2015 International Conference on Circuit, Power and Computing Technologies [ICCPCT]
Evaluating Optimal Generation using different Multi– Criteria Decision Making Methods Javeed Kittur, Poornanand C, Prajwal R, Pavan R.P, Pavankumar M.P, Vishal P, Vijeta B, Vijaykumar S and Jagadish B Department of Electrical & Electronics Engineering B. V. Bhoomaraddi College of Engineering & Technology, Hubli, India
[email protected],
[email protected] Abstract—In the present day scenario the energy demand is going on increasing. It is expensive to import electricity from the generation far from load centers because of the cost of power loss. It is therefore more economical to use electricity generated by local distributed generators. In this paper power generation from wind, Combined Heat Power (CHP) and utility for a complete day is considered. This paper proposes different methods to evaluate the optimal generation of a particular day. The methods considered are Simple Additive Weighting (SAW) method, Weighted Product (WP) Method and Analytic Hierarchy Process (AHP) multi-criteria decision making technique. The results obtained by the multi-criteria evaluation using the presented method, gives the possibility of identification and evaluation of the optimal generation in a particular day. Keywords—Analytic Hierarchy Process, Multi – criteria Decisions, Optimal Generation, Simple Additive Weighting, Weighted Product
I.
INTRODUCTION
In the past, new methods have been found and the methodology of decision-making process has been improving. Decision-making problems generally imply the selection of the best compromise solution. Besides the real criteria values by which a decision is made, the selection of the best solution also depends on the decision maker, that is, on his individual preferences [1]. In order to simplify the decision-making process, many mathematical methods have been suggested. The Analytic Hierarchy Process (AHP) represents one of the most frequently used methods of multi-criteria decisions. Besides this method, other methods are also available like Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) technique, combinatorial mathematics based method, etc. The authors in [2], discuss the application of AHP and TOPSIS method for supplier selection problem. In this paper the weights are calculated and verified for each criterion based on AHP method. In [3], the authors discuss about evaluating potential freight using multi-criteria decision making techniques, the authors have considered an example of evaluating freight villages and selecting one of them using AHP and PROMETHEE technique. The authors in [4], make a comparative analysis of different multi-criteria decision
978-1-4799-7075-9/15/$31.00 ©2015 IEEE
making techniques like ELECTRE, TOPSIS, PROMETHEE and VIKOR. The aim of this paper is to find the optimal generation with respect to cost in a day. Here a logistic evaluation of the generation is proposed using Simple Additive Weighting (SAW), Weighted Product (WP) and Analytic Hierarchy Process (AHP) method. Subjective and objective opinions of experts turn into quantitative form with Analytic Hierarchy Process [5]. AHP is applied to determine the relative weights of the evaluation criteria. In this study the weights are assigned considering relative importance of different attributes (Wind, CHP, Utility and Cost). For calculating the optimal generation TOPSIS method is used. This paper is arranged in six sections. The second, third and fourth section describes the proposed approach and gives information about SAW, WP and AHP methodologies. The next section discusses the implementation of the considered methods using an example which includes generation using different attributes like wind, CHP, utility and purchasing cost. Results and discussion and conclusions of the study are followed. II.
SIMPLE ADDITIVE WEIGHTING METHOD
This method is also called as weighted sum method and is the simplest and the widest used method [6]. Here each attribute is given a weight and sum of all the weights must be 1. Each alternative is assessed with regard to every attribute. The overall or composite performance score of an alternative is given by below expression,
Pi =
M
∑ w j (mij ) normal
(1)
j =1
where, (mij)normal represents the normalized value of an attribute and Pi is the overall score of the alternative Ai. The alternative with the highest value of Pi is considered as the best alternative. The attributes can be beneficial or non-beneficial. When objective values of the attribute are available, normalized values are calculated by
2015 International Conference on Circuit, Power and Computing Technologies [ICCPCT]
(mij )K (mij )L
(2) •
where, (mij)K is the measure of the attribute for the K-th alternative and (mij)L is the measure of the attribute for the Lth alternative that has the highest measure of the attribute out of all alternatives considered. This ratio is valid only for beneficial attributes. For the non – beneficial attributes, the lower measures are desirable and the normalized values are calculated by
(mij )L (mij )K III.
(3)
This method is similar to simple additive weighting method. The main difference is that, instead of addition in the method, there is multiplication. The overall score of an alternative is given by the following equation, M
wj
(4)
j =1
The normalized values are calculated as explained under the SAW method. Each normalized value of an alternative with respect to an attribute, i.e., (mij)normal, is raised to the power of the relative weight of the corresponding attribute. The alternative with the highest value of Pi is considered as the best alternative. IV.
•
λ −M CI = max M −1 • •
WEIGHTED PRODUCT METHOD
Pi = ∏ [(mij ) normal ]
•
ANALYTIC HIERARCHY PROCESS METHOD
One of the most popular analytical techniques for complex decision-making problems is Analytic Hierarchy Process [6]. In 1980, 2000 Saaty developed AHP, which decomposes a decision-making problem into a system of hierarchies of objectives, attributes (or criteria) and alternatives [6][7]. AHP can efficiently deal with objective and subjective attributes, especially where the subjective judgments of different individuals constitute an important part of the decision process. The main procedure of AHP is as follows [6][8]: Step 1: Determine the objective and the evaluation attributes. Step 2: Determine the relative importance of different attributes with respect to the objective. • Construct a pair-wise comparison matrix using a scale of relative importance (this gives matrix A1). • Find the relative normalized weight of each attribute by calculating the geometric mean of each row and
by normalizing the geometric means of rows (this gives matrix A2). Calculate matrices A3 and A4 using A3 = (A1 x A2) and A4 = (A3 / A2). Determine the maximum eigen value λmax, that is the average of matrix A4. Calculate the Consistency Index (CI), the smaller the value of CI, the smaller is the deviation from the consistency (5)
Obtain the Random Index (RI) for the number of attributes used in decision making, table 3.2 given in [6]. Calculate the consistency ratio (CR), usually a CR of 0.1 or less is considered as acceptable.
Step 3: Obtain the overall performance scores for the alternatives by multiplying the relative normalized weight of each attribute. Step 4: Give the ranking to the performance scores and the alternative with the highest value of Pi is considered as the best alternative i.e., first rank. V.
IMPLEMENTATION AND RESULTS
The implementation of SAW, WP and AHP is done using the generation details from wind, CHP, utility and the purchasing cost for a particular day. The data is taken from [1] is shown in table 1, which is considered as input. The weights assigned to the attributes wind, CHP, utility and cost are 0.0909, 0.27272, 0.18181 and 0.45454 respectively (chosen on the basis of relative importance). The attribute wind, CHP and utility should be high and the attribute purchasing cost should be low. To calculate the normalized values highest values of attributes wind, CHP and utility are chosen (wind: 0.6, CHP: 2.35, utility: 1.41) and lowest value of attribute purchasing cost is chosen (purchasing cost: 181.98). Consider each alternative and divide it with the chosen value for the respective attribute, the table 2 shows the normalized values. Using these normalized values, the performance score is calculated as discussed in SAW method. The ranking is also done i.e., the alternative with highest value is ranked first and so on and this is shown in table 3. Similarly, the performance score is also calculated using WP method and the rankings are as shown in table 5. In simple additive weighting method and weighted product method the weights chosen based on relative importance may or may not be correct. There is no any procedure to validate the weights chosen in SAW and WP method. In AHP method the weights chosen can be validated by the consistency ratio, if the consistency ratio is well within the range then we get a
2015 International Conference on Circuit, Power and Computing Technologies [ICCPCT] confirmation that the weights chosen are correct. This is not possible in both SAW and WP method.
14:00
0.1
0.88936170
0.8297872
0.6922550
15:00
0.5
0.92340425
0.8794326
0.6600892
TABLE 1. Generation and Purchasing cost for a day
16:00
0.4
0.96170212
0.9432624
0.5178124
17:00
0.6
0.97021276
0.9503546
0.3696601
18:00
0.2
0.99148936
1
0.3844187
TIME 0:00
WIND (MW) 0.12
CHP (MW) 1.77
UTILITY (MW) 0.88
PURCHASING COST (£/H) 187.55
19:00
1
1
1
0.4488456
1:00
0.06
1.76
0.88
181.98
20:00
1
0.94468085
0.9148936
0.5057388
2:00
0.24
1.78
0.90
184.69
21:00
1
0.89361702
0.8297872
0.5910360
192.66
22:00
0.9
0.83404255
0.751773
0.6758021
23:00
1
0.77446808
0.6595744
0.8008625
3:00
0.30
1.82
0.94
4:00
0.24
1.94
1.05
200.52
5:00
0.36
2.13
1.22
228.57
6:00
0.36
2.18
1.24
268.57
7:00
0.42
2.15
1.21
311.28
8:00
0.30
1.93
1.01
283.31
TABLE 3. Performance Scores for SAW method TIME
PERFORMANCE SCORE 0.77811888
RANK
9:00
0.18
2.10
1.15
313.67
0:00
10:00
0.24
2.06
1.12
328.01
1:00
0.78136686
7
11:00
0.10
2.08
1.15
316.62
2:00
0.806869999
4
12:00
0.30
2.06
1.14
315.88
3:00
0.807233215
3
13:00
0.48
2.05
1.12
314.01
4:00
0.809423584
2
14:00
0.06
2.09
1.17
262.88
5:00
0.820952979
1
15:00
0.30
2.17
1.24
275.69
6:00
0.77543523
6
16:00
0.24
2.26
1.33
351.44
7:00
0.734916787
14
17:00
0.36
2.28
1.34
492.29
8:00
0.691648196
19
18:00
0.12
2.33
1.41
473.39
9:00
0.682988734
20
19:00
0.60
2.35
1.41
405.44
10:00
0.672040046
21
20:00
0.60
2.22
1.29
359.83
11:00
0.666089402
22
21:00
0.60
2.10
1.17
307.90
12:00
0.693393887
18
22:00
0.54
1.96
1.06
269.28
13:00
0.718486562
16
23:00
0.60
1.82
0.93
227.23
14:00
0.71717588
15
TABLE 2. Normalized values TIME
WIND (MW)
CHP (MW)
UTILITY (MW)
PURCHASING COST (£/H)
0:00
0.2
0.75319148
0.6241134
0.9703012
1:00
0.1
0.74893617
0.6241134
1
2:00
0.4
0.75744680
0.6382978
0.9853267
3:00
0.5
0.77446808
0.6666666
0.9445655
4:00
0.4
0.82553191
0.7446808
0.9075403
5:00
0.6
0.90638297
0.8652482
0.7961674
6:00
0.6
0.92765957
0.8794326
0.6775887
7:00
0.7
0.91489361
0.8581560
0.5846183
8:00
0.5
0.82127659
0.7163120
0.6423352
9:00
0.3
0.89361702
0.8156028
0.5801638
10:00
0.4
0.87659574
0.7943262
0.5548001
11:00
0.1667
0.88510638
0.8156028
0.5747583
12:00
0.5
0.87659574
0.8085106
0.5761048
13:00
0.8
0.87234042
0.7943262
0.5795356
8
15:00
0.75722947
9
16:00
0.705517577
17
17:00
0.659968029
23
18:00
0.645141993
24
19:00
0.749475318
10
20:00
0.744774899
13
21:00
0.75414598
11
22:00
0.753153132
12
23:00
0.786078727
5
Using AHP method a pair-wise comparison matrix using a scale of relative importance is constructed which gives matrix A1 as shown in table 4. Table 4 : Relative Importance Matrix Wind Wind
1
CHP Utility Cost
CHP
Utility
Cost
1/4
1/2
1/7
4
1
2
1/2
2
1/2
1
1/4
7
2
4
1
2015 International Conference on Circuit, Power and Computing Technologies [ICCPCT] Table 6. Geometric Mean of each attribute
⎡1 1 / 4 1 / 2 1 / 7 ⎤ ⎢4 1 2 1 / 2⎥⎥ A1 = ⎢ ⎢2 1 / 2 1 1 / 4⎥ ⎢ ⎥ 4 1 ⎦ ⎣7 2
Wind
From matrix A1 it is understood that, • • • •
Attribute wind is 1/4, 1/2 and 1/7 times important than attribute CHP, utility and cost respectively. Attribute CHP is 4, 2 and 1/2 times important than attribute wind, utility and cost respectively. Attribute utility is 2, 1/2 and 1/4 times important than attribute wind, CHP and cost respectively. Attribute cost is 7, 2 and 4 times important than the attribute wind, CHP and utility respectively. TABLE 5. Performance Scores for WP method TIME
RANK
0:00
PERFORMANCE SCORE 0.723951817
1:00
0.688055984
7
2:00
0.780820717
4
3:00
0.792660367
3
4:00
0.791926194
2
5:00
0.816136373
1
8
6:00
0.76552499
6
7:00
0.720007099
14
8:00
0.684835892
19
9:00
0.653990576
20
10:00
0.651238231
21
11:00
0.61572043
22
12:00
0.678244234
18
13:00
0.706546274
16
14:00
0.642485864
15
15:00
0.743106864
9
16:00
0.667827758
17
17:00
0.596727529
23
18:00
0.55810991
24
19:00
0.694803989
10
20:00
0.710652176
13
21:00
0.738129417
11
22:00
0.748965266
12
23:00
0.781681507
5
Considering matrix A1 (of table 5) and calculating the Geometric Mean (GM) of each attribute gives table 6. To determine the weight matrix A2, divide the GM of each attribute by its total, this gives,
CHP
Utility
Cost
GM
Wind
1
1/4
1/2
1/7
0.36558
CHP
4
1
2
1/2
1.41421
Utility
2
1/2
1
1/4
0.70711
Cost
7
2
4
1
2.73556 5.22247
Total
⎡0.07 ⎤ ⎢0.27079⎥ ⎥ [ A2] = ⎢ ⎢0.1354 ⎥ ⎢ ⎥ ⎣0.52381⎦ Matrix A3 is obtained by multiplying A1 and A2, and matrix A4 is obtained by dividing A3 by A2, given below
⎡0.2803 ⎤ ⎢1.0835 ⎥ ⎥ [ A3] = [ A1 * A2] = ⎢ ⎢0.5417 ⎥ ⎢ ⎥ ⎣2.0970⎦ ⎡4.003477 ⎤ ⎥ ⎢ [ A3] ⎢4.001192 ⎥ = [ A4] = [ A2] ⎢4.001192 ⎥ ⎢ ⎥ ⎣4.003377 ⎦ Average of A4 = 4.002309 The average value of the matrix A4 is λmax = 4.002309, this value should be close to the size of the matrix A1 (in this study, it is 4). The Consistency Index (CI) is calculated using equation (5) and the Consistency Ratio (CR) using equation (6), Consistency Index = 0.000769841 Consistency ratio is given by,
CR =
CI *100 RI
(6)
where, RI is the Random Index and its values is chosen from [6], given below which in table 7 is equal to 0.89 for four attributes (wind, CHP, utility and purchasing cost).
2015 International Conference on Circuit, Power and Computing Technologies [ICCPCT] TABLE 7. Random Index (RI) values
VI.
Attributes
3
4
5
6
7
8
9
10
RI
0.52
0.89
1.11
1.25
1.35
1.4
1.45
1.49
Now substituting the values of CI and RI in equation (6), we get CR = 0.086498945 %. The calculated CR is less than 0.1 % which is as per the requirement [6][9]. With CR being in the acceptable range the weights are also considered acceptable. Now using step 3 and step 4 of the Analytic Hierarchy Process method, the performance scores and the rankings are determined and are as shown in table 8. From the rank column of table 3 and table 5, it is observed that at 5:00 hours of the day optimal generation occurs when the generation by wind is 0.36MW, generation by CHP is 2.13MW and generation by utility is 1.22MW. For the total generation of 3.71MW, the cost of the generation at 5 hours of the day is 228.57 £/h. From the rank column of table 8 it is observed that the at 2:00 hours of the day optimal generation occurs when the generation by wind is 0.24MW, generation by CHP is 1.78MW and generation by utility is 0.90MW. For the total generation of 2.92MW, the cost of the generation at 6hours of the day is 184.69 £/h. TABLE 8. Performance Scores for AHP method TIME
RANK
0:00
PERFORMANCE SCORE 0.810713852
1:00
0.818117756
5
2:00
0.835657538
1
3:00
0.829757038
2
4:00
0.827753488
3
5:00
0.821634422
4
6:00
0.767204146
8
7:00 8:00
0.719168081 0.69084402
13 17
9:00
0.67731088
20
10:00
0.663535334
21
11:00
0.662841235
22
12:00
0.683615594
19
13:00 14:00
0.703340415 0.722792835
16 12
15:00
0.749885292
9
16:00
0.687372732
18
17:00
0.62703482
23
6
18:00
0.61924814
24
19:00
0.711301559
15
20:00
0.714599316
14
21:00
0.733927657
11
22:00
0.744633225
10
23:00
0.788525098
7
CONCLUSIONS
In this paper SAW, WP and AHP methods are discussed to evaluate the optimal generation of a particular day. The weights assigned to the attributes wind, CHP, utility and cost based on their relative importance is validated using analytic hierarchy process method. From the decision making methods SAW and WP method it is found that the optimal generation happens at 5:00 hours of the day. The consistency ratio obtained from AHP method is 0.086498945% which is less than 0.1%, is considered acceptable and it reflects a good judgment for the considered example. From the decision making method AHP it is found that the optimal generation happens at 2:00 hours of the day. ACKNOWLEDGEMENTS The authors would like to thank the Principal and Head of the department (Electrical & Electronics Engineering) of B.V.Bhoomaraddi College of Engineering and Technology, Hubli for providing with the necessary training and facilities to work on this paper. REFERENCES [1]
Vojislav Tomic, Zoran Marinkovic, Dragoslav Janosevic, “PROMETHEE method implementation with multi-criteria decisions”, FACTA UNIVERSITATIS, Mechanical Engineering, Vol. 9, No. 2, 2011, pp. 193 – 202.
[2]
Pema Wangchen Bhutia, Ruben Phipon, “Application of AHP and TOPSIS method for supplier selection problem”, IOSR Journal of Engineering, Volume 2, Issue 10 (October 2012), PP 43-50
[3]
Bahadir Fatih Yildirim, Emrah Onder, “Evaluating Potential Freight Villages in Istanbul using Multi Criteria Decision Making Techniques”, Journal of Logistics Management 2014, 3(1): 1-10
[4]
N. Caterino, I. Iervolino, G. Manfredi and E.Cosenza, “A Comparative Analysis of Decision Making Methods for the Seismic Retrofit of RC Buildings”, The 14th World Conference on Earthquake Engineering October 12-17, 2008, Beijing, China.
[5]
Shuanghong Qu, Hua Li, Yunxia Pei, “Decision Making in Investing: Application of Interval – PROMETHEE based on the Composite Weight”, Journal of Theoretical and Applied Information Technology 15th November 2012. Vol. 45 No.1
[6]
R.Venkata Rao, “Decision Making in the Manufacturing Environment: Using Graph Theory and Fuzzy Multiple Attribute Decision Making Methods” (Springer series in advanced manufacturing).
[7]
Ihab Sbeity, Mohamed Dbouk and Habib Kobeissi, “Combining the Analytical Hierarchy Process and the Genetic Algorithm to solve the time table problem”, International Journal of Software Engineering & Applications (IJSEA), Vol.5, No.4, July 2014
[8]
Alireza Arabameri, “Application of the Analytic Hierarchy Process (AHP) for locating fire stations: Case Study Maku City”, Merit Research Journal of Art, Social Science and Humanities (ISSN: 2350-2258) Vol. 2(1) pp. 001-010, January, 2014.
[9]
Evangelos Triantaphyllou, “Multi-Criteria Decision Making Methods: A Comparative Study”, Springer
