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:
2)Department of Electrical Engineering, Faculty of Industrial Technology ITS Surabaya Indonesia 60111, email:
3)Department of Electrical Engineering, Universitas Borneo Tarakan (UBT)Tarakan Indonesia, email:
4)Department of Electrical Engineering, Faculty of Industrial Technology ITS Surabaya Indonesia 60111, email:
5)Department of Electrical Engineering, Faculty of Industrial Technology ITS Surabaya Indonesia 60111, email:
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 byvoltage 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 undervoltage 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 decreasedmore than another bus in the system when load changingoccurs.
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 low-voltage 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:
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
(1)
(2)
From equation 1 and 2 can be obtain
(3)
Let
(4)
(5)
(6)
Equation (4), (5), and (6) substitute in equation (3) than equation (3) become:
(7)
Voltage value in the node two have four possible answer, they are:
•
•
•
•
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.
(8)
From the equation above, it can be noted that the power flow solution for radial distribution system is feasible if:
(9)
If the value of b and c are inserted into the equation above, obtained the following equation
(10)
The above equation can be simplified to
(11)
The value of voltage stability index on the bus is as follows
(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:
(13)
So the value of voltage stability index can be determined using the following equation
(14)
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.
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.
Flowchart for Catastrophe method described in the figure 2.
4.RESULTSANDDISCUSSIONS
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 / P(kW) / Q(kVar) / Voltage(p.u)1 / 0 / 0 / 1
2 / 0 / 0 / 0.9889
3 / 74 / 21 / 0.9889
4 / 0 / 0 / 0.9865
5 / 58 / 19 / 0.9865
6 / 95 / 31 / 0.9864
7 / 0 / 0 / 0.9862
8 / 64 / 19 / 0.9859
9 / 0 / 0 / 0.9859
10 / 312 / 80 / 0.9847
Total / 603 / 170 / -
Figure 3. Single Line Diagram of Kaliasin Feeder
TABLE II. Load Data Of Basuki Rahmat Feeder
Bus No / P(MW) / Q(MVar)1 / 0 / 0
2 / 0 / 0
3 / 0.279 / 0.061
4 / 0.029 / 0.006
5 / 0.039 / 0.009
6 / 0 / 0
7 / 0.342 / 0.087
8 / 0.601 / 0.1
9 / 0.066 / 0.018
10 / 0.054 / 0.025
11 / 0 / 0
12 / 0.025 / 0.005
13 / 0.455 / 0.127
14 / 0 / 0
15 / 0.012 / 0.003
16 / 0 / 0
17 / 0.317 / 0.086
18 / 0 / 0
19 / 0.067 / 0.018
20 / 0.108 / 0.029
21 / 0.083 / 0.023
22 / 0.146 / 0.058
23 / 0.129 / 0.034
24 / 0.078 / 0.018
25 / 0.097 / 0.028
26 / 0.092 / 0.022
27 / 0.04 / 0.006
28 / 0.038 / 0.012
29 / 0.097 / 0.02
Total / 3.194 / 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 / P(kW) / Q(kVar)1 / 0 / 0
2 / 0 / 0
3 / 674 / 160
4 / 0 / 0
5 / 1558 / 419
6 / 695 / 131
7 / 0 / 0
8 / 64 / 19
9 / 0 / 0
10 / 1312 / 280
Total / 4303 / 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 / P(MW) / Q(MVar)1 / 0 / 0
2 / 0 / 0
3 / 0.279 / 0.061
4 / 0.029 / 0.006
5 / 0.039 / 0.009
6 / 0 / 0
7 / 0.342 / 0.087
8 / 0.601 / 0.1
9 / 0.066 / 0.018
10 / 0.054 / 0.025
11 / 0 / 0
12 / 0.025 / 0.005
13 / 0.455 / 0.127
14 / 0 / 0
15 / 0.012 / 0.003
16 / 0 / 0
17 / 0.317 / 0.086
18 / 0 / 0
19 / 0.067 / 0.018
20 / 0.108 / 0.029
21 / 0.083 / 0.023
22 / 1.646 / 0.258
23 / 0.129 / 0.034
24 / 0.078 / 0.018
25 / 0.097 / 0.028
26 / 0.092 / 0.022
27 / 0.04 / 0.006
28 / 0.038 / 0.012
29 / 0.097 / 0.02
Total / 4.694 / 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 / Catastrophe Rank Bus Sequence10 / 10
5 / 5
6 / 6
8 / 8
3 / 3
9 / 9
7 / 7
4 / 4
2 / 2
1 / 1
TABLE VI. Bus Ranking for Basuki Rahmat Feeder
Loss Sensitivity Rank Bus Sequence / Catastrophe Rank Bus Sequence22 / 22
13 / 8
3 / 3
8 / 13
17 / 7
7 / 17
25 / 25
10 / 29
21 / 21
29 / 10
20 / 20
24 / 24
19 / 5
23 / 9
9 / 19
5 / 23
26 / 26
28 / 28
27 / 27
12 / 12
15 / 4
4 / 15
18 / 18
16 / 16
14 / 14
11 / 11
6 / 6
2 / 2
1 / 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 / Shedded LoadP(kW) / Q(kVar)
10 / 25% / 328 / 70
TABLE VIII. Kaliasin Feeder Load Shedding data from non-weakest bus Ranking
Bus No / Load Shedding Value / Shedded LoadP(kW) / Q(kVar)
5 / 15% / 233.7 / 62.85
6 / 13% / 90.35 / 17.03
8 / 12% / 7.68 / 2.28
3 / 12% / 80.88 / 19.2
Total / 412.61 / 101.36
TABLE IX. Voltage porfile after Load Shedding Mechanism in Kaliasin Feeder
Bus No / Voltage profile after LS mechanism from weakest bus (p.u) / Voltage profile after LS mechanism from non-weakest bus (p.u)1 / 1 / 1
2 / 0.9222 / 0.924
3 / 0.9219 / 0.9237
4 / 0.906 / 0.9078
5 / 0.9047 / 0.9068
6 / 0.9054 / 0.9074
7 / 0.9049 / 0.9064
8 / 0.9046 / 0.9062
9 / 0.9039 / 0.9051
10 / 0.9001 / 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 / Shedded LoadP(MW) / Q(MVar) / S (MVA)
8 / 0.1 / 0.1 / 0.14142136
13 / 0.1 / 0.1 / 0.14142136
TABLE XI. Voltage porfile after Load Shedding Mechanism in Basuki Rahmat Feeder
Bus No. / Voltage profile after Load Shedding in bus 8 (Bus Ranking using Catastrophe Theory) / Voltage profile after Load Shedding in bus 13 (Bus Ranking using Loss Sensitivity) / Difference (%)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
9 / 0.9432 / 0.9424 / 0.0848176
10 / 0.9432 / 0.9424 / 0.0848176
11 / 0.9369 / 0.9363 / 0.064041
12 / 0.9364 / 0.9359 / 0.053396
13 / 0.936 / 0.9355 / 0.0534188
14 / 0.9207 / 0.9201 / 0.0651678
15 / 0.9207 / 0.92 / 0.0760291
16 / 0.9137 / 0.9131 / 0.0656671
17 / 0.9134 / 0.9127 / 0.0766367
18 / 0.9107 / 0.9101 / 0.0658834
19 / 0.9107 / 0.91 / 0.076864
20 / 0.9106 / 0.91 / 0.0658906
21 / 0.9065 / 0.9058 / 0.0772201
22 / 0.9018 / 0.9011 / 0.0776225
23 / 0.9015 / 0.9008 / 0.0776484
24 / 0.9012 / 0.9005 / 0.0776742
25 / 0.9006 / 0.9 / 0.0666223
26 / 0.9005 / 0.8999 / 0.0666297
27 / 0.9005 / 0.8998 / 0.0777346
28 / 0.9004 / 0.8998 / 0.0666371
29 / 0.9105 / 0.9099 / 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 methodis 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.
REFERENCES
[1] Mahmoud, G.A., “Voltage Stability Analysis of Radial Distribution Network Using Catastrophe Theory,” IET Generation, Transmission & Distribution, Vol. 6 Iss.7, pp.612-618. 2012.
[2]Takahashi,K., Nomura, Y., “The power system failure on July 23rd 1987 in Tokyo”, CIGRE SC-37 Meeting 37.87(JP)07(E),1987.
[3]PT PLN Distribusi Area Surabaya
[4]Van Cutsem, T.: ‘Voltage instability: phenomena, countermeasures,and analysis methods’, Proc. IEEE, 2000, 88, (2), pp. 208–2227.
[5]Parker,C.J., Morrison, I.F., Sutanto, D.,"Simulation of Load Shedding as a corrective action against voltage collapse," Electric Power Systems Research 46 (1998) 235–241
[6]Deng, Jiyu., Liu, Junyong., “A Study on a Centralized Under-Voltage Load Shedding Scheme Considering the Load Characteristics,” International Conference on Applied Physics and Industrial Engineering. 2012.
[7]Liu Bin, Chen Lei, Min Yong., “Determination of the location of under-voltage load shedding considering transient voltage Stability.” Automation of Electric Power Systems, 2008, 32(5): 11-14.
[8]Tuan T Q, Fandino J., “Emergency load shedding to avoid risks of voltage instability using indicators.” IEEE Trans on Power Systems,1994,9(1): 341-351.
[9]Ma Ping, Cai Xing-guo, Yu Ji-lai.,”A study on a under voltage load shedding strategy based minimum mismatch function,”.Proceedings of the CSEE,2005,25(1)：27-31.
[10]Uman P. Dimas Fajar,, Penangsang Ontoseno, Soeprijanto Adi,Abdillah Muhammad.,” Intelligent Underfrequency Load Shedding for 500kV Java-Bali Electrical Power System.”,3rd APTECS 2011.
[11]Chakravorty,M., Das,D.,” Voltage stability analysis of radial distribution networks.,” Electrical Power and Energy Systems 23, 2001.
[12]U. Eminoglu M. H. Hocaoglu.,” A Voltage Stability Index For Radial Distribution Networks.”, UPEC 2007
[13]Sayonsom Chanda, Bappa Das.,” Identification of Weak Buses in a Power Network Using Novel Voltage Stability Indicator in Radial Distribution System.”, India International Conference on Power Electronics (IICPE), 2010
[14]PT PLN P3B Jawa-Bali, “Greed Code(aturan Jaringan)” PT PLN, 2007.