This research study provides a methodology to solve the multi-objective optimal placement of automatic line switches in distribution networks. SAIFI, SAIDI, and TCOST represent the three objective functions to be minimized simultaneously. Furthermore, each feasible solution for the optimization problem is represented by a different combination of number and locations of automatic switches.
In this study, the distribution network is modeled using set operation theory in order to determine the presence of any switching device between the faulted section and the customers upstream or downstream. This technique helps us calculate easily the reliability indices SAIFI and SAIDI for a certain combination of switch locations.
We proposed an integer version of NSGA-II to solve the multi-objective optimization problem by sorting a population of feasible solutions in order to identify the set of Pareto-optimal solutions, which constitute the best trade-offs between system reliability and utility investment.
The person in charge of the network design-planning can select a final solution from the Pareto-set by considering the different objective function trade-offs according to his/her professional experience. However, a selection approach has also been presented in this study in order to choose the final solution based on Max-Min method.
The proposed version of NSGA-II was tested using two case studies, and the results have showed that this methodology guarantees a very good approximation to the true Pareto-front and diversity of the solutions is also ensured.
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In Case 1, the beneficial impact of automatic line switches in distribution networks was illustrated through simulation in a one-line distribution network.
Case 2 considered the simulation of an actual distribution system with notable results for reliability indexes. Although, as expected, they involved higher investment cost for the utility.
In conclusion, the present methodology will indicate where the utility should invest resources for switching automation in order to improve the reliability of the system, proving this way its application as an important decision tool for distribution utilities.
This study is strongly related to sustained interruptions. It is suggested that a future research study includes an additional objective function that accounts for the effects of momentary interruptions in distribution networks. Another interesting objective function worth being evaluated is CIC (Customer Interruption Costs) given that it accounts for the economic losses of customers due to power outages.
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Appendix
Appendix 1: SF6 Gas Insulated Automatic Sectionalizing Switch for
distribution systems Specifications datasheet
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77
78
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Appendix 2: Fitness Evaluation for Solution 1 in Table 4-1
1. SAIFI
80
81 3. TCOST
ܰݑ݉ ൌ Ͷ
ܰݑ்݉ൌ ͳ
ܥ ൌ ܥ்ൌ ܷܵ̈́ͻǡͲͳ െ ͳͷݕ݁ܽݎݏ
ܶܥܱܵܶ ൌ ܰݑ݉ൈ ܥ ܰݑ்݉ൈ ܥ்
ܶܥܱܵܶ ൌUS$45355
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Appendix 3:
1. Crossover Operator Procedure Parent 1:
0 0 1 0 1 1 2 0 1 0
Parent 2:
1 1 1 0 2 1 1 1 1 1
ܿݎݏݏݒ݁ݎܨݎܽܿݐ݅݊ ൌ ͲǤ
ݎܽݐ݅ ൌ ͳǤͷ
݄݈ܿ݅݀ͳ ൌ ܽݎ݁݊ݐͳ ݎܽ݊݀ ൈ ݎܽݐ݅ ൈ ሺܽݎ݁݊ݐͳ െ ܽݎ݁݊ݐʹሻ
݄݈ܿ݅݀ʹ ൌ ܽݎ݁݊ݐʹ െ ݎܽ݊݀ ൈ ݎܽݐ݅ ൈ ሺܽݎ݁݊ݐʹ െ ܽݎ݁݊ݐͳሻ
Child 1:
1
-0.04681 0
-0.28801
2.37631 1
-1.2423Child 2:
1
0.18921 0
1.49791
2.01201 1
-0.2352After rounding and setting lower and upper bounds:
Child 1:
0 0 1 0 0 1 2 0 1 0 Child 2:
1 0 1 0 1 1 2 1 1 0
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2. Mutation Operator Procedure Parent:
0 0 1 2 1 0 0 0 0 1
݉ݑݐܽݐ݅݊ܨݎܽܿݐ݅݊ ൌ ͲǤͶ ݏ݈ܿܽ݁ ൌ ͲǤͷ
ݏ݄ݎ݅݊݇ ൌ Ͳ
݄݈ܿ݅݀ ൌ ܽݎ݁݊ݐ ܵ ൈ ݎܽ݊݀݊ ൈ ሺݑܾ െ ݈ܾሻ
Child:
0
1.31451 2
1.08720
0.97800
-0.57471
After rounding and setting lower and upper bounds:
Child:
0 1 1 2 1 0 1 0 0 1
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Appendix 4: Load and Number of Customers of Load points for Case 1 (Chen, et al., 2006)
Load Points Load (Kw) Total Customers
L1 69 40
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App e ndi x 5: P a ret o -opt im a l S o lu ti on s fo r Cas e 1
Var1Var2Var3Var4Var5Var6Var7Var8Var9Var10 Var11 Var12 Var13 Var14 Var15 Var16 Var17 Var18 Obj1Obj2Obj3 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1.26531 303.674 604.73 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 0.0178926 4.29422 10885.1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1.26531 303.674 604.73 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 0.0178926 4.29422 10885.1 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0.830824 199.398 1209.46 0 0 0 1 0 0 0 0 0 2 0 0 0 1 0 0 0 0 0.551969 132.473 1814.19 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0.830824 199.398 1209.46 0 1 0 0 0 1 0 0 0 2 0 0 0 1 0 0 0 0 0.419294 100.631 2418.92 0 0 0 1 0 0 0 0 0 2 0 0 0 1 0 0 0 0 0.551969 132.473 1814.19 0 1 0 0 0 1 0 0 0 2 0 0 1 0 0 1 0 0 0.329831 79.1595 3023.65 0 1 0 0 0 1 0 0 0 2 0 0 0 1 0 0 0 0 0.419294 100.631 2418.92 0 1 0 1 0 1 0 0 0 2 0 0 1 0 0 1 0 0 0.269739 64.7374 3628.38 0 1 0 0 0 1 0 0 0 2 0 0 1 0 0 1 0 0 0.329831 79.1595 3023.65 0 1 0 1 0 1 0 0 0 2 0 0 1 0 0 1 0 0 0.269739 64.7374 3628.38 0 1 0 1 0 0 1 0 0 2 0 1 0 1 0 0 1 0 0.21201 50.8825 4233.11 0 1 0 1 0 0 1 0 0 2 0 1 0 1 0 0 1 0 0.21201 50.8825 4233.11 1 1 0 1 0 0 1 0 0 2 0 1 0 1 0 0 1 0 0.173524 41.6458 4837.84 1 1 0 1 0 1 0 1 0 2 0 1 0 1 0 0 1 0 0.144153 34.5968 5442.57 1 1 0 1 0 0 1 0 0 2 0 1 0 1 0 0 1 0 0.173524 41.6458 4837.84 1 1 0 1 0 1 0 1 0 2 0 1 0 1 0 1 0 1 0.119509 28.6821 6047.3 1 1 0 1 0 1 0 1 0 2 0 1 0 1 0 0 1 0 0.144153 34.5968 5442.57 1 1 0 1 0 1 0 1 0 2 0 1 0 1 0 1 0 1 0.119509 28.6821 6047.3 1 1 1 1 0 1 0 1 0 2 0 1 0 1 0 1 0 1 0.0975652 23.4157 6652.03 1 1 1 1 0 1 1 0 2 1 1 0 1 1 0 1 0 1 0.0671816 16.1236 7861.49 1 1 1 1 0 1 0 1 0 2 0 1 0 1 0 1 0 1 0.0975652 23.4157 6652.03 1 1 1 1 0 1 0 1 0 2 0 1 1 1 0 1 0 1 0.0823734 19.7696 7256.76 1 1 1 1 0 1 0 1 0 2 0 1 1 1 0 1 0 1 0.0823734 19.7696 7256.76 1 1 1 1 0 1 1 0 2 1 1 1 1 1 0 1 0 1 0.0543529 13.0447 8466.2286
1 1 1 1 0 1 1 0 2 1 1 0 1 1 0 1 0 1 0.0671816 16.1236 7861.49 1 1 1 1 0 1 1 0 2 1 1 1 1 1 0 1 0 1 0.0543529 13.0447 8466.22 1 1 1 1 0 1 1 0 1 1 2 1 1 1 1 1 0 1 0.0442251 10.614 9070.95 1 1 1 1 0 1 1 0 1 1 2 1 1 1 1 1 1 1 0.0340972 8.18332 9675.68 1 1 1 1 0 1 1 0 1 1 2 1 1 1 1 1 0 1 0.0442251 10.614 9070.95 1 1 1 1 1 1 1 0 1 2 1 1 1 1 1 1 1 1 0.0259949 6.23877 10280.4 1 1 1 1 1 1 1 0 1 2 1 1 1 1 1 1 1 1 0.0259949 6.23877 10280.4 1 1 1 1 0 1 1 0 1 2 1 1 1 1 1 1 1 1 0.0340972 8.18332 9675.68 0 0 0 1 0 0 0 0 0 2 0 0 0 1 0 0 0 0 0.551969 132.473 1814.19 0 1 0 0 0 1 0 0 0 2 0 0 1 0 0 1 0 0 0.329831 79.1595 3023.65 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0.830824 199.398 1209.46 0 1 0 1 0 1 0 0 0 2 0 0 1 0 0 1 0 0 0.269739 64.7374 3628.38 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0.830824 199.398 1209.46 1 1 0 1 0 1 0 1 0 2 0 1 0 1 0 1 0 1 0.119509 28.6821 6047.3 1 1 0 1 0 1 0 1 0 2 0 1 0 1 0 1 0 1 0.119509 28.6821 6047.3 0 0 0 1 0 0 0 0 0 2 0 0 0 1 0 0 0 0 0.551969 132.473 1814.19 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0.830824 199.398 1209.46 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0.830824 199.398 1209.46 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0.830824 199.398 1209.46 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0.830824 199.398 1209.46 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1.26531 303.674 604.73 1 1 0 1 0 1 0 1 0 2 0 1 0 1 0 1 0 1 0.119509 28.6821 6047.3
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Appendix 5: Original Diagram for Taipower System in Case 2 (Chen, et al., 2006)
Manual Sectionalizing Switch Manual Tie-point Switch
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Appendix 5: Max-Min Algorithm – Matlab Implementation
function MaxMin = DecisionMaking (data)
%Function that returns the final solution from the set of non-dominated
%solutions