Engineering, 2013, 5, 168-173
doi:10.4236/eng.2013.51b031 Published Online January 2013 (http://www.SciRP.org/journal/eng)
Utilizing Stability Index Tracing for Precise Load Buses
Identification in Load Shedding Problem
Z. Hamid1, I. Musirin2, M. M. Othman3
Faculty of Electrica l Engineering, Uni ver siti Teknologi MAR A, Selangor, Malaysia
Received 2013
Abstract
This pap er propo ses a new approach for suitable load buses id entificatio n via stability index tracing in performing cor-
rective load shedding. The proposed identification technique is called the Fast Voltage Stability Index Load Tracing
(FVSI-LT). By implementing a power tracing algorithm, a group of major contributors on the stress experienced by a
power system is able to be precisely identified by a system operator (SO) based on the traced values of FVSI. To be
precise, the traced FVSI via FVSI-LT can be used to form a ranking list indicating the priority of buses committed for
shedding purpose. After designing a Fuzzy Inference System (FIS) for deciding the allowable load powers to be shed
and performing experiment on IEEE 57-Bus reliability test system (RT S), it is revealed t hat the ra nki ng list pro vided b y
FVSI-LT re sults to the most consis te nt improvement in terms of voltage stability and losses minimization.
Keywords: fuzzy logic, FVSI-LT, load shedding, stability index trac ing
1. Introduction
Adequacy of reactive power support plays a significant
role in guarantying the health of a power system from
any disturb ance s [1] . Sudd en line and ge nera tors o utages
and extreme demand increases will cause reactive power
insufficiency. As a result, the operating point of a power
system moves very close to a critical point known as
Saddle No te Bifurcation (S NB) of Q-V cur ve. Whe n such
disturbances dominate, any further reduction on reactive
power support will lead to the worst phenomenon;
namely voltage collapse or ‘black-out’ [2]. Scheduling on
generators output powers, sizing on capacitor banks and
transformers tap settings, and power flow control via
Flexible Alternating Current Transmission System
(FACTS) devices are the instances for counteracting any
instability problems. However if all of them are ex-
hausted, the only way for system recovery is by per-
forming load shedding. Article [3] – [5] reported the
techniques for rehabilitating the power system from be-
ing do mina ted b y vol tage c ollapse via under voltage load
shedding (UVLS).
Meanwhile, various electricity tracing theories or
simply power tracing algorithms have been proposed for
solving tr ansmission service pricing problems. Article [6]
is considered as the pioneered method for tracing algo-
rithm. A circuit theory based power tracing has been
proposed by [7]. A unique tracing algorithm was pro-
posed by [8] without requiring any assumptions like PSP
or matrix inversion process. Next, optimization approach
for real power tracing was firstly demonstrated by [9].
Because of involving too difficult problem formulation
(too many constraints to be considered), the technique is
less preferred for solving deregulated market problems.
An Artificial Intelligence (AI) based tracing algorithm
was firstly pr esented by [10] – [11].
This paper proposes a new approach for suitable load
buses identification using stability index tracing. Instead
of tracing the magnitude of powers as what others did,
the proposed technique traces the Fast Voltage Stability
Index (FVSI) contributed by load buses for better accu-
racy using any tracing algorithms; hence it is named as
FVSI-Load Tracing (FVSI-LT). From the traced FVSI, a
ranking list indicating the priority of load buses to be
shed can be formed by a system operator (SO) for pre-
cise load buses selection prior to load shedding.
2. The Stability Index Tracing
In this paper, the Fast Voltage Stability Index (FVSI) is
selected for the purpose of stability index tracing [12] –
[13]. Since FVSI is a line based index (which means that
it is only used to indicate stress experienced by a
particular line), there is a need to modify the index for
indicating load bus that contributes high stress on that
line. This can be achieved by performing load tracing
algorithm or sp ecificall y calle d FVSI-LT. The FVSI of an

Z. HAMID ET AL .
169
l-th line can be represented in (1) .
(1)
For a stable power system, the value of FVSI shall not
exceed unity. Otherwise, the voltage collapse phenome-
non will dominate.
2.1. FVSI Modification for FVSI-LT
Load tracing is defined as a task to trace t he powers (ge-
nerators power, line flows, and losses) extracted by an
individual load. Due to such fact, tracing the stability
index is termed FVSI-Load Tracing (FVSI-LT). Accord-
ing to [9], a power to be traced can be expressed as a
summation of indiv idual load p articipa tion in that power.
Thus, an l-th line FVSI can also be expressed as a sum-
mation of individ ual load participation, as in (2).
(2)
Substituting (1) into (2 ) in the context of load trac ing:
(3)
(4)
(5)
According to [9], the participa tion of a loa d with po w-
er QLi in receiving end line flow can be expressed as in
(6).
(6)
Thus, substituting (6) into (5):
(7)
It can be deduced that from (7), the FVSI of l-th line
contributed by i-th load of power QLi can be mathemati-
cally represented as in (8).
(8)
Thus, the only way for tracing FVSI contributed by a
load bus is by tracing the receiving end power fraction,
xri via any power tracing algorithms, as proposed in [6],
[11] and [14]. It is recommended to explore article [15]
for a brief explanation on how to perform FVSI-LT using
the existing tracing algorithms. By determining the
traced FVSI as in (8) , the syst em operator ( SO) is able to
make a ranking list of load buses precisely indicating
their priority to be shed.
2.2. Application of F VSI-LT
This section demonstrates the method for ranking load
buses according to their priority based on the traced FVSI.
Consider an IEEE 6-Bus reliability test system (RTS) as
in Figure 1 with the calculate d FVSI on line between bus
3 and 4 (FVSI3 – 4), bus 4 and 6 (FVSI6 – 4) , and bus 5 and
6 (FVSI6 – 5). After performing FVSI-LT, the traced FVSI
values contributed by each load are also included in
Figure 1. For example, FVSI on line between bus 4 and
6 contributed by load at bus 6 is noted as FVSI6 – 4(L6).
Fro m these value s, a ra nkin g list is tabul ated a s in Table
1.
Table 1. Bus and Line R anking Bas e d on FVSI-LT
Ran k
Lines
Bu ses
Traced FVSI
1
6 – 4
3
0.50
2
6 – 5
3
0.40
3
3 – 4
3
0.30
4
6 – 4
5
0.25
5
6 – 4, 6 – 5, 3 – 4
4, 5
0.20
6
3 – 4, 6 – 5, 6 – 5, 3 – 4
4, 5, 6
0.10
7
6 – 4
6
0.05
1
6
4
5
3
2
FVSI 6 – 4 = 1.00
FVSI
6 – 4 (L3) = 0.50
FVSI
6 – 5 (L3)
= 0.40
FVSI
3 – 4 (L3)
= 0.30
FVSI 3 – 4 = 0.70
FVSI 6 – 5 = 0.80
FVSI 6 – 4 (L4) = 0.20
FVSI 6 – 5 (L4) = 0.20
FVSI 3 – 4 (L4) = 0.10
FVSI 6 – 4 (L5) = 0.25
FVSI 6 – 5 (L5) = 0.10
FVSI 3 – 4 (L5) = 0.20
FVSI 6 – 4 (L6) = 0.05
FVSI 6 – 5 (L6) = 0.10
FVSI 3 – 4 (L6) = 0.10
Figure 1. IEEE 6-bus system wit h single line outage
From Table 1, bus 3 possesses the highest traced FVSI
and f ol l ow e d by bus 5, 4, an d 6. F rom th is e x ample, bus 3
becomes the major contributor for the stress experienced
ls
rl
l
XV
QZ
FVSI
2
2
4
=
( )
Li
i
r
ls
l
i
l
Qx
XV
Z
FVSI .
4
2
2
=
nloadi
l
lll FVSIFVSIFVSIFVSI ,
...+++= 21
Li
i
r
i
r
QxQ .=
∑
=
=∴
nload
i
Li
i
r
ls
l
l
Qx
XV
Z
FVSI
1
2
2
4.
ls
nloadi
rl
ls
rl
ls
rl
lXV
QZ
XV
QZ
XV
QZ
FVSI 2
2
2
22
2
12 444 ,
...+++=
( )
nloadi
rrr
ls
l
l
QQQ
XV
Z
FVSI
,21
2
2
...
4+++=
∑
=
=∴
nload
i
i
r
ls
l
l
Q
XV
Z
FVSI
1
2
2
4

Z. HAMID ET AL .
170
by tra nsmis sion li ne bet ween b us 4 and 6. The SO has to
perform load shedding by prioritizing bus 3 as the first
location t o be s hed, fol l owed by bus 5, 4, and last l y bus 6.
3. Problem Formulation via Fuzzy System
The purpose of performing FVSI-LT is to create a rank-
ing list for precise load buses identification committed
for shedding purpose. However, deciding suitable
amount of load powers to b e shed is the most critical task
in load shedding problem as this will not only affect the
post shedding condition, but also economical factors.
Too many load buses inter rupt ed dur ing load shedd ing is
not very effective. Hence, for fair amount of load powers
decided for shedding with satisfactory voltage stability
improvement, a decision making system has to be im-
plemented, namely Fuzzy Inference System (FI S). For
the purpose of this paper, only intuitive
3.1. Fuzzy Logic Concept
At first, it was proposed as a fuzzy set theory by L. A.
Zadeh in 1965. Contrary to binary logic that takes only
two values (either 0 or 1), designing a system via fuzzy
logic can have the value in between; that is the mapped
value from a crisp value is between 0 and 1. This en-
hances the flexibility of a FIS to be a good decision
maker besides requiring only simple problem formula-
tion. In deciding a crisp output value, a FIS infers one or
more inputs based on fuzzy decision rule or if-then rule.
There are two parts in the rule which are antecedent (in-
put parts) and consequent (output part). The crisp values
of input and output are mapped between 0 and 1 using
membership functions; a group of linguistic variables
plotted in graph form. A fuzzy rule consists of two-input
antecedent and one output con sequent is as follows.
Ri: IF x1 IS A AND x2 IS B, THEN y IS C
Where, Ri is the i-th rule, x1 and x2 are the inp uts, y is the
output, A, B, and C are the linguistic values specified
within the input and output space. The basic decision
making process of a FIS is divided to five steps; (1) fuz-
zify input; (2) apply fuzzy operator; (3) apply implica-
tion method; (4) aggregate a ll outputs; ( 5) defuzzi fication
[16].
3.2. Proposed Load Shedding Scheme
There are various techniques implemented for designing
membership functions of FIS. Intuition, rank ordering,
and probabilistic approach (optimization technique) [17]
are the examples of techniques utilized for better mem-
bership functions design. Due to simplicity during prob-
le m for mulatio n, intui tive tec hnique is prefe rable. In this
paper, the inputs to the designed FIS are the maximum
FVSI (FVSImax) and minimum voltage magnitude (Vmin)
of the system, whereas the output is the percentage of
allowable load powers to be shed (SL). The fuzzy rules
are constructed based on the decisions as tabulated in
Table 2.
Table 2. Fuzzy decision table
V
min
EL
VL
L
M
S
VS
ES
FVSImax
VL
L
L
L
VL
VL
EL
EL
L
M
M
L
L
VL
VL
EL
M
H
M
M
M
L
L
VL
H H H M M M L L
VH
VH
H
H
H
M
M
L
S
EH
VH
VH
VH
H
H
M
VS
EH
EH
EH
VH
VH
H
H
In addition, there are seven linguistic variables for each
input and output, as follows.
• FVSImax: ver y lo w (VL), lo w (L), medium (M) , high
(H), very high (VH), stress (S), very stress (VS).
• Vmin: extremely low (EL), very low (VL), low (L),
medium (M), stable (S), very stable (VS), extreme-
ly stable (ES).
• SL: extremely low (EL), very low (VL), low (L),
medium (M), high (H), very high (VH), extremely
high (EH).
Based on heuristic approach, seven linguistic variables
were selected for better output. In addition, the trape-
zoidal and triangular membership functions were se-
lected due to good sensitivity on to the change in input
value s. As rep orted in [17] – [18], the maximum allowa-
ble percentage of load power to be shed is 60 percents to
80 percents.
Since the proposed load shedding scheme is performed
iteratively (stage-by-stage), it is better to limit the per-
centage of shed load for each stage to a certain value. For
the purpose of this paper, 20 percents (or 0.2) of shed
load (SL) per stage is used and it is for both real and
reactive load power. The proposed membership functions
for the designed FIS are depicted in Figure 2. For the
Figure 2 . Proposed membership functions for F IS

Z. HAMID ET AL .
171
algorithm, the iterative strategy for performing load
shedding via FIS is illustrated in Figure 3.
Initiation of
contingencies
Condition
Satisfied?
Start
Yes
No
Run power flow
program
Perform FVSI-LT
Load buses ranking
Decision making via
FIS
Perform load shedding
Record FIS’s inputs
Record FIS’s inputs
End
Figure 3. L o ad shedding s trategy via IFIS
The algorith m start s by initiating disturba nces to a test
system. A power flow program is simulated to obtai n the
stability condition at pre load shedding. Thus, the re-
sulted FVSImax and Vmin are re corded and will be assigned
as the inputs to fuzzy system. Later, a power tracing al-
gorithm is implemented to perform FVSI-LT and the
traced FVSI values are used for ranking load buses ac-
cording to their priority. At this stage, an iterative load
shedding begins by feeding inputs to the designed FIS
for determining suitable amount of shed load powers, SL.
Next, Nshed (number of loads) loads are selected based on
the created ranking list; that is, the topmost load bus is
firstly selected pr ior to selecting t he next l oad b us. Then,
the power of selected load bus is shed based on FIS out-
put ( S L values) acc ording to (9).
(9)
After that, the cond ition of tes t system is eval uate d vi a
power flow program and the resulted FVSImax and Vmin
are recorded. If the stability condition at post shedding is
still unsatisfactory, similar looping process as illustrated
in Figure 3 is required. Otherwise, the overall algorithm
is terminated.
4. Results and Discussion
The proposed technique was implemented using MAT-
LAB software and validated on IEEE 57-Bus RTS. For
this paper, there are five ranking methods for load buses
identification before performing load shedding. Two of
them are based on FVSI-LT with different tracing algo-
rithms. Whereas the remaining three (non FVSI-LT) are
Loss Sensitivity (LS) [19], Risk of Voltage Instability
Index (RVI) [17], and Voltage Magnitude based ranking
(VM) [20]. The first FVSI-LT is marked as FVSI-LTA in
which the tracing algorithm is based on optimization
technique as proposed in [15]. The second one is
FVSI-LTB with TGLDF [6] as the tracing algorithm. In
conducting the experiment, all ranking methods are ana-
lyzed under four levels of contingencies (marked as C L)
as follows.
• CL1: Line outage: line 11, 15, 24, 51, 59, 75
• CL2: Generator outage: bus 2, 3, 6, 9
• CL3: Line outage: line 11, 15, 24, 51, 59, 75
Generator outage: bus 2, 3, 6, 9
• CL4: Line outage: line 11, 15, 24, 51, 59, 75
Generator outage: bus 2, 3
Load increase: 5% of total load power
The result details for post load shedding in terms of
Vmin, FVSImax, and losse s Ploss are tabulated in Appendix,
Table A.
In the table, the pre load shedding condition (marked
as ‘pre’) means the condition before load shedding was
performed. From Table A, the graphical illustrations
concerning Vmin, FVSImax, and Ploss are depicted in Figure
4, Figure 5, and Figure 6 respectively. Firstly, by look-
ing at Figure 4 all methods provide significant im-
provement on voltage profile throughout the contingen-
cies levels. As compared to pre condition, Vmin has been
improved to satisfactory magnitude of above than 0.90
p.u. It is seen that FVSI-LTA, LS, and VM provide op-
timal improvement on Vmin with magnitude of approx-
imately 1.00 p.u. for all levels. The resulted trend of
FVSImax at post load shedding is depicted in Figure 5.
This time, both FVSI-LTA and FVSI-LTB are the best
ranking methods with the lowest trend of FVSImax
through all contingencies levels (below than 0.20). The
conve ntional r ankin g metho ds (LS, RVI , and V M) resul t
to unstable trend of reduction as there exists fluctuation
Figure 4 . Vmin trend a t pos t load s hedding
).(
DDshedshedshed
jQPSLjQPS+=+=

Z. HAMID ET AL .
172
at CL1 and CL2 with magnitude of FVSImax of above
than 0.20.
Figure 5 . FVSI
max
trend at post loa d shedding
Similar trend as FVSImax is observed for losses trend in
Figure 6. The most consistent improvement on Ploss is
resulted by both FVSI-LT methods with reduced losses
of about 10 MW, however there is still no result at CL2
for FVSI-LTB. Unstable trend of losses reduction is de-
picted by conventional ranking methods through all le-
vels; implying that they are not very consistent as
FVSI-LT. Moreover, the reduced Ploss is not as good as
the proposed technique especiall y at CL2 and CL3. From
all analysis, it is revealed that the most consistent im-
provement can only be provided via FVSI-LT A. Based on
Figure 4 to Fig ure 6, the impro vement trend r esult ed b y
this method is stable and optimal regardless of contin-
gencie s sever ity. As c an be se en in Figure 5 and Figure
6, thei r i mprovement tr end c onsists of large fluctuat ion at
CL1 to CL3 and the resulted FVSImax and Ploss at those
levels is not as good as FVSI-LTA. Moreover in provid-
ing satisfactory voltage stability improvement, the num-
ber of loads involved for load shedding, Nshed requi re d b y
conventional ranking methods are higher than that of
FVSI-LT. From Table A, VM is the only method that
requires high Ns hed at all contingencies levels, followed
by LS at CL2 and CL4, and RVI at CL3. Too many loads
involved for shedding means large interruption occurs at
consumer sites and this is not good for an efficient load
sheddin g s cheme.
5. Conclusion
In brief, a new approach for precise load buses identifi-
cati on has b een proposed. The technique applied stability
index tracing namely FVSI-LT for creating a useful
ranking list of load buses. Based on the traced FVSI, the
load buses are ranked according to their p riority and this
will help the system operator (SO) to perform accurate
load buses selection prior to performing any corrective
actions against voltage instability. After validating the
reliability of ranking list in load shedding problem, it
was justified that FVSI-LT is reliable as the improvement
on voltage stability condition at post load shedding is
consistent regardless of contingencies severity. As com-
pared to other methods, ranking list via FVSI-LT pro-
vides satisfactory improvement in terms of voltage mag-
nitude, line stress, and losses minimization. Such dis-
covery has proven the capability of power tracing to be
an alternative for voltage stability improvement besides
solving power system economics prob lems as what other
researches proposed.
6. Acknowledgemen t
The authors would like to acknowledge The Research
Manage ment I nstitute (RMI) UiT M, Shah A lam, Human
Resource Department of UiTM and Ministry of Higher
Education Malaysia (MOHE) for the financial support of
this research. This research is jointly supported by Re-
search Management Institute (RMI) via the Excellence
Research Grant Scheme UiTM with project code:
600-RMI/ST/DANA 5/3/Dst (164/2011) and MOHE
under the Exploratory Research Grant Scheme (ERGS)
with project code: 600-RMI/ERGS 5/3 (14/2011).
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Appendix: Table A. Post load shedding performance under various contingencies levels – IEEE 57-Bus RTS
CL Method Nshed Top 10 load buses (based on priority)
V
min
(p.u.) FVSImax
P
loss
(MW)
1
Pre
-
0.492
1.253
56.213
FVSI
-LT
A
16 30, 25 , 31, 35 , 38, 47, 49, 28, 15, 18 0.979 0.146 12.921
FVSI-LTB
16
30 , 31, 50, 25, 42, 49, 9, 41 , 47, 18
0.984
0.095
11.852
LS
18
31, 30, 25, 33, 32, 23, 20, 35, 57, 19
0.983
0.274
12.848
RVI 23 8, 12, 3, 6, 9, 1, 2, 17, 18, 19 0.902 0.395 20.596
VM
29
30, 31, 25, 33, 32, 23, 35, 57, 20, 56
1.003
0.146
11.051
c
2
Pre
-
0.510
1.381
38.451
FVSI-LTA
19
30, 25, 38, 50, 2, 31, 35, 53, 14, 3
0.968
0.102
11.007
FVSI-LTB
-
-
-
-
-
LS
30
31, 30, 25, 33, 32, 35, 57, 56, 23, 42
0.963
0.139
21.087
RVI 22 8, 1, 12, 2, 13, 17, 3, 5, 6, 14 0.929 0.192 26.171
VM
31
30, 31, 25, 33, 32, 35, 57, 56, 23, 42
0.936
0.158
19.857
c
3
Pre
-
0.485
1.184
69.528
FVSI-LTA
15
31 , 30, 25 ,49, 9, 2, 3, 14, 35 ,38
0.950
0.098
13.211
FVSI-LTB
15
30, 31, 50, 42, 25, 2, 49 , 3, 47, 41
0.957
0.091
13.723
LS
16
31, 30, 25, 33, 32, 23, 20, 35, 57, 19
0.969
0.298
21.599
RVI 30 8, 12, 1, 17, 3, 5, 6, 13, 14, 15 0.914 0.192 24.459
VM
32
30, 31, 25, 33, 32, 23, 35, 57, 20, 56
0.957
0.189
13.758
c
4
Pre
-
0.464
1.209
89.738
FVSI-LTA
20
30, 25, 2, 3 1, 3, 14, 38, 49, 15, 28
0.957
0.107
13.955
FVSI-LTB
21
30, 31, 50, 42, 25, 2, 49, 9, 3, 47
0.959
0.098
13.671
LS
30
31, 30, 25, 33, 32, 23, 20, 35, 57, 19
1.000
0.163
10.701
RVI
20
8, 12, 6, 9, 1, 17, 3, 15, 16, 18
0.959
0.198
15.035
VM
33
31, 30, 25, 33, 32, 35, 23, 57, 20, 56
1.005
0.187
11.587