An Improved, Negatively Correlated Search for Solving the Unit Commitment Problem’s Integration with Electric Vehicles
Abstract
:1. Introduction
2. Problem Formulation
2.1. Basic Unit Commitment
2.1.1. Objective Function
Fuel cost
Start-up cost
2.1.2. Constraints
Power balance constraint
Generation limit
Minimum up and minimum down time constraint
Ramp rates constraint
Spinning reserve constraint
2.2. Unit Commitment Integrated with EV
2.2.1. Constraints of UC Combined with EVs
Power Balance Constraint
Spinning reserve constraint
2.2.2. Different Charging Models
Off-peak charging mode (OPCM)
Peak charging mode (PCM)
Electric Power Research Institute Charging Mode (EPRICM)
Stochastic charging mode (SCM)
3. Negatively Correlated Search
3.1. Negatively Correlated Search
3.2. Global Best Inspired Binary Negatively Correlated Search
3.3. The Proposed Algorithm for UC Problem
- Step 1
- Initialize the parameters including the step size , , , r, (total number of cost function evaluations), and population size.
- Step 2
- Randomly generate a population consisting binary variables (0, 1) representing the on/off status of units.
- Step 3
- Handle the minimum up/down time and spinning reserve constraints by adjusting the population.
- Step 4
- Solve the economic load dispatch (ELD) sup-problem, where a lambda iteration method is used to solve this problem [36].
- Step 5
- Calculate the objective function using Equation (3).
- Step 6
- While stopping criterion is not met,
- Step 6.1
- Step 6.2
- Handle the minimum up/down time and spinning reserve constraints by adjusting the population.
- Step 6.3
- Solve the economic load dispatch (ELD) sub-problem, where a lambda iteration method is used to solve this problem.
- Step 6.4
- Calculate the objective function of the new population.
- Step 6.5
- Calculate the Hamming distance between each solution and the best solution.
- Step 6.6
- Select the solution with better quality using Equation (18).
- Step 7
- End while.
4. Experimental Results
4.1. Knapsack Problem
4.2. Basic UC
4.3. UC with EVs
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Time Period | Charging Probability | |||||
---|---|---|---|---|---|---|
01:00–06:00 | 18.5% | 18.5% | 9% | 9% | 4% | 4% |
07:00–12:00 | 0% | 0% | 0% | 0% | 0% | 0% |
13:00–18:00 | 0% | 0% | 0% | 0% | 0% | 0% |
19:00–24:00 | 0% | 0% | 0% | 0% | 18.5% | 18.5% |
Time Period | Charging Probability | |||||
---|---|---|---|---|---|---|
01:00–06:00 | 0% | 0% | 0% | 0% | 0% | 0% |
07:00–12:00 | 0% | 0% | 0% | 0% | 9% | 9% |
13:00–18:00 | 18.5% | 18.5% | 18.5% | 18.5% | 0% | 0% |
19:00–24:00 | 4% | 4% | 0% | 0% | 0% | 0% |
Time Period | Charging Probability | |||||
---|---|---|---|---|---|---|
01:00–06:00 | 10% | 10% | 9.5% | 7% | 5% | 3% |
07:00–12:00 | 1% | 0.3% | 0.3% | 1.3% | 2% | 2% |
13:00–18:00 | 2% | 2% | 2% | 1% | 0.3% | 0.3% |
19:00–24:00 | 1.5% | 3% | 5% | 9.5% | 10% | 10% |
Time Period | Charging Probability (Scenario1) | |||||
---|---|---|---|---|---|---|
01:00–06:00 | 5.70% | 4.90% | 4.80% | 2.40% | 2.60% | 9.70% |
07:00–12:00 | 8.70% | 4.80% | 1.10% | 3.20% | 2.10% | 5.70% |
13:00–18:00 | 3.80% | 2.20% | 2.10% | 6.10% | 3.20% | 2.20% |
19:00–24:00 | 2.80% | 2.20% | 5.50% | 2.50% | 3.50% | 8.20% |
Time period | Charging probability (scenario2) | |||||
01:00–06:00 | 9.98% | 5.81% | 6.92% | 2.04% | 3.22% | 3.62% |
07:00–12:00 | 6.36% | 3.60% | 5.56% | 0.06% | 3.45% | 2.51% |
13:00–18:00 | 1.01% | 5.18% | 4.72% | 4.23% | 1.49% | 6.41% |
19:00–24:00 | 4.86% | 3.56% | 4.21% | 3.64% | 3.97% | 3.59% |
Time period | Charging probability (scenario3) | |||||
01:00–06:00 | 3.40% | 3.96% | 6.53% | 2.78% | 5.42% | 4.65% |
07:00–12:00 | 3.79% | 2.47% | 3.71% | 4.02% | 2.84% | 4.47% |
13:00–18:00 | 2.84% | 4.01% | 4.70% | 2.71% | 3.70% | 4.72% |
19:00–24:00 | 1.22% | 5.82% | 8.04% | 5.07% | 3.65% | 4.85% |
Time period | Charging probability (scenario4) | |||||
01:00–06:00 | 3.10% | 4.58% | 2.47% | 5.82% | 3.07% | 8.16% |
07:00–12:00 | 2.32% | 4.51% | 1.57% | 2.91% | 3.15% | 4.84% |
13:00–18:00 | 5.76% | 4.67% | 3.53% | 5.55% | 5.52% | 4.36% |
19:00–24:00 | 5.13% | 4.86% | 2.48% | 5.45% | 3.04% | 3.13% |
Time period | Charging probability (scenario5) | |||||
01:00–06:00 | 4.35% | 4.91% | 4.33% | 8.90% | 2.18% | 1.01% |
07:00–12:00 | 2.22% | 2.30% | 3.42% | 3.87% | 3.79% | 5.08% |
13:00–18:00 | 4.82% | 5.44% | 7.18% | 6.24% | 1.98% | 0.77% |
19:00–24:00 | 5.69% | 1.04% | 4.27% | 4.22% | 7.95% | 4.04% |
Parameters | U1 | U2 | U3 | U4 | U5 | U6 | U7 | U8 | U9 | U10 |
---|---|---|---|---|---|---|---|---|---|---|
455 | 455 | 130 | 130 | 162 | 80 | 85 | 55 | 55 | 55 | |
150 | 150 | 20 | 20 | 25 | 20 | 25 | 10 | 10 | 10 | |
1000 | 970 | 700 | 680 | 450 | 370 | 480 | 660 | 665 | 670 | |
16.19 | 17.26 | 16.6 | 16.5 | 19.7 | 22.26 | 27.74 | 25.92 | 27.27 | 27.79 | |
0.00048 | 0.00031 | 0.002 | 0.00211 | 0.00398 | 0.00712 | 0.00079 | 0.00413 | 0.00222 | 0.00173 | |
8 | 8 | 5 | 5 | 6 | 3 | 3 | 1 | 1 | 1 | |
8 | 8 | 5 | 5 | 6 | 3 | 3 | 1 | 1 | 1 | |
4500 | 5000 | 550 | 560 | 900 | 260 | 260 | 30 | 30 | 30 | |
9000 | 10000 | 1100 | 1120 | 1800 | 520 | 520 | 60 | 60 | 60 | |
5 | 5 | 4 | 4 | 4 | 2 | 2 | 0 | 0 | 0 | |
8 | 8 | −5 | −5 | −6 | −3 | −3 | −1 | −1 | −1 |
dim | opt.value | BNCS | GBNCS | |||||
---|---|---|---|---|---|---|---|---|
Best | Mean | Best Times | Best | Mean | Best Times | |||
F1 | 10 | 295 | 295 | 286.8 | 9 | 295 | 295 | 30 |
F2 | 20 | 1024 | 1016 | 988 | 0 | 1024 | 1024 | 30 |
F3 | 4 | 35 | 35 | 35 | 30 | 35 | 35 | 30 |
F4 | 4 | 23 | 23 | 23 | 30 | 23 | 23 | 30 |
F5 | 15 | 481.0694 | 481.0694 | 425.9331 | 4 | 481.0694 | 481.0694 | 30 |
F6 | 10 | 50 | 52 | 51.6 | 21 | 50 | 50 | 30 |
F7 | 7 | 107 | 107 | 103.6 | 27 | 107 | 107 | 30 |
F8 | 23 | 9767 | 9752 | 9733.4 | 0 | 9767 | 9763.1 | 6 |
F9 | 5 | 130 | 130 | 130 | 30 | 130 | 130 | 30 |
F10 | 20 | 1025 | 1025 | 991.9 | 3 | 1025 | 1025 | 30 |
Hour | |||||||
---|---|---|---|---|---|---|---|
1 | 700 | 7 | 700 | 13 | 1400 | 19 | 1200 |
2 | 750 | 8 | 1150 | 14 | 1300 | 20 | 1400 |
3 | 850 | 9 | 1200 | 15 | 1200 | 21 | 1300 |
4 | 950 | 10 | 1300 | 16 | 1050 | 22 | 1100 |
5 | 1000 | 11 | 1400 | 17 | 1000 | 23 | 900 |
6 | 1100 | 12 | 1500 | 18 | 1100 | 24 | 800 |
Method | Best | Worst | Mean | std |
---|---|---|---|---|
DP [15] | 565825 | - | - | - |
LR [15] | 565825 | - | - | - |
GA [15] | 565,825 | 507,732 | 570,032 | - |
EP [39] | 564,551 | 566,231 | 565,325 | - |
SA [18] | 565,825 | 566,260 | 565,988 | - |
IPSO [39] | 563,954 | 564,579 | 564,162 | - |
BPSO [40] | 563,977 | 563,977 | 563,977 | - |
QPSO [41] | 563,977 | 563,977 | 563,977 | - |
IQEA [42] | 563,977 | 563,977 | 563,977 | - |
EQA-UC [43] | 563,937 | 564,012 | 564,711 | - |
BDE [44] | 563,937 | 564,253 | 564,088 | - |
brGA [45] | 563,937 | - | - | - |
HAS [46] | 563,977 | - | 564,168 | - |
HHS [47] | 563,937 | 563,995 | 563,965 | - |
BGSA [36] | 563,937 | 564,241 | 564,031 | - |
BSPSO1 [48] | 563,977 | 564,018 | 563,980 | 0.002 |
BSPSO2 [48] | 563,937 | 563,977 | 563,976 | 0.001 |
BSPSO3 [48] | 563,937 | 563,977 | 563,973 | 0.002 |
BSPSO4 [48] | 563,937 | 563,977 | 563,964 | 0.003 |
BSPSO5 [48] | 563,937 | 563,977 | 563,960 | 0.003 |
BNCS | 563,937 | 563,977 | 563,941 | 8.455 |
GBNCS | 563,937 | 563,937 | 563,937 | 0 |
Item | Value |
---|---|
Average battery capacity of an electric vehicle | 0.015 |
Maximum battery capacity of an electric vehicle | 0.025 |
Minimum battery capacity of an electric vehicle | 0.010 |
Departure state of charge | 50% |
Charging efficiency | 85% |
OFF-PEAK | PEAK | EPRI | stochastic | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Best | Mean | Worst | Best | Mean | Worst | Best | Mean | Worst | Best | Mean | Worst | |
GAH [50] | 577,405 | 579,632 | - | - | - | - | - | - | - | 578,884 | 580,254 | - |
577,932 | 580,082 | - | ||||||||||
578,564 | 581,332 | - | ||||||||||
580,087 | 582,258 | - | ||||||||||
580,028 | 583,821 | - | ||||||||||
GAD [50] | 571,085 | 572,577 | - | - | - | - | - | - | - | 572,403 | 573,400 | - |
572,435 | 573,184 | - | ||||||||||
573,364 | 574,439 | - | ||||||||||
573,543 | 574,738 | - | ||||||||||
574,663 | 576,152 | - | ||||||||||
BNCS | 568,372 | 568,373 | 568,374 | 568,894 | 569,120 | 569,210 | 568,201 | 568,202 | 568,210 | 568,086 | 568,102 | 568,155 |
568,281 | 568,283 | 568,284 | ||||||||||
568,460 | 568,764 | 569,032 | ||||||||||
569,581 | 569,811 | 569,862 | ||||||||||
569,648 | 569,755 | 569,834 | ||||||||||
GBNCS | 568,370 | 568,371 | 568,374 | 568,894 | 569,032 | 569,180 | 568,199 | 568,202 | 568,203 | 568,085 | 568,099 | 568,146 |
568,279 | 568,282 | 568,283 | ||||||||||
568,440 | 568,772 | 568,960 | ||||||||||
569,562 | 569,806 | 569,862 | ||||||||||
569,627 | 569,738 | 569,820 |
Hour | U1 | U2 | U3 | U4 | U5 | U6 | U7 | U8 | U9 | U10 |
---|---|---|---|---|---|---|---|---|---|---|
1 | 455 | 245 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 455 | 295 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
3 | 455 | 370 | 0 | 0 | 25 | 0 | 0 | 0 | 0 | 0 |
4 | 455 | 455 | 0 | 0 | 40 | 0 | 0 | 0 | 0 | 0 |
5 | 455 | 390 | 130 | 0 | 25 | 0 | 0 | 0 | 0 | 0 |
6 | 455 | 360 | 130 | 130 | 25 | 0 | 0 | 0 | 0 | 0 |
7 | 455 | 410 | 130 | 130 | 25 | 0 | 0 | 0 | 0 | 0 |
8 | 455 | 455 | 130 | 130 | 30 | 0 | 0 | 0 | 0 | 0 |
9 | 455 | 455 | 130 | 130 | 85 | 20 | 25 | 0 | 0 | 0 |
10 | 455 | 455 | 130 | 130 | 162 | 33 | 25 | 10 | 0 | 0 |
11 | 455 | 455 | 130 | 130 | 162 | 73 | 25 | 10 | 0 | 10 |
12 | 455 | 455 | 130 | 130 | 162 | 80 | 25 | 43 | 10 | 10 |
13 | 455 | 455 | 130 | 130 | 162 | 58 | 25 | 10 | 10 | 0 |
14 | 455 | 455 | 130 | 130 | 120 | 20 | 25 | 0 | 0 | 0 |
15 | 455 | 455 | 130 | 130 | 45 | 20 | 0 | 0 | 0 | 0 |
16 | 455 | 345 | 130 | 130 | 25 | 0 | 0 | 0 | 0 | 0 |
17 | 455 | 277 | 130 | 130 | 25 | 0 | 0 | 0 | 0 | 0 |
18 | 455 | 377 | 130 | 130 | 25 | 0 | 0 | 0 | 0 | 0 |
19 | 455 | 443 | 130 | 130 | 25 | 0 | 25 | 0 | 0 | 0 |
20 | 455 | 455 | 130 | 130 | 162 | 31 | 25 | 10 | 10 | 0 |
21 | 455 | 455 | 130 | 130 | 85 | 20 | 25 | 0 | 0 | 0 |
22 | 455 | 455 | 130 | 0 | 40 | 20 | 0 | 0 | 0 | 0 |
23 | 455 | 450 | 0 | 0 | 25 | 0 | 0 | 0 | 0 | 0 |
24 | 455 | 345 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Hour | U1 | U2 | U3 | U4 | U5 | U6 | U7 | U8 | U9 | U10 |
---|---|---|---|---|---|---|---|---|---|---|
1 | 455 | 280 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 455 | 330 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
3 | 455 | 387 | 0 | 0 | 25 | 0 | 0 | 0 | 0 | 0 |
4 | 455 | 357 | 130 | 0 | 25 | 0 | 0 | 0 | 0 | 0 |
5 | 455 | 397 | 130 | 0 | 25 | 0 | 0 | 0 | 0 | 0 |
6 | 455 | 367 | 130 | 130 | 25 | 0 | 0 | 0 | 0 | 0 |
7 | 455 | 410 | 130 | 130 | 25 | 0 | 0 | 0 | 0 | 0 |
8 | 455 | 455 | 130 | 130 | 30 | 0 | 0 | 0 | 0 | 0 |
9 | 455 | 455 | 130 | 130 | 85 | 20 | 25 | 0 | 0 | 0 |
10 | 455 | 455 | 130 | 130 | 162 | 33 | 25 | 10 | 0 | 0 |
11 | 455 | 455 | 130 | 130 | 162 | 73 | 25 | 10 | 10 | 0 |
12 | 455 | 455 | 130 | 130 | 162 | 80 | 25 | 43 | 10 | 10 |
13 | 455 | 455 | 130 | 130 | 162 | 33 | 25 | 10 | 0 | 0 |
14 | 455 | 455 | 130 | 130 | 85 | 20 | 25 | 0 | 0 | 0 |
15 | 455 | 455 | 130 | 130 | 30 | 0 | 0 | 0 | 0 | 0 |
16 | 455 | 310 | 130 | 130 | 25 | 0 | 0 | 0 | 0 | 0 |
17 | 455 | 260 | 130 | 130 | 25 | 0 | 0 | 0 | 0 | 0 |
18 | 455 | 340 | 130 | 130 | 25 | 20 | 0 | 0 | 0 | 0 |
19 | 455 | 440 | 130 | 130 | 25 | 20 | 0 | 0 | 0 | 0 |
20 | 455 | 455 | 130 | 130 | 162 | 33 | 25 | 10 | 0 | 0 |
21 | 455 | 455 | 130 | 130 | 85 | 20 | 25 | 0 | 0 | 0 |
22 | 455 | 455 | 130 | 0 | 35 | 0 | 25 | 0 | 0 | 0 |
23 | 455 | 455 | 0 | 0 | 25 | 0 | 0 | 0 | 0 | 0 |
24 | 455 | 355 | 0 | 0 | 25 | 0 | 0 | 0 | 0 | 0 |
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Niu, Q.; Jiang, K.; Yang, Z. An Improved, Negatively Correlated Search for Solving the Unit Commitment Problem’s Integration with Electric Vehicles. Sustainability 2019, 11, 6945. https://doi.org/10.3390/su11246945
Niu Q, Jiang K, Yang Z. An Improved, Negatively Correlated Search for Solving the Unit Commitment Problem’s Integration with Electric Vehicles. Sustainability. 2019; 11(24):6945. https://doi.org/10.3390/su11246945
Chicago/Turabian StyleNiu, Qun, Kecheng Jiang, and Zhile Yang. 2019. "An Improved, Negatively Correlated Search for Solving the Unit Commitment Problem’s Integration with Electric Vehicles" Sustainability 11, no. 24: 6945. https://doi.org/10.3390/su11246945