Application of Hybrid MOPSO Algorithm to Optimal Reactive Power Dispatch Problem Considering Voltage Stability

Table 4

Optimal settings of control variables for 𝑃_𝐿 and 𝐿_max minimization in IEEE 30-bus system (Case  2(b): contingency state).

Variable	Initial	MOPSO		NSGA-II		MOEA/D		HMOPSO
		Best 𝑃𝐿	Best 𝐿max	Best 𝑃𝐿	Best 𝐿max	Best 𝑃𝐿	Best 𝐿max	Best 𝑃𝐿	Best 𝐿max
𝑉𝐺1	1.05	1.0844	1.0837	1.0848	1.0803	1.0888	1.0754	1.0772	1.0512
𝑉𝐺2	1.04	1.0735	1.0729	1.0723	1.0689	1.0734	1.0668	1.0733	1.0451
𝑉𝐺5	1.01	1.0537	1.0533	1.0525	1.0456	1.0504	1.0297	1.0624	1.0175
𝑉𝐺8	1.01	1.0558	1.0566	1.0525	1.0475	1.0506	1.0413	1.0555	1.0136
𝑉𝐺13	1.05	1.0963	1.0962	1.0688	1.0674	1.0762	1.0771	1.0862	1.0747
𝑉𝐺1	1.05	1.0793	1.0788	1.0805	1.0758	1.0649	1.0656	1.0646	1.0531
𝑇6--9	1.078	1.0125	1.0125	0.9875	0.9875	0.9875	1.0375	1.0125	0.9875
𝑇6--10	1.069	0.9	0.9	0.9125	0.925	0.9	0.9375	0.9875	0.9125
𝑇4--12	1.032	0.9875	0.9875	1	1	1	1.05	1.025	1.05
𝑇27-28	1.068	0.95	0.95	0.95	0.9375	0.95	0.925	0.95	0.925
𝑄10	0.0	0.01	0	0.01	0.02	0.02	0.01	0.02	0.02
𝑄24	0.0	0.04	0.3	0.02	0.02	0.01	0.05	0.01	0.03
𝑃𝐿 (MW)	6.5179	5.4436	5.5493	5.5094	5.5548	5.4504	5.6932	5.3076	5.9774
𝐿max	0.2956	0.2162	0.2061	0.2177	0.2168	0.2197	0.1980	0.2386	0. 1842