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

Table 3

Optimal settings of control variables for 𝑃_𝐿 and 𝐿_max minimization in IEEE 30-bus system (Case  2(a): heavy load).

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	1.1000	1.0965	1.0978	1.0947	1.1000	1.0959	1.0923	1.0714
𝑉𝐺2	1.04	1.0807	1.0844	1.0865	1.0882	1.0871	1.0771	1.0871	1.0545
𝑉𝐺5	1.01	1.0496	1.0393	1.0547	1.0522	1.0400	1.0241	1.0400	1.0142
𝑉𝐺8	1.01	1.0522	1.0547	1.0346	1.0313	1.0502	1.0525	1.0502	1.0103
𝑉𝐺13	1.05	1.0962	1.1000	1.0864	1.0897	1.0831	1.0626	1.0831	1.0881
𝑉𝐺1	1.05	1.0918	1.0784	1.0323	1.0344	1.0560	1.0815	1.0560	1.0678
𝑇6--9	1.078	1.0125	1	0.9875	0.9875	1.0125	1	1.0125	0.9875
𝑇6--10	1.069	0.95	0.9625	0.9	0.9	0.925	0.9	0.925	0.925
𝑇4--12	1.032	1.025	0.9375	0.9375	0.9	0.9875	1	0.9875	0.9375
𝑇27-28	1.068	0.95	0.9	0.925	0.925	0.925	0.9	0.925	0.925
𝑄10	0.0	0.03	0.03	0	0.01	0.02	0.02	0	0.02
𝑄24	0.0	0.03	0.03	0.04	0.03	0.01	0.03	0.01	0.01
𝑃𝐿 (MW)	13.9971	12.1380	12.5101	12.8269	13.0480	12.1136	12.7399	12.0156	12.9451
𝐿max	0.2410	0.1837	0.1715	0.1856	0.1824	0.1858	0.1739	0.1883	0.1636