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Risky Group Decision-Making Method for Distribution Grid Planning

  • Cunbin Li , Jiahang Yuan EMAIL logo and Zhiqiang Qi
Published/Copyright: November 6, 2015

Abstract

With rapid speed on electricity using and increasing in renewable energy, more and more research pay attention on distribution grid planning. For the drawbacks of existing research, this paper proposes a new risky group decision-making method for distribution grid planning. Firstly, a mixing index system with qualitative and quantitative indices is built. On the basis of considering the fuzziness of language evaluation, choose cloud model to realize “quantitative to qualitative” transformation and construct interval numbers decision matrices according to the “3En” principle. An m-dimensional interval numbers decision vector is regarded as super cuboids in m-dimensional attributes space, using two-level orthogonal experiment to arrange points uniformly and dispersedly. The numbers of points are assured by testing numbers of two-level orthogonal arrays and these points compose of distribution points set to stand for decision-making project. In order to eliminate the influence of correlation among indices, Mahalanobis distance is used to calculate the distance from each solutions to others which means that dynamic solutions are viewed as the reference. Secondly, due to the decision-maker’s attitude can affect the results, this paper defines the prospect value function based on SNR which is from Mahalanobis-Taguchi system and attains the comprehensive prospect value of each program as well as the order. At last, the validity and reliability of this method is illustrated by examples which prove the method is more valuable and superiority than the other.

Funding statement: Funding: This study is funded by the National Natural Science Foundation of China (Grant Number: 71271084) and supported by Science and Technology Project of SGCC (Grant Number: “521820140017”).

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Appendix

Table 3:

11 Fuzzy language and 11 cloud.

Fuzzy languageCloudExEnHe
PLY5(0,43.68,1.10)XminEn+40.618He+40.618
ALY4(11.8,26.99,0.68)Ex00.382Xmax+XminEn+30.618He+30.618
VLY3(21.35,16.68,0.42)Ex00.382Xmax+Xmin×34En+20.618He+20.618
LY2(30.9,10.31,0.26)Ex00.382Xmax+Xmin2En+10.618He+10.618
FLY1(40.45,6.37,0.16)Ex00.382Xmax+Xmin40.382(XmaxXmin)6He00.618
MY0(50,3.39,0.1)Xmax+Xmin20.618En+1He0=0.1
FHY+1(59.55,6.37,0.16)Ex0+0.382Xmax+Xmin40.382(XmaxXmin)6He00.618
HY+2(69.1,10.31,0.26)Ex0+0.382Xmax+Xmin2En+10.618He+10.618
VHY+3(78.65,16.68,0.42)Ex0+0.382Xmax+Xmin×34En+20.618He+20.618
AHY+4(88.2,26.99,0.68)Ex0+0.382Xmax+XminEn+30.618He+30.618
PHY+5(100,43.68,1.10)XmaxEn+40.618He+40.618
Table 4:

The decision-making information of each solution under quantitative index.

SolutionQuantitative index
Electricity supply reliability (I1)Electricity supply Quality (I2)Investment (I3)Grid loss rate (I4)
A1[230,280][0.16,0.23][3.86,3.92][0.27,0.43]
A2[210.250][0.09,0.14][5.78,5.81][0.22,0.31]
A3[270,310][0.32,0.38][6.12,6.20][0.19,0.25]
A4[200,220][0.21,0.25][5.94,6.01][0.24,0.29]
Table 5:

The decision-making information of each solution under qualitative index.

SolutionQualitative index
Influence on environment (I5)Compatibility of solutions and load growth (I6)Expandability (I7)Achievability (I8)
A1Expert 1HFHHAL
Expert 2VHMHVL
Expert 3HMML
A2Expert 1FHLFLVL
Expert 2AHVLAHAL
Expert 3VHVLMM
A3Expert 1AHMLL
Expert 2HMMFL
Expert 3VHFLFHAL
A4Expert 1MHMH
Expert 2FHFLVHM
Expert 3MFHLVL
Table 6:

Normalizing matrix.

A1A2A3A4
I1[0.2727,0.7273][0.0909,0.4545][0.6361,1][0,0.1824]
I2[0.2413,0.4827][0,0.1724][0.7931,1][0.4137,0.5517]
I3[0.9744,1][0.1667,0.1794][0,0.0342][0.0812,0.1111]
I4[0,0.6667][0.5,0.875][0.75,1][0.5833,0.7917]
I5[0.3007,0.5551][0.1330,0.5386][0,0.5794][0.7770,1]
I6[0.7227,0.8021][0,0.3068][0.5563,0.7047][0.6467,1]
I7[0.6546,0.8825][0.4093,1][0.1026,0.4434][0,0.9296]
I8[0,0.3028][0.1295,0.4519][0.0529,0.5071][0.3743,1]
Table 7:

Orthogonal array of L12(211).

I1I2I3I4I5I6I7I8I9I10I11
111111111111
211122222222
322211112222
422222221112
512211221122
612222112211
711222222211
812121212121
912212121212
1012112211221
1112122212112
1211221121221
Table 8:

Mahalanobis distance squared form each solution to reference point.

Reference pointMahalanobis distance squared
t1t2t3t4t5t6t7t8t9t10t11t12
A1A23.5773.5773.7373.7373.6683.6683.7983.7983.6403.6403.8653.612
A32.0762.0762.4262.4262.0362.0362.3422.3422.0372.0372.3152.317
A41.1141.1141.2771.2771.0491.0491.2041.2040.9300.9301.2171.099
A2A11.2931.2931.5971.5971.4851.4851.4531.4531.2071.2071.7831.199
A34.5384.5384.8534.8534.0254.0254.7694.7694.8144.8143.7795.617
A41.3161.3161.2511.2511.0561.0561.1071.1070.6970.6971.1550.981
A3A14.6294.6295.1835.1834.6044.6044.9734.9734.6884.6884.8594.919
A24.5324.5324.8334.8333.8673.8674.2254.2254.1784.1783.7495.073
A42.3932.3934.2754.2752.8702.8704.7384.7387.0487.0482.4796.939
A4A14.3394.3394.5564.5564.2884.2884.3324.3323.4773.4775.1463.654
A21.8291.8291.7101.7101.3191.3191.4211.4211.1121.1121.4971.537
A32.2602.2603.5943.5943.1583.1583.3413.3418.1028.1020.8527.986
Published Online: 2015-11-6
Published in Print: 2015-12-1

©2015 by De Gruyter

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