Elsevier

Energy

Volume 138, 1 November 2017, Pages 355-373
Energy

A hybrid evolutionary algorithm for secure multi-objective distribution feeder reconfiguration

https://doi.org/10.1016/j.energy.2017.07.102Get rights and content

Highlights

  • Introduce a novel hybrid algorithm based on MSFLA and PSO to solve the MODFR problem.

  • Develop an efficient mutation operator to modify the performance of the SFLA.

  • Consider power loss, VSI and switching number as various objective functions.

  • Three criterions are used to analyze the obtained Pareto-optimal solutions.

  • Report the numerical results on IEEE 33-node and 95-node distribution networks.

Abstract

Distribution Feeder Reconfiguration (DFR) is an important technique to improve the performance of distribution networks. The common objectives considered in the DFR problem are power loss and voltage deviation which are important objectives for traditional distribution systems. Security issues cause by Distributed Generations (DGs) in modern distribution systems which can potentially jeopardize power system security has almost neglected in power system operation problem. Toward this end, this study considers the power loss, Voltage Stability Index (VSI), and number of switching as objective functions which can satisfy both operation and security expectations. The Backward-Forward Sweep (BFS) method known for easy convergence has been employed for power flow calculations. Because of the increase in DG penetration in distributed systems, the impacts of these units are investigated. A powerful optimization algorithm based on hybridization of Shuffled Frog Leaping Algorithm (SFLA) and Particle Swarm Optimization (PSO) is proposed to solve the proposed problem. The proposed algorithm is a combination of strong mutation operator, original SFLA and original PSO algorithms which has high population diversity and search ability. The proposed algorithm has been applied to a complex multimodal benchmark function and also two different distribution networks including 33- and 95-bus test systems.

Introduction

The concept of reconfiguration process is modifying the structure of distribution feeders in order to optimize certain objective functions subject to satisfy a set of constraints and limitations [1]. Generally, the Distribution Feeder Reconfiguration (DFR) is carried out by managing the states of tie-switches and sectionalizes components in a distribution feeder without removing the section of the system as an island. Because of the inherit characteristic of the DFR problem such as having discontinuous variables and etc., the Mathematical-based optimization algorithms are not proper candidate to solve this problem. Toward this end, special attentions have been paid to heuristic algorithms to solve the DFR problem. Advantages of heuristic algorithms in solving the optimization problem make these algorithms popular candidate to solve optimization problems. Therefore proposing more efficient algorithm has become an ongoing research topic.

The power loss and voltage deviation objectives are further studied by researchers in solving the DFR problem in conventional form [2]. But, investigation the conventional DFR problem cannot take care of other issues in the distribution systems. Therefore the results of conventional DFR are not acceptable in modern distribution systems where the penetration of Distributed Generations (DGs) is being increased and the system suffers from security issues.

Recently, the share of DG resources in distribution networks has been rapidly increased [2]. The increasing utilization of these resources is due to their characteristics such as closing to load points, small-scale, reducing the active power transmission loss and etc. Although there is a vast body of research on the DFR problem without consideration of DGs effect, little attention has been paid to the consideration of DGs influence on DFR problem. Beside several benefits that DGs have brought to distribution systems, they can jeopardize the stability of distribution systems by decreasing the short circuit level. This issue is corresponding to the operation and design of the distribution networks. Also, the Short Circuit Current (SCC) level is directly proportional to the sub-station voltage. The SCC can be increased by reconfiguring the structure of distribution system. To this end, the security issues caused by DG implementation are taken into account beside the conventional objective function and constraints. It is notable that considering the security issues in the proposed DFR modeling and formulation makes the proposed study more practical from operation and planning point of views.

Another important objective in operation of distribution system, which this study focuses on, is reducing the number of switching operations which can have negative effect on the overall operation cost of network. It is necessary to note that number of switching is usually ignored or not considered simultaneously with other objectives. The substantial decreasing in the number of switching leads to the reduction of operation and maintenance cost.

Considering security objectives and switching cost along with the traditional objective function necessitate the optimization problem to be solved as a Multi-Objective Optimization Problem (MOOP). In other words, evaluating the DFR problem as a MOOP covers different aspects and needs a tool to optimize all objective simultaneously. Toward this end Pareto-based approach, which can obtain a set of optimal solutions instead of one, is employed in which enables the power system operators to select one of these solutions based on their desires. Furthermore, a fuzzy decision making is utilized to find the best compromise solution. To verify the suitability of the presented algorithm it is applied to 33- and 95-bus test systems. Simulation results prove the ability of the proposed algorithm in solving the proposed optimization problem.

During the years, different numerical algorithms have been utilized to solve the network reconfiguration problem such as, distance measurement method [3], brute-force solution [4], Integer Programming (IP) [5], [6] and G-Net inference mechanism approach [7]. But, these numerical algorithms cannot guarantee to recognize the global optimal solution of DFR problem. On the other side, these optimization algorithms have extra restrictions including continuation and derivability of the objective functions, the discrete inherence of the switches status and also constraint for radial configuration of distribution feeders. Toward this end, these numerical-based and mathematical algorithms are not suitable candidate for solving the DFR and more specifically MODFR problems. Recently many heuristic and meta-heuristic algorithms have been introduced to ameliorate these restrictions.

A literature survey manifest that, various evolutionary-based optimization algorithms have been utilized to solve the different forms of the network reconfigurations.

Particle Swarm Optimization (PSO) algorithm for solving the DFR problem was implemented in Ref. [8]. In Ref. [9], a hybrid approach based on Discrete PSO (DPSO) and Honey Bee Mating Optimization (HBMO) was presented to solve Multi-Objective DFR (MODFR) problem. A Guaranteed Convergence PSO (GCPSO) algorithm for solving the DFR problem was proposed in Ref. [10]. A Multi-objective HBMO (MHBMO) algorithm was employed to solve the DFR problem in Ref. [11]. A combination of Bacterial Foraging Algorithm (BFA) and Nelder-Mead (NM) method was used to solve DFR with phase balancing restriction in Ref. [12]. A New Fuzzy Adaptive PSO (NFAPSO) algorithm was employed in Ref. [13] to evaluate the DFR problem. Teacher Learning Algorithm (TLA) was proposed in Ref. [14] to solve the Stochastic DFR (SDFR) problem considering Fuel Cell Power Plants (FCPP) and Probabilistic Load Flow (PLF) based on Point Estimate Method (PEM). In Ref. [15], an Adaptive Modified PSO (AMPSO) was presented to solve the DFR problem considering Wind Power Plant (WPP). A Multi-objective modified HBMO (MHBMO) algorithm was presented in Ref. [16] to solve the DFR problem considering renewable energy resources. A probabilistic approach based on the Genetic Algorithm (GA) for solving the DFR problem was proposed in Ref. [17]. An Improved Shuffled Frog Leaping Algorithm (ISFLA) was introduced in Ref. [18] to solve the MODFR problem for reliable operation of distribution system. An Interval Multi-Objective Evolutionary Algorithm (IMOEA) was presented in Ref. [19] to solve the DFR problem. A new Self Adaptive Modified Bat Algorithm (SAMBA) and Teacher Learning Optimization (SAMTLO) were introduced in Refs. [20], [21], respectively to solve the DFR problem from reliability and probabilistic points of view.

Ref. [22] presented a Multi-Objective Invasive Weed Optimization (MOIWO) algorithm for solving Optimal Network Reconfiguration (ONR) problem in radial distribution systems. In Ref. [23] a Quantum PSO (QPSO) algorithm was presented to solve the DFR problem in distribution system equipped with DG units. A GA algorithm was utilized in Ref. [24] for solving the DFR problem considering DG resources and hourly Locational Marginal Prices (LMPs) of wholesale market. A θ-Modified Bat Algorithm was introduced in Ref. [25] to solve the DFR problem in a stochastic framework. In Ref. [26], a Social Spider Optimization (SSO) algorithm was proposed to solve the DFR problem considering Plug-in Electric Vehicles (PEVs) and Vehicle-to-Grid (V2G). A heuristic approach according to Uniform Voltage Distribution Algorithm (UVDA) based constructive reconfiguration was proposed in Ref. [27] to solve the optimal allocation and sizing of DG units by DFR. A Multi-objective Hybrid Big Bang-Big Crunch (MOHBB-BC) algorithm was presented in Refs. [28], [29] for solving the multi-objective optimal DFR problem in distribution networks while DG allocation and load uncertainty were considered in Ref. [28] and capacitor placement was taken into account in Ref. [29] and finally, a comprehensive review on network reconfiguration in distribution systems to decrease the power loss and improve the system reliability was presented in Ref. [30].

A general outline of these references has been organized and presented in Table 1 to ease the access of essential information of the researches such as merits, demerits and etc.

According to Table 1, only one of the presented studies considers the security objective i.e. the voltage stability in DFR problem. Also, most of them neglected the switching cost which can play an important role in decreasing the operation and maintenance cost in distribution systems. Toward this end, the suitability of the proposed approach in this study for solving different versions of DFR problems is much more require. In this regard, the contribution of this study is twofold which are related to the presented evolutionary algorithm and the considered objective functions.

Solving the MODFR problem requires an accurate and powerful optimization algorithm especially in DG resources included distribution system. To this end, a novel Hybrid Modified Shuffled Frog Leaping Algorithm-Particle Swarm Optimization (HMSFLA-PSO) is proposed to cope with the complexities of the proposed DFR problem. The original PSO and SFLA algorithms have few drawbacks such as; (1) premature converge or trapped into local optimal and (2) converge to global optimal in a long period of time. Toward this end, an appropriate and strong strategy of mutation operator is added to the hybrid algorithm to increase the diversity of population and search ability of the algorithm.

Moreover, three different objective functions including power loss, Voltage Stability Index (VSI) and number of switching are considered in this study. Also, Backward-Forward Sweep (BFS) algorithm has been employed for the load flow analysis. This BFS method utilizes complete advantage of ladder structure of distribution network, to achieve high speed, robust convergence, low memory requirements and does not need any Jacobian matrix.

In the proposed MOOP, obtains a set of optimal solutions instead of one because the considered objectives are not in line with each other. This is done by utilizing a repository to save all non-dominated solutions (Pareto-optimal solutions) at each iterate. Also, a fuzzy decision making strategy is used for sorting all Pareto-optimal solutions based on their importance.

Finally, three different criterions are implemented to analyze the obtained Pareto-optimal solutions. These criterions include Generational Distance (GD), Spacing Parameter (SP) and Diversity Metric (DM). The proposed approach is simple, easy to implement and also high computationally efficient. Yet another it has a stable operation for solving the DFR and MODFR problems in which the obtained outcomes approve this statement.

In this regard, the highlighting characteristic features of this study are outlined as follows;

  • The MODFR is modeled considering three different objective functions including power loss, Voltage Stability Index (VSI) and, number of switching.

  • Utilizing the Backward-Forward Sweep (BFS) procedure for power flow calculations without considering Jacobian matrix.

  • Considering the stability objective function based on the short circuit capacity.

  • Presenting a novel and powerful hybrid algorithm, HMSFLA-PSO, for solving the MODFR problem.

  • Introducing the robust and strong mutation operator to improve the algorithm performance.

  • Considering the effect of DG resources in different aspects.

The remaining of this paper is conducted as follows;

Section 2 presents DFR problem formulation. Multi-objective solution methodology is provided in detail in section 3. The comprehensive descriptions of the proposed approach are developed in section 4. Section 5 presents case studies and numerical results and finally, section 6 concludes the paper.

Section snippets

Problem formulation

Three different objective functions along with several constraints are needed to implement the proposed DFR problem. All these functions and constraints are introduced and explained in this section.

Multi-objective solution methodology

Most of the time in the real applications we have to solve a set of objective functions simultaneously as a Multi-Objective Optimization Problem (MOOP). It is notable that, the objective functions may not in line with each other in which leads to deal with a set of optimal solutions instead of one. Generally, a sample MOOP can be formulated as follows [41];SubjecttoMinimizefi(X),i=1,2,,NOFhj(X)=0,j=1,2,,Hgk(X)0,k=1,2,,K

Where, fi(X) is ith objective function. hj(X) and gk(X) are vectors of

Original SFLA

The SFLA was introduced by Eusuff, Lanssey and Pasha in 2006 [44]. This algorithm is extracted from social life of frogs when they are searching their food. In the SFLA, at first the frog population is divided into several memeplexes equally. SFLA consists of two searching strategy; the first one is called local search occurs in each memeplex, while the second one is exchange the data between memeplexes [45]. The following steps should be taken to implement the original SFLA [46];

  • Step 1.

Numerical and simulation outcomes

In order to evaluate the ability of the proposed algorithm, it is employed to optimize Schaffer's function and solve the DFR in two different and independent studies. It is worth mentioning that, all test cases are coded and performed in MATLAB environment on a quad-core processor laptop machine with 1.6 GHz clock frequency and 4.0 GB of RAM.

Conclusions

A novel hybrid evolutionary algorithm has been successfully implemented in this paper to solve single- and multi-objective versions of Distribution Feeder Reconfiguration (DFR) problem. Stability challenges emerged by increasing penetration level of Renewable Energy Sources (RES) in distribution systems which has been neglected in most studies is investigated in this paper. A voltage stability index related to the short circuit capacity of the system is considered as an objective function

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