Table 16 Statistical results of the proposed LSDO and its competitors for case studies with RESs.
Systems | Cases | LSDO | SDO | ABC | AEO | DE | PSO | |
|---|---|---|---|---|---|---|---|---|
IEEE 30 | Case 5 | Min | 781.0465 | 781.0633 | 781.5679 | 781.5613 | 781.8429 | 781.8984 |
Mean | 781.0777 | 781.1211 | 781.6922 | 781.7967 | 781.9374 | 785.7463 | ||
Max | 781.1041 | 781.3601 | 781.9680 | 782.8320 | 782.0656 | 813.5669 | ||
SD | 1.8922e−02 | 7.9737e−02 | 9.9345e−02 | 2.5226e−01 | 5.4209e−02 | 5.5157e+00 | ||
p_value | N/A | 7.2253e−02 | 2.7792e−11 | 2.7792e−11 | 2.7792e−11 | 2.7792e−11 | ||
Case 6 | Min | 809.5379 | 809.5406 | 810.2063 | 810.3869 | 810.3891 | 810.6643 | |
Mean | 809.5686 | 809.5534 | 810.2226 | 810.4587 | 810.4189 | 812.5426 | ||
Max | 809.6433 | 809.6613 | 810.2596 | 810.5989 | 810.4526 | 828.2575 | ||
SD | 2.4758e−02 | 2.9860e−02 | 1.2469e−02 | 6.0906e−02 | 1.7633e−02 | 3.1834e+00 | ||
p_value | N/A | 2.1627e−05 | 2.8538e−11 | 2.8538e−11 | 2.8538e−11 | 2.8538e−11 | ||
IEEE 57 | Case 10 | Min | 26491.8072 | 26529.4584 | 30539.0423 | 26496.6212 | 27458.7947 | 26565.5122 |
Mean | 26509.1985 | 26544.8073 | 35120.4814 | 29735.3255 | 29253.3064 | 34947.4702 | ||
Max | 26571.5093 | 26577.9994 | 40518.7080 | 41637.2155 | 32302.3813 | 56398.4406 | ||
SD | 2.0740e+01 | 1.6977e+01 | 2.5649e+03 | 3.4953e+03 | 1.1643e+03 | 7.6620e+03 | ||
p_value | N/A | 4.0707e−08 | 2.2204e−11 | 1.9203e−08 | 2.2204e−11 | 2.4579e−11 | ||
Case 11 | Min | 26490.4174 | 26560.9184 | 28755.3530 | 26500.9984 | 27247.6331 | 26695.5204 | |
Mean | 26513.1831 | 26561.6940 | 35555.4767 | 29647.0590 | 29235.2903 | 33617.4824 | ||
Max | 26547.1563 | 26563.0338 | 51597.0759 | 45841.5302 | 31924.7822 | 54730.8211 | ||
SD | 2.4701e+01 | 1.0368e+00 | 4.9651e+03 | 4.5404e+03 | 1.1092e+03 | 6.8201e+03 | ||
p_value | N/A | 9.9140e−12 | 2.4446e−11 | 6.0580e−09 | 2.4446e−11 | 2.4446e−11 |
