. 2023 Dec 5;13:21446. doi: 10.1038/s41598-023-48479-6

Table 10.

Optimum control variables for the 30-bus system for minifying fuel cost and voltage deviation.

Control variables	AHA	HHO	mAHA	RUN	SCA	SMA	TSA	WOA	GWO³⁷
$P_{G 1}$ (MW)	175.5229	165.2596	174.9996	180.2959	152.897	176.000	152.3759	175.6838	63.4100
$P_{G 2}$ (MW)	48.78027	54.90978	47.908	43.11046	46.21225	49.3706	51.20082	42.94417	77.7900
$P_{G 5}$ (MW)	21.95667	19.35698	21.18578	24.74529	23.88146	21.9316	21.44287	21.97456	39.8500
$P_{G 8}$ (MW)	21.46253	23.8677	23.89826	19.11117	35	19.29766	32.45254	23.89286	45.4400
$P_{G 11}$ (MW)	13.18521	13.86115	13.32854	13.73714	15.75959	13.41639	10.82703	15.50411	30.3100
$P_{G 13}$ (MW)	12.32151	15.39698	12.00118	12.49682	18.01988	13.34685	23.45908	12.97393	30.4100
$V_{1}$ (pu)	1.039515	1.063826	1.031421	1.034383	1.056401	1.0364	1.071509	1.03843	1.0720
$V_{2}$ (pu)	1.02771	1.043007	1.014417	1.02032	1.02664	1.015553	1.047492	1.024674	1.0710
$V_{5}$ (pu)	1.014143	0.993806	1.013213	1.017806	1.011091	1.01422	0.984239	0.996189	1.0310
$V_{8}$ (pu)	1.004954	0.996013	1.009208	1.010292	0.981409	0.99934	0.996136	1.010137	1.0041
$V_{11}$ (pu)	1.007247	1.047857	1.014779	1.001898	1.059162	1.04089	1.1	1.020358	1.0400
$V_{13}$ (pu)	0.996524	1.011814	0.998543	1.007497	1.073992	1.018594	1.032821	1.027376	1.0820
$T_{11}$ (6–9)	1.012959	1.000785	1.030949	1.006006	0.950253	1.054622	1.060472	0.954086	1.043
$T_{12}$ (6–10)	0.913714	0.94624	0.9	0.9000	1.1	0.903902	0.914689	0.93967	0.99
$T_{15}$ (4–12)	0.952708	0.947149	0.967012	0.955314	1.048264	0.989138	1.02256	0.973295	0.99
$T_{36}$ (28–27)	0.95967	0.959914	0.970758	0.958486	0.96805	0.96049	0.978803	0.963043	0.965
$Q_{10}$ (MVAR)	4.648409	2.36515	2.173401	1.51318	4.10456	4.259120	3.0328	2.0042	18.93
$Q_{12}$ (MVAR)	0.609357	3.4281	3.8315	1.82596	3.8632	0.579030	4.5746	3.06927	0
$Q_{15}$ (MVAR)	4.843797	0.239426	4.93276	1.8356	0.02045	4.11300	1.63617	0.89053	0
$Q_{17}$ (MVAR)	1.4157006	1.35966	4.0660	3.97469	0.01532	1.103097	1.9630	0.29389	0
$Q_{20}$ (MVAR)	4.869775	3.910071	4.99048	2.26118	0.4833	4.928113	1.7889	2.41299	0
$Q_{21}$ (MVAR)	4.4165256	1.666834	5	3.9316	4.6215	4.341355	3.74594	2.2095	0
$Q_{23}$ (MVAR)	4.918944	3.8529345	4.9518	4.08318	1.70689	4.951307	2.47034	2.07403	0
$Q_{24}$ (MVAR)	4.610539	3.4359845	4.9373	4.99936	3.86399	4.858122	4.77817	1.028523	15.52
$Q_{29}$ (MVAR)	1.73194	2.169675	2.73016	1.31833	0.002345	1.930208	3.3332	2.539075	0
Objective function	824.9193	839.7303	824.0697	829.941	882.0512	825.729	856.5994	839.5122	916.1964
Fuel cost ($/h)	803.9283	805.3913	804.5488	805.9561	810.8618	804.2747	811.2805	804.7557	916.1764
Power losses (MW)	9.829075	9.252214	9.921366	10.09684	8.370063	9.963252	8.358272	9.573489	–
Voltage deviations (pu)	0.104955	0.171695	0.097605	0.119924	0.355947	0.107271	0.226594	0.173782	0.4935
Iterations time (s)	28.144	289.74	34	48	27.6	25.2	29.4	38.5	–