The most important measures which can improve the performance in the operation of a distribution system are: (i) reconfiguration of the system, exchanging the functional links between its elements (system/network/feeder reconfiguration problem); (ii) variation and control of the reactive power flow through the system (optimal reactive power dispatch problem), using bank capacitors, power generators, etc.; (iii) variation and control of the voltage by using on-load tap-changers for power transformers (by using automatic voltage regulators); and (iv) changing the operating scheme of the parallel connected power transformers, etc. This paper focuses on optimization through the reconfiguration of power distribution systems.

The reconfiguration problem is one of the multi-criteria optimization types, where the solution is chosen after the evaluation of some indices (e.g., active power losses, reliability indices, branch load limits, voltage drop limits,

etc.), which represent multiple purposes. These criteria can be grouped in two different categories: (i)

objective functions: criteria that must be minimized; and (ii)

constraints (restrictions): criteria that must be included within some bounds. On the other hand, the criteria are incompatible from the point of view of measurement units and are often conflicting. Moreover, some criteria can be (or it is important for them to be) modeled, at the same time as objectives and constraints. For instance, the active power losses must be minimized but we can simultaneously impose a maximal acceptable value (constraint). Thus, in order to solve the problem, first of all,

a proper model has to be chosen. The problem of optimization through the reconfiguration of a power distribution system, in terms of its definition, is a historical

single objective problem with constraints. Since 1975, when Merlin and Back [

1] introduced the idea of distribution system reconfiguration for active power loss reduction, until nowadays, a lot of researchers have proposed diverse methods and algorithms to solve the reconfiguration problem

as a single objective problem. The most frequently used one is

the main criterion method (ε-constraint) where the problem is defined in the following conditions: a main criterion is chosen, concomitantly indicating acceptable values for the other criteria. Usually, active power losses are adopted as the main criterion [

1,

2,

3,

4,

5,

6,

7,

8,

9,

10,

11,

12,

13,

14,

15,

16,

17,

18,

19,

20,

21,

22]. This approach has a major weakness because there is more than one index that must be taken into account in the optimization process and, without any prior information about the different criteria, choosing the acceptable value can be problematic. Additionally, this approach alters the essence of the original technical problem. On the other hand, some authors have studied this problem using

aggregation functions, converting the multi-objective problem into a single objective one that assumes a (weighted or not) sum of the selected objective functions [

23,

24,

25,

26,

27,

28,

29,

30]. The major difficulty in this kind of problem consists in the incompatibility of different criteria. To create a global function, all criteria must be converted to the same measurement unit; a frequently used method is to convert them into costs, which is usually a tricky and often inaccurate operation. In addition, subjectivity appears, caused by the introduction of weighting factors for different criteria. Thus, the existence of a model that could take into consideration more objective functions and constraints at the same time is of great interest. To eliminate the subjectivity and rigidity of the classic methods, the authors propose an original approach to formulate this problem using the

Pareto optimality concept that defines a dominate relation among solutions.

Regardless of the problem formulation,

searching for the solution is also a very complex issue due to its combinatorial nature. An absolute (e.g., “brute force” [

10]) method which generates the entire space of candidate solutions in order to choose the best one, requires a prohibitive execution time. In order to avoid the evaluation of the entire space of the candidate solutions and to minimize the computation burden, several algorithms have been developed. Most authors have used different well known heuristics (branch exchange [

2,

3,

21], branch and bound [

1,

4], simulated annealing [

5]), other heuristic rules or meta-heuristics [

7,

8,

9,

11,

12,

13,

15,

17,

22,

23,

25,

27,

28] or multi-agent technologies [

20]. On the other hand, some authors have developed methods based on evolutionary computation techniques [

6,

14,

16,

18,

19,

24,

26,

29,

30]. An important drawback of these methods is the fact that

they solve the reconfiguration problems as single objective problems. Nevertheless, some authors have proposed Pareto optimality based approaches (including active power losses and reliability indices as objectives). With these approaches, linear programming cannot be used because we have more than one objective function. Thereby, different artificial intelligence based methods have been used: evolutionary [

31], branch exchange [

32] and particle swarm optimization [

33].

Taking into account these considerations, we can observe the fact that this problem is arduous particularly from two points of view: (i)

the formulation of the problem, because there is more than one objective; (ii)

the search for the optimal solution, because of the prohibitive execution time demanded by applying an absolute method. In this paper an original method, aiming the optimization through the reconfiguration of distribution systems, is proposed. The novelty of the method consists in:

the criteria for optimization are evaluated on active power distribution systems (containing distributed generators connected directly to the main distribution system and microgrids operated in grid-connected mode);

the original formulation of the optimization problem, as a Pareto optimal one, with two objective functions (active power losses and system average interruption frequency index);

an original genetic algorithm (based on NSGA-II) to solve the problem (as a Pareto optimal one) in a non-prohibitive execution time.