WO2014109666A1

WO2014109666A1 - A method for determining a placement of protection devices in an energy distribution network

Info

Publication number: WO2014109666A1
Application number: PCT/RU2013/000027
Authority: WO
Inventors: Yury Sergeevich CHISTYAKOV; Elena Vladimirovna KHOLODOVA; Kirill Ivanovich NETREBA
Original assignee: Siemens Aktiengesellschaft
Priority date: 2013-01-14
Filing date: 2013-01-14
Publication date: 2014-07-17
Also published as: RU2015134134A3; RU2015134134A; RU2667662C2

Abstract

A method for determining a placement of protection devices (16) in an energy distribution network (10) is provided. The distribution network (10) is represented by a graph consisting of nodes (12) and edges (14), wherein each node (12) represents a derivation or an interconnection or a load point and wherein each edge (14) represents a transmission line or a feeder section, wherein at least some of the feeder sections comprise a protection device (16), comprising the steps of: a) providing a first number (s) of initial solutions of the distribution network (10) equipped with protection devices (16), wherein each solution is represented by a vector set (Xi) indicating an information about the presence of a protection device (16) in at least some, in particular each, of the feeder sections; b) determining at least one reliability index (RI) for each of the first number (s) of initial solutions, wherein the at least one reliability index (RI) represents a measure about a failure safety of a solution;

Description

A METHOD FOR DETERMINING A PLACEMENT OF PROTECTION DEVICES IN AN ENERGY DISTRIBUTION NETWORK

The invention relates to a method for determining a placement of protection devices in an energy distribution network. In particular, the energy distribution network is a power supply network of same or different voltage levels. However, the distribution network may be used for the distribution of any kind of energy, such as gas or oil. A distribution network may be represented by a graph consisting of nodes and edges . Each node represents a derivation or an interconnection or a load point. Each edge represents a transmission line or a feeder section, wherein at least some of the feeder sections comprise a protection device.

Reliability of distribution systems is a continuous concern for electric utilities. In particular, it is an aim to minimize sustained outages. The optimal placement of

protection (protective) devices in a distribution network allows better operation and improvement of the system reliability. Protection devices may be, for example, in the form of a fuse saving recloser, a fuse blowing recloser, a sectionalizer, a fuse or a switch. However, allocation of protection devices is a combinatorial constrained problem, difficult to solve due its nonlinear, discontinuous and non- differentiable characteristics. It would be desirable to find a global optimum solution within a reasonable computation time, even for complex network structures .

It is therefore an object of the present invention to provide an improved method for allocation of protection devices in an energy distribution network. This object is solved by a method according to the features of claim 1 and a computer program product according to the features of claim 9.

According to the invention, a method for determining a placement of protection devices in an energy distribution network, in particular a power supply network, is suggested. The energy distribution network (also referred to as a distribution network) is represented by a graph consisting of nodes and edges, wherein each node represents a derivation or an interconnection or a load point and wherein each edge represents a transmission line or a feeder section. At least some of the feeder sections comprise a protection device, such as a fuse saving recloser, a fuse blowing recloser, a sectionalizer, a fuse or a switch. ' The method comprises the steps of: a) Providing a first number of initial solutions of the

distribution network equipped with protection devices, wherein each solution is represented by a vector set indicating an information about the presence of a

protection device in at least some of the feeder sections. Preferably, the vector set indicates an information about the presence of a protection device in each of the feeder sections. Indicating an information comprises the

information whether or not a protection device is provided in a respective feeder section. Furthermore, the vector set may comprise the information about what kind of protection device (fuse saving recloser, fuse blowing recloser, sectionalizer, fuse or switch and so on) is provided in a respective feeder section. b) Determining at least one reliability index for each of the first number of initial solutions, wherein the at least one reliability index represents a measure about a failure safety of a solution. The higher the failure safety is, the better the solution. c) Selecting a second number of best solutions and a third number of perspective solutions out of the number of first solutions, wherein the second number of best solutions provides the highest failure safety according to their at least one reliability index, and wherein the third number of perspective solutions provides a failure safety according to their at least one reliability index being lower compared to the second number of best solutions . The selected second number of solutions corresponds to the best solutions of the initial number of solutions and will be the basis for new, modified solutions. The same is with the third number of solution. However, the third number of solutions does not contain a solution which is part of the second number of solution, but such solutions which are worse with respect to their failure safety. d) Creating a fourth number of solutions by modifying the second number of best solutions and creating a fifth number of solutions by modifying the third number of perspective solutions, wherein the forth and the fifth number of solutions is within a predetermined patch size in the neighborhood of the respective best and perspective solution. A patch is a number which characterizes the area around some solution for generation of neighbor solutions. In other words, the patch size defines the maximum

differences between some selected solution and new adjacent solutions. Modifying the second and third number of best and perspective solutions can be made by moving randomly chosen protective device on n positions and adjacency list, where 1 < n < patch size is preferred. The patch size defines the size of the neighborhood around the corresponding solution of the second and third number of solution. The step of creating a fourth and fifth number of solution aims to form new, further solutions. e) Creating a sixth number of random solutions of the

distribution network equipped with protection devices. This step ensures that a global minimum for the at least on reliability index can be found. The sixth number of random solutions should therefore be independent from the solutions of the fourth and fifth number of solutions. f) Proceeding with step b) at least once to determine the at least one reliability index for the solutions of the second to sixth number of solutions and form new sets of the second and third number of solutions. This step enables to find the best solution of each of the patches, created in step d) . g) Terminating the calculation steps b) to f) in case the at least one reliability index is considered to reach its global optimum. The global optimum (i.e. minimum in terms of the at least one reliability index or maximum in terms of the failure safety) is reached if no or no significant improvement can be achieved in the following cycles.

The suggested method allows to find a global optimum of the placement of protection devices in an energy distribution network with low computational effort even if the

distribution network is complex.

The method is based on the idea to apply a modified ABC (Artificial Bee Colony) algorithm to the problem of the optimal placement of switches and protective devices in distribution networks. The proposed algorithm's parameters are transparent and clear for the specified type of problems so they are easy to adjust. The method may be used in setting up new distribution networks. The method may also be used in grid modernization purposes because it has key factors for efficient usage of the existing grid configuration.

According to a preferred embodiment, the at least one initial solution in step a) is random. Each initial solution may differ from each other.

According to a further preferred embodiment, the second number of solutions is smaller than the third number of solutions. According to a further preferred embodiment, the forth number of solutions is greater than the fifth number of solutions. This is to examine the best solutions.

Accordingly, more solutions in its neighborhood are created. But it is always a question of computation time so that the best solutions have to be chosen carefully. This carefulness results in a small number of best solutions. Opposite, not so good but perspective solutions should not be missed. But due to limited computation resources (time for example) they are not very carefully studied. That's why the number of

perspective solutions is great, but the number of solutions in neighborhood is smaller.

According to a further preferred embodiment, the at least one reliability index is one or more of System Average

Interruption Duration Index (SAIDI) or System Average

Interruption Frequency Index (SAIFI) or Momentary Average Interruption Frequency Index (MAIFI) or any other reliability index defined by IEEE Std. 1366-2003. Usage of concrete indices depends on aims of the calculation.

According to a further preferred embodiment, creating the fourth and fifth number of solutions may be executed in parallel. This enables a faster converging to the global optimum.

According to a further preferred embodiment, in a step h) being executed instead of step e) the solutions of the forth number of solutions and the solutions of the fifth number of solutions are subject to a crossover procedure in which a substring of the best solution of a patch is exchanged with a substring of the best solution of another patch wherein a substring is a subset of the vector set. The condition for crossover may be chosen beforehand, for example, "every g cycles", where g is a predetermined parameter.

The invention further provides a computer program product directly loadable into the internal memory of a digital computer, comprising software code portions for performing the steps of the invention as set out above when said product is run on a computer.

The invention and its advantages will be described in more detail by reference to the accompanying figures.

Fig. 1 shows a diagram illustrating the method according to the invention. Fig. 2 shows an exemplary energy distribution network with an initial allocation of protection devices.

Fig. 3 shows a diagram illustrating a general procedure of neighborhood solutions generation within a patch in scope of ABC algorithm.

Fig. 4 shows a further distribution network illustrating an interpretation of a patch concept specified for the optimum replacement problem.

Fig. 5 shows a schematic diagram of a multiple-population parallel genetic algorithm, in which a communication between the populations is used for improving the result of the genetic algorithm.

Fig. 6 shows different patches and a communication between the patches for a crossover optimization.

Fig. 7 shows a diagram in which an improvement of a

reliability index in dependency of the number of cycles is illustrated by making use of the method according to the invention.

Fig. 8 shows a table illustrating an initial solution, a

final solution after applying a base algorithm of the invention, and a final solution after applying a preferred algorithm of the invention. The method proposed for the allocation of protection devices in an energy distribution network is based on the so called ABC (Artificial Bee Colony) -algorithm. In particular, the energy distribution network is a power supply network of same or different voltage levels. Before describing the method in detail, some basic information about the ABC-algorithm is given .

The Artificial Bee Colony (ABC) algorithm uses a colony of artificial bees. The bees are classified into three types: 1. Employed bees, 2. Onlooker bees, and 3. Scout bees. Each employed bee is associated with a food source, which it exploits currently. A bee waiting in the hive to choose a food source is an onlooker bee . The employed bees share information about the food sources with onlooker bees in the dance area. Each onlooker bee then chooses a food source. More follower bees are sent to more promising patches. A scout bee carries out a random search to discover new food sources. The position of a food source represents a solution for an optimization problem. The nectar amount of the food source is the fitness of the solution. The patch which includes food source and its neighborhood is a region within problem parameters' tolerance range. The basic ABC-algorithm is as outlined below:

1. Initialize population with random solutions.

2. Evaluate fitness of the population.

3. While (stopping criterion not met)

//Forming new population.

4. Select sites for neighborhood search.

5. Recruit bees for selected sites (more bees for best

sites) and evaluate fitnesses.

6. Select the fittest bee from each patch.

7. Assign remaining bees to search randomly and evaluate

their fitnesses.

8. End While. This basic algorithm will be used in a modified form to propose an optimal allocation of the protection devices in an energy distribution network 10 as outlined in Fig. 2. Generally, the distribution network (electrical grid) 10 is represented by the graph, where nodes 12 represent

derivation, interconnection or load points and edges 14 represent transmission lines or feeder sections. In this example, in total there are 51 edges 14 and each edge 14 is provided with a unique number "1", "2", "3" and so on. In some of the edges 14 protection devices 16 are arranged.

Protection devices are, for example, fuse blowing reclosers 18 (inside feeder connections), fuse blowing reclosers 20, sectionalizers (not shown), fuses 22 and switches 24. Fig. 2 shows a random, initial arrangement of the protection devices 16. In case that the distribution network has to be

modernized, the network arrangement may be that arrangement before an optimization. In order to identify the sections of the feeder where a specific protection device, i.e. a fuse saving recloser 18, a fuse blowing recloser 20, a sectionalize , a fuse 22 and a switch 24 is located, this information is stored in

information sets R_s, Rb, S, F and D which are defined for each type of protection device. In case that a specific protection device is in a specific edge, the number of this edge is stored in the corresponding information set. This is outlined in the table of Fig. 8 in which cases CA for the initial solution B and for a first and an improved second solution Kl, K2 the information sets together with a

reliability index RI (here-. SAIDI (System Average

Interruption Duration Index) ) are outlined.

For example, the information set R_s comprises information about the fuse saving reclosers. In the initial configuration of Fig. 2, there are no fuse saving reclosers. Hence, R_s does not contain any edge number (^w-^w in Fig. 8) . The information set R_b comprises information about the fuse blowing

reclosers. In the initial configuration of Fig. 2, there are fuse blowing reclosers in the edges 1, 8 and 39. Hence, R_b contains edge numbers "1", "8" and "39" in Fig. 8. The information set S comprises information about the

sectionalizers. In the initial configuration of Fig. 2, there are no sectionalizers. Hence, the information set S does not contain any edge number ("-" in Fig. 8) . The information set F comprises information about fuses. In the initial

configuration of Fig. 2, there are fuses in the edges 4, 6, 10, 12, 16, 18, 20, 24, 27, 29, 34, 37, 40, 42, 44, 46, 48, and 50. Hence, F contains edge numbers "4", "6", "10", "12", "16", "18", "20", "24", "27", "29", "34", "37", "40", "42", "44", "46", "48", and "50" in Fig. 8. The information set D comprises information about switches. In the initial

configuration of Fig. 2, there are switches in the edges 14, 15, 22, 23, 33, 36, and 51. Hence, D contains edge numbers "14", "15", "22", "23", "33", "36", "51" in Fig. 8.

The application of the ABC algorithm in solving a specific problem depends initially on defining the representation of potential solutions to the problem. Let Xi be the i-th solution belonging to the current algorithm's cycle. The individual Xi is composed by the information sets R_a, R_b , S, F and D, concatenated in this order in a vector set, also named as row vector, Xi = [R_s | ¾ | S | F | D] .

Given a set of possible locations in the edges 16 (i.e. the feeder sections) and sets of various protective devices 18, 20, 22 and switches 24 (which as well is a protection device), the proposed single (or multi-) objective

optimization problem is to define a subset of the locations (i.e. edges) at which to install a specific device. The specific objective of the minimization procedure can be defined by one or more reliability indices, such as SAIDI (System Average Interruption Duration Index) , SAIFI (System Average Interruption Frequency Index) or MAIFI (Momentary Average Interruption Frequency Index) , or any other

reliability index which are formally defined in [1] . Referring now to Fig. 1, the steps according to the method of the invention will be described.

In step SI, a first number s of initial solutions of the distribution network equipped with protection devices will be provided. The first step can be regarded as an

initialization. The initial solutions may be determined randomly. Each solution is represented by a vector set Xi (i = l...s) indicating the information about the presence of a protection device in each of the feeder sections. As already set out, indicating the information also comprises the information whether or not a protection device is provided in a respective feeder section. Furthermore, the vector set Xi comprises the information about what kind of protection device (fuse saving recloser - R₃, fuse blowing recloser -

Rb, sectionalizer - S, fuse - F or switch - D) is provided in a respective feeder section. The allocation for one of the initial solutions may be, for example, as shown in Fig. 2 and outlined in the table of Fig. 8 for CA = "B" . The first number s corresponds to the number of scouts. For example, s may be chosen to s = 10.

In step S2, at least one reliability index for each of the first number of initial solutions will be determined. In the example of Fig. 8, only SAIDI is determined. However, SAIFI and AIFI could be determined, as well as other indices from [1] . In general, the at least one reliability index (here: SAIFI) represents a measure about a failure safety of a solution. The higher the failure safety is, the better the solution. This determination can be seen as an evaluation of the so called fitness of each of the first number s of initial solutions.

In step S3, the best solutions identified in step S2 are stored.

In step S4, a second number n of best solutions and a third number m of perspective solutions out of the number of the best first solutions (stored in step S3) are selected. The second number n of best solutions provides the highest failure safety according to their at least one reliability index. The third number m of perspective solutions provides a failure safety according to their at least one reliability index being lower compared to the second number n of best solutions. The second number n determines the number of best patches to be considered, the third number m determines the number of perspective patches. Thereby, the condition m > n should be fulfilled. For example, n might be chosen to be n = 2, m might be chosen to be m = 5.

The selected second number n of solutions corresponds to the best solutions of the initial number s of solutions and will be the basis for new, modified solutions. The same is with the third number m of solutions.

In step S5, a fourth number N of solutions will be created by modifying the second number of best solutions. The forth number N of solutions is within a predetermined patch size r (for example, r =2) in the neighborhood of the respective best solution n_j (j=l, 2 according to the example) . This means for each of the n best solutions which were selected in step S4 , N additional solutions will be created. For example, N can be chosen to be N = 20. The resulting solutions (N+l for each patch n) will be assessed according to step S2.

Correspondingly, in step S6 a fifth number M of solutions will be created by modifying the third number of perspective solutions. The fifth number M of solutions is within the predetermined patch size r (or a different patch size) in the neighborhood of the respective best solution m_k (k=l, 5 according to the example) . This means for each of the m perspective solutions which were selected in step S4 , M additional solutions will be created. It is to be noted that the condition M < N should be fulfilled. For example, M can be chosen to be M = 10. The resulting solutions (M+l for each perspective patch m) will be assessed according to step S2. Modifying the second and third number n, m of best, and perspective solutions can be made by moving randomly chosen protective device on n positions in adjacency list, where 1 < n < patch size is preferred.

Referring to Fig. 3, the patch size r of a patch 34 defines the size of the neighborhood around the corresponding solution of the second and third number n, m of solution. Reference numeral 30 depicts the best solution of n_j or m_k in which the protection devices 16 are in a corresponding specific edges 14. The patch size r defines a radius around the best solution 30 of the patch 34. The stars 32 whose number corresponds to N or M (depending on the fact whether 30 is a best solution n_j or a perspective solution m_k) represent the fourth or fifth number of created solutions in step S5 or S6. The steps S5 and S5 of creating a fourth and fifth number N, M of solutions aim to form new, further solutions . Step S7 in conjunction with step S9 which will be explained lateron in more detail is optional. In step S7, it will be checked whether a condition for so called crossover is fulfilled. If this condition is fulfilled ("y"), it will be proceeded with step S9. Otherwise ("n") , step S8 will follow.

In step S8, a sixth number s (s may correspond to the first number of initial solutions) of random solutions of the distribution network equipped with protection devices is created which will be assessed according to step S2. This step ensures that in step S2 a global minimum for the at least on reliability index can be found. The sixth number s of random solutions should therefore be independent from the solutions of the fourth and fifth number of solutions. Steps S2 to S8 and S2 to S9, respectively, are called a cycle c. The maximum number of cycles may be chosen to be c = 100. The algorithm will be terminated (in step S2 or S3) when the reliability index of one of the assessed solutions has reached its global optimum. The global optimum (i.e. minimum in terms of the at least one reliability index or maximum in terms of the failure safety) is considered to be reached if no improvement can be achieved in the following cycles. It is to be noted that at steps S5 and S6 (see Fig. 1) N and M solutions are generated in the neighborhood (patch in nature analogy) of each n_j best solution and for each perspective m_k solution, respectively. The size r of the patch is one of the algorithm's parameters. For an ordered dimension of the problem neighborhood conception causes no difficulties (see Fig. 3) . Opposite, when a graph

representation of the problem with randomly numbered edges is used, the definition of the neighbor solution needs to be redefined.

For the distribution network 40 shown in Fig. 4 and

consisting of nodes 42, edges 44, and protection devices 46 (fuse blowing breaker 48, fuse blowing reclosers 50, fuses 52 and switches 54) edges with numbers "11" and "12" are physically located quite far from each other while as numbers which appear in the solution they are the nearest. For this class of problems, an adjacency list has to be used to generate a new solution in the neighborhood of the specified solution. An adjacency list is a data structure for representing graphs. In an adjacency list

representation, for each vertex in the graph, a list of all other vertices which has an edge to (that vertex's

"adjacency list") is kept. In this case, the patch size r is the number of edges 44 adjacent with each other on which a current protection device 46 may be moved. For example, if the patch size r is 2 for Fig. 4, it means the device that is located in the edge number "8" can be moved sequentially to the edge number "7" and then to the edge number "5" .

Thus, the edge numbers which form each solution do not apply at algorithm's operations at themselves and in fact they are just device's placement pointers.

In Fig. 8, the obtained solution found with the proceeding described is indicated by Kl . Fig. 7 shows a diagram in which the improvement of the reliability index SAIDI in dependency of the number of cycles is illustrated. Kl depicts the development according to the proceeding described above. As can be seen, SAIDI can be reduced about 40 % within less than 100 cycles. This result can be achieved by considering only the relocation of two reclosers R_S( five fuses F and six of the existing switches D in a feeding section (cf. case CA =P "Kl" in Fig. 8) . The solution can be even more improved if a crossover which is an optimization technology used in Genetic Algorithms (GA) is applied. Referring to Fig. 1, crossover is carried out in step S9 among the N and solutions created in steps S5 and S6. Step S9 is carried out if in step S8 a condition for crossover is found to be true.

In general, crossover is a combining method of genetic algorithms. Crossover modification is based on a patch conception (feature of ABC algorithm) and a parallel

computation of patches. Parallel computation usually refers to a multiprocessing optimization where several processors access globally shared memory. Using genetic algorithm (GA) as a well-known example, a set of populations (i.e. patches 60 in Fig. 5) is placed in the local memory of each

processor. During each cycle a population (patch 60) tries to improve itself in the local memory. At the end of the cycle the fittest member from each sub-GA 60 is broadcast to each other sub-GA 60, with a certain probability. This is

illustrated by the communication paths 62 in Fig. 5.

Usage of patches in an ABC algorithm (cf . Fig. 6) makes it possible to draw an analogy to the parallel computation. In Fig. 6, a schematic snapshot of an ABC algorithm is shown. One can consider a patch as a sub-GA 60 and an employed bee 64 as the fittest member of the sub-GA. 66 represents an onlooker bee, 68 a scout bee, r is the patch size.

The combining is done by random substrings exchange between two solutions (patches) . A crossover operator is chosen to provide a communication 62 between patches 60 due to next features of the protective devices optimum placement problem;

1. An optimum placement of several (not all) types of

protective devices can allow a solution to be near the global (local) optimum.

2. Each type of protective devices influences on reliability indices with a different power.

3. Each substring of the problem solution contains positions of the one type of the protective devices.

The first feature of the problem solution is critical for a single-ob ective optimization. If one solution includes optimal positions of the reclosers under two schemes (fuse saving and fuse blowing) , this allows the solution to be the fittest within the patch and elevates it to the employed bee. Opposite, in another solution fuses and switches are located at the optimal places. During patch communication this two solutions can be chosen to be the parents to produce a new solution as shown below. For example,

Parent 1 = [R_sl | R_bl | Si | Fi | DJ

Parent 2 = [R_s2 | R_b2 | S₂ | F₂ | D₂]

Offspring = Parent 1 + Parent 2 = [R_sl | R_bl | S₂ | F₂ | D₂]

After crossover, the offspring will be better than both previous solutions. It means that a communication between the patches in an ABC algorithm, when applied to the optimum protective devices placement problem, increases algorithm convergence. It also makes an application of algorithm more robust, preventing it from a local optimum and capable to find the global one. Hence, crossover between the patches helps to increase algorithm convergence.

In Figs. 7 and 8, the effect of crossover on SAIDI compared to Kl can be seen. The result is depicted with K2. In this example which is based on the initial Case CA = "B" and the distribution network in Fig. 2, SAIDI could be reduced around 69% in relation to the base case. Here, the maximum numbers of the protection devices of each type were chosen to: R_max = 4, Smax = 2, Fmax = 18, O_max = 7. For the modified algorithm (^WK2") a patch exchange occurs every 10^th cycle. Fig. 7 shows that the algorithm modification with crossover applied to the described problem increases its convergence and allows finding a better solution.

The main advantages of the suggested approach are: An optimal solution is found faster compared to classical ABC-algorithm.

The quality of the final solution is improved since a global optimum can be found.

A stack in local optima can be prevented, resulting in an increased robustness.

It allows an aggregation of the best single and

multiprocessing optimization techniques.

The method can be carried out with usage of only one CPU while results are similar to multiprocessing optimization.

References

[1] IEEE Guide for Electric Power Distribution Reliability- Indices, IEEE Std. 1366-2003.

List of Reference Signs

10 distribution network

12 node

14 edge

16 protection device

18 fuse blowing breaker

20 fuse blowing recloser

22 fuse

24 switch

30 best solution ni

32 neighbour to best solution ni

40 distribution network

42 node

44 edge

46 protection device

48 fuse blowing breaker

50 fuse blowing recloser

52 fuse

54 switch

60 patch

62 communication between patch

64 employed bee (best solution)

66 onlooker bee (neighbor solution)

68 scout bee

r patch size

s first number of initial solutions

n second number of best soltions

m third number of best soltions

N fourth number of solutions which are neighbours to a respective best solution ni

M fifth numer of solutions which are neighbours to a respective perspective solution mi

RI reliability index

CA case

B initial solution

Kl first solution K2 second solution

Xi vector set

R_s fuse saving recloser

R_b fuse blowing recloser

S sectionalizer

F fuse F

D switch

Claims

Patent Claims

1. A method for determining a placement of protection devices (16) in an energy distribution network (10) , which is represented by a graph consisting of nodes (12) and edges (14) , wherein each node (12) represents a derivation or an interconnection or a load point and wherein each edge (14) represents a transmission line or a feeder section, wherein at least some of the feeder sections comprise a protection device (16), comprising the steps of:

a) providing a first number (s) of initial solutions of the distribution network (10) equipped with protection devices

(16) , wherein each solution is represented by a vector set (Xi_.) indicating an information about the presence of a protection device (16) in at least some, in particular each, of the feeder sections;

b) determining at least one reliability index (RI) for each of the first number (s) of initial solutions, wherein the at least one reliability index (RI) represents a measure about a failure safety of a solution;

c) selecting a second number (n) of best solutions and a

third number (m) of perspective solutions out of the number of first solutions (s) , wherein the second number (n) of best solutions provides the highest failure safety according to their at least one reliability index, and wherein the third number (m) of perspective solutions provides a failure safety according to their at least one reliability index being lower compared to the second number (n) of best solutions;

d) creating a fourth number (N) of solutions by modifying the second number (n) of best solutions and creating a fifth number (M) of solutions by modifying the third number (m) of perspective solutions, wherein the forth and the fifth number (N, M) of solutions is within a predetermined patch size (r) in the neighborhood of the respective best and perspective solution;

e) creating a sixth number (s) of random solutions of the distribution network (10) equipped with protection devices (16) ;

f) proceeding with step b) at least once to determine the at least one reliability index for the solutions of the second to sixth number of solutions;

g) terminating the calculation steps b) to f) in case the at least one reliability index is considered to reach its global optimum.

2. The method according to claim 1, wherein the at least one initial solution in step a) is random.

3. The method according to claim 1 or 2, wherein each initial solution is differing from each other.

4. The method according to one of the preceding claims, wherein the second number (n) of solutions is smaller than the third number (m) of solutions.

5. The method according to one of the preceding claims, wherein the forth number (N) of solutions is greater than the fifth number ( ) of solutions.

6. The method according to one of the preceding claims, wherein the at least one reliability index is one or more of

- System Average Interruption Duration Index (SAIDI) ;

- System Average Interruption Frequency Index (SAIFI) ;

- Momentary Average Interruption Frequency Index (MAIFI) ;

7. The method according to one of the preceding claims, wherein creating the fourth and fifth number (N, M) of solutions is executed in parallel.

8. The method according to claim 7, wherein in a step h) being executed instead of step e) the solutions of the forth number (N) of solutions and the solutions of the fifth number (M) of solutions are subject to a crossover procedure in which a substring of the best solution of a patch is

exchanged with a substring of the best solution of another patch wherein a substring is a subset of the vector set (Xi) .

9. Computer program product directly loadable into the internal memory of a digital computer, comprising software code portions for performing the steps of one of the

preceding claims when said product is run on a computer.