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

Table 5.

Optimum control variables for IEEE 30-bus grid for minifying fuel cost.

Control variables	AHA	HHO	mAHA	RUN	SCA	SMA	TSA	WOA	CGSCE⁵⁰
$P_{G 1}$ (MW)	176.906	178.999	177.1779	177.306	172.6857	176.7942	179.9009	175.5387	177.120
$P_{G 2}$ (MW)	48.051	48.558	48.7003	48.511	49.5774	48.3917	47.2028	47.5454	48.6931
$P_{G 5}$ (MW)	21.279	20.884	21.4732	21.220	25.9249	21.1671	21.0713	20.6348	21.3708
$P_{G 8}$ (MW)	21.719	13.578	21.0560	20.643	22.2514	21.2451	18.4862	21.4456	21.2720
$P_{G 11}$ (MW)	11.990	17.119	11.6398	11.817	10	12.4284	13.9516	14.6936	11.9708
$P_{G 13}$ (MW)	12.066	13.407	12	12.564	13.0287	12	12	12.1966	12.0011
$V_{1}$ (pu)	1.0998	1.1	1.1	1.0997	1.08018	1.1	1.1	1.1	1.0848
$V_{2}$ (pu)	1.0876	1.0893	1.08753	1.0854	1.05307	1.08743	1.07431	1.08822	1.0653
$V_{5}$ (pu)	1.0617	1.0770	1.05989	1.0593	1.00887	1.06122	1.06045	1.06419	1.0338
$V_{8}$ (pu)	1.0670	1.0652	1.06828	1.0656	1.01128	1.06968	1.06601	1.06895	1.0384
$V_{11}$ (pu)	1.0945	1.0757	1.09523	1.0986	1.1	1.1	1.06663	1.1	1.0993
$V_{13}$ (pu)	1.0994	1.0632	1.09950	1.0993	1.1	1.09995	1.1	1.04947	1.0462
$T_{11}$ (6–9)	1.0073	1.0651	1.03251	1.0002	1.1	1.01595	0.99058	1.06601	1.0377
$T_{12}$ (6–10)	0.9569	1.0104	0.91963	0.9523	1.1	0.94796	0.9	1.03469	0.9539
$T_{15}$ (4–12)	1.0034	1.0272	0.99351	0.9916	0.9	1.00276	1.1	1.03139	0.9687
$T_{36}$ (28–27)	0.9739	0.9991	0.96845	0.9681	0.92811	0.96587	0.93863	1.01569	0.9741
$Q_{10}$ (MVAR)	4.70492	2.2025	4.99909	4.70924	0	2.817585	2.684852	0.448918	1.5896
$Q_{12}$ (MVAR)	4.24528	0.16911	4.98579	4.42300	0	3.946360	1.910281	1.919497	1.1263
$Q_{15}$ (MVAR)	3.79860	0.49680	2.70386	4.060068	3.142928	0	3.171857	0.678525	4.2301
$Q_{17}$ (MVAR)	3.3856	0.0429	3.61731	4.408631	0.090808	4.52756	0.950972	2.036575	4.9719
$Q_{20}$ (MVAR)	4.23117	1.49543	4.99426	4.50550	3.120945	4.041979	4.116303	2.995657	4.0218
$Q_{21}$ (MVAR)	4.82997	2.37321	4.81975	4.73517	2.399678	4.949713	3.747557	1.134746	4.9972
$Q_{23}$ (MVAR)	4.3502	0.11461	4.99194	4.11112	1.385095	4.843498	2.152461	1.896188	2.9141
$Q_{24}$ (MVAR)	3.9253	1.30597	4.9990	4.72998	0.340715	4.954122	0.384783	4.131996	5
$Q_{29}$ (MVAR)	2.69775	0.81080	1.11435	2.57926	1.766579	0.412344	0.010386	2.672235	2.4753
Fuel cost ($/h)	799.18	801.60	799.135	799.17	807.179	799.193	800.877	799.962	800.5106
Power losses (MW)	8.6151	9.1477	8.64736	8.6636	10.0683	8.62662	9.21300	8.65502	–
Voltage deviations (pu)	1.6377	0.6024	1.71252	1.7326	0.57608	1.63148	1.36734	0.63584	–
Iterations time (s)	50.8	418	52	91.2	85.097	52.1	53.8	55.2	–