
G
Capacity =
L
P
= 40
BUS  BUS 
T
Figure 3. A 2-Bus sample power system.
Table 2. Quality indices for 2-Bus sample system.
(Needed, Exists, Can-reac h)
G
P T P L P G
P T P LNS 000 001 010 011 100 101110111
70 40 50 90 100 10 40 10 0 0 0 20 0 20
forms the bases for analyzing and evaluating the quality
indices. For example, the Load Supply Reliability can be
evaluated as follows:
LNSl = Load Not-Served at Load Bus


(1)
ll lPP
LNS = Total System Load Not-Served =

(1)
1
L
n
ll
l
PP



where the bus loads at the solution of the master linear
program are termed as , and Pl denotes the solution
load value at bus (l).

1
l
P
On the other hand, generation quality indices are de-
fined in terms of the previously defined “1/0” states in-
dicating the (Needed, Exists, Can-reach) true/false values
associated with each quality metaphor. We shall use the
symbol Qgijk to indicate the generation quality index state.
Also, in the following expressions, we shall use


min, ,,
x
yz to indicate the minimum of ,,,
x
yz.
The notation
x
will be used to denote


0,max
x
, that
is the maximum of x and zero (=x if , or 0 other-
wise). For example, the generation Utilized Capacity
index is given by
0x
Qg111 = Utilized Capacity
≡ {needed, exists, can reach} =

(1)
1
L
n
l
l
P


Similarly, the generation Bottled Capacity index is
given by
Qg110 = Bottled Capacity
≡ {needed, exists, cannotreach}
=
 


11
11 1
min,max 0,
nl nGnG
lg gg
lg g
PP PP
 



 






 



 

 
4. Practical Application
4.1. SEC Quality Indices
The newly developed methodology for power system
performance quality assessment has been applied to a
practical power system comprising a portion of the in-
terconnected Saudi power grid. The power system con-
sists of two main regions, namely the Central region and
the Eastern region.
The two systems are interconnected through two 380
kV and one 230 kV double-circuit lines. The system
model used in the current application is shown in Figure
4. Three zones are identified in the present analysis, two
in the Central region (Riyadh and Qassim zones) and one
in the Eastern region.
In this application, three reliability and quality indices
are considered, namely the system Load Not-Served
(LNS), Bottled Generation Capacity (Qg110) and Surplus
Generation Capacity (Qg011). The Surplus Generation

M. A. EL-KADY ET AL. 503
10
20
3
13 33
117 102 101
118
64
9
73
19
1
23
5
4
1415 7
8
63
77
74
76
114
115 113
116
95 88
96
98
100
2
12
6
41
40
34
78
42
35
37
38
75
80
79
43
36
81
44
82
48
47
84 85
103
110
111
112
83
87
49
61 62
89 92
91
90
93
94104
105 106
107
50
86
108
99
109
56
30
16
26
54
53
24
25
97
27
32 31
52
119
72
58
69 70
59 65
66
71
57
39
60
18
11 22
21
51
6768
45 46
29 28
55
17
78
SEC EAST
GAZLAN
BERI
JSWCC
DAMMAM
SHED GUM
FARAS
QUR AIA H
SOUTH AREA
DAMAMAM AREA
NORTH AREA
PP5
PP9
PP4
PP7A
LAYLA
PP7B
PP8X
PP8A
PP8B
QPP2
QPP3
QASSIM AREA
AL-KAH AR J ARE A
RIYADH AREA
SEC CENTRAL
Figure 4. Single-line diagram of study pow er system.
Capacity (Qg011) is calculated as
Qg011 = Surplus Capacity
≡ {not need ed , exists, can reach}
11
11
minmax 0,,
max 0,
nG nL
ll
gl
nG nL
gl
gl
PP
PP





 


  

 










 
 

 










where the generation output values Pg are calculated at the
solution of the linear program with open limits on the loads.
Table 3 summarizes some of the performance quality
measures applied to the power system for three operating
scenarios evaluated at the system peak-demand level
(including reserve requirement). The first scenario repre-
sents the base system status with all facilities available,
the second scenario represents the loss of a major Cen-
tral-East interface for extended duration, while the third
scenario represents the loss of a major generating station
in the Eastern region for extended duration. The results
of the first operating scenario indicate that the integrity
of the supply-demand pattern is preserved in the base-
case scenario with no un-served demand or generation
bottling. However, there is 130 MW of surplus genera-
tion in the Eastern region, where most of the generation
facilities of the interconnected system are located.
The results obtained for the second operating scenario
reveal that the Load Not-Served in the Central-Riyadh is
450 MW. On the other hand, no Load Not-Served exists
in the Central-Qassim zone for the same operating sce-
nario, indicating that this zone has sufficient backup
generation with adequate transmission facilities that en-
able the zone to be somehow shielded from the loss of an
interface between the Central and Eastern regions. Also
for this scenario, there are 420 MW and 30 MW of bot-
tled generation capacity in the Eastern and Qassim re-
gions, respectively, which would be sufficient to supply
the Central-Riyadh zone if the interface facility had not
been lost causing separation of the the two intercon-
nected system regions.
It is also of interest to note that no Surplus generation
Capacity exists in the Eastern region for this operating
scenario, which confirms that the loss of the East-
ern-Central interface is the sole reason (causing genera-
tion bottling) for the Load Not-Served in the Cen-
tral-Riyadh zone.
The third operating scenario impacts directly on the
generation availability at the Eastern region. The results
for this scenario show that there are Load Not-Served in
both the Central-Riyadh and Eastern region of 375 MW
and 105 MW, respectively. On the other hand, a 30 MW
of bottled generation capacity would exist in the Qassim
regions, where the flows over transmission lines toward
the Central-Riyadh region had already reached their lim-
its.
Incidentally, the total system generation shortfall
(Qg101) in this scenario, which measures the needed-

M. A. EL-KADY ET AL. 504
Table 3. System performance quality assessment measures for three operating scenarios.
{PRIVATE} Power Grid Zone First Operating Scenario
(Base-Case Scenario—All Facilities are Available)
Load Not Served (NLS) Bottled Generation
Capacity (Qg110) Surplus Generation Capacity (Qg011)
1. (Central-Riyadh) - - -
2. (Central-Qassim) - - -
3. (Eastern) - - 130 MW
{PRIVATE} Power Grid Zone Second Operating Scenario
(Loss of a Major Central-East Interface for Extended Duration)
Load Not Served (NLS) Bottled Generation
Capacity (Qg110) Surplus Generation Capacity (Qg011)
1. (Central-Riyadh) 450 MW - -
2. (Central-Qassim) - 30 MW -
3. (Eastern) - 420 MW -
{PRIVATE} Power Grid Zone Third Operating Scenario
(Loss of a Major Generating Station for Extended Duration)
Load Not Served (NLS) Bottled Generation
Capacity (Qg110) Surplus Generation Capacity (Qg011)
1. (Central-Riyadh) 375 MW - -
2. (Central-Qassim) - 30 MW -
3. (Eastern) 105 MW - -
yet does not exist—generation capacity which indeed can
reach the demand is 345 MW. This shortfall generation
is solely attributed to absence of sufficient generation
capacity that transmission would otherwise have been
able to deliver to the loads had such generation capacity
been available.
4.2. Sensitivity Evaluation
While the system reliability and quality indices are
valuable on their own, their sensitivities with respect to
variations in the system operating parameters represent
powerful information, which can be used to assess the
level of degradation in the quality index under considera-
tion.
In order to demonstrate this point, Figure 5 shows the
variations of two quality indices, namely the Load Not-
Served in the Central-Riyadh area and the total Bottled
Generation Capacity in the system, with respect to in-
crease in the system demand level under the first (base-
case) operating scenario.
As is expected, the Load Not-Served increases steadily
with the increase in system demand. Below the 110%
load level (with respect to the base-case level), both the
Load Not-Served and Bottled Generation Capacity are
equal, indicating that during this range the generation
bottling represents the sole reason for demand non-ful-
fillment. Beyond the 110% load level, the two indices are
different. While the Load Not-Served keeps increasing,
the Bottled Generation saturates at 125 MW at 115%
load level. At this point, the generation insufficiency—
rather than the transmission limitation—becomes the
sole reason for unsupplied demand in the system.
5. Conclusions
This paper has shared the findings and results of a recent
major study to formulate—and develop the general the-
ory for—the overall integrated quality indices, and lay
the foundation for practical large-scale, network-oriented
composite adequacy and reliability determination and
assessment. The paper has also taken an important step
towards effective and meaningful evaluation of the over-
all system quality measures by offering a general frame-
work for evaluation of power system performance qual-
ity indices. The novel framework is based on three meta-
phors (dimensions) representing the relationship between
certain system generation capacity and the demand. The
first metaphor defines whether or not the capacity exists,
the second metaphor defines whether or not the capacity
is needed, and the last metaphor defines whether or not
the capacity can reach (delivered to) the demand. The
eight possible combinations associated with the 0/1
(Yes/No) values of the thre metaphors would, in turn, e

M. A. EL-KADY ET AL.505
LN S/ C ( M W )
Qg110 ( M W)
100 102 104106 108 110 112 114116 118 120
0
50
100
150
200
250
300
Sy st em Demand Level ( % )
Load N ot - Served in C- R iyadh (M W) , Bot t led G ene r at ion in East er n (M W)
Senstivity of Quality In dices w.r.t. System Demand Level
Figure 5. Sensitivity analysis of quality indices.
define a set of powerful system-wide performance qual-
ity measures relating to deficiency, redundancy, bottling,
etc.
Through the quality assessment formulation intro-
duced in the paper, a general, comprehensive framework
is established together with a proper methodology to
assess the harmony and compatibility of generation,
transmission and demand in power systems. This com-
puter-aided assessment can reveal, in an efficient and
reliable manner, areas of deficiencies and bottle-necks in
various portions of the system. Furthermore, using the
method proposed, integrated system quality assessment
can be performed globally on the whole system or locally
on portions or even nodes (buses) in the power grid. It
can be applied to the nominal system or subject to con-
tingencies.
Based on the solution of the basic linear program de-
scribed in this paper, a more realistic (less conservative)
flow pattern can be established. The more realistic nature
of such a flow pattern comes from the fact that when
load curtailments are anticipated, all system generation
resources would be re-dispatched in such a way which
minimizes such load cuts. The feasible flow pattern es-
tablished from the Master Linear Program is then used to
evaluate various integrated system quality indices th-
rough a set of subsequent sub-problems. In the practical
application presented for the Saudi electricity system,
three reliability and quality indices were considered in
the paper, namely the load-not-served (LNS), bottled
generation capacity (Qg110) and surplus generation ca-
pacity (Qg011).
The performance quality measures were applied to
three operating scenarios evaluated at the system peak-
demand level constituting the base-case system (with all
facilities available), the loss of a major Central-East in-
terface and the loss of a major generating station in the
Eastern region. While adequate supply-demand pattern
was preserved in the base-case scenario, notable levels of
un-served demand and generation bottling were observed
in the two other operating scenarios.
While the system reliability and quality indices are
valuable on their own, their sensitivities with respect to
variations in the system operating parameters represent
powerful information, which can be used to assess the
level of degradation in the quality index under considera-
tion. This fact was also demonstrate in the paper where
the impacts on two quality indices, namely the Load
Not-Served in the Central-Riyadh area and the total Bot-
tled Generation Capacity in the system, were evaluated
with respect to potential increase in the system demand
level.
6. Acknowledgements
This work was supported by the Saudi Electricity Com-
pany.

M. A. EL-KADY ET AL. 506
7. References
[1] S. Torre, A. Conejo and J. Contreras, “Transmission Ex-
pansion Planning in Electricity Markets,” IEEE Transac-
tions on Power Systems, Vol. 23, No. 1, 2008, pp. 238-
248. doi:10.1109/TPWRS.2007.913717
[2] M. El-Kady, M. El-Sobki and N. Sinha, “Reliability
Evaluation for Optimally Operated Large Electric Power
Systems,” IEEE Transactions on Reliability, Vol. R35,
No. 1, 1986, pp. 41-47. doi:10.1109/TR.1986.4335340
[3] M. El-Kady, M. El-Sobki and N. Sinha, “Loss of Load
Probability Evaluation Based on Real Time Emergency
Dispatch,” Canadian Electrical Engineering Journal, Vol.
10, 1985, pp. 57-61.
[4] Q. M. Chen, L. Yan and J. McCalley, “The Risk of
High-Order Transmission Contingencies,” Proceedings of
the IEEE Power Engineering Society General Meeting,
Norristown, 23 July 2007, pp. 1-7.
[5] M. El-Kady, B. Alaskar, A. Shaalan and B. Al-Shammri,
“Composite Reliability and Quality Assessment of Inter-
connected Power Systems,” International Journal for
Computation and Mathematic in Electrical and Elec-
tronic Engineering (COMPEL), Vol. 26, No. 1, 2007,
Paper #SSD05-PES-12.
[6] B. Alshammari, M. El-Kady and Y. Al-Turki, “Com-
puter-Aided Optimization of Power System Performance
Quality Indices,” Proceedings of 3rd Global Conference
on Power Control and Optimization, Gold Coast, 2-4
February 2010, p. 51.
[7] J. Choi, T. Mount and R. Thomas, “Transmission Expan-
sion Planning Using Contingency Criteria,” IEEE Trans-
actions on Power Systems, Vol. 22, No. 4, 2007, pp.
2249-2261. doi:10.1109/TPWRS.2007.908478
[8] P. Jirutitijaroen and C. Singh, “Reliability Constrained
Multi-Area Adequacy Planning Using Stochastic Pro-
gramming with Sample-Average Approximations,” IEEE
Transactions on Power Systems, Vol. 23, No. 2, 2008, pp.
405-513. doi:10.1109/TPWRS.2008.919422
[9] R. Billinton and D. Huang, “Effects of Load Forecast
Uncertainty on Bulk Electric System Reliability Evalua-
tion,” IEEE Transactions on Power Systems, Vol. 23, No.
2, 2008, pp. 418-425. doi:10.1109/TPWRS.2008.920078
[10] H. Jun, Y. Zhao, P. Lindsay and P. Kit, “Flexible Trans-
mission Expansion Planning with Uncertainties in an
Electricity Market,” IEEE Transactions on Power Sys-
tems, Vol. 24, No. 1, 2009, pp. 479-488.
doi:10.1109/TPWRS.2008.2008681
[11] P. Gill, W. Murray and M. Wright, “Practical Optimiza-
tion,” Academic Press, London, 1981.

M. A. EL-KADY ET AL.507
Appendix
Quality Indices for 2-Bus Sample System
GENERATION INDICES
(Needed-Exist-Can-reach)
L
P G P T P G
PT P LNS
SA
000
SP
001
RE
010
SU
011
DE
100
SF
101
BO
110
UT
111
50 70 40 90 100 10 20 0 20 0 0 0 10 40
105 70 100 90 110 35 0 0 0 0 0 20 0 70
105 70 100 120 110 35 15 0 0 0 5 30 0 70
100 10 70 95 90 90 0 0 0 0 25 60 0 10
100 10 70 195 90 90 95 0 0 0 30 60 0 10
100 10 70 95 130 90 0 0 0 0 25 60 0 10
100 10 70 195 130 90 95 0 0 0 30 60 0 10
100 80 70 95 110 30 0 0 0 0 15 0 10 70
100 80 70 115 110 30 51 0 0 0 20 0 10 70
90 70 100 95 120 20 0 5 0 0 0 20 0 70
90 70 100 145 120 20 45 10 0 0 0 20 0 70
90 120 100 125 135 0 5 0 20 10 0 0 0 90
50 70 300 80 305 0 0 10 0 20 0 0 0 50
50 70 300 310 305 0 10 230 0 20 0 0 0 50
90 100 40 100 80 50 0 0 10 0 0 0 50 40
90 100 40 130 80 50 30 0 10 0 0 0 50 40
90 100 40 100 250 50 0 0 10 0 0 0 50 40
90 100 40 130 250 50 30 0 10 0 0 0 50 40
140 130 70 140 135 70 0 0 0 0 10 0 60 70
140 130 70 170 135 70 30 0 0 0 10 0 60 70
140 130 70 140 145 70 0 0 0 0 10 0 60 70
140 130 70 170 145 70 30 0 0 0 10 0 60 70
130 70 140 80 150 60 0 0 0 0 0 10 0 70
130 70 140 150 150 60 10 10 0 0 0 60 0 70
90 200 190 210 220 0 10 0 10 100 0 0 0 90
50 90 100 95 105 0 0 5 0 40 0 0 0 50
50 90 100 105 105 0 5 10 0 40 0 0 0 50
G = Generation T = Transmission L = Load LNS = load Not Served
UT = Utilized BO = Bottled SF = Short-fall DE = Deficient
SU = Surplus RE = Redundant SP = Spared SA = Saved