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 includes: a random generation (E1) of a first-generation population of solutions corresponding to a set of possible sensor positions within the set of nodes of the network, a solution being associated with a vector, called a gene, and at least one reproduction iteration of the population, including a tournament selection (E3) of solutions within the population, by random drawing of pairs of solutions from the population and selection of a solution with the best performance within each randomly drawn pair.At the end (E6) of the reproduction iteration(s), the process includes a placement (E7) of the sensors within the network at positions determined by a predominant gene associated with 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] This disclosure falls within the field of electricity distribution and transmission network management. It applies in particular, but not exclusively, to the state estimation of such networks, which is especially useful for voltage regulation in the presence of decentralized electricity generation. Previous technique

[0002] Voltage regulation of a distribution network in the presence of decentralized generation requires a reliable estimation of the voltages at each node of the network. The voltage at each node of the network can, in particular, be determined by applying the laws of electrical engineering to actual measurements provided by voltage sensors positioned on nodes of the distribution network and to pseudo-measurements calculated from a load model of consumers and MV / LV substations not instrumented by sensors.

[0003] The reliability of 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 control method because the accuracy of the voltage estimation at any node of the network will not meet the technical constraints, namely a maximum deviation of 1% between the voltage estimate and the actual, unknown value of that voltage. However, for cost reasons, it is not feasible to instrument a very 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 ensure a good state estimation.

[0005] To date, sensor placement is often carried out based on expert opinion, with the expert using their electrotechnical knowledge to achieve efficient placement. This placement can be relevant, but it is not always optimal, particularly because it is impossible for the expert to exhaustively test all possible sensor placement combinations on the network. Furthermore, such expert-based sensor placement is often time-consuming to implement. Moreover, such a method is not generalizable for scaling up, in the event that the distribution network operator wishes to place sensors for all network feeders, which would require calling upon a very large number of experts. It should be noted that The connection between the transmission network and the distribution network is located at a high-voltage / medium-voltage substation, consisting of one or more transformers, behind which several lines branch off to connect multiple consumers and producers. A "feeder" is one of these lines and everything it connects.

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

[0007] Such a method is advantageous because it guarantees the reliability of the state estimation associated with a given sensor positioning in the network. However, it does not guarantee that this positioning is optimal. Furthermore, finding a suitable positioning can be time-consuming, given the iterative nature of the method, which requires successively and randomly exploring a set of voltage sensor position configurations, which can be tedious.

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

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

[0010] Although few details are given in this prior art document regarding the implementation of this genetic algorithm, it nevertheless appears that the described method for optimizing the position of voltage sensors has several drawbacks. In particular, the proposed method does not provide a solution to the problem of optimal positioning of voltage sensors when the network operator has a limited number of voltage sensors available. 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 network nodes. Furthermore, this method does not guarantee sufficient exploration of the space of possible solutions and may therefore converge to a local optimum, which, in terms of state estimation, will provide a suboptimal response in terms of reliability and accuracy.Finally, this method appears suboptimal in that it does not take into account the topology of the network under consideration.

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

[0012] This disclosure improves the situation.

[0013] A method for optimizing the positioning of sensors in an electrical network comprising a set of nodes is proposed, 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 sensor positions within the network node set, each solution being associated with a vector, called a gene, representing the sensor positions within the network, and b. at least one reproduction iteration of the population, producing from a generation population of rank is 1 a generation population of rank i+1, the reproduction comprising: i. An evaluation of the performance of the solutions in the population of generation i ii. A tournament selection of solutions within the population of generation 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 crossover of at least some pairs of selected solutions, each generating two daughter solutions; iv. A production of a generation population of rank i+1 comprising at least some tournament-selected solutions from 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 process includes 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, an electrical network is proposed 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 implementation of the process as described above.

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

[0017] The features described in the following paragraphs may optionally be implemented independently of each other or in combination with each other:

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

[0019] Reproduction also includes a gene mutation in at least some of the selected solutions not having undergone crossing.

[0020] The gene is a vector containing the sensor positions within the network, ranked by distance to the most upstream node in the network, and of a length equal to a number of sensors.

[0021] Evaluating the performance of a solution from the population of generation i involves calculating an objective function defined by: D fi i\ — / \ loadflow(n)-estiniatioi^ii,sol) \\ reri (SOI) - | 7oadf7ow(n) IJ , where Perf denotes the performance of the soil solution, N is the number of operating points studied, and loadflow(l^) associates with an operating point n the value of the electrical variables of the nodes of said network calculated from of known production and consumption data for said network and estimation, SOI) designates, for the operating point n, the value of the electrical variables of the network nodes estimated from the measurements provided by the sensors placed at the set of positions defined by the gene of the soil solution. A solution exhibits better performance the more it minimizes the value of the calculated objective function.

[0022] The crossing of pairs of selected solutions implements a single 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 from the initial node.

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

[0025] Other features, details and advantages will become apparent from reading the detailed description below and from analyzing the accompanying drawings, in which: Fig. 1

[0026] [Fig.1] 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 regulation 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 process of [Fig.2] according to an embodiment. Fig. 4

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

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

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

[0032] [Fig.7] presents a curve representing the probability of mutation as a function of the distance to the sensor in the context of the optimization process of [Fig.2] according to an embodiment. Fig. 8

[0033] [Fig.8] presents a synoptic 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 process of [Fig.2] according to an embodiment. Fig. 9

[0034] [Fig.9] shows an example of sensor placement obtained by applying the optimization process 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 process according to [Fig. 2]. Description of embodiments

[0036] Reference is now made to [Fig. 1], which illustrates an electrical network referenced 1. Such a network 1 can 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 on a local scale, from distribution centers to the end customer.

[0037] Such a network 1 comprises a set of nodes organized in a tree structure from a source node. Each branch of the network topology includes one or more nodes, which may correspond to MV / LV substations, switching devices, consumers, or decentralized producers. In the example in [Fig. 1], the source node is numbered "0", and each node in the tree structure is numbered, with the number incrementing along each branch of the tree. The electrical network in [Fig. 1], for example, comprises 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 studied starting point, including the position of the sensors already present and the Operational Information Exchange Devices (DEIE), which enable remote control and remote monitoring of decentralized production facilities; - 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, we propose, in one embodiment, to optimize the placement of sensors in the network 1 according to a process which is based on the use of a genetic algorithm, the general synoptic diagram of which is illustrated in [Fig.2],

[0040] In a first step, referenced El, a first-generation population of sensor positioning solutions in network 1 is randomly generated. Each solution in this population corresponds to a set of possible sensor positions within the set of nodes in network 1. Each solution is associated with a vector, called a gene, representing the sensor positions 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, which is five in this example. Each component of the vector contains the number of one of the nodes in network 1 on which a sensor is proposed to be placed 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 the gene [0, 123, 40, 77, 100] corresponds to a solution in which five sensors are respectively placed on the 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 tree-structured network, in particular because it allows us to keep the topological structure of the network and 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 under consideration than 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 of 0 or 1, depending on the absence or presence of sensors on the node under consideration.

[0041] The genetic algorithm implemented in the optimization process illustrated in [Fig. 2] uses mechanisms of natural selection so that the population of solutions considered (i.e., the sensor positions considered) improves over time, retaining only the highest-performing solutions, which can then pass on their "genes" to subsequent generations. It is therefore necessary to evaluate the performance of each solution in a population. This is done in a step referenced E2.

[0042] Indeed, in order to compare the different sensor positions, it is necessary to evaluate their performance in order to maximize it, and thus obtain the best state estimate of 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. It should be noted that a loadflow is a numerical calculation.

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[0052] Energy flows in an electrical network allow us to obtain the value of an electrical variable, for example, the voltage across all network nodes, or the active and reactive power on each network segment. Load flow is calculated by taking into account the consumption and production of the various network elements as well as the characteristics of the lines, using a technique known to those skilled in the art, which we will not detail further here. In one embodiment, the optimization process of [Fig.2] aims to minimize the objective function defined as follows: [Math.l] D ?x _ X?fl 1 oadflow(n)-estimation(n,sol) Ii r^OrtySOl)— loadflowtn) | / where Perf denotes the performance of the soil solution, N the number of operating points studied, and the functions loadflow(lî) and est i mn t innin soi) 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 soil solution. In one embodiment, this objective function relies on the use of operating points, that is, levels of production and consumption on the network, intelligently distributed across the various producers and loads of the network. In another embodiment, this objective function relies on the use of N time steps. Next, we calculate the absolute value of the relative difference between these two network states, keeping the maximum relative difference. Finally, we sum the values ​​for all operating points or time steps. The optimal position for the sensors is the one that will minimize this objective function. In an embodiment where we are more specifically interested in the tension at each of the nodes of network 1, this objective function can also be expressed as: [Math.2] T p J = li=0^X HO, L.,NJ Where Nn denotes the number of nodes in the network, Np denotes the number of operating points, y^ denotes the actual voltage at node n for operating point i and y1 denotes the estimated voltage at node n for operating point i. With this objective function defined and the input data known, it is possible to proceed to optimization, that is, to the search for the optimal solution. according to an iterative process corresponding to the repetition of successive steps E2 to E6 of evaluation, selection, crossing and mutation, production of the next generation and final test.

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

[0054] In one embodiment, the number of solutions in a population is fixed and remains constant from generation to generation. It can be set by the user when the algorithm is launched. 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 made during the step referenced E3, which will be used to supply the next generation of the population.

[0056] In one embodiment, this selection relies on the use of a referenced tournament logic 2, schematically illustrated in [Fig. 3]. To do this, pairs of individuals are randomly drawn from the population, their performances are compared pairwise, and the better of the two individuals is retained each time. In effect, the best individual of generation i is guaranteed to be retained for the next generation of rank i+1; similarly, the worst individual of generation i is guaranteed to be eliminated. This also ensures that not only the best individuals are retained, but also "average" individuals to avoid local optima.Thus, this tournament-based selection logic allows for a good exploration of the solution space, better in particular than a roulette-based selection which has two main drawbacks: on the one hand, it does not guarantee that the best individual will be kept for the next generation and on the other hand, it can lead to convergence of the algorithm towards a local minimum in the case where one solution has 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 solution "1", with performance fl, and solution "8", with performance f8, which leads to the selection of solution "8" whose performance f8, evaluated during step E2, is greater than that fl of solution "1". Similarly, tournaments are organized between solutions "2" and "9", between solutions "3" and "10", between solutions "4" and "11", between solutions "5" and "12", between solutions "6" and " 13” and between solutions “7” and “14”, which lead to the selection referenced 3 of 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 in the subsequent crossing step E4 as parents of new daughter solutions, and possibly of mutation, which will feed the next generation population.

[0060] These selected solutions are also subjected to a second tournament to determine which solutions can be directly integrated into the next generation of the solution population. This second tournament also relies on a random selection of solution pairs from among the selected solutions: for each tournament, the pair of selected solutions with the best performance, i.e., the one that most minimizes the objective function, is retained. At the end of this second tournament, 25% of the solutions from the population under consideration are selected to directly populate the next generation population.

[0061] The referenced step E4 is a mutation and crossover step 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 single crossing (daughter solutions referenced 6 and 7 on [Fig.4]) or double crossing (daughter solutions referenced 9 and 10 on [Fig.5]) of their genes.

[0063] This cross, also called a "crossover," allows the genes of two parent solutions 4 and 5 to be mixed to produce a daughter solution. The gene of a daughter solution is obtained by taking a portion of the gene from the first parent solution, referenced as 4 (i.e., certain sensor positions), with a portion of the gene from the second parent solution, referenced as 5 (i.e., certain other sensor positions), from a pair of solutions 4 and 5 drawn randomly. 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]) will be used, chosen with equal probability for each pair of individuals.

[0064] This crossover takes place with a certain defined probability, which, in one embodiment, is fixed at 0.8. Thus, there is an 80% chance of carrying out a crossover on a pair of parent solutions: the parent solutions which do not undergo a crossover can be subject to a mutation during the subsequent step, without having been crossed.

[0065] For example, a simple crossover of a referenced parent solution 4 whose gene is expressed [0, 123, 40, 77, 100] with a referenced parent solution 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, a gene mutation in a solution can also occur with a certain defined probability. This intentionally induced mutation allows exploration of the solution space. 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 moving sensor has a probability of mutating, and therefore changing position, of approximately 0.4.

[0067] In the event of a mutation in 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 neighborhood. 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 adjacent to the node “135” in network 1 of [Fig. 1].

[0068] As illustrated by the curve in [Fig. 7], a decreasing probability of mutation is imposed with increasing distance from the final node to the initial node, up to a maximum distance of 15 nodes. [Fig. 6] illustrates this probability of mutation for a gene carrying sensor positioning information at node "74". The probability that this gene mutates at "73" or "75" is highest, at 0.3, but decreases with increasing distance from node "74" according to the network topology, becoming zero beyond node "23", which is fifteen nodes from node "74".

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

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

[0071] Through this E4 crossover and mutation operation, the 50% of solutions selected by tournaments during the E3 step allow the generation of as many daughter solutions, which constitute 50% of the next generation population.

[0072] In [Fig.2], the step referenced E5 corresponds to a production step of 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 schematically in [Fig.8].

[0073] As indicated above, the population of each generation is defined by a given number of solutions, fixed by the user at the start of the algorithm, and for example equal to 64 for satisfactory optimization and convergence of the process according to one embodiment. Each new generation, Gen_i+1, is composed of solutions directly from the previous generation (via two successive tournaments performed during step E3), daughter solutions created by crossing over the parent solutions and possible mutation during step E4, and new random solutions, referenced 14, to provide "genetic diversity" and avoid convergence towards a local but not global optimum. As can be seen in [Fig. 8], the best solution of generation Gen_i, referenced 13, is guaranteed, thanks to the tournament selection E3, to always appear in the following generation Gen_i+1.In an advantageous embodiment, the new generation, Gen_i+1, is populated 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 sensor positioning and convergence speed of the genetic algorithm.

[0074] During the referenced step E6, it is determined whether it is appropriate to terminate the population reproduction iterations, or whether this generation population of rank i+1, newly generated during step E5, should in turn be used 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 Nb_cap denotes the number of sensors. For example, for a population of 64 individuals and a maximum of five sensors, steps E2 to E5 are iterated until a generation of rank j = 48 is produced. This number of successive generations represents 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 population solutions of the latest generation. The predominant gene within the latest generation is the one that minimizes the objective function defined and evaluated during step E2.

[0077] An example of optimal sensor positioning obtained by implementing the process of [Fig.2] according to an embodiment is illustrated in [Fig.9], on 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 includes a processing circuit connected to the electrical network for implementing the optimization process presented above.

[0079] With reference to [Fig. 10], this processing circuit may include: - an input interface (IN) for signals received from the electrical network, allowing the processing circuit to receive data and information about the network, such as the topology of the studied feeder, the position of existing sensors and DEIEs, as well as production and consumption data on network 1, - a memory module (MM) capable of storing, at least temporarily, voltage values, solution vectors and their performance, as well as instruction data from a computer program for implementing the above process. The MMM 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 instructions stored in memory to execute the steps necessary for implementing the process defined above. Thus, the PROC processor can, among other things, calculate the performance of solutions, perform crossovers and mutations, carry out tournament selection, etc. - 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 displayed on a human / machine interface (display on a screen for example), and to send CMD commands to execute sensor positioning according to the optimal solution delivered in the electrical network.

[0080] Figure 10 illustrates only one particular way, among several possible ways, of implementing a device for optimizing the positioning of sensors in an electrical network, so that it performs the steps of the process 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 performed interchangeably on a reprogrammable computing machine (a PC, a DSP processor, or a microcontroller) executing a program comprising a sequence of instructions, or on a dedicated computing machine (for example, a 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 any electricity distribution or transmission network. They eliminate the need for an expert to plan sensor installation, thus resulting in substantial time savings. Furthermore, the results obtained during tests on approximately 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 approximately 150 nodes), which therefore represents significant cost savings.

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

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

[0084] - 1: electrical network - 2: tournament - 3: Selected solutions - 4, 5: parent solutions - 6, 7: daughter solutions via simple crossover - 8: simple crossing point - 9, 10: solutions for girls via double crossover - 11, 12: double intersection 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: Sensor placement. List of documents cited Patent documents

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

Claims

1. Demands A 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 a gene, representative of said sensor positions within said network, and b. at least one iteration of reproduction of said population, producing from a generation population of rank i 1 (Gen_i) a generation population of rank i+1 (Gen_i+1), said reproduction comprising: i. An evaluation (E2) of the performance of the solutions in the population of generation i ii. A selection (E3) by tournament of solutions within said population of generation i, by random draws of pairs of solutions in said population and selection of a solution with the best performance within each pair drawn randomly; iii. A crossover (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 some tournament-selected solutions from 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 positions determined by a predominant gene associated with maximum evaluated performance within the latest generation population solutions.

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 includes a gene mutation of at least some of the selected solutions not having 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, ranked by distance to the 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 from the population of generation i implements a calculation of an objective function defined by: reriysoi)— ioadfiow(n) U , where Perf denotes the performance of the solution sol, N is a number of operating points studied, loâdf associates to an operating point n the value of the electrical variables of the nodes of said network calculated from production and consumption data known for said network and eStimâtiOU^n,SO1) designates, for the operating point 12, 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 soil solution, and in that a solution exhibits a performance that is all the better the more 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 crossover of pairs of selected solutions implements a single crossing or a double crossing of the genes of the chosen solutions in an equiprobable manner at each pair of selected solutions.

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

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

9. A computer program comprising instructions for carrying out the method according to any one of claims 1 to 8 when this program is executed by a processor.

10. A non-transient, computer-readable recording medium on which a program is recorded for the implementation of the method according to any one of claims 1 to 8 when this program is executed by a processor.

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