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. 2025 Jul 19;15:26206. doi: 10.1038/s41598-025-06555-z

Table 2.

Optimal combination of control variables for all the cases (modified IEEE 30-bus system).

Control variables M1 M2
ESDE-MC SKH ESDE-EC KH ESDE ESDE-MC SKH ESDE-EC KH ESDE
P G1 1.552 156.12 1.54 1.55 1.51 1.627 163.09 1.651 1.500 1.690
P G2 0.436 42.64 0.43 43.55 0.46 0.454 46.26 0.462 41.72 0.416
P G5 0.19 19.74 0.211 19.74 0.19 0.206 20.34 0.192 19.59 0.196
P G8 0.100 10.00 0.100 10 0.10 0.137 12.99 0.120 15.281 0.129
P G11 0.100 10.02 0.100 10 0.11 0.100 10.25 0.100 10.00 0.100
P G13 0.120 12.14 0.120 12.25 0.12 0.120 12.11 0.120 12 0.1200
P sch22 0.400 39.99 0.399 40 0.40 0.263 26.03 0.265 25.49 0.2630
V G1 1.10 1.09 1.10 1.1 1.09 1.10 1.10 1.10 1.1 1.09
V G2 1.08 1.08 1.08 1.092 1.08 1.08 1.08 1.08 1.082 1.07
V G5 1.05 1.05 1.06 1.049 1.03 1.05 1.05 1.049 1.05 1.04
V G8 1.07 1.06 1.07 1.072 1.05 1.07 1.07 1.05 1.063 1.05
V G11 1.10 1.10 1.10 1.1 1.09 1.09 1.09 1.04 1.1 1.10
V G13 1.10 1.08 1.10 1.064 1.08 1.10 1.07 1.07 1.1 1.094
t 6–9 1.03 1.02 1.05 1.05 0.98 1.04 1.02 1.05 1.03 1.050
t 6–10 0.95 0.90 0.93 0.93 1.05 0.94 0.95 1.00 0.93 0.93
t 4–12 1.01 0.96 0.99 0.94 1.05 0.98 1.01 1.02 0.98 0.940
t 28–27 0.96 0.98 0.94 0.95 0.97 0.96 0.975 0.95 0.93 0.94
Q C10 0.120 18.00 0.06 0.05 0.24 0.20 3.00 0.21 0.25 0.00
Q C24 0.150 8.009 0.03 0.04 0.13 0.10 10.00 0.07 0.24 0.11
Total cost ($/h) 732.55 732.754 733.12 733.28 733.78 786.96 787.2152 787.6704 787.78 788.27
Wind cost ($/h) 72.47 72.456 72.39 72.47 72.47 80.84 79.64206 81.4316 77.81 80.57
Thermal cost ($/h) 660.08 660.248 660.78 660.81 661.31 706.12 707.5731 706.2388 709.97 707.69
APL 0.0721 7.273 0.072 0.0742 0.073 0.075 7.6877 0.079701 0.078 0.081
Q wG22 − 0.205 − 20.611 − 0.204 − 0.020 − 0.204 − 0.165 − 15.7741 0.156603 − 0.156 − 0.1596

*All Powers, voltages, transformer taps, reactive powers are in p.u.

Significant values are in bold.