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      where PV and solari are the solar PV installed capacity and solar power generation (in pu) for load hour of i. GF is the generation factor, having a value of (3.52/6.628) [68].

In this study, the biomass DG has been considered as the LPF DG having power factor being the same as the load demand. On the other hand, shunt capacitors available in the market are of standard size only. So, in this work, the sizes of shunt capacitors are considered to be as an integer multiple 25 kVAr. Table 1.5 presents the cost of different DGs and their lifetime. Using the mixed discrete SPBO, the location of the biomass DG, solar PV, and shunt capacitor has been optimized. As the location of the installed plants can’t be moved from one bus to another bus, the locations of the considered DGs need to be kept constant.

Table 1.4 Variation of load demand (pu) and solar power generation (pu) with load hours.

Load hour	Load demand (pu)	Solar power generation (pu) [68]	Load hour	Load demand (pu)	Solar power generation (pu) [68]
1	0.64	0	13	0.99	1
2	0.6	0	14	1	0.9309
3	0.58	0	15	1	0.7424
4	0.56	0	16	0.97	0.5491
5	0.56	0	17	0.96	0.2827
6	0.58	0	18	0.96	0.0593
7	0.64	0.015	19	0.93	0
8	0.76	0.2143	20	0.92	0
9	0.87	0.5331	21	0.92	0
10	0.95	0.7653	22	0.93	0
11	0.99	0.894	23	0.87	0
12	1	0.9968	24	0.72	0

Figure 1.2 Variation of load demand (pu) and solar power generation (pu) with load hour.

Table 1.5 Cost and lifetime of different DGs.

	Biomass DG	Solar PV	Shunt capacitors
Cost ($)	3000/kW [60]	770/kW [60]	9/kVAr
Lifetime (years)	40	20	5

      1.5.1 Optimum Placement of RDGs and Shunt Capacitors to 33-Bus Distribution Network

In this section, the optimum placement of biomass DG, solar PV, and shunt capacitors, to the 33-bus distribution network is discussed. Table 1.6 presents the optimum sizes and locations of biomass DG, solar PV, and shunt capacitors for different load hours of the 33-bus distribution networks. The reductions of active power loss and VDI for different load hours have been shown in Figures 1.3 and 1.4, respectively. From Table 1.6 and Figure 1.3, it may be noticed that the active power loss reduction after the placement of biomass DG, solar PV, and shunt capacitor is quite significant for all the load hours. After the placement of RDGs and shunt capacitors to bus numbers 14, 31, and 30, respectively, the active power loss of the 33-bus distribution network reduces from 202.6771 kW to 36.8247 kW for the 15^th load hour. It may also be noticed that in presence of solar radiation, the active power loss reduction is higher compared to the same when the solar power generation is less or absent.

From Table 1.6 and Figure 1.4, it may be noticed that the improvement of the voltage profile of the 33-bus distribution network is very good for all the load hours of the day. Improvement of the voltage profile of the distribution network leads to the reduction of VDI. From Table 1.6 and Figure 1.4, the reduction of the VDI for all the load hours of the day may be noticed quite prominently. The voltage profile before and after the placement of DG to the 33-bus distribution network, for the 15^th load hour, has

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