Combined Economic and Emission Dispatch Problem of Wind-Thermal Power System Using Gravitational Particle Swarm Optimization Algorithm

Table 8

Statistical results of the minimum fuel cost, minimum emission, and best compromise solution by different algorithms on three cases.

Algorithm	Minimum fuel cost				Minimum emission level				ASD values for best compromise solution
	Best	Worst	Average	Std.	Best	Worst	Average	Std.	Best	Worst	Average	Std.
Case 1 (conventional thermal test system)
GPSOA	600.29	600.31	600.29	2.5601e − 03	0.1942	0.1942	0.1942	4.0891e − 09	0.8203	0.5809	0.7016	6.8199e − 03
PSOGSA	600.44	601.02	600.96	2.7367e − 02	0.1942	0.1942	0.1942	5.7842e − 08	0.8065	0.5296	0.7045	4.6413e − 03
TV-MOPSO	605.06	608.57	606.35	3.5274e − 00	0.1942	0.1943	0.1942	5.6532e − 04	0.7632	0.6534	0.6962	3.7624e − 03
PSO	600.57	607.13	603.13	1.5618e − 00	0.1947	0.1990	0.1964	1.1037e − 03	0.7477	0.5876	0.6896	7.2215e − 03
GSA	602.23	615.30	609.05	3.4189e − 00	0.1954	0.2057	0.2004	2.6205e − 03	0.7327	0.5164	0.6587	1.0174e − 02
OGSA	601.02	604.73	601.53	2.6352e − 01	0.1942	0.1944	0.1942	6.5624e − 04	0.7524	0.6028	0.6835	4.6441e − 03
Case 2 (lossless wind-thermal test system)
GPSOA	285.61	285.61	285.61	4.8224e − 08	0.1941	0.1942	0.1942	7.2534e − 07	0.6751	0.6011	0.6356	5.0026e − 03
PSOGSA	286.52	286.82	286.66	3.6226e − 06	0.1941	0.1944	0.1943	3.6518e − 02	0.6624	0.5628	0.6164	2.7538e − 03
PSO	288.12	289.69	288.62	1.4625e − 02	0.1945	0.1947	0.1946	1.0231e − 04	0.6630	0.6026	0.6268	5.0167e − 03
GSA	324.40	419.02	366.44	2.6899e+01	0.1967	0.2156	0.2063	4.6911e − 03	0.6598	0.4353	0.5794	4.8831e − 02
GA	422.64	462.62	436.62	3.3943e+01	0.1972	0.2208	0.2176	2.7521e − 02	0.5873	0.4261	0.5207	8.7264e − 02
Case 3 (wind-thermal test system with loss)
GPSOA	286.02	286.05	286.03	4.5555e − 03	0.1941	0.1943	0.1942	4.9695e − 05	0.7466	0.6052	0.6318	4.9998e − 03
PSOGSA	288.24	290.51	289.43	2.7536e − 02	0.1943	0.1950	0.1946	1.6253e − 02	0.6825	0.5844	0.6275	6.6253e − 02
PSO	288.52	289.15	288.07	3.6977e − 02	0.1944	0.1948	0.1945	1.6181e − 04	0.6748	0.5964	0.6423	5.5679e − 03
GSA	296.85	324.92	367.50	6.1065e+01	0.1969	0.2145	0.2070	4.1027e − 03	0.6647	0.4831	0.6163	3.6581e − 02
GA	306.15	384.63	326.73	1.6259e+02	0.1970	0.2186	0.2092	3.0726e − 03	0.6026	0.4222	0.5726	5.7529e − 02