**5. Results and Discussion**

The DG location, DG size, and EDS reliability are obtained and analyzed. The 33 bus EDS (Figure A1 of Appendix A.1) is considered in this study. The branch and load data for this EDS are adopted from [76]. It contains 33 buses and 32-branches with a total of 3.715 MW and 2.3 MVAr AP and RP loads, respectively. This EDS operates at 12.66 kV, 100 MVA base values. The APL and RPL for without DG case are obtained as 0.211009 MW and 0.143056 MVAr, respectively. The objective function (OF) minimization is done by implementing the CF-based PSO, as explained in Section 2. The following steps are followed to obtain the results.


#### *5.1. DG Location and DG Rating*

The bus number is obtained to allocate WTG, SPV, and BSS. The two indexes are implemented to obtain the locations as described in Section 2.1. It is observed from the analysis that Index-1 provides the location suitable for a single DG. This index examines the effective apparent power injection to the buses. The Load Factor value of *lth* line depends on whether the *lth* is in the path of the *ith* bus to the source node or not. The multiplication of Load Factor and injected apparent power provides the APL and RPL of *lth* line due to the *ith* bus *APa* injection. Thus, the maximum value of Index-1 at *ith* bus indicates the candidate bus to place one DG. The first six values of this index for respective buses are provided in Table 3.

The optimal siting for several DGs are found by implementing the Index-2. This index provides the hierarchy of weak buses in the EDS. It shows the sensitivity of the bus towards voltage collapse. The value of Index-2 must be greater than or equals to zero for ensuring the stable operation of the distribution system. The minimum value of this index depicts more sensitivity to the voltage collapse and thus, referred to as the weak bus. The optimal location(s) and size(s) of WTG, SPV, and BSS for three cases are obtained and reproduced in Table 7. The DGs are accommodated according to the locations obtained from the indexes, as mentioned in Section 2.1. The DG size and minimum APL are then evaluated, implementing CF-PSO as described in Section 2.


**Table 7.** DG location and DG size obtained.

#### *5.2. APL, RPL, and Bus Voltages*

The accommodation of DG at an optimal location with optimal size reflects in VP improvement and minimization of APL and RPL. Most of the research has concentrated on APL minimization because of the dominance of *I*2*R* losses in the EDS. In contrast, the RPL minimization for overall voltage improvement of all the 32 buses of the EDS has also been observed. The estimation of APL, RPL, and VP is considered before analyzing the system's reliability. This is done to analyze the system's reliability with the optimal DG size, DG location, minimum power loss, and better VP.

Several kinds of research are performed to obtain APL minimization, which is cited in Table 2 for single and multiple DGs, respectively. It is observed from Table 2 that the authors of the mentioned literature have not dealt with the cases considering various DGs combination. Therefore, it is vital to observe that the results obtained considering several types of DGs are compared with the conventional DGs [77]. The output results obtained for the APL are tabulated in Table 8. This table shows that the APL value is better for Case 1, and comparable for Case 2 and Case 3. The slight variations in APL for Case 2 and Case 3 are observed because the authors have considered the pf of WTG only. Furthermore, the bus voltage profile with one DG and multiple DGs is drawn in Figure 7. The voltages at all the buses vary according to the real power loss and reactive power loss in the distribution system. Therefore, the system requires real power support for active power loss minimization, which improves the bus voltages by compensating the *I*2*R* losses. Furthermore, it is concluded from Table 8 that the active power loss minimization is not reduced significantly for Case 3 as compared to Case 2. Thus, there is a marginal improvement in bus voltage profile for Case 3 as compared to Case 2, which is depicted in Figure 7. Also, the improvement in bus voltages is observed when multiple DGs are placed. This VP is further improved at 0.85 and 0.82 pfs. This is because of increment in reactive power support at system buses. It is the point of interest to know about the two voltage peaks when the system is operated with single DG. The two voltage peaks appear at bus number 7 and 26 because these buses are directly connected to bus 6, at which single DG is placed optimally. Also, the size of the single DG is greater than the sum of the size of two DG and slightly lesser than the sum of the size of three DG, as obtained in Table 8. A comparison between present work and the best available method is made for ELM. Simultaneously, from Table 9 it can be inferred that the minimum bus voltage is improved and RPL is minimized with the implementation of multiple DGs at different pfs as illustrated. The graphical representation of APL and RPL for without DG, one DG, and multiple DGs are represented in Figure 8.

**Figure 7.** Voltage profile for 33 bus system (WTG at 0.9 pf).



**Table 9.** Minimum voltage, DG location, and RPL (MVAr) obtained.


**Figure 8.** Active and Reactive power losses (WTG at UPF).

#### *5.3. Reliability Assessment*

The indices obtained show the improvement in the system's reliability. The indices are calculated for two different reliability data of DGs. It is observed that the indices are dependent on two reliability data, namely *λp* and RT of the system's elements. The present work has considered different reliability data for DG only. The best reliability improvement is observed for 0.2 of *λp* and 12 h of RT. A detailed description of the DG reliability data effect on indices is given as per the following Scenarios.


Scenarios 1, 2, and 3 are considered by fixing the RT and varying *λp*. The appropriate case from the first three cases is then considered for variable RT to extract the best case from the top Five Scenarios. The values of these reliability data are fed manually in the optimization technique to get the values of indices for the system's reliability improvement. Furthermore, the following key assumptions are considered to assess the reliability of the EDS.


#### 5.3.1. Effect on Load-Oriented Indices

The EENS and AENS are obtained and tabulated in Tables 10 and 11 for all cases as illustrated in Figure 9a–d, respectively. It is important to note that the EENS and AENS decrease with the number of DGs, and these are also decreased with decreasing values of *λp* and RT. As the increasing number of DGs are integrated into an EDS, the supplied energy is improved in the EDS, and thus, the indices related to the energy not supplied are reduced. This reduction is more while integrating the DGs with lesser *λp* and RT values. The reducing EENS and AENS are desirable, and thus, the EDS reliability enhances with the integration of DGs with appropriate reliability data values.

**Table 10.** EENS (MWh per year) evaluated for different Scenarios.



#### 5.3.2. Effect on System-Oriented Indices

The SAIDI, and SAIFI are obtained and tabulated in Tables 12 and 13 for all cases considering all scenarios as shown in Figure 10a–d, respectively. The important point to be noted here that the SAIDI, and SAIFI, decreases with the increasing number of DGs; SAIDI is also decreased with the decreasing values of *λp* and RT. It is worthy to note that the SAIFI is not affected by the RT of the DG. It is because this index is independent of RT as shown in Equation (43). As the increasing number of DGs are incorporated into the EDS, the duration of the interruption and the number of interruptions occurred are reduced in the system. Thus, the SAIDI, and SAIFI are reduced. Customer Average Interruption Duration Index can be determined using the ratio of SAIDI, and SAIFI as shown in Equation (45). The reduction in the value of indices is more while integrating the DGs with lesser *λp* and RT values. Moreover, reducing SAIDI and SAIFI are desirable for EDS reliability enhancement.

**Figure 9.** Load-oriented indices for different DG reliability data (**a**) EENS at different *λp*, (**b**) EENS at different RT, (**c**) AENS at different *λp*, and (**d**) AENS at different RT.



**Table 13.** SAIFI (failure per customer per year) evaluated for different Scenarios.


The ASAI is determined and tabulated in Table 14 for all cases considering six scenarios as illustrated in Figure 11a,b. The electrical power service availability for all loads increases with the integration of multiple DGs. This index is further increased when DGs have a lower *λp* and RT values. The increment in ASAI increases leads to the decrement in ASUI as given in Equations (46a) and (46c) which is desirable for the EDS reliability improvement.

**Table 14.** ASAI (pu) evaluated for different Scenarios.


**Figure 10.** System-oriented indices for different DG reliability data (**a**) SAIDI at different *λp*, (**b**) SAIDI at different RT, (**c**) SAIFI at different *λp*, and (**d**) SAIFI at different RT.

**Figure 11.** System-oriented indices for different DG reliability data (**a**) ASAI at different *λp*, (**b**) ASAI at different RT.
