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”).
Reference
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Appendix
11 Fuzzy language and 11 cloud.
Fuzzy language | Cloud | |||
PL | ||||
AL | ||||
VL | ||||
L | ||||
FL | ||||
M | ||||
FH | ||||
H | ||||
VH | ||||
AH | ||||
PH |
The decision-making information of each solution under quantitative index.
Solution | Quantitative index | |||
Electricity supply reliability ( | Electricity supply Quality ( | Investment ( | Grid loss rate ( | |
[230,280] | [0.16,0.23] | [3.86,3.92] | [0.27,0.43] | |
[210.250] | [0.09,0.14] | [5.78,5.81] | [0.22,0.31] | |
[270,310] | [0.32,0.38] | [6.12,6.20] | [0.19,0.25] | |
[200,220] | [0.21,0.25] | [5.94,6.01] | [0.24,0.29] |
The decision-making information of each solution under qualitative index.
Solution | Qualitative index | ||||
Influence on environment ( | Compatibility of solutions and load growth ( | Expandability ( | Achievability ( | ||
Expert 1 | H | FH | H | AL | |
Expert 2 | VH | M | H | VL | |
Expert 3 | H | M | M | L | |
Expert 1 | FH | L | FL | VL | |
Expert 2 | AH | VL | AH | AL | |
Expert 3 | VH | VL | M | M | |
Expert 1 | AH | M | L | L | |
Expert 2 | H | M | M | FL | |
Expert 3 | VH | FL | FH | AL | |
Expert 1 | M | H | M | H | |
Expert 2 | FH | FL | VH | M | |
Expert 3 | M | FH | L | VL |
Normalizing matrix.
[0.2727,0.7273] | [0.0909,0.4545] | [0.6361,1] | [0,0.1824] | |
[0.2413,0.4827] | [0,0.1724] | [0.7931,1] | [0.4137,0.5517] | |
[0.9744,1] | [0.1667,0.1794] | [0,0.0342] | [0.0812,0.1111] | |
[0,0.6667] | [0.5,0.875] | [0.75,1] | [0.5833,0.7917] | |
[0.3007,0.5551] | [0.1330,0.5386] | [0,0.5794] | [0.7770,1] | |
[0.7227,0.8021] | [0,0.3068] | [0.5563,0.7047] | [0.6467,1] | |
[0.6546,0.8825] | [0.4093,1] | [0.1026,0.4434] | [0,0.9296] | |
[0,0.3028] | [0.1295,0.4519] | [0.0529,0.5071] | [0.3743,1] |
Orthogonal array of
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
3 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
4 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 2 |
5 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 2 |
6 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 1 |
7 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | 1 |
8 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 |
9 | 1 | 2 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 |
10 | 1 | 2 | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 1 |
11 | 1 | 2 | 1 | 2 | 2 | 2 | 1 | 2 | 1 | 1 | 2 |
12 | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 1 | 2 | 2 | 1 |
Mahalanobis distance squared form each solution to reference point.
Reference point | Mahalanobis distance squared | ||||||||||||
3.577 | 3.577 | 3.737 | 3.737 | 3.668 | 3.668 | 3.798 | 3.798 | 3.640 | 3.640 | 3.865 | 3.612 | ||
2.076 | 2.076 | 2.426 | 2.426 | 2.036 | 2.036 | 2.342 | 2.342 | 2.037 | 2.037 | 2.315 | 2.317 | ||
1.114 | 1.114 | 1.277 | 1.277 | 1.049 | 1.049 | 1.204 | 1.204 | 0.930 | 0.930 | 1.217 | 1.099 | ||
1.293 | 1.293 | 1.597 | 1.597 | 1.485 | 1.485 | 1.453 | 1.453 | 1.207 | 1.207 | 1.783 | 1.199 | ||
4.538 | 4.538 | 4.853 | 4.853 | 4.025 | 4.025 | 4.769 | 4.769 | 4.814 | 4.814 | 3.779 | 5.617 | ||
1.316 | 1.316 | 1.251 | 1.251 | 1.056 | 1.056 | 1.107 | 1.107 | 0.697 | 0.697 | 1.155 | 0.981 | ||
4.629 | 4.629 | 5.183 | 5.183 | 4.604 | 4.604 | 4.973 | 4.973 | 4.688 | 4.688 | 4.859 | 4.919 | ||
4.532 | 4.532 | 4.833 | 4.833 | 3.867 | 3.867 | 4.225 | 4.225 | 4.178 | 4.178 | 3.749 | 5.073 | ||
2.393 | 2.393 | 4.275 | 4.275 | 2.870 | 2.870 | 4.738 | 4.738 | 7.048 | 7.048 | 2.479 | 6.939 | ||
4.339 | 4.339 | 4.556 | 4.556 | 4.288 | 4.288 | 4.332 | 4.332 | 3.477 | 3.477 | 5.146 | 3.654 | ||
1.829 | 1.829 | 1.710 | 1.710 | 1.319 | 1.319 | 1.421 | 1.421 | 1.112 | 1.112 | 1.497 | 1.537 | ||
2.260 | 2.260 | 3.594 | 3.594 | 3.158 | 3.158 | 3.341 | 3.341 | 8.102 | 8.102 | 0.852 | 7.986 |
©2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- Research Articles
- Association Analysis of System Failure in Wide Area Backup Protection System
- Interdependency Assessment of Coupled Natural Gas and Power Systems in Energy Market
- Determination of the Prosumer’s Optimal Bids
- A Mathematical Model to Predict Voltage Fluctuations in a Distribution System with Renewable Energy Sources
- The Effect of Plug-in Electric Vehicles on Harmonic Analysis of Smart Grid
- A Computational Methodology to Support Reimbursement Requests Analysis Concerning Electrical Damages
- Optimal Scheduling Method of Controllable Loads in DC Smart Apartment Building
- Risky Group Decision-Making Method for Distribution Grid Planning
Articles in the same Issue
- Frontmatter
- Research Articles
- Association Analysis of System Failure in Wide Area Backup Protection System
- Interdependency Assessment of Coupled Natural Gas and Power Systems in Energy Market
- Determination of the Prosumer’s Optimal Bids
- A Mathematical Model to Predict Voltage Fluctuations in a Distribution System with Renewable Energy Sources
- The Effect of Plug-in Electric Vehicles on Harmonic Analysis of Smart Grid
- A Computational Methodology to Support Reimbursement Requests Analysis Concerning Electrical Damages
- Optimal Scheduling Method of Controllable Loads in DC Smart Apartment Building
- Risky Group Decision-Making Method for Distribution Grid Planning