Assessment of the voltage stability of the power system using stability indices and artificial neural network | Science and Technology for Energy Transition (STET)

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Table 6

Comparison of LVSI, Lmn, and FVSI indices for NR and ANN methods with different active power loading at bus 44.

Load at Bus No. 44	LVSI			Lmn			FVSI
Load at Bus No. 44	NR method	ANN approach	Error ( $\hat{e} - 4$ $Mathematical equation: $ \widehat{e}-4$$ )	NR method	ANN approach	Error ( $\hat{e} - 4$ $Mathematical equation: $ \widehat{e}-4$$ )	NR method	ANN approach	Error ( $\hat{e} - 4$ $Mathematical equation: $ \widehat{e}-4$$ )
0.4039	1.90598	1.90571	−2.66	0.01436	0.01482	4.65	0.01423	0.01469	4.67
0.4852	1.85611	1.85611	0.04	0.01621	0.01624	0.23	0.01615	0.01616	0.20
0.5665	1.80806	1.80829	2.28	0.01845	0.01829	−1.56	0.01845	0.01829	−1.58
0.702	1.73163	1.73136	−2.70	0.02306	0.02306	−0.01	0.02323	0.02323	0.06
0.8375	1.65925	1.65997	7.18	0.02888	0.02892	0.46	0.02928	0.02932	0.46
1.0272	1.56374	1.56273	−10.04	0.03931	0.03925	−0.65	0.04018	0.04010	−0.82
1.1898	1.48641	1.49060	41.90	0.05071	0.05009	−6.24	0.05215	0.05150	−6.56
1.2711	1.44908	1.45310	40.25	0.05739	0.05696	−4.36	0.05920	0.05875	−4.51
1.2982	1.43681	1.44013	33.19	0.05978	0.05948	−3.02	0.06172	0.06141	−3.08
1.3524	1.41252	1.41394	14.23	0.06481	0.06479	−0.14	0.06703	0.06703	−0.02
1.4879	1.35308	1.35127	−18.13	0.07900	0.07920	1.98	0.08208	0.08230	2.22
1.5692	1.31819	1.31700	−11.87	0.08878	0.08867	−1.05	0.09246	0.09237	−0.97
1.5963	1.30667	1.30595	−7.17	0.09227	0.09205	−2.16	0.09618	0.09596	−2.14
1.7318	1.24973	1.25062	8.84	0.11170	0.11144	−2.55	0.11688	0.11663	−2.50
1.8402	1.20480	1.20472	−0.76	0.12998	0.13032	3.37	0.13641	0.13678	3.76
1.9486	1.16015	1.15952	−6.32	0.15125	0.15163	3.82	0.15916	0.15956	4.02
2.0299	1.12669	1.12722	5.35	0.16957	0.16923	−3.44	0.17877	0.17838	−3.90
2.0841	1.10432	1.10544	11.26	0.18313	0.18235	−7.76	0.19328	0.19243	−8.54
2.1925	1.05921	1.05812	−10.93	0.21412	0.21403	−0.90	0.22647	0.22639	−0.77
2.2467	1.03636	1.03601	−3.46	0.23195	0.23203	0.84	0.24555	0.24569	1.46
2.3551	1.09228	1.10137	90.83	0.27365	0.27646	28.03	0.29012	0.29244	23.17
2.4364	1.08368	1.08346	−2.25	0.31184	0.31198	1.36	0.33085	0.33033	−5.20
2.5448	1.07222	1.06975	−24.66	0.37628	0.37443	−18.46	0.39932	0.39718	−21.33
2.6532	1.05496	1.05492	−0.49	0.46592	0.46598	0.60	0.49395	0.49513	11.86
2.7616	1.03303	1.03516	21.32	0.60847	0.60780	−6.69	0.64271	0.64518	24.66
2.8593	1.00560	1.00570	0.99	0.91388	0.92000	61.28	0.95408	0.94295	−111.28

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