A Quasioppositional-Chaotic Symbiotic Organisms Search Algorithm for Distribution Network Reconfiguration with Distributed Generations

Abstract

This study suggests an enhanced metaheuristic method based on the Symbiotic Organisms Search (SOS) algorithm, namely, Quasioppositional Chaotic Symbiotic Organisms Search (QOCSOS). It aims to optimize the network configuration simultaneously and allocate distributed generation (DG) subject to the minimum real power loss in radial distribution networks (RDNs). The suggested method is developed by integrating the Quasiopposition-Based Learning (QOBL) as well as Chaotic Local Search (CLS) approaches into the original SOS algorithm to obtain better global search capacity. The proposed QOCSOS algorithm is tested on 33-, 69-, and 119-bus RDNs to verify its effectiveness. The findings demonstrate that the suggested QOCSOS technique outperformed the original SOS and provided higher-quality alternatives than many other methods studied. Accordingly, the proposed QOCSOS algorithm is favourable in adapting to the DG placement problems and optimal distribution network reconfiguration.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

In distribution networks, reconfiguration is a traditional technique to minimize power loss in the system by opening/closing switches to establish the latest optimal network structure. Recently, distributed generation (DG) has been swiftly implemented in distribution networks caused by its great economic, environmental, and technical benefits. The DG unit’s optimal allocation in the distribution network can reduce power loss and other risks such as excess reverse power flow, harmonic distortion, overload in line, and overvoltage in the operation of the network [1]. It is realized that the combination of the optimal network reconfiguration and DG placement problems would significantly decrease power loss and enhance the performance of the distribution network. Nevertheless, the distribution network reconfiguration (DNR) is a complex optimization problem since this problem has 2ⁿ candidate solutions (n is the number of switches) [2]. Finding the optimal solution among these solutions while satisfying the radial structure and operating constraints is a barrier to problem-solving techniques. In addition, the optimal DG placement (ODGP) problem refers to a complex mixed-integer nonlinear optimization problem. Moreover, this is deemed as an obstacle for optimization methods. Therefore, the issues with ODGP and DNR in combination (DNG-DG) become a more complex optimization problem for the optimization solving approach. This research aims to propose a successful optimization method in solving the DNR-DG problem.

Merlin and Back initially solved the DNR problem for power loss decrement [3]. In this study, the authors expressed the DNR as a mixed-integer nonlinear optimization problem and overcame it with a discrete branch-and-bound method. In [4], Civanlar et al. recommended a branch exchange scheme to address the DNR problem for minimizing balancing load and power loss. In [5], Martín and Gil developed a novel heuristic methodology of branch exchange depending on the branch power flow’s direction to decrease the real power loss for the DNR issue. In [6], Gohokar et al. formulated the DNR problem by a network topology concept, in which nodes and branches can be numbered in any order. The single loop optimization procedure was developed to find the optimum network topology. The aforementioned heuristic methods are simple implementation and provide an excellent solution for small-scale problems. Nevertheless, they expose limitations when facing complex optimization problems of changing objective functions. Therefore, these methods have not really attracted researchers.

Advanced optimization methods (i.e., metaheuristics) have been developed and applied to various engineering fields. They are capable of handling various complex constraints and different objective functions. Genetic algorithm (GA) is deemed a well-known metaheuristic, thrivingly implemented on the DNR problem. In [7], a modified GA was suggested for the DNR alongside the power loss reduction objective for 16- and 33-bus RDNs. In [8], GA was enhanced by utilizing the edge-window-decoder encoding system to minimize the power loss via the DNR problem. Another famous metaheuristic approach is particle swarm optimization (PSO). In [9], an adaptive PSO was presented for the RDN’s reconfiguration for the real power loss reduction. In [10], the niche binary PSO algorithm was developed to optimally reconfigure the RDN. This algorithm overcame the prematurity of the original PSO for a better-obtained solution. In [11], improved selective binary PSO was offered as an alternative to the DNR to decrease the power loss. Other metaheuristic algorithms have been implemented effectively to the DNR problem, for instance, ant colony search algorithm [12], cuckoo search algorithm (CSA) [13], fireworks algorithm [14], honeybee mating optimization [15], stochastic fractal search [16], and binary group search optimization [17].

The DNR problem becomes more complex when DG units are integrated into distribution networks. Thus, the metaheuristic-based approaches are more suitable than heuristic methods for an optimal solution. Several metaheuristic methods have been recommended for the DNR-DG problem. In [2], a harmony search algorithm (HSA) was proposed in solving the DNR-DG problem for the 33- and 69-bus RDNs. The aim of this research was voltage profile increment and real power loss reduction. Also, in studies [18,19], fireworks algorithm (FWA) and adaptive cuckoo search algorithm (ACSA) were, respectively, presented for the DNR-DG within the similar coverage in the research [2]. In [20], the DNR-DG problem was fixed by the adaptive shuffled frogs leaping algorithm (ASFLA). In this study, the simulated outcomes from 33-bus and 69-bus RDNs for various circumstances found that the ASFLA was efficient than ACSA, FWA, and SFLA. In [21], the salp swarm algorithm (SSA) was suggested for handling the DNR problem with the DG placement. The effectiveness of SSA was also tested on 33- and 69-bus RDNs. Generally, the aforementioned metaheuristic methods were implemented in small- and medium-scale test systems. The research did not take into account large-scale systems. Moreover, the majority of the research employed metaheuristic approaches to tackle the DNR-DG issue. Despite these techniques having a significant search capacity for an optimal solution, there is no guarantee that they would be effective for all optimization problems. A metaheuristic method can effectively solve a specific optimization problem; however, it may not be effective for others. Therefore, there is always room to suggest new effective metaheuristic methods for dealing with complex optimization problems.

This research suggests a powerful optimization strategy to manage the DNR-DG problem towards minimum real power loss. The suggested approach is the Quasioppositional Chaotic Symbiotic Organisms Search (QOCSOS) method developed in our previous work [22]. The QOCSOS algorithm embedded QOBL and CLS search strategies to boost the obtained solution quality and convergence speed of the original SOS. In QOCSOS, the QOBL strategy helps the algorithm to explore more promising domains; thus, it increases the chance of obtaining a better solution. As a result, the algorithm’s exploration capacity is enhanced. In addition to QOBL, the CLS strategy also helps the algorithm to avoid trapping in local optima. It locally explores the neighbourhood of the current best solution for better exploitation. Consequently, the integration of both QOBL and CLS strategies would keep a balance between exploration and exploitation and significantly improve the performance of the SOS algorithm. The suggested QOCSOS technique is applied to simultaneously obtain the optimal configuration and DG placement in the 33-, 69-, and 119-bus RDNs.

This research’s contributions are outlined as the statements as follows:

(i) The QOCSOS was modified to the DNR-DG problem for power loss decrement.

(ii) The QOCSOS was successfully applied to 119-bus large-scale system for the DNR-DG problem.

(iii) The simulation results showed that the simultaneous consideration of optimal network reconfiguration and DG placement substantially enhanced the distribution networks’ performance with regard to voltage profile and power loss compared to only network reconfiguration or DG placement.

(iv) The outcome comparison illustrated that the QOCSOS technique is more successful than the original SOS and other compared approaches for the acquired excellent solution standard.

The remaining sections of the paper are as follows. Section 2 describes the problem formulation of the DNR-DG. Section 3 presents the QOCSOS algorithm, in which the original SOS, QOBL, and CLS are introduced. Section 4 explains the implementation of the proposed QOCSOS to the DNR-DG problem. The results of numerical simulations are presented in Section 5. Finally, the conclusions are given in Section 6.

2. Problem Formulation

The main goal of the DNR-DG problem is to minimize real power loss (P_L) in RDNs, while all operating constraints are satisfied as follows:$$\begin{array}{c}\text{(1)}& OF=\text{Min}{P}_L=\text{Min}{\displaystyle \sum _{k=1}^{N_L}{R}_k{I}_k^2},\end{array}$$where R_k is the resistance of the k^th branch, I_k is the current passing through that branch, and N_L is the number of branches in an RDN.

The operational constraints for the objective function in equation (1) are given as follows:

i. Power balance constraints:$$\begin{array}{c}\text{(2)}& P_{SS}+{\displaystyle \sum _{i=1}^{N_{DG}}{P}_{DG,i}}={\displaystyle \sum _{j=1}^{N_B}{P}_{D,j}+{\displaystyle \sum _{k=1}^{N_L}{P}_{L,k}},}{Q}_{SS}+{\displaystyle \sum _{i=1}^{N_{DG}}{Q}_{DG,i}}={\displaystyle \sum _{j=1}^{N_B}{Q}_{D,j}+{\displaystyle \sum _{k=1}^{N_L}{Q}_{L,k}}},\end{array}$$

  where N_DG is the number of DGs; N_B is the number of buses in RDN; P_D,j and Q_D,j are the active and reactive power of load demands at the j^th bus, respectively; P_L,k and Q_L,k are the active and reactive power losses in the k^th branch, respectively; P_SS and Q_SS are the active and reactive power outputs at the slack bus, respectively; P_DG,i and Q_DG,i are the active and reactive power outputs of the i^th DG, respectively.

ii. Voltage constraint:$$\begin{array}{}\text{(3)}& V_{\text{min},i}\le V_i\le V_{\text{max},i};\hspace{1em}i=1,\dots ,N_B,\end{array}$$

  where V_min,i and V_max,i denote the voltage bounds at the i^th bus.

iii. Thermal limit:$$\begin{array}{}\text{(4)}& I_k\le I_{\text{max},k};\hspace{1em}k=1,\dots ,N_L,\end{array}$$

  where I_max,k represents the maximum current allowed to flow through the k^th branch.

iv DG generation constraint:$$\begin{array}{}\text{(5)}& P_{DG\text{min},i}\le P_{DG,i}\le P_{DG\text{max},i};\hspace{1em}i=1,\dots ,N_{DG},\end{array}$$

  where P_DGmin,i and P_DGmax,i denote the capacity limit of the i^th DG, respectively.

v DG penetration constraint:$$\begin{array}{}\text{(6)}& {\displaystyle \sum _{i=1}^{N_{DG}}{P}_{DG,i}}\le {\displaystyle \sum _{j=1}^{N_B}{P}_{D,j}}.\end{array}$$

vi Radial configuration constraint:

The radial topology must be maintained after reconfiguration as follows [23]:$$\begin{array}{}\text{(7)}& \text{det}A=1\mathrm{or}-1,\end{array}$$where A represents a matrix for the connection of branches and buses in the RDN [23]:$$\begin{array}{}\text{(8)}& A_{ij}=\begin{array}{cc}1,& \text{if\hspace{0.17em}branch}i\text{connects\hspace{0.17em}from\hspace{0.17em}bus\hspace{0.17em}\hspace{0.17em}}j,\\ -1,& \text{if\hspace{0.17em}branch}i\text{connects\hspace{0.17em}to\hspace{0.17em}bus\hspace{0.17em}\hspace{0.17em}}j,\\ 0,& \mathrm{otherwise}\text{.}\end{array}\end{array}$$

3. QOCSOS Algorithm

3.1. Original SOS Algorithm

The SOS method was developed based on a natural ecosystem with symbiotic relations between two different organisms [24]. The search process is started by randomly generating a population of organisms (ecosystem) as follows:$$\begin{array}{}\text{(9)}& O_i=O_{i\text{min}}+\text{rand}\mathrm{0,1}\times O_{i\text{max}}-O_{i\text{min}}\text{,}\hspace{1em}i=\mathrm{1,2},\&,N,\end{array}$$where O_i = [o_i1, o_i2, …, o_iD]; D is the dimension of optimization problem; O_imin and O_imax are the upper and lower limits of the i^th organism, respectively; N is the size of the ecosystem.

In the population, each organism represents a solution. For each iteration, the population is updated based on mutualism, commensalism, and parasitism phases. Each phase is defined as follows.

3.1.1. Mutualism

Based on mutualistic relationships, the j^th random organism is assigned from the population to associate with the i^th organism during this phase. Vectors O_i and O_j are the i^th and j^th organisms in the population, respectively. New organisms are created as follows [24]:$$\begin{array}{c}\text{(10)}& O_i^{\text{new}}=O_i+\text{rand}\mathrm{0,1}\times O_{\text{best}}-MV\times b{f}_1,O_j^{\text{new}}=O_j+\text{rand}\mathrm{0,1}\times O_{\text{best}}-MV\times b{f}_2,\\ MV=\frac{O_i+O_j}{2},\end{array}$$where MV is the average of the i^th and j^th organisms, representing a mutualistic relationship; bf₁ and bf₂ are randomly chosen as 1 or 2; O_best denotes the best organism in the population.

The fitness value is calculated for each organism. The new organism is updated as follows:$$\begin{array}{}\text{(11)}& O_i=\begin{array}{cc}{O}_i^{\text{new}},& \mathrm{if}f{O}_i^{\text{new}}<f{O}_i,\\ O_i,& O_i\mathrm{otherwise}\text{.}\end{array}\end{array}$$

3.1.2. Commensalism

In this phase, the i^th organism interacts with the j^th organism, which is randomly selected from the population based on commensalism interaction. A new organism is generated as follows [24]:$$\begin{array}{}\text{(12)}& O_i^{\text{new}}=O_i+\text{rand}-\mathrm{1,1}\times O_{\text{best}}-O_j.\end{array}$$

The new organism is updated as described by equation (10).

3.1.3. Parasitism

In this phase, the i^th organism acts as a parasite, and the j^th random organism acts as the host. In the parasitism interaction of two different organisms, the parasite gets benefits, while the host gets harm. Vector O_i is duplicated to create a Parasite_Vector (PV). A new candidate solution (O_PV) is created by randomly modifying some variables of the PV vector [24]. The O_PV vector is updated or discarded as follows:$$\begin{array}{}\text{(13)}& O_j=\begin{array}{cc}{O}_{PV},& \mathrm{if}f{O}_{PV}<f{O}_j,\\ O_j,& O_i\mathrm{otherwise}\text{.}\end{array}\end{array}$$

3.2. QOBL Strategy

The QOBL strategy is performed when SOS generates a new population of organisms. The QOBL approach is also applied when the initial population is randomly initialized. The opposite point $O_i^o$ of each organism O_i is calculated as follows [25]:$$\begin{array}{}\text{(14)}& O_i^o=O_{i\text{min}}+O_{i\text{max}}-O_i.\end{array}$$

Then, the quasiopposite point $O_i^{qo}$ is given by the following equation [22]:$$\begin{array}{}\text{(15)}& O_i^{qo}=\text{rand}\frac{O_{i\text{min}}+O_{i\text{max}}}{2},O_i^o.\end{array}$$

The pseudocode of QOBL (Algorithm 1) is illustrated in Figure 1.

[figure omitted; refer to PDF]

In this case, QOCSOS outperformed the comparable techniques with regard to the solution quality, demonstrating its suitability for a large-scale system.

6. Conclusion

In the study, the improved QOCSOS is successfully implemented to solve the simultaneous problems of network reconfiguration and DG allocation in RDNs to reduce the real power loss. The efficacy of QOCSOS has been carried out on the 33-bus, 69-bus, and 119-bus RDNs. It was found that Case 3 (combination of optimal network reconfiguration and DG allocation) offered the best real power loss and minimum voltage amplitude compared to Case 1 (only network reconfiguration) or Case 2 (only optimal DG placement). For this case, the power loss reductions were 74.57%, 84.37%, and 56.47% for the 33-bus, 69-bus, and 119-bus RDNs. Furthermore, the findings showed that the suggested QOCSOS algorithm delivered higher solution quality with regard to loss minimization than the original SOS and several other optimization approaches, particularly for large-scale systems, as seen from the outcome evaluations. As a result, the QOCSOS algorithm provides a viable solution for the DNR-DG problem in RDNs.

Acknowledgments

This research was funded by the Ho Chi Minh City University of Technology, VNU-HCM (Grant no. T-ÐÐT-2020-31).

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