Method for optimizing the placement of voltage sensors on an electrical network using a genetic algorithm

Abstract

A method for optimizing the positioning of sensors configured to provide measurements of electrical variables in an electrical network comprising a set of nodes comprises: a random generation (E1) of a first generation population of solutions corresponding to a set of possible positions of the sensors within the set of nodes of the network, a solution being associated with a vector, called gene, and at least one iteration of reproduction of the population, comprising a selection (E3) by tournaments of solutions within the population, by random drawings of pairs of solutions in the population and selection of a solution having the best performance within each pair drawn randomly.At the end (E6) of the reproduction iteration(s), the method comprises a placement (E7) of the sensors within the network at the positions determined by a predominant gene associated with a maximum evaluated performance within the solutions of the last generation population. Abstract figure: Figure 2.

Description

Title of the invention: Method for optimizing the placement of voltage sensors on an electrical network using a genetic algorithm Technical field

[0001] The present disclosure relates to the field of the management of electricity distribution and transmission networks. It applies in particular, but not exclusively, to the estimation of the state of such networks, which is particularly useful for carrying out voltage adjustment in the presence of decentralized electricity production. Prior art

[0002] The voltage adjustment of a distribution network in the presence of decentralized production requires a reliable estimation of the voltages at any node of the network. The voltage at any node of the network can in particular be determined by applying the laws of electrical engineering to real measurements provided by voltage sensors positioned on nodes of the distribution network and to pseudo-measurements calculated from a load model of consumers and HTA / LV transformer stations not instrumented by sensors.

[0003] The reliability of the voltage estimation depends directly on the number of sensors in the network. If the number of sensors in the network is too low, it is not possible to guarantee the operation of a voltage adjustment method because the accuracy of the voltage estimation at any node in the network will not comply with the technical constraints, namely a maximum difference of 1% between the voltage estimation and the actual, unknown, value of this voltage. However, it is not possible, for cost reasons, to instrument a large number of measurement points on a distribution network.

[0004] It is therefore important, given a limited number of voltage sensors available to a network operator, to optimize their placement on the network to guarantee a good state estimation.

[0005] To date, the placement of sensors is often carried out according to expert opinion, the latter using his electrotechnical knowledge to obtain an efficient placement. This placement may be relevant, but it is not always optimal, in particular because it is impossible for the expert to exhaustively test all the possible sensor positioning combinations on the network. In addition, such expert-determined sensor placement is often time-consuming to set up. Such a method is also not generalizable in the event of scaling up, in the case where the distribution network operator would like to place sensors for all the network outlets, which would require calling on a large number of experts. It should be recalled that The connection between the transmission network and the distribution network is located in an HTB / HTA substation, consisting of one or more transformers behind each of which several lines depart, making it possible to connect several consumers and producers. One of these lines and everything it connects is called a "feeder".

[0006] Patent document FR 3 006 818 A1 in the name of the Applicant describes an iterative method for determining a minimum number of sensors to be installed in a network and their position to ensure a sufficiently reliable estimate of the voltages at all nodes of the network. Such a method is based on a comparison of a first series of simulated values ​​of electrical variables of the network, by simulation of its operation, and a second series of estimated values ​​of these variables, corresponding to measurements of theoretical sensors, obtained by state estimation from a subset of the first series of simulated values. In the event of a divergence less than a threshold value, sensors are installed in the network at the locations of the theoretical sensors. Otherwise, the method is repeated by changing the subset of values ​​corresponding to measurements of theoretical sensors.

[0007] Such a method is interesting in that it makes it possible to guarantee the reliability of the state estimation associated with a given positioning of sensors in the network. However, it does not make it possible to guarantee that this positioning is optimal. In addition, the search for an adequate positioning can prove to be costly in terms of time, given the iterative nature of the method, which requires successively and randomly exploring a set of configurations of positions of voltage sensors, which can prove to be tedious.

[0008] Patent document CN107563550A proposes a method for real-time state estimation in an electricity distribution network, including in particular wind and photovoltaic energy producers. This state estimation method is based on the use of a set of voltage sensors. The measurements made by these sensors make it possible to reconstruct the voltages across the entire network.

[0009] This document also briefly discusses the idea of ​​using a genetic algorithm to optimize the positioning of voltage sensors in the electrical distribution network. It is recalled that genetic algorithms belong to the family of evolutionary algorithms. Their goal is to obtain an approximate solution to an optimization problem, when there is no exact method or the solution is unknown, to solve it in a reasonable time. Genetic algorithms use the notion of natural selection and apply it to a population of potential solutions to the given problem (in this case, the evaluated voltage sensor positions).

[0010] Although few details are given in this prior art document regarding the implementation details of this genetic algorithm, it nevertheless appears that the described method for optimizing the position of the voltage sensors has several drawbacks. Indeed, the proposed method does not allow in particular to obtain a solution to the problem of the optimal positioning of the voltage sensors with a constrained number of voltage sensors available by the network operator. However, these sensors are often limited in number and it is important to take this operational constraint into account when optimizing their placement at different nodes of the network. In addition, this method does not guarantee sufficient exploration of the space of possible solutions, and can therefore converge towards a local optimum, which will give, in terms of state estimation, a suboptimal response in terms of reliability and precision.Finally, this method appears suboptimal in that it does not take into account the topology of the network considered.

[0011] There is therefore a need for a technique for optimizing the positioning of sensors in an electrical network which does not have these various drawbacks of the prior art. Summary

[0012] The present disclosure improves the situation.

[0013] A method is proposed for optimizing the positioning of sensors in an electrical network comprising a set of nodes, the sensors being configured to provide measurements of electrical variables of the network. Such a method comprises: a. a random generation of a first generation population of solutions corresponding to a set of possible positions of the sensors within the set of nodes of the network, a solution being associated with a vector, called gene, representative of the positions of sensors within the network, and b. at least one iteration of reproduction of the population, producing from a generation population of rank i £ 1 a generation population of rank i+1, the reproduction comprising: i. An evaluation of a performance of the solutions of the population of the generation of rank i; ii. A tournament selection of solutions within the population of the generation of rank i, by randomly drawing pairs of solutions from the population and selecting a solution with the best performance within each randomly drawn pair; iii. A crossing of at least some selected pairs of solutions each generating two daughter solutions; iv. A production of a generation population of rank i+1 including at least some solutions selected by tournaments of the generation population of rank i, the daughter solutions, and randomly generated solutions, the generation population of rank i+1 comprising the same number of solutions as the generation population of rank i;

[0014] At the end of the reproduction iterations, such a method comprises placing the sensors within the network at positions determined by a predominant gene associated with a maximum evaluated performance within the solutions of the last generation population.

[0015] According to another aspect, there is provided an electrical network comprising a set of nodes on at least some of which are placed sensors configured to provide measurements of electrical variables of the network, the positioning of the sensors being optimized by implementing the method as described previously.

[0016] According to another aspect, there is provided a computer program comprising instructions for implementing all or part of a method as defined herein when this program is executed by a processor. According to another aspect, there is provided a non-transitory, computer-readable recording medium on which such a program is recorded.

[0017] The features set out in the following paragraphs may, optionally, be implemented, independently of one another or in combination with one another:

[0018] Reproduction also includes mutation of the gene of at least some of the daughter solutions.

[0019]

[0020]

[0021] Reproduction also includes mutation of the gene of at least some of the selected solutions that have not undergone crossbreeding. The gene is a vector containing the positions of sensors within the network, ranked by distance to an upstream node in the network, and of length equal to a number of sensors. The evaluation of a performance of a solution of the population of the generation of rank i implements a calculation of an objective function defined by: |Y where Perf denotes the per-loadflow\n) |j formance of the ground solution, N is a number of operating points studied, loadflow(n) associates with an operating pointn the value of the electrical variables of the nodes of said network calculated from known production and consumption data for said network and estimatio^n, ground) designates for the operating pointn the value of the electrical variables of the nodes of the network estimated from the measurements provided by the sensors placed at the set of positions defined by the gene of the ground solution. A solution presents a performance of as much better than it minimizes the value of the calculated objective function.

[0022] The crossing of pairs of selected solutions implements a simple crossing or a double crossing of the genes of the chosen solutions, in an equiprobable manner for each pair of selected solutions.

[0023] The mutation of the gene of a solution implements a displacement of at least one of the sensors from an initial node to a final node of the network located in a neighborhood of the initial node, according to a probability decreasing with a distance of the final node relative to the initial node.

[0024] The population reproduction is iterated until reaching a generation of rank j = 0.15*Nb_sol*Nb_cap, where Nb_sol denotes the number of solutions in the population and where Nb_cap denotes the number of sensors. Brief description of the drawings

[0025] Other characteristics, details and advantages will appear on reading the detailed description below, and on analyzing the attached drawings, in which: Fig.l

[0026] [Fig.l] illustrates an electrical distribution network according to one embodiment. Fig. 2

[0027] [Fig.2] illustrates a method for optimizing the positioning of voltage sensors in a distribution network for voltage adjustment in the presence of decentralized production according to one embodiment. Fig. 3

[0028] [Fig.3] illustrates a tournament selection of solutions within the framework of the optimization method of [Fig.2] according to one embodiment. Fig. 4

[0029] [Fig.4] illustrates the crossing of selected solutions with simple crossing over within the framework of the optimization method of [Fig.2] according to one embodiment. Fig. 5

[0030] [Fig.5] illustrates the crossing of selected solutions with double crossing within the framework of the optimization method of [Fig.2] according to one embodiment. Fig. 6

[0031] [Fig.6] illustrates the principle of gene mutation within the framework of the optimization method of [Fig.2] according to one embodiment. Fig. 7

[0032] [Fig.7] presents a curve representative of the mutation probability as a function of the distance to the sensor within the framework of the optimization method of [Fig.2] according to one embodiment. Fig. 8

[0033] [Fig-8] presents a block diagram of the generation of a generation population of rank n+1 from a generation population of rank n within the framework of the optimization method of [Fig.2] according to one embodiment. Fig. 9

[0034] [Fig.9] shows an example of sensor placement obtained by applying the optimization method of [Fig.2] according to one embodiment. Fig. 10

[0035] [Fig. 10] schematically illustrates the structure of a sensor positioning optimization device configured to implement the method according to [Fig.2]. Description of the embodiments

[0036] Reference is now made to [Fig. 1], which illustrates an electrical network referenced 1. Such a network 1 may be a transmission network, which carries electricity from production centers to large industrial sites and distribution networks, or a distribution network which allows electrical energy to be transported locally, from distribution centers to the end customer.

[0037] Such a network 1 comprises a set of nodes organized according to a tree structure from a source node. Each branch of the network topology comprises one or more nodes, which may correspond to HTA / LV substations, operating devices, consumers or even decentralized producers. In the example of [Fig.l], the source node has the number “0”, and each of the nodes of the tree structure has a number, which increments step by step along a branch of the tree structure. The electrical network of [Fig.l] comprises for example 153 nodes.

[0038] It is assumed that certain data and information are available on the electrical network 1, and in particular: - the topology of the departure studied, including the position of the sensors already present and the Operating Information Exchange Devices (DEIE), which allow the remote control and remote monitoring of decentralized production installations; - production and consumption data on network 1. This data must be sufficiently numerous and varied to guarantee a certain exhaustiveness of the situations encountered on network 1.

[0039] Knowing these different elements, it is proposed, in one embodiment, to optimize the placement of sensors in the network 1 according to a method which is based on the use of a genetic algorithm, the general block diagram of which is illustrated in [Fig.2],

[0040] During a first step referenced E1, a random generation of a first generation population of sensor positioning solutions is carried out. in network 1. Each solution in this population corresponds to a set of possible positions of the sensors within the set of nodes in network 1. Each solution is associated with a vector, called a gene, representing the positions of the sensors within network 1. For example, the gene of one of these solutions is expressed in the form [0, 123, 40, 77, 100]. The length of the gene corresponds to the number of sensors that can be placed in network 1, five in this example. Each component of the vector contains the number of one of the nodes in network 1 on which it is proposed to place a sensor according to this solution, these nodes being ordered in the vector according to their distance from the source node "0". In this example, the solution associated with gene [0, 123, 40, 77, 100] corresponds to a solution in which five sensors are respectively placed on nodes “0”, “123”, “40”, “77” and “100” of network 1.Such encoding of the gene by sensor position is well suited to the problem of optimizing the positioning of sensors in a network with a tree structure, in particular because it allows the topological structure of the network to be kept and to take advantage of it in solving the optimization problem. This way of representing a solution in vector form is notably much better suited to the problem considered than could be a binary encoding, of the type [1, 0, 0, 0, ... 1, 0, 1, 0, 0] in which the length of the vector would be equal to the number of nodes in the network 1, and in which each component of the vector could take a value 0 or 1, depending on the absence or not of sensors on the node considered.

[0041] The genetic algorithm implemented in the optimization process illustrated in [Fig.2] uses natural selection mechanisms so that the population of solutions considered (i.e. the sensor positions considered) improves over time, retaining only the most efficient solutions, which will be able to transmit their “genes” to the following generations. It is therefore necessary to evaluate the performance of each of the solutions in a population. This is what is done during a step referenced E2.

[0042] Indeed, in order to compare the different sensor positions, it is necessary to be able to evaluate their performance in order to maximize it, and thus obtain the best estimate of the state of the network 1. In this case, we seek to minimize the difference between the state estimate obtained with the given sensor position and a reference situation obtained via a "loadflow". We recall that a loadflow is a digital calculation of the energy flows in an electrical network making it possible to obtain the value of an electrical variable, for example the voltage on all the nodes of the network, or the active and reactive powers on each section of the network. The loadflow is calculated by taking into account the consumption and production of the different elements of the network as well as the characteristics of the lines, according to a technique known to those skilled in the art which we will therefore not detail here further.

[0043] In one embodiment, the optimization method of [Fig.2] aims to minimize the objective function defined as follows:

[0044] [Math.l] Per f (sol) = L,max —-—-77------JK 7 “ / 7=1 \| loadflow{Ti) 1 /

[0045] where Perf denotes the performance of the ground solution, N the number of operating points studied, and the functions loadflow(n) and estimaiionin, sol) associate with each operating point the voltage of the nodes of the network studied calculated respectively using a loadflow and a state estimation for which the placement of the voltage sensors is given by the ground solution.

[0046] In one embodiment, this objective function is based on the use of operating points, i.e. production and consumption levels on the network, intelligently distributed over the different producers and loads of the network. In another embodiment, this objective function is based on the use of N time steps.

[0047] We then calculate the absolute value of the relative difference between these two states of the network, for which we keep the maximum relative difference. We finally sum for all the operating points or time steps.

[0048] The optimal position of the sensors is the one which will minimize this objective function.

[0049] In an embodiment where we are more specifically interested in the voltage at each of the nodes of the network 1, this objective function can still be expressed:

[0050] [Math.2]

[0051] Where N„ denotes the number of nodes in the network, N p denotes the number of operating points, y1 denotes the actual voltage at node n for operating point i and Vlest / l denotes the estimated voltage at node n for operating point i.

[0052] This objective function being defined and the input data being known, it is possible to move on to optimization, that is to say to the search for the optimal solution, according to an iterative process corresponding to the repetition of the successive steps E2 to E6 of evaluation, selection, crossing and mutation, production of the next generation and final test.

[0053] Each solution of the first generation population generated during step E1 has, as indicated above, a gene, which corresponds to a vector representation of the sensors in the network, and a performance, calculated during step E2. The performance of a solution is inversely proportional to the value of the objective function for the position of sensors on the network 1 given by its gene. Thus, the more a solution is efficient, and the more it minimizes the value of the objective function.

[0054] In one embodiment, the number of solutions in a population is fixed and is retained from generation to generation. It may be set by the user when launching the algorithm. For example, a population of 64 individuals, or solutions, has given satisfactory results.

[0055] After evaluating the performance of each solution in the population, the population is reproduced. To do this, a selection of solutions is first carried out during the step referenced E3, which will enable the next generation of the population to be fed.

[0056] In one embodiment, this selection is based on the use of a tournament logic referenced 2, illustrated schematically in [Fig.3]. To do this, pairs of individuals are randomly drawn from the population, their performances are compared two by two and the best of the two individuals is kept each time. In fact, the best individual of the generation of rank i is guaranteed to be kept for the following generation of rank i+1; similarly, the worst individual of the generation of rank i is guaranteed to be eliminated. This also guarantees that not only the best individuals are kept but also “average” individuals to avoid local optima.Thus, this tournament selection logic allows for a good exploration of the solution space, better in particular than a roulette selection which has two main drawbacks: on the one hand, it does not guarantee keeping the best individual for the next generation and on the other hand, it can lead to a convergence of the algorithm towards a local minimum in the case where a solution presents a much better performance than the others.

[0057] Thus, in the example of [Fig.3] for this step E3, a tournament 2 is organized between the solution “1”, of performance fl and the solution “8”, of performance f8, which leads to the selection of the solution “8” whose performance f8, evaluated during the step E2, is higher than that fl of the solution “1”. Similarly, tournaments are organized between the solutions “2” and “9”, between the solutions “3” and “10”, between the solutions “4” and “11”, between the solutions “5” and “12”, between the solutions “6” and “13” and between the solutions “7” and “14”, which lead to the selection referenced 3 of the solutions “9”, “3”, “4”, “12”, “6” and “7” which each win their tournament.

[0058] Thus, at the end of step E3, 50% of the solutions from the population considered are selected.

[0059] These selected solutions referenced 3 are used during the subsequent step E4 of crossing as parents of new daughter solutions, and possibly of mutation, which will feed the population of the next generation.

[0060] These selected solutions are also the subject of a second tournament, in order to complete the solutions that can be directly integrated into the next generation of the solution population. This second tournament is also based on a random selection of pairs of solutions from among the selected solutions: for each tournament, we keep the one of the two selected solutions that presents the best performance, i.e. that minimizes the objective function the most. At the end of this second tournament, we therefore select 25% of the solutions from the population considered, which are directly fed into the next generation population.

[0061] The step referenced E4 is a step of mutation and crossing of the solutions selected by tournaments during step E3.

[0062] A two-by-two crossover is carried out of some of the solutions selected during step E3, as illustrated in Figures 4 and 5. Each pair of solutions, called parent solutions referenced 4 and 5, gives rise to two daughter solutions, which are obtained by simple crossing (daughter solutions referenced 6 and 7 in [Fig.4]) or double crossing (daughter solutions referenced 9 and 10 in [Fig.5]) of their genes.

[0063] This crossing, also called in English "crossover", makes it possible to mix the genes of two parent solutions 4 and 5, to give a daughter solution. The gene of a daughter solution is obtained by taking a part of the gene of the first parent solution referenced 4 (therefore certain sensor positions) with a part of the gene of the second parent solution referenced 5 (therefore certain other sensor positions) of a pair of solutions 4, 5 drawn randomly. We will use a simple crossover (a single cut 8 in the gene, illustrated in [Fig.4]) or a double crossover (two cuts 11 and 12 in the gene, illustrated in [Fig.5]), chosen in an equiprobable manner for each pair of individuals.

[0064] This crossover occurs with a certain defined probability, which, in one embodiment, is set at 0.8. Thus, there is an 80% chance of performing a crossover on a pair of parent solutions: parent solutions that do not undergo crossover may be mutated during the subsequent step, without having been crossed.

[0065] For example, the simple crossover crossing of a parent solution referenced 4 whose gene is expressed [0, 123, 40, 77, 100] with a parent solution referenced 5 whose gene is expressed [5, 126, 47, 104, 102] can give two daughter solutions referenced 6, 7 whose genes are expressed [0, 123, 47, 104, 102] and [5, 126, 40, 77, 100],

[0066] During this step E4, the mutation of the gene of a solution can also appear with a certain defined probability. This intentionally caused mutation makes it possible to explore the space of solutions. In one embodiment, this probability is set between approximately 0.2 and 0.7. In an advantageous embodiment, this probability is set at 0.4, which means that each mobile sensor has a pro- ability to mutate, and therefore change position, by approximately 0.4.

[0067] In case of mutation of the gene of a solution, this mutation moves one or more of the sensors, from their initial position defined in the gene of the solution, to a new final position in one of the nodes of their neighborhoods. For example, the gene of the solution [0, 123, 40, 77, 100] can mutate to [0, 135, 40, 77, 100], the node "123" being directly neighbor of the node "135" in the network 1 of [Fig.l].

[0068] As illustrated by the curve in [Fig.7], we choose to impose a mutation probability that decreases with the distance of the final node from the initial node, up to a maximum distance of 15 nodes. [Fig.6] illustrates this mutation probability for a gene that would carry sensor positioning information on node "74". The probability that this gene mutates into "73" or "75" is the highest, and equal to 0.3, but decreases as we move away from node "74" according to the network topology, and becomes zero beyond node "23", which is at a distance of fifteen from node "74".

[0069] This probability of mutating as a function of the distance to the node makes it possible to respect the topology of the network and to explore the neighborhood of the solutions, which allows good convergence towards the local minimum around a solution. In particular, it gives more satisfactory results than a probability of mutating which would be fixed for example at 0.01 for each of the bits of a gene corresponding to a binary encoding, of type [1, 0, 0, 0, ...1,0, 1,0, 0],

[0070] This mutation preferably occurs on the daughter solutions generated during the crossing of step E4. The solutions selected during step E3 which would not have been used as parent solutions during the crossing can also undergo a mutation of their gene, before being integrated into the population of the next generation.

[0071] By this crossing and mutation operation E4, the 50% of solutions selected by tournaments during step E3 make it possible to generate as many daughter solutions, which constitute 50% of the population of the next generation.

[0072] In [Fig.2], the step referenced E5 corresponds to a step of producing a population of generation solutions of rank i+1, Gen_i+1, from the population of generation solutions of rank i, Gen_i. It is illustrated in schematic form in [Fig.8].

[0073] As indicated above, the population of each generation is defined by a given number of solutions, set by the user at the launch of the algorithm, and for example equal to 64 for satisfactory optimization and convergence of the method according to one embodiment. Each new generation, Gen_i+1, is composed of solutions directly derived from the previous generation (via two successive tournaments carried out during step E3), daughter solutions created by crossover of the solutions parents and possible mutation during step E4, and new random solutions, referenced 14, to provide "genetic diversity" and not converge towards a local but not a global optimum. As seen in [Fig.8], the best solution of the generation Gen_i, referenced 13, is ensured, thanks to the selection by tournaments E3, to always appear in the following generation Gen_i+1. In an advantageous embodiment, we choose to populate the new generation, Gen_i+1, with 25% of solutions selected during step E3, 50% of daughter solutions from step E4 and 25% of new random solutions, these proportions having given satisfactory results in terms of optimization of the positioning of the sensors and speed of convergence of the genetic algorithm.

[0074] During the step referenced E6, it is determined whether it is appropriate to terminate the reproduction iterations of the population, or whether this generation population of rank i+1, newly generated during the step E5, must be used in turn to iterate the steps E2 to E5 described above.

[0075] For example, steps E2 to E5 are iterated until a sufficient number of successive generations have been produced during the iteration cycles to ensure good convergence of the algorithm towards the optimal solution. In one embodiment, this number of successive generations is j= 0.15*Nb_sol*Nb_cap, where Nb_sol denotes the number of solutions in the population and where Nb_cap denotes the number of sensors. For example, for a population of 64 individuals and a maximum number of five sensors, steps E2 to E5 are iterated until a generation of rank j=48 is produced. This number of successive generations constitutes a good compromise between satisfactory convergence of the algorithm towards the optimal solution and a sufficiently moderate computation time for the number of successive population generations.

[0076] During the step referenced E7, the sensors are then placed within the network 1 at the positions determined by a predominant gene within the solutions of the last generation population. The predominant gene within the last generation is the one which minimizes the objective function defined and evaluated during step E2.

[0077] An example of optimal positioning of sensors obtained by implementing the method of [Fig.2] according to one embodiment is illustrated in [Fig.9], in which the optimal positioning of the sensors is indicated by a triangle.

[0078] [Fig. 10] schematically illustrates the structure of a DIS device for optimizing the positioning of sensors in an electrical network 1. Such a DIS device comprises a processing circuit connected to the electrical network for implementing the optimization method presented above.

[0079] With reference to [Fig. 10], this processing circuit may comprise: - an IN input interface for signals received from the electrical network, allowing the processing circuit to receive data and information on the network, such as the topology of the departure studied, the position of the sensors already present and of the DEIE, as well as production and consumption data on the network 1, - a MEM memory capable of storing at least temporarily voltage values, solution vectors and their performances, as well as instruction data of a computer program for implementing the above method. The MEM memory can be of the ROM (Read Only Memory) or RAM (Random Access Memory) type or even Flash, - a PROC processor capable of cooperating with the MEM memory and in particular of reading the instructions stored in the memory to execute in particular the steps necessary for the implementation of the method defined above. Thus, the PROC processor can in particular calculate the performance of the solutions, carry out crossovers and mutations, carry out a selection by tournaments, etc. And - an output interface OUT cooperating with the processor PROC to deliver the result of the optimization process in the form of an optimal sensor positioning solution, intended to be returned on a human / machine interface (display on a screen for example), and to send CMD commands to execute a sensor positioning according to the optimal solution returned in the electrical network.

[0080] [Fig. 10] illustrates only one particular way, among several possible ways, of producing a device for optimizing the positioning of sensors in an electrical network, so that it performs the steps of the method detailed above, in relation to Figures 2 to 9 (in any one of the different embodiments, or in a combination of these embodiments). Indeed, these steps can be carried out indifferently on a reprogrammable computing machine (a PC computer, a DSP processor or a microcontroller) executing a program comprising a sequence of instructions, or on a dedicated computing machine (for example a set of logic gates such as an FPGA or an ASIC, or any other hardware module). Industrial application

[0081] These technical solutions can be applied in particular in any electricity distribution or transmission network. They make it possible to dispense with the need for an expert to plan the installation of sensors, which therefore allows for a substantial saving of time. In addition, the results obtained during tests on around ten existing networks have confirmed good convergence towards an optimal solution, even with a limited number of sensors (for example only three sensors for a network of around 150 nodes), which therefore represents a significant financial gain.

[0082] The implementation of such optimization solutions makes it possible to carry out an optimal state estimation with a fixed number of sensors, which makes it possible to maximize the efficiency of the levers linked to the estimation, such as the Advanced Network Functions which deal with voltage (FAR-U), and therefore a financial gain for the network operator.

[0083] It is also possible to carry out several successive optimizations, with different numbers of sensors (for example, one, then two, then three sensors, etc.); a statistical analysis on the results obtained with these different optimizations makes it possible to determine the optimum number of sensors required to obtain, for example, a precision of 1% on the estimation of the voltage. An optimal state estimation is then carried out with a variable number of sensors by including this iteration on the sensors and this validation process. List of reference signs

[0084] - 1: electrical network - 2: tournament - 3: selected solutions - 4, 5: parent solutions - 6, 7: daughter solutions by simple crossover - 8: simple crossing point - 9, 10: daughter solutions by double crossover - 11, 12: double crossing points - 13: best solution - 14: randomly generated solutions - El: initial population generation - E2: performance evaluation - E3: selection by tournament - E4: mutation and crossing - E5: next generation production - E6: end of iteration test - E7: placement of sensors. List of cited documents Patent documents

[0085] For all useful purposes, the following patent document(s) is (are) cited: - patcitl: FR 3 006 818 Al (publication number); - patcit2: CN107563550A (publication number).

Claims

Claims

1. Method for optimizing the positioning of sensors in an electrical network (1) comprising a set of nodes, said sensors being configured to provide measurements of electrical variables of said network, said method comprising: a. a random generation (El) of a first generation population of solutions corresponding to a set of possible positions of said sensors within said set of nodes of the network, a solution being associated with a vector, called gene, representative of said sensor positions within said network, and b. at least one iteration of reproduction of said population, producing from a population of generation of rank i 1 (Gen_i) a population of generation of rank i+1 (Gen_i+1), said reproduction comprising: i. An evaluation (E2) of a performance of the solutions of the population of the generation of rank i; ii. A selection (E3) by tournaments of solutions within said population of the generation of rank i, by random drawings of pairs of solutions from said population and selection of a solution presenting the best performance within each pair drawn randomly; iii. A crossing (E4) of at least some pairs of selected solutions each generating two daughter solutions; iv. A production (E5) of a generation population of rank i+1 comprising at least certain solutions selected by tournaments of the generation population of rank i, said daughter solutions, and randomly generated solutions (14), said generation population of rank i+1 comprising the same number of solutions as the generation population of rank i; and said method comprising, at the end (E6) of said at least one reproduction iteration, a placement (E7) of said sensors within said network at the positions determined by a predominant gene associated with a maximum evaluated performance within the solutions of the last generation population.

2. Optimization method according to claim 1, characterized in that said reproduction also comprises a mutation of the gene of at least some of the daughter solutions.

3. Optimization method according to any one of claims 1 and 2, characterized in that said reproduction also comprises a mutation of the gene of at least some of the selected solutions which have not undergone crossing.

4. Optimization method according to any one of claims 1 to 3, characterized in that said gene is a vector containing said sensor positions within said network, classified by distance to a most upstream node in said network, and of length equal to a number of said sensors.

5. Optimization method according to any one of claims 1 to 4, characterized in that said evaluation (E2) of a performance of a solution of the population of the generation of rank i implements a calculation of an objective function defined by: Ptrflwl} - VN k>adflcw(n)-estim.aticm(n^ pù Perf ret j ( soi ) - ^jindxq.....................................JJ denotes the performance of the ground solution, N is a number of operating points studied, loadflorin) associates with an operating point n the value of the electrical variables of the nodes of said network calculated from known production and consumption data for said network and estimation(n, ground) denotes for the operating point 11 the value of the electrical variables of the nodes of said network estimated from the measurements provided by said sensors placed at the set of positions defined by the gene of the ground solution and in that a solution presents a performance all the better as it minimizes the value of said calculated objective function.

6. Optimization method according to any one of claims 1 to 5, characterized in that said crossing of pairs of selected solutions implements a simple crossing or a double crossing of the genes of the solutions chosen in an equiprobable manner to each pair of selected solutions.

7. Optimization method according to any one of claims 1 to 6, characterized in that the mutation of the gene of a solution implements a displacement of at least one of said sensors from an initial node to a final node of said network located in a neighborhood of said initial node, according to a probability decreasing with a distance of said final node relative to said initial node.

8. Optimization method according to any one of claims 1 to 7, characterized in that said population reproduction is iterated until reaching a generation of rank j = 0.15*Nb_sol*Nb_cap, where Nb_sol denotes the number of solutions of the population and where Nb_cap denotes the number of sensors.

9. Computer program comprising instructions for implementing the method according to one of claims 1 to 8 when this program is executed by a processor.

10. Non-transitory recording medium readable by a computer on which is recorded a program for implementing the method according to one of claims 1 to 8 when this program is executed by a processor.

11. Electrical network (1) comprising a set of nodes on at least some of which are placed sensors configured to provide measurements of electrical variables of said network, said positioning of said sensors being optimized by implementing the method according to any one of claims 1 to 8.

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