Multiple DGs for Reducing Total Power Losses in Radial Distribution Systems Using Hybrid WOA-SSA Algorithm

Table 5

Performance of WOA-SSA compared with those of the standard case, WOA, and SSA on an IEEE 13-bus RDN with multiple DGs.

DG no.	Particulars	Base case without DG	Algorithms
			WOA	SSA	WOA-SSA
2	Candidate buses	—	645, 675	645, 675	611, 675
	Optimal DG size (kW)	—	438.9; 2090.454	1794.687; 2007.456	361.804; 2024.676
	Total DG size (kW)	—	2529.354	3802.143	2386.48
	Total power losses (kW)	110.948	74.871	74.85	74.838
	% power loss reduction	—	32.5%	32.5%	32.6%
	Minimum voltage (p.u.), bus	0.97288, 611	0.99202, 634	0.99293, 634	0.99294, 634
	Maximum voltage (p.u.), bus	1.04, 675	1.0394, 632	1.0387, 632	1.0385, 632
	Mean voltage (p.u.)	1.0037	1.0115	1.0113	1.0113
	Standard deviation voltage (p.u.)	0.020686	0.014066	0.013567	0.013665
	Computational time (S)	—	450	506	440
3	Candidate buses	—	680, 611, 675	645, 646, 675	611, 645, 675
	Optimal DG size (kW)	—	4705.369; 1434.894; 2039.296	2877.887; 2928.977; 1982.26	1673.064; 665.587; 2022.381
	Total DG size (kW)	—	8179.559	7789.124	4361.032
	Total power losses (kW)	110.948	74.838	74.852	74.832
	% power loss reduction	—	32.6%	32.5%	32.6%
	Minimum voltage (p.u.), bus	0.97288, 611	0.99257, 634	0.9922, 634	0.99276, 634
	Maximum voltage (p.u.), bus	1.04, 675	1.039, 632	1.0389, 632	1.0389, 632
	Mean voltage (p.u.)	1.0037	1.0114	1.0113	1.0112
	Standard deviation voltage (p.u.)	0.020686	0.013757	0.013427	0.013658
	Computational time (S)	—	475	550	539
4	Candidate buses	—	646, 692, 611, 675	652, 611, 645, 675	645, 646, 634, 675
	Optimal DG size (kW)	—	32.418; 8.923; 2879.988; 2013.935	631.618; 664.226; 646.792; 2004.942	2786.184; 3093.839; 1591.05; 1921.799
	Total DG size (kW)	—	4935.264	3947.578	9392.872
	Total power losses (kW)	110.948	74.937	74.834	72.762
	% power losses reduction	—	32.5%	32.6%	34.4%
	Minimum voltage (p.u.), bus	0.97288, 611	0.99285, 634	0.99295, 634	0.99008, 634
	Maximum voltage (p.u.), bus	1.04, 675	1.0388, 632	1.0387, 632	1.0341, 632
	Mean voltage (p.u.)	1.0037	1.0113	1.0113	1.0099
	Standard deviation voltage (p.u.)	0.020686	0.013609	0.013558	0.012129
	Computational time (S)	—	542	550	540
5	Candidate buses	—	632, 684, 611, 634, 675	634, 633, 632, 611, 675	611, 684, 634, 692, 675
	Optimal DG size (kW)	—	3124.516; 4176.683; 2663.978; 1.041; 2036.525	4020.34; 3095.887; 1498.569; 3793.034; 2007.206	1252.741; 720.198; 1922.402; 265.501; 2042.348
	Total DG size (kW)	—	12002.743	14415.036	6203.19
	Total power losses (kW)	110.948	74.845	74.839	74.834
	% power losses reduction	—	32.5%	32.6%	32.6%
	Minimum voltage (p.u.), bus	0.97288, 611	0.99259, 634	0.99291, 634	0.99252, 634
	Maximum voltage (p.u.), bus	1.04, 675	1.039, 632	1.0387, 632	1.039, 632
	Mean voltage (p.u.)	1.0037	1.0114	1.0113	1.0114
	Standard deviation voltage (p.u.)	0.020686	0.013745	0.013574	0.013781
	Computational time (S)	—	626	658	614
6	Candidate buses	—	652, 680, 645, 633, 671, 675	646, 680, 632, 671, 684, 675	645, 652, 633, 684, 671, 675
	Optimal DG size (kW)	—	1760.35; 982.198; 2423.365; 3418.675; 3279.92; 1991.147	3087.157; 1820.051; 887.208; 1812.839; 1620.26; 2025.412	1704.998; 2942.587; 3221.933; 818.585; 188.281; 2032.203
	Total DG size (kW)	—	13855.655	11252.927	10908.587
	Total power losses (kW)	110.948	74.872	74.869	74.864
	% power loss reduction	—	32.5%	32.5%	32.5%
	Minimum voltage (p.u.), bus	0.97288, 611	0.99306, 634	0.99269, 634	0.99261, 634
	Maximum voltage (p.u.), bus	1.04, 675	1.0386, 632	1.0389, 632	1.039, 632
	Mean voltage (p.u.)	1.0037	1.0113	1.0114	1.0114
	Standard deviation voltage (p.u.)	0.020686	0.013496	0.01369	0.013731
	Computational time (S)	—	677	692	659