Research Article
An Enhanced Moth-Flame Optimization with Multiple Flame Guidance Mechanism for Parameter Extraction of Photovoltaic Models
Table 1
Solution accuracy of EMFO and compared algorithms.
| | Func. | Results | EMFO | MFO | AMFO | GMFO | CMFO | LMFO | OMFO |
| | F1 | Mean | 1.29E-24 | 4.10E-22∼ | 8.36E+03ǂ | 6.32E-11ǂ | 1.17E-10ǂ | 1.11E-10ǂ | 1.62E-10ǂ | | Std. | 1.86E-24 | 2.04E-21 | 9.74E+02 | 1.00E-10 | 1.34E-10 | 1.25E-10 | 2.08E-10 | | value | — | 3.21E-01 | 6.03E-40 | 2.78E-03 | 6.57E-05 | 5.26E-05 | 3.07E-04 | | H value | — | 0 | 1 | 1 | 1 | 1 | 1 |
| | F2 | Mean | 3.17E-02 | 5.32E-02∼ | 1.94E+04ǂ | 3.14E+01ǂ | 3.44E+01ǂ | 3.05E+01ǂ | 2.98E+01ǂ | | Std. | 3.15E-02 | 5.24E-02 | 2.88E+03 | 2.07E+01 | 2.06E+01 | 1.75E+01 | 3.49E+01 | | value | — | 8.46E-02 | 5.21E-35 | 8.73E-10 | 6.22E-11 | 2.18E-11 | 9.14E-05 | | H value | — | 0 | 1 | 1 | 1 | 1 | 1 |
| | F3 | Mean | 1.51E+06 | 1.84E+06∼ | 1.30E+08ǂ | 4.35E+06ǂ | 4.26E+06ǂ | 4.10E+06ǂ | 3.89E+06ǂ | | Std. | 9.36E+05 | 7.07E+05 | 2.54E+07 | 1.48E+06 | 1.95E+06 | 2.27E+06 | 1.58E+06 | | value | — | 1.70E-01 | 1.93E-29 | 1.56E-10 | 7.29E-08 | 3.35E-06 | 4.76E-08 | | H value | — | 0 | 1 | 1 | 1 | 1 | 1 |
| | F4 | Mean | 1.91E+00 | 1.16E+03ǂ | 2.47E+04ǂ | 3.46E+03ǂ | 4.01E+03ǂ | 2.99E+03ǂ | 3.29E+03ǂ | | Std. | 2.70E+00 | 1.03E+03 | 3.74E+03 | 1.93E+03 | 2.42E+03 | 1.52E+03 | 2.72E+03 | | value | — | 8.18E-07 | 1.32E-34 | 8.00E-12 | 8.39E-11 | 4.37E-13 | 2.12E-07 | | H value | — | 1 | 1 | 1 | 1 | 1 | 1 |
| | F5 | Mean | 2.90E+04 | 2.73E+04ξ | 2.80E+04ξ | 2.75E+04ξ | 2.29E+04ξ | 2.29E+04ξ | 2.71E+04ξ | | Std. | 2.88E+01 | 2.24E+03 | 1.66E+03 | 2.63E+03 | 3.40E+02 | 4.55E+02 | 2.55E+03 | | value | — | 3.47E-04 | 2.40E-03 | 6.67E-03 | 4.62E-55 | 4.76E-49 | 5.31E-04 | | H value | — | 1 | 1 | 1 | 1 | 1 | 1 | | F6 | Mean | 5.03E+01 | 1.38E+02ǂ | 6.14E+08ǂ | 2.31E+02ǂ | 3.05E+02∼ | 2.23E+02∼ | 1.60E+02ǂ | | Std. | 3.75E+01 | 2.13E+02 | 1.23E+08 | 3.71E+02 | 8.97E+02 | 5.32E+02 | 2.65E+02 | | value | — | 4.92E-02 | 3.82E-29 | 1.93E-02 | 1.63E-01 | 1.12E-01 | 4.52E-02 | | H value | — | 1 | 1 | 1 | 0 | 0 | 1 |
| | F7 | Mean | 4.70E+03 | 4.70E+03∼ | 4.61E+03ξ | 4.69E+03∼ | 3.92E+03ξ | 3.90E+03ξ | 4.65E+03∼ | | Std. | 2.83E-12 | 2.42E-12 | 1.13E+02 | 3.61E+01 | 1.75E+02 | 1.95E+02 | 1.53E+02 | | value | — | 1.00E+00 | 2.33E-04 | 3.22E-01 | 6.08E-27 | 1.94E-25 | 1.61E-01 | | H value | — | 0 | 1 | 0 | 1 | 1 | 0 |
| | F8 | Mean | 2.09E+01 | 2.02E+01ξ | 2.10E+01∼ | 2.09E+01∼ | 2.09E+01∼ | 2.09E+01∼ | 2.09E+01∼ | | Std. | 6.02E-02 | 7.48E-02 | 6.03E-02 | 4.58E-02 | 7.21E-02 | 4.95E-02 | 6.25E-02 | | value | — | 1.02E-38 | 3.72E-01 | 7.15E-01 | 8.44E-01 | 6.48E-01 | 9.54E-01 | | H value | — | 1 | 0 | 0 | 0 | 0 | 0 |
| | F9 | Mean | 2.13E+01 | 4.92E+01ǂ | 2.33E+02ǂ | 5.10E+01ǂ | 4.82E+01ǂ | 5.32E+01ǂ | 4.94E+01ǂ | | Std. | 3.95E+00 | 1.16E+01 | 1.62E+01 | 1.59E+01 | 1.20E+01 | 1.87E+01 | 1.60E+01 | | value | — | 2.83E-15 | 5.38E-48 | 5.37E-12 | 3.53E-14 | 6.58E-11 | 3.42E-11 | | H value | — | 1 | 1 | 1 | 1 | 1 | 1 |
| | F10 | Mean | 3.46E+01 | 1.13E+02ǂ | 2.96E+02ǂ | 1.23E+02ǂ | 1.13E+02ǂ | 1.26E+02ǂ | 1.13E+02ǂ | | Std. | 9.31E+00 | 2.89E+01 | 1.42E+01 | 3.59E+01 | 3.17E+01 | 3.10E+01 | 2.82E+01 | | value | — | 3.50E-17 | 6.81E-52 | 7.04E-16 | 6.26E-16 | 9.43E-19 | 1.28E-17 | | H value | — | 1 | 1 | 1 | 1 | 1 | 1 |
| | F11 | Mean | 6.14E+00 | 2.64E+01ǂ | 3.93E+01ǂ | 2.61E+01ǂ | 3.97E+01ǂ | 2.75E+01ǂ | 2.39E+01ǂ | | Std. | 1.78E+00 | 4.25E+00 | 1.25E+00 | 4.33E+00 | 1.20E+00 | 5.33E+00 | 3.95E+00 | | value | — | 1.17E-26 | 8.48E-52 | 3.52E-26 | 2.74E-52 | 5.63E-24 | 2.20E-25 | | H value | — | 1 | 1 | 1 | 1 | 1 | 1 |
| | F12 | Mean | 8.78E+05 | 7.81E+03ξ | 1.02E+06ǂ | 1.15E+04ξ | 9.42E+05ǂ | 3.15E+04ξ | 9.38E+03ξ | | Std. | 8.30E+04 | 5.31E+03 | 1.51E+05 | 7.89E+03 | 1.24E+05 | 6.18E+04 | 5.85E+03 | | value | — | 5.52E-44 | 1.25E-04 | 7.60E-44 | 3.61E-02 | 5.78E-39 | 6.14E-44 | | H value | — | 1 | 1 | 1 | 1 | 1 | 1 |
| | F13 | Mean | 2.67E+00 | 7.29E+00ǂ | 3.16E+01ǂ | 7.06E+00ǂ | 7.11E+00ǂ | 7.17E+00ǂ | 7.48E+00ǂ | | Std. | 4.69E-01 | 2.23E+00 | 1.76E+00 | 2.59E+00 | 2.78E+00 | 2.20E+00 | 2.00E+00 | | value | — | 1.54E-13 | 1.27E-52 | 6.73E-11 | 3.17E-10 | 2.34E-13 | 1.15E-15 | | H value | — | 1 | 1 | 1 | 1 | 1 | 1 |
| | F14 | Mean | 1.29E+01 | 1.33E+01ǂ | 1.34E+01ǂ | 1.28E+01ξ | 1.33E+01ǂ | 1.27E+01ξ | 1.30E+01∼ | | Std. | 2.28E-01 | 3.10E-01 | 1.45E-01 | 2.85E-01 | 1.85E-01 | 3.16E-01 | 2.49E-01 | | value | — | 5.94E-06 | 1.54E-12 | 2.01E-02 | 8.44E-07 | 2.59E-02 | 1.03E-01 | | H value | — | 1 | 1 | 1 | 1 | 1 | 0 |
| | F15 | Mean | 3.88E+02 | 3.61E+02∼ | 5.70E+02ǂ | 3.96E+02∼ | 2.68E+02ξ | 2.63E+02ξ | 4.00E+02∼ | | Std. | 7.84E+01 | 6.62E+01 | 2.95E+01 | 8.08E+01 | 7.77E+01 | 9.45E+01 | 8.73E+01 | | value | — | 1.85E-01 | 1.77E-14 | 7.51E-01 | 1.79E-06 | 5.95E-06 | 6.25E-01 | | H value | — | 0 | 1 | 0 | 1 | 1 | 0 |
| | F16 | Mean | 6.02E+01 | 2.05E+02ǂ | 3.29E+02ǂ | 1.83E+02ǂ | 1.66E+02ǂ | 1.83E+02ǂ | 1.59E+02ǂ | | Std. | 2.48E+01 | 1.18E+02 | 1.42E+01 | 9.51E+01 | 8.01E+01 | 8.56E+01 | 6.62E+01 | | value | — | 2.36E-07 | 7.77E-42 | 1.00E-07 | 7.85E-08 | 1.15E-08 | 7.20E-09 | | H value | — | 1 | 1 | 1 | 1 | 1 | 1 |
| | F17 | Mean | 6.83E+01 | 1.81E+02ǂ | 3.64E+02ǂ | 1.79E+02ǂ | 1.73E+02ǂ | 1.55E+02ǂ | 1.49E+02ǂ | | Std. | 2.79E+01 | 1.04E+02 | 2.18E+01 | 8.75E+01 | 8.97E+01 | 6.53E+01 | 7.23E+01 | | value | — | 3.16E-06 | 2.29E-39 | 2.43E-07 | 1.08E-06 | 1.82E-07 | 3.79E-06 | | H value | — | 1 | 1 | 1 | 1 | 1 | 1 |
| | F18 | Mean | 9.04E+02 | 9.11E+02ǂ | 1.01E+03ǂ | 9.11E+02ǂ | 9.13E+02ǂ | 9.13E+02ǂ | 9.11E+02ǂ | | Std. | 1.04E+00 | 3.37E+00 | 8.57E+00 | 3.36E+00 | 4.18E+00 | 5.38E+00 | 3.04E+00 | | value | — | 1.18E-13 | 1.99E-46 | 4.57E-12 | 2.29E-13 | 6.98E-10 | 2.79E-13 | | H value | — | 1 | 1 | 1 | 1 | 1 | 1 |
| | F19 | Mean | 9.04E+02 | 9.13E+02ǂ | 1.00E+03ǂ | 9.12E+02ǂ | 9.10E+02ǂ | 9.11E+02ǂ | 9.13E+02ǂ | | Std. | 8.55E-01 | 4.32E+00 | 1.07E+01 | 3.03E+00 | 3.27E+00 | 4.05E+00 | 3.32E+00 | | value | — | 2.87E-13 | 2.02E-41 | 4.50E-16 | 2.41E-12 | 1.73E-10 | 2.52E-16 | | H value | — | 1 | 1 | 1 | 1 | 1 | 1 |
| | F20 | Mean | 9.04E+02 | 9.12E+02ǂ | 1.00E+03ǂ | 9.12E+02ǂ | 9.12E+02ǂ | 9.12E+02ǂ | 9.12E+02ǂ | | Std. | 9.78E-01 | 3.26E+00 | 9.76E+00 | 3.56E+00 | 5.70E+00 | 2.68E+00 | 3.27E+00 | | value | — | 2.76E-15 | 1.34E-43 | 3.77E-14 | 1.31E-08 | 6.84E-19 | 2.52E-15 | | H value | — | 1 | 1 | 1 | 1 | 1 | 1 |
| | F21 | Mean | 5.00E+02 | 5.27E+02∼ | 1.13E+03ǂ | 5.79E+02∼ | 5.48E+02ǂ | 5.00E+02∼ | 5.77E+02∼ | | Std. | 8.29E-14 | 1.33E+02 | 3.30E+01 | 2.19E+02 | 1.12E+02 | 1.41E-10 | 1.95E+02 | | value | — | 3.22E-01 | 1.94E-56 | 7.67E-02 | 3.76E-02 | 7.98E-02 | 5.39E-02 | | H value | — | 0 | 1 | 0 | 1 | 0 | 0 |
| | F22 | Mean | 8.76E+02 | 9.56E+02ǂ | 1.07E+03ǂ | 9.67E+02ǂ | 9.60E+02ǂ | 9.65E+02ǂ | 9.46E+02ǂ | | Std. | 1.87E+01 | 3.75E+01 | 1.69E+01 | 5.35E+01 | 4.56E+01 | 3.40E+01 | 3.50E+01 | | value | — | 1.52E-12 | 1.95E-37 | 2.36E-10 | 3.58E-11 | 2.97E-15 | 1.28E-11 | | H value | — | 1 | 1 | 1 | 1 | 1 | 1 |
| | F23 | Mean | 5.34E+02 | 5.77E+02∼ | 1.12E+03ǂ | 5.84E+02∼ | 5.77E+02∼ | 5.77E+02∼ | 5.50E+02∼ | | Std. | 4.29E-04 | 1.49E+02 | 2.97E+01 | 1.34E+02 | 1.51E+02 | 1.51E+02 | 8.06E+01 | | value | — | 1.57E-01 | 3.04E-57 | 6.91E-02 | 1.60E-01 | 1.64E-01 | 3.22E-01 | | H value | — | 0 | 1 | 0 | 0 | 0 | 0 |
| | F24 | Mean | 2.00E+02 | 2.00E+02∼ | 1.12E+03ǂ | 2.00E+02∼ | 2.00E+02∼ | 2.00E+02∼ | 2.00E+02∼ | | Std. | 6.21E-13 | 6.21E-13 | 1.99E+01 | 1.29E-10 | 8.46E-11 | 6.37E-11 | 1.56E-10 | | value | — | 4.58E-21 | 8.07E-75 | 3.42E-03 | 8.09E-04 | 1.46E-05 | 6.54E-03 | | H value | — | 1 | 1 | 1 | 1 | 1 | 1 |
| | F25 | Mean | 9.75E+02 | 9.85E+02ǂ | 1.27E+03ǂ | 9.86E+02ǂ | 9.86E+02ǂ | 9.86E+02ǂ | 9.87E+02ǂ | | Std. | 4.74E+00 | 9.61E+00 | 1.60E+01 | 8.71E+00 | 7.81E+00 | 7.50E+00 | 1.05E+01 | | value | — | 2.07E-05 | 1.38E-54 | 4.71E-07 | 2.94E-07 | 6.27E-08 | 1.64E-06 | | H value | — | 1 | 1 | 1 | 1 | 1 | 1 |
| | ǂ/ξ/∼ | | — | 14/3/8 | 22/2/1 | 16/3/6 | 18/3/4 | 15/5/5 | 16/2/7 |
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