Introduction
Problem statement
Objective functions
Total operation cost of DGs
Emission cost objective function
Constraints
Load balance
DGs’ ramp rate constraints
Generating unit limits
Charging and discharging of the storage device
Main concepts of krill herd and ant lion algorithms
Krill herd optimization algorithm
Ant lion optimizer
Simulation results and analysis
Generating unit | Bid (€ct/kWh) | Start-up/shut-down (€ct) | CO2 (kg/MWh) | SO2 (kg/MWh) | NOx (kg/MWh) | Minimum power (kW) | Maximum power (kW) |
---|---|---|---|---|---|---|---|
PV | 2.584 | 0 | 0 | 0 | 0 | 0 | 25 |
WT | 1.073 | 0 | 0 | 0 | 0 | 0 | 15 |
MT | 0.457 | 0.96 | 720 | 0.0036 | 0.1 | 6 | 30 |
FC | 0.294 | 1.65 | 460 | 0.003 | 0.0075 | 3 | 30 |
Battery | 0.38 | 0 | 10 | 0.0002 | 0.001 | − 30 | 30 |
Grid | Figure 5 | 0 | 0 | 0 | 0 | − 30 | 30 |
Operation of DGs with specified limits (first scenario)
Hour | Pd (kW) | Ppv (kW) | Pwt (kW) | PMt (kW) | PFC (kW) | PBatt (kW) | Pgrid (kW) |
---|---|---|---|---|---|---|---|
1 | 52 | 0 | 0.01 | 12.96 | 25.24 | − 4.94 | 18.73 |
2 | 50 | 0 | 0.005 | 17.18 | 21.72 | 11.44 | − 0.36 |
3 | 50 | 0 | 0.002 | 10.00 | 25.36 | 0.624 | 14.01 |
4 | 51 | 0 | 0.005 | 8.03 | 19.88 | − 0.52 | 23.60 |
5 | 56 | 0 | 0.001 | 19.08 | 21.15 | 6.34 | 9.43 |
6 | 63 | 0 | 0.001 | 11.99 | 28.69 | 3.27 | 19.04 |
7 | 70 | 0 | 0.02 | 23.24 | 29.04 | 7.85 | 9.84 |
8 | 75 | 0.0003 | 0.004 | 18.99 | 25.74 | 12.27 | 17.99 |
9 | 76 | 0.007 | 1.12 | 21.23 | 29.99 | 15.77 | 7.88 |
10 | 80 | 7.52 | 3.09 | 29.99 | 30.00 | 29.99 | − 20.61 |
11 | 78 | 9.23 | 8.77 | 30.00 | 30.00 | 30.00 | − 30.00 |
12 | 74 | 3.59 | 10.41 | 30.00 | 29.99 | 30.00 | − 30.00 |
13 | 72 | 0.0004 | 0.93 | 29.98 | 27.43 | 24.10 | − 10.45 |
14 | 72 | 9.63 | 2.37 | 29.99 | 30.00 | 30.00 | − 29.99 |
15 | 76 | 0.0001 | 1.78 | 30.00 | 29.99 | 29.99 | − 15.79 |
16 | 80 | 0.0005 | 0.67 | 27.37 | 29.78 | 29.03 | − 6.85 |
17 | 85 | 2.2e–05 | 0.005 | 19.93 | 29.70 | 20.03 | 15.33 |
18 | 88 | 0 | 0.01 | 21.27 | 29.48 | 12.99 | 24.25 |
19 | 90 | 0 | 0.01 | 20.89 | 24.69 | 22.47 | 21.93 |
20 | 87 | 0 | 0.001 | 24.12 | 29.62 | 6.063 | 27.19 |
21 | 78 | 0 | 0.03 | 22.97 | 29.99 | 23.23 | 1.78 |
22 | 71 | 0 | 0.005 | 22.01 | 28.51 | 25.06 | − 4.58 |
23 | 52 | 0 | 0.017 | 17.54 | 22.24 | 8.17 | 17.03 |
24 | 50 | 0 | 0.008 | 21.87 | 20.10 | 4.97 | 9.05 |
Algorithm | Average (€ct) | Standard deviation (€ct) | Worst (€ct) | Best (€ct) | Computational time (s) |
---|---|---|---|---|---|
FSAPSO [4] | 125.91 | 0.006 | 125.92 | 125.91 | NA |
GA | 151.89 | 36.23 | 210.46 | 125.91 | 114.67 |
GWO | 151.57 | 40.20 | 824.30 | 128.93 | 132.17 |
PSO | 145.28 | 53.52 | 830.83 | 126.16 | 556.64 |
WOA | 129.05 | 8.99 | 307.55 | 126.09 | 149.17 |
KH | 148.57 | 0.009 | 1337.7 | 105.94 | 104.17 |
Algorithm | Average (Kg) | Standard deviation (Kg) | Worst (Kg) | Best (Kg) | Computational time (s) |
---|---|---|---|---|---|
FSAPSO | 422.02 | 0.005 | 422.03 | 422.02 | NA |
GA | 506.78 | 89.25 | 680.33 | 422.02 | 119.85 |
GWO | 580.88 | 300.97 | 2699.2 | 451.54 | 167.44 |
PSO | 500.44 | 216.42 | 2943.4 | 425.43 | 523.87 |
WOA | 428.79 | 68.54 | 2135.3 | 423.25 | 124.92 |
KH | 436.59 | 0.004 | 118.97 | 420.57 | 79.41 |
Hour | P (kW) | Ppv (kW) | Pwt (kW) | PMt (kW) | PFC (kW) | PBatt (kW) | Pgrid (kW) |
---|---|---|---|---|---|---|---|
1 | 52 | 0 | 0.88 | 15.09 | 27.09 | 27.42 | − 18.49 |
2 | 50 | 0 | 0.08 | 6.84 | 4.65 | 13.45 | 24.99 |
3 | 50 | 0 | 1.69 | 17.09 | 25.63 | 6.64 | − 1.07 |
4 | 51 | 0 | 0.05 | 7.19 | 4.38 | 28.81 | 10.57 |
5 | 56 | 0 | 0.89 | 29.06 | 28.46 | 27.57 | − 29.98 |
6 | 63 | 0 | 0.92 | 19.68 | 30.00 | 3.54 | 8.86 |
7 | 70 | 0 | 1.00 | 6.00 | 18.47 | 26.72 | 17.81 |
8 | 75 | 0.20 | 1.31 | 29.99 | 29.99 | 17.45 | − 3.95 |
9 | 76 | 3.75 | 1.79 | 30.00 | 30.00 | 30.00 | − 19.54 |
10 | 80 | 6.32 | 3.09 | 30.00 | 30.00 | 30.00 | − 19.41 |
11 | 78 | 10.14 | 8.76 | 29.99 | 29.99 | 29.12 | − 29.99 |
12 | 74 | 11.43 | 10.27 | 29.03 | 30.00 | 23.27 | − 30.00 |
13 | 72 | 7.50 | 3.92 | 30.00 | 30.00 | 7.02 | − 6.44 |
14 | 72 | 20.28 | 2.22 | 28.47 | 27.74 | 23.00 | − 29.70 |
15 | 76 | 7.88 | 1.79 | 30.00 | 30.00 | 30.00 | − 23.66 |
16 | 80 | 2.75 | 1.31 | 30.00 | 30.00 | 29.99 | − 14.05 |
17 | 85 | 0.22 | 1.79 | 30.00 | 30.00 | 29.99 | − 7.00 |
18 | 88 | 0 | 0.54 | 17.34 | 29.99 | 29.88 | 10.24 |
19 | 90 | 0 | 0.36 | 30.00 | 30.00 | 29.92 | − 0.27 |
20 | 87 | 0 | 1.79 | 29.99 | 30.00 | 29.99 | − 4.78 |
21 | 78 | 0 | 0.56 | 30.00 | 30.00 | 30.00 | − 12.56 |
22 | 71 | 0 | 1.30 | 25.11 | 30.00 | 28.47 | − 13.88 |
23 | 65 | 0 | 0.92 | 30.00 | 30.00 | − 23.61 | 27.69 |
24 | 56 | 0 | 0.61 | 29.78 | 29.77 | − 8.38 | 4.22 |
Operation of PV and WT at maximum limits (second scenario)
Algorithm | Average (€ct) | Standard deviation (€ct) | Worst (€ct) | Best (€ct) | Computational time (s) |
---|---|---|---|---|---|
FSAPSO [4] | 599.99 | 0.007 | 600.00 | 599.99 | NA |
GA | 632.72 | 45.37 | 664.8 | 600.64 | 83.14 |
GWO | 317.20 | 658.54 | 8337.5 | 687.77 | 134.57 |
PSO | 1293.7 | 7.90 | 2164.3 | 645.26 | 473.22 |
WOA | 683.87 | 204.57 | 5853.9 | 647.09 | 111.47 |
KH | 629.63 | 0.001 | 268.91 | 592.86 | 74.23 |
Algorithm | Average (€ct) | Standard deviation (€ct) | Worst (€ct) | Best (Kg) | Computational time (s) |
---|---|---|---|---|---|
FSAPSO | 350.52 | 0.008 | 350.53 | 350.52 | NA |
GA | 370.24 | 27.82 | 389.91 | 350.57 | 80.29 |
GWO | 561.55 | 1.54 | 46800 | 409.85 | 167.44 |
PSO | 523.46 | 984.85 | 2443.5 | 404.02 | 454.74 |
WOA | 477.09 | 68.84 | 2189.9 | 458.14 | 110.94 |
KH | 365.17 | 0.004 | 814.51 | 339.72 | 75.83 |
Hour | Pd (kW) | Ppv (kW) | Pwt (kW) | PMt (kW) | PFC (kW) | PBatt (kW) | Pgrid (kW) |
---|---|---|---|---|---|---|---|
1 | 52 | 0 | 1.78 | 6.00 | 3.00 | 18.80 | 22.41 |
2 | 50 | 0 | 1.78 | 26.33 | 7.09 | − 10.44 | 25.24 |
3 | 50 | 0 | 1.78 | 6.00 | 17.36 | − 5.14 | 29.99 |
4 | 51 | 0 | 1.78 | 11.04 | 12.03 | 28.98 | − 2.84 |
5 | 56 | 0 | 1.78 | 6.89 | 24.95 | 8.10 | 14.27 |
6 | 63 | 0 | 0.90 | 22.04 | 4.50 | 5.56 | 29.99 |
7 | 70 | 0 | 1.78 | 12.48 | 4.76 | 22.37 | 28.59 |
8 | 75 | 0.19 | 1.30 | 27.80 | 12.08 | 29.17 | 4.44 |
9 | 76 | 3.75 | 1.79 | 15.01 | 8.63 | 29.25 | 17.57 |
10 | 80 | 7.52 | 3.09 | 6.00 | 24.21 | 29.99 | 9.25 |
11 | 78 | 10.44 | 8.77 | 19.23 | 23.71 | 28.43 | − 12.58 |
12 | 74 | 11.95 | 10.41 | 15.61 | 3.74 | 29.53 | 2.76 |
13 | 72 | 23.90 | 3.92 | 17.11 | 18.94 | 4.73 | 3.41 |
14 | 72 | 21.05 | 2.37 | 23.83 | 26.95 | 27.80 | − 30.00 |
15 | 76 | 7.88 | 1.79 | 12.28 | 29.28 | 22.21 | 2.57 |
16 | 80 | 4.23 | 1.31 | 30.00 | 30.00 | 30.00 | − 15.53 |
17 | 85 | 0.55 | 1.79 | 30.00 | 30.00 | 30.00 | − 7.34 |
18 | 88 | 0 | 1.79 | 16.36 | 18.49 | 21.44 | 29.93 |
19 | 90 | 0 | 1.30 | 6.33 | 22.98 | 29.54 | 29.84 |
20 | 87 | 0 | 1.78 | 29.97 | 29.97 | 1.51 | 23.77 |
21 | 78 | 0 | 1.30 | 26.62 | 27.38 | 6.71 | 15.99 |
22 | 71 | 0 | 1.30 | 29.69 | 29.77 | 28.76 | − 18.51 |
23 | 65 | 0 | 0.91 | 12.05 | 4.22 | 28.88 | 18.93 |
24 | 56 | 0 | 0.61 | 26.71 | 28.52 | 10.56 | − 10.40 |