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1.5 Optimum Placement of RDG and Shunt Capacitor to the Distribution Network
ОглавлениеIn 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 | 1.0264×108 | -450.0000 | |
| Std. Dev | 0 | 8.1216×10-2 | 0 | 3.0745×108 | 0 | |
| Rank | 2 | 4 | 3 | 5 | 1 | |
| F5 | Best FF | 1.4051×104 | 1.0443×104 | 1.1914×104 | 7.9132×103 | 7.5236×103 |
| Worst FF | 3.6183×104 | 1.7420×104 | 5.3257×104 | 1.8809×104 | 9.7728×103 | |
| Mean | 2.3954×104 | 1.3856×104 | 2.8358×104 | 1.1950×104 | 8.4225×103 | |
| Std. Dev | 7.0703×104 | 2.2846×103 | 1.0637×104 | 3.2094×103 | 3.1287×103 | |
| Rank | 5 | 3 | 4 | 2 | 1 | |
| F6 | Best FF | 390.0070 | 405.8698 | 390.0033 | 390.0007 | 390.0002 |
| Worst FF | 462.3391 | 407.8258 | 449.3571 | 457.6640 | 390.0492 | |
| Mean | 412.4370 | 406.5812 | 403.1944 | 401.5661 | 390.0157 | |
| Std. Dev | 25.1252 | 0.5722 | 16.8726 | 18.9630 | 0.0176 | |
| Rank | 4 | 5 | 3 | 2 | 1 | |
| F7 | Best FF | -179.9926 | 4.2916×103 | -179.9926 | -179.9926 | -180.0000 |
| Worst FF | -179.9803 | 8.2175×103 | -179.9459 | -179.8050 | -179.9901 | |
| Mean | -179.9764 | 5.8506×103 | -179.9754 | -179.9596 | -179.9943 | |
| Std. Dev | 1.8121×10-2 | 1.2183×103 | 1.7129×10-2 | 5.3002×10-2 | 3.7955×10-3 | |
| Rank | 2 | 5 | 3 | 4 | 1 | |
| F8 | Best FF | -119.5245 | -119.3254 | -119.9887 | -120.6199 | -119.5256 |
| Worst FF | -119.0590 | -119.0550 | -119.9010 | -120.2961 | -119.3143 | |
| Mean | -119.2094 | -119.1229 | -119.9549 | -120.4613 | -119.3801 | |
| Std. Dev | 0.1392 | 7.3253×10-2 | 2.3401×10-2 | 0.1028 | 7.3663×10-2 | |
| Rank | 4 | 5 | 2 | 1 | 3 | |
| F9 | Best FF | -321.0454 | -164.8339 | -172.7972 | -293.1865 | -330.0000 |
| Worst FF | -302.1412 | -129.4599 | -55.3934 | -184.5407 | -330.0000 | |
| Mean | -313.3842 | -147.5225 | -123.7465 | -241.1199 | -330.0000 | |
| Std. Dev | 5.4141 | 11.0234 | 41.4742 | 42.6722 | 0 | |
| Rank | 2 | 4 | 5 | 3 | 1 | |
| F10 | Best FF | -217.5703 | -150.7517 | -100.1658 | -225.9089 | -256.3699 |
| Worst FF | -92.2075 | -104.3583 | 91.8576 | -100.6526 | -184.7313 | |
| Mean | -153.3029 | -125.7336 | -9.2147 | -151.2863 | -213.3927 | |
| Std. Dev | 38.9758 | 14.0585 | 62.1465 | 38.1157 | 17.6163 | |
| Rank | 3 | 4 | 5 | 2 | 1 |
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 | 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 |
