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 sensor positioning, by randomly selecting an initial solution corresponding to a set of sensor positions within the network nodes, and an initial temperature parameter T0; an evaluation (E2) of the performance of the initial solution; and at least one iteration of the evolution of said sensor positioning, producing, from a positioning solution of rank i, a positioning solution of rank i+1, by means of a 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.Figure from the summary: Figure 2.

Description

Title of the invention: Optimization of the placement of voltage sensors on an electrical network by simulated annealing. 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, the latter using their electrotechnical knowledge to achieve efficient sensor 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. This method is also not generalizable for scaling up, for example, if the distribution network operator wanted to place sensors for all feeders in the network, which would require a large number of experts. It is important to remember that a substation is located at the connection between the transmission and distribution networks. HTB / HTA, consisting of one or more transformers, behind each of which several lines branch off to connect multiple consumers and producers. A "branch" 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] This described method for optimizing the position of voltage sensors has several drawbacks. In particular, it does not provide a solution to the problem of optimally positioning voltage sensors when the network operator has a limited number of sensors available. These sensors are often limited in number, and it is important to consider this operational constraint 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 will provide a suboptimal response in terms of reliability and accuracy for state estimation. Moreover, this method appears suboptimal because it does not take into account the topology of the network under consideration. Finally, the computation time required by 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 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. an initialization of the sensor positioning, by randomly drawing an initial solution corresponding to a set of sensor positions within the network node set, and an initial temperature parameter To, b. an evaluation of the performance of said initial solution, and c. at least one iteration of the 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 the performance of a given 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 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 in the temperature parameter according to the equation TM - aTjt where a is a determined coefficient strictly less than 1, as long as Ti+l is greater than a determined minimum temperature parameter Tmin; and the method includes 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, 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.

[0015] 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.

[0016] The features described in the following paragraphs may optionally be implemented independently of each other or in combination with each other:

[0017] The initialization includes: - a random selection of k>2 solutions, each comprising the same determined number of sensors; - determining 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, Emisk; - a calculation of an expected average deviation according to the equation: AF esp = ----$--- and the initial temperature parameter is initialized to To = 100* A Eesp and the minimum temperature parameter is determined by Tmin = 0.01* A Eesi>.

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

[0019] A neighborhood of a position includes the set of nodes located at a distance less than or equal to one from that 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] Evaluating the performance of a solution involves calculating an objective function defined by: "r ïWoadflowin^stimtâ^ l\, where Perf denotes performance (S® ' \| loadflmdn) 1 / of the ground solution, N is a number of operating points studied, loadflo^n} associates to an operating pointn the value of the electrical variables of the nodes of said network calculated from production and consumption data known for said network and estimation^n, ground) designates 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 the more it minimizes the value of said calculated objective function. Brief description of the drawings

[0022] Other features, details and advantages will become apparent from reading the detailed description below and from analyzing the accompanying drawings, in which: Fig. 1

[0023] [Fig.1] 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 regulation 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.1] to illustrate the principle of determining neighboring solutions according to an embodiment. Fig. 4

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

[0027] [Fig.5] shows an example of sensor placement obtained by applying the optimization process 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 process according to [Fig.2]. Description of the implementation methods

[0029] 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.

[0030] 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.

[0031] 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.

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

[0033] Such a simulated annealing optimization method relies on the Metropolis-Hastings algorithm, which describes the evolution of a thermodynamic system. By analogy with the physical process, the objective function that we seek to minimize in the optimization is considered to be the energy E of the system. We also introduce a fictitious parameter, called 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 we are trying 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 vicinity of the initial state. Accepting a state that degrades the performance criterion allows us to... It allows him to explore a larger part of the state space and tends to avoid getting too quickly stuck in the search for a local optimum.

[0034] With reference to [Fig. 2], during a first step referenced El, the entire process parameters are initialized. This initialization step is particularly delicate, as choosing 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, that 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 we wish to optimize on the network of [Fig.1]. For example, Nb_cap=5.

[0036] During the initialization El, an initial solution So for positioning these Nb_cap sensors in network 1 is randomly generated. 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 sensors Nb_cap 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 of 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 vector [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 a vector structure is well suited to the problem of optimizing sensor positioning in a tree-structured network, particularly because it allows the topological structure of the network to be preserved and leveraged in solving the optimization problem.

[0037] During this initialization step El, it is also necessary 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] Once this initialization step El has 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 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. 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.

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

[0041] [Math.l] Perf (ground) = L„=1max( |----------1)

[0042] where Perf denotes the performance of the ground solution, N the number of operating points studied, and the functions loadflow(n) and estimation(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 relies on the use of operating points, i.e., production and consumption levels 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.

[0044] The absolute value of the relative difference between these two network states is then calculated, for which the maximum relative difference is retained. Finally, the values ​​are summed for all operating points or time steps.

[0045] The optimal position of the sensors is that 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 network 1, this objective function can also be expressed as follows:

[0047] [Math.2] \ J = Li-( / tiax ......ÿ;-.......

[0048] Where Nn denotes the number of nodes in the network, Np denotes the number of operating points, y1 denotes the actual voltage at node n for operating point i and denotes the estimated voltage at node n for point CxJl- function i.

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

[0050] [Math.3] J = ^i=^j=Qy. ((Vj)ML jyj)

[0051] Where N„ denotes the number of nodes in the network, Np denotes the number of operating points, y1 denotes the actual voltage at node n for operating point i and y1 denotes the estimated voltage at node n for operating point i, and where:

[0052] [Math.4] . [1 if V1, if V'i is in the 20% of voltages that deviate most from 1 for operating point i । i) 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 should be noted that in the French electricity distribution network, the network operator must ensure that the voltage remains within a range of + / - 5% around a target voltage of 20 kV for a major part of the network.

[0054] The three equations above allow the calculation of 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 Eil' the energy associated with the current solution Si.

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

[0056] To do this, we therefore proceed with 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 positioning solution of the Nb_cap sensors.

[0057] During a referenced step 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]. We consider, for example, 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. 1]. We define the neighborhood of a node as the set consisting of that node itself and all the nodes located at a distance of The distance less than or equal to an integer h from this node, this distance being expressed as the number of nodes. The value of h can be chosen according to the topology of the network under consideration, and a compromise to be reached between a fast convergence speed of the optimization process and convergence towards a global rather than local optimum. In the embodiment illustrated in [Fig. 3], h=l was chosen. Thus, in [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 Operational Information Exchange Device (OIE), installed at the producers' premises and already enabling measurement of 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 p0 and pl; however, node p0 is a forbidden node. Therefore, the neighborhood of node p is extended to include the direct neighbor of the forbidden node p0, namely node p2. The neighborhood of node p, in the example in [Fig. 3], therefore includes nodes p, pl, and p2.

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

[0062] During a step referenced E4, the performance of the neighboring solution Svois, i.e., its energy Evois, is evaluated using the same objective function as that used to evaluate the performance of the initial solution during step E2. The energy change induced by the transition from the current solution to the neighboring solution is also calculated:

[0063] [Math.5] ^E = Emis-Ei

[0064] The referenced step E5 is an evaluation step of this energy variation 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 state estimation of the network.

[0066] Otherwise, if AE>0, the neighbouring solution Svois is conserved 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 referenced step E6, the current temperature is compared to the minimum temperature determined at the initialization El. If the determined minimum temperature is not reached, the temperature is decreased during a referenced step E7, so that Ti+1 = aTb where a is a determined coefficient 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 El.

[0068] The steps E3 to E6 described above are then repeated with this new temperature value 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 process ends and it is considered that we have converged towards the optimal solution.

[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, achieving convergence of such an optimization process towards an optimal solution is difficult and results from an appropriate choice of initial parameters during the initialization step EL. A method of advantageous implementation of this step, which allows such an optimization process based on simulated annealing to be used simply on any electrical network.

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

[0073] A neighborhood is determined for each of these k solutions, 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 equations Math. 1, Math. 2 and Math. 3 for example: the energy Esoi of each of these k solutions is thus obtained.

[0075] Similarly, the performance of each of the solutions neighboring these k solutions is evaluated, in order 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 the set of k solutions and their neighbors from the equation below:

[0077] [Math.6] FF ] * “ps soT^vois / AJ^esp = £

[0078] The initial temperature T0 and final temperature Tmin are then chosen during this initialization step E1, so that at the beginning of the iterations AE < T, and therefore the probability of accepting a solution that degrades the system, is close to 1. This makes it easier to traverse all the solutions and thus avoid converging too quickly towards a local optimum. This should also ensure that at the end of the iterations AE > T, and therefore the probability g-ef is close to 0, in order to converge towards the optimum, i.e., the sensor positioning solution with minimum energy.

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

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

[0081] Fig. 4 illustrates, in the form of a curve representing the Metropolis rule, the evolution over time (i.e. as the temperature decreases during successive steps E7) of the probability of accepting a change which degrades the value of the objective function, in the embodiment described above by way of 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 that degrades performance is close to 1. On the other hand, over time, the temperature decreases and gets closer and closer to the minimum temperature Tmin: for these low temperatures, changes that degrade the system have a very low probability, close to zero, of being accepted, which ensures the convergence of the optimization process.

[0083] The process described above in relation to figures 1 to 4 has been tested on about ten electrical networks, with reproducible results which allow us to conclude that the optimum is indeed reached.

[0084] An example of optimal sensor positioning obtained by implementing the process of [Fig.2] according to an embodiment is illustrated in [Fig.5], on 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 includes a processing circuit connected to the electrical network for implementing the optimization process presented above.

[0086] With reference to [Fig. 6], 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 the instructions stored in memory to execute the steps necessary for implementing the process 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 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.

[0087] Figure 6 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 5 (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 set of logic gates such as an FPGA or an ASIC, or any other hardware module). Industrial application

[0088] 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.

[0089] 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.

[0090] 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

[0091] - 1: electrical network - E1: Initialization - E2: Performance evaluation - E3: Determination of a neighboring solution - E4: Calculation of performance variation - E5: Evaluation of performance variation - E6: Temperature test - E7: Temperature decrease - E8: Sensor placement. List of documents cited Patent documents

[0092] 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 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 randomly drawing 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 the performance of said initial solution, and c. at least one iteration of the 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 (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, a neighborhood of a position comprising the set of nodes located at a distance less than or equal to one from said position; ii. an evaluation (E4) of a performance of the determined neighboring solution, and of a difference, A E., 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 neighbor solution is kept as a positioning solution of rank i+1; 2. If said difference AE is positive, said neighboring solution is retained as a positioning solution of rank i+1 with a probability equal to where is a value of the temperature parameter at rank i; iii. a decrease (E7) of the temperature parameter according to the equation TM = aTit where a is a determined coefficient strictly less than 1, as long as said temperature parameter is greater than a determined minimum temperature parameter T rnm 9 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 draw of k>2 solutions each comprising the same determined number of sensors; - a determination of a neighboring solution of each of the k solutions; - an evaluation of a performance of each of the k solutions, E^ and of each of their neighboring solutions, E^^; - a calculation of an expected average deviation according to the equation: A Eesp - k and in that said initial temperature parameter is initialized to T0 = 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 close to the solution of rank i comprises, for each position in the solution of rank i, an equiprobable random draw of a position located in its neighborhood, and in that said close 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, if said neighborhood of a position includes at least one forbidden node, said neighborhood of said position is supplemented by a neighborhood of said at least one forbidden node.

5. Optimization method according to any one of claims 1 to 4, characterized in that said evaluation (E2, E4) of a solution performance implements a calculation of an objective function defined by: „ / . / / 1 loadflmrfn)^stinurtion(njsol) 1 \ WHERE Petf Per f (son,max , z.J v ^«=1 \| loadflmAn) 1 / designates the performance of the soil solution, N is a number of operating points studied, load, florin) associates to an operating point the value of the electrical variables of the nodes of said network calculated from production and consumption data known for said network and estimatior^n, sol) designates for the operating point 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 soil solution and in that a solution presents a performance all the better as it minimizes the value of said calculated objective function.

6. A computer program comprising instructions for carrying out the method according to any one of claims 1 to 5 when this program is executed by a processor.

7. 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 5 when this program is executed by a processor.

Images