Optimum Network Reconfiguration using Grey Wolf Optimizer

The objective of this paper is to determine an optimal network reconfiguration that presents the minimum losses considering network constraints using Grey Wolf Optimizer (GWO) algorithm. The proposed algorithm was tested using some standard networks (33_bus, 69_bus, 84_busand 118_bus).


Introduction
A power system can be divided to different phases, generation phase, transmission phase and distribution phase. The distribution phase is the important one that presents liaison between transmission system and consumer. Distribution networks are in many cases exploited in a radial configuration [1], power flux has just a way to transit from source to load. Radial configuration allows insuring easily network maintenance and fast fault detection with short-term network restoring. To move from a configuration to another it is enough to change switchers states (opened or closed) so as to reduce active losses, balance loads between feeder or maximize, in case of line fault the number of restored customers [2]. Distribution network reconfiguration was proposed the first time by A. Merlin et al [3]. The distribution network reconfiguration is considered as a non-linear and/or discreet combinatory programming problem. To determine an optimal reconfiguration, one has to perform a sequence of adequate commutation operation by considering all aspects of network constraints (technique, security and topology) [4].Distribution network reconfiguration can minimize active losses [5].
To determine optimal distribution network reconfiguration, different methods based meta-heuristic optimization proposed in literature as, Modified Tabu Search Algorithm [6].Modified PSO Algorithm [7,8]. Adaptive Particle Swarm Optimization [9]. Genetic Algorithm [10]. Artificial Bee Colony Algorithm [11]. Differential Evolution [12]. Artificial Immune Systems [13]. Gravitational Search Algorithm [14]. Harmony Search algorithm [15]. Hybrid Big Bang-Big Crunch Algorithm [16]. Biogeography Based Programming Algorithm [17]. Cuckoo Search Algorithm [18]. Runner-root Algorithm [19].Stochastic Dominance Concepts [20]. In this paper, a metaheuristic technique called (GWO) based on graphs theory is proposed to find the optimal reconfiguration of an electrical network in order to minimize active losses. This is concretized by an adequate adjustment of switches states. The remainder is organized as follows: The second section is dedicated to distribution network reconfiguration problem, definitions and methods associated. In the third section, we gives the mathematical programming model of the proposed problem. In the fourth section, we shows the application of GWO technique to network reconfiguration problem. The fifth section presents some simulation results relative to standard networks.

Problem Formulation 2.1. Objective Function
In distribution network level, active losses reduction can be established by network topology changing. Active power losses, due to current flow in an electrical conductor, is given by (1) with ( ) and where , refer toactive and reactive power sat bus i. , refer to active and reactive powers at bus j. is the branch resistance between buses i and j.
are voltage and angle at bus i. are voltage and angle at bus j. N represents the number of buses in the network. To insure a steady operation of the network is necessary to respect network exploitation constraints such as equality and inequality constraints given in the following section.

Equality Constraints
Its defined by load flow equations, corresponding to one operation point of the network, for a given load and generation. They are given as follows: where: is the admittance matrix corresponding to buses i and j.

Inequality Constraints
The nodal voltages in all network remains within admissible limits, which are given by (3) where: and are the extremal (Min/Max) voltages of i th bus. (i) The transiting currents are limited by the line thermal limits so that (4) where is the apparent power flow at distribution system lines between buses i and j, is permitted rating of lines ij.

Radiality Constraint
This constraint is relative to network topology that indicates radiality conservation of exploitation schemes, so there is no power loop in the scheme [21].

Connectivity Constraint
Obviously, it is necessary to have all buses under electrical voltage.

Constraints-Handling Mechanism 2.6.1. EqualityConstraints
In distribution networks, Newton-Raphson and Gauss-Seidel methods are not more appropriate to solve the power flow problem because, in cases, they diverge due to different typical characteristics related to transmission network where, the configuration is generally radial with, high ratio R/X [22]. For that raison, backward-forward sweep(BFS) technique is used in this work to analyze the power flow.

Inequality Constraints
Physical problems enclose generally constraints that have to be fulfilled. The constraints' set defines the feasible set. Indeed, a solution that not verify one or many constraints is said to be non-feasible and cannot be considered as ideal solution, even if it optimizes the objective function. Therefore, penalty function is necessary to favor feasible solutions. Hence the objective function must be replaced by the following function see [23][24][25][26].
where: F is the objective function value, and are expressed as: Where: and represent the penalty factors which are selected as 10.000. So, a penalty function is used (for topology constraints) in the case of existing power loops or isolated loads as follows: (8) where is the existing power loops number, is the number of isolated loads, and are penalty factors.

Grey Wolf Optimizer Algorithm
S_Mirjalili et al, proposed a novel population based meta-heuristic optimization algorithm namely "Grey Wolf Optimizer" [27]. The main inspiration of this algorithm is the social leadership and hunting technique of grey wolves. Similarly to other meta-heuristics, it initializes the process by a set of random candidate solutions (wolves). During every iteration, the first three best wolves are considered as (α), (β), and (δ) which lead other wolves (ω) toward promising zones of the search space. Grey wolves tend to encircle the prey when the hunt. The encircling behavior can be formulate as follows: where: t is the iteration number, ⃗ and ⃗ are the coefficient vectors, ⃗ the prey position vector, ⃗⃗⃗⃗⃗ refers tothe grey wolf position vector. are random vectors in the interval [0, 1] and the variable ⃗ decreases linearly from 2 to 0 with iteration steps given by Is worth noticing that each mega wolf is required to update its position with respect to , and simultaneously as follows: It was argued by S_Mirjalili et al that the parameters A and C force the grey wolf optimizer algorithm to explore and exploit the search space [27]. Half of the iterations is devoted to exploration (| | ) and the rest is used for exploitation (| | ). The parameter C also changes randomly to solve the local optima stagnation during optimization.

Application of the GWO to the Proposed Problem 4.1. Decision variables
Because of the design of the network, the fundamental loops are numbered from 1 to BL, respectively. One switch from every BL loops is opened to keep the network radial with considering constraints. This contributes to reduce the generation of non feasible configurations during each steps of the algorithm. (20) where: X is the state variables and represents the open switch number that is selected from the i th fundamental loop. So, the size of X is equal to the number of distribution system fundamental loops. The number of network fundamental loops is identical to the tie switches number. Moreover, Figure 2 show the encoding of individuals, where each candidate switch is denoted by discrete integer corresponding to the respective loop vector. Figure 3 shows the flow chart for Grey Wolf Optimizer algorithm.

Proposed Method Steps
The pseudo codes the GWO algorithm are given by following steps: Step 1: Define the input data including the system base configuration, branch impedance and bus data (load real and reactive power) and switches devices states.
Step 3: Runload flow analysis using BFS technique, for each control variables vector. According to the results of the distribution load flow, evaluate the fitness function value (1) and (5).
Step 4: Update leader wolves , , and (the first three best search agents).
Step 6: Update the wolves position using (9). Repeat procedure from step 3 to step 6 up to maximum number iteration. The last present the solution of problem.

Simulations and Discussion
In order to test the efficiency of the proposed technique, the application is performed on some standard networks with different sizes such as 33_bus network [28], 69_bus [29], 84_bus [30] and 118_bus [31].
From the comparison of the second and the fifth columns in Table 1, we can see that, for all test system, the total active power losses are reduced significantly after reconfiguration. Figure 4, represent the voltage profiles of all test systems. So, we can note that, for all nodes, the voltage levels of the radial distribution systems are improved and placed in an acceptable margin. The results obtained using GWO method is compared with Particle Swarm Optimization(PSO) method and the results are given in Table 2.

Conclusion
This paper presents GWO technique to determine the optimal distribution networker configuration. The objective function considered in this study is, minimizing active losses under technique and topologic constraints. This technique is based on Grey Wolf Optimizer which, was tested on different standard networks (33_bus, 69_bus, 84_bus and 118_bus). Compared to PSO method, the simulation results proved the superiority of the proposed method (GWO) in terms of robustness and quality improvement.