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

Table 8.

Optimal control variables for IEEE 30-bus test system for minimizing voltage deviation.

Control variables	AHA	HHO	mAHA	RUN	SCA	SMA	TSA	WOA	AHA⁴⁹
$P_{G 1}$ (MW)	122.681	88.5591	147.117	75.2296	184.529	134.813	161.712	72.1794	–
$P_{G 2}$ (MW)	62.3952	76.2285	57.4035	72.5051	28.1335	60.5820	40.6097	73.5926	9.7903
$P_{G 5}$ (MW)	42.4997	38.4568	34.7601	47.9036	24.0555	23.3362	37.3022	45.4916	45.8976
$P_{G 8}$ (MW)	25.3713	32.2721	11.8578	32.3474	21.0647	31.0750	14.2072	31.2644	21.7849
$P_{G 11}$ (MW)	23.9567	16.1774	27.3105	28.0929	14.9899	27.0478	15.0217	27.2625	28.3488
$P_{G 13}$ (MW)	12.9713	36.8881	13.0244	31.8296	20.5300	14.0200	22.9069	37.9501	18.0528
$V_{1}$ (pu)	1.01725	1.02372	1.02223	1.00262	1.08376	1.03034	1.03565	1.01670	1.01222
$V_{2}$ (pu)	1.00930	1.02097	1.01398	1.00015	1.04039	1.02543	1.02329	1.01209	0.99700
$V_{5}$ (pu)	1.01912	1.00979	1.0160	1.01700	0.97922	1.01881	0.97742	1.01899	1.01962
$V_{8}$ (pu)	1.00651	1.00760	1.00794	1.00759	1.00015	1.00403	1.01344	1.00446	1.00738
$V_{11}$ (pu)	0.99973	0.99193	1.02722	1.03076	1.08171	1.0063	1.03549	1.01549	1.03968
$V_{13}$ (pu)	1.01772	1.01021	0.99954	1.01332	1.06184	0.99320	1.04831	1.001288	1.03656
$T_{11}$ (6–9)	1.0117	0.96021	1.04337	1.04569	0.95573	1.01075	1.1	0.957383	0.99107
$T_{12}$ (6–10)	0.91206	0.96042	0.90460	0.90003	1.08799	0.9	0.91578	0.976089	0.93416
$T_{15}$ (4–12)	0.99164	0.96411	0.95435	0.98536	1.09168	0.94867	1.01159	0.979018	1.00823
$T_{36}$ (28–27)	0.96299	0.97707	0.95676	0.97327	0.95721	0.97493	0.95270	0.971677	0.95622
$Q_{10}$ (MVAR)	3.27787	1.97271	4.18088	4.42679	4.69157	1.787223	3.36870	4.739554	3.99263
$Q_{12}$ (MVAR)	1.15581	4.12753	1.33663	4.20977	2.12152	4.430132	2.61065	4.453511	1.90580
$Q_{15}$ (MVAR)	4.69677	3.76231	4.48546	2.95974	1.27970	3.666590	4.70315	4.372774	4.12228
$Q_{17}$ (MVAR)	4.51875	2.59322	1.51701	4.45045	0.27270	3.545235	2.41784	4.383086	2.42501
$Q_{20}$ (MVAR)	4.74382	2.45081	4.93432	4.72581	4.07621	4.950436	5	4.293828	4.99457
$Q_{21}$ (MVAR)	4.45496	4.94036	4.07387	2.92357	4.96282	1.487236	4.10688	4.354775	4.84730
$Q_{23}$ (MVAR)	4.92754	4.97427	4.63567	4.48689	3.58842	5	2.28231	4.839135	4.21244
$Q_{24}$ (MVAR)	4.82808	4.99962	4.84966	4.60890	3.25991	4.999492	3.934234	3.941876	4.38256
$Q_{29}$ (MVAR)	2.31166	4.41481	1.58313	4.62710	3.29670	5	1.557113	4.941514	1.33206
Fuel cost ($/h)	851.678	885.835	827.401	920.571	814.934	820.855	826.089	922.282	860.1368
Power losses (MW)	6.47578	5.18227	8.07451	4.50839	9.90363	7.47450	8.36049	4.34096	10.44553
Voltage deviations (pu)	0.09841	0.14498	0.09783	0.10214	0.24245	0.10708	0.20299	0.12508	0.120906
Iterations time (s)	27.5	277.36	36	47.358	33	28	27.2	32	–