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The Selection Algorithm for Connection Modes of Medium Voltage Power Distribution Network Based on FAHP-GRA
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Physics Procedia
Physics Procedia (2011)24 000–000 Physics 00 Procedia (2012) 345 – 353
www.elsevier.com/locate/procedia
2012 International Conference on Applied Physics and Industrial Engineering
The Selection Algorithm for Connection Modes of Medium Voltage Power Distribution Network Based on FAHP-GRA Wu Han1, Lin Han1, Chen Bin1,Wu Han2, Wen Bu ying2 1
Research and Development Center Fujian Electric Power Company Limited Fuzhou, China 2 College of Electrical Engineering ＆ Automation Fuzhou University Fuzhou, China
Abstract This paper used fuzzy analytic hierarchy process (FAHP) and gray relational analysis (GRA) to solve the selection for the connection modes of medium voltage (MV) power distribution network. Firstly, it established the comprehensive evaluation indicator system from technicality, economy, and adaptability. Secondly, FAHP can evaluate the indicator weights, and avoid the ambiguity and uncertainty of judgment matrix. Finally, it combined with GRA to complete the comprehensive decision-making. This method also solves the error of the fuzzy albino number caused by fuzzy comprehensive evaluation theory. In the end, a practical example verified the reasonable and practical of this method. ©©2011 by Elsevier B.V.Ltd. Selection and/orand/or peer-review under responsibility of ICAPIEofOrganization Committee. 2011Published Published by Elsevier Selection peer-review under responsibility [name organizer] Keywords:medium voltage power distribution network; connection modes; fuzzy analytic hierarchy process; gray relational analysis
1.
Introduction
How to choose the best connection mode is an important piece of work in the planning and construction of MV power distribution network structure. Reasonable choice of connection modes need to consider not only the reliability of supply, economy, but also need to consider the line utilization, operational flexibility etc. Thus the multi-objective decision theory has been gradually integrated into the choice of the connection modes. Some scholars have made studies in this field. For example reference [1] adopted strength and weakness analysis method to select the connection mode from four aspects: reliability, economy, actionability and expansibility. However, this method applies only to the choice of two options. Some introduced the blind number theory into the measure and calculation of all risk factors for the final solution
1875-3892 © 2011 Published by Elsevier B.V. Selection and/or peer-review under responsibility of ICAPIE Organization Committee. doi:10.1016/j.phpro.2012.02.051
346
Wu Han et al. / Physics Procedia 24 (2012) 345 – 353
Author name / Physics Procedia 00 (2011) 000–000
[2]. But the main problem is the pre-collection of uncertainty information and computation is too large. In previous studies, many scholars used the fuzzy theory to make the selection of connection modes. Reference [3-5] established the comprehensive evaluation model of connection modes based on the fuzzy comprehensive evaluation method. But it has some limitations, mainly due to fuzzy comprehensive evaluation method is established based on the membership function to indirectly judge. To be able to find the membership function of each indicator, the indicator value must be characterized; the value of some of the original albino is set into a fuzzy value, bringing a certain amount of error. 2.
The Theory of FAHP and GRA
In order to adapt to the ambiguity and uncertainty of the judgment matrix, this paper uses the triangular fuzzy number proposed by Dutch scholar Van Laarhoven to give the fuzzy judgment matrix. It is expressed with an interval, instead of a single judgment value [6]. Through this, the establishment of FAHP triangle fuzzy numbers can determine the weight of each indicator. Meanwhile GRA which was proposed by Chinese scholar Julong Deng in 1982 is combined into the connection modes selection [7-9]. Through calculating the grey relational grade between the alternative connection modes and the ideal mode to judge which mode is a better one. Different indicator weights have different effects on grey relational grade. So far, this paper establishes a selection algorithm of connection modes based on FAHP-GRA theory. 3.
Connection Modes Indicator System Indicator System Hierarchy Structure
The choice of connection modes is affected by many factors, after the investigation of the actual situation of various planning decisions, identify technicality, economy, adaptability as the selection basis. Hierarchy structure of indicator system is shown in Figure 1, each indicator contains a number of subsidiary indicators. Indicator Analysis 1) Technicality: Failure mode effect analysis (FMEA) is used to evaluate the reliability through calculating the average supply availability indicator (ASAI). On the other hand, through the power flow calculation, the voltage drop of power supply line can be used to assess the voltage quality of connection modes. 2) Economy: For a particular area, supposing use different connection modes to construct, separately calculate the economy of each period, including construction cost, operation cost, life cycle cost (LCC). 3) Adaptability: The connection mode which has better applicability can be judged by the following aspects: line utilization factor, operational flexibility, and transitivity.
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Wu Han et al. / Physics Procedia 24 (2012) 345 – 353
Author name / Physics Procedia 00 (2011) 000–000
Figure 1. Hierarchy structure of indicator system
4.
Steps of FAHP-GRA Algorithm Steps of FAHP Algorithm
1) Build fuzzy triangle judgment matrix Pairwise comparing the indicators of each level, build the fuzzy triangle judgment matrix A=(aij) nk×nk whose element aij=(lij,mij,uij) is a closed interval. uij: upper bound, lij: lower bound, mij: median, use the integer ‘1-9’ , the uij－lij: the blur length, nk: the number of the ‘k’ level of indicator system. i,j=1,2,…,nk. The schematic diagram of the triangular fuzzy number is shown in Figure 2 (a).
μ
μ
Si
Sj
μ (d )
lij
mij
uij
X
li
mi l j d ui m j
uj
X
Figure 2. Triangular fuzzy number schematic diagram
2) Calculate comprehensive judgement matrix aijt=(uijt,mijt,lijt), represents for the fuzzy numbers which are obtained through comparing the indicators i and j by the decision maker ‘t’, t=1,2,…, T. 1 M ij = ⊗ (aij1 + aij 2 + " aij T ) T
(1)
⊗ : the multiplication principle of triangular fuzzy number. The specific fuzzy algorithms can be referred in [6]. From the above equation, the comprehensive judgement matrix Mij can be calculated. 3) Calculate comprehensive fuzzy degree Calculate comprehensive fuzzy degree Si, the equation is as follows:
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Wu Han et al. / Physics Procedia 24 (2012) 345 – 353
Author name / Physics Procedia 00 (2011) 000–000 nk ⎛ nk nk ⎞ = Si ∑ M ij ⊗ ⎜ ∑ ∑ M ij ⎟ =j 1 ⎝=i 1 =j 1 ⎠
−1
(2)
4) Calculate indicator weight The better scalar measure of indicator Ci is given by equation = d ' (Ci ) min V ( Si ≥ S j )
(3)
where 0≤V(Si≥Sj) ≤1, i,j=1,2,…,nk V(Si≥Sj) represent for the possibility degree of Si≥Sj, as shown in Figure 2 (b). It is calculated by the following equation: l j − ui ⎧ , l j ≤ ui ⎪ V ( Si ≥ S j ) = μ (d ) = ⎨ (mi − ui ) − (m j − l j ) ⎪0 , others ⎩
(4)
Indicator weight in single level : W ' = (d ' (C1 ), d ' (C2 ), d ' (C3 ), " d ' (Cn )) k
(5) Indicator weight normalized: W = (d (C1 ), d (C2 ), d (C3 ), " d (Cn ))
(6)
k
5) Calculate comprehensive indicator weight After calculating all indicator weights of each level, the total weight can be easily got by multiplication of each level. Compared the traditional FHP, the triangular FAHP need not consistency test. Steps of GRA Algorithm 1) Build initial indicator matrix Suppose there are ‘m’ pieces of alternative modes, each mode has ‘n’ pieces of evaluating indicators. Sign the alternative mode as row subscript ‘i’, while sign the evaluating indicator as column subscript ‘j’, then build the initial indicator matrix: = Aij (= aij ) m× n (i 1, 2,..., = m, j 1, 2,..., n)
(7)
Quantitative indicators, such as technicality, economy use the actual value. For qualitative indicators, such as operational flexibility, adaptability use five-point Likert scale. The indicator value is 5, 4, 3, 2, 1, separately express very good, well, general, bad, and very bad. When the target rank is situated between two adjacent ranks, corresponding value is 4.5, 3.5, 2.5, and 1.5. 2) Confirm ideal series The ideal series is: A0=[a01, a02,…,a0k, …,a0n] (k=1,2,…,n) .It is got from the best indicator of alternative modes using equations as follow: = a0 j
{(max a 1≤ i ≤ m
ij
}
j ∈ J1 ), (min aij j ∈ J 2= ) j 1, 2,..., n 1≤ i ≤ m
(8)
J1 presents for beneficial indicator (the more the better), such as the reliability indicator; while J2 is on the contrary, such as the economy indicator. 3) Nondimensionalize additive indicator matrix
349
Wu Han et al. / Physics Procedia 24 (2012) 345 – 353
Author name / Physics Procedia 00 (2011) 000–000
Combine the initial indicator matrix with ideal series to form the additive indicator matrix A=(aij)(m+1)×n. As a result of the different meaning and purpose of each indicator, which usually have different dimension and magnitude, for further comparison, it is necessary to nondimensionalize the additive indicator matrix. In this paper, the data-average method is chose. X ij =
= aj
aij
(9)
aj
1 m = ∑ aij , j 1, 2,..., n m + 1 i =0
(10)
additive indicator matrix of nondimensionalization: ⎡ X 01 ⎢X ⎢ 11 = X (= X ij )( m +1)× n ⎢ X 21 ⎢ ⎢ # ⎢⎣ X m1
X 02
X 0n ⎤ X 1n ⎥⎥ ... X 2 n ⎥ ⎥ # # ⎥ ... X mn ⎥⎦ ...
X 12
...
X 22 # X m2
(11)
4) Calculate grey relational grade Each row of Xij is a compared series, calculate grey relational grade between the alternative connection modes and the ideal mode.
ξi ( j ) =
min min X 0 j − X ij + ρ max max X 0 j − X ij i
j
i
i
= H
j
X 0 j − X ij + ρ max max X 0 j − X ij
(12)
j
X 0 j − X ij , ρ is correlation coefficient, which is between 0 and 1, commonly set ρ=0.5
(i=1,2,…,m, j=1,2,…,n) grey relational matrix: ⎡ ξ11 ξ12 ⎢ξ ⎢ 21 ξ 22 ) E (ξ= = ij m× n ⎢ # # ⎢ ⎣ξ m1 ξ m 2
... ξ1n ⎤ ... ξ 2 n ⎥⎥ # # ⎥ ⎥ ... ξ mn ⎦
(13)
5) Comprehensive evaluation The final comprehensive evaluation result can be obtained through the following equation: P= E × W
The steps of FAHP-GRA algorithm is show in Figure 3.
(14)
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Wu Han et al. / Physics Procedia 24 (2012) 345 – 353
Author name / Physics Procedia 00 (2011) 000–000
Figure 3. FAHP-GRA algorithm steps
5.
Example Analysis
A specific example is given to further introduce the application of this method. A suburb, load density: 10MW/km2, plans to build a 110kV substation with capacity of 2×50MVA. There are four connection modes to choose, as shown in Figure 4, the specific connection modes refer to [10]. The calculated results of specific indicators parameters are shown Table 1. Here, mode1,2,3,4 respectively stand for ‘cable single radiation’, ‘cable with three contact’, ‘cable with two full load line and one unload line’, ‘2-1 switching station’.
substation
mode 1
mode 2
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Wu Han et al. / Physics Procedia 24 (2012) 345 – 353
Author name / Physics Procedia 00 (2011) 000–000
mode 3
mode 4
Figure 4. Connection modes schematic diagram TABLE I.
INDICATOR PARAMETERS
Evaluation indicator Reliability Voltage qualified rate Construction economy ￥104/MW Operational economy￥104/MW Life cycle economy ￥104/MW Line utilization rate
Connection modes Mode 1
Mode 2
Mode 3
Mode 4
99.9938% 99.9952% 99.9965% 99.9983% 3.5%
2.1%
0.8%
0.6%
105
123
133
153
10.6
12.4
8.5
8.8
24
26
27
32
100%
75%
67%
50%
Operational flexibility
1
3
3.5
3.5
Transitivity
4
2.5
3.5
3
Indicator weight calculation According to the FAHP algorithm, it can get all indicator weights in each index level. The first level weights: WB-A=(0.46,0.33,0.21), technicality weights: WC-B1=(0.46,0.33,0.21), economy weights: WC-B2=(0.25,0.25,0.5), adaptability weights: WC-B3=(0.55,0.23,0.12). The final comprehensive indicator weight: T W = [ 0.31 0.15 0.08 0.08 0.16 0.14 0.05 0.03] GRA Calculation ideal serie : A0 = [99.9983% 0.6% 105 8.5 24 100% 3.5 4]
additive indicator matrix :
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⎡99.9983% ⎢99.9938% ⎢ A = ⎢99.9952% ⎢ ⎢99.9965% ⎢⎣99.9983%
0.6% 3.5% 2.1% 0.8% 0.6%
nondimensionalization: ⎡1.2928 ⎢0.5919 ⎢ X = ⎢0.8100 ⎢ ⎢1.0125 ⎢⎣1.2928
Author name / Physics Procedia 00 (2011) 000–000 105 8.5 24 100% 3.5 4 ⎤ 105 10.6 24 100% 1 4 ⎥⎥ additive indicator matrix of 123 12.4 26 75% 3 2.5⎥ ⎥ 133 8.5 27 67% 3.5 3.5 ⎥ 153 8.8 32 50% 3.5 3 ⎥⎦
0.3947 0.8481 0.8709 0.9023 1.2755 1.2069 1.1765 ⎤ 2.3026 0.8481 1.0861 0.9023 1.2755 0.3448 1.1765 ⎥ ⎥ 1.3816 0.9935 1.2705 0.9774 0.9566 1.0345 0.7353⎥ ⎥ 0.5263 1.0743 0.8709 1.0150 0.8546 1.2069 1.0294 ⎥ 0.3947 1.2359 0.9016 1.2030 0.6378 1.2069 0.8824 ⎥⎦
grey relational grade matrix:
1 0.8160 1 1 0.5253 1 ⎤ ⎡0.5764 0.3333 ⎢0.6639 0.4915 0.8677 0.7048 0.9269 0.7495 0.8469 0.6838⎥ ⎥ E=⎢ ⎢0.7729 0.8788 0.8083 1 0.8943 0.6938 1 0.8664⎥ ⎢ ⎥ 1 0.7110 0.9688 0.7303 0.5993 1 0.7643⎦ ⎣ 1
Comprehensive Evaluation P = E × W =[ 0.7302 0.7214 0.8323 0.872 ]
T
Through the comprehensive evaluation, the results shows the prioritization of connection modes is: mode 4 > mode 3 > mode 1> mode 2, thus connection mode of ‘2-1 switching station’ can be the first choice of MV distribution network construction. Conclusion A new selection algorithm based on FAHP and GRA theory is put forward to solve the choice of connection modes. The principle is relatively simple, the evaluation results is objective and reliable. It not only has strong practicability but also avoid the error caused by fuzzy comprehensive evaluation method. The decision-making process of the connection modes in a actual area shows that this method is reasonable and practical. References [1]
Zheng Hewei, Yu Ji-hui, and SUN Yu-jiang, “Application of Comprehensive Weight Method to Choosing the
Connection Mode of 10 kV Distribution Network,”Journal of Chongqing University(Natural Science Edition), vol.29, no.7, pp.4145, 2006. [2]
He Yongxiu, Wang Wei, and Yang Weihong, “Assessment of Connection Mode in Distribution Network Based on Blind
Number Theory,”Transactions of China Electrotechnical Society, vol.24, no.7, pp.139-144, 2009. [3]
Zhang Chi, Cheng Haozhong, and Xi Xun, “A Study of Distribution Network Feeding Modes Selection Based on
Analytic Hierarchy Process and Fuzzy Comprehensive Evaluation,” Power System Technology, vol.30, no.22,pp.67-71,2006. [4]
Pan Feng, Zhang Yujun, and Zhou Min, “A Comprehensive Evaluation Hierarchy for MV Distribution Network based
on Connection Modes,” Power System Protection and Control, vol.37, no.19, pp.19-21,2009. [5]
Mo-yuen Chow, and Hahn Tram, “Application of fuzzy logic technology for spatial load forecasting,” IEEE Tansactions
on Power System, vol.12, no.3, pp.1360-1366,1997. [6]
Zhu Kejun, Zhang Xinlan, and Xiao Lijin, “The Method and Application of Fuzzy AHP,” Systems Engineering-
Theory&Practice, vol.12, no.12, pp.64-69,1997. [7]
Shi Bingli, “The Choice of Water Resources and Hydropower Planning based on Grey Correlation Analysis,” Journal of
Hydraulic Engineering, vol.9, no.1, pp.66-69.1990.
Wu Han et al. / Physics Procedia 24 (2012) 345 – 353
Author name / Physics Procedia 00 (2011) 000–000 [8]
Cao Guoqing, Xing Jincheng, and Guangbei, “ Grey Method with Use of an Analytic Hierarchy Process for Performance
Evaluation of Flue Gas Desulfurization Technology,” Power System Technology, vol.26, no.4, pp.51-55,2006. [9]
Deng Jurong, Grey Prediction and Grey Decision, CA: Huazhong University of Science Press,2000.
[10]
Wang Chengshan, Wang Saiyi, and Ge Shaoyun, “Economy and Reliability Analysis of Different Connection Modes in
MV Distribution Systems,” Automation of Electric Power Systems, vol.26,no.24, pp.34-39,2002.
353
Physics Procedia
Physics Procedia (2011)24 000–000 Physics 00 Procedia (2012) 345 – 353
www.elsevier.com/locate/procedia
2012 International Conference on Applied Physics and Industrial Engineering
The Selection Algorithm for Connection Modes of Medium Voltage Power Distribution Network Based on FAHP-GRA Wu Han1, Lin Han1, Chen Bin1,Wu Han2, Wen Bu ying2 1
Research and Development Center Fujian Electric Power Company Limited Fuzhou, China 2 College of Electrical Engineering ＆ Automation Fuzhou University Fuzhou, China
Abstract This paper used fuzzy analytic hierarchy process (FAHP) and gray relational analysis (GRA) to solve the selection for the connection modes of medium voltage (MV) power distribution network. Firstly, it established the comprehensive evaluation indicator system from technicality, economy, and adaptability. Secondly, FAHP can evaluate the indicator weights, and avoid the ambiguity and uncertainty of judgment matrix. Finally, it combined with GRA to complete the comprehensive decision-making. This method also solves the error of the fuzzy albino number caused by fuzzy comprehensive evaluation theory. In the end, a practical example verified the reasonable and practical of this method. ©©2011 by Elsevier B.V.Ltd. Selection and/orand/or peer-review under responsibility of ICAPIEofOrganization Committee. 2011Published Published by Elsevier Selection peer-review under responsibility [name organizer] Keywords:medium voltage power distribution network; connection modes; fuzzy analytic hierarchy process; gray relational analysis
1.
Introduction
How to choose the best connection mode is an important piece of work in the planning and construction of MV power distribution network structure. Reasonable choice of connection modes need to consider not only the reliability of supply, economy, but also need to consider the line utilization, operational flexibility etc. Thus the multi-objective decision theory has been gradually integrated into the choice of the connection modes. Some scholars have made studies in this field. For example reference [1] adopted strength and weakness analysis method to select the connection mode from four aspects: reliability, economy, actionability and expansibility. However, this method applies only to the choice of two options. Some introduced the blind number theory into the measure and calculation of all risk factors for the final solution
1875-3892 © 2011 Published by Elsevier B.V. Selection and/or peer-review under responsibility of ICAPIE Organization Committee. doi:10.1016/j.phpro.2012.02.051
346
Wu Han et al. / Physics Procedia 24 (2012) 345 – 353
Author name / Physics Procedia 00 (2011) 000–000
[2]. But the main problem is the pre-collection of uncertainty information and computation is too large. In previous studies, many scholars used the fuzzy theory to make the selection of connection modes. Reference [3-5] established the comprehensive evaluation model of connection modes based on the fuzzy comprehensive evaluation method. But it has some limitations, mainly due to fuzzy comprehensive evaluation method is established based on the membership function to indirectly judge. To be able to find the membership function of each indicator, the indicator value must be characterized; the value of some of the original albino is set into a fuzzy value, bringing a certain amount of error. 2.
The Theory of FAHP and GRA
In order to adapt to the ambiguity and uncertainty of the judgment matrix, this paper uses the triangular fuzzy number proposed by Dutch scholar Van Laarhoven to give the fuzzy judgment matrix. It is expressed with an interval, instead of a single judgment value [6]. Through this, the establishment of FAHP triangle fuzzy numbers can determine the weight of each indicator. Meanwhile GRA which was proposed by Chinese scholar Julong Deng in 1982 is combined into the connection modes selection [7-9]. Through calculating the grey relational grade between the alternative connection modes and the ideal mode to judge which mode is a better one. Different indicator weights have different effects on grey relational grade. So far, this paper establishes a selection algorithm of connection modes based on FAHP-GRA theory. 3.
Connection Modes Indicator System Indicator System Hierarchy Structure
The choice of connection modes is affected by many factors, after the investigation of the actual situation of various planning decisions, identify technicality, economy, adaptability as the selection basis. Hierarchy structure of indicator system is shown in Figure 1, each indicator contains a number of subsidiary indicators. Indicator Analysis 1) Technicality: Failure mode effect analysis (FMEA) is used to evaluate the reliability through calculating the average supply availability indicator (ASAI). On the other hand, through the power flow calculation, the voltage drop of power supply line can be used to assess the voltage quality of connection modes. 2) Economy: For a particular area, supposing use different connection modes to construct, separately calculate the economy of each period, including construction cost, operation cost, life cycle cost (LCC). 3) Adaptability: The connection mode which has better applicability can be judged by the following aspects: line utilization factor, operational flexibility, and transitivity.
347
Wu Han et al. / Physics Procedia 24 (2012) 345 – 353
Author name / Physics Procedia 00 (2011) 000–000
Figure 1. Hierarchy structure of indicator system
4.
Steps of FAHP-GRA Algorithm Steps of FAHP Algorithm
1) Build fuzzy triangle judgment matrix Pairwise comparing the indicators of each level, build the fuzzy triangle judgment matrix A=(aij) nk×nk whose element aij=(lij,mij,uij) is a closed interval. uij: upper bound, lij: lower bound, mij: median, use the integer ‘1-9’ , the uij－lij: the blur length, nk: the number of the ‘k’ level of indicator system. i,j=1,2,…,nk. The schematic diagram of the triangular fuzzy number is shown in Figure 2 (a).
μ
μ
Si
Sj
μ (d )
lij
mij
uij
X
li
mi l j d ui m j
uj
X
Figure 2. Triangular fuzzy number schematic diagram
2) Calculate comprehensive judgement matrix aijt=(uijt,mijt,lijt), represents for the fuzzy numbers which are obtained through comparing the indicators i and j by the decision maker ‘t’, t=1,2,…, T. 1 M ij = ⊗ (aij1 + aij 2 + " aij T ) T
(1)
⊗ : the multiplication principle of triangular fuzzy number. The specific fuzzy algorithms can be referred in [6]. From the above equation, the comprehensive judgement matrix Mij can be calculated. 3) Calculate comprehensive fuzzy degree Calculate comprehensive fuzzy degree Si, the equation is as follows:
348
Wu Han et al. / Physics Procedia 24 (2012) 345 – 353
Author name / Physics Procedia 00 (2011) 000–000 nk ⎛ nk nk ⎞ = Si ∑ M ij ⊗ ⎜ ∑ ∑ M ij ⎟ =j 1 ⎝=i 1 =j 1 ⎠
−1
(2)
4) Calculate indicator weight The better scalar measure of indicator Ci is given by equation = d ' (Ci ) min V ( Si ≥ S j )
(3)
where 0≤V(Si≥Sj) ≤1, i,j=1,2,…,nk V(Si≥Sj) represent for the possibility degree of Si≥Sj, as shown in Figure 2 (b). It is calculated by the following equation: l j − ui ⎧ , l j ≤ ui ⎪ V ( Si ≥ S j ) = μ (d ) = ⎨ (mi − ui ) − (m j − l j ) ⎪0 , others ⎩
(4)
Indicator weight in single level : W ' = (d ' (C1 ), d ' (C2 ), d ' (C3 ), " d ' (Cn )) k
(5) Indicator weight normalized: W = (d (C1 ), d (C2 ), d (C3 ), " d (Cn ))
(6)
k
5) Calculate comprehensive indicator weight After calculating all indicator weights of each level, the total weight can be easily got by multiplication of each level. Compared the traditional FHP, the triangular FAHP need not consistency test. Steps of GRA Algorithm 1) Build initial indicator matrix Suppose there are ‘m’ pieces of alternative modes, each mode has ‘n’ pieces of evaluating indicators. Sign the alternative mode as row subscript ‘i’, while sign the evaluating indicator as column subscript ‘j’, then build the initial indicator matrix: = Aij (= aij ) m× n (i 1, 2,..., = m, j 1, 2,..., n)
(7)
Quantitative indicators, such as technicality, economy use the actual value. For qualitative indicators, such as operational flexibility, adaptability use five-point Likert scale. The indicator value is 5, 4, 3, 2, 1, separately express very good, well, general, bad, and very bad. When the target rank is situated between two adjacent ranks, corresponding value is 4.5, 3.5, 2.5, and 1.5. 2) Confirm ideal series The ideal series is: A0=[a01, a02,…,a0k, …,a0n] (k=1,2,…,n) .It is got from the best indicator of alternative modes using equations as follow: = a0 j
{(max a 1≤ i ≤ m
ij
}
j ∈ J1 ), (min aij j ∈ J 2= ) j 1, 2,..., n 1≤ i ≤ m
(8)
J1 presents for beneficial indicator (the more the better), such as the reliability indicator; while J2 is on the contrary, such as the economy indicator. 3) Nondimensionalize additive indicator matrix
349
Wu Han et al. / Physics Procedia 24 (2012) 345 – 353
Author name / Physics Procedia 00 (2011) 000–000
Combine the initial indicator matrix with ideal series to form the additive indicator matrix A=(aij)(m+1)×n. As a result of the different meaning and purpose of each indicator, which usually have different dimension and magnitude, for further comparison, it is necessary to nondimensionalize the additive indicator matrix. In this paper, the data-average method is chose. X ij =
= aj
aij
(9)
aj
1 m = ∑ aij , j 1, 2,..., n m + 1 i =0
(10)
additive indicator matrix of nondimensionalization: ⎡ X 01 ⎢X ⎢ 11 = X (= X ij )( m +1)× n ⎢ X 21 ⎢ ⎢ # ⎢⎣ X m1
X 02
X 0n ⎤ X 1n ⎥⎥ ... X 2 n ⎥ ⎥ # # ⎥ ... X mn ⎥⎦ ...
X 12
...
X 22 # X m2
(11)
4) Calculate grey relational grade Each row of Xij is a compared series, calculate grey relational grade between the alternative connection modes and the ideal mode.
ξi ( j ) =
min min X 0 j − X ij + ρ max max X 0 j − X ij i
j
i
i
= H
j
X 0 j − X ij + ρ max max X 0 j − X ij
(12)
j
X 0 j − X ij , ρ is correlation coefficient, which is between 0 and 1, commonly set ρ=0.5
(i=1,2,…,m, j=1,2,…,n) grey relational matrix: ⎡ ξ11 ξ12 ⎢ξ ⎢ 21 ξ 22 ) E (ξ= = ij m× n ⎢ # # ⎢ ⎣ξ m1 ξ m 2
... ξ1n ⎤ ... ξ 2 n ⎥⎥ # # ⎥ ⎥ ... ξ mn ⎦
(13)
5) Comprehensive evaluation The final comprehensive evaluation result can be obtained through the following equation: P= E × W
The steps of FAHP-GRA algorithm is show in Figure 3.
(14)
350
Wu Han et al. / Physics Procedia 24 (2012) 345 – 353
Author name / Physics Procedia 00 (2011) 000–000
Figure 3. FAHP-GRA algorithm steps
5.
Example Analysis
A specific example is given to further introduce the application of this method. A suburb, load density: 10MW/km2, plans to build a 110kV substation with capacity of 2×50MVA. There are four connection modes to choose, as shown in Figure 4, the specific connection modes refer to [10]. The calculated results of specific indicators parameters are shown Table 1. Here, mode1,2,3,4 respectively stand for ‘cable single radiation’, ‘cable with three contact’, ‘cable with two full load line and one unload line’, ‘2-1 switching station’.
substation
mode 1
mode 2
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Wu Han et al. / Physics Procedia 24 (2012) 345 – 353
Author name / Physics Procedia 00 (2011) 000–000
mode 3
mode 4
Figure 4. Connection modes schematic diagram TABLE I.
INDICATOR PARAMETERS
Evaluation indicator Reliability Voltage qualified rate Construction economy ￥104/MW Operational economy￥104/MW Life cycle economy ￥104/MW Line utilization rate
Connection modes Mode 1
Mode 2
Mode 3
Mode 4
99.9938% 99.9952% 99.9965% 99.9983% 3.5%
2.1%
0.8%
0.6%
105
123
133
153
10.6
12.4
8.5
8.8
24
26
27
32
100%
75%
67%
50%
Operational flexibility
1
3
3.5
3.5
Transitivity
4
2.5
3.5
3
Indicator weight calculation According to the FAHP algorithm, it can get all indicator weights in each index level. The first level weights: WB-A=(0.46,0.33,0.21), technicality weights: WC-B1=(0.46,0.33,0.21), economy weights: WC-B2=(0.25,0.25,0.5), adaptability weights: WC-B3=(0.55,0.23,0.12). The final comprehensive indicator weight: T W = [ 0.31 0.15 0.08 0.08 0.16 0.14 0.05 0.03] GRA Calculation ideal serie : A0 = [99.9983% 0.6% 105 8.5 24 100% 3.5 4]
additive indicator matrix :
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⎡99.9983% ⎢99.9938% ⎢ A = ⎢99.9952% ⎢ ⎢99.9965% ⎢⎣99.9983%
0.6% 3.5% 2.1% 0.8% 0.6%
nondimensionalization: ⎡1.2928 ⎢0.5919 ⎢ X = ⎢0.8100 ⎢ ⎢1.0125 ⎢⎣1.2928
Author name / Physics Procedia 00 (2011) 000–000 105 8.5 24 100% 3.5 4 ⎤ 105 10.6 24 100% 1 4 ⎥⎥ additive indicator matrix of 123 12.4 26 75% 3 2.5⎥ ⎥ 133 8.5 27 67% 3.5 3.5 ⎥ 153 8.8 32 50% 3.5 3 ⎥⎦
0.3947 0.8481 0.8709 0.9023 1.2755 1.2069 1.1765 ⎤ 2.3026 0.8481 1.0861 0.9023 1.2755 0.3448 1.1765 ⎥ ⎥ 1.3816 0.9935 1.2705 0.9774 0.9566 1.0345 0.7353⎥ ⎥ 0.5263 1.0743 0.8709 1.0150 0.8546 1.2069 1.0294 ⎥ 0.3947 1.2359 0.9016 1.2030 0.6378 1.2069 0.8824 ⎥⎦
grey relational grade matrix:
1 0.8160 1 1 0.5253 1 ⎤ ⎡0.5764 0.3333 ⎢0.6639 0.4915 0.8677 0.7048 0.9269 0.7495 0.8469 0.6838⎥ ⎥ E=⎢ ⎢0.7729 0.8788 0.8083 1 0.8943 0.6938 1 0.8664⎥ ⎢ ⎥ 1 0.7110 0.9688 0.7303 0.5993 1 0.7643⎦ ⎣ 1
Comprehensive Evaluation P = E × W =[ 0.7302 0.7214 0.8323 0.872 ]
T
Through the comprehensive evaluation, the results shows the prioritization of connection modes is: mode 4 > mode 3 > mode 1> mode 2, thus connection mode of ‘2-1 switching station’ can be the first choice of MV distribution network construction. Conclusion A new selection algorithm based on FAHP and GRA theory is put forward to solve the choice of connection modes. The principle is relatively simple, the evaluation results is objective and reliable. It not only has strong practicability but also avoid the error caused by fuzzy comprehensive evaluation method. The decision-making process of the connection modes in a actual area shows that this method is reasonable and practical. References [1]
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