Optimization of voltage sensor placement on an electrical network by simulated annealing

Abstract

The invention relates to a method 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. According to the invention, such a method comprises: an initialization (E1) of the positioning of the sensors, by random drawing of an initial solution corresponding to a set of positions of the sensors within the nodes of the network, and of an initial temperature parameter T0, an evaluation (E2) of a performance of the initial solution, and at least one iteration of evolution of the positioning of said sensors, producing from a positioning solution of rank a positioning solution of rank i+1, by simulated annealing algorithm. Such a method also comprises a placement (E8) of the sensors within the network at the positions determined by the positioning solution of rank i+1 obtained at the end of the evolution iterations.Abstract figure: Figure 2.

Description

Title of the invention: Optimization of the placement of voltage sensors on an electrical network by simulated annealing 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 possible sensor positioning combinations on the network. In addition, such expert-determined sensor placement often takes a long time 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 network outlets, which would require calling on a large number of experts. It should be remembered that at the connection between the transmission network and the distribution network, there is a substation HTB / HTA, consisting of one or more transformers behind each of which several lines depart, connecting 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] This described method of optimizing the position of the voltage sensors presents several drawbacks. In particular, it does not allow a solution to be obtained to the problem of optimal positioning of voltage sensors with a limited 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. In addition, this method appears suboptimal in that it does not take into account the topology of the network considered. Finally, the computation time required according to this method is too long.

[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. an initialization of the positioning of the sensors, by randomly drawing an initial solution corresponding to a set of positions of the sensors within the set of nodes of the network, and an initial temperature parameter T o, b. an evaluation of a performance of said initial solution, and c. at least one iteration of evolution of the positioning of said sensors, producing from a positioning solution of rank i £ 0 a positioning solution of rank i+1, said evolution comprising: i. a determination of a solution close to the solution of rank i, comprising a set of positions of said sensors chosen in a neighborhood of the positions of the solution of rank i; ii. an evaluation of a performance of the determined neighboring solution, and of a difference, AE, between the performance of the neighboring solution and the performance of the solution of rank i, and: 1. if the difference AE is negative or zero, the neighboring solution is chosen as the positioning solution of rank i+1; 2. if the difference AE is positive, the neighboring solution is kept as the rank positioning solution i+1 with a probability equal to where T {is a value of the temperature parameter at rank i; iii. a decrease in the temperature parameter according to the equation where a is a determined coefficient and strictly less than 1, as long as TM is greater than a determined minimum temperature parameter Tmin; and the method comprises placing the sensors within the network at the positions determined by the positioning solution of rank i+1 obtained at the end of said at least one evolution iteration.

[0014] 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.

[0015] 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.

[0016] The features set out in the following paragraphs may, optionally, be implemented, independently of one another or in combination with one another:

[0017] Initialization includes: - a random draw of k>2 solutions each comprising the same determined number of sensors; - a determination of a solution close to each of the k solutions; - an evaluation of the performance of each of the k solutions, E^ and of each of their neighboring solutions, EV(jisk ; - a calculation of an expected average deviation according to the equation: AP' Egsp — k and the initial temperature parameter is initialized to To = 100* A EesP and the minimum temperature parameter is determined by Tmin = 0.01* A EesP.

[0018] The determination of a solution neighboring the solution of rank i comprises, for each position in the solution of rank i, an equiprobable random drawing of a position located in its neighborhood, and the neighboring solution differs from the solution of rank i for at least one of its positions.

[0019] A neighborhood of a position comprises the set of nodes located at a distance less than or equal to one from this position.

[0020] If the neighborhood of a position includes at least one forbidden node, the neighborhood of the position is completed by a neighborhood of the forbidden node(s).

[0021] The evaluation of a solution's performance implements a calculation of an objective function defined by: Perf(wl) = maxfl loadPow^11 where Perf denotes the performance of the ground solution, N is a number of operating points studied, loadflo^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 estimation(n, ground) denotes for the operating pointn 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 ground solution and in that a solution presents a performance all the better as it minimizes the value of said calculated objective function. Brief description of the drawings

[0022] Other characteristics, details and advantages will appear on reading the detailed description below, and on analyzing the attached drawings, in which: Fig.l

[0023] [Fig.l] illustrates an electrical distribution network according to one embodiment. Fig. 2

[0024] [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

[0025] [Fig.3] shows a simplified synthetic diagram of the network of [Fig.l] to illustrate the principle of determining neighboring solutions according to one embodiment. Fig. 4

[0026] [Fig.4] shows a representative curve of the Metropolis rule illustrating a probability of evolution of the solutions according to an embodiment. Fig. 5

[0027] [Fig.5] shows an example of sensor placement obtained by applying the optimization method of [Fig.2] according to one embodiment. Fig. 6

[0028] [Fig.6] schematically illustrates the structure of a sensor positioning optimization device configured to implement the method according to [Fig.2]. Description of the embodiments

[0029] Reference is now made to [Fig.l], which illustrates an electrical network referenced 1. Such a network 1 may be a transmission network, which carries electricity from production centres to large industrial sites and distribution networks, or a distribution network which allows electrical energy to be transported locally, from distribution centres to the end customer.

[0030] 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.

[0031] 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.

[0032] 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 an optimization method called simulated annealing, the general block diagram of which is illustrated in [Fig.2].

[0033] Such a simulated annealing optimization method is based on the Me-tropolis-Hastings algorithm, which allows the evolution of a thermodynamic system to be described. By analogy with the physical process, the objective function that we seek to minimize in the context of optimization is assimilated to the energy E of the system considered. We also introduce a fictitious parameter, which we call the temperature T of the system. Starting from a given state of the system, by modifying it, we obtain a neighboring state, which can improve the criterion that we seek to optimize (it then lowers the energy of the system) or which can degrade it. If we accept a state that improves the criterion, we thus tend to seek the optimum in the neighborhood of the initial state. Accepting a state that degrades the performance criterion allows us to explore a larger part of the state space and tends to avoid getting too quickly locked into the search for a local optimum.

[0034] With reference to [Fig.2], during a first step referenced E1, an initialization of all the parameters of the process is carried out. This initialization step is particularly delicate, because the choice of inappropriate initial parameters can lead to difficulties or slow convergence of the optimization process. In particular, it is important to define initial parameters, or at least a method for initializing them, which allows the principle of simulated annealing to be used on any electrical network considered, regardless of its topology.

[0035] For example, we consider that we have a number of sensors Nb_cap (3, 5 or even 10 sensors) whose positioning on the network of [Fig. 1] we wish to optimize. For example, Nb_cap=5.

[0036] During initialization El, a random generation of an initial solution So for positioning these Nb_cap sensors in network 1 is carried out. This initial solution is associated with a vector representing the positions of the sensors within network 1, for example [0, 123, 40, 77, 100]. The length of the vector corresponds to the number of Nb_cap sensors that can be placed in network 1, i.e. five in this example. Each component of the vector contains the number of one of the nodes of 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 the vector [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 a vector structure is well suited to the problem of optimizing the positioning of sensors in a tree-structured network, particularly since it allows the topological structure of the network to be kept and taken advantage of in solving the optimization problem.

[0037] During this initialization step E1, it is also appropriate to set the values ​​of certain other parameters, such as an initial temperature parameter To and a minimum temperature parameter Tmin. An advantageous embodiment for setting these values ​​will be described in more detail below.

[0038] This initialization step El having been carried out, the performance of the initial solution So for positioning the sensors is evaluated during a step referenced E2.

[0039] 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 numerical 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. a profession that we will therefore not detail further here.

[0040] In one embodiment, the optimization method of [Fig.2] aims to minimize the objective function defined as follows:

[0041] [Math.l] Perf(sol) - |)

[0042] where Perf denotes the performance of the ground solution, N the number of operating points studied, and the functions loadflow(n) and estimation(n, ground) 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.

[0043] 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.

[0044] 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.

[0045] The optimal position of the sensors is the one which will minimize this objective function.

[0046] 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:

[0047] [Math.2]

[0048] 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 VlesU1 denotes the estimated voltage at node n for operating point i.

[0049] In another embodiment, one can consider only the estimation error made on the nodes having voltages which deviate the most from the nominal voltage, which is 1 pu (per unit). The objective function can then be expressed:

[0050] [Math.3] y)

[0051] Where Nn denotes the number of nodes in the network, N p denotes the number of points of operation, y1 denotes the actual voltage at node n for the operating point operation i and Vle« / t denotes the estimated voltage at node n for operating point i, and where:

[0052] [Math.4] / z . \ _ fl if VJ if V'i is in the 20% of the voltages which are most distant from 1 for the operating point i A ' / [ 0 otherwise

[0053] Such a formulation of the objective function has the advantage of optimizing the placement of the sensors, so as to make the best possible voltage estimate where the voltage is most likely to fall outside the contractual + / - 5% band. It is recalled that in the French electricity distribution network, the network manager must ensure that the voltage remains within a range of + / - 5% around a target voltage of a major part of the network of 20kV.

[0054] The three equations above make it possible to calculate the performance, and therefore the energy E, of a sensor positioning solution, as evaluated for example during step E2 for the initial solution. We will denote Ei the energy associated with the current solution Si.

[0055] The objective of simulated annealing is to move from near to near on the solution space, always accepting a movement in the neighborhood which improves the performance, and accepting a movement in the neighborhood which degrades the performance with a certain decreasing probability over time, which is a function of the temperature.

[0056] To do this, we therefore carry out one or more iterations of steps E3 to E7, until the temperature has reached the fixed limit temperature Tmin: we then consider that we have converged towards the optimal solution for positioning the Nb_cap sensors.

[0057] During a step referenced E3, a solution close to the current solution is therefore determined (for example a solution close to the initial solution So for the first iteration of step E3).

[0058] To do this, we consider the set of nodes of network 1, which is illustrated in simplified schematic form in [Fig.3]. For example, we consider a common solution S;=[m, n, p], according to which Nb_cap= 3 sensors are respectively positioned on nodes m, n and p of network 1, where m, n and p are integers between 0 and 152 in the example of the network in [Fig.l]. We define as the neighborhood of a node the set constituted by this node itself and all the nodes located at a distance less than or equal to an integer h from this node, this distance being expressed in number of nodes. The value of h can be chosen according to the topology of the network considered, and a compromise to be reached between a rapid convergence speed of the optimization method and a convergence towards a global and not local optimum. In the embodiment illustrated in [Fig.3], we have chosen h=l. Thus, on the [Fig.3], the neighborhood of node m includes node m itself and its direct neighbors ml and m2. In other embodiments, one could also choose h=2 or h=3 for example.

[0059] Furthermore, if one of the nodes in this neighborhood is a forbidden node (i.e. a node on which it is not possible to place a sensor, for example because this node already receives an Operating Information Exchange Device (DEIE), installed at the producers and already allowing measurement of the voltage, active power and reactive power), the neighborhood is completed by adding the direct neighbors of the forbidden node. Thus, the neighborhood of node p includes node p itself and its direct neighbors pO and pl; however, node pO is a forbidden node. We therefore extend the neighborhood of node p to include the direct neighbor of the forbidden node pO, namely node p2. The neighborhood of node p, in the example of [Fig.3], therefore includes nodes p, pl and p2.

[0060] In the following, a neighbor of a position is called a node located in the neighborhood of this position, as defined above. To construct a neighboring solution to the current solution Si=[m, n, p], a neighbor of each position m, n and p is randomly and equiprobably drawn. Thus, in the example of [Fig.3]: - the sensor placed in position m in the current solution Si will have a 33% chance of being moved to node ml in the neighboring solution of Si, a 33% chance of being moved to node m2 in this neighboring solution, and a 33% chance of not being moved, and therefore of remaining on node m in the neighboring solution determined during step E3; - similarly, the sensor placed in position n in the current solution Si will have a 50% chance of being moved to node ni in the neighboring solution of S;, and a 50% chance of not being moved, and therefore of remaining on node n in the neighboring solution determined during step E3; - finally, the sensor placed in position p in the current solution Si will have a 33% chance of being moved to node pl in the neighboring solution of Si, a 33% chance of being moved to node p2 in this neighboring solution, and a 33% chance of not being moved, and therefore of remaining on node p in the neighboring solution determined during step E3.

[0061] For example, during step E3, a neighboring solution Svois of the current solution Si is determined such that Svois=[m, ni, p2]. During this step E3, it is ensured that at least one of the positions of the solution vector changes in the neighboring solution with respect to the current solution.

[0062] During a step referenced E4, the performance of the neighboring solution Svois, iæ- its energy EVOiS, is evaluated using the same objective function as that used to evaluate the performance of the initial solution during step E2. We also calculate the energy variation induced by the transition from the current solution to the neighboring solution:

[0063] [Math.5] A p — p - p.

[0064] The step referenced E5 is a step of evaluating this variation in energy AE.

[0065] If AE<0, the neighboring solution Svois is kept as the new current solution Si+ i for a new iteration of steps E3 and following, since it minimizes the error of the network state estimation.

[0066] Otherwise, if AE>0, the neighboring solution Svois is preserved with a probability equal to where T; is the temperature at the current step i, according to the so-called Metropolis rule.

[0067] During a step referenced E6, the current temperature is compared to the minimum temperature determined at initialization E1. If the minimum temperature determined is not reached, the temperature is reduced during a step referenced E7, so that T;+1 — aT it where a is a determined coefficient and strictly less than 1, for example a=0.99 or a=0.95. In an advantageous embodiment, a=0.97 is chosen during the initialization step E1.

[0068] Steps E3 to E6 described above are then repeated with this new temperature value Ti+^ and we start moving again in the vicinity of a current solution.

[0069] On the other hand, when it is determined during step E6 that the current temperature has reached the fixed limit temperature Tmin, the optimization method ends and it is considered that the optimal solution has been converged.

[0070] In this case, during a step referenced E8, the sensors are positioned in the network 1, on the nodes whose positions are given by the vector of the last solution explored during the iterations of steps E3 to E5.

[0071] As mentioned above, the convergence of such an optimization method towards an optimal solution is difficult to obtain and results from an appropriate choice of the initial parameters, during the initialization step EL. An advantageous embodiment of this step is described below, which makes it possible to simply use such an optimization method based on simulated annealing on any electrical network.

[0072] To do this, during step E1, k solutions are randomly drawn, i.e. k positioning vectors of the Nb_cap sensors. For example, k=20 is chosen, i.e. 20 sets of positions of the Nb_cap sensors.

[0073] A neighborhood of each of these k solutions is determined, using the notion of neighborhood defined above in relation to step E3 of [Fig.2].

[0074] The performance of each of the k randomly drawn solutions is evaluated using one of the objective functions proposed above in relation to the equations Math. 1, Math. 2 and Math. 3 for example: we thus obtain the energy Esoi of each of these k solutions.

[0075] Similarly, we evaluate the performance of each of the neighboring solutions to these k solutions, to obtain the energy Evois of each of these k neighboring solutions.

[0076] We then calculate an expected average deviation for the simulated annealing on all k solutions and their neighbors from the equation below:

[0077] [Math.6] VA / ;1 J7 *> Ajy ] / - SOr1-' ','Oisf esp “ £

[0078] The initial temperatures To and final Tmin are then chosen during this initialization step El, so that at the start of the iterations ^E and therefore the probability of accepting a solution that degrades the system is close to 1, which makes it easier to browse through all the solutions, and therefore to avoid converging too quickly towards a local optimum. This must also make it possible to ensure that at the end of the iterations SE > T and therefore the probability is close to 0, in order to converge towards the optimum, i.e. the sensor positioning solution with minimal energy.

[0079] In an embodiment which gives satisfactory results, both in terms of reaching the optimum and convergence time, we choose: - To = 100* A Eesp ; -Tmin = 0.01* SE^P- -a = 0.97.

[0080] The initial solution So corresponds to a random position of the Nb_cap sensors on network 1, and the temperature decreases according to the law TM = aT^

[0081] [Fig.4] illustrates, in the form of a curve representative of the Me-tropolis rule, the evolution over time (i.e. over the course of the decrease in the temperature decided during the successive steps E7) of the probability of accepting a change which degrades the value of the objective function, in the embodiment described above as an example.

[0082] Thus, at the initialization of the optimization process, for temperatures close to the initial temperature To, the probability of accepting a neighboring solution which degrades the performance is close to 1. On the other hand, over time, the temperature decreases and approaches more and more the minimum temperature Tmin: for these low temperatures, the changes which degrade the system have a very low probability, close to zero, of being accepted, which makes it possible to ensure the convergence of the optimization process.

[0083] The method described above in relation to figures 1 to 4 was tested on around ten electrical networks, with reproducible results which allow us to conclude that the optimum is well reached.

[0084] An example of optimal positioning of sensors obtained by implementing the method of [Fig.2] according to one embodiment is illustrated in [Fig.5], in which the optimal positioning of the sensors is indicated by a triangle.

[0085] [Fig.6] 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.

[0086] With reference to [Fig.6], this processing circuit may comprise: - an input interface IN 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 and their neighbors, and proceed to reduce the current temperature. 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.

[0087] [Fig. 6] 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 5 (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 module material). Industrial application

[0088] 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.

[0089] 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.

[0090] 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

[0091] - 1: electrical network - El: initialization - E2: performance evaluation - E3: determination of neighboring solution - E4: calculation of performance variation - E5: performance variation assessment - E6: temperature test - E7: decrease in temperature - E8: placement of sensors. List of cited documents Patent documents

[0092] 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

1. Claims Method for optimizing the positioning of sensors in an electrical network (1) comprising a set of nodes (m, n, p), said sensors being configured to provide measurements of electrical variables of said network, said method comprising: a. an initialization (El) of the positioning of said sensors, by random drawing of an initial solution corresponding to a set of positions of said sensors within said set of nodes of the network, and an initial temperature parameter To, b. an evaluation (E2) of a performance of said initial solution, and c. at least one iteration of evolution of the positioning of said sensors, producing from a positioning solution of rank i 4 0 a positioning solution of rank i+1, said evolution comprising: i. a determination (E3) of a solution close to the solution of rank i, comprising a set of positions of said sensors chosen in a neighborhood of the positions of the solution of rank i; ii. an evaluation (E4) of a performance of the determined neighboring solution, and of a difference, AE, between the performance of said neighboring solution and the performance of the solution of rank i, and:

1. if said difference AE is negative or zero, said neighboring solution is chosen as a positioning solution of rank i+1; 2. if said difference AE is positive, said neighboring solution is kept as a positioning solution of rank i+1 with a probability equal to , where T} is a value of the temperature parameter at rank i; iii. a decrease (E7) of the temperature parameter according to the equation Tf+1 = aTit where a is a coefficient determined and strictly less than 1, as long as said temperature parameter is greater than a determined minimum temperature parameter Tmin; and said method comprising a placement (E8) of said sensors within said network at the positions determined by said positioning solution of rank i+1 obtained at the end of said at least one evolution iteration.

2. Optimization method according to claim 1, characterized in that said initialization comprises: - a random drawing of k>2 solutions each comprising the same determined number of sensors; - a determination of a solution close to each of the k solutions; - an evaluation of a performance of each of the k solutions, Esol^ and of each of their close solutions, Evoijj.; - a calculation of an expected average deviation according to the equation: A F. ' Za Lesp — and in that said initial temperature parameter is initialized at To = 100* A EesP and said minimum temperature parameter is determined by Tmin = 0.01* A Eesp.

3. Optimization method according to any one of claims 1 and 2, characterized in that said determination (E3) of a solution neighboring the solution of rank i comprises, for each position in the solution of rank i, an equiprobable random drawing of a position located in its neighborhood, and in that said neighboring solution differs from the solution of rank i for at least one of its positions.

4. Optimization method according to any one of claims 1 to 3, characterized in that a neighborhood of a position comprises all the nodes located at a distance less than or equal to one from said position.

5. Optimization method according to claim 4, characterized in that, if said neighborhood of a position comprises at least one forbidden node, said neighborhood of said position is completed by a neighborhood of said at least one forbidden node.

6. Optimization method according to any one of claims 1 to 5, characterized in that said evaluation (E2, E4) of a performance of a solution implements a calculation of an objective function defined by: Ptrflwl} - VN k>adflow(.n)-estimatio^ol) j\, where Perf fetp ( soi ) - Z^max^.....................................| / denotes the performance of the ground solution, N is a number of operating points studied, loadflowln) 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 n 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 ground solution and in that a solution presents a performance all the better as it minimizes the value of said calculated objective function.

7. Computer program comprising instructions for implementing the method according to one of claims 1 to 6 when this program is executed by a processor.

8. 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 6 when this program is executed by a processor.

9. 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 6.

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