An Improved Human-Inspired Algorithm for Distribution Network Stochastic Reconfiguration Using a Multi-Objective Intelligent Framework and Unscented Transformation
Abstract
:1. Introduction
1.1. Motivation
1.2. Literature Review and Research Gap
- The review of the literature has shown that the operation of the distribution network is based on the optimization of the network configuration with various goals, including the minimization of losses and voltage deviations, as well as the improvement of reliability and power quality in various studies, but the investigation of these goals is scattered and single- or double-objective. Moreover, it has not been evaluated as a comprehensive objective function;
- From the evaluation of the literature, it is clear that the lack of a multi-objective optimization structure consisting of various objectives of minimizing power losses, improving reliability indicators, and also improving distribution network power quality indicators in solving the reconfiguration problem to achieve the optimal network configuration by creating a compromise between different goals is felt;
- In previous studies, the reconfiguration of distribution networks has been performed using various intelligent optimization methods to determine the optimal configuration of the network. Considering that an optimization method cannot achieve successful performance for all different problems with different objective function structure, it is important to present an intelligent optimization method with the ability to robustly avoid premature convergence to determine the optimal configuration of the network and achieve the best goals;
- Moreover, one of the challenges facing the reconfiguration problem in the distribution network is the uncertainty of the network load, and in the literature evaluating its effect on the network operators decision-making and also integrating the reconfiguration with power quality and reliability objectives are not addressed well.
1.3. Contributions
- The stochastic reconfiguration of a 33-bus electrical distribution network is performed using a multi-objective intelligent framework (MOIF) to minimize power losses and improve power quality and reliability indices considering the network load uncertainty using an unscented transformation (UT) [38]. Two power quality indicators, the decline in voltage sags and the system’s average RMS fluctuation frequency, are considered. Also, the average system interruption frequency index, the instantaneous average interruption frequency index, and the system average interruption frequency index are reliability indices;
- The UT is used to model the uncertainty of the network load in the stochastic reconfiguration problem. Compared with the Monte Carlo simulation (MCS) with high computational cost, the UT has low calculation time, and no assumptions are required to simplify the model,
- To validate the IMTBO, it has been compared to conventional MTBO, particle swarm optimization, and the artificial electric field algorithm [41] in solving the reconfiguration problem based on the MOIF;
- Moreover, the deterministic and stochastic MOIF results are compared to evaluate the effect of the uncertainty consideration on solving the reconfiguration problem.
1.4. Paper Structure
2. Problem Statement
2.1. Objective Function
2.2. Constraints
2.2.1. Power Flow
2.2.2. Voltage
2.2.3. Current
2.2.4. Radiality Condition
3. Proposed Optimizer
3.1. Overview of the MTBO
3.1.1. Inspiration
3.1.2. First Phase: Coordinated Mountaineering
3.1.3. Second Phase: Impact of Natural Catastrophes
3.1.4. Third Phase: Concerted Action by Many People to Prevent Catastrophes
3.1.5. Fourth Phase: Potential Demise of Members
Algorithm 1: Mountaineering Team-Based Optimization (MTBO) |
1: Setting MTBO control parameters: scaling factors including Li, Ai, and Mi, the number of iterations of the Itermax, and the number of its population NP and set the number of iterations for individuals Iter = 0; 2: Random generation of the initial population NP (I = 1, 2, …, NP); 3: ; 4: Assessing the level of physical fitness of each individual; 5: while the i till maximum no of iterations Itermax do 6: Setting the number of iterations Iter = Iter + 1; 7: for i = 1 to NP do 8: ; 9: 10: 11: 12: 13: ; 14: 15: else 16: ; 17: end if 18: if 19: ; 20: end if 21: if 22: ; 23: end if 24: end for 25: end while Return the best solution is obtained via MTBO: |
3.2. Overview of the Improved MTBO (IMTBO)
3.3. Implementation of the IMTBO
4. Uncertainty Modeling Based on the UT
- -
- Step 1: Choose 2n + 1 samples from the uncertain input data:
- -
- Step 2: Assess the weighting factor of individual sample points:
- -
- Step 3: Sample 2n + 1 points to the nonlinear function to obtain output samples as per Equation (31).
- -
- Step 4: Assess and of the output variable θ.
5. Results and Discussions
5.1. Results of the Base Network (Case 1)
5.2. Results of Dual-Objective Reconfiguration (Cases 2 and 3)
5.3. Results of MOIF for Reconfiguration (Case 4)
5.4. Analysis of Different Cases
5.5. Results of MOIF for Reconfiguration Considering Demand Uncertainty (Case 5)
6. Conclusions
- According to the results, buses 6, 7, 23, 24, and 29 were the most sensitive to the spread of voltage sag across the entire network, with bus 29 affecting the plurality of network buses;
- In terms of power quality and reliability indicators, as well as an objective function value, simulation results demonstrated that the IMTBO optimization method was preferable to PSO, AEFA, and conventional MTBO;
- The results showed that the success of the proposed MOIF reduced active losses by 30.94%, improved the SARFI index by 33.68%, and enhanced the ASIFI and MAIFI indices by 6.43% and 44.57%, respectively;
- The MOIF for reconfiguration has enhanced network performance in terms of power quality and reliability in comparison to single-objective reconfiguration, whereas single-objective reconfiguration cannot produce a desirable compromise between all objectives. In addition, the superior efficacy of the proposed IMTBO-based method compared to Refs. [42,43,44,45] is validated;
- Moreover, the results of the stochastic reconfiguration based on the UT, clearly showed that the losses were increased, and also the power quality and reliability indices were weakened compared to the deterministic MOIF without uncertainty. The results illustrated that considering the demand uncertainty allows the network operator to make accurate decisions and to be aware of the network’s optimal configuration. The results showed that the UT was able to model the uncertainty simply with a low number of sampling points.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Algorithm | Parameter |
---|---|
MTBO | -- |
PSO [32] | C1 = C2 = 2 and W: Linear decline from 0.9 to 0.1 |
AEFA [33,34] | Initial value used in Coulomb’s constant (K0) = 100 |
Item | Base Network |
---|---|
Opened Switches | 33, 34, 35, 36, 37 |
(kW) | 202.68 |
16,104 | |
8.2331 | |
2.3508 | |
4.6479 | |
1.3614 | |
1 |
Item/Method | Base Network | Loss + Power Quality (Case 2) | Loss + Reliability (Case 3) |
---|---|---|---|
Opened Switches | 33, 34, 35, 36, 37 | 7, 9, 14, 28, 32 | 7, 8, 9, 16, 28 |
(kW) | 202.68 | 149.9782 | 153.5122 |
16,104 | 10,680 | 11,016 | |
8.23 | 5.46 | 5.63 | |
2.35 | 2.33 | 2.11 | |
4.64 | 3.95 | 2.98 | |
1.36 | 1.36 | 1.33 | |
1 | 0.7629 | 0.81934 |
Item/Method | Base Network | IMTBO | PSO | AEFA | MTBO |
---|---|---|---|---|---|
Opened Switches | 33, 34, 35, 36, 37 | 7, 9, 14, 28, 32 | 7, 10, 14, 28, 32 | 7, 9, 14, 17, 28 | 9, 28, 32, 33, 34 |
(kW) | 202.68 | 139.97 | 166.94 | 146.28 | 144.77 |
16,104 | 10,680 | 11,520 | 10,848 | 10,848 | |
8.23 | 5.46 | 5.88 | 5.54 | 5.54 | |
2.35 | 2.19 | 2.35 | 2.19 | 2.16 | |
4.64 | 2.57 | 2.99 | 2.95 | 2.81 | |
1.36 | 1.35 | 1.36 | 1.39 | 1.37 | |
1 | 0.74372 | 0.74594 | 0.76256 | 0.75876 | |
- | 142.36 | 144.11 | 148.57 | 150.68 |
Item/Method | IMTBO | MFO [47] | EGA [48] | SSA [49] | BWOA [50] |
---|---|---|---|---|---|
Opened Switches | 7, 9, 14, 28, 32 | 7, 10, 14, 28, 36 | 10, 13, 16, 28, 33 | 7, 14, 30, 35, 37 | 7, 9, 14, 28, 32 |
(kW) | 139.97 | 142.42 | 164.41 | 115.73 | 139.98 |
1.35 | -- | 2.158 | 2.2716 | -- |
Objective Function | Lines | (kW) | SARFI | ASIFI | MAIFI | SAIFI | |
---|---|---|---|---|---|---|---|
Base network (Case 1) | 33, 34, 35, 36, 37 | 16,104 | 202.68 | 8.23 | 2.35 | 4.64 | 1.36 |
6, 9, 14, 16, 28 | 10,512 | 154.81 | 5.39 | 2.20 | 2.96 | 1.06 | |
7, 9, 14, 17, 28 | 10,848 | 139.95 | 5.54 | 2.09 | 2.95 | 1.39 | |
6, 10, 15, 27, 34 | 10,760 | 163.63 | 5.37 | 2.20 | 2.99 | 1.35 | |
10, 13, 16, 28, 33 | 12,696 | 161.58 | 6.49 | 1.99 | 3.01 | 1.08 | |
6, 10, 13, 26, 31 | 11,832 | 174.14 | 6.04 | 2.52 | 2.56 | 1.06 | |
6, 9, 14, 17, 24 | 11,208 | 184.60 | 5.73 | 2.50 | 3.23 | 1.05 | |
Case 2 | 7, 9, 14, 28, 32 | 10,680 | 149.97 | 5.48 | 2.33 | 3.95 | 1.36 |
Case 3 | 7, 8, 9, 16, 28 | 11,016 | 153.51 | 5.63 | 2.11 | 2.98 | 1.33 |
Case 4 | 7, 9, 14, 28, 32 | 10,680 | 139.97 | 5.46 | 2.19 | 2.57 | 1.35 |
Case | Lines | SARFI | ASIFI | MAIFI | SAIFI | ||
---|---|---|---|---|---|---|---|
Deterministic (Without uncertainty, Case 4) | 7, 9, 14, 28, 32 | 10,680 | 139.97 | 5.46 | 2.19 | 2.57 | 1.35 |
Stochastic (With uncertainty, Case 5) | 7, 10, 28, 32, 34 | 11,256 5.39 | 150.64 7.62 | 5.75 5.31 | 2.24 2.28 | 2.74 6.61 | 1.37 1.48 |
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Zhu, M.; Arabi Nowdeh, S.; Daskalopulu, A. An Improved Human-Inspired Algorithm for Distribution Network Stochastic Reconfiguration Using a Multi-Objective Intelligent Framework and Unscented Transformation. Mathematics 2023, 11, 3658. https://doi.org/10.3390/math11173658
Zhu M, Arabi Nowdeh S, Daskalopulu A. An Improved Human-Inspired Algorithm for Distribution Network Stochastic Reconfiguration Using a Multi-Objective Intelligent Framework and Unscented Transformation. Mathematics. 2023; 11(17):3658. https://doi.org/10.3390/math11173658
Chicago/Turabian StyleZhu, Min, Saber Arabi Nowdeh, and Aspassia Daskalopulu. 2023. "An Improved Human-Inspired Algorithm for Distribution Network Stochastic Reconfiguration Using a Multi-Objective Intelligent Framework and Unscented Transformation" Mathematics 11, no. 17: 3658. https://doi.org/10.3390/math11173658
APA StyleZhu, M., Arabi Nowdeh, S., & Daskalopulu, A. (2023). An Improved Human-Inspired Algorithm for Distribution Network Stochastic Reconfiguration Using a Multi-Objective Intelligent Framework and Unscented Transformation. Mathematics, 11(17), 3658. https://doi.org/10.3390/math11173658