2015 [EEE [nternational Conference on Technological Advancements in Power & Energy
Optimal Generation Evaluation using SAW, WP, AHP and PROMETHEE Multi - Criteria Decision Making Techniques Javeed Kittur 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
methods
like
Simple
Weighted
considered.
Product
Organization (PROMETHEE)
This
Additive
(WP)
paper
method
Method
for
multi-criteria
discusses
Weighting and
method,
Preference
Ranking
Enrichment decision
different
(SAW)
Evaluation
making technique
to
evaluate the optimal generation of a particular day. The Analytic Hierarchy Process (AHP) method is used to verify the weights' selections. The results obtained by the multi-criteria evaluation using the presented methods, gives the possibility of identification and evaluation of the optimal generation in a particular day. Keywords:
Analytic
Hierarchy
Process;
Multi-criteria
Decisions; Optimal Generation; PROMETHEE; Simple Additive Weighting; Weighted Product
I.
[NTRODUCTION
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] . [n 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 TOPS[S method for supplier selection problem. [n this paper the weights are calculated and verified for each criterion based on AHP method. [n [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
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AHP and PROMETHEE technique. The authors in [4] , make a comparative analysis of different multi-criteria decision making techniques like ELECTRE, TOPS[S, PROMETHEE and V[KOR. 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 TOPS[S method is used. This paper is arranged in seven sections. The second, third, fourth and fifth section describes the proposed approach and gives information about SAW, WP, AHP and PROMETHEE 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. [I.
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 I. Each alternative is assessed with regard to every attribute. The overall or composite performance score of an alternative is given by below expression, M
Pt
=
I Wj (my )normal
(1)
)=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
304
2015 IEEE International Conference on Technological Advancements in Power & Energy •
(mij )K (mij )L where, (mijh is the measure of the attribute for the K-th alternative and (mij)r is the measure of the attribute for the L th 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
III.
WEIGHTED PRODUCT METHOD
M
� = II [(mij ) normal tl
(2)
)= 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., (m;)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. 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 AI). • 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 (AI x A2) and A4 (A3 1 A2). • Determine the maximum eigen value Amax, that is the average of matrix A4. =
=
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CI= •
•
Amax -M M-l
(3)
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.
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,
IV.
Calculate the Consistency Index (CI), the smaller the value of CI, the smaller is the deviation from the consistency
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.
PREFERENCE RANKING ORGANIZTION METHOD FOR ERICHMENT EVALUATION
(PROMETHEE)
PROMETHEE has been developed at the beginning of the I980s and has been extensively studied and refined since then. It has particular application in decision making, and is used around the world in a wide variety of decision scenarios, in fields such as business, governmental institutions, transportation, healthcare and education. An advantage of this technique is that there is no need to convert the qualitative data into quantitative data. The main procedure of PROMETHEE is as follows: Step I: Determine the objective and the evaluation attributes. Step 2: Determine 1 Select the weights for different attributes by relative comparison of attributes. Step 3: Create the dominance matrices for each of the attributes by comparing the alternatives. • If the attribute is non-beneficial and when AI> A2, assign'0' when Al < A2, assign' l' • If the attribute is beneficial and when Al > A2, assign' l' when Al < Az, assign'0' • If Al Az, then neither Al nor A2 are dominating each other, hence assign '0' in the dominance matrix when comparing Al with Az and A2 with AI. =
where, Al - Alternative I A2 - Alternative 2 Step 4: Multiply the dominance matrices of each attributes with its relevant attribute weight. Step 5: Add all the dominance matrices after having multiplied with the weights of the respective attribute.
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2015 IEEE International Conference on Technological Advancements in Power & Energy Step 6: Consider the updated dominance matrix obtained from step 5 and compute flow scores, that is, • Add the elements of a row (and then store the sum in +) for each alternative. • Add the elements of a column (and then store the sum in -) for each alternative. Step 7: Compute the net flow, that is, subtract - from + and the highest element value in the net flow column will be assigned first rank, the second highest element value will be assigned with second rank and so on. VI.
IMPLEMENTATION AND RESULTS
The implementation of SAW, WP, AHP and PROMETHEE 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 I, 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 TABLE 1 Generation and Purchasing cost for a day TIME
of attribute purchasing cost is chosen (purchasing cost: 18l.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 4. 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 confirmation that the weights chosen are correct. This is not possible in both SAW and WP method. TABLE 2 Normalized values TIME
WIND
CHP
lJTILITY
PURCHASING
(MW)
(MW)
(MW)
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 0.7961674
WIND
CHP
UTILITY
PURCHASING
(MW)
(MW)
(MW)
COST (£/H)
0.88
187.55
5:00
0.6
0.90638297
0.8652482
1:00
0.06
1.76
0.88
181.98
6:00
0.6
0.92765957
0.8794326
0.6775887
2:00
0.24
1.78
0.90
184.69
7:00
0.7
0.91489361
0.8581560
0.5846183
0:00
0.12
1.77
3:00
0.30
1.82
0.94
192.66
8:00
0.5
0.82127659
0.7163120
0.6423352
4:00
0.24
1.94
1.05
200.52
9:00
0.3
0.89361702
0.8156028
0.5801638
5:00
0.36
2.13
l.22
228.57
10:00
0.4
0.87659574
0.7943262
0.5548001
6:00
0.36
2.l8
l.24
268.57
11:00
0.l667
0.88510638
0.8156028
0.5747583 0.5761048
7:00
0.42
2.15
1.21
311.28
12:00
0.5
0.87659574
0.8085106
8:00
0.30
1.93
1.01
283.31
13:00
0.8
0.87234042
0.7943262
0.5795356
9:00
0.l8
2.l0
l.l5
313.67
14:00
0.1
0.88936170
0.8297872
0.6922550 0.6600892
10:00
0.24
2.06
l.l2
328.01
15:00
0.5
0.92340425
0.8794326
11:00
0.10
2.08
1.15
316.62
16:00
0.4
0.96170212
0.9432624
0.5l78124
12:00
0.30
2.06
1.14
315.88
17:00
0.6
0.97021276
0.9503546
0.3696601
13:00
0.48
2.05
l.l2
314.01
18:00
0.2
0.99148936
1
0.3844187
14:00
0.06
2.09
l.l7
262.88
19:00
1
1
1
0.4488456
20:00
1
0.94468085
0.9148936
0.5057388
15:00
0.30
2.17
1.24
275.69
16:00
0.24
2.26
1.33
351.44
17:00
0.36
2.28
l.34
492.29
18:00
0.l2
2.33
1.4 1
473.39
19:00
0.60
2.35
1.41
405.44
1.29
359.83
20:00
0.60
2.22
21:00
0.60
2.l0
l.l7
307.90
22:00
0.54
l.96
l.06
269.28
23:00
0.60
1.82
0.93
227.23
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21:00
1
0.8936l702
0.8297872
0.5910360
22:00
0.9
0.83404255
0.751773
0.6758021
23:00
1
0.77446808
0.6595744
0.8008625
Using AHP method a pair-wise comparison matrix using a scale of relative importance is constructed which gives matrix A1 as shown in table 5.
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2015 [EEE [nternational Conference on Technological Advancements in Power & Energy TABLE 4. Performance Scores for WP method
TABLE 3. Perfonnance Scores for SAW method TIME
PERFORMANCE
RANK
TIME
SCORE
PERFORMANCE
RANK
SCORE
0:00
0.77811888
8
0:00
0.723951817
8
1:00
0.78136686
7
1:00
0.688055984
7
2:00
0.806869999
4
2:00
0.780820717
4
3:00
0.807233215
3
3:00
0.792660367
3
4:00
0.809423584
2
4:00
0.791926194
2
5:00
0.820952979
t
5:00
0.816136373
t
6:00
0.77543523
6
6:00
0.76552499
6
7:00
0.734916787
14
7:00
0.720007099
14
8:00
0.684835892
19
9:00
0.653990576
20 21
8:00
0.691648196
19
9:00
0.682988734
20
10:00
0.672040046
21
10:00
0.651238231
11:00
0.666089402
22
11:00
0.61572043
22
12:00
0.693393887
18
12:00
0.678244234
18
13:00
0.718486562
16
13:00
0.706546274
16
14:00
0.71717588
15
14:00
0.642485864
15
15:00
0.75722947
9
15:00
0.743106864
9
16:00
0.705517577
17
16:00
0.667827758
17
0.596727529
23
17:00
0.659968029
23
17:00
18:00
0.645141993
24
18:00
0.55810991
24
19:00
0.749475318
10
19:00
0.694803989
10
20:00
0.744774899
13
20:00
0.710652176
13
21:00
0.75414598
11
21:00
0.738129417
11
22:00
0.753153132
12
22:00
0.748965266
12
23:00
0.786078727
5
23:00
0.781681507
5
TABLE 5. Relative Importance Matrix Wind
Utility
CHP
Cost
Wind
1
114
112
117
CHP
4
1
2
112
Utility
2
112
1
114
Cost
7
2
4
1
Al=
[
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, TABLE 6. Geometric Mean of each attribute Wind
1 4
114 1
2 112 7
2
112 117 2
112
1
114
4
1
CHP
Utility
Cost
GM
Wind
1
114
112
117
0.36558
CHP
4
1
2
112
1.41421
Utility
2
112
1
114
0.70711
Cost
7
2
4
1
2.73556
Total
5.22247
From matrix Al it is understood that, 0.07 •
•
•
•
Attribute wind is [/4, 112 and [/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, CRP and cost respectively. Attribute cost is 7, 2 and 4 times important than the attribute wind, CRP and utility respectively.
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[A2] =
0.27079 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
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2015 IEEE International Conference on Technological Advancements in Power & Energy
0.2803 [A3]
=
[AI * A2]
1.0835 =
0.5417 2.0970
[A4]
=
[A3] [A2]
=
Average of A4
4.003477 4.001192 4.001192 4.003377 =
4. 002309
The average value of the matrix A4 is "-max 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 (3) and the Consistency Ratio (CR) using equation (4), =
Consistency Index
=
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 CRP 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 I . 78MW and generation by utility is 0. 90MW. For the total generation of 2.92MW, the cost of the generation at 2 hours of the day is 184.69 £/h. From the ranking column of table 9, it is observed that at 6 hours of the day optimal generation occurs where the generation by wind is 0.36MW, generation by CHP is 2.18MW and generation by utility is 1. 24MW. For the total generation of 3. 78MW, the cost of the generation at 6hours of the day is 268.57 £/h. TABLE 7. Random Index (RI) values
0.000769841
Consistency ratio is given by,
TABLE 8. Performance Scores for AHP method
(4)
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, CRP, utility and purchasing cost). Now substituting the values of CI and RI in equation (4), 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. Let us consider the same weights and proceed with PROMETHEE technique. The initial mathematical calculations done in AHP method can be used for PROMETREE technique as well. The next step in PROMETREE method is to construct the dominance matrices for each attribute and then multiply it by its weights accordingly. After obtaining the dominance matrices for all the four attributes, the matrices are added which gives a complete dominant matrix. The next step is to compute flow scores, that is, add the elements of a row (and then store the sum in +) for each alternative. Add the elements of a column (and then store the sum in -) for each alternative. Table 9 gives the details of flow scores considering rows and columns separately. Table 9 also has net flow column which is the difference between the flow scores. This net flow plays a very important role in deciding the ranking or the priority of optimal generation. The last column of table 7 gives the ranking or priority of optimal generation for the 24hours of a particular day. =
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TIME
PERFORMANCE
RANK
SCORE
0:00
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
0.719168081
13
8:00
0.69084402
17
9:00
0.67731088
20 21
6
10:00
0.663535334
11:00
0.662841235
22
12:00
0.683615594
19
13:00
0.703340415
16
14:00
0.722792835
12
15:00
0.749885292
9
16:00
0.687372732
18
17:00
0.62703482
23
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
308
2015 IEEE International Conference on Technological Advancements in Power & Energy SAW and WP method are very simple and there is no validation of the weights selected, therefore the results obtained by these methods may be inaccurate. In AHP method after the validation of weights, the process that is followed is same as SAW method, hence even this method is not considered as an accurate method. PROMETHEE method is a detailed stepwise method which considers all the aspects into account, hence is considered as a comparatively accurate method.
at 2:00 hours of the day and by the PROMETHEE technique the optimal generation happens at 6:00 hours of the day. 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]
Perna 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): l-lO
[4]
N. Caterino, I. lervolino, G. Manfredi and E.Cosenza, "A Comparative Analysis of Decision Making Methods for the Seismic Retrofit of RC Buildings"', The 141h 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
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R.Venkata Rao, "Decision Making in the Manufacturing Environment: Using Graph Theory and Fuzzy Multiple Attribute Decision Making Methods'" (Springer series in advanced manufacturing).
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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), Vo1.5, No.4, July 2014
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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. OOl-OlO,January,2014.
[9 ]
Evangelos Triantaphyllou, "Multi-Criteria Methods: A Comparative Study"',Springer
TABLE 9 Flow scores,net flow and ranking Flow scores
(
