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 3

Comparison of LVSI, Lmn, and FVSI indices for NR and ANN methods with different active power loading at bus 14.

Active load at bus No. 14 (in p.u.)	LVSI			Lmn			FVSI
Active load at bus No. 14 (in p.u.)	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$$
0.17363	1.87546	1.87542	−0.42	0.04251	0.04248	−0.23	0.04342	0.04339	−0.23
0.21058	1.85047	1.85063	1.60	0.04413	0.04440	2.74	0.04528	0.04556	2.76
0.22290	1.84221	1.84236	1.56	0.04474	0.04496	2.14	0.04598	0.04620	2.15
0.24753	1.82576	1.82585	0.85	0.04608	0.04606	−0.27	0.04751	0.04748	−0.27
0.29560	1.79402	1.79399	−0.34	0.04915	0.04888	−2.73	0.05098	0.05071	−2.75
0.32143	1.77713	1.77709	−0.41	0.05106	0.05087	−1.89	0.05313	0.05294	−1.92
0.38302	1.73732	1.73731	−0.12	0.05635	0.05648	1.26	0.05909	0.05921	1.21
0.43228	1.70588	1.70589	0.03	0.06140	0.06163	2.39	0.06478	0.06501	2.31
0.44460	1.69808	1.69808	0.05	0.06278	0.06302	2.42	0.06634	0.06657	2.34
0.48155	1.67477	1.67478	0.10	0.06721	0.06741	1.99	0.07135	0.07154	1.90
0.54313	1.63628	1.63630	0.19	0.07565	0.07567	0.17	0.08094	0.08095	0.12
0.58008	1.61336	1.61339	0.23	0.08139	0.08128	−1.12	0.08748	0.08737	−1.10
0.59240	1.60575	1.60577	0.24	0.08342	0.08327	−1.52	0.08980	0.08965	−1.46
0.62935	1.59056	1.58300	−75.57	0.08767	0.08964	19.70	0.09466	0.09698	23.17
0.66630	1.56030	1.56031	0.11	0.09695	0.09665	−2.99	0.10532	0.10506	−2.61
0.74020	1.51513	1.51509	−0.43	0.11301	0.11279	−2.15	0.12391	0.12377	−1.44
0.74020	1.51513	1.51509	−0.43	0.11301	0.11279	−2.15	0.12391	0.12377	−1.44
0.81410	1.47008	1.46998	−0.97	0.13201	0.13205	0.43	0.14608	0.14618	1.07
0.88800	1.42495	1.42490	−0.52	0.15446	0.15469	2.31	0.17250	0.17270	2.08
0.93727	1.39472	1.39478	0.59	0.17167	0.17185	1.86	0.19290	0.19297	0.76
0.97422	1.37192	1.37208	1.55	0.18593	0.18599	0.58	0.20989	0.20979	−0.98
1.03580	1.33357	1.33376	1.92	0.21267	0.21249	−1.83	0.24192	0.24165	−2.70
1.04812	1.32583	1.32600	1.64	0.21852	0.21831	−2.09	0.24896	0.24870	−2.52
1.17128	1.24669	1.24643	−2.61	0.28841	0.28844	0.26	0.33369	0.33391	2.28
1.18360	1.23855	1.23834	−2.06	0.29677	0.29678	0.15	0.34389	0.34402	1.33
1.22055	1.21378	1.21384	0.56	0.32372	0.32362	−0.98	0.37687	0.37661	−2.62
1.29445	1.16239	1.16243	0.39	0.38782	0.38808	2.60	0.45576	0.45612	3.63
1.33140	1.13547	1.13557	0.98	0.42643	0.42692	4.83	0.50351	0.50389	3.81
1.38067	1.09786	1.09738	−4.82	0.48715	0.48531	−18.42	0.57887	0.57745	−14.22
1.46688	1.02491	1.02091	−40.01	0.63220	0.62294	−92.54	0.75982	0.75454	−52.80
1.51615	1.01132	1.01064	−6.81	0.74380	0.74290	−8.96	0.84483	0.84548	6.49
1.60237	1.00650	1.00653	0.32	0.94163	0.94244	8.10	0.96494	0.96531	3.73

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