DOI : 10.17577/IJERTV6IS090108
- Open Access
- Total Downloads : 195
- Authors : Trong Nghia Le, Giang Tran Tung , Ngoc Au Nguyen, Anh Quyen Huy , Do Ngoc An
- Paper ID : IJERTV6IS090108
- Volume & Issue : Volume 06, Issue 09 (September 2017)
- Published (First Online): 19-09-2017
- ISSN (Online) : 2278-0181
- Publisher Name : IJERT
- License:
This work is licensed under a Creative Commons Attribution 4.0 International License
Emergency control of load shedding based on Fuzzy- AHP algorithm
L.T. Nghia1, T.T. Giang1, N.N. Au1,
Q.H. Anp, Do.Ngoc. An1
1Faculty of Electrical and Electronics Engineering, HCMC University of Technology and Education Hochiminh city, Vietnam
AbstractLoad shedding is considered one of the methods used in emergency situations to avoid instability and quickest recovery. In load shedding, anti-instability and spreading, it is important to quickly propose a reasonable load shedding strategy that will allow rapid recovery frequencies and the frequency values are acceptable. This paper presented the building of load shedding strategy that includes pre-designed rules based on the Fuzzy-AHP algorithm. The Fuzzy-AHP algorithm calculates the importance factor of the load in the electrical system. Load shedding are performed with low priority loads to help reduce the economic losses. When the electrical system is determined to be unstable, immediately, the load shedding control commands is executed, so the decision-making time is shortened and the damage caused by the load shedding is reduced compared to the traditional methods. The effectiveness of the proposed method is checked on the IEEE 39-bus system.
Keywords Load Shedding; fuzzy-AHP; power system stability; UFLS
-
INTRODUCTION
Controlling the load shedding in the electrical system requires both economic and technical efficiency. Thereby, it must ensure the power system continues to maintain stability and cause the least damage when the load has to be shed. The method of load shedding by under frequency relay (R81), or under voltage relay (R27) is the most commonly used method for frequency and voltage stability control, and maintenance stability of the system under the necessary conditions [1,2].
In conventional load-shedding, when the frequency or voltage fluctuates outside the pre-set operating range, the under frequency/under voltage relay will cut the load. Therefore, it will prevent the frequency/voltage reduce and its effects. The under frequency load shedding relays are set to cut a predetermined load capacity of 3-5 steps when the frequency reduce below the set threshold in order to keep the power system stable.
To improve the effectiveness of the load shedding, some load shedding methods are based on the declining frequency (df/dt) [3], or are used the second derivative to forecast the frequency and load shedding [4]. These methods mainly restore the frequency of allowable values and prevent the black out. To optimize the amount of load shedding, some intelligent methods were proposed such as: artificial neural networks (ANNs) [5,6], fuzzy logic, neuro-fuzzy, particle swarm optimization (PSO), genetic algorithm (GA) [7-9]. These publications are focused on under frequency load shedding in
the steady state of operation of the power system. However, due to the complexity of the electrical system, in the emergency operating mode, these cases had a problem of the burden of calculation; the processing speed of the algorithm program was slow or has to shed the passive load after the frequency was under the threshold. It took much time and caused delay in load shedding decision leading to the instable power system. In particular, in the electricity market today, the need to ensure quality of power and reduce the economic losses associated with load shedding should be addressed.
In order to overcome the limitations of traditional methods, it is necessary to propose a new model for load shedding control based on rules that pre-design according to the Fuzzy- AHP algorithm. When the power system is unstable, the load shedding control commands immediately executes, so the decision-making time is shortened. The effectiveness of the proposed method is test on the IEEE 39-bus electrical system diagram.
-
MATERIALS AND METHODS
-
Analytic Hierarchy Process (AHP)
Analytic Hierarchy Process (AHP) is one of Multi Criteria decision making method that was originally developed by Prof. Thomas L. Saaty. In short, it is a method to derive ratio scales from paired comparisons [10, 11]. This method presents assessment method and criteria, and works collectively to arrive at a final decision. AHP is particularly well suited for case studies involving quantitative and analytical, making decisions when there are multiple standards-dependent alternatives with multiple interactions.
The steps of the AHP algorithm can be expressed as follows:
Step 1: Set up a decision hierarchy model.
Fig. 1. AHP model of the arrangement of units
Step 2: Build judgment matrix LC and LN that show the important factor between load centers (LC) and load nodes (LN) each other of the power system. The value of elements in the judgment matrix reflects the users knowledge about the relative importance between every pair of factors.
W *
n
i
W i , i = 1, …, n (6)
j
W *
j 1
w D1/w D1 w D1/w D2 ….. wD1/w Dn
w /w w /w ….. w /w
D2 D1 D2 D2 D2 Dn
In this way, there are eigenvectors of matrix A,
T
. .
LC
W W1 ,W2 ,…,Wn
(7)
. .
. .
(4) Calculation of the largest eigenvalues of matrix A
w Dn /w D1 wDn /w D2 ….. w Dn /w Dn
w K1/w K1 w K1/w K2 ….. w K1/w Kn
;
max
( AW ) j
n
, j= 1, …, n (8)
nW
w
K2 /w K1
w K2 /w K2
….. w
K2 /w Dn
i1 i
.
LN
.
.
w Kn /w K1
w Kn /w K2
.
.
.
….. w Kn /w Kn
(1)
Where, AWi represents the i-th component of the vector AW.
Step 4: Hierarchy ranking and check the consistency of the results.
where, wDi/wDj is the relative importance of the ith load node compared with the jth load node; wki /wkjis the relative
-
The definition of the triangular fuzzy number and the operational laws of triangular fuzzy numbers [12]
importance of the ith load center compared with the jth load
center. The value of wki /wkj, wDi/wDj can be obtained
The membership function
~
M (x) : R [0,1]
of the triangular
~
according to the experience of electrical engineers or system operators by using some 1 9 ratio scale methods.
fuzzy number M (l, m, u) defined on R is equal to
According to the principle of AHP, the weighting factors of the loads can be determined through the ranking computation
x
m l
-
, x [l, m] m l
of a judgment matrix, which reflects the judgment and comparison of a series of pair of factors. Therefore, the unified weighting factor of the load nodes of the power system can be
~
x u
M (x) m u m u , x [m, u]
obtained from the following equation:
wij = wKj x wDi Di Kj (2)
0,
otherwise
(9)
where, Di Kj means load node Di is located in load center
Where, l m u and, l and u are respectively lower and
~
Kj.
bound values of the support of M . According to Zadehs
Step 3: Calculate the largest eigenvalue and corresponding
extension principle given two triangular fuzzy numbers
eigenvectors of judgment matrix.
~
(l , m , u ) and
~
(l , m , u )
( l and l 0).
To calculate the eigenvalue of matrix largest jdgment, can use the root methods.
-
Multiply all the components in each row of the judgment matrix.
Mi i X ij , i = 1, , n; j = 1, , n (3)
Here, n is the dimension of the judgment matrix A, Xij is the element of the matrix A.
M1 1 1 1
M 2 2 2 2 1 2
-
Calculate the n th root of Mi
~
Fig. 2. The comparison of two fuzzy numbers M 1
~
and M 2
Mi i X ij
i = 1, …, n (4)
The extended addition is defined as:
, ~ ~
* * * * T
M1 M2 (l1 l2 , m1 m2 ,u1 u2 )
(10)
Vector W *: W
W1 ,W2 ,…,Wn
(5)
The extended multiplication is defined as:
-
Standardize vector W * ~ ~
(11)
M1 M 2 (l1l2 , m1m2 ,u1u2 )
~
The inverse of triangular fuzzy number M 1
is defined as:
Step 4: Calculate the weights in the sub-factors (load units) for the whole system. This weight is calculated by multiplying
~ 1
M 1
1
1
1
, ,
u1 m1 l1
(12)
the numerator by the weighted coefficients by the weight of the respective principal factors.
-
-
-
Fuzzy – AHP Model
The conventional AHP approach may not fully reflect a
According to Chang's Fuzzy-AHP method [15-17],
style of human thinking. One reason is that decision makers
-
~ n m
~ 1
usually feel more confident to give interval judgments rather than expressing their judgments in the form of single numeric values. As a result, fuzzy AHP and its extensions are developed to solve alternative selection and justification problems. Fuzzy-AHP method determines the significance of the load units in the power system, is performed by following
S M j j1
gi
i
where,
M j
gi
i1 j1
(13)
these steps [12]:
Step 1: Identify main factors and sub-factors.
m ~ m m m
M
gi
j
j j
j l , m , u
Step 2: Develop an AHP model based on these factors determined in Step 1.
Step 3: Calculate the weighting of the important factor of
j1
j1
n
j1
j1
;
these load centers together and the important factor of load
n m ~ 1 1 1 1
units in the same load center based on the judgment matrix
M j
, ,
(14)
was been fuzzy. Percentage of fuzzy about the important
gi
n n
factor to measure the relevant weighting is given in Fig 3 and Table I. This rate was proposed by Kahraman [13] and was
i 1 j 1
ui
i1
mi
i1
ui l
i1
used to resolve the problems fuzzy implementation of decisions [13,14].
The degree of possibility of
~ ~
M 2 (l2 , m2 ,u2 ) M1 (l1 , m1 ,u1 )
is defined as:
~ ~ ~ ~
V (M 2 M1) sum[min(M 1 (x), M 2 ( y))]
~ ~ ~ ~ ~
1,
if m2 m1
V (M 2 M1) hgt(M1 M 2 ) M 2 (d ) 0, if l2 u1
l1 u2
m u m l ,
otherwise
2 2 1 1
~ ~
(15)
Fig. 3. Linguistic scale for relative importance
See Fig. 3 V (M 2 M1) in case
m2 l1 u2 m1 where d
TABLE I. LINGUISTIC SCALES FOR DIFFICULTY AND IMPORTANCE
is the ordinate of the highest intersection point D between
Linguistic scale for difficulty
Linguistic scale for
importance
Triangular fuzzy scale
Triangular fuzzy reciprocal scale
Just equal
Just equal
(1,1,1)
(1,1,1)
Equally difficult
Equally important (EI)
(1/2,1,3/2)
(2/3,1,2)
(ED)
Weakly more important
(1,3/2,2)
(1/2,2/3,1)
Weakly more
(WMI)
difficult (WMD)
Strongly more
Strongly more important (SMI)
(3/2,2,5/2)
(2/5,1/2,2/3)
difficult (SMD)
Very strongly more
Very strongly more difficult (VSMD)
important (VSMI)
Absolutely more important (AMI)
(2,5/2,3)
(5/2,3,7/2)
(1/3,2/5,1/2)
(2/7,1/3,2/5)
Absolutely more
difficult (AMD)
~ ~
M1 and M 2
~
. To compare M1
~
and M 2
need to both the values of
~ ~ ~ ~
V (M1 M2 ) andV (M 2 M 1 ) . The degree possibility for a
convex fuzzy number to be greater than k convex fuzzy numbers Mi (i = 1,2,. . .,k) can be defined by
~ ~ ~ ~ ~ ~
V (M
M1, M 2 ,…M k ) minV (M
M i )
, i
= 1,2,,k (16)
Finally,
W (min V (S1
Sk
), min V (S2
Sk
),…,V (Sn
Sk
))T
(17)
is the weight vector, for k=1,2,,n.
The weighting importance of the load units of the system is calculated by multiplying the weights of the load nodes with the weight of the corresponding load center.
Step 5: Sort by descending order of importance of each load unit to implement load shedding strategy by priority.
TABLE II. SORT BY DESCENDING ORDER OF IMPORTANCE OF THE LOAD UNITS
Load Center
Load
W
Notes
LC1
LC1 LC3 LC4
L1
L2
….
W1
W2
…
W1>W2> ….
-
-
Proposed method
Fig. 4. Flowchart of steps using Fuzzy-AHP method to load shedding
-
-
SIMULATIONS AND RESULTS
To compare the effectiveness of load shedding base on Fuzzy-AHP, we simulation the proposed algorithm on the IEEE 39 bus system for using case proposed method and using traditional method.
Considering the loss of a generator causes the system to become unstable (frequency decreases less than 59.7 Hz or rotor deviation greater than 1800 at the bus). Corresponding to each case, it will develop a "control strategy" in the load shedding to restore the parameters back to the initial stable state. This paper simulations using PowerWorld and observes the results obtained when applying the proposed load shedding.
Calculate the importance factor of load based on the Fuzzy
– AHP algorithm:
Fig. 5. Diagram of the power system 39 bus 10 generators for case study Based on the grid of the elements and the number of the loads, divide the system into 4 load centers. This system is similar to a National grid, in which each loading area is a province (or possibly a cluster of provinces). The number of loads in the area is the transformer stations in that province.
Use the Fuzzy – AHP method to determine load and load center weights in the system. Follow the steps of the Fuzzy- AHP algorithm model:
Step 1: Identify the load centers and load units in the load center (main factors and sub-factors).
In this model, the system has four load centers LC1, LC2, LC3, LC4 and has 19 load units as shown in Table III.
TABLE III. SYNTHESIZE DIVISION OF LOAD CENTERS, GENERATORS AND LOADS
LC
GEN
LOAD
N. OF LOAD
LC1
G30,31,32
L4, 7, 8, 12, 31, 39
6
LC2
G33, 34, 35, 36
L15, 16, 20, 21, 23,
24
6
LC3
G38
L26, 27, 28, 29
4
LC4
G37, 39
L3, 18, 25
3
Step 2: Develop a hierarchical AHP model based on load centers and units Load identified in Step 1.
Fig. 6. Fuzzy-AHP model includes load centers and load units
Step 3: Determine the weighting coefficients of importance of load centers and load units using the judgment matrix. To do that, the matrices should be constructed between the load centers and between the loads together in each load center. Based on Table I and the experienced operators of electrical systems determine the main and the sub-factors. These factors were shown in the tables Table IV, Table V, Table VI, Table VII, and Table VIII.
3/2
2/5
1/1
2/3
5/2
2/3
L21
5/2
2/3
3/2
1/1
2/7
2/7
3/1
1/1
2/1
1/1
1/3
1/3
7/2
3/2
5/2
1/1
2/5
2/5
L23
3/2
2/3
2/5
5/2
1/1
2/3
2/1
1/1
1/2
3/1
1/1
1/1
5/2
3/2
2/3
7/2
1/1
3/2
L24
2/3
2/3
3/2
5/2
2/3
1/1
1/1
1/1
2/1
3/1
1/1
1/1
3/2
3/2
5/2
7/2
3/2
1/1
TABLE IV. THE MAIN AND SUB-FACTOR MATRIX OF THE LOAD CENTER.
Ci
C1
C2
C3
C4
C1
1/1
3/2
2/7
2/5
1/1
2/1
1/3
1/2
1/1
5/2
2/5
2/3
C2
2/5
1/1
2/3
3/2
1/2
1/1
1/1
2/1
2/3
1/1
3/2
5/2
C3
5/2
2/3
1/1
2/5
3/1
1/1
1/1
1/2
7/2
3/2
1/1
2/3
C4
3/2
2/5
3/2
1/1
2/1
1/2
2/1
1/1
5/2
2/3
5/2
1/1
Where, Ci is the center of load i, i = 1 – 4. This is the 4 row x 4 column, with the value in each row consists of the main position in the middle row and two sub values in the two adjacent rows it. Similarly, the judgment matrices of load in LC1, LC2, LC3, LC4 load centers are calculated.
TABLE V. MAIN AND SECONDARY COEFFICIENTS MATRIX OF LOAD CENTER 1, LC1
LC1
L4
L7
L8
L12
L31
L39
L4
1/1
2/3
2/3
2/7
2/5
5/2
1/1
1/1
1/1
1/3
1/2
3/1
1/1
3/2
3/2
2/5
2/3
7/2
L7
2/3
1/1
5/2
2/3
3/2
2/3
1/1
1/1
3/1
1/1
2/1
1/1
3/2
1/1
7/2
3/2
5/2
3/2
L8
2/3
2/7
1/1
2/5
2/3
2/5
1/1
1/3
1/1
1/2
1/1
1/2
3/2
2/5
1/1
2/3
3/2
2/3
L12
5/2
2/3
3/2
1/1
2/7
2/7
3/1
1/1
2/1
1/1
1/3
1/3
7/2
3/2
5/2
1/1
2/5
2/5
L31
3/2
2/5
2/3
5/2
1/1
2/3
2/1
1/2
1/1
3/1
1/1
1/1
5/2
2/3
3/2
7/2
1/1
3/2
L39
2/7
2/3
3/2
5/2
2/3
1/1
1/3
1/1
2/1
3/1
1/1
1/1
2/5
3/2
5/2
7/2
3/2
1/1
Load Center 1 includes 6 loads: L4, L7, L8, L12, L31,
TABLE VII. MAIN AND SECONDARY COEFFICIENTS MATRIX OF LOAD CENTER 3, LC3
LC3
L26
L27
L28
L29
L26
1/1
2/5
2/3
2/3
1/1
1/2
1/1
1/1
1/1
2/3
3/2
3/2
L27
3/2
1/1
5/2
2/7
2/1
1/1
3/1
1/3
5/2
1/1
7/2
2/5
L28
2/3
2/7
1/1
2/3
1/1
1/3
1/1
1/1
3/2
2/5
1/1
3/2
L29
2/3
5/2
2/3
1/1
1/1
3/1
1/1
1/1
3/2
7/2
3/2
1/1
TABLE VIII. MAIN AND SECONDARY COEFFICIENTS MATRIX OF LOAD CENTER 4, LC4
LC4
L3
L18
L25
L3
1/1
2/3
2/3
1/1
1/1
1/1
1/1
3/2
3/2
L18
2/3
1/1
5/2
1/1
1/1
3/1
3/2
1/1
7/2
L25
2/3
2/7
1/1
1/1
1/3
1/1
3/2
2/5
1/1
According to Chang's Fuzzy-AHP method [15], the formula (13) computes:
L39, matrix obtained for load center 1 is matrix 6 rows x 6 columns.
TABLE VI. MAIN AND SECONDARY COEFFICIENTS MATRIX OF LOAD CENTER 2, LC2
S1 = (3.19, 3.83, 4.57) x
1
,
1
,
1
23.57
1
,
19.33
1
,
15.72
1
23.57
1
,
19.33
1
,
15.72
1
23.57
1
,
19.33
1
,
15.72
1
0.20, 0.29)
S2 = (3.57, 4.5, 5.67) x
0.23, 0.36)
= (0.14,
= (0.15,
LC2
L15
L16
L20
L21
L23
L24
L15
1/1
2/3
2/3
2/7
2/5
2/3
1/1
1/1
1/1
1/3
1/2
1/1
1/1
3/2
3/2
2/5
2/3
3/2
L16
2/3
1/1
5/2
2/3
2/3
2/3
1/1
1/1
3/1
1/1
1/1
1/1
3/2
1/1
7/2
3/2
3/2
3/2
L20
2/3
2/7
1/1
2/5
3/2
2/5
1/1
1/3
1/1
1/2
2/1
1/2
S3 = (2.73, 3.50, 4.67) x = (0.19,
0.28, 0.42)
S4 = (3.45, 4.33, 5.40) x
0.28, 0.42)
Using (15), (16):
23.57
19.33
15.72
= (0.19,
7
L16
0,2162023778
LC2
0,2318391143
0,0501241678
8
L26
0,1371793201
LC3
0,3037660388
0,0416704187
9
L7
0,2152410974
LC1
0,1606288080
0,0345739209
10
L28
0,1122063232
LC3
0,3037660388
0,0340844703
11
L31
0,2023422316
LC1
0,1606288080
0,0325019915
12
L39
0,1976879287
LC1
0,1606288080
0,0317543763
13
L12
0,1767634431
LC1
0,1606288080
0,0283933012
14
L20
0,1111338061
LC2
0,2318391143
0,0257651632
15
L4
0,1519630935
LC1
0,1606288080
0,0244096506
16
L21
0,1002503983
LC2
0,2318391143
0,0232419636
17
L15
0,0992308192
LC2
0,2318391143
0,0230055852
18
L25
0,0478793425
LC4
0,3037660388
0,0145441182
19
L8
0,0560022057
LC1
0,1606288080
0,0089955675
V S S = 0.15 0.29 0.80 ; similar
1 2 (0.20 0.29) (0.23 0.15)
V S1 S3 =0.53; V S1 S4 =0.55;
V S2 S1=1;
V S S = 0.19.0.36 0.76 ;
2 3
(0.23 0.36) (0.29 0.19)
similar V S2 S4 =0.77;
V S3 S1 =1; V S3 S2 =1; V S3 S4 =1
V S4 S1 =1; V S4 S2 =1; V S4 S3 =1.
Using (16):
d(C1)= V S1 S2 ,S 3, S4 =min(0.80,0.53,0.55)=0.53 d(C2)= V S2 S1,S 3, S4 =min(1,0.76,0.77)=1 d(C3)= V S3 S1,S 2, S4 =min(1,1,1)=1
d(C4)= V S1 S4 ,S 2, S3 = min(1,1,1)=1
Thus, W=(0.53,0.76,1,1), from which the weights or vectors are calculated W=(0.16,0.23,0.30,0.30) based on the formula
.
W *
W
i
i W *i
Similar to such calculation, find the weights of each load center and of each load in the center. The results for the remaining cases are shown in Table IX.
TABLE IX. WEIGHT OF LOADS IN EACH CENTER.
Weight
LC1
LC2
LC3
LC4
W1
0,1519630935
0,0992308192
0,1371793201
0,2895529185
W2
0,2152410974
0,2162023778
0,3872652285
0,6625677390
W3
0,0560022057
0,1111338061
0,1122063232
0,0478793425
W4
0,1767634431
0,1002503983
0,3633491282
–
W5
0,2023422316
0,2294871676
–
–
W6
0,1976879287
0,2436954311
–
–
After obtaining the values Wkj and Wdi, compute the coefficients of gross coefficient combined Wij of each load. The value is calculated by the formula W ij = Wkj.x Wdi, that is, multiply by two the weighted values of the load and the weight of the center together. Weights Wkj in the same load center is the same and equal to the value Wkj. After calculating the important factor of each load unit at each stage from Fuzzy-AHP calculations, arrange loading units in descending order of priority as shown in Table X. The more important loads are, the greater the Wij are.
TABLE X. ARRANGE LOADING UNITS BY THE WEIGHT FACTOR OF THE LOAD FACTOR WIJ
No
Loads
The important
factor of load units
LC
The important
factor of load centers
The important factors
1
L18
0,6625677390
LC4
0,3037660388
0,2012655775
2
L27
0,3872652285
LC3
0,3037660388
0,1176380244
3
L29
0,3633491282
LC3
0,3037660388
0,1103731254
4
L3
0,2895529185
LC4
0,3037660388
0,0879563431
5
L24
0,2436954311
LC2
0,2318391143
0,0564981329
6
L23
0,2294871676
LC2
0,2318391143
0,0532041017
From Table X, it is found that load L8 has the largest order number (19th) that is the load has the lowest priority and will be cut off first. Load L18 with the smallest ordinal number (numbered 1st), meaning that this load has the highest priority and will be cut off in the end in any case.
From here, the following order can be given: L8, L25, L15, L21, L4, L20, L12, L39, L31, L28, L7, L26, L16, L23, L24, L3, L29, L27, L18.
The Fuzzy-AHP method is used to determine the arrangement of load units in priority order at all times and the load shedding system will cut the load on the system smallest number before.
Apply the proposed method proceed to load shedding the load until the frequency of recovery return to a value greater than 59.7Hz. The results of frequency simulation were shown in Fig. 7.
Fig. 7. Compares the effectiveness of the traditional method and the proposed method
Compared the load shedding methods based on traditional method (under frequency load shedding) and Fuzzy-AHP algorithm, in both cases the frequencies were restored to allowed values. However, the load shedding according to Fuzzy-AHP algorithm had total load shedding capacity lower than under frequency load shedding. Especially, the frequency recovery time and rotor angle of Fuzzy-AHP method are faster than traditional method.
-
CONCLUSIONS
Load shedding based on Fuzzy-AHP algorithm is applied in the emergency situations to maintain stability of the power system. This paper proposed a new method to build load shedding strategies according to the pre-designed rules based on Fuzzy-AHP algorithm. The implementation of load shedding was made immediately after evaluating the instability of the power system, helping the system to recover faster in emergency. Simulation results on the IEEE 39 bus system showed that the effectiveness of the proposed method.
ACKNOWLEDGMENT
This research was supported by Ho Chi Minh City University of Technology and Education under a research at the Power System and Renewable Lab.
REFERENCES
-
Florida Reliability Coordinating Council Inc, FRCC standards handbook (2011)
-
IEEE Guide for the Application of Protective Relay used for Abnormal Frequency Load Shedding and Restoration, IEEE StdC37.117-2007, 2007.
-
Seyedi, H., and Sanaye-Pasand, M., Design of new load shedding special protection schemes for a double area power system, Amer. J. Appl. Sci., Vol. 6, No. 2, pp. 317327,2009.
-
Urban Rudez, Rafael Mihalic, A novel approach to underfrequency load shedding, Electric Power Systems Research, 636-643 (2011)
-
Hsu, C. T., Kang, M. S., and Chen, C. S., Design of adaptive load shedding by artificial neural networks,IEE Proc. Generat.Transm. Distrib., Vol. 152, No. 3, pp. 415421, 2005.
-
Hooshmand, R., and Moazzami, M., Optimal design of adaptive under frequency load shedding using artificial neural networks in isolated power system, Int. J. Power Energy Syst., Vol. 42, No. 1, pp. 220228, 2012.
-
J.A. Laghari , H. Mokhlis, A.H.A. Bakar, Hasmaini Mohamad, Application of computational intelligence techniques for load shedding in power systems: A review, Energy Conversion and Management, vol. 75, pp130-140, 2013.
-
Sasikala, J., and Ramaswamy, M., Fuzzy based load shedding strategies for avoiding voltage collapse, Appl. Soft Comput., Vol. 11, No. 3, pp. 31793185, 2011.
-
Sadati, M., Amraee, T., and Ranjbar, A. M., A global particle swarm- based-simulated annealing optimization technique for under-voltage load shedding problem, Appl. Soft Comput., Vol. 9, pp. 652657, 2009.
-
T.L. Saaty.: The Analytic Hierarchy Process. McGraw-Hill, New York, (1980)
-
J. Z. Zhu, Optimal Load Shedding Using AHP and OKA, International Journal of Power and Energy Systems, Vol.25, No.1, pp40-49, 2005.
-
Y.C. Erensal, T. O¨ zcan, M.L. Demircan, Determining key capabilities in technology management using fuzzy analytic hierarchy process, A case study of Turkey, Information Sciences 176, 27552770 (2006)
-
C. Kahraman, T. Ertay, G. Bu¨yu¨ko¨zkan, A fuzzy optimization model for QFD planning process using analytic network approach, European Journal of Operational Research 171, 390411 (2006)
-
E. Tolga, M.L. Demircan, C. Kahraman, Operating system selection using fuzzy replacement analysis and analytic hierarchy process, International Journal of Production Economics 97, 89117 (2005)
-
D.Y. Chang, Extent Analysis and Synthetic Decision, Optimization Techniques and Applications, World Scientific, Singapore, 352 (1992)
-
D.Y. Chang, Applications of the extent analysis method on fuzzy AHP, European Journal of Operational Research 95, 649655(1996)
-
P.J.M. Van Laarhoven, W. Pedrycz, A fuzzy extension of Saatys priority theory. Fuzzy Sets and Systems 11, 229241 (1983)