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

Table 13.

Optimum control variables for the 30-bus grid for minifying multi-objective function with emission.

Control variables	AHA	HHO	mAHA	RUN	SCA	SMA	TSA	WOA	FKH⁴⁰
$P_{G 1}$ (MW)	165.400	166.8056	166.4721	166.5516	166.724	164.969	156.645	168.9629	123.6836
$P_{G 2}$ (MW)	47.79336	46.25959	48.60795	51.88644	45.45169	48.78904	50.36477	49.08558	51.5998
$P_{G 5}$ (MW)	23.99595	18.1686	22.54116	22.11936	15.25348	23.20754	24.91179	19.7571	31.4264
$P_{G 8}$ (MW)	26.37857	27.31501	30.67165	20.14404	26.94864	26.89674	30.9148	20.74778	34.9189
$P_{G 11}$ (MW)	15.4945	21.15653	11.53718	15.24274	20.02407	15.25062	10.21388	17.12666	27.1416
$P_{G 13}$ (MW)	13.17305	12.81335	12.60599	16.63903	18.62736	13.05962	19.2427	16.99289	20.0125
$V_{1}$ (pu)	1.039098	1.040652	1.039056	1.047613	1.035358	1.043882	1.036548	1.04753	1.1
$V_{2}$ (pu)	1.020842	1.024997	1.022437	1.03056	1.007994	1.027929	1.019686	1.023413	1.0883
$V_{5}$ (pu)	1.007009	1.014929	1.007678	1.010245	0.95	1.004604	0.95	1.004138	1.0626
$V_{8}$ (pu)	1.002955	1.002843	1.007759	1.005067	0.984175	1.001507	0.981303	1.003892	1.0723
$V_{11}$ (pu)	1.027677	1.029506	1.005235	1.049557	1.073876	1.027916	1.1	1.072832	1.0661
$V_{13}$ (pu)	1.01166	1.059816	1.001543	0.990098	1.075011	1.00591	1.018861	1.018827	1.0220
$T_{11}$ (6–9)	1.025236	0.973647	1.012411	1.048338	1.003556	1.023669	1.1	1.022662	1.0909
$T_{12}$ (6–10)	0.909392	0.960301	0.914416	0.90002	0.982152	0.923891	0.9	0.94292	1.0210
$T_{15}$ (4–12)	0.982708	0.992372	0.950994	0.934678	0.991057	0.974637	0.995898	0.987179	1.0619
$T_{36}$ (28–27)	0.959825	0.985456	0.967399	0.968509	0.928281	0.962299	0.9	0.954627	1.0283
$Q_{10}$ (MVAR)	2.75864	0.893957	4.50358	3.88395	1.9883	4.72861	3.7866	2.54853	0.3568
$Q_{12}$ (MVAR)	0.848113	1.099	0.07098	0.965388	0	3.9491	0.0750	3.74059	4.6954
$Q_{15}$ (MVAR)	4.97757	2.832	2.4058	2.3171	2.43085	3.45173	2.6479	1.18119	3.6401
$Q_{17}$ (MVAR)	1.13727	3.328	2.348087	2.8309	0	0.23348	5	2.301628	3.1174
$Q_{20}$ (MVAR)	4.99764	0.975976	5	4.9971	0.83895	4.92498	4.83476	0.974147	0.8760
$Q_{21}$ (MVAR)	4.36739	0.831048	4.995866	0.78898	3.43964	4.86885	1.5173	1.48059	4.9595
$Q_{23}$ (MVAR)	4.7651	3.02398	4.9535	4.29237	0	4.93974	4.6711	4.1572	3.9324
$Q_{24}$ (MVAR)	4.84673	0.84786	5	3.29885	0.56658	4.91916	2.6284	1.3137	5
$Q_{29}$ (MVAR)	1.626306	3.607	2.39323	3.41025	2.51957	1.95153	0.41082	4.1195	1.9857
Objective function	865.0322	879.4284	864.735	867.2717	888.6845	864.9008	885.6557	873.5397	–
Fuel cost ($/h)	804.8632	807.3554	804.8359	804.9669	811.4686	804.3571	810.2148	805.1315	828.3271
Power losses (MW)	8.835931	9.118731	9.036036	9.183196	9.629671	8.772594	8.893501	9.272956	5.3828
Voltage deviations (pu)	0.113104	0.226543	0.106119	0.125655	0.267482	0.118206	0.236763	0.184763	0.4925
Iterations time (s)	46.6	290	56	72.23	45.4	48.6	47.62	57.6	–