Method for managing an electrical network, device and computer program for implementing the method

Abstract

A computer-implemented method of managing an electrical network comprising a set of nodes is provided, which comprises: obtaining voltage measurements for each node of a subset of the set of nodes of the electrical network; configuring a graph neural network based on data representative of a topology of the electrical network; and determining, by the configured graph neural network, an estimate of the respective voltage magnitudes of the nodes of the set of nodes based on the voltage measurements of the nodes of the subset. Abstract Figure: Figure 2b

Description

Title of the invention: Method for managing an electrical network, device and computer program for implementing the method Technical field

[0001] The present invention relates to a method for managing an electrical network, to a device and computer software for implementing this method. It applies in particular to low-voltage electrical networks, in particular to the state management of a low-voltage electrical network. Prior art

[0002] Low voltage (LV) electricity distribution networks are facing major challenges, including the increasing integration of photovoltaic (PV) producers into the LV electricity network, the introduction of new uses such as charging Electric Vehicles (EVs) and the increasingly widespread use of heat pumps.

[0003] However, since LV networks were initially designed to primarily (or even exclusively) transport electricity to consumers (residential, professional, tertiary, etc.), the integration of decentralized electricity production on these networks risks placing these networks under new constraints of increases in voltage levels. In addition, new uses such as EV charging risk placing LV networks under other new constraints of significant voltage drops in the event of uncontrolled simultaneous charging.

[0004] The deployment of smart meters improves the observability of LV networks. However, the collection of measurement data from these meters in real time and simultaneously is limited by communication constraints.

[0005] There is thus a need for an electrical network management method making it possible to observe and monitor the state of an electrical network subject to these new constraints. Summary

[0006] The present disclosure improves the situation.

[0007] According to a first aspect, there is provided a computer-implemented method for managing an electrical network comprising a set of nodes. The proposed method comprises: obtaining voltage measurements for each node of a subset of the set of nodes of the electrical network, configuring a graph neural network based on data representative of a topology of the electrical network, and determining, by the configured graph neural network, an estimate of the voltage amplitudes respective nodes of the node set based on the voltage measurements of the nodes of the subset.

[0008] Thanks in particular to the use of a graph representation to represent complex data structures corresponding to the electrical networks, the proposed method advantageously allows the implementation of a state estimator which makes it possible to estimate the amplitudes of the voltages of a LV network from a small number of measurements sent back, for example in real time (or quasi-real time).

[0009] Furthermore, the proposed method can advantageously be implemented on any electrical network, including a large electrical network comprising a large number of low-voltage networks, such as for example the French electrical network which has more than 700,000 HTA / LV public distribution stations (and therefore the same number of LV networks).

[0010] The proposed method also advantageously makes it possible to provide Distribution Network Managers (DNMs) with a tool for observing voltage levels in real time (or quasi-real time) on all the nodes of a LV network, for example advantageously making it possible to maintain the voltage level within a regulated range (for example a range of ± 10% around a nominal network voltage).

[0011] The features set forth in the following paragraphs may, optionally, be implemented. They may be implemented independently of one another or in combination with one another. In one or more embodiments, the measurements obtained further comprise one or more of active power measurements and reactive power measurements, for each node of the subset of the set of nodes of the electrical network, and wherein the estimation of the voltage amplitudes is further determined based on one or more of the active power measurements and the reactive power measurements of the nodes of the subset.Collecting one or more of active power measurements and reactive power measurements, for each node of the subset of the set of nodes of the electrical network, allows this data to be used as input data to the graph neural network in the inference phase to improve the determination of the estimate of the voltage amplitudes. For example, this collected data can be used to configure the graph neural network to determine an estimate of the voltage amplitudes under the constraint of compliance with predefined physical laws, as explained in more detail in one or more embodiments below.

[0012] In one or more embodiments, the graph neural network may be configured with N neural network layers. In these embodiments, one or more (e.g., each) neural network layers i may comprise one or several of: an encoder £( / ) configured to receive voltage measurement data as input and operatively coupled to one of one or more neural networks and a decoder operatively coupled to one of the one or more neural networks and configured to produce voltage amplitude estimation data as output. In one or more embodiments, the number A' neural network layers can be chosen to correspond to the number of nodes in the electrical network.

[0013] In one or more of the embodiments in which the graph neural network is configured with A' neural network layers, the proposed method may further comprise: performing a training phase of the one or more neural networks jjk. / ) of the layers of the graph neural network, following which each neural network layer * comprises the encoder £( / ), one or more trained neural networks / JX f), and the decoder / X / )-

[0014] In one or more embodiments, one or more of the encoder and the decoder jXz) are trained neural networks, for example following a training phase of one or more layers of the graph neural network.

[0015] In one or more embodiments, the proposed method further comprises: performing a training phase of the graph neural network on the basis of data respectively representative of the topology of one or more training electrical networks. Advantageously, the training of the graph neural network can be performed on the basis of data of a set of training electrical networks which does not include the electrical network to be managed for which the graph neural network is used in the inference phase. Thus, the present disclosure proposes, according to different embodiments, to configure a graph neural network on the basis of data of an electrical network to be managed. The graph neural network used for this configuration may comprise one or more neural network layers which will have been previously trained on the training electrical networks.The implementation of embodiments of the proposed method is thus particularly flexible and facilitated by the configuration of a graph neural network comprising layers which may have been trained beforehand.

[0016] In one or more embodiments, the proposed method further comprises: performing a learning phase of the graph neural network on the basis of data respectively representative of topology of one or more learning electrical networks and data respectively representative of electrotechnical characteristics of the one or more learning electrical networks, in which the estimation is further determined on the basis data representative of electrotechnical characteristics of the electrical network. Thus, advantageously, the training (of one or more layers) of the graph neural network can take into account data representative of electrotechnical characteristics of the one or more learning electrical networks, so as to use this data in the inference phase, for example to configure the graph neural network to determine an estimate of the voltage amplitudes subject to compliance with predefined physical laws, as explained in more detail in one or more embodiments below.

[0017] In one or more embodiments, wherein the graph neural network performs a self-configuration phase based on data representative of the topology of the electrical network. Thus, advantageously, the configuration of the graph neural network, based on data representative of the topology of the electrical network, and possibly (in certain embodiments) based on data representative of electrotechnical characteristics of the electrical network, can be automated, for example by software.

[0018] For example, in one or more embodiments, the self-configuration of the graph neural network may comprise: generating, based on data representative of the topology of the electrical network comprising a connection in the electrical network between a first and a second node of the electrical network, a neural connection between a neural network j) of a first layer i1 of the graph neural network and a neural network L(j, i1) of a second layer i2 of the graph neural network, the first and second nodes of the electrical network corresponding respectively to the first and second layers i1 and i2 of the graph neural network and the neural connection between the neural networks j) and j2) corresponding to the connection in the electrical network between the first and second nodes.

[0019] In one or more embodiments, configuring the graph neural network may comprise: configuring, based on data representative of the topology of the electrical network comprising a connection in the electrical network between a first and a second node of the electrical network, a neural connection between a neural network £(^ f]) of a first layer 11 of the graph neural network and a neural network / 2) of a second layer i2 of the graph neural network, the first and second nodes of the electrical network corresponding to the first and second layers 11 and 12 of the graph neural network, respectively, and the neural connection between the neural networks £(£ / 1) and £Q( / 2) corresponding to the connection in the electrical network between the first and second nodes.

[0020] In one or more of the embodiments in which the graph neural network is configured with one or more neural network layers respectively corresponding to one or more nodes of the electrical network, the configuration of the graph neural network may comprise: configuring one or more neural connections between layers of the graph neural network respectively corresponding to one or more connections between nodes of the electrical network, the layers of the graph neural network respectively corresponding to the nodes of the electrical network.

[0021] In one or more of the embodiments in which the graph neural network is configured with one or more neural network layers respectively corresponding to one or more nodes of the electrical network, the self-configuration of the graph neural network may comprise: generating one or more neural connections between layers of the graph neural network respectively corresponding to one or more connections between nodes of the electrical network, the layers of the graph neural network respectively corresponding to the nodes of the electrical network.

[0022] In one or more embodiments, the electrical grid may be managed based on estimating the respective voltage magnitudes of the nodes of the set of nodes. According to another aspect, an electrical grid management device is provided, which includes a processor, a data communications interface and a memory operatively coupled to the processor, the processor being configured to implement a method according to one of the embodiments provided in the present application.

[0023] Another aspect relates to a computer program, loadable into a memory associated with a processor, and comprising portions of code for implementing a method according to one of the embodiments proposed in the present application during the execution of said program by the processor.

[0024] Another aspect relates to a data set representing, for example by compression or encoding, a computer program as proposed in the present application.

[0025] Another aspect relates to a non-transitory storage medium for a computer-executable program, comprising a data set representing one or more programs, said one or more programs comprising instructions for, upon execution of said one or more programs by a computer comprising a processor operatively coupled to a memory and to a data communication input / output interface, causing the computer to manage an electrical network according to a method according to one of the embodiments proposed in the present application.

[0026] Another aspect relates to a non-transitory storage medium of a computer-executable program, comprising a data set representing one or several programs, said one or more programs comprising instructions for, during the execution of said one or more programs by a computer comprising a processing unit operatively coupled to memory means and to an input / output interface module, causing the computer to implement a method according to one of the embodiments proposed in the present application. Brief description of the drawings

[0027] Other features and advantages of the present disclosure will appear in the following description of non-limiting exemplary embodiments, with reference to the appended drawings, in which: Fig.l

[0028] [Fig.l] is a diagram illustrating an example of an electrical network architecture comprising low-voltage (LV) networks for implementing the method proposed according to one or more embodiments; Fig. 2a

[0029] [Fig.2a] is a diagram illustrating a proposed method of configuring a graph neural network according to one or more embodiments; Fig. 2b

[0030] [Fig.2b] is a diagram illustrating a proposed method of managing an electrical network according to one or more embodiments; Fig. 2c

[0031] [Fig.2c] is a diagram illustrating a proposed method of managing an electrical network according to one or more embodiments; Fig. 3

[0032] [Fig.3] is a diagram illustrating an example of a graph neural network comprising Ngnn layers according to one or more embodiments; Fig. 4

[0033] [Fig.4] is a diagram illustrating an example of the constitution of a learning database according to one or more embodiments; Fig. 5a

[0034] [Fig.5a] illustrates an example of an electrical network according to one or more embodiments; Fig. 5b

[0035] [Fig.5b] illustrates an example of a graph representation obtained for an example of an electrical network according to one or more embodiments; Fig. 6

[0036] [Fig.6] illustrates an example of a graph neural network architecture according to one or more embodiments; Fig. 7

[0037] [Fig.7] illustrates an example of implementation of learning of the graph neural network according to one or more embodiments; Fig. 8

[0038] [Fig.8] illustrates an example of implementation of a method for managing an electrical network according to one or more embodiments; Fig. 9a

[0039] [Fig.9a] is a diagram illustrating an example of equipment architecture for implementing a method of configuring a graph neural network according to one or more embodiments. Fig. 9b

[0040] [Fig.9b] is a diagram illustrating an example of equipment architecture for implementing the proposed method according to one or more embodiments. Description of the embodiments

[0041] In the following detailed description of embodiments of the invention, numerous specific details are presented to provide a more complete understanding. However, those skilled in the art may realize that embodiments can be practiced without these specific details. In other instances, well-known features are not described in detail to avoid unnecessarily complicating the present description.

[0042] The present application refers to functions, engines, units, modules, platforms, and diagram illustrations of the methods and devices according to one or more embodiments. Each of the described functions, engines, modules, platforms, units and diagrams can be implemented in hardware, software (including in the form of embedded software ("firmware"), or "middleware"), microcode, or any combination thereof.In the case of a software implementation, the functions, engines, units, modules and / or diagram illustrations may be implemented by computer program instructions or code, which may be stored or transmitted on a computer-readable medium, including a non-transitory medium, or a medium loaded into the memory of a generic, specific computer, or any other programmable data processing apparatus or device to produce a machine, such that the computer program instructions or code executed on the computer or the programmable data processing apparatus or device, constitute means of implementing these functions.

[0043] Embodiments of a computer-readable medium include, but are not limited to, computer storage media and communication media, including any medium that facilitates the transfer of a computer program from one location to another. By "computer storage medium(s)" is meant any physical medium that can be accessed by a computer.Examples of computer storage media include, but are not limited to, flash memory disks or components or any other flash memory devices (e.g., USB keys, memory keys, memory sticks, key disks), CD-ROMs or other optical data storage devices, DVDs, magnetic disk data storage devices or other magnetic data storage devices, data memory components, RAM, ROM, EEPROM, memory cards ("smart cards"), SSD ("Solid State Drive") type memories, and any other form of media usable for carrying or storing or memorizing data or data structures that can be read by a computer processor.

[0044] Furthermore, various forms of computer-readable media may transmit or carry instructions to a computer, such as a router, gateway, server, or any data transmission equipment, whether wired (via coaxial cable, fiber optics, telephone wires, DSL cable, or Ethernet cable), wireless (via infrared, radio, cellular, microwave), or virtualized transmission equipment (virtual router, virtual gateway, virtual tunnel endpoint, virtual firewall).The instructions may, depending on the embodiments, include code of any computer programming language or computer program element, such as, without limitation, assembly languages, C, C++, Visual Basic, HyperText Markup Language (HTML), Extensible Markup Language (XML), HyperText Transfer Protocol (HTTP), Hypertext Preprocessor (PHP), SQL, MySQL, Java, JavaScript, JavaScript Object Notation (JSON), Python, and bash scripting.

[0045] Furthermore, the terms "notably", "for example", "example", "typically" are used in the present description to designate examples or illustrations of non-limiting embodiments, which do not necessarily correspond to preferred or advantageous embodiments compared to other aspects or possible embodiments.

[0046] The terms “operably coupled,” “coupled,” “mounted,” “connected,” and their various variations and forms as used herein refer to couplings, connections, assemblies, which may be direct or indirect, and include, in particular, connections between electronic equipment or between portions of such equipment that enable operations and functioning as described in the present application. In addition, the terms “connected” and “coupled” are not limited to physical or mechanical connections or couplings. For example, an operationally coupled connection may include one or more wired connections and / or one or more wireless connections between two or more devices that enable simplex and / or duplex communication links between the devices or portions of the devices. In another example, an operationally coupled connection may include a wired and / or wireless coupling to enable data communications between a server of the proposed system and other equipment of the system.

[0047] The terms "LV network" as used herein refer to all electrical networks comprising one or more components located downstream of an HTA / LV distribution station, such as, for example, one or more HTA / LV transformers, LV overhead lines, LV underground cables, consumers and producers connected to the network.

[0048] The term "training network" as used herein refers to an electrical network used to constitute a training database when implementing a training phase of the graph neural network. For example, a training network may correspond to an electrical network whose data is used in the database used during the training phase of the neural network-based model.

[0049] The terms "application network" and "electrical network under consideration" as used interchangeably herein refer to an electrical network to which a method proposed according to an embodiment of the present disclosure is applied. For example, an application network is a network to which a trained graph neural network model is applied to make a state estimation in order to determine an estimate of the respective voltage amplitudes of all the nodes of the application network on the basis of voltage measurements of the nodes of a subset of the nodes of this network.

[0050] The terms "graph neural network" and "graph neural networks" (or "GNN") as used interchangeably herein refer to any neural network (or neural network) configured for processing data that can be represented by a graph.

[0051] The term "graph" as used herein refers to any data structure representing objects and relationships (links) between those objects. A graph data structure typically includes a set of nodes (or vertices) and links (sometimes referred to as "edges"). A link in the graph may represent a relationship between two nodes of the graph and can be, depending on the graph considered, directed or undirected.

[0052] [Fig.l] illustrates an example of an electrical network architecture (1) comprising low-voltage (LV) networks (3) for implementing the method proposed according to one or more embodiments.

[0053] With reference to [Fig.l], the electrical network (1) comprises a transmission network (2) electrically coupled to a distribution network (3). The transmission network (2) comprises a high-voltage network (2a) comprising production units (PI, P2, P3) (2al, 2a2, 2a3), electrically connected by one or more high-voltage (HT) to medium-voltage (MV) transformers (2cl) to a medium-voltage network (2b) comprising medium-voltage infrastructures (II, 12) (2bl, 2b2).

[0054] The MV network (2b) is electrically connected to two low-voltage networks (3a, 3b) via transformers (TF1 MV->LV, TF2 MV->LV) (2c2, 2c3) MV to LV, respectively.

[0055] Each of the low-voltage networks (3a and 3b) comprises several nodes (3a1 to 3a6 for network 3a, and 3b1 to 3b5 for network 3b) which may be, depending on the embodiment, consumer and / or producer nodes of electrical energy.

[0056] Those skilled in the art will understand that the proposed methods and systems are not limited to one or more particular types of LV electrical network, whether for the type of node of the electrical network or the type of link for transporting electricity between different nodes of the network or for supplying power to the network. Similarly, the proposed methods and systems are not limited to one or more LV electrical network architecture(s).

[0057] In one or more embodiments, a graph data structure may be generated from data of an electrical network used in the embodiment. In embodiments where multiple electrical networks are used, a respective graph data structure may be generated for one or more (each) of those electrical networks.

[0058] A graph data structure corresponding to an electrical network may then be used to configure a graph neural network corresponding to the electrical network for implementing one or more embodiments. The configuration of a graph neural network corresponding to an electrical network may for example use topology data of the electrical network (if applicable reflected by the graph data structure), in particular for example data describing nodes of the electrical network and links between the nodes of the electrical network.

[0059] In one or more embodiments, an electrical network may be described by a graph-type data structure G = (y, Ej, in which the set V of nodes of the graph G represents the network nodes of the electrical network, and the set E of links of the graph G represents electrical links between two nodes of the electrical network.

[0060] [Fig.2a] is a diagram illustrating a method (10a) of configuring a graph neural network according to one or more embodiments.

[0061] With reference to [Fig.2a], we envisage an electrical network comprising a set of nodes, such as for example a low-voltage (LV) type electrical network.

[0062] In one or more embodiments, data representative of topology of the electrical network may be obtained (10a_l). In certain embodiments, the data representative of topology may comprise information relating to a number A of nodes.

[0063] In one or more embodiments, Ngnn neural network layers of the graph neural network may be configured (10a_2), each neural network layer comprising one or more neural networks and the number Ngnn neural network layers corresponding to the number N of nodes of the electrical network.

[0064] In one or more embodiments, the Ngnit neural network layers of the graph neural network may have an identical or similar structure from one layer to another. For example, in some embodiments, the Ngnn neural network layers of the graph neural network may be generated by duplicating Ngnn times a neural network layer (referred to as a "model" or "matrix") comprising one or more neural networks.

[0065] In one or more embodiments, a neural connection is configured (10a_3), based on the data representative of the topology of the electrical network comprising one or more connections in the electrical network, for each connection among the one or more connections in the electrical network existing between a first and a second node of the electrical network corresponding respectively to the connection, between a neural network ufo f]) of a first layer il of the graph neural network and a neural network [jj, / 2) of a second layer ï'2 of the graph neural network. In some embodiments, the first and second nodes of the electrical network may correspond respectively to the first and second layers il and i2 of the graph neural network.In some embodiments, the neural connection between the neural networks £(&, il) and jjj* i2) may correspond to the connection in the electrical network between the first and second nodes. Thus, the graph neural network may be configured with a structure of layers and neural connections that corresponds to the structure . of the electrical network to be managed, or in certain embodiments to a graph data structure representing the electrical network to be managed.

[0066] In one or more embodiments, the graph neural network thus configured can be used (10a_4) for the management of the electrical network, for example according to an embodiment of an electrical network management method described in the present disclosure.

[0067] [Fig.2b] is a diagram illustrating a proposed method of managing an electrical network (10b) according to one or more embodiments.

[0068] With reference to [Fig.2b], we envisage an electrical network comprising a set of nodes, such as for example a low-voltage (LV) type electrical network.

[0069] In one or more embodiments, voltage measurements are obtained (10b_l) for each node of a subset of the set of nodes of the electrical network. Advantageously, the subset of nodes contains a number of nodes (Vs) much lower than the total number NT of nodes of the electrical network (Ars) so that the proposed method can advantageously be implemented by carrying out measurements on a number of nodes of the electrical network considered which is small compared to the total number of nodes of the network, thus avoiding the constraint of carrying out measurements on all or almost all of the nodes of the electrical network considered.

[0070] In one or more embodiments, a graph neural network is configured (10b_2) based on data representative of a topology of the electrical network.

[0071] We therefore have data representative of a topology of the electrical network considered, describing for example the architecture of the network, such as for example data describing each node of the network as well as the electrical connections respectively connecting one or more pairs of nodes of the network.

[0072] In one or more embodiments, this data representative of the topology of the electrical network can be used to configure a graph neural network, for example during a phase of self-configuration of the graph neural network as described below.

[0073] In one or more embodiments, the graph neural network can further be configured on the basis of data respectively representative of electrotechnical characteristics of the electrical network considered. In these embodiments, the estimation of the voltage amplitudes can advantageously be further determined on the basis of the data respectively representative of electrotechnical characteristics of the electrical network considered.

[0074] In one or more embodiments, the graph neural network once configured can be used to determine (10b_3) an estimate of the amplitudes of respective voltages of the nodes of the node set based on the voltage measurements of the nodes of the subset.

[0075] The voltage measurements obtained on the nodes of the subset can thus be used to generate data provided as input data to the configured graph neural network. In one or more embodiments, the graph neural network can then determine an estimate of the respective voltage amplitudes of the nodes of the set of nodes of the electrical network (for example, determine an estimate of the respective voltage amplitudes of all the nodes of the electrical network, or, depending on the embodiment, of one or more nodes of the electrical network for which a voltage measurement has not been carried out).

[0076] Advantageously, the proposed method thus makes it possible to obtain an estimate of the voltage amplitudes of one or more nodes of an electrical network (for example a LV electrical network) for which no voltage measurement is carried out, so that it is possible, by using a graph neural network that is configured from topology data of the electrical network considered and to which voltage measurements carried out on a number of nodes (of a subset of a set of nodes) of the network that is strictly lower (for example very low compared to) the total number (of the set) of nodes of the electrical network, to obtain (depending on the embodiment, in real time or quasi-real time) voltage amplitude data for nodes (of the set of nodes) of the network, in particular for nodes for which the voltage measurement has not been carried out.

[0077] In one or more embodiments, the obtained voltage measurements may further comprise one or more of active power measurements and reactive power measurements of one or more of 3 phases, for each node of the subset of the set of nodes of the electrical network. In these embodiments, the estimation of the voltage amplitudes may be further determined based on one or more of the active power measurements and the reactive power measurements of the nodes of the subset.

[0078] In one or more embodiments, the graph neural network may be configured with Argnn neural network layers, each neural network layer 7 ( 1 < / < Ngm) comprising an encoder £( / ) configured to receive voltage measurement data as input and operatively coupled to one of one or more neural networks £(£ f) (1 S k < K\ and a decoder £)( / ) operatively coupled to one of the one or more neural networks £(£ f) and configured to output voltage amplitude estimation data. In one or more embodiments, the number Ngnn of network layers neural network can be chosen corresponding to the number of nodes of the electrical network considered.

[0079] Figure 3 is a diagram illustrating an example of a graph neural network comprising Ngm layers.

[0080] In the illustrated example, each neural network layer is configured according to a structure comprising a set of neural networks comprising an encoder neural network £(f) configured to receive voltage measurement data as input, and operatively coupled to a sequence of K neural networks £(£ ÿ (1 S k < Æ) operatively coupled to each other according to the sequence [ lik / )]: The neural network £( / ) is coupled to a first network neural network £({, f) of the sequence, which is coupled to a second neural network £(2, i) of the sequence of layer z, itself coupled to the following network of the sequence [L(k, / )} 'c neural network [Jk, i) is coupled to the neural network which follows it in the sequence j / k + 1, / )• The last neural network L(K, i) of the sequence {L(k, i)} operationally coupled to the decoder neural network / )( / ) of layer h which is configured to produce as output data for estimating the voltage amplitudes.

[0081] In one or more embodiments, as illustrated by Figure 3, the graph neural network, used to implement the proposed method for an electrical network comprising nodes, can be generated by duplicating a layer (sometimes referred to in the present disclosure as a "base layer") (for example of a structure corresponding to that illustrated in Figure 3) a number of times corresponding to the number Nt of nodes of the electrical network considered. For example, to carry out the processing of an electrical network comprising Nt nodes according to the proposed method, a graph neural network can be generated by duplicating a base layer at least Nt times, in order to use a graph neural network comprising at least Nt layers (Ngnu 4 Nh for example Ngnn =

[0082] [Fig.2c] provides another example diagram illustrating a proposed method of managing an electrical network according to one or more embodiments, which are referred to in the following description of embodiments of a training phase of the graph neural network and embodiments of an inference phase of the graph neural network according to the present disclosure.

[0083]

[0084] In the context of the present disclosure, a graph neural network is considered, without limitation on the type of this graph neural network. For example, the graph neural network used may be of any type suitable for the implementation of embodiments of the present disclosure, known or future, such as for example (architecture) of the type MPGNN (from the English "Message-Passing Graph Neural Network"), MPNN (from the English "Message-passing Neural Network"), GCNN (from the English "Graph Convolutional Neural Network"), GCN (from the English "Graph Convolutional Network"), and graph attention neural network GAT (from the English "Graph Attention Network"), or may comprise a combination of one or more neural networks of different types (for example among these types of graph neural networks).

[0085] The methods and systems described in the present disclosure are particularly suitable for the management and maintenance of electrical networks, by estimating the respective voltage amplitudes of nodes of an electrical network (estimation that can be obtained on all the nodes of an electrical network (with the possible exception of nodes for which a voltage measurement is carried out) on the basis of a measurement of these voltages on a small number of nodes compared to the number of nodes of the network on which an estimation is obtained).

[0086] Depending on the chosen embodiment, different types or architectures of graph neural network may be envisaged for implementing the proposed methods. Thus, in one or more embodiments, the proposed method may be implemented using a graph neural network of the MPNN (or MPGNN) type. Those skilled in the art will however understand that the proposed method is not limited to implementations using one or more MPGNN-type neural networks, and that it may be advantageously used with any graph neural network suitable for its implementation for managing an electrical network according to one or more embodiments described in the present disclosure.

[0087] In the following, the non-limiting example of an implementation using a graph neural network of the MPGNN type is considered. Nevertheless, those skilled in the art will be able to realize that any graph neural network can be used for the implementation of embodiments of the proposed method instead of or in addition to a neural network of the MPGNN type, which is described only by way of example.

[0088] Graph neural networks are neural networks whose architecture is configured to be suitable for processing data that can be associated with a corresponding graph data structure. Thus, graph neural networks are configured with an architecture particularly suitable for processing data that can be represented as a set of one or more nodes, and a set of one or more links between these nodes. Depending on the data description chosen, one or more nodes may have one or more of input characteristics and output characteristics, and one or more links may have one or more of input characteristics and output characteristics.

[0089] Graph neural networks can be used to perform a task (classification, prediction or regression) that can be applied at one or more of: the graph, one or more of the links, and one or more of the nodes.

[0090] For example, a graph-level task may consist of graph classification (e.g., predicting the type of the graph from its structure).

[0091] For example, a link-level task may consist of a prediction of one or more links (e.g., predicting whether a link between two nodes exists) or - another example - a regression that consists of predicting one or more output feature values ​​of one or more links.

[0092] For example, a node-level task may consist of a classification of one or more nodes (e.g., predicting the type of a node from its features) or - as another example - a regression that consists of predicting one or more output feature values ​​of one or more nodes.

[0093] In one or more embodiments, one (or more) graph neural network(s) may advantageously be used to apply a regression at one or more nodes of an electrical network to be managed to which the graph neural network corresponds by configuring the graph neural network on the basis of topology data (for example to predict the voltages of one or more of the nodes of the electrical network considered).

[0094] Depending on the chosen embodiment, the learning of the (each of the) graph neural networks used can be done in a supervised or unsupervised manner.

[0095] In one or more embodiments, the supervised learning may comprise: training one (or more) of the graph neural networks used to produce, from an input, an output that aligns with a (predetermined) target value. In this case, the objective function to be minimized during the training phase may be defined based on a deviation between the output and the target value.

[0096] In one or more embodiments, the unsupervised learning may comprise: learning one (or more) of the graph neural networks used to produce, from an input, an output that complies with a predefined objective function according to the application considered, by exploiting the structure of the graph, but without knowing the target value.

[0097] In one or more embodiments, the graph neural network used may be configured with a number Ngm of neural network layers of the graph neural network, each neural network layer 1 comprising one or more (e.g. example K) neural networks î) (with l^k <K et l<i< Ngmt). Par exemple, une couche de réseau neuronal comprenant un ou plusieurs (par exemple réseaux de neurones £(£) (avec 1S k < K\ dite (indifféremment) couche de base, couche modèle ou couche matrice, peut être dupliquée pour configurer le réseau neuronal en graphe avec Ngim de couches de réseau neuronal. Dans un ou plusieurs modes de réalisation, le nombre de couches du réseau neuronal en graphe peut être choisi sur la base d’un nombre N de nœuds du réseau électrique.

[0098] In one or more embodiments, topology data of the electrical network to be managed comprising a number N of nodes of the electrical network may be used to determine a number Ngm of neural network layers to be configured. For example, the number Ngnn of neural network layers to be configured may be determined based on the number N of nodes of the electrical network to be represented (e.g. N gnn - N).

[0099] For example, in one or more embodiments, a neural network layer comprising one or more (e.g., neural networks £(£) (with l <k<K\ dite (indifféremment) couche de base, couche modèle ou couche matrice, peut être dupliquée Ngm fois pour configurer le réseau neuronal en graphe avec Ngnn de couches de réseau neuronal comprenant au moins N couches de réseau neuronal correspondant respectivement à N nœuds du réseau électrique à gérer.

[0100] In one or more embodiments in which the graph neural network used is of the message passing type (e.g., of the MPGNN type), each neural network layer * may further comprise an encoder configured to receive input data from the graph neural network and operatively coupled to a first of one or more neural networks j), and a decoder operatively coupled to a second of the one or more neural networks £(£ and configured to output output data from the graph neural network.

[0101] In one or more embodiments in which the graph neural network used is of the message passing type (e.g. MPGNN type), each neural network layer i further comprising an encoder Efy configured to receive input data from the graph neural network and operatively coupled to one of the one or more neural networks / ), and a decoder operatively coupled to one of the one or more neural networks £(& and configured to output output data from the graph neural network, the encoder E(i) may comprise a fully connected neural network configured to generate a message by encoding data provided in input of layer 1 of the graph neural network, and the decoder may comprise a fully connected neural network configured to generate output data of layer i of the graph neural network by decoding a message received from a neural network of layer 1 of the graph neural network.

[0102]

[0103] In one or more embodiments, a learning phase (20a) of the graph neural network is carried out on the basis of data respectively representative of the topology of one or more learning electrical networks (20al).

[0104] For example, in one or more embodiments, the training phase may be configured to perform unsupervised learning that aims to produce output data that complies with one or more physical equations of the electrical system on which the training is performed.

[0105] In the embodiments in which data representative of electrotechnical characteristics are used (for example in the embodiments in which the graph neural network is further configured on the basis of data respectively representative of electrotechnical characteristics of the electrical network considered), the training phase of the graph neural network can further be carried out on the basis of data respectively representative of electrotechnical characteristics of the one or more training electrical networks.

[0106] In one or more embodiments, a phase of training one or more of the neural networks of at least one layer * of the graph neural network (e.g., training one or more neural networks of the base layer ib) may be performed. For example, in one or more embodiments, a phase of training the neural networks [L^k, ï)} <k^ d’au moins une couche du réseau neuronal en graphe (par exemple d’un ou plusieurs réseaux neuronaux de la couche de base peut être effectuée avant de générer (par exemple par duplication) les autres couches du réseau neuronal en graphe, pour obtenir un réseau neuronal en graphe dans lequel chaque couche 1 de réseau neuronal comprends un ou plusieurs réseaux de neurones / ) entrainés.

[0107] In one or more embodiments, the graph neural network used may be configured with a number Ngmi of neural network layers of the graph neural network, each neural network layer comprising one or more (e.g. ^) neural networks j] (with 1 k < K and 1 i Ngnn). For example, a neural network layer comprising one or more (e.g. K) neural networks neurons £(£) (with 1 k < K), called (indifferently) base layer, model layer or matrix layer, can be duplicated to configure the graph neural network with Ngnn of neural network layers. In one or more embodiments, the number of layers of the graph neural network can be chosen based on a number N of nodes of the electrical network.

[0108] In one or more embodiments, topology data of the electrical network to be managed comprising a number N of nodes of the electrical network may be used to determine a number Ngnn of neural network layers to be configured. For example, the number Ngmt of neural network layers to be configured may be determined based on the number N of nodes of the electrical network to be represented (e.g. N gtm N).

[0109] For example, in one or more embodiments, a neural network layer comprising one or more (for example, Ijfy neural networks (with 1 k < K) called (indifferently) base layer, model layer or matrix layer, can be duplicated Ngnn times to configure the neural network in a graph with Ngnn of neural network layers comprising at least N neural network layers corresponding respectively to N nodes of the electrical network to be managed.

[0110] In one or more embodiments in which the graph neural network used is of the message passing type (for example of the MPGNN type), each neural network layer * may further comprise an encoder e(î) configured to receive input data from the graph neural network and operatively coupled to a first of one or more neural networks £(£ i\ and a decoder Dfy operatively coupled to a second of the one or more neural networks £(£ and configured to output output data from the graph neural network.

[0111] In one or more embodiments in which the graph neural network used is of the message passing type (e.g. MPGNN type), each neural network layer further comprising an encoder e(i) configured to receive input data from the graph neural network and operatively coupled to one of the one or more neural networks £(£ f), and a decoder Dfy operatively coupled to one of the one or more neural networks £(£ f ) and configured to output output data from the graph neural network, the encoder E(i) may comprise a fully connected neural network configured to generate a message by encoding data provided as input to layer 1 of the graph neural network, and the decoder may comprise a fully connected neural network configured to generate output data of layer i of the graph neural network by decoding a message received from a neural network of layer 1 of the graph neural network.

[0112] In one or more embodiments, the configuration of the encoder and decoder networks can also be performed using training. Thus, in one or more embodiments, a training phase of one or more of the encoder and decoder neural networks of one or more layers of the graph neural network can be performed, so as to configure the encoder neural networks to receive voltage measurement data as input, and to configure the decoder neural networks to produce voltage amplitude estimation data as output. For example, in one or more embodiments, a training phase of the encoder and decoder neural networks of each layer of the graph neural network can be performed.Advantageously, in certain embodiments, a training phase of the encoder neural networks Eiij) and decoder of the base layer can be carried out before generating (for example by duplication) the other layers of the graph neural network, to obtain a graph neural network in which each layer ï of the neural network comprises a trained encoder neural network e(i), a trained decoder neural network (as well as, in certain embodiments in which one or more of the neural networks L(k, i) of the layer J have been trained, one or more trained neural networks).

[0113] In one or more embodiments in which one or more of these training phases are implemented, one or more of these training phases are performed based on (using) data representative of respective topologies of one or more electrical networks from which one or more trainings are performed (referred to in the present disclosure as training electrical networks).

[0114] Thus, in one or more embodiments, data from one or more electrical learning networks are used to constitute a database used during the learning phase of one or more of the neural networks of the graph neural network model used.

[0115] In one or more embodiments, the training phase may use one or more training electrical networks, for example chosen because they have distinct typical topologies or other distinct relevant characteristics, in order to enrich the training database.

[0116] For example, in one or more embodiments, offline learning is performed on a database consisting of measurement histories (e.g. example comprising voltage amplitude measurements on one or more nodes of the learning electrical network) for Nrés learning electrical networks over a predetermined period of time T (for example of a few months), with a predetermined measurement time step A t: measurements (for example comprising voltage amplitude measurements on one or more nodes of a learning electrical network) are carried out on each of the one or more learning electrical networks every A t of a first unit of time for a duration of T of a second unit of time, so as to generate a learning database.

[0117] The number of measurement samples obtained for each learning electrical network can then be determined by: = , where T is the period in course of the history considered and A t is the time step in minutes.

[0118] The total number of samples constituting the training database is then: Néeh = Nrés x Nt.

[0119] [Fig.4] illustrates an example of constitution (30) of a learning database which can be implemented in one or more embodiments.

[0120] Figure 4 illustrates a set (30a) of N training network sets on which measurements can be performed in one or more embodiments to constitute a training database.

[0121] In the example illustrated in Figure 4, Nt measurement samples (30b) are collected for each of the N sets of learning electrical networks, which makes it possible to constitute in one or more embodiments a learning database (30c) comprising Nes = N sets x Nt samples. A sample of the learning database then corresponds to the data of one of the N sets of learning electrical networks which were collected at a certain measurement time.

[0122]

[0123] In one or more embodiments, data representative of a network topology may be collected (1.1) for one or more of the one or more training electrical networks (20al). For example, in some embodiments, data representative of network topology may be collected for each of the one or more training electrical networks.

[0124] In one or more embodiments, the topology representative data may comprise one or more of data representative of the nodes of the electrical network (here the training electrical network) and data representative of the links of the electrical network. For example, in some embodiments, the data representative of the nodes of the electrical network may include a list of the nodes of the electrical network, for example numbered from 1 to M. For example, in certain embodiments, the data representative of the links of the electrical network may comprise a matrix of dimension N nuisonsx 2, for example consisting of the indices of the two nodes of the two ends of the ^links links of the electrical network.

[0125] [Fig.5a] illustrates a simplified example of an electrical network (31).

[0126] The electrical network (31) of [Fig.5a] comprises 3 nodes 31a_l, 31a_2 and 31a_3 electrically connected (coupled) by 2 links 3 lb_l and 31b_2: a first electrical link 3 lb_l between the nodes 31a_l and 31a_2, and a second electrical link 31b_2 between the nodes 31a_l and 31a_3.

[0127] In the case of the electrical network (31) of Figure 5 comprising 3 nodes and 2 links, the data representative of the links of the electrical network can comprise the following 2x2 matrix: ( 1 2 \, which represents the links of the network U 3 / electrical (31) according to the following table: Node Link 1-2 1 2 Link 1-3 1 3

[0129]

[0130] In one or more embodiments, measurement data is collected (1.3) on one or more of the one or more training electrical networks, for example by performing measurements on these one or more training networks. In some embodiments, measurement data is collected on each of the one or more training electrical networks, for example by performing measurements on each of these one or more training networks.

[0131] In one or more embodiments, the measurements performed may include voltage measurements (e.g., including voltage amplitude measurements) performed on one or more of the nodes of the one or more of the training electrical networks. In some embodiments, the measurements performed may include voltage measurements (e.g., including voltage amplitude measurements) performed on each of the nodes of the one or more of the training electrical networks.

[0132] In one or more embodiments, the measurements performed may further include one or more of active power measurements and three-phase reactive power measurements performed on one or more of the nodes of the one or more of the training power networks. In some embodiments, the measurements performed may further include one or more of active power(s) and reactive power(s) measurements of one or more of the three phases carried out on each of the nodes of one or more of the learning electrical networks.

[0133]

[0134] In embodiments in which data respectively representative of electrotechnical characteristics of the electrical network under consideration are used (1.2) (for example, the graph neural network may further be configured on the basis of data respectively representative of electrotechnical characteristics of the electrical network under consideration), data representative of electrotechnical characteristics may be collected for one or more of the one or more training electrical networks. For example, in some embodiments, data representative of electrotechnical characteristics may be collected for each of the one or more training electrical networks.

[0135] In one or more embodiments, the data representative of electrotechnical characteristics may comprise, for a learning network comprising M nodes, an admittance matrix Y (which is a complex matrix NphM X Np^M). In certain embodiments, the admittance matrix may relate the currents to the voltages of Nph phases among the 4 phases (the three phases and the neutral) ( 1 < Np^ < 4) of the M nodes of the network. Depending on the embodiment, the admittance matrix may be predetermined, or be determined from data provided by the distribution network manager and making it possible to construct it.

[0136]

[0137] In one or more embodiments, the data collected on one or more of the one or more training networks (comprising topology data and voltage V measurement data performed on nodes, and possibly in some embodiments one or more of active power P measurement data and reactive power Q measurement data of one or more of the three phases on these nodes and electrotechnical parameter data) can be used (20a2-1, 20a2-2, 20a2-3) to construct a graph representation of one or more samples (of each sample) of the database.

[0138] Thus, in one or more embodiments, the present disclosure provides for training (1.4) of at least one layer of a graph neural network (20a3) (such as for example the graph neural network illustrated by [Fig.3]) using a training database constituted from topology data and measurement data carried out on one or more training electrical networks.

[0139] Advantageously, due to the use of a graph neural network configurable according to topology data of an application network, this Graph neural network training can be used during an inference phase applied to an application electrical network without requiring that this application network have an identical or similar topology, or an identical or similar size, to those of one or more of the training electrical networks. The proposed method therefore advantageously makes it possible to carry out an inference phase, possibly in real time (or near real time) on any electrical network, thanks to the use of a graph neural network configured and trained according to an embodiment of the present disclosure, using measurements carried out on a subset of the electrical network (and not on all or almost all of the nodes of this network).The implementation of the proposed method is therefore not limited to an electrical network or type of electrical network (of similar topology or size) used to perform the training of one or more of the layers of the graph neural network.

[0140]

[0141] In one or more embodiments, the proposed method uses a graph neural network (GNN) architecture, which advantageously makes it possible to represent the interactions between the different nodes of the electrical network considered (for example by configuring the graph neural network on the basis of topology data of the electrical network considered). In certain embodiments, a training phase (1) of the graph neural network can be carried out, using topology data (20a2-l) of one or more training networks (20al) and measurement data (20a2-3) ((voltage amplitudes)) carried out on the one or more training networks.In certain embodiments, the use (in addition to topology data (20a2-l) and measurement data (20a2-3)) of data representative of electrotechnical characteristics (20a2-2) can advantageously make it possible to carry out learning which aims to penalize the violation of physical laws.

[0142] In one or more embodiments, an inference phase (2) is performed during which the model (20b3) (graph neural network) is used on the considered electrical network (20b 1) to determine an estimate (20b4) of the amplitudes of the voltages of the nodes of the considered electrical network, from input data comprising voltage measurements (20b2-3) carried out (2.3) on a subset of nodes of the considered electrical network (typically only a few nodes of the considered electrical network, the subset of nodes comprising a number of nodes being substantially less than the total number of nodes of the considered electrical network). In one or more embodiments, the proposed method can advantageously be implemented in real time or quasi-real time, in the case where the voltage measurements are sent in real time or near real time, and the estimate is determined in real time or near real time.

[0143] In one or more embodiments, the model (graph neural network) may have been trained (for example by performing a learning phase) prior to and / or in parallel with the inference phase during a learning phase (1). For example, in one or more embodiments, the model previously trained on one or more (Nrés) training electrical networks (20al) (for example of size M (comprising M nodes)) can be applied to an (application) electrical network (20b 1) (for example of size M' different from M) to determine (2.4) an estimate (20b4) of the amplitudes of the voltages of the nodes of this network (20b 1) using as input data voltage measurements (20b2-3) carried out (2.3) on a number of nodes of this network which is (significantly) less than the total number of nodes of the (application) network (20b 1) (for example reported in real time or quasi-real time).The proposed method therefore advantageously makes it possible to avoid, on the one hand, taking measurements on all the nodes of the electrical network considered (by advantageously using a number of nodes on which measurements are carried out which can be small compared to the total number of nodes of the network), which can be particularly long and complex, but also on the other hand the use of a neural network specifically configured for the configured electrical network. Once the graph neural network has been trained on one or more learning electrical networks, this graph neural network can advantageously be configured on the basis of topology data (20b2-l) of the electrical network considered (20bl), then be applied to this network (20bl) by using voltage measurements (20b2-3) carried out (2.3) on nodes of this network whose number is (significantly) lower than the total number of nodes of the network (20b 1) to generate (2.4) an estimation (20b4) of the voltage amplitudes for all the nodes of this network. The proposed method thus has a hybrid character, in that it uses a neural network (but which is not specifically trained on the electrical network considered) as well as voltage measurements carried out on the electrical network considered (but on a (small) number of nodes (possibly very) lower than the total number of nodes in the network).

[0144]

[0145] In one or more embodiments, data (20b2-l) representative of a network topology may be collected (2.1) for the considered electrical network (20b 1), and provided to the graph neural network (20b3) for configuration, possibly after transcoding.

[0146] In one or more embodiments, the topology representative data (20b2-l) may comprise one or more of representative data nodes of the electrical network considered and data representative of the links of the electrical network considered. For example, in certain embodiments, the data representative of the nodes of the electrical network may comprise a list of the nodes of the electrical network considered, for example numbered from 1 to M. For example, in certain embodiments, the data representative of the links of the electrical network may comprise a matrix of dimension . x 0' for example consisting of the indices of the two nodes of the two ends of the m' links of the electrical network.

[0147] Advantageously, in one or more embodiments, the network topology data collected for the electrical network considered (inference phase) and for one or more of the learning networks used (learning phase) may be in the same format or in a similar format. The electrical network (31) of [Fig.5a] and the example of representative data of links is applicable to any electrical network, whether it is the electrical network considered or a learning electrical network.

[0148]

[0149] In one or more embodiments, measurement data (20b2-3) are collected (2.3) on the electrical network considered (20bl), for example by carrying out measurements on a subset of nodes of this network (20b 1) comprising a number of nodes (possibly very) lower than the total number of nodes of this network (20b 1).

[0150] In one or more embodiments, the measurements performed may comprise voltage measurements (for example comprising voltage amplitude measurements) performed on a subset of nodes of the electrical network considered, typically comprising a number of nodes small compared to the total number of nodes of the electrical network considered. In certain embodiments, these measurements may be performed in real time or near real time.

[0151] In one or more embodiments, the measurements performed may further comprise one or more of active power measurements and reactive power measurements on one or more of the three phases performed on the subset of nodes of the electrical network considered.

[0152] For example, in one or more embodiments, the measurements carried out on the subset of nodes of the electrical network considered may comprise measurements of the voltage amplitudes, and possibly in certain embodiments measurements of the active powers and reactive powers of one or more of the three phases of one or more of: the secondary of the HTA / LV transformer considered as a node of the electrical network considered (in the embodiments in which the secondary of the HTA / LV transformer is instrumented in measurement sensors, for example capable of sending measurements in real time or near real time) and a predetermined number of network nodes of another type (for example nodes equipped with smart electricity meters capable of sending measurements in real time or near real time). The proposed method can advantageously be implemented with a small number of these meters (in comparison with the total number of meters in the network), which makes it possible to overcome the communication constraints that may arise on certain networks with these smart meters.

[0153]

[0154] In embodiments in which data respectively representative of electrotechnical characteristics of the electrical network considered are used (for example the graph neural network can further be configured on the basis of data respectively representative of electrotechnical characteristics of the electrical network considered), data (20b2-2) representative of electrotechnical characteristics can be collected (2.2) for the electrical network considered (20b 1).

[0155] In one or more embodiments, the data representative of electrotechnical characteristics may comprise, for a considered electrical network comprising M' nodes, an admittance matrix Y' (which is a complex matrix N^M' X Np^M''). In certain embodiments, the admittance matrix may link the currents to the voltages of Nph phases among the 4 phases (the three phases and the neutral) (1 < Nph < 4) of the M' nodes of the considered electrical network. Depending on the embodiment, the admittance matrix may be predetermined, or be determined from data provided by the distribution network manager and making it possible to construct it.

[0156]

[0157] In one or more embodiments, data relating to the (description of the) considered electrical network (20b 1) comprising topology data (20b2-l) of the considered electrical network can be used to construct (2.4) a graph representation of the considered electrical network, which makes it possible, in one or more embodiments, to configure a graph neural network using one or more neural network layers (for example as illustrated by [Fig.3]) based on the topology data (20b2-l) of the considered electrical network.

[0158] In one or more embodiments, once configured on the basis of the data representative of the topology of the electrical network considered (20bl), the graph neural network (20b3), trained in certain embodiments according to a learning phase (1), determines (2.4) (during an inference phase) an estimate (20b4) of the respective voltage amplitudes of the nodes of the set of nodes on the basis of the voltage measurement data (20b2-3) of the nodes of the subset of nodes. In the embodiments in which data (20b2-2) of electrotechnical parameters are further used for the configuration of the graph neural network, the determination (2.4) (in the inference phase) of the estimation (20b4) of the respective voltage amplitudes of the nodes of the set of nodes can further be carried out on the basis of measurements of active power(s) and measurements of reactive power(s) of one or more of the three phases on the nodes of the subset of nodes (data included in the measurement data (20b2-3) fed back (in certain embodiments in real time (or quasi-real time)) to the graph neural network.

[0159]

[0160] Advantageously, embodiments of the present disclosure use a graph neural network representation of the complex data structures corresponding to one or more electrical networks managed according to the proposed scheme.

[0161] According to the embodiment, a graph representation can be applied to one or more (or even all) samples of the training database as well as to one or more (or even all) samples of the electrical network considered (electrical network of the real-time application). As indicated in connection with Figure 4, a sample of the training database then corresponds to the data of one of the N training electrical networks which were collected at a certain measurement time:

[0162] In one or more embodiments, the data collected during one or more of collecting topological data of the training networks, collecting measurement histories of the training networks, and collecting electrical parameters of the training networks may be organized according to a predefined graph neural network structure. The data collected on the training networks may thus be transformed into a graph.

[0163] In one or more embodiments, the data collected during one or more of the collection of topological data of the electrical network considered, the collection of measurement histories (measurements possibly collected in real time (or quasi-real time)) of the electrical network considered and the collection of electrotechnical parameters of the electrical network considered can be organized according to a predefined graph neural network structure. The data collected on the electrical network considered can thus also be transformed into a graph.

[0164] In one or more embodiments, data collected for an electrical network to be represented (training network or considered electrical network) can be used to configure a graph neural network.

[0165] For example, in one or more embodiments, the topology representative data may be used to configure a graph G = (y, e) representative of the electrical network to be represented, in which V is a set of nodes of the electrical network to be represented and E is a set of connections between the nodes of the electrical network to be represented. The data of the sets V and E may be obtained based on the topology representative data of the electrical network to be represented.

[0166] In one or more embodiments, the electrical network topology representative data that is used to configure the graph neural network is comprised in a data structure corresponding to a graph representation Q — (y, e) of the electrical network, wherein V denotes a set of graph nodes respectively representing nodes of the electrical network and E denotes a set of graph connections respectively representing electrical connections between the nodes of the electrical network. In these embodiments the graph neural network may be configured by establishing respective mappings between one or more of the nodes of the set V of the graph and the neural network layers of the graph neural network and the connections of the set E of the graph and the neural connections of the graph neural network.

[0167] In one or more embodiments, the graph neural network used may be configured with a number Ngnn of neural network layers of the graph neural network, each neural network layer comprising one or more (e.g., EE j neural networks) (with 1 k < K and 1 i Ngnn), the number Ngnn being determined based on a number of nodes of a graph G = (V, E) representing the electrical network. For example, a neural network layer comprising one or more (e.g., K) L(k) neural networks (with 1 k < K), called (indifferently) a base layer, a model layer, or a matrix layer, may be duplicated to configure the graph neural network with Ngnn of neural network layers, the number Ngnn being determined based on a number of nodes of a graph G = (V, E) representing the electrical network.

[0168] In one or more embodiments, topology data of the electrical network to be managed that is used to configure the graph neural network may be included in a data structure corresponding to a graph representation G = (V, E) of the electrical network, the number of nodes of the graph corresponding to the number N of nodes of the electrical network, may be used to determine a number N gnn of neural network layers to be configured. For example, the number Ngm of neural network layers to be configured may be determined based on the number N of nodes of the electrical network to be represented (e.g. example N gnn N) via the number of nodes of a graph data structure Q = (y, E) representing the electrical network to be managed.

[0169] In one or more embodiments, a node of the graph G can be configured to represent one or more phases of this node (for example the 3 phases of this node).

[0170]

[0171] In one or more embodiments, electrotechnical characteristics of one or more links of the electrical network to be represented can be represented, for a link / ()e F between the nodes of index a and P of the set V, by a matrix A = comprising the real (yre ) and imaginary (Yim^) parts of the 4x4 admittance matrix corresponding to the indices “and 4: Yreap • In one or more embodiments, the dimension of the electrotechnical characteristics of a connection can thus be: dA = 4 x 4 + 4 x 4 = 32. In one or more embodiments, electrotechnical characteristics of one or more nodes of the electrical network to be represented may be represented, for an index node, by a matrix B = ( Ba ) ^ comprising one or several measurements (amplitudes) of voltages (Va), active power (PA and reactive power (Q^ of one or more phases (^w, bn and Cn) (for example of the three phases) measured with respect to the neutral (”): kq“ v? and Kr and c]-In one or more embodiments, the dimension of the electrotechnical characteristics of a node can thus be: dB - 9.

[0172] In the embodiments in which the scheme proposed in the present disclosure is implemented in real time (or, depending on the embodiment, quasi-real time), it is possible that the matrix B corresponding to a node of the electrical network to be represented has missing values ​​due to problems of feedback of measurements in real time (or, depending on the embodiment, quasi-real time).

[0173] In one or more embodiments, output data (for example representing electrotechnical characteristics) corresponding to one of the nodes of the electrical network to be represented can be represented, for a node of index a GV, by a matrix U = (Ua) ^ comprising the real and imaginary parts of the voltages of one or more phases (for example of the three phases) with respect to the neutral (y «ni an > bn y bn ymyc«\ and of the voltage of the neutral with respect to the earth V “re aim are V afe V (VZ VO-U„=\voan V™ Vabn Vbn V™ vam V*e K'HIn one or more embodiments, the dimension of the electrotechnical characteristics of the outputs corresponding to a node can thus be: dv = 8.

[0174] In one or more embodiments, the proposed method provides for performing a training phase of the graph neural network once configured, the training phase being configured to penalize the violation of physical laws. In these embodiments, a representation format of the output data comprising the real and imaginary parts of the four voltages (the three phases and the neutral) (as illustrated above) can advantageously be used in order to express physical equations corresponding to the physical laws for which it is desired to train the graph neural network. In one or more embodiments, output data organized according to this representation format can be used to perform training of the graph neural network configured to penalize the violation of physical laws.

[0175] In one or more embodiments, the representations used of the input and output data of a node of the electrical network to be represented may be configured by including the neutral-to-ground voltage data in the representation of the output data, without including this neutral-to-ground voltage data in the representation of the input data. For example, in one or more embodiments, the neutral-to-ground voltages are included only in the output data.

[0176] Therefore, advantageously, in one or more embodiments, measurements of these voltages (of the neutral) are not required as input data, which is consistent with the fact that in practice the neutral is not often measured.

[0177] In one or more embodiments, neutral voltage estimates can be obtained at the output of the graph neural network, and be used in the physical equations that one wishes to respect during the learning phase, which advantageously makes it possible to use for the learning phase of the graph neural network physical equations that use the 4 phases (including the neutral), which advantageously make it possible to take into account a possible imbalance between the 3 phases in the definition of the physical laws to be respected.

[0178] In the embodiments in which the graph neural network is not configured to generate neutral voltage estimates as output, it will be possible to use, for the learning phase of the graph neural network, physical equations which use, among the 4 phases, only the 3 phases other than the neutral. To move from physical equations which use the 4 phases to physical equations which do not use the neutral, it will be possible to consider in one or more embodiments the hypothesis that the system is balanced. However, to the extent that certain LV networks may be unbalanced, this approximation may possibly degrade the performance of the proposed method.

[0179] [Fig.5b] illustrates an example of graph representation obtained for an example of electrical network (40a-4) (corresponding to the example of network (31) illustrated by [Fig.5a]) comprising 3 nodes and two links (one link between nodes 1 and 2 and one link between nodes 1 and 3).

[0180]

[0181] In one or more embodiments, the graph neural network architecture used may comprise N neural network layers, each neural network layer i = 1, ..., N comprising an encoder E configured to perform encoding, one or more neural networks ÿ (with indices &) configured to perform message propagation, and a decoder D configured to perform decoding. The graph neural network architecture may thus comprise an encoding portion comprising the respective encoders of each layer, a message propagation portion comprising the respective neural network(s) of each layer, and a decoding portion comprising the respective decoders of each layer.

[0182] According to the embodiments, the encoders of one or more of the neural network layers may be configured to perform an identical encoding operation, and the decoders of one or more of the neural network layers may be configured to perform an identical decoding operation.

[0183] [Fig.6] illustrates an example of a graph neural network architecture (50) corresponding to the example of a 3-node electrical network (40a-4) of [Fig.5b].

[0184]

[0185] In one or more embodiments, an encoding (50-1) is performed by each neural network layer encoder on the received input data. In some embodiments, the encoder of a neural network layer may be configured to transcode input data (for example, with reference to the 3-node network example of Figures 5a and 5b, 9-dimensional data corresponding to voltage (L), active power (P) and reactive power (ô) measurement data for the three phases (VPQ x 3)) to a 4-dimensional latent space, corresponding to a hyperparameter to be optimized.

[0186] For example, in some embodiments, for a node the information Ba of dimension dB may be encoded into a message ^o) of dimension 4. This encoding may be performed by an encoder device, which may be implemented by a fully connected neural network.

[0187] In one or more embodiments, an encoder performing the same encoding operation (transformation) may be configured for several of the nodes (in some embodiments, all nodes) of the graph neural network. By denoting this encoder y? • -> p4, the encoded message corresponding to node a may be represented by: j / h) — E(Ba)-The dimension of the latent space and the number of hidden layers are hyperparameters to be adjusted.

[0188]

[0189] In one or more embodiments, message propagation (50-2) is performed by the neural networks of the neural network layers of the graph neural network on the received messages. In one or more embodiments, the neural networks (of indices k = 0, .... K - 1) of the neural network layers are configured to iteratively update (the neural networks of index k = 0, .... K - 1 performing an update iteration) the message corresponding to each node by taking into account the messages of neighboring nodes.

[0190] In one or more embodiments, the graph neural network may be configured to perform K message propagation iterations. In some embodiments, the graph neural network may be configured to apply, at each iteration k = 0, ..., K - 1, a same neural network jHA) to one or more (in some embodiments, to each) of the M nodes of the electrical network considered. By denoting this neural network -> p^, the corresponding message at node a after each message propagation iteration can be represented by: the characteristics of the links A at the input of the neural network allow us to consider the messages from the neighborhood of node a. Although for an iteration A, the same neural network is applied to each of the M nodes of the electrical network considered, this neural network varies from one iteration to another.

[0191] In one or more embodiments, the number of message propagations K is a hyperparameter, which can be preconfigured or dynamically configured, for example according to characteristics of the electrical network considered.

[0192]

[0193] In one or more embodiments, decoding (50-3) is performed by each neural network layer decoder of the graph neural network on the received final messages. In one or more embodiments, the decoder of a neural network layer may be configured to transcode (decode) the final message from the latent space to the output data space.

[0194] For example, in some embodiments, for a node a, the final message (K-th iteration) may be decoded into an output t / Æ) corresponding to node a. a U a This decoding can be done by a decoder device, which can be implemented by a fully connected neural network. j. In this representation,

[0195] In one or more embodiments, a decoder D performing the same decoding operation (transformation) may be configured for several of the nodes (in some embodiments, all nodes) of the graph neural network. Denoting this encoder p. prf j / r, the output data pOO generated by decoding the final message / / ^0 corresponding to node a may be represented P^-Up^D^}

[0196] In one or more embodiments, a decoder may be applied to an iteration k <K pour passer d’un message intermédiaire latent pWcorrespondant à l’itération k à une sortie intermédiaire jr / A).

[0197] Thus, advantageously, in embodiments in which a learning loop of the graph neural network configured to respect physical equations is used, the learning loop may be configured to respect said physical equations progressively throughout the message propagation iterations (1 k < K\ and not just at the last propagation (k - K).

[0198] The present disclosure proposes to use a graph neural network whose architecture allows interaction between different neural networks to explore the neighborhood of the different nodes by propagating messages, which makes this architecture advantageously modular.

[0199] Thus, advantageously, in one or more embodiments, a trained neural network model corresponding to a network of size M nodes can be used to manage an electrical network of size M according to an embodiment of the present disclosure by adding (modifying, or deleting), according to the embodiments, one or more blocks of trained neural networks to apply the trained model to a network of size M * M, and by filling in the links between the nodes in the characteristics of the links A on the basis of characteristics (for example electrotechnical) of links of the electrical network of size M'.

[0200]

[0201] In one or more embodiments, a training loop is performed to train the model (graph neural network) to produce an output that complies with physical laws.

[0202] For example, in some embodiments, a training phase may be performed on the graph neural network to configure the neural network so that the complex voltages output from the model meet one or more conditions, such as one or more of the following example conditions:

[0203] Example of condition 1: The values ​​of the amplitudes of the voltages calculated from the complex voltages are close to the values ​​of the amplitudes of the voltages which appear in the characteristics of the nodes B. For example, the deviations between the values

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[0213] amplitudes of the voltages calculated from the complex voltages and the values ​​of the amplitudes of the voltages which appear in the characteristics of the nodes B are less than a threshold, for example predetermined. Example condition 2: The values ​​of the active powers calculated from the complex voltages are close to the values ​​of the active powers which appear in the characteristics of the nodes B. For example, the differences between the values ​​of the active powers calculated from the complex voltages and the values ​​of the active powers which appear in the characteristics of the nodes B are less than a threshold, for example predetermined. Example condition 3: The reactive power values ​​calculated from the complex voltages are close to the reactive power values ​​that appear in the characteristics of the B nodes. For example, the differences between the reactive power values ​​calculated from the complex voltages and the reactive power values ​​that appear in the characteristics of the B nodes are less than a threshold, for example a predetermined one. Example condition 4: The calculated values ​​of the three-phase complex voltages respect one or more of the phase shift between phases and the phase shift induced by the transformer coupling: The real parts of the voltages are located around the values ​​corresponding to each of the 3 phases and the neutral given by: cos{ô), if (p = a _ cos(<5+Ÿ ), if (pb Vre “ / . 4;t \ . cos(o + — ), if (p = c , 0 , if (pn Where 5 is the phase shift due to transformer coupling. The imaginary parts of the voltages must be located around the values ​​corresponding to each of the 3 phases and the neutral given by: sin ( 5 ) , if (p = a - sin(<5 + ^X if (pb v"= । ' im . / s \ sin((5 + —J, si(p = c L 0 , if (p = n Where 5 is the phase shift due to transformer coupling. Depending on the embodiment, the learning phase may be configured so that one or more predefined conditions, for example one or more (for example all) of the example conditions 1 to 4, are met on one or more of: one or more (for example all) of the samples in the database

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[0225] (t S pV- J)' one or more (for example all) of the nodes (a £ [d / ]) and on one or more of the 3 phases ((p £ {a, b, c} ). In one or more embodiments, the training phase may further be configured so that one or more of the one or more conditions are met at the output of the model and are further progressively ensured throughout one or more of the message propagation iterations (fa g [k])• [Fig.7] illustrates an example of graph neural network learning implementation. In the example illustrated in [Fig.7], the learning phase of the graph neural network is configured to minimize the error corresponding to the difference between the values ​​calculated by the model and the corresponding values ​​respecting certain predetermined conditions. For example, in one or more embodiments, the training phase may use a training function expressed as follows: In one or more embodiments, for a sample f, a node a and at the iteration the output of the model can be written: rAk ) _ [17 17 17 bii'k TZ bn^ cnik) T / cnik) ntWd znrW] ^ta— 'te * ta. * ta V ta ta * ta Y ta 'ta The characteristics of node a of sample f can be represented by: o Fit®” \7bn nb” V^n P^n O™] Qt a Vt.a *7« The learning phase may be configured so that the calculations of one or more of the voltage amplitudes, active powers, and reactive powers as a function of the elements of jyW are close to the corresponding values ​​in BCa. For example, the learning phase may be configured so that the deviations between one or more of the voltage amplitudes, active powers, and reactive powers as a function of the elements of yik) calculated from the elements of lj(k) and the corresponding values ​​in Bt a are less than a threshold, for example a predetermined one. In one or more embodiments, for a sample, a node, a phase, and at iteration k, the voltage amplitude may be calculated from the complex voltages, for example as follows: L y U ~^t,are Referring to the example of condition 1, the deviation to be minimized AV t,a on the voltage amplitude can be expressed by any function

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[0238] appropriate distance between A <pn{k) et y?7”, telle que par exemple y. ka r t,a ta [ | r ta F ta | In one or more embodiments, the active power may be calculated from the complex voltages, for example as follows: y pW [ pnfk) p^k) (wW-, j. TZ ^'tz tz = Lm^ v„m +Vt^im}+BttP[vt,am -v^ JJ Referring to the example of condition 2, the deviation A vg>^k) to be minimized on the active power at the iteration can be expressed by any appropriate distance function between A and p^', such as for example n rt,a min ► PY" your " * your In one or more embodiments, reactive power may be calculated from the complex voltages, for example as follows: = yWre +ytM.mv,^ -yKUre v,^ j] Referring to the example of condition 3, the deviation ^^k) to be minimized on the reactive power at iteration * can be expressed by any suitable function of distance between A <pm et o(pn, telle que par exemple 0, ^there <pnik) t.a In one or more embodiments, with reference to example condition 4, the constraint on the real part of the voltage may be expressed as: . TT (pnfâ) - T apn . In one or more embodiments, with reference to example condition 4, the stress on the imaginary part of the tension can be expressed by: im tptik) ipn Vt^im ' Vim

[0239] In one or more embodiments, an example Loss objective function for minimizing the deviations and constraints expressed for condition examples 1-4 may be expressed as follows:

[0240] r, _ * M. ■ <, . / 7 AAA L +lo2(*)(apL + A0fo + AV,^ +AV74 J,

[0241] According to the embodiment, all appropriate weight functions a'i and a,2 may be used in the loss function Loss^ such as the weight functions — yK-k and — 1-yK-k, P being a predefined hyperparameter, chosen for example between 0 and 1.

[0242] For example, in one or more embodiments, it will be possible to choose a first weight function (applied to the values ​​of the voltage amplitudes) ü'i increasing (as a function of the variable & designating the message propagation iteration index) on the domain considered, and a second weight function "'2 decreasing (as a function of the variable & designating the message propagation iteration index), so that an increasing weight is given for compliance with the values ​​of the voltage amplitudes and, conversely, a decreasing weight is given for compliance with the other conditions, during the message propagation iterations.

[0243]

[0244] In embodiments aiming to use a method proposed according to the present disclosure with real-time or near-real-time performance, cases arise in which the number of measurements (of voltages, active powers and reactive powers obtained in real-time (or, depending on the embodiment, near-real-time) for the electrical network considered) is deemed too low for the estimation by the graph neural network of the amplitudes of the respective (unmeasured) voltages of the nodes of the set of nodes of the electrical network considered to have the desired performance (for example, have the desired accuracy). In particular, the characteristics of the nodes B of the electrical network considered on which the measurements are obtained may have missing values.

[0245] In one or more embodiments, a replacement of the missing measurements can be carried out in order to generate data capable of replacing these missing values ​​and supplementing the input data of the trained model, so as to obtain a better estimation by the graph neural network of the amplitudes of the respective (unmeasured) voltages of the nodes of the set of nodes of the electrical network considered during an inference phase of the graph neural network.

[0246] In one or more embodiments, pseudo-measurements of one or more of one or more unmeasured active powers and one or more unmeasured reactive powers may be used to address the absence of these measures.

[0247] In one or more embodiments, any missing voltage measurements (amplitudes) may be considered as variables to be optimized by an optimization engine configured to employ the trained model as an objective function.

[0248] Depending on the embodiment, any appropriate optimization technique may be used for this optimization, such as for example the particle swarm optimization technique known as PSO (from the English Particles Swarm Optimization).

[0249] [Fig.8] shows a diagram illustrating an example of a method (60) for managing an electrical network designed for real-time (or, depending on the embodiment, quasi-real-time) use.

[0250] [Fig.8] shows a trained model (MOD) of a graph neural network, configured on the basis of data representative of a topology of the electrical network considered according to one or more embodiments of the present disclosure. The trained model (MOD) of a graph neural network is further configured to receive voltage measurements (AMP_V_MES) (for example, measured voltage amplitude data), one or more of active power measurements and reactive power measurements (P_MES) (for example, measured active and / or reactive power data), these measurements being fed back in real time (or, depending on the embodiment, quasi-real time) from the nodes of a subset of a set of nodes of the electrical network considered, according to one or more embodiments of the present disclosure.

[0251] As illustrated by [Fig.8], in certain embodiments where the measurement feedbacks made in real time (or, depending on the embodiment, quasi-real time) are provided as input to the trained model (MOD) to perform data inference based on these measurements, one or more measurements among the voltage measurements (AMP_V_N_MES) (for example, measured voltage amplitude data), the active power measurements and the reactive power measurements (P_N_MES) (for example, measured active and / or reactive power data) may not be provided quickly enough to be included in the real-time (or, depending on the embodiment, quasi-real-time) measurement feedbacks provided as input to the trained model (MOD). Depending on the embodiment, these measurements not provided in real time may be considered missing, and may be replaced for provision as input to the trained model (MOD).

[0252] For example, in one or more embodiments, one or more of the missing power measurement(s) (active power measurement and / or reactive power measurement) (P_N_MES) may be replaced by corresponding pseudo-measurements (PM_P) that are provided as input to the trained model to address the absence of these measurements.

[0253] For example, in one or more embodiments, one or more of the missing voltage measurement(s) (amplitudes) (P_N_MES) may be replaced by corresponding pseudo-measurements (PM_P) that are provided as input to the trained model (MOD) to compensate for the absence of these power measurements.

[0254] In some embodiments, one or more of the missing voltage (amplitude) measurements (AMP_V_N_MES) may be replaced by corresponding pseudo-measurements (PM_V) that are provided as input to an optimization engine (Init., PSO), preferably configured to employ the trained model (MOD) as an objective function, and whose output data is provided to the trained model (MOD) to address the absence of these voltage (amplitude) measurements.

[0255] In one or more embodiments, a proposed method usable for determining, by a graph neural network, in real time (or, depending on the embodiment, quasi-real time) an estimate of the respective voltage amplitudes of the nodes of a set of nodes of an electrical network considered may comprise one or more of the following actions, depending on the embodiment:

[0256] Providing one or more of (in some embodiments all) the measurements (AMP_V_MES, P_MES) reported in real time (or, depending on the embodiment, quasi-real time) for certain nodes of a subset of nodes of the electrical network considered as input data of the trained model (MOD) (graph neural network).

[0257] The graph neural network (illustrated for example by the trained model (MOD) of [Fig.8]) will have been previously configured on the basis of data representative of a topology of the electrical network considered, and trained using one or more training electrical networks, according to one or more of the embodiments described in the present disclosure.

[0258] Calculate or, depending on the embodiment, obtain pseudo-measurements of one or more of the active and reactive powers when these are not measured (for those of the nodes of the subset of nodes of the electrical network considered for which power measurements are not sent in real time (or, depending on the embodiment, quasi-real time).

[0259] Calculate or, depending on the embodiment, obtain pseudo-measurements of the (amplitudes of the) voltages when these are not measured (for those nodes of the subset of nodes of the electrical network considered for which measurements of the (amplitudes of the) voltages are not sent in real time (or, depending on the embodiment, quasi-real time)).

[0260] Use one or more of the pseudo-measurements of the (amplitudes of the) unmeasured voltages to initialize an optimization engine (e.g. to initialize the particles of a PSO optimizer), and then execute the optimization engine (e.g. launch the PSO optimizer).

[0261] Include in the input data of the trained model (MOD) provided as input to the model (MOD) one or more of the pseudo-measurements of one or more of the active and reactive powers and the pseudo-measurements of the (amplitudes of the) voltages, possibly in certain embodiments after optimization by the optimization engine.

[0262] Determine, by the trained model (MOD) (graph neural network) an estimate of the respective voltage amplitudes of the nodes of a set of nodes of the electrical network considered including the subset of nodes for which measurements or pseudo-measurements have been provided.

[0263] Advantageously, the proposed method can therefore make it possible to obtain an estimate of the respective voltage amplitudes of the nodes of a set of nodes of the electrical network considered on the basis of measurements carried out in real time (or, depending on the embodiment, quasi-real time) or pseudo-measurements (to compensate for the absence of real-time measurements) for a subset of nodes of the set of nodes (comprising a number (much) lower than the number of nodes of the set of nodes of the electrical network considered).Thus, in one or more embodiments, the proposed method can be used to obtain an estimate of the respective voltage amplitudes of all the nodes of a set of nodes of the electrical network considered on the basis of a subset of nodes (comprising a number (very) lower than the number of nodes of the electrical network considered) for which measurements are obtained in real time (or, depending on the embodiment, quasi-real time), or failing that, pseudo-measurements are determined.

[0264] Depending on the embodiment, different schemes for constituting pseudo-measurements of the active and reactive powers and the amplitudes of the voltages may be used. For example, in certain embodiments, statistical or machine learning techniques that are based on a history of measurements of these quantities may be used.

[0265] According to one aspect of the present disclosure, a method for generating pseudo-measurements is proposed, which has the advantage of being inexpensive in terms of data. Indeed, in one or more embodiments, the proposed method is based on measurements reported in real time (or, depending on the embodiment, quasi-real time) without using a measurement history.

[0266] Respective examples of generation of different pseudo-measurements (active power, reactive power and voltage) according to one or more embodiments of the proposed method are described below:

[0267]

[0268] In one or more embodiments, in the case of a measurement of the active power p^ of a phase of a node a which is not available (for example because this measurement is not carried out or is not reported in real time (or, depending on the embodiment, quasi-real time)), it can be replaced by a pseudo-measurement which corresponds to the fraction of the measured active power of a transformer (high voltage / low voltage, or HTA / LV), depending on the power connected to the phase and the node in question.

[0269] In one or more embodiments, this pseudo-measurement may be calculated as follows:

[0270] <pn               fsoùsmtea *pseudoa — *tr y „ ? subscribed

[0271] Where p9" corresponds to the active power measured at the secondary of the HTA / LV transformer, p 9 corresponds to the load power connected to the node and phase x subcntea ri er in question, and yM'p iP corresponds to the sum of the charge powers subscribed connected to all nodes of the phase in question.

[0272]

[0273] In one or more embodiments, in the case of a measurement of the reactive power of a phase of a node "which is not available (for example because this measurement is not carried out or is not reported in real time (or, depending on the embodiment, quasi-real time)), it can be replaced by a pseudo-measurement which corresponds to the fraction of the measured reactive power of the transformer (high voltage / low voltage, or HTA / LV), according to the power connected to the phase and the node in question.

[0274] In one or more embodiments, this pseudo-measurement may be calculated as follows:

[0275] pseudoa ,-jpn = Q x pwr süUKcritef,

[0276] Where: (pm corresponds to the reactive power measured at the secondary of the transformer ^tr HTA / BT, p 9 corresponds to the load power connected to the node and the subscribed phase iic r in question, and yM< pv corresponds to the sum of the subscribed load powers p connected to all nodes of the phase in question.

[0277]

[0278] In one or more embodiments, in the case of a measurement of the voltage y^n of a phase of a node a which is not available (for example because this measurement is not carried out or is not reported in real time (or, depending on the embodiment, quasi-real time)), it can be replaced by a pseudo-measurement which can for example correspond to the average of the voltages of its first measured neighborhood.

[0279] In one or more embodiments, this pseudo-voltage measurement can be used to initialize an optimization engine configured to provide as input to a graph neural network configured according to an embodiment of the present disclosure replacement data for the corresponding unavailable voltage measurement. For example, in embodiments in which the optimization engine used is of the PSO type, the pseudo-voltage measurement can be used to initialize the particles of the PSO around this value.

[0280]

[0281] An embodiment is described below in which a PSO type optimization engine is used to optimize one or more pseudo-voltage measurements before providing input to a graph neural network.

[0282] The PSO technique is inspired by the living world. It is based on the collaboration of individuals to organize themselves to find an optimal position. At the start of the algorithm, each particle (one-dimensional or multidimensional) is initialized (randomly or not) in the search space of the problem.

[0283] At an iteration \ the position xlt of a particle 1 is updated according to 3 components: its current speed y1, its best solution X- and the best solution obtained in its neighborhood ss.

[0284] The velocity of the particle can be updated according to the following equation:

[0285] y J+i = + ^(^-^)+^(^-^)

[0286] Where a\ bY and b2 are predefined hyperparameters, which allow to define the exploration strategy of the search space, by fixing the degree of dependence of each particle on itself or on its surroundings.

[0287] The position of the particle can be updated according to the following equation:

[0288] ^+i = X- + Vj+1

[0289] In one or more embodiments, the (amplitudes of) voltages for which a measurement is not available may be used as an optimization variable of the PSO algorithm. In this context, the dimension of each particle considered may correspond to the number of (amplitudes of) voltages for which a measurement is not available. In some embodiments,

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[0300] These particles can be initialized around the pseudo-measurements of the amplitudes of the voltages determined previously. In these embodiments, for a particle, "at an iterationx\ can correspond to a set of values ​​(amplitudes) of the unmeasured voltages, in the search space of the problem. In one or more embodiments, by injecting x\ into the missing positions of the features of the nodes B, we note the features of the nodes corresponding to the particle » at iteration l. In one or more embodiments, may include one or more of: measurements (of the magnitudes) of the measured voltages, measurements of one or more of the measured active and reactive powers, pseudo-measurements of one or more of the unmeasured (or unavailable) active and reactive powers, and values ​​of xi that represent the values ​​(of the magnitudes) of the unmeasured voltages for the particle" at iteration &. In one or more embodiments, by applying the trained model GNNentrained on the data corresponding to a particle, at one iteration we obtain an estimate of the amplitudes of the voltages y* which is separated into V^jmes ct y* to respectively designate the estimate (of the amplitudes) of the non-mes voltages. measured and unmeasured. r helots. ilnon mes.. GNNen[raitté The objective of this iterative optimization is to minimize the gap between the amplitudes of the measured voltages and the estimate of the amplitudes of the measured voltages. For a particle », at iteration l, the solution s< corresponding to one of the iterations l < l where the following deviation is minimal can be considered optimal (for the particle): He Ï<1 Where Vmes groups the amplitudes of the measured voltages. At iteration l, the global solution ss corresponding to one of the particles i E [ N particles ] °where the gap is minimal can be considered optimal: min 11Vmes. "Vumes 11 » [N partit-nies]

[0301] The implementation of iterations of a position update loop allows, for each particle, to converge towards the best position of the particle. At the end of this approach, we are interested in the estimation of the amplitudes of the unmeasured voltages v* obtained at the output of the trained model having as input data the F non J characteristics of the nodes corresponding to the best position of the particles.

[0302] [Fig.9a] illustrates an example of equipment architecture for implementing a method of configuring a graph neural network according to one or more embodiments of the proposed method.

[0303] With reference to [Fig.9a], the device 100a comprises a controller 104a, operatively coupled to a memory 101, which drives a neural network management module 102a, and a neural network module 103a.

[0304] The controller 104a is configured to control the neural network management module 102a, and the neural network module 103a for implementing one or more embodiments of the proposed method.

[0305] The neural network management module 102a is configured for implementing the method proposed by the device 100a. In particular, the neural network management module 102a may be configured to perform the functions and perform the acts described in the present description for implementing the configuration of a graph neural network according to one or more embodiments of the method proposed in the present disclosure. In certain embodiments, the neural network management module 102a may be further configured to perform the functions and perform the acts described in the present description for implementing a training phase of the graph neural network, comprising for example a training phase of one or more neural networks of layers of the graph neural network, according to one or more embodiments of the method proposed in the present disclosure.

[0306] The neural network module 103a is configured for implementing the method proposed by the device 100a. In particular, the neural network module 103a may comprise a graph neural network, for example of the message transmission type, which may be configured according to one or more embodiments of the method proposed in the present disclosure.

[0307] The device 100a may be a computer, a computer network, an electronic component, or other apparatus comprising a processor operably coupled to a memory, as well as, depending on the embodiment selected, a data storage unit, and other associated hardware such as a network interface and a media reader for reading and writing to a removable storage medium (not shown in the figure). The removable storage medium may be, for example, a compact disc (CD), a digital video / versatile disc (DVD), a flash disk, a USB stick, an SSD memory, etc. Depending on the embodiment, the memory, the data storage unit or the removable storage medium contains instructions which, when executed by the controller 104a, cause this controller 104a to perform or control the neural network management module 102a and neural network module 103a parts for implementing one or more embodiments of the proposed method. The controller 104a may be a component implementing a processor or a computing unit for configuring a graph neural network according to the proposed method and controlling the modules 101 to 103a of the device 100a.

[0308] The device 100a may be implemented in software form, in hardware form, such as an application-specific integrated circuit (ASIC), or in the form of a combination of hardware and software elements. Similarly, each of the modules 101a to 103a may be implemented in software form, in hardware form, such as an ASIC, or in the form of a combination of hardware and software elements. [Fig.9b] illustrates an example of an equipment architecture configured for implementing the proposed method according to one or more embodiments.

[0309] With reference to [Fig.9b], the device 100b comprises a controller 105b, operatively coupled to a memory 101b, which controls a module 102b for obtaining voltage measurements, a module 103b for managing a neural network, and a module 104b for the neural network.

[0310] The controller 105b is configured to control the module 102b for obtaining voltage measurements, module 103b for managing the neural network, and module 104b for implementing one or more embodiments of the proposed method.

[0311] The module 102b for obtaining voltage measurements is configured for implementing the method proposed by the device 100b. In particular, the module 102b for obtaining voltage measurements may be configured to perform the functions and accomplish the acts described in the present description for implementing the obtaining of voltage measurements for each node of a subset of the set of nodes of the electrical network according to one or more embodiments of the method proposed in the present disclosure.In some embodiments, the module 102b for obtaining voltage measurements may be further configured to perform the functions and perform the acts described in the present description for implementing the obtaining of active power measurements and reactive power measurements, for each node of the subset of the set of nodes of the electrical network, according to one or more embodiments of the method proposed in the present disclosure.

[0312] The neural network management module 103b is configured for implementing the method proposed by the device 100b. In particular, the neural network management module 103b may be configured to perform the functions and accomplish the acts described in the present description for implementing the configuration of a graph neural network based on data representative of a topology of the electrical network according to one or more embodiments of the method proposed in the present disclosure.In some embodiments, the neural network management module 103b may be further configured to perform the functions and accomplish the acts described in the present description for implementing a learning phase of the graph neural network, comprising for example a learning phase of one or more neural networks / ) of layers of the graph neural network, according to one or more embodiments of the method proposed in the present disclosure.

[0313] The neural network module 104b is configured for implementing the method proposed by the device 100b. In particular, the neural network module 104b may be configured to perform the functions and perform the acts described in the present description for implementing the determination, by the configured graph neural network, of an estimate of the respective voltage amplitudes of the nodes of the set of nodes on the basis of the voltage measurements of the nodes of the subset according to one or more embodiments of the method proposed in the present disclosure.

[0314] The device 100b may be a computer, a computer network, an electronic component, or other apparatus comprising a processor operably coupled to a memory, as well as, depending on the embodiment selected, a data storage unit, and other associated hardware such as a network interface and a media reader for reading and writing to a removable storage medium (not shown in the figure). The removable storage medium may be, for example, a compact disc (CD), a digital video / versatile disc (DVD), a flash drive, a USB flash drive, a solid-state memory, etc.Depending on the embodiment, the memory, the data storage unit or the removable storage medium contains instructions which, when executed by the controller 105b, cause this controller 105b to perform or control the module 102b for obtaining voltage measurements, module 103b for managing a neural network, and module 104b for the neural network for implementing one or more embodiments of the proposed method. The controller 105b may be a component implementing a processor or a computing unit for managing electrical networks and controlling the modules 101b to 104b of the device 100b.

[0315] The device 100b may be implemented in software, in hardware, such as an application-specific integrated circuit (ASIC), or as a combination of hardware and software elements. Similarly, each of the modules 102b to 104b may be implemented in software, in hardware, such as an ASIC, or as a combination of hardware and software elements.

[0316] In the embodiments using a message transmission type graph neural network, the proposed configuration method makes it possible to advantageously use an iterative propagation of messages with the neighborhood of each node, which has the double advantage of an interaction between neural networks to explore the neighborhood and propagate messages and of a modular architecture which can be applied to networks of different sizes, as opposed to conventional methods which only use a single neural network which processes all the data of the electrical network to be managed and whose application is thus limited to this same electrical network.

[0317] The methods proposed in the present disclosure further have the following user advantages:

[0318] The proposed method for managing an electrical network makes it possible to use only a limited number of measurements (for example real time or quasi-real time) to observe LV networks.

[0319] The proposed method for managing an electrical network does not require strengthening telecommunications networks to collect a large number of measurements in real time.

[0320] The proposed method for managing an electrical network can use data from sensors already present, and is thus immediately applicable to electrical networks to be managed which are equipped with measurement feedback sensors. Thus, the proposed method makes it possible to avoid additional costs for the installation of additional sensors.

[0321] The proposed methods for managing an electrical network and configuring a graph neural network advantageously use a modular and generalizable model.

[0322] The proposed method for managing an electrical network makes it possible to observe an operator's LV networks. In particular, it makes it possible to activate control, piloting and adjustment actions, to accommodate producers and new consumption, to operate the network close to its dimensioning point, and to avoid the additional costs of reinforcement work.

[0323] Depending on the embodiment chosen, certain acts, actions, events or functions of each of the methods described herein may be performed or occur in a different order than that in which they were described, or may be added, merged, or not performed or not occur, as the case may be. Furthermore, in certain embodiments, certain acts, actions, or events are performed or occur concurrently and not successively.

[0324] Although described through a number of detailed exemplary embodiments, the proposed method and the apparatus for implementing an embodiment of the method include various variations, modifications, and improvements that will be apparent to those skilled in the art, it being understood that these various variations, modifications, and improvements are within the scope of the invention, as defined by the following claims.In addition, various aspects and features described above may be implemented together, or separately, or substituted for each other, and all various combinations and subcombinations of the aspects and features are within the scope of the invention. Furthermore, some systems and equipment described above may not incorporate all of the modules and functions described for the preferred embodiments.< / pn> < / pm>

Claims

Claims

1. A computer-implemented method of managing an electrical network comprising a set of nodes, the method comprising: Obtaining voltage measurements for each node of a subset of the set of nodes of the electrical network; Configuring a graph neural network based on data representative of a topology of the electrical network; and Determining, by the configured graph neural network, an estimate of the respective voltage amplitudes of the nodes of the set of nodes based on the voltage measurements of the nodes of the subset.

2. The method of claim 1, wherein the obtained measurements further comprise one or more of active power measurements and reactive power measurements, for each node of the subset of the set of nodes of the electrical network, and wherein the estimation of the voltage amplitudes is further determined based on one or more of the active power measurements and the reactive power measurements of the nodes of the subset.

3. A method according to any preceding claim, wherein the graph neural network is configured with V neural network layers, each neural network layer comprising an encoder e(i) configured to receive voltage measurement data as input and operatively coupled to one of one or more neural networks £(£. / ), and a decoder Dfy operatively coupled to one of the one or more neural networks j) and configured to output voltage amplitude estimation data, and wherein the number V neural network layers corresponds to the number of nodes in the electrical network.

4. Method according to claim 3, comprising: carrying out a training phase of the one or more neural networks £(£ of the layers of the graph neural network, following which each layer 1 of the neural network comprises the encoder £( / ), one or more trained neural networks £(£ ÿ, and the decoder / Xi)-

5. A method according to any one of claims 3 and 4, wherein one or more of the encoder and the decoder £)( / ) are trained neural networks.

6. Method according to any one of the preceding claims, comprising: carrying out a learning phase of the graph neural network on the basis of data respectively representative of the topology of one or more learning electrical networks.

7. Method according to any one of the preceding claims, comprising: carrying out a training phase of the graph neural network on the basis of data respectively representative of topology of one or more training electrical networks and data respectively representative of electrotechnical characteristics of the one or more training electrical networks, in which the estimation is further determined on the basis of data representative of electrotechnical characteristics of the electrical network.

8. Method according to any one of the preceding claims, in which the graph neural network performs a self-configuration phase on the basis of data representative of the topology of the electrical network.

9. The method of claim 8, wherein the self-configuration of the graph neural network comprises: generating, based on data representative of the topology of the electrical network comprising a connection in the electrical network between a first and a second node of the electrical network, a neural connection between a neural network fJk. z'1) of a first layer il of the graph neural network and a neural network [ / jt / 2) of a second layer i2 of the graph neural network, the first and second nodes of the electrical network corresponding respectively to the first and second layers il and i2 of the graph neural network and the neural connection between the neural networks L(k, il) and iJj, i2) corresponding to the connection in the electrical network between the first and second nodes.

10. A method according to any one of claims 8 to 9, wherein the graph neural network is configured with one or more neural network layers respectively corresponding to one or more nodes of the electrical network, and wherein the self-configuration of the graph neural network comprises: generating one or more neural connections between layers of the graph neural network corresponding respectively to one or more connections between nodes of the electrical network, the layers of the graph neural network corresponding respectively to the nodes of the electrical network.

11. A method according to any preceding claim, comprising: managing the electrical network based on the estimation of the respective voltage amplitudes of the nodes of the set of nodes.

12. An electrical network management device, comprising a processor, a data communications interface and a memory, operatively coupled to the processor, wherein the processor is configured to implement a method according to any one of claims 1 to 11.

13. Computer program, loadable into a memory associated with a processor, and comprising portions of code for implementing a method according to any one of claims 1 to 11 during the execution of said program by the processor.

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