Simple Quadratic Interpolation-Inspired Symbiosis Organisms Search Algorithm for Optimal Placement of Capacitors in Radial Distribution Networks with Different Loading Models

Table 14

Optimal siting and sizing of capacitors for the 119-bus system with the CP load model at different load levels.

Item	Load level—light 50%
Method	CSA [16]	IHA [17]	FPA [18]	ABC [19]	MGABC [30]	SOSc	SQI-SOSc	SOS	SQI-SOS
Locations (kVArs)	32 (0)	39 (1200)	32 (0)	32 (500)	33 (300)	96 (561.52)	50 (977.53)	42 (400)	32 (850)
	39 (1100)	43 (0)	40 (1100)	35 (0)	35 (750)	107 (636.82)	96 (548.25)	111 (750)	80 (800)
	40 (0)	70 (900)	70 (750)	40 (0)	45 (300)	80 (807.44)	32 (899.34)	80 (800)	74 (750)
	70 (350)	74 (0)	74 (1100)	50 (0)	46 (150)	50 (982.00)	80 (811.47)	74 (750)	111 (800)
	74 (500)	86 (0)	89 (500)	70 (0)	49 (900)	74 (753.84)	107 (626.67)	96 (550)	96 (550)
	86 (450)	91 (600)	104 (0)	73 (750)	54 (450)	42 (393.18)	42 (392.52)	107 (600)	107 (550)
	108 (0)	107 (0)	109 (0)	79 (500)	71 (750)	32 (904.33)	111 (733.85)	50 (950)	50 (1000)
	118 (1000)	109 (0)	112 (0)	105 (300)	76 (150)	111 (753.84)	74 (751.84)	33 (750)	42 (400)
		118 (1000)	118 (1000)	106 (0)	86 (750)
				109 (0)	94 (300)
				110 (950)	101 (750)
					110 (600)
					111 (450)
					114 (150)
					115 (150)
Total kVAr	3400	3700	3350	3900	6900	5777.11	5741.51	5550	5700
Total kVAr demand	8520.55
Load level—medium 75%
Locations (kVArs)	32 (900)	39 (1500)	32 (0)	32 (0)	33 (600)	96 (804.70)	50 (1499.95)	42 (550)	32 (1050)
	39 (1500)	43 (0)	40 (1500)	35 (800)	35 (1200)	107 (903.13)	96 (820.33)	111 (1100)	80 (1100)
	40 (0)	70 (900)	70 (750)	40 (1200)	45 (300)	80 (1107.43)	32 (1137.43)	80 (1100)	74 (1150)
	70 (600)	74 (600)	74 (600)	50 (450)	46 (150)	50 (1497.64)	80 (1087.39)	74 (1150)	111 (1150)
	74 (750)	86 (0)	89 (1500)	70 (550)	49 (1350)	74 (1146.86)	107 (904.62)	96 (800)	96 (800)
	86 (700)	91 (1500)	104 (0)	73 (750)	54 (750)	42 (553.04)	42 (556.16)	107 (950)	107 (900)
	108 (750)	107 (0)	109 (0)	79 (850)	71 (1050)	32 (1122.45)	111 (1132.41)	50 (1500)	50 (1500)
	118 (1100)	109 (0)	112 (0)	105 (0)	76 (300)	111 (1133.50)	74 (1145.73)	33 (1000)	42 (600)
		118 (1200)	118 (1000)	106 (0)	86 (1050)
				109 (800)	94 (450)
				110 (1000)	101 (1200)
					110 (900)
					111 (600)
					114 (150)
					115 (150)
Total kVAr	6300	5700	5350	6400	10200	8268.79	8284.06	8150	8250
Total kVAr demand	12780.83
Load level—full 100%
Locations (kVArs)	32 (1500)	39 (1500)	32 (1500)	32 (850)	33 (900)	96 (804.85)	50 (1499.95)	42 (550)	32 (1050)
	39 (1500)	43 (1000)	40 (1500)	35 (1050)	35 (1500)	107 (903.63)	96 (820.46)	111 (1400)	80 (1100)
	40 (550)	70 (1000)	70 (850)	40 (1300)	45 (450)	80 (1107.66)	32 (1137.43)	80 (1100)	74 (1400)
	70 (950)	74 (1000)	74 (1100)	50 (800)	46 (450)	50 (1499.53)	80 (1087.45)	74 (1400)	111 (1450)
	74 (750)	86 (900)	89 (1500)	70 (550)	49 (1500)	74 (1395.53)	107 (904.64)	96 (800)	96 (800)
	86 (1050)	91 (1500)	104 (500)	73 (1300)	54 (1050)	42 (553.16)	42 (556.20)	107 (950)	107 (900)
	108 (1500)	107 (850)	109 (900)	79 (1200)	71 (1200)	32 (1122.81)	111 (1435.61)	50 (1500)	50 (1500)
	118 (1200)	109 (850)	112 (250)	105 (700)	76 (450)	111 (1436.75)	74 (1408.13)	33 (1000)	42 (600)
		118 (1200)	118 (1150)	106 (250)	86 (1350)
				109 (800)	94 (750)
				110 (1200)	101 (1500)
					110 (1350)
					111 (750)
					114 (150)
					115 (150)
Total kVAr	9000	9800	9250	10000	13500	8823.94	8849.91	8700	8800
Total kVAr demand					17041.1
Fixed capacitors	SOS	(42, 400); (111, 750); (80, 800); (74, 750); (96, 550); (107, 600); (50, 950); (33, 750)
	SQI-SOS	(32, 850); (80, 800); (74, 750); (111, 800); (96, 550); (107, 550); (50, 1000); (42, 400)
Switched capacitors	SOS	(42, 150); (111, 650); (80, 300); (74, 650); (96, 250); (107, 350); (50, 550); (33, 250)
	SQI-SOS	(32, 200); (80, 300); (74, 650); (111, 650); (96, 250); (107, 350); (50, 500); (42, 200)