In this section, the proposed BO technique for enhancement of the system loadability ((lambda_{{{text{max}}}})) and real power loss mitigation is applied on 33 & 69 bus distribution test systems for the scenarios and cases shown in Table 1. In turn, each case is divided into two sub-cases a) optimal connection of DGs in the initial network without application of ODNR problem b) Optimal connection of DGs in the optimal reconfigured network which is obtained from the ODNR problem. The tuned BO algorithm parameters are shown in Table 2. All the simulations are implemented in MATLAB R2017a platform and carried out in computer having Core i7 7200U 3.10 GHz, 16 GB RAM.

Table 1 Scenarios and cases considered in this paper
Table 2 BO algorithm parameters

33 Bus radial distribution system

The line & load data of the system is taken from [29]. The system has 33 section switches and 5 tie switches. Normally tie switches are in open condition. The load on the system is 3.715 MW + j 2.3 MVAR. The base case real power loss is 210.98 kW, system loadability is 3.4, and the minimum voltage is 0.9038 p.u.

From the results of the ODNR problem, the points observed are.

  1. 1.

    In case of (f_{1}) optimization, the real power loss is reduced to 138.5513 kW. And also, in this case, system loadability is improved to 4.87. For this case, switches given by the algorithm are 7, 9, 14, 32, and 37.

  2. 2.

    In case of (f_{2}) optimization, the system loadability is enhanced to 5.23. And also, in this case, system network power loss is reduced to 139.9782 kW. For this case, switches given by the algorithm are 7, 9, 14, 28, and 32.

  3. 3.

    From the above observations, it is perceived that in the case of (f_{2}) maximization, both objectives is improved. Therefore, the optimal switches determined by the algorithm for enhancement of (f_{2}) are considered for case-3b.

Table 3 shows the outcomes of the OCDG problem for scenario 1. From the outcomes tabulated in Table 3, the succeeding points are observed. In case-1a & case-1b, the real power loss is reduced to 12.7458 kW & 18.7531 kW, respectively. It is observed that the real power loss of the system is reduced to the lowest value in the case of DGs placed in the initial configured network. In Case-2a & case-2b, system loadability is improved to 5.1 & 7.23 from 3.4 & 5.23, respectively. It is noticed that system loadability is improved to the utmost value in the case of DGs connected optimally in the optimal reconfigured network, i.e., in case-2b. From the outcomes of case-2a & case-2b, it is also noticed that real power loss is only reduced to 86.5804 kW and 98.8904 kW, respectively. To improve both loss reduction and system loadability, a multi-objective approach with the Max–Min method is taken in case-3. For case-3a, the minimum ( left( {F_{k}^{max} } right)) and maximum ( (F_{k}^{min} ) ) objective function values taken for real power loss are 12 kW,210.98 kW and for maximum loadability are 1/5.1, 1/3.4. For case-3b, the minimum and maximum objective function values taken for real power loss are 18 kW, 139.9782 kW, for maximum loadability are 1/7.23,1/5.23. The convergence graphs for all cases of scenario-1 are shown in Fig. 2.

Table 3 Simulation results of 33 bus system for scenario-1
Fig. 2
figure 2

Scenario-1 outcomes convergence graphs for 33 bus system

From the results of case-3a & 3b, the points observed are as follows.

  1. 1.

    In case-3a, the system loadability is enhanced to 4.78 from 3.4, and loss is reduced to 39.1317 kW from 210.98 kW shows an improvement in both the objectives unlike in case-1a & case-2a.

  2. 2.

    In case-3b, the system loadability is enhanced to 6.76 from 5.23 and loss is reduced to 42.7188 kW from 139.9782 kW shows an improvement in both the objectives unlike in case-1b & case-2b.

  3. 3.

    In scenario-1, the utmost percentage of improvement in both the objectives is observed in case-3b, i.e., in the case of DGs optimally connected in the optimal reconfigured network while optimizing (f_{1}) and (f_{2}) using the Max–Min method.

The minimum (left( {F_{k}^{min} } right) ) and maximum ( left( {F_{k}^{max} } right)) objective function values taken in scenario-2 for case-1a are 12 kW,210.98 kW, for case-1b are 1/5.1, 1/3.4, for case-2a are 18 kW, 139.9782 kW and for case-2b are 1/7.23,1/5.23 for system loadability. The minimum limit for DGs real power injection is taken as 50% of the system real power demand i.e., 3715*0.5 = 1857 kW, and the maximum real power injective power limit by DGs is taken as 100% injection level.

Table 4 shows the outcomes of the OCDG problem for scenario 2. Figure 3 depicts the comparison between the performance indices of scenario-1 & 2. From Fig. 3 it is observed that even though there is a significant difference between the % KVA injection by DGs into the distribution system in scenario-1 & scenario-2 cases, but the difference between the performance indices is very less. Therefore, it can be concluded that the optimal placement of DGs in scenario-2 gives a better improvement in objectives (% PLR & % MLI) with less amount of % KVA injection by the DGs into the system.

Table 4 Simulation results of 33 bus system for scenario-2
Fig. 3
figure 3

Comparison between the performance indices of scenario 1 & 2 for 33 bus system

From Table 4, the succeeding points are noticed. In the case of (f_{1}) and (f_{3}) optimization, loss is reduced to 23.715 kW & 23.446 kW in case-1a & case-1b, respectively. It is noticed that the amount of loss reduction is almost the same for both cases. In the case of (f_{2}) and (f_{3}) optimization, system loadability is improved to 4.73 & 6.69 in case-2a & case-2b, respectively, but the loss is reduced to 55.4613 kW and 56.2606 kW only. Therefore, to improve the real power loss reduction along with loadability, optimization of (f_{1, } f_{2}), and (f_{3}) are considered in case-3a & case-3b. The points observed from case-3a & case-3b are real power loss is reduced to 45.1702 kW, 46.3242 kW, respectively, system loadability is increased to 4.7, 6.64. From case-3a & 3b of scenario-2, it is concluded that the optimal connection of DGs in the reconfigured network shows better improvement in both the objectives, i.e., loss reduction and system loadability enhancement. The convergence graphs for all cases of scenario-2 are shown in Fig. 4. Based on the above discussions it can be concluded that among all the cases in scenario-1 & 2, the highest percentage of improvement in both the objectives is observed in case-3b of scenario-1, i.e., by the injection of 74.92% kVA into the system, real power loss is reduced to 79.75%, system lodability is increased by 98.92%. An almost equal percentage of improvement in both objectives with less amount of % kVA injection by DGs into the system is observed in case-3b of scenario-2, i.e., with 64.69% kVA injection into the system, the loss is reduced to 78.04%, system loadability is increased by 95.29%.

Fig. 4
figure 4

Scenario-2 outcomes convergence graphs for 33 bus system

To access the capability of the BO optimization technique to the proposed methodology, the results obtained are contrasted with the befitting methods and algorithms that are accessible in the literature and shown in Table 5. From Table 5, it is observed that in case of power loss minimization by the optimal placing of DGs in the initial configured case & optimal reconfigured case, the proposed BO algorithm reduces the real power loss to 93.95% & 91.11, respectively, whereas HTLBO-GWO, HAS-PABC, UVDA reduces real power loss to 93.51%, 92.51%, and 87.98%, respectively. In the case of loadability maximization, the BO algorithm improves it to 50% whereas HPSO improves it to 48.23% only. In scenario-2, in the case of loss minimization, the loss is reduced to 88.76% with 53.01 kW injection by DGs into the system, whereas the BSOA algorithm reduces it to 85.94% with % 50 kW real power injection by DGs into the system. In [29], with 40% kW or 47.05 kVA injection by DGs into the system, real power loss reduced to 71.75%, system loadability increased to 26.76%. But with the proposed method in this paper, with 64.69% kVA injection by DGs into the system, real power loss reduced to 78.09%, maximum loadabilty increased to 95.29% that shows an improvement in both the objectives unlike the method in [29] which shows the efficacy of the proposed method.

Table 5 Comparison results of 33 bus system

69 Bus radial distribution System

The line & load data of the system are taken from [29]. The system has 69 section switches and 5 tie switches. Normally tie switches are in open condition. The load on the system is 3.801 MW + j 2.693 MVAR. The base case real power loss is 224.9515 kW, loadability of the system is 3.21 and the minimum voltage is 0.9091 p.u.

From the results of the ODNR problem, the following points are observed. In the case of individual optimization of objective functions (f_{1}) & (f_{2}), switches given by the algorithm are the same, i.e., they are 14, 58, 61, 69, and 70. For these switch combinations real power loss is mitigated to 98.55 kW, lodability enhanced to 5.23. Therefore, the above-mentioned optimal switches are considered for the OCDG problem in the optimal reconfigured network case.

Table 6 shows the outcomes of the OCDG problem for scenario 1. In case-1a & 1b, the power loss is reduced to 4.487 kW & 5.3082 kW. It is observed that the power loss is reduced to the lowest value in the case of DGs connected optimally in the initial configured network. In case-2a & case-2b, the system loadability is improved to 4.91 &7.71, respectively, but the real power loss is only reduced to 89.8601 kW & 93.9651 kW. In case-3a & 3b, the system loadability is improved to 4.61 & 7.07 and real power loss is reduced to 30.2921 kW & 25.313, respectively. From scenario-1 outcomes, it can be deduced that both the loadability and real power loss reduction are well improved in case-3b. The convergence graphs for all cases of scenario-1 are shown in Fig. 5. Figure 6 depicts the comparison between the performance indices of scenario-1 & 2. From Fig. 6, it is noticed that the optimal connection of DGs in scenario-2 gives a better improvement in objectives (% PLR & % MLI) with less amount of % KVA injection by the DGs into the system.

Table 6 Simulation results of 69 bus system for scenario-1
Fig. 5
figure 5

Scenario-1 outcomes convergence graphs for 69 bus system

Fig. 6
figure 6

Comparison between the performance indices of scenario 1 & 2 for 69 bus system

Table 7 shows the outcomes of the OCDG problem for scenario 2. In case-1a & 1b, the real power loss is reduced to 9.6078 & 7.0345 kW, respectively, but the system loadability is improved to 4.09 & 6.4 only. In case-2a & 2b, the system loadability is enhanced to 4.51 & 7.04, respectively, but the power loss is reduced to 35.096 kW & 46.448 kW only. Among case-3a & case-3b, better enhancement in both objectives is observed in optimal connection of DGs in optimal network reconfigured case, i.e., real power loss is reduced to 23.8112 kW and system loadability is enhanced to 6.94. The convergence graphs for all cases of scenario-2 are shown in Fig. 7. Based on the above discussions it can be concluded that among all the cases in scenario-1 & 2, better improvement in both objectives with less % KVA injection by DGs is observed in case-3b of scenario-2, i.e., real power loss is reduced to 89.414%, maximum loadability is increased to 116.19%.

Table 7 Simulation results of 69 bus system for scenario-2
Fig. 7
figure 7

Scenario-2 outcomes convergence graphs for 69 bus system

To access the capability of the BO optimization technique to the proposed methodology, the results obtained are contrasted with the befitting methods and algorithms that are accessible in the literature and shown in Table 8. The proposed algorithm yields to produce the same result produced by the HPSO algorithm in the literature concerning loadabilty of the system as an objective function and the proposed algorithm performs well in mitigating the real power with comparison to the HTLBO-GWO algorithm. In [29], with 40% KW or 47.06 KVA injection by DGs into the system, real power loss reduced to 87.206%, system loadability increased to 27.72%. But with the proposed method in this paper, with 63.98% KVA injection by DGs into the system, real power loss reduced to 89.414%, system loadabilty increased to 116.19% that shows an improvement in both the objectives unlike the method in [29] which shows the efficacy of the proposed method.

Table 8 Comparison results of 69 bus system

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Disclaimer:

This article is autogenerated using RSS feeds and has not been created or edited by OA JF.

Click here for Source link (https://www.springeropen.com/)