For the study purpose, two different distribution networks are considered. The first distribution network is a 33-bus distribution network having a total active power demand of 3715 kW with active power loss of 202.6771 kW [65] at the peak load level. The other one is 69-bus distribution network having active power demand as 3802.2 kW and, reactive power demand as 2694.6 kVAr [67]. The active power loss at the peak load level of the 69-bus distribution network is 224.96 kW.
The size of the solar PV can’t be varied. The installed capacity of solar PV is constant. So, the size of the solar PV has been optimized for a particular hour. In this study, the size of the solar PV has been optimized for the 15th hour of the day correspond to which the load demand is 1.0 pu, and solar PV power generation is 0.7424 pu. The solar PV system generates and injects the active power to the distribution network. The active power injection from a solar PV plant for any particular hour can be expressed as in (Equation 1.33)
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 |
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