A Scatter Search Heuristic for the Optimal Location, Sizing and Contract Pricing of Distributed Generation in Electric Distribution Systems
Abstract
:1. Introduction
2. Mathematical Model
2.1. Decision-Making Problem of the Distribution Company
2.2. Decision-Making Problem of the Distributed Generation Owner
2.3. Bilevel Modeling Framework
2.4. Upper Level Optimization Problem
2.5. Lower Level Optimization Problem
2.6. Illustrative Example
3. Solution Approach
3.1. Scatter Search General Structure
Algorithm 1. Scatter search for DG optimization | |
1 | |
2 | While do |
3 | |
4 | If then |
5 | |
6 | End-if |
7 | End-While |
8 | Evaluate the solutions in and sort them by non-increasing profit (Equation (1)) |
9 | Build with the best solutions of , |
10 | Add to the most diverse solutions in with respect to those already in |
11 | Sort by non-increasing profit (Equation (1)) |
12 | |
13 | While (new) do |
14 | |
15 | For all do |
16 | If ( has not been combined before) then |
17 | |
18 | |
19 | |
20 | End-if |
21 | End-For all |
22 | End-While |
23 | Return |
3.2. Scatter Search Components
3.2.1. Solution Representation and Objective Function Evaluation
3.2.2. Distance Measure
3.2.3. Diversification Generator Method
3.2.4. Solution Combination Method
3.2.5. Improvement Method
3.2.6. Reference Set Update Method
4. Tests and Results
4.1. Diversification Generator Method Comparison
4.2. Comparison against Other Metaheuristics
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A
Bus | P (MW) | Q (Mvar) | Bus | P (MW) | Q (Mvar) |
---|---|---|---|---|---|
1 | 0 | 0 | 18 | 0 | 0 |
2 | 0.1555 | 0.0820 | 19 | 0.0113 | 0.0057 |
3 | 0.1555 | 0.0820 | 20 | 0.0424 | 0.0198 |
4 | 0.0452 | 0.0226 | 21 | 0 | 0 |
5 | 0.0452 | 0.0226 | 22 | 0.1385 | 0.0707 |
6 | 0 | 0 | 23 | 2.5438 | 1.2719 |
7 | 0 | 0 | 24 | 0.5031 | 0.2544 |
8 | 0 | 0 | 25 | 0.0057 | 0.0028 |
9 | 0.0141 | 0.0057 | 26 | 0.9836 | 0.5992 |
10 | 0.0961 | 0.0480 | 27 | 0.0254 | 0.0141 |
11 | 0.1385 | 0.0678 | 28 | 0.3448 | 0.1781 |
12 | 0.4777 | 0.2459 | 29 | 2.4421 | 1.8598 |
13 | 0.0311 | 0.0141 | 30 | 0.0791 | 0.0396 |
14 | 0.1131 | 0.0565 | 31 | 0.2657 | 0.1752 |
15 | 0.3816 | 0.1979 | 32 | 0.1922 | 0.0961 |
16 | 0.2742 | 0.1215 | 33 | 0.0791 | 0.0396 |
17 | 0.0113 | 0.0057 | 34 | 0.4042 | 0.3024 |
Line | R (Ω) | X (Ω) | Line | R (Ω) | X (Ω) |
---|---|---|---|---|---|
1–2 | 0.0026 | 0.0025 | 17–18 | 0.0078 | 0.0064 |
2–3 | 0.0018 | 0.0013 | 18–20 | 0.0004 | 0.0003 |
3–4 | 0.0170 | 0.0138 | 20–21 | 0.0053 | 0.0038 |
4–5 | 0.0004 | 0.0003 | 20–22 | 0.0071 | 0.0071 |
4–6 | 0.0036 | 0.0033 | 21–23 | 0.0007 | 0.0004 |
6–7 | 0.0010 | 0.0009 | 22–25 | 0.0004 | 0.0003 |
7–8 | 0.0076 | 0.0057 | 22–24 | 0.0007 | 0.0005 |
8–9 | 0.0003 | 0.0003 | 24–26 | 0.0105 | 0.0065 |
9–10 | 0.0105 | 0.0074 | 24–27 | 0.0037 | 0.0037 |
9–11 | 0.0190 | 0.0172 | 26–28 | 0.0004 | 0.0003 |
10–12 | 0.0086 | 0.0065 | 28–30 | 0.0005 | 0.0004 |
12–15 | 0.0095 | 0.0065 | 30–33 | 0.0037 | 0.0034 |
11–14 | 0.0037 | 0.0037 | 28–31 | 0.0070 | 0.0052 |
11–13 | 0.0077 | 0.0064 | 27–29 | 0.0014 | 0.0013 |
13–16 | 0.0017 | 0.0011 | 29–32 | 0.0038 | 0.0035 |
16–17 | 0.0038 | 0.0037 | 32–34 | 0.0047 | 0.0034 |
17–19 | 0.0103 | 0.0103 | - | - | - |
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SS Variant | DG Owner Profit | Average Running Time (s) | Best Profit | ||
---|---|---|---|---|---|
Solution 1 | Solution 2 | Solution 3 | |||
SS-Sist | 165,036 | 165,036 | 165,036 | 422 | 165,036 |
SS-Rand | 165,952 | 166,303 | 166,731 | 407 | 166,731 |
SS-SistRand | 165,339 | 165,484 | 165,119 | 607 | 165,484 |
SS Variant | DG Unit (Bus, Price($/MWh), Size (MW)) | DG Owner Profit | ||
---|---|---|---|---|
1 | 2 | 3 | ||
SS-Sist | (24, 77.0, 1.5) | (29, 77.0, 1.5) | (30, 77.0, 1.5) | 165,036 |
SS-Rand | (27, 77.0, 1.5) | (29, 77.0, 1.5) | (30, 77.0, 1.5) | 166,731 |
SS-SistRand | (24, 77.0, 1.5) | (27, 77.0, 1.5) | (31, 77.0, 1.5) | 165,484 |
Method | DG Owner Profit | Average Running Time (s) | Best Profit | ||
---|---|---|---|---|---|
Solution 1 | Solution 2 | Solution 3 | |||
SS-Rand | 165,952 | 166,303 | 166,731 | 407 | 166,731 |
SS-Sist | 165,036 | 165,036 | 165,036 | 422 | 165,036 |
MA | 156,128 | 157,601 | 155,423 | 302,400 | 157,601 |
GA | 25,100 | 21,500 | 35,000 | 1200 | 35,000 |
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Pérez Posada, A.F.; Villegas, J.G.; López-Lezama, J.M. A Scatter Search Heuristic for the Optimal Location, Sizing and Contract Pricing of Distributed Generation in Electric Distribution Systems. Energies 2017, 10, 1449. https://doi.org/10.3390/en10101449
Pérez Posada AF, Villegas JG, López-Lezama JM. A Scatter Search Heuristic for the Optimal Location, Sizing and Contract Pricing of Distributed Generation in Electric Distribution Systems. Energies. 2017; 10(10):1449. https://doi.org/10.3390/en10101449
Chicago/Turabian StylePérez Posada, Andrés Felipe, Juan G. Villegas, and Jesús M. López-Lezama. 2017. "A Scatter Search Heuristic for the Optimal Location, Sizing and Contract Pricing of Distributed Generation in Electric Distribution Systems" Energies 10, no. 10: 1449. https://doi.org/10.3390/en10101449