This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Reconfiguration, by exchanging the functional links between the elements of the system, represents one of the most important measures which can improve the operational performance of a distribution system. The authors propose an original method, aiming at achieving such optimization through the reconfiguration of distribution systems taking into account various criteria in a flexible and robust approach. 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 (Pareto optimality) of the optimization problem and an original genetic algorithm (based on NSGA-II) to solve the problem in a non-prohibitive execution time. The comparative tests performed on test systems have demonstrated the accuracy and promptness of the proposed algorithm.

The most important measures which can improve the performance in the operation of a distribution system are: (i)

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,

Regardless of the problem formulation,

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

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 (

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

Active power losses represent the most important criterion and cannot be ignored in reconfiguration problems [

The essential attributes of interruptions in the power supply of the customers are the frequency and duration. While duration is predominantly influenced by the distribution system structure (radial, meshed, weak meshed) and the existing automations, the frequency is mainly influenced by the adopted operational configuration; it can be minimized by the suitable choice of the effective configuration. In other words, through reconfiguration, we can improve those reliability indices which refer to the interruption frequency [

Reliability of

Reliability of

For any fault that will lead to the interruption of the power supply from the main distribution system, the existing distributed generators will be switched off owing to a variety of reasons. We point out only two of them: (i) an operation of a power island purely with dispersed generators is usually considered unacceptable; (ii) it is important to

A distribution smart grid with a distributed generator and a microgrid.

Knowing the failure rates at the level of each supplied node (load point), we can estimate the _{i}_{ti} is the total failure rate of the equivalent element corresponding to the reliability block diagram at the level of node ^{−}^{1}].

The total failure rate at the level of a node _{ti} = λ_{i} + _{i}’, where λ_{i} is the failure rate when the restoring of supply is performed after the fault repair; while λ_{i}’ is the failure rate when the restoring of supply is performed after the fault isolation through non-automatic maneuvers; and ^{−}^{1}], on each supplied node there are 30 customers and the microgrid connected to node 3 (which contains 30 customers and DG units) behaves as a source. In this case we will have (

λ_{t2}_{2} = 0.5 ∙ 30 = 15;

λ_{t3}_{3} = 0.5 ∙ 3 ∙ 0 = 0 (three branches, the microgrid is expected to operate as an island and customers from a microgrid will be supplied even if a fault has occurred in the main distribution system);

λ_{t4}_{4} = 0.5 ∙ 3 ∙ 30 = 45 (three branches, if a fault occurs on the path 1-7-4-3, the DG unit will be switched off and the customers will be not supplied);

λ_{t5}_{5} =_{t6}_{6} = 0.5 ∙ 2 ∙ 30 = 30 (two branches);

λ_{t7}_{7} = 0.5 ∙ 3 ∙ 30 = 45;

_{i}

_{ij}

_{ij}

The criteria presented above are not unique, but we consider them to be the most important ones. Taking into account these criteria, we can begin to perceive the real dimensions of the problem. These criteria are incompatible from the point of view of measurement units and can be grouped in two different categories:

A Pareto front for a bi-objective reconfiguration problem.

As a Pareto optimal multi-objective problem, we propose the following form:

In the case of multi-objective problems, the literature proposes several Pareto-based genetic algorithms:

Logical diagram of the proposed algorithm (

In this implementation, the representation using the

A power distribution system: (

The operation scheme of the system will be obtained by making the preservation of the corresponding branch value equal 1 (in operation). For instance, by decoding the chromosome a, the radial operation scheme will be obtained (with corresponding α and β lists) (

The goal of the selection operator is to assure more chances to replicate for the best chromosomes of a population. The selection is performed taking into account the fitness of the chromosomes. The most used selection methods are Monte Carlo and tournament. For this multi-objective optimization problem, the author has used the ecological niche method [

Choosing the number and position of crossover points for the crossover operator depends on the system topology. If these points are selected in an inadequate mode we will obtain “bad” chromosomes: (i) un-connected systems with isolated nodes; or (ii) connected systems with loops (meshed). In order to reduce the number of these cases, we propose that the number of cut points be equal to

One of the two conditions in order to have a tree or a forest is to assure

The second condition in order to have a tree or a forest is to have a connected graph

The Pareto front allows an informed decision to be made by visualizing an extensive range of options since it contains the solutions that are optimal from an overall standpoint. The proposed algorithm was implemented in the

In order to test the correctness and convergence speed of the proposed algorithm, the authors studied, first of all, five well known

Test distribution systems: (

The proposed algorithm has an excellent behavior obtaining good quality solutions in reduced computation times (seconds); usually, a reduced number of generations is necessary for convergence. Performing reconfiguration for the test system B [

The evolution of the active power losses along the searching process (in the case of minimum CPU runtime): (

Results for different single-objective reconfiguration (test cases with DGs).

System | Configuration | Open branches (tie lines) | Active power losses | CPU runtime for 100 runs | Population/Generations | |
---|---|---|---|---|---|---|

A | Base case | 8–21, 9–15, 12–22, 18–33, 25–29 | 169.881 | kW | - | |

MOReco | 7–8, 9–10, 14–15, 28–29, 32–33 | 115.748 | kW | Minimum (3 s: 804 ms) |
10/4 | |

B | Base case | 5–55, 7–60, 11–43, 12–72, 13–76, 14–18, 16–26, 20–83, 28–32, 29–39, 34–46, 40–42, 53–64 | 425.131 | kW | - | |

MOReco | 6–7, 12–13, 32–33, 38–39, 41–42, 54–55, 62–63, 71–72, 82–83, 11–43, 14–18, 16–26, 28–32 | 380.656 | kW | Minimum (6 s: 202 ms) |
10/8 |

Results for Pareto reconfiguration with two objectives.

System | Open branches (tie lines) | Active power losses | SAIFI | CPU runtime for 100 runs | Population/Generations | |
---|---|---|---|---|---|---|

B with DGs | 6–7, 12–13, 32–33, 38–39, 41–42, 54–55, 62–63, 71–72, 82–83, 11–43, 14–18, 16–26, 28–32 | 380.656 | kW | 1.143 | Minimum (6 s: 952 ms) |
10/9 |

5–55, 6–7, 11–43, 12–72, 13–76, 14–18, 16–26, 20–83, 28–32, 29–39, 32–33, 40–42, 53–64 | 396.143 | kW | 0.751 | - | ||

5–55, 6–7, 11–43, 12–72, 13–76, 14–18, 16–26, 20–83, 28–32, 29–39, 34–46, 40–42, 53–64 | 409.526 | kW | 0.648 | - | ||

5–55, 7–60, 11–43, 12–72, 13–76, 14–18, 16–26, 20–83, 28–32, 29–39, 34–46, 40–42, 53–64 | 425.131 | kW | 0.472 | - | ||

B with microgrids | 6–7, 12–13, 32–33, 38–39, 41–42, 54–55, 62–63, 71–72, 82–83, 11–43, 14–18, 16–26, 28–32 | 380.656 | kW | 0.988 | Minimum (7 s: 114 ms) |
10/9 |

5–55, 6–7, 11–43, 12–72, 13–76, 14–18, 16–26, 20–83, 28–32, 29–39, 32–33, 40–42, 53–64 | 396.143 | kW | 0.619 | - | ||

5–55, 7–60, 11–43, 12–72, 13–76, 14–18, 16–26, 20–83, 28–32, 29–39, 34–46, 40–42, 53–64 | 425.131 | kW | 0.427 | - |

The Pareto front (in the case of minimum CPU runtime): (

It is important to mention the fact that, in the case of the proposed algorithm, we obtained the same results for 100 runs. The differences consist only in the execution time required (e.g., between 6 s

The proposed algorithm tries to exploit the fundamental properties of a distribution system,

Reconfiguration represents one of the most important measures which can improve the performance in the operation of a distribution system. Optimization through the reconfiguration (or optimal reconfiguration) of a power distribution system is not a new problem but still represents a difficult one and nowadays has new valences. Besides active power losses, the average number of interruptions to the power supply represents an essential criterion which must be taken into consideration in the optimization problem. The criteria for optimization have been evaluated on active power distribution systems (containing distributed generators connected directly to the main distribution system and microgrids operated in grid-connected mode). The simulation studies on test systems have highlighted that the

The original formulation of the optimization problem, as a Pareto optimal one, with two objective functions (

Usually, the existing reconfiguration methods used nowadays either demand prohibitive execution times or result in non-optimal solutions (in the case of most common heuristics). The authors propose an original genetic algorithm (based on NSGA-II) to solve the problem (as a Pareto optimal one) in a non-prohibitive execution time. The comparative tests performed on some active test systems have demonstrated the accuracy and promptness of the proposed algorithm.

This work was supported by the project “Development and support of multidisciplinary postdoctoral programmes in major technical areas of national strategy of Research-Development-Innovation” 4D-POSTDOC, contract no. POSDRU/89/1.5/S/52603, a project co-funded by the European Social Fund through Sectoral Operational Programme Human Resources Development 2007–2013. We would like to thank the IREC—Catalonia Institute for Energy Research for hosting Bogdan Tomoiagă during his postdoctoral research stage. We would also like to thank Jennifer Fink for her English review.

Failure rates of system B (

Branch | λ [^{−1}] |
Branch | λ [^{−1}] |
Branch | λ [^{−1}] |
||||||
---|---|---|---|---|---|---|---|---|---|---|---|

1 | B1 | 1 | 0.071 | 37 | 36 | 37 | 0.016 | 73 | B10 | 73 | 0.019 |

2 | 1 | 2 | 0.096 | 38 | 37 | 38 | 0.024 | 74 | 73 | 74 | 0.082 |

3 | 2 | 3 | 0.078 | 39 | 38 | 39 | 0.064 | 75 | 74 | 75 | 0.009 |

4 | 3 | 4 | 0.035 | 40 | 39 | 40 | 0.065 | 76 | 75 | 76 | 0.091 |

5 | 4 | 5 | 0.065 | 41 | 38 | 41 | 0.095 | 77 | B11 | 77 | 0.065 |

6 | 5 | 6 | 0.082 | 42 | 41 | 42 | 0.046 | 78 | 77 | 78 | 0.017 |

7 | 6 | 7 | 0.059 | 43 | B6 | 43 | 0.085 | 79 | 78 | 79 | 0.017 |

8 | 7 | 8 | 0.012 | 44 | 43 | 44 | 0.075 | 80 | 79 | 80 | 0.091 |

9 | 7 | 9 | 0.012 | 45 | 44 | 45 | 0.062 | 65 | B9 | 65 | 0.042 |

10 | 7 | 10 | 0.011 | 46 | 45 | 46 | 0.036 | 66 | 65 | 66 | 0.054 |

11 | B2 | 11 | 0.007 | 47 | B7 | 47 | 0.065 | 67 | 66 | 67 | 0.017 |

12 | 11 | 12 | 0.039 | 48 | 47 | 48 | 0.093 | 68 | 67 | 68 | 0.016 |

13 | 12 | 13 | 0.095 | 49 | 48 | 49 | 0.019 | 69 | 68 | 69 | 0.085 |

14 | 12 | 14 | 0.036 | 50 | 49 | 50 | 0.065 | 70 | 69 | 70 | 0.066 |

15 | B3 | 15 | 0.048 | 51 | 50 | 51 | 0.017 | 71 | 70 | 71 | 0.052 |

16 | 15 | 16 | 0.076 | 52 | 51 | 52 | 0.017 | 72 | 71 | 72 | 0.052 |

17 | 16 | 17 | 0.023 | 53 | 52 | 53 | 0.051 | 73 | B10 | 73 | 0.019 |

18 | 17 | 18 | 0.094 | 54 | 53 | 54 | 0.026 | 74 | 73 | 74 | 0.082 |

19 | 18 | 19 | 0.056 | 55 | 54 | 55 | 0.055 | 75 | 74 | 75 | 0.009 |

20 | 19 | 20 | 0.067 | 56 | B8 | 56 | 0.026 | 76 | 75 | 76 | 0.091 |

21 | 20 | 21 | 0.099 | 57 | 56 | 57 | 0.017 | 77 | B11 | 77 | 0.065 |

22 | 21 | 22 | 0.045 | 58 | 57 | 58 | 0.032 | 78 | 77 | 78 | 0.017 |

23 | 21 | 23 | 0.073 | 59 | 58 | 59 | 0.017 | 79 | 78 | 79 | 0.017 |

24 | 23 | 24 | 0.046 | 60 | 59 | 60 | 0.068 | 80 | 79 | 80 | 0.091 |

25 | B4 | 25 | 0.049 | 61 | 60 | 61 | 0.055 | 84 | 5 | 55 | 0.052 |

26 | 25 | 26 | 0.062 | 62 | 61 | 62 | 0.061 | 85 | 7 | 60 | 0.051 |

27 | 26 | 27 | 0.066 | 63 | 62 | 63 | 0.098 | 86 | 11 | 43 | 0.072 |

28 | 27 | 28 | 0.059 | 64 | 63 | 64 | 0.017 | 87 | 12 | 72 | 0.061 |

29 | 28 | 29 | 0.099 | 65 | B9 | 65 | 0.042 | 88 | 13 | 76 | 0.069 |

30 | B5 | 30 | 0.034 | 66 | 65 | 66 | 0.054 | 89 | 14 | 18 | 0.049 |

31 | 30 | 31 | 0.114 | 67 | 66 | 67 | 0.017 | 90 | 16 | 26 | 0.036 |

32 | 31 | 32 | 0.074 | 68 | 67 | 68 | 0.016 | 91 | 20 | 83 | 0.045 |

33 | 32 | 33 | 0.065 | 69 | 68 | 69 | 0.085 | 92 | 28 | 32 | 0.066 |

34 | 33 | 34 | 0.059 | 70 | 69 | 70 | 0.066 | 93 | 29 | 39 | 0.085 |

35 | 34 | 35 | 0.025 | 71 | 70 | 71 | 0.052 | 94 | 34 | 46 | 0.061 |

36 | 35 | 36 | 0.026 | 72 | 71 | 72 | 0.052 | 95 | 40 | 42 | 0.042 |