Under Voltages Load Shedding Based on Catastrophe Theory
Method for Surabaya Electrical Distribution Systems
Dimas Fajar Uman P1) Fitriana Suhartati2) A. Budiman3) Ontoseno Penangsang4)Adi
Soeprijanto5)
1) Department of Electrical Engineering, Faculty of Industrial Technology ITS Surabaya Indonesia
60111, email: dimasfup@gmail.com
2) Department of Electrical Engineering, Faculty of Industrial Technology ITS Surabaya Indonesia
60111, email: fitriana_unibraw@yahoo.com
3) Department of Electrical Engineering, Universitas Borneo Tarakan (UBT) Tarakan Indonesia, email:
achmad_b75@yahoo.co.id
4) Department of Electrical Engineering, Faculty of Industrial Technology ITS Surabaya Indonesia
60111, email: zenno_379@yahoo.com
5) Department of Electrical Engineering, Faculty of Industrial Technology ITS Surabaya Indonesia
60111, email: adisup@ee.its.ac.id
Abstract - Voltage stability problem has received
much attention of distribution companies because of
the serious consequences on distribution systems.
This problem is associated with a rapid voltage drop
because of heavy system load, which might result in
system collapse. One of the actions to prevent this
serious consequence is Under Voltage Load
Shedding (UVLS). In this paper, Catastrophe theory
is used to determine the ranking of system buses
based on voltage stability index. Basuki Rahmat
feeder and Kaliasin feeder of Surabaya Utara
electrical distribution system are used to implement
the proposed method, and the results are compared
with Loss Sensitivity method to determine the best
locations for load shedding. For a simple radial
distribution system like Kaliasin feeder, the Loss
Sensitivity and Catastrophe theory result in the same
bus ranks. However, for a complex one like Basuki
Rahmat feeder, Loss Sensitivity and Catastrophe
theory result in different best locations for load
shedding. Then, the same amount of loads are shed
for the different best locations, and the results show
that the application of Catastrophe theory method for
load shedding gives a better voltage profile than the
Loss Sensitivity method.
Keywords: under voltages, electrical distribution
system, voltage stability index, load shedding,
catastrophe theory.
1. INTRODUCTION
In electrical power system, there are two ways
delivering electrical energy from one place to another
place. First, using transmission system, second is
distribution system. During the delivery process,
disturbance often occurs both on the transmission and
distribution. Disturbance occurs frequently in
distribution system rather than transmission system.
Moreover, the distribution system directly connected to
the consumer, so it’s received much attention to
prevent distribution system from collapse. Much of
disturbance in the distribution system caused by
voltage stability problem [1, 2].
Under voltage in the electrical distribution system
caused by few things, they are: short circuit, overload,
and long distribution lines [3]. From the list above,
most common disturbance is heavy system load [3]. If
this phenomenon can’t be stopped, it might result in
system collapse. To prevent this condition, there are
several ways: switching to change a network
configuration of distribution system and under voltage
load shedding (UVLS) [14].
To optimize the load shedding value, there are two
factor [1], they are: the determination of the location of
the load shedding and load shedding techniques. To
determine the optimal location of UVLS, voltage
stability index used to determine the weakest bus. A
bus called “weakest bus” if the voltage in the bus
decreased more than another bus in the system when
load changing occurs.
Many researchers have developed method to optimize
UVLS in transmission systems [4-8], but there still a
few concern of researcher develop method for UVLS
in the distribution systems [9-11]. Some researchers
that had developed several theories for determining
voltage stability index values [11-13] in the electrical
distribution system. Newest method to find the value
of the stability index of electrical distribution system
by using catastrophe theory. In this paper will be
developed UVLS methods based on the stability index
value obtained from catastrophe theory method to
determine the optimize location for under voltage load
shedding mechanism. Two Feeders from Surabaya
electrical distribution system will used to obtain the
simulation result.
In Section II, A brief discussion is presented on
problem formulation of the system. In Section III,
proposed method is described. Meanwhile, Section IV
applying the proposed method to the system and
simulation results is discussed
2. STUDY LITERATURE
A. Voltage Stability Index
Voltage instability in distribution networks of a
power system is a local phenomenon and it occurs at
buses in an area with high variation in loads and lowvoltage profiles [1]. In this condition, the system will
become unstable if significant jump occur in the
increasing phase [1]. This phenomenon can be
analyzed by using voltage stability index to identify
the critical point in the system due to load change.
To find the voltage stability index equation, it needed
to derive the radial distribution power flow formula.
Figures 1 illustrate the power flow in the radial
distribution system:
N1
Nk
N2
Ik
The completion of the second and third for the fourth
answer above probably not used since the value of
voltage is negative, while for the voltage value from
the first completion approaching zero. From the
fourth possible answer the most appropriate solution
is number four.

V2  0.707 bk  bk  4ck

2

0.5


0.5
(8)
From the equation above, it can be noted that the
power flow solution for radial distribution system is
feasible if:
bk2  4ck  0
Zk
(9)
If the value of b and c are inserted into the equation
above, obtained the following equation
V1
P(2)+jQ(2)
V2
V
2
1
Figure 1. Electrical Radial Distribution Systems
In [11] a way to earn the power flow results in
electrical radial distribution system given. From
figure 1 may be obtained
Ik 
V1  V2
(1)
Rk  jX k
P2  jQ2  V2* I k
(2)
From equation 1 and 2 can be obtain

V2  2 P2 Rk  Q2 X k  0.5 V2
4


 P2  Q2 Z
2
2

Let
2
k
2
V
2
2
(3)
0
bk  2 P2 Rk  Q2 X k  0.5 V2

ck  Z k2 P2 2  Q2 2
2


(4)
(5)
hk  0
(6)
Equation (4), (5), and (6) substitute in equation (3)
than equation (3) become:
V2  bk V2  hk V2  ck  0
4
2
(7)
Voltage value in the node two have four possible
answer, they are:

•
0.707 bk  bk  4ck
•
0.707 bk  bk  4ck
•
•

2
 
0.707 b   b

0.707 b   b

2
k
2
k
2
k
k

0.5

 4c 
 4c 
k
k


0.5


0.5 0.5


0.5 0.5


0.5
0.5
 2 P2 Rk  2Q2 X k

2
 4  P2 Rk  Q2 X k  V1
2
 0 (10)
The above equation can be simplified to
V1  4  P2 X k  Q2 Rk   4  P2 Rk  Q2 X k  V1
4
2
2
 0 (11)
The value of voltage stability index on the bus is as
follows
SI  2   V
1
4
 4PX  Q R
2
k
2
k

2
 4PR  Q X
2
k
2
k
V
1
2
(12)
Using the above equation, the stability index value
can be determined for each bus. Bus with minimum
value of stability index have more sensitive to the
voltage changes [1].
B. Catastrophe theory
In bifurcation theory there is branch that study about
dynamic stability, it called catastrophe theory.
Catastrophe theory firstly introduced by a French
scientist named René Thom in the 1960’s. In 1970s
catastrophe theory is popular because a scientist
named Christopher Zeeman found that the value of
long-run stability can be identified smoothly by using
potential function (lyapunov function) that governed
by catastrophe theory.
Load fluctuation is very often In the electrical
distribution system, the phenomenon of the load
fluctuation is very often happened with large
fluctuation range. This phenomenon can be analyzed
using catastrophe theory to determine the value of
stability after a sudden load changes. The value of
stability that is calculated from catastrophe theory is
a representation of the stability value on every bus in
the electrical distribution system. This stability value
is also represents stability index of every bus.
From the (3) can be derived from catastrophe theory
is as follow:
 bk   c  0
  k
2
2
(13)
So the value of voltage stability index can be
determined using the following equation
VSI cat
 2   P R
2
k
 Q2 X k  0.5 V1
2

2

2
START

 Z k P2  Q2 (14)
2
2
Determine System
Parameters
In addition, catastrophe theory can be used to
determine critical voltage in a bus and maximum
loading in the bus.
In this paper, catastrophe theory used to determine
the voltage stability index value in every bus, and to
determine the bus rank from the upper to lower
stability index. This is to get bus rank to decide
priority of the load shedding.
Running Distribution Power
Flow
3. METHODOLOGY
Method for solving under voltage problem shown
below:
1. First determine the systems parameter: load and
impedance at each bus.
2. Running distribution power flow for knowing
current flow each node.
3. Check the voltage each bus, if there are voltage
value under the normal condition.
4. If there is under voltage condition then check
voltage stability index using catastrophe theory.
5. Determine bus rank for highest loss sensitivity
value till the lowest value.
6. Bus with the highest sensitivity value is the bus
to be shed for the first time.
7. Execute load shedding depending on the bus
ranking from the catastrophe theory.
8. Do load shedding mechanism until the voltage
on the system in the normal condition.
V < Vmin
Yes
No
Calculate Bus
Ranking using
Catastrophe and loss
sensitivity
Determine Load
Shedding Value
Yes
V < Vmin
No
Flowchart for Catastrophe method described in the
figure 2.
System Stable
4. RESULTS AND DISCUSSIONS
STOP
A. Surabaya Utara Electrical Distribution Data
Surabaya Utara Electrical Distribution Data that used
in this paper is Kaliasin and Basuki Rahmat 20 kV
Distribution Feeder. Kaliasin feeder represents a small
and simple model of radial distribution feeder and
Basuki Rahmat represent a large and complex radial
distribution feeder.
1)
Kaliasin Feeder Data
For a normal condition kaliasin feeder have 10
buses with 5 loads. Nominal power for Kaliasin
feeder is 626.5 KVA, 603 KW and 170 KVAR
2)
Basuki Rahmat Feeder Data
For a normal condition Basuki Rahmat feeder
have 29 buses with 22 loads. Nominal power
for Basuki Rahmat feeder is 3.29 MVA, 3.19
MW and 0.795 MVAR.
Figure 2. Flowchart for Under Voltages Load Shedding for
Surabaya
TABLE I. LOAD DATA OF KALIASIN FEEDER
Bus No
1
2
3
4
5
6
7
8
9
10
Total
P(kW)
0
0
74
0
58
95
0
64
0
312
603
Q(kVar)
0
0
21
0
19
31
0
19
0
80
170
Voltage(p.u)
1
0.9889
0.9889
0.9865
0.9865
0.9864
0.9862
0.9859
0.9859
0.9847
-
20 kV
20 kV
Node
1
Node
1
20 kV
20 kV
20 kV
Node
5
20 kV
Node
6
20 kV
Node
2
Node
4
Node
3
20 kV
Node
2
20 kV
20 kV
Node
7
20 kV
Node
11
Node
3
20 kV
Node
8
20 kV
Node
4
20 kV
Node
12
20 kV
Node
9
20 kV
20 kV
Node
14
Node
13
20 kV
Node
15
Node
5
20 kV
20 kV
20 kV
20 kV
Node
18
20 kV
20 kV
Node
7
Node
21
Node
6
Node
16
20 kV
20 kV
Node
19
20 kV
20 kV
Node
22
Node
17
20 kV
Node
20
Node
8
Node
10
Node
29
20 kV
20 kV
20 kV
20 kV
Node
9
Node
23
20 kV
Node
10
Node
24
20 kV
20 kV
Node
25
Node
26
20 kV
20 kV
Node
27
Figure 3. Single Line Diagram of Kaliasin Feeder
TABLE II. LOAD DATA OF BASUKI RAHMAT FEEDER
Bus No
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
Total
P(MW)
0
0
0.279
0.029
0.039
0
0.342
0.601
0.066
0.054
0
0.025
0.455
0
0.012
0
0.317
0
0.067
0.108
0.083
0.146
0.129
0.078
0.097
0.092
0.04
0.038
0.097
3.194
Q(MVar)
0
0
0.061
0.006
0.009
0
0.087
0.1
0.018
0.025
0
0.005
0.127
0
0.003
0
0.086
0
0.018
0.029
0.023
0.058
0.034
0.018
0.028
0.022
0.006
0.012
0.02
0.795
Figure 4. SLD of Basuki Rahmat Feeder
B. UVLS for Kaliasin and Basuki Rahmat Feeder
In this section, load increment case added in Kaliasin
and Basuki Rahmat feeder to make the voltage under
the normal condition. In PLN standard book/grid code
book [14] for 20 kV distribution system, normal
condition range is +5% and -10%. To make Kaliasin
feeder voltages under normal condition, 626.5 KVA
load added. Detail of additional load given in table 3
TABLE III. KALIASIN FEEDER DATA AFTER LOAD ADDITION
No Bus
1
2
3
4
5
6
7
8
9
10
Total
P(kW)
0
0
674
0
1558
695
0
64
0
1312
4303
Q(kVar)
0
0
160
0
419
131
0
19
0
280
1009
For Basuki Rahmat feeder, to make under voltage
condition 1507 KVA load added in bus 22. Detail of
additional load given in table 4
TABLE IV. BASUKI RAHMAT FEEDER DATA AFTER LOAD
ADDITION
No Bus
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
Total
P(MW)
0
0
0.279
0.029
0.039
0
0.342
0.601
0.066
0.054
0
0.025
0.455
0
0.012
0
0.317
0
0.067
0.108
0.083
1.646
0.129
0.078
0.097
0.092
0.04
0.038
0.097
4.694
Q(MVar)
0
0
0.061
0.006
0.009
0
0.087
0.1
0.018
0.025
0
0.005
0.127
0
0.003
0
0.086
0
0.018
0.029
0.023
0.258
0.034
0.018
0.028
0.022
0.006
0.012
0.02
0.995
Under abnormal voltage conditions during load
addition, UVLS needed to restore the voltage
magnitude in normal range condition.
Before determining load shedding value, first step of
the load shedding mechanism is make a ranking of the
system buses from the weakest until the strongest bus.
For Kaliasin feeder, loss sensitivity and catastrophe
method have an equal sequence of the bus ranking.
But in Basuki Rahmat feeder, the sequences for loss
sensitivity and catastrophe bus ranking are different.
TABLE V. BUS RANKING FOR KALIASIN FEEDER
Loss Sensitivity Rank Bus
Sequence
10
5
6
8
3
9
7
4
2
1
Catastrophe Rank Bus
Sequence
10
5
6
8
3
9
7
4
2
1
TABLE VI. BUS RANKING FOR BASUKI RAHMAT FEEDER
Loss Sensitivity Rank Bus
Sequence
22
13
3
8
17
7
25
10
21
29
20
24
19
23
9
5
26
28
27
12
15
4
18
16
14
11
6
2
1
Catastrophe Rank Bus
Sequence
22
8
3
13
7
17
25
29
21
10
20
24
5
9
19
23
26
28
27
12
4
15
18
16
14
11
6
2
1
For the bus rank sequence of Kaliasin feeder, weakest
buses are bus 10 and the sequence rank number two
until five are bus 5, bus 6, bus 8 and bus 3.
After knowing the bus ranking, load shedding
mechanism value set as below
TABLE VII. KALIASIN FEEDER LOAD SHEDDING DATA FOR
WEAKEST BUS RANKING
Bus No Load Shedding Value
10
25%
Shedded Load
P(kW)
Q(kVar)
328
70
TABLE VIII. KALIASIN FEEDER LOAD SHEDDING DATA FROM
NON-WEAKEST BUS RANKING
Bus No Load Shedding Value
5
6
8
3
15%
13%
12%
12%
Total
Shedded Load
P(kW)
Q(kVar)
233.7
62.85
90.35
17.03
7.68
2.28
80.88
19.2
412.61
101.36
TABLE IX.
VOLTAGE PORFILE AFTER LOAD SHEDDING
MECHANISM IN KALIASIN FEEDER
Voltage profile after LS
Bus
mechanism from weakest
No
bus (p.u)
1
1
2
0.9222
3
0.9219
4
0.906
5
0.9047
6
0.9054
7
0.9049
8
0.9046
9
0.9039
10
0.9001
Voltage profile after LS
mechanism from nonweakest bus (p.u)
1
0.924
0.9237
0.9078
0.9068
0.9074
0.9064
0.9062
0.9051
0.9
From table VI, VII and VIII load shedding amount
based on the weakest bus ranking is 328 kW and 70
kVar, but if random bus used for load shedding
mechanism is 412.61 kW and 101.36 kVar. Can be
concluded that load shedding mechanism using
weakest bus rank it need less amount of load to be
shed.
In Basuki Rahmat feeder, bus rank sequences were
calculated by loss sensitivity and catastrophe theory is
different. To know what is the best method to search
bus stability ranking, loss sensitivity and catastrophe
theory will used to make load shedding mechanism for
Basuki Rahmat feeder. From table VI bus 8 and 13 is
at the different rank for loss sensitivity and
catastrophe theory. To compare which is the best
method for determining location for load shedding
mechanism, Table X shows the load shed for bus 8
and 13 and table XI shows the load shedding result
TABLE X.
BASUKI RAHMAT FEEDER LOAD SHEDDING DATA
IN BUS 8 AND 13
Bus No
8
13
P(MW)
0.1
0.1
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
Shedded Load
Q(MVar)
S (MVA)
0.1
0.14142136
0.1
0.14142136
VOLTAGE PORFILE AFTER LOAD SHEDDING
MECHANISM IN BASUKI RAHMAT FEEDER
TABLE XI.
Voltage profile
Voltage profile
after Load
after Load
Shedding in bus
Shedding in bus
Bus No. 8 (Bus Ranking
Difference (%)
13 (Bus Ranking
using
using Loss
Catastrophe
Sensitivity)
Theory)
1
1
1
0
2
0.9513
0.9506
0.0735835
3
0.9509
0.9502
0.0736145
4
0.9513
0.9506
0.0735835
5
0.9513
0.9506
0.0735835
6
0.9432
0.9425
0.0742154
7
0.9429
0.9421
0.0848446
8
0.9428
0.9419
0.0954603
0.9432
0.9432
0.9369
0.9364
0.936
0.9207
0.9207
0.9137
0.9134
0.9107
0.9107
0.9106
0.9065
0.9018
0.9015
0.9012
0.9006
0.9005
0.9005
0.9004
0.9105
0.9424
0.9424
0.9363
0.9359
0.9355
0.9201
0.92
0.9131
0.9127
0.9101
0.91
0.91
0.9058
0.9011
0.9008
0.9005
0.9
0.8999
0.8998
0.8998
0.9099
0.0848176
0.0848176
0.064041
0.053396
0.0534188
0.0651678
0.0760291
0.0656671
0.0766367
0.0658834
0.076864
0.0658906
0.0772201
0.0776225
0.0776484
0.0776742
0.0666223
0.0666297
0.0777346
0.0666371
0.0658979
From the simulation if bus 8 used for load shedding,
minimum voltage is 0.9004 p.u at bus 28. If bus 13
used for load shedding, minimum voltage is 0.8998
p.u at bus 28. It’s mean that bus 8 has weaker bus
stability than bus 13. Determining bus stability
ranking using catastrophe theory is better than using
loss sensitivity.
5. CONCLUSIONS
For Kaliasin feeder, bus ranking sequence by using
loss sensitivity and catastrophe theory has the same
sequence, but for Basuki Rahmat feeder the bus
ranking sequence is different. Minimum voltage is
0.9004 p.u at bus 28 by using Catastrophe ranking
and 0.8998 p.u at bus 28 by using loss sensitivity
method. From the simulation can be shows that
catastrophe theory method is more accurate than
loss sensitivity method.
ACKNOWLEDGEMENT
The authors wish a highly grateful to the JICA
PREDICT PHASE 2 Batch 1, Power System
Simulation Laboratory, Department of Electrical
Engineering, Sepuluh Nopember Institute of
Technology (ITS), Surabaya, Indonesia to all facilities
and founded during this research.
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