Although most of the middle voltage distribution networks have mashed topology in all or some parts of the network, they are usually kept in radial operation by opening sectionalizing and tie-switches [

1,

2,

3,

4]. This is done for pure economic reasons to avoid the additional investments in more expensive substation primary equipment and to simplify the network protection scheme. On the other hand, keeping the distribution networks in radial operation reduces network reliability. Spatially enclosed structure in some parts of the distribution networks generally provide numerous feasible topologies, that can be implemented to assure the reliable supply of the distribution system load. Topology changes can be implemented by different switching layouts of sectionalizing and tie-line switches that are placed along the distribution network. The distribution network optimal reconfiguration represents an optimization problem that identifies the optimal radial topology of the distribution network from the set of feasible radial network topologies [

5]. In normal operating conditions, distribution network reconfiguration is usually conducted with a goal to minimize the total network power/energy losses [

1,

2,

3,

4], harmonize network voltage profile [

5,

6,

7,

8] and unify network loading [

3], or to achieve a combination of the mentioned criteria through a multi-objective framework [

9,

10,

11]. In achieving these goals, it is necessary to assure the radial topology of distribution networks, as well as to satisfy different physical and operational constraints. However, in certain specific subsections of the distribution network, mashed operation is required to maintain normal operating conditions. These are usually areas distant from main supply points with low voltage conditions, or areas of network with higher supply reliability requirements. If such areas are present in the network, given that they remain mashed, they can be simply left out and not considered in the reconfiguration process, or they can be made mashed after detecting the optimal radial structure. For the distribution networks of a realistic size, a simple examination of the whole set of feasible topologies is usually not possible, due to the computational requirements of such an approach [

12].

So far, different sets of approaches have been developed for solving the optimal distribution network problem under different sets of objective functions. These approaches can be clustered into four major categories depending on the solution methods used: heuristic approaches [

1,

2,

3], metaheuristic approaches [

4,

5,

6,

7,

8,

9,

10,

11], mathematical programming [

13,

14], fuzzy logic. Heuristic approaches use a different set of heuristic rules [

1,

2] or approximate analytical expressions [

3], which can be applied on segments of distribution network to partially improve network conditions and objective function. The most heuristic approaches use simple logic to detect optimal branch exchange, by examining voltage difference across tie switches to identify the optimal tie-line for branch exchange [

2]. Different sets of heuristic approaches use analytical expression to approximate objective function change under single branch exchange in a single network cycle [

3]. Using analytical expression, one can approximately determine objective function change under all feasible branch exchanges in a single network cycle. These approximate calculations don’t require load flow analysis calculation for each considered branch exchange, but rather use the results for present network topology. Only after implementation of branch exchange in single cycle, do load flow results need to be updated. This approach is computationally very effective, but due to the “greedy” nature of such approaches, it can lead to local optimum solutions. Metaheuristic methods represent a set of methods for detecting global optimum solutions which use the iterative improvement of population of solution by employing different improvement strategies based on evolution theory concepts, social interaction and learning concepts, as well as a different set of approaches simulating animal behavior. Different sets of metaheuristics approaches have been applied so far to solve the optimal distribution network problem, ranging from genetic algorithms, particle swarm optimization, simulate annealing, ant-colony optimization, bacterial foraging, bee swarm optimization, etc. Most of the approaches, regardless of the method applied and objective function, demonstrate challenges in maintaining network radial topology in the process of the initialization or modification of candidate solutions [

5,

8,

10,

11]. Most of the approaches use simple generic methods for candidate solution modification, not respecting the topological nature of the problem. In the case of genetic algorithms, the candidate solution modification in the form of crossover process, uses, for example, a simple single [

5,

8,

10] or multipoint [

11] crossover method, which in a large number of cases results in an infeasible candidate solution. These infeasible solutions usually include isolated parts of a distribution network or parts of network connected to a main supply point containing cycles (meshed network). In order to solve these issues, different strategies are used: penalization of objective function for unfeasible topologies, repeating crossover process until radial topology is achieved, application of graph traversal algorithm and modification of candidate solution. All these approaches significantly increase computational burden and usually don’t provide mechanisms necessary for the transfer of “good” genetic material to a new set of candidate solutions. These issues become even more pronounced on a large scale distribution network, given the low probability of generating a feasible candidate solution using described strategies. The set of methods based on mathematical programming [

13,

14] represent a more formal way of defining network radiality constraints, as well as network operating constraints related to maximum element loading and bus voltages. By linearizing power flow equations, we can reduce the optimal distribution network reconfiguration problem to classical mixed-integer linear programming (MILP) [

14], mixed-integer quadratic programming (MIQP) [

13], and mixed integer second order cone programming (MISOCP). The linearization of the optimization problem assures the detection of a global optimum with a sufficiently small gap, as well as the application of efficient solution techniques. These approaches have shown the best solution quality and computational performance for smaller distribution networks. However, they demonstrate a slow convergence rate for large scale distribution networks.

This paper proposes a novel algorithm for the optimal reconfiguration of distribution networks, based on the combination of heuristic method and genetic algorithms, with specific adjustments due to the nature of the given problem. The proposed algorithm introduces several improvements related to the generation of the initial set of possible solutions as well as crossover and mutation steps in the genetic algorithm. Although genetic algorithms are often used in the optimal reconfiguration of a distribution networks [

15,

16,

17,

18,

19,

20,

21,

22,

23,

24], most of the approaches [

16,

17,

18,

19,

20,

21,

22,

23] don’t provide an effective means of creating an initial population, as well as effective operators to implement a crossover and mutation process over the set of population individuals. Due to this, during the evolution process, a large number of generated individuals is often rejected and power flow calculations are often conducted for unfeasible individuals (network topologies), that don’t provide the radial network topology or include the isolated parts of the network. Additionally, testing individuals in the population to check if the distribution network has radial structure, or to identify isolated parts of the networks, and impose such criteria on individuals which do not conform to such conditions, can be time consuming and computationally ineffective. Such an approach is not applicable for the realistic and complex distribution networks.

The approach proposed in this paper provides significant improvements precisely in these segments, yielding the method that can be used on the distribution networks of realistic size and level of complexity. The major contribution of the work relates to:

This paper is organized as follows:

Section 2 gives a general overview of the proposed algorithm;

Section 3 defines algorithms for the efficient initial population generation based on a successive branch-exchange algorithm and stochastic Kruskal’s algorithm;

Section 4 describes and illustrates the main modifications introduced in the genetic algorithm process (crossover, mutation), specifically adjusted for the distribution network reconfiguration problem;

Section 5 provides results of the proposed method on different test case networks, as well as a comparison with other state-of-the-art approaches;

Section 6 gives main paper conclusions.