Grid state estimation, and control of an electric grid

Abstract

The invention relates to a computer-supported method for estimating the state of an electric grid comprising a plurality of grid nodes and lines, said method being characterized at least by the following steps: - (S1) ascertaining an a priori distribution P(x) for state variables x of the electric grid, said a priori distribution P(x) being ascertained using a mixed distribution with respect to a plurality of grid topologies g of the electric grid; - (S2) providing a measurement distribution P(z|x) of measurement variables z for a given grid state x of the electric grid; - (S3) forming an a posteriori distribution P(x|z) for the state variables x using the a priori distribution P(x) and the measurement distribution P(z|x); and - (S4) carrying out the grid state estimation on the basis of the a posteriori distribution P(x|z) for one or more grid nodes and / or lines of the electric grid. The invention additionally relates to a method for controlling an electric grid, to a control unit for controlling an electric grid, and to a computer program product.

Description

[0001] 202305748 1 Description Network state estimation and control of a power grid The invention relates to a method according to the preamble of patent claim 1, a method according to the preamble of patent claim 12, a device according to the preamble of patent claim 14 and a computer program product according to the preamble of patent claim 15. Due to the progressive installation of additional consumers in the context of electromobility and volatile decentralized generation units, for example photovoltaic systems and wind turbines, within medium-voltage networks and low-voltage networks, critical operating states will increasingly occur due to the higher capacity utilization of the power grid in the two lower voltage levels.In addition to cost-intensive grid expansion, attractive operating approaches are those that specifically control the aforementioned generators / consumers in critical grid situations, such as violations of the voltage range or the triggering of fuses due to exceeding maximum power, in order to avoid overloads. However, these operating approaches require sufficiently accurate knowledge of the grid status of the power grid. Therefore, state estimation, i.e., an estimate of the status or grid status, is becoming increasingly relevant at the lower voltage levels mentioned. However, very few real-time measurements are typically available for medium-voltage and low-voltage grids. This fundamentally requires additional prior knowledge for conventional state estimators, which use this as input data.Prior knowledge can be determined from historical and / or predicted data. 202305748 2 However, the aforementioned input data exhibits uncertainties that can be accounted for using probabilistic state estimations. Using probabilistic state estimators, it is possible to consider the uncertainties of the input data and generate output data with a probabilistic statement (state estimation), i.e., a probability distribution. The disadvantage of known state estimation methods is that they require a known grid topology. For medium-voltage and low-voltage grids, their topology is typically not known with sufficient accuracy, or in the worst case, such topology data is not available. This is the case because distribution grids are typically designed and expanded over decades.While individual assets are at least partially recorded in geoinformation systems, complete network models are rarely maintained. Furthermore, the switching states that determine the topology, which can be used to accurately calculate the network states, are not always updated. Even if information about a network topology is available, the topology data is typically not up-to-date due to the numerous changes to the distribution network that have been implemented over decades. In order for a network operator with uncertain or little knowledge of the network topology to be able to estimate the network state for the operation of the power grid, a state estimation is required that takes the uncertainties regarding the network topology into account. The present invention is based on the object of enabling a network state estimation when information about the topology of the power grid is unknown or incomplete.202305748 3 The object is achieved by a method having the features of independent patent claim 1, by a method having the features of independent patent claim 12, by a control unit having the features of independent patent claim 14, and by a computer program product having the features of independent patent claim 15. Advantageous embodiments and developments of the invention are specified in the dependent patent claims.The inventive method for network state estimation of a power grid with multiple network nodes and lines is characterized by the following steps: - determining an a priori distribution ^^^ ^^^ for state variables ^^ of the power grid, wherein the a priori distribution ^^^ ^^^ is determined by means of a mixed distribution with respect to multiple (possible) network topologies ^^ ൌ 1, … , ^^ of the power grid; - providing a measurement distribution ^^^ ^^| ^^^ of measurement variables ^^ for a given network state ^^ of the power grid; - forming an a posteriori distribution ^^^ ^^| ^^^ for the state variables ^^ by means of the a priori distribution ^^^ ^^^ and the measurement distribution ^^^ ^^| ^^^; and - carrying out the network state estimation based on the a posteriori distribution ^^^ ^^| ^^^ for one or more network nodes and / or lines of the power grid. The order of the steps of the procedure does not imply a chronological order of the steps.In particular, these can – as far as possible – be carried out in parallel. In other words, one or more steps of the method are preferably carried out in parallel. The method according to the invention and / or one or more functions, features and / or steps of the method according to the invention and / or one of its embodiments can be computer-aided. In particular, a control unit provided for controlling or regulating the power grid comprises one or more computing units which are designed and configured, for example by means of commands, to carry out the method and to determine the distributions. The power grid is an electrical distribution network, in particular a low-voltage network and / or a medium-voltage network. The power grid has a plurality of network nodes. Furthermore, the power grid typically has a plurality of lines which extend from one of the network nodes to another of the network nodes.The topology of the power grid can comprise strands and / or rings. The power grid also has one or more state variables, with one or more state variables typically being assigned to each network node and / or each branch (line). In particular, each network node has one or more complex-valued voltages, i.e., voltage magnitudes and voltage angles (angles), as state variables. The power grid can be designed as multi-phase. State variables of the power grid can be complex-valued voltages, complex-valued currents, phase asymmetries, higher harmonics, for example, by modeling the systems / devices connected to the grid, and / or transformer rated powers. The state variables are particularly preferably complex-valued voltages. In particular, the complex-valued voltages are described by magnitude and angle or by real and imaginary parts.The distributions or probability distributions can be provided discretely and / or as a probability density. In principle, the distributions can be integrated over their associated variables. In the discrete case, integration is understood to mean a corresponding summation. The distributions are typically multidimensional due to the number of network nodes and / or lines. In particular, they are designed as multidimensional normal distributions or Gaussian distributions. 202305748 5 In a first step of the method, an a priori distribution ^^^ ^^^ for state variables ^^ of the power grid is determined using a mixed distribution of several possible network topologies ^^ ൌ1, … , ^^ of the power grid. In other words, several possible network topologies of the power grid are provided (ensemble of network topologies), with a respective a priori distribution being provided for each network topology.The a priori distribution ^^^ ^^^ is then formed by the mixed distributions of the provided a priori distributions of the grid topologies. Thus, an associated a priori distribution is provided for each grid topology. In this case, a grid topology can be possible if it appears to be fundamentally suitable, i.e. plausible, from a technical and / or physical perspective and / or taking known topology data into account for the power grid. Providing an a priori distribution for each of the considered grid topologies is advantageous because, typically, in low-voltage or medium-voltage grids, complete data on the actual grid topology is not available. Thus, according to the first step of the method, several possible grid topologies are considered via their mixed distribution.A selection of possible or considered network topologies can be made, for example, based on typical design criteria and / or operating criteria of the power grids. Thus, only network topologies that are technically sensible or feasible are preferably considered. In other words, technically realistic network topologies are advantageously used. For example, topologies that are compatible with existing measured values ​​and / or topologies that take into account known network information, such as the location of distribution boxes, transformers and / or local network stations. 202305748 6 Furthermore, geodata, for example from a GIS system of distribution network operators, street layouts, and / or information about end users, can be used to determine the network topologies used. Publicly accessible sources, such as OpenStreetMap, can be used for this purpose.Furthermore, known impedance per unit lengths of lines and / or transformers can be taken into account by the topologies used, i.e., topologies consistent with the aforementioned information are used for the mixed distributions. Furthermore, line measurements can be used to reduce the number of possible topologies. The assumption is made that, despite an uncertain topology, a line is highly likely to be present wherever a line measurement is installed. According to a second step of the invention, a measurement distribution ^^^ ^^| ^^^ (English: likelihood) of measured variables ^^ for a given state ^^ of the power grid is provided. In other words, the measurement distribution is given by ^^^ ^^| ^^^, i.e., by the probability distribution of the measurements ^^ for a given state ^^ of the power grid.In a third step of the method according to the invention, a posterior distribution ^^^ ^^| ^^^ is formed for the state variables ^^ for given measurements ^^ using the prior distribution ^^^ ^^^ and the measurement distribution ^^^ ^^| ^^^. For this purpose, the Bayesian approach (Bayes' theorem) is particularly preferably used, according to which ^^^ ^^| ^^^ ∝ ^^^ ^^| ^^^ ∙ ^^^ ^^^. Thus, after the third step, the statistical distribution of the state variables for given measurements or measured values ​​is determined. The distribution ^^^ ^^| ^^^ is advantageous because it contains the information about the probability that a network state exists for given measurements. Typically, this posterior distribution, i.e. after knowledge of the measured values, is not readily known.However, according to the invention it can be determined from the distribution 202305748 7 of the state variables and the measurement distribution, which can be determined a priori, by using Bayes' theorem. According to a fourth step of the method according to the invention, the network state is estimated based on the a posteriori distribution ^^^ ^^| ^^^ for one or more network nodes and / or lines of the power grid. In other words, the a posteriori distribution ^^^ ^^| ^^^ designed according to the invention is used for state estimation. Here, the term state estimation comprises at least determining expected values ​​and / or variances and / or determining marginal distributions for one or more network nodes by marginalizing the a posteriori distribution ^^^ ^^| ^^^.In particular, as a network state estimate for one or more network nodes, their respective expected values ​​as an estimated state and / or their respective variances (measure of uncertainty) can be determined from the posterior distribution ^^^ ^^| ^^^. Furthermore, as a network state estimate for one or more network nodes, the most probable network state ^^^௭ ൌarg max௫ ^^^ ^^| ^^^ can be determined. It is crucial that the network state estimate is based on the posterior distribution ^^^ ^^| ^^^, which according to the invention takes several possible network topologies into account. Furthermore, a probability for a critical state (critical probability) for one or more of the network nodes could be determined using the respective marginal distributions determined from the posterior distribution for the network nodes.Advantageously, in contrast to known methods which, for example, only use expected values, the entire distribution of the states is used to determine the probability 202305748 8 for a critical state of the power grid or the network node. In order to obtain a distribution for each network node, the a posterior distribution is marginalized in each case, i.e. the other network nodes are integrated or the results are summed over the other network nodes. This allows the marginal distribution or marginal distribution to be determined for each network node. The probability of a critical state of the network node is then determined from the determined marginal distribution for at least one of the network nodes. The determination is based on the entire distribution. For example, the probability is determined using an integral over a sub-range of the marginal distribution.The entire distribution is advantageously included here. Furthermore, a probabilistic prediction of the presence of a critical grid state can be determined. The method according to the invention thus provides a grid state estimator (state estimator) that takes into account several possible grid topologies of the power grid via the a posteriori distribution generated according to the invention. Thus, according to the invention, a topology estimation and a probabilistic state estimation are synergistically combined.The present invention has at least one or more of the following advantages: - Determination, use and / or provision of topology information and states of a distribution network by means of existing system measurements and / or known data, for example open source data; - Advantageous use of historical data for state estimation and consideration of their uncertainty; - Modular structure of the method, comprising two estimators, which could also be executed separately if the appropriate information is available; 202305748 9 - Coherent approach that integrates heterogeneous data sources with open source data; - Integration of existing, real information for topology estimation and state estimation.The more real information about the actual grid topology is provided, the more reliable the state estimation becomes; - state estimation even with incomplete information about the grid topology; and - implementation of operating paragraphs for the targeted control / regulation of producers / consumers and the avoidance of overloads. The inventive method for controlling a power grid with multiple grid nodes and lines by means of a control unit is characterized by the following steps: - grid state estimation using a method for grid state estimation according to the present invention and / or one of its embodiments; and - implementation of grid-friendly and / or system-friendly control measures by the control unit depending on the determined grid state. The grid state can in particular be the expected value of the voltage magnitude of the respective grid node.System-beneficial measures include, in particular, control interventions or adjustments relating to frequency maintenance, voltage maintenance, safe operation, and / or supply restoration of the power grid. These are typically carried out by a grid operator of the power grid, so that the control unit can be included in a grid control device of the grid operator. Grid-beneficial measures can include the control of individual or multiple electrical systems, in particular generators, consumers, and / or storage systems, which, through their controlled operation, contribute to reducing grid bottlenecks, the need for grid expansion, and / or optimized grid management. In this case, the control unit typically exercises control indirectly via local control units of the systems.The control unit according to the invention is thus designed and / or configured to carry out system-supporting and / or grid-supporting measures. This can occur directly or indirectly. For example, the control unit determines control signals based on the determined probability, which it transmits to system-supporting systems, for example transformers, and / or grid-supporting systems, for example within energy systems. The systems are then controlled according to the transmitted control signals. This results in indirect control of the power grid by the control unit. According to the present invention, probabilistic approaches, in particular Bayesian methods, are used. This makes it possible to transfer stochastic input variables (values ​​subject to uncertainty) as well as multiple grid topologies to a state estimator.The output variable of the present invention is also a stochastic distribution (a posteriori distribution), which is evaluated accordingly. This informs the grid operator which outgoing feeders and / or grid nodes are likely to be affected by a critical condition. The control unit then reacts accordingly with control and / or regulation interventions. Similar, equivalent, and equally effective advantages and / or embodiments of the inventive method for controlling a power grid result from the inventive method for grid state estimation. The inventive control unit for controlling a power grid with multiple network nodes and lines comprises a computing unit and is characterized in that the computing unit is configured to carry out a method according to the present invention and / or one of its embodiments.In particular, a network control device of a network operator of the power grid comprises the control unit according to the invention. Similar, equivalent and equivalently effective advantages and / or embodiments of the control unit according to the invention result from the method for state estimation according to the invention. The computer program product according to the invention is characterized in that it comprises instructions which, when the program is executed by a computing unit, in particular a computer, cause the latter to carry out a method for state estimation and / or steps of the method according to the present invention and / or one of its embodiments. According to an advantageous embodiment of the invention, the a priori distribution ^^^ ^^^ is replaced by the mixed distribution ^^^ ^^^ ൌ. ∙ ^^ ^ ^ ^^^ determined, where ^^ ^ ^ ^^^ the a priori distribution associated with one of the network topologies ^^ and ^^ ^normalized weights of the respective network topology ^^ ^ In other words, for each possible network topology ^^ an a priori distribution ^^ ^ ^ ^^^ provided. This can be done, for example, using a topology estimator that generates and provides consistent network topologies using existing data / information about the actual network topology. For each of these consistent network topologies, an a priori distribution can then be determined, for example, using the admittances associated with the network topology. The admittances can be determined from historical and / or predicted data, for example, regarding load profiles. 202305748 12 Furthermore, the network topologies are weighted differently. Here, ൌ 1 and 0 ^ ^^ ^^ 1, so that the weights can be interpreted as probabilities for the respective network topology. In an advantageous development of the invention, the weights ^^ ^ depending on the aggregated line length of the respective network topologies ^^, depending on design and / or operational criteria, and / or through an analysis and evaluation of measured data relating to the network topology ^^. This is advantageous because networks are typically built with the shortest possible line length. This is the case because it can reduce effort and costs. In this sense, a topology is all the more likely the shorter its aggregated line length. For example, an ensemble of network topologies with ^^ ^ generated, where ^^ is the dependence of the probability on the aggregate line length ^^ ^modeled. For the state estimation according to the invention, the possible topologies are sampled according to the aforementioned probability distribution for the weights. According to an advantageous embodiment of the invention, each of the a priori distributions of the network topologies ^^ ^ ^ ^^^ from an empirical load distribution of the power grid and an admittance corresponding to the respective grid topology ^^ ^^ ^In other words, the a priori distributions of the respective grid topologies are determined from a background distribution, which was determined from historical load data, for example from smart meters (load distribution), using the admittances associated with the respective topology. The load distribution forms a distribution of active power and reactive power at one or more grid nodes of the power grid. Using an affine linear transformation, which is essentially determined by the admittances ^^ ^is determined, the a priori distributions of the state variables for each of the network nodes under consideration can be determined from the load distribution. Due to the different network configurations, the admittances are different for each of the topologies. In other words, the associated admittance is essentially determined by the topology. In an advantageous development of the invention, the a priori distributions of the network topologies are determined ^^ ^ ^ ^^^ from the empirical load distribution and the respective admittance ^^ ^ by means of a load flow calculation. In other words, the linear affine transformation advantageously forms a load flow calculation. This way, the a priori distributions ^^ ^^ ^^^ determined from the distributions of active power and / or reactive power using load flow calculation. According to an advantageous embodiment of the invention, the empirical load distribution is approximated as a multidimensional normal distribution (Gaussian distribution). This advantageously achieves sufficient accuracy. Furthermore, the a priori distributions of the grid topologies ^^ ^ ^ ^^^ advantageously also designed as a multidimensional normal distribution. This is the case because the a priori distributions of the network topology gien ^^^ ^ ^^ ^ are each determined from the load distribution by a linear affine transformation. In other words, the a priori distributions ^^ ୮୰୧୭୰୧,^ ≡ ^^ ^ ^ ^^^ each by a multidimensional normal distribution ^^^ ^^ ^ , Σ ^ ^ approximated, that is, it is valid ^^ ^ ^ ^^^ ≡ ^^ ୮୰୧୭୰୧,^ ~ ^^^ ^^ ୮୰୧୭୰୧,^ , Σ୮୰୧୭୰୧,^ ^. Here ^^ denotes ୮୰୧୭୰୧,^ the expected value vector (vector of expected values) and Σ ୮୰୧୭୰୧,^ the covariance matrix of the measured values. For example, 202305748 is 14 where ^^ denotes the vector of state variables. For example, ^^ ൌ ^Re ^ ^^ ^^ , Im^ ^^ ^ ^^ ^, where ^^ denotes the vector of complex-valued voltages. The a priori distribution of the complex-valued voltage is thus determined from the background distribution of the complex-valued powers (active power and reactive power), i.e., from the load distribution, via the linear affine transformation, which includes the result of a linear load flow calculation. This transformation is typically implemented in the form of matrices. In this case, the measurement distribution is particularly preferably also implemented as a multidimensional normal distribution. As a result, the a posteriori distribution is advantageously also a multidimensional normal distribution. In an advantageous development of the invention, the grid topologies ^^ are determined using a random growth algorithm, taking into account known topology data of the power grid.Particularly preferably, a random growth method (growth algorithm) in combination with a method for deriving a radial topology is used to determine the topologies. The method can be structured as follows: 1) For example, the geographical information regarding the network components, for example about local network stations, end users and road routes, known lines, for example lines with measurements, and the line parameters, for example admittances, are provided. Based on the data provided, an ensemble of network topologies that are as realistic as possible is created. 202305748 15 In principle, two different network topologies are sufficient for the method according to the invention. A network topology typically defines the radial connectivity.This is particularly advantageous for low-voltage or medium-voltage grids, as these are essentially operated radially. Ring circuits, especially in medium-voltage grids, are typically only activated in the event of a fault. Thus, the power grid between end users and distribution substations can be mathematically described as an acyclic graph. ୰ୟ^୧ୟ୪ ൌ ^ ^^, ^^^ are modeled, where ^^ denotes the set of network nodes, for example, local network stations, end users, and intermediate nodes connecting the end users to the local network stations, and ^^ denotes the set of edges, for example, electrical lines and / or connections to the end users. The graph ^^ ୰ୟ^୧ୟ୪ is typically a collection of ^^ disjoint trees ( ^^ corresponds to the number of available local network stations) and each tree ^^ ^ includes one of the local network stations ^^ as a so-called root node, a subset of the nodes ^^^^ೖ ⊂ ^^ connected to a subset of the edges ^^ ^^ೖ ⊂ ^^. The procedure for determining ^^ ୰ୟ^୧ୟ୪ can now be constructed as follows: - Starting from a basic graph ^^ ୠୟ^^ , which describes the network region, a random growth model generates a random, yet technically realistic, and particularly coherent, allocation between available local network stations and end users. - According to the allocation, ^^ ୠୟ^^ then segmented into ^^ subgraphs. Finally, each subgraph becomes a radial topology ^^ ^derived, for example, using a Steiner tree problem formulation. - The growth model together with the derivation of a radial network topology is iterated to generate an ensemble of ^^ radial 202305748 16 network topologies and make them available for network state estimation. 2) The network topologies are weighted in the next step. The weighting is based on an estimate of how likely one of the generated network topologies corresponds to the real network topology. This can be achieved, for example, by evaluating how well a generated network topology fulfills common design and / or operational criteria, such as costs of the respective topology, and / or by analyzing and evaluating measurement data in the context of the generated topology and / or its aggregated line length.In summary, after the above steps, an ensemble of ^^ radial network topologies is available that meet common design and / or operational criteria and with probability weights ^^. ^are weighted. The topologies generated and provided in this way can be used for state estimation according to the present invention. According to an advantageous embodiment of the invention, the measurement distribution ^^^ ^^| ^^^ is determined and provided by measured values ​​of the state variables ^^, by measured values ​​of electrical power, in particular active power and reactive power, and / or by measured values ​​of electrical currents and the respective associated measurement deviations. In this case, it is again particularly advantageous if the measurement distribution is determined approximately by using a multidimensional normal distribution, wherein the associated expected values ​​and the variances are determined from the measured values ​​and the associated measurement deviations. In other words, the measurement distribution can be approximately durch ^^^ ^^^ ^ where ^^ denotes a 202305748 17 measurement function that maps the expected values ​​to the measured values. Furthermore, ^^ is the Jacobian matrix of the measurement function (English: mapping matrix). This linearizes the measurement function around the expected value. ൌ be used, whereby underlined quantities indicate complex quantities. Furthermore, the apparent power ^^ୠ^^ ൌdiag൫ ^^൯ ^^∗ ∗ ୠ^^ ^^ , ^^^ ൌ ^^^ ^^ for ^^ ^ 1 network nodes and^^ lines, that is ^^ ∈ ^ 0 … ^^ ^, ^^ ^^ ∈ ^0 … ^^^ and ^^ ^^ ∈ ^0 … ^^^.In an advantageous development of the invention, the posterior distribution ^^^ ^^| ^^^ is determined by a product of the prior distribution ^^^ ^^^ and the measurement distribution ^^^ ^^| ^^^. Advantageously, a Bayesian approach is thereby used to determine the posterior distribution of the state variables. If the prior distribution and the measurement distribution are designed as a multidimensional Gaussian distribution, then the posterior distribution advantageously also forms a multidimensional Gaussian distribution, i.e. ist ^^൫ ^^୮୰୧୭୰୧, Σ୮୰୧୭୰୧൯ ൌ The expected value vector^^୮୭^^^୰୧୭୰୧and the covariance matrix Σ ୮୭^^^୰୧୭୰୧ are clearly identified by ^^୫^ୟ^^୰^|^୰^^, ^^ ୮୰୧୭୰୧ and Σ ୫^ୟ^^୰^|^୰^^ and Σ ୮୰୧୭୰୧determinable and determined. In other words, the product of two Gaussian distributions again results in a Gaussian distribution. In particular, the posterior distribution is again a mixture of the posterior distributions associated with the topologies. In other words, in this case, ^^୮୭^^^୰୧୭୰୧ൌ ∑ ^ୀ^ ^^ ^ ⋅ ^^୮୭^^^୰୧୭୰୧,^. It is crucial that the a prior distributions are developed, i.e., linearized, around each expected value of the ^^: 202305748 18 Definition ^^ ^ ൌ According to an advantageous embodiment of the invention, the expected value and / or the variance of the network state of a network node is / are determined by the marginal distribution of the a posterior distribution ^^^ ^^| ^^^ associated with the respective network node. This advantageously allows a critical state of one or more network nodes to be detected. The marginal distribution (edge ​​distribution) of a network node is determined by forming a trace (integration or sum) over the other network nodes. The marginal distribution is thus a one-dimensional distribution. If the a posterior distribution is a multidimensional normal distribution, then the marginal distribution forms a one-dimensional normal distribution. The probability of a critical state can now be determined via the expected value and / or the variance and / or advantageously according to d ^^ can be determined if a lower threshold ^^୪୭^^୰ ୪୧୫୧^(limit value) is specified for the state variable ^^ of the network node, or ∞ according to ^^ ୡ୰୧^୧ୡୟ୪ ൌ^ ^౫౦౦^౨ ^^^^౪^^୮୭^^^୰୧୭୰୧d ^^, if an upper threshold ^^^୮୮^୰ ୪୧୫୧^(limit value) is specified for the state variable ^^ of the network node. The probabilities can be specified as a percentage, whereby the mentioned integrals include a factor of 100%. For several network nodes, the probabilities for a critical state can be combined into a vector ^^ ୡ୰୧^୧ୡୟ୪be summarized. In this case, the lower limit value ^^୪୭^^୰ ୪୧୫୧^or upper limit value ^^^୮୮^୰ ୪୧୫୧^of a permissible value range for the state variable is preferably used as the threshold value. 202305748 19 The state variable is particularly preferably the magnitude of the voltage, i.e. ^^ ൌ | ^^|. The permissible value range for the voltage magnitude or the voltage extends, for example, in Germany from 207 volts (lower limit value) to 253 volts (upper limit value). Thus, the permissible range is characterized by േ10 percent of the nominal value of 230 volts. Other countries, for example the USA, also have a symmetrical percentage band around their respective nominal value as the permissible range. Preferably, the permissible value range is defined as ±X percent of a nominal value of the state variable, where X has a value between 0 and 10, or, if not specified as a percentage, between 0 and 0.1.This advantageously creates a symmetrical permissible percentage band for the state variable. In particular, according to an advantageous embodiment of the invention, the permissible value range is formed by ±10 percent, ±6 percent, ±5 percent, or ±4 percent of a nominal value of the state variable. In particular, different grid operators can have different permissible value ranges. Typically, grid operators in Germany use the values ​​±10 percent, ±6 percent, or ±4 percent, so that the limit value used to determine the critical probability is advantageously matched to the permissible value ranges used. In an advantageous development of the invention, complex-valued voltages, in particular their magnitude and angle, are used as state variables ^^. This advantageously uses the state variables preferred for electrical grids.In this case, the power grid can be multi-phase, i.e., each phase of each network node has a voltage magnitude and an angle. The angles of the multiple phases can be dependent on one another. According to an advantageous embodiment of the invention, the power grid is designed as a medium-voltage grid or a low-voltage grid. This is advantageous because, in particular, no or incomplete information is available about the actual network topology of medium-voltage and low-voltage grids. The present invention solves this technical problem by taking several possible network topologies into account in the probabilistic state estimation. Further advantages, features, and details of the invention emerge from the exemplary embodiments described below and from the drawings.The figure shows a schematic flow chart of a method for state estimation according to one embodiment of the present invention. Similar, equivalent, or equivalently acting elements can be provided with the same reference symbols in the figure. The figure shows a flow chart of a method for state estimation for a power grid, wherein the power grid has several network nodes and lines. In particular, complex-valued voltages, for example by means of their magnitude and angle, are used below as state variables ^^. The start of the method is marked with the reference symbol S. The end of the method is marked with the reference symbol E.In a first step S1, an a priori distribution ^^^ ^^^ for state variables ^^ of the power grid is determined, wherein the a priori distribution ^^^ ^^^ is determined using a mixed distribution with respect to several possible network topologies ^^ ൌ 1, ... , ^^ of the power grid. For this purpose, the first step S1 according to the present embodiment comprises three sub-steps S1a, S1b, S1c. First, a so-called background distribution ^^. ୗ(load distribution) of the apparent power or the complex-valued voltages is provided (sub-step S1a). The background distribution can be determined from historical data 11 (historical data batches), for example, using power / energy consumption measurement data. In sub-step S1b, a linear affine transformation (affine linear power flow transformation) is provided or performed. For each provided grid topology, the corresponding admittance ^^ ୠ^^,^ by the linear affine transformation (load flow calculation) from the background distribution one of the a priori distributions of the network topologies ^^ ^^ ^^^ determined. The determination and / or provision of the admittances is designated by reference numeral 22. These are calculated or determined for each of the network topologies in a step 21 (English: Make bus admittance matrix for ^^). In sub-step S1c, a respective a priori distribution ^^ is thus determined for each provided network topology ^^ ^ ^ ^^^ is determined from the background distribution. This is symbolized by the loop ^^ ൌ ^^ ^ 1, which is executed until for each of the generated and provided network topologies ^^ ൌ 1, … , ^^ an a priori distribution ^^ ^ ^ ^^^ was generated. In the first step S1, the several a priori distributions ^^ ^ ^ ^^^ the mixed distribution is formed, which forms the a priori distribution ^^^ ^^^ of the state variables. This is advantageous because the actual network topology is typically unknown. In other words, 202305748 22 ∙ ^^^ ^ ^^^, where ^^ ^ ^ ^^^ the a priori distribution associated with one of the network topologies ^^ and ^^ ^ normalized weights of the respective network topology ^^ ^The network topologies can be determined using a growth method. The determination of the ensemble of network topologies is designated by reference numeral 34. Probabilistic growth algorithms and / or MST methods can be used for this purpose (see reference numeral 33). The aforementioned methods for determining the possible network topologies can take into account, as input data 31, data on installed measuring devices 51 (placement data and / or type data), branch impedances 41, as well as the locations of distribution network transformers and / or street data and / or development data (summarized by reference numeral 32) when generating the most realistic topologies possible. After the topologies have been generated, the weights for the respective topology are determined. This is designated by reference numeral 35. For example, a topology has a higher weighting if it has a shorter aggregate line length.The provision of the determined weights for forming the a priori distribution is identified by the reference numeral 36. In a second step S2 of the method, a measurement distribution ^^^ ^^| ^^^ (English: Measurement Distribution) is generated and / or provided. The measurement distribution can be determined using placement data and / or type data 51 of measuring devices installed for the power grid. As an approximation, the measurement distribution is described by a normal distribution which has an expected value (vector) and a variance matrix 53. The variance matrix 53 can be determined from the known measurement accuracies 51 of the placed measuring devices using placement data and / or type data of the respective measuring device. The generation of the so-called variance matrix 202305748 23. is marked with the reference symbol 52. The impedances 41 are provided for determining the expected value, whereby these are provided for calculating a measurement function ^^^ ^^^ and its associated Jacobian matrix ^^. This is marked with the reference symbol 42 (English: Build Measurement Function & Jacobian Matrix). The provision of the measurement function and its Jacobian matrix ^^ is marked with the reference symbol 43. According to a third S3, by means of Bayes' theorem, a posterior distribution ^^^ ^^| ^^^ is determined from the measurement distribution ^^^ ^^| ^^^ and the multiple prior distributions ^^^ ^^^ by means of ^^^ ^^| ^^^ ൌ ^^^ ^^| ^^^ ^^^ ^^^ / ^^^ ^^^. Thus, ^^^ ^^| ^^^ ∝ ^^^ ^^| ^^^ ^^^ ^^^, that is, the posterior distribution ^^^ ^^| ^^^ is equal to the product of the measurement distribution and the posterior distribution, up to a constant factor.Thus, the posterior distribution is again a mixture of the individual posterior distributions of the network topologies, i.e. ^^^ ^^| ^^^ ∝. mit ^^^ ^ ^^ | ^^ ^∝ ^^^ ^^| ^^^ ^^^^ ^^^.Here, real-time data (real-time measurements) 54 can be taken into account when determining the posterior distribution ^^^ ^^| ^^^. In particular, the posterior distribution ^^^ ^^| ^^^ is updated by new measurements or new measurement data for each time step in which the method is carried out. In a fourth step S4, the posterior distribution ^^^ ^^| ^^^ is marginalized. In this case, a linear approximation using a Taylor expansion can be provided for the magnitude and angle of the voltages. In a sub-step S4a of the fourth step S4, the distribution of the network states for each network node is thus available (Estimated system state distribution for ^^ ୫ୟ^ and ^^ ୟ୬^at all buses). 202305748 24 The method according to the present embodiment can thus be summarized in simplified form as follows: To determine the distribution of the estimated state (posterior distribution), a Bayesian approach is used, which is structured as follows: 1) Bayes' theorem ^^^ ^^| ^^^ ൌ ^^^ ^^| ^^^ ^^^ ^^^ / ^^^ ^^^ is used to determine the posterior distribution ^^^ ^^| ^^^, where ^^^ ^^| ^^^ denotes the posterior distribution for the state variable ^^ given measurements ^^, ^^^ ^^^ the prior distribution, and ^^^ ^^| ^^^ the measurement distribution (likelihood) ^^ given ^^. The prior distribution ^^^ ^^^ is determined by a mixture distribution over the prior distribution of the network topologies ^^ ^^ ^^^ determined. 2) Linear Bayesian state estimator: a) The determination of the a priori distribution of complex voltages can be carried out as follows: i) From the background distribution (distribution for active and reactive power at each node in the network) by means of an affine transformation of a linear load flow, which has the bus admittance matrix ^^ as input. ^ a topology. ii) This step is performed for each of the topologies from the ensemble to create ^^ prior distributions. iii) Using the weights ^^ ^ For the probabilistic topology estimation, a mixture distribution (Gaussian Mixture Prior Distribution) is generated from the individual prior distributions of the network topologies. b) Distribution for real-time measurements (measured value and uncertainty): i) Possible measurements: ^^, ^^, ^^ ୫ୟ^ , ^^ ୟ୬^ , ^^ ୫ୟ^ , ^^ ୟ୬^with any number and placement of measurements; 202305748 25 ii) With linearized measurement function ^^^ ^^^, the expected value for likelihood measurement distribution is given by ∙ ൫ ^^ െ where ^^ is the Jacobian matrix of the measurement function. c) Formation of the posterior distribution: Using Bayes' theorem, the posterior distribution results from the product of the prior distribution of the complex voltages and the likelihood measurement distribution. Since the prior distribution is a Gaussian mixture distribution with respect to the network topologies, the posterior distribution is also a Gaussian mixture distribution. It is crucial that the prior distributions are expanded, i.e., linearized, around each expected value of the ^^: ^^^ ^^ ^^୮୰୧୭୰୧,^ with the appropriate definition ^^^ ൌ^^ ୰୧,^ ^^ ் ൫ ^^ ୮୰୧୭୰୧,^ ் ି^ ୮ ୰୧୭ ^^ ^^ ^ ^^ ୫^ୟ^|^୰^^d) The posterior distribution can then be marginalized, and the variance determined using a linear approximation. The result is the marginalized distribution of the state variables in polar coordinates (magnitude and angle). 3) The described method is particularly advantageous for North American medium-voltage grids, which are often asymmetrically constructed. In this case, the method can be extended to determine possible phase assignments. These phase assignments are then used in the Bayesian estimator analogously to the topology information. This makes it possible to estimate grid states despite unknown phase assignments of consumers. The method thus provides a grid state estimation or state estimator that takes several possible grid topologies into account using the posterior distribution generated according to the invention.Thus, according to the invention, a topology estimation and a state estimation are synergistically combined. The method thus makes it possible to provide an advantageous state estimator with improved accuracy in a medium-voltage ring with local network stations and low-voltage networks for which no topology information is available and very few real-time measurements are installed. Although the invention has been illustrated and described in detail by the preferred embodiments, the invention is not limited by the disclosed examples, and other variations may be derived therefrom by a person skilled in the art without departing from the scope of the invention.

[0002] 202305748 27 List of reference symbols S Start E End S1 First step (determining a priori distribution) S1a Sub-step (empirical load distribution) S1b Sub-step (load flow calculation) S1c Sub-step (a priori distribution of network topologies) S2 Second step (providing measurement distribution) S3 Third step (forming a posteriori distribution) S4 Fourth step (marginalization) S4a Sub-step (network state estimation) 11 Historical data 12 Empirical determination 21 Determining admittance 22 Admittance 31 Measurement data 32 Topology data 33 Growth algorithm 34 Ensemble of network topologies 35 Determining weights of network topologies 36 Weights of network topologies 41 Line impedances 42 Determining measurement function / Jacobi matrix measurement function 43 Measurement function / Jacobi matrix measurement function 51 Placement data and type data 52 Variance measurement distribution 53 Measurement accuracies 54 Real-time measurement data

Claims

202305748 28 patent claims 1. Computer-aided method for network state estimation of a power grid with several network nodes and lines, characterized by the following steps: - (S1) determining an a priori distribution ^^^ ^^^ for state variables ^^ of the power grid, wherein the a priori distribution ^^^ ^^^ is determined by means of a mixed distribution with respect to several network topologies ^^ ൌ 1, ... , ^^ of the power grid; - (S2) providing a measurement distribution ^^^ ^^| ^^^ of measurement variables ^^ for a given network state ^^ of the power grid; - (S3) forming an a posteriori distribution ^^^ ^^| ^^^ for the state variables ^^ by means of the a priori distribution ^^^ ^^^ and the measurement distribution ^^^ ^^| ^^^; and - (S4) performing the grid state estimation based on the posterior distribution ^^^ ^^| ^^^ for one or more grid nodes and / or lines of the power grid. 2.Method according to claim 1, characterized in that the a priori distribution ^^^ ^^^ is replaced by the mixed distribution ^^^ ^^^ ൌ ∙ ^^. ^ ^ ^^^ is determined, where ^^ ^ ^ ^^^ the a priori distribution associated with one of the network topologies ^^ and ^^ ^ normalized weights of the respective network topology ^^ ^ 3. Method according to claim 2, characterized in that the weights ^^ ^ depending on the aggregated line length of the respective network topologies ^^, depending on design and / or operating criteria, and / or through an analysis and evaluation of measurement data relating to the network topology ^^.

4. Method according to claim 2 or 3, characterized in that each of the a priori distributions of the network topologies ^^ ^ ^ ^^^ from an empirical load distribution of the power grid and an admittance corresponding to the respective grid topology ^^ ^^ ^ is determined. 202305748 29 5. Method according to claim 4, characterized in that the determination of the a priori distributions of the network topology ^^ ^ ^ ^^^ each from the empirical load distribution and the respective admittance ^^ ^by means of a load flow calculation.

6. Method according to claim 4 or 5, characterized in that the empirical load distribution is approximated as a multidimensional normal distribution.

7. Method according to one of the preceding claims, characterized in that the network topologies ^^ are determined using a random growth algorithm, wherein known topology data of the power grid are taken into account.

8. Method according to one of the preceding claims, characterized in that the measurement distribution ^^^ ^^| ^^^ is determined and provided by measured values ​​of the state variables ^^, by measured values ​​of electrical power and / or by measured values ​​of electrical currents and the respectively associated measurement deviations. 9.Method according to one of the preceding claims, characterized in that the a posteriori distribution ^^^ ^^| ^^^ is determined by a product of the a priori distribution ^^^ ^^^ and the measurement distribution ^^^ ^^| ^^^.

10. Method according to one of the preceding claims, characterized in that the expected value and / or the variance of the network state of a network node is / is determined by the marginal distribution of the a posteriori distribution ^^^ ^^| ^^^ associated with the respective network node.

11. Method according to one of the preceding claims, characterized in that complex-valued voltages, in particular their magnitude and angle, are used as state variables ^^. 202305748 30 12. A method for controlling a power grid with multiple network nodes and lines by means of a control unit, characterized by the following steps: - estimating the grid state using a method according to one of the preceding claims; and - implementing grid-friendly and / or system-friendly control measures by the control unit depending on the determined grid state.

13. The method according to claim 12, characterized in that the power grid is designed as a medium-voltage grid or a low-voltage grid.

14. A control unit for controlling a power grid with multiple network nodes and lines, comprising a computing unit, characterized in that the computing unit is designed and configured to implement a method according to one of the preceding claims. 15.Computer program product, comprising instructions which, when the program is executed by a computing unit, in particular a computer, cause the latter to carry out a method and / or steps of the method according to one of claims 1 to 13.

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