A Novel Binary Competitive Swarm Optimizer for Power System Unit Commitment
Abstract
:1. Introduction
- (1)
- To solve the problem of binary switching in the engineering application, a novel binary competitive swarm optimization (BCSO) algorithm has been proposed based the framework of CSO algorithm.
- (2)
- The proposed BCSO algorithm was applied to solve the UC problem with different unit number, which provided a new method for solving large-scale optimization problems.
- (3)
- The feasibility and practicability of the proposed algorithm and the applicability for large-scale, mixed-integer problems was validated, through the comprehensive experimental analysis.
2. Problem Formulation
2.1. Objective Function
2.1.1. Fuel Cost
2.1.2. Start-Up Cost
2.2. Constraints
2.2.1. Power Balance Constraint
2.2.2. Generation Limit Constraint
2.2.3. Minimum Up/Down-Time Limit Constraint
2.2.4. Spinning Reserve Limit Constraint
3. Proposed Binary Competitive Swarm Optimizer
3.1. Competitive Swarm Optimization
3.2. Proposed Binary CSO
4. BCSO Application to UC
4.1. Constraints Processing
4.2. Applied BCSO to UC
4.2.1. Initialization
- Set the parameters of the power system such as the load demand, the fuel cost coefficients of the unit, generation capacity and minimum up/down time, etc.;
- Initialize for the parameters of BCSO such as and maximum iteration time;
- Initialize and boundary check of the particles and their velocity, generate the value of the particle according to Equations (10) and (11), then check the constraints;
4.2.2. BCSO Process
- Divide particles into couples, compute objective function of each particle in couple, determine the loser and winner;
- Update the velocity of the loser according Equation (8) and check the boundary;
- Update the value of the loser according to Equations (10) and (11), and check the constraints to generated the new swarm;
- If the iteration is less than the maximum value of the iteration, go back to the first step of BCSO process. Otherwise, end the process and output the result.
5. Experimental Results and Analysis
5.1. Parameter of BCSO and Data Setting
5.2. The Experimental Results of BCSO
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Unit 1 | Unit 2 | Unit 3 | Unit 4 | Unit 5 | Unit 6 | Unit 7 | Unit 8 | Unit 9 | Unit 10 | |
---|---|---|---|---|---|---|---|---|---|---|
Pmax (MW) | 455 | 455 | 130 | 130 | 162 | 80 | 85 | 55 | 55 | 55 |
Pmin (MW) | 150 | 150 | 20 | 20 | 25 | 20 | 25 | 10 | 10 | 10 |
a ($/MW h) | 1000 | 970 | 700 | 680 | 450 | 370 | 480 | 660 | 665 | 670 |
b ($/MW h) | 16.19 | 17.26 | 16.6 | 16.5 | 19.7 | 22.26 | 27.74 | 25.92 | 27.27 | 27.79 |
c ($/MW h) | 0.00048 | 0.00031 | 0.002 | 0.00211 | 0.00398 | 0.00712 | 0.000793 | 0.00413 | 0.002221 | 0.00173 |
MU (h) | 8 | 8 | 5 | 5 | 6 | 3 | 3 | 1 | 1 | 1 |
MD (h) | 8 | 8 | 5 | 5 | 6 | 3 | 3 | 1 | 1 | 1 |
Hot Start Cost (\$) | 4500 | 5000 | 550 | 560 | 900 | 170 | 260 | 30 | 30 | 30 |
Cold Start Cost (\$) | 9000 | 10,000 | 1100 | 1120 | 1800 | 340 | 520 | 60 | 60 | 60 |
Initial Status (h) | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Methods | Trials | Population | Iteration | Best ($) | Mean ($) | Worst ($) | STDV | Time (s) |
---|---|---|---|---|---|---|---|---|
IBPSO | 10 | 20 | 2000 | 563,777 | 564,155 | 565,312 | 143 | 27 |
IPSO | 50 | 40 | 1000 | 563,954 | 564,162 | 564,579 | - | - |
HPSO | 100 | 20 | 1000 | 563,942.3 | 564,772.3 | 565,785.3 | - | - |
QBPSO | 50 | - | 1000 | 563,977 | 563,977 | 563,977 | 0.00 | 18 |
GA | 20 | 50 | 500 | 565,852 | - | 570,032 | - | 221 |
SA | - | - | 50 | 565,828 | 565,988 | 566,260 | - | 3.35 |
brGA | 30 | - | 1000 | 563,938 | 564,253 | 564,088 | 18 | - |
DBDE | 20 | 40 | 1000 | 563,977 | 564,028 | 564,241 | 103 | 3.6 |
BDE | 50 | 20 | 1000 | 563,977 | 563,977 | 563,977 | 0.00 | - |
BGSO | 50 | 50 | - | 563,938 | 563,952 | 564,226 | - | 3 |
BPSO | 30 | 150 | 200 | 563,955.99 | 564,000.40 | 564,053.73 | 21.63 | 25.45 |
BLPSO | 30 | 150 | 200 | 563,977.01 | 563,982.09 | 563,987.16 | - | 22.09 |
NBPSO | 30 | 150 | 200 | 563,937.68 | 563,962.59 | 563,977.01 | - | 21.91 |
BCSO | 30 | 150 | 200 | 563,937.68 | 563,937.68 | 563,937.68 | 0.00 | 11.58 |
Units | Best ($) | Mean ($) | Worst ($) | Time (s) |
---|---|---|---|---|
10 | 563,937.68 | 563,937.68 | 563,937.68 | 11.58 |
20 | 1,124,389.73 | 1,124,477.52 | 1,124,524.29 | 20.15 |
40 | 2,246,837.71 | 2,247,351.83 | 2,247,675.59 | 35.02 |
60 | 3,367,348.99 | 3,367,466.61 | 3,367,535.33 | 49.45 |
80 | 4,491,212.46 | 4,491,574.93 | 4,491,717.60 | 66.91 |
100 | 5,610,281.71 | 5,610,624.74 | 5,610,986.92 | 85.01 |
Units | Methods | Best ($) | Mean ($) | Worst ($) | Time (s) |
---|---|---|---|---|---|
10 | BCSO | 563,937.68 | 563,937.68 | 563,937.68 | 12.51 |
BPSO | 563,955.99 | 564,000.40 | 564,053.73 | 21.56 | |
BLPSO | 563,777.01 | 563,982.09 | 563,987.16 | 21.01 | |
NBPSO | 563,937.68 | 563,962.59 | 563,977.01 | 21.05 | |
20 | BCSO | 1,124,389.73 | 1,124,477.52 | 1,124,524.29 | 20.15 |
BPSO | 1,127,588.66 | 1,129,897.11 | 1,131,708.18 | 32.32 | |
BLPSO | 1,126,027.27 | 1,126,195.45 | 1,126,748.06 | 31.32 | |
NBPSO | 1,128,147.58 | 1,128,157.00 | 1,128,218.22 | 33.28 | |
40 | BCSO | 2,246,837.71 | 2,247,351.83 | 2,247,675.59 | 35.02 |
BPSO | 2,260,669.13 | 2,267,206.95 | 2,273,667.73 | 51.77 | |
BLPSO | 2,254,213.53 | 2,254,289.66 | 2,254,967.89 | 51.72 | |
NBPSO | 2,261,696.75 | 2,261,696.75 | 2,261,696.75 | 53.17 | |
60 | BCSO | 3,367,348.99 | 3,367,466.61 | 3,367,535.33 | 49.45 |
BPSO | 387,761.20 | 3,395,743.16 | 3,404,382.46 | 69.09 | |
BLPSO | 3,384,093.39 | 3,393,103.18 | 3,395,468.84 | 66.68 | |
NBPSO | 3,395,480.43 | 3,395,480.43 | 3,395,480.43 | 69.39 | |
80 | BCSO | 4,491,212.46 | 4,491,574.93 | 4,491,717.60 | 66.91 |
BPSO | 4,524,683.47 | 4,538,115.06 | 4,547,525.84 | 103.94 | |
BLPSO | 4,513,521.52 | 4,520,667.44 | 4,522,452.92 | 98.97 | |
NBPSO | 4,530,843.70 | 4,530,843.70 | 4,530,843.70 | 101.33 | |
100 | BCSO | 5,610,281.71 | 5,610,624.74 | 5,610,986.92 | 85.01 |
BPSO | 566,545.61 | 5,482,671.50 | 5,692,414.71 | 112.45 | |
BLPSO | 5,655,610.14 | 5,655,610.14 | 5,655,610.14 | 113.54 | |
NBPSO | 5,648,702.49 | 5,648,702.49 | 5,648,702.49 | 121.56 |
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Wang, Y.; Yang, Z.; Guo, Y.; Zhou, B.; Zhu, X. A Novel Binary Competitive Swarm Optimizer for Power System Unit Commitment. Appl. Sci. 2019, 9, 1776. https://doi.org/10.3390/app9091776
Wang Y, Yang Z, Guo Y, Zhou B, Zhu X. A Novel Binary Competitive Swarm Optimizer for Power System Unit Commitment. Applied Sciences. 2019; 9(9):1776. https://doi.org/10.3390/app9091776
Chicago/Turabian StyleWang, Ying, Zhile Yang, Yuanjun Guo, Bowen Zhou, and Xiaodong Zhu. 2019. "A Novel Binary Competitive Swarm Optimizer for Power System Unit Commitment" Applied Sciences 9, no. 9: 1776. https://doi.org/10.3390/app9091776