entry “NA” means not applicable.
So, it may be inferred that the proposed novel SPBO method works fine to solve ten CEC-2005 benchmark functions considered in this book chapter.
1.5 Optimum Placement of RDG and Shunt Capacitor to the Distribution Network
In this current book chapter, optimum placement of RDG (biomass and solar PV) and shunt capacitor has been considered for the study purpose. The DG optimization problem may be divided into two sections, such as optimization of the location of DG and optimization of the size of DG. To optimize both the location and size of the DGs simultaneously, mixed discrete SPBO has been used in this study. In the mixed discrete SPBO, the sizes of the DGs are considered as the continuous variables, and locations of the DGs are considered as the discrete variables. To optimize the sizes and locations of the biomass, solar PV, and shunt capacitor, a multi- objective function is considered in this study. The objective function is described in (Equation 1. 12). The study has been carried out for a variable load demand for a day. Load demand of a network is not constant throughout the day. It varies with time, so as the power generation of the solar PV. Table 1.4 shows the load demand and electrical power generation from the solar PV for a day. The graphical representation of the variation of load demand (pu) and power generation from PV (pu) with respect to the different load hours of a day has been portrayed in Figure 1.2.
Table 1.3 Optimization result of CEC-2005 benchmark functions.
| Functions | Attributes | PSO | TLBO | CS | SOS | SPBO |
|---|---|---|---|---|---|---|
| F1 | Best FF | -450.0000 | 4.3423×103 | 285.0288 | -450.0000 | -450.0000 |
| Worst FF | -450.0000 | 1.2868×104 | 2.6304×104 | -450.0000 | -450.0000 | |
| Mean | -450.0000 | 6.1561×103 | 9.2000×103 | -450.0000 | -450.0000 | |
| Std. Dev | 0 | 2.4294×103 | 8.1507×103 | 0 | 0 | |
| Rank | 3 | 5 | 4 | 2 | 1 | |
| F2 | Best FF | -450.0000 | -450.0000 | -450.0000 | -450.0000 | -450.0000 |
| Worst FF | -450.0000 | -450.0000 | -449.9989 | 7.8615×108 | -450.0000 | |
| Mean | -450.0000 | -450.0000 | -449.9998 | 7.8615×107 | -450.0000 | |
| Std. Dev | 0 | 0 | 3.3800×10-4 | 2.3584×108 | 0 | |
| Rank | 2 | 3 | 4 | 5 | 1 | |
| F3 | Best FF | 2.4082×106 | 1.2404×107 | 2.7113×106 | 1.4156×106 | 1.1252×106 |
| Worst FF | 1.4310×107 | 9.0300×107 | 4.4354×106 | 6.8667×106 | 5.5039×106 | |
| Mean | 5.9320×106 | 7.4449×107 | 3.5213×106 | 3.0747×106 | 3.6913×106 | |
| Std. Dev | 3.6300×106 | 1.2404×107 | 7.8163×105 | 1.4156×106 | 1.2379×106 | |
| Rank | 3 | 5 | 4 | 2 | 1 | |
| F4 | Best FF | -450.0000 | -449.9981 | -450.0000 | -449.9957 | -450.0000 |
| Worst FF | -450.0000 | -449.7224 | -450.0000 | 1.025×109 | -450.0000 | |
| Mean | -450.0000 | -449.9655 |
-450.0000
|
