Determining the aging state of electrical operating means

Abstract

The invention relates to a method for determining the aging state (A, AHI) of a number of electrical operating means (4) in a power grid (1), the method having the following steps: a) carrying out a computer-aided calculation of a probabilistic distribution (p(x|z)) for at least one physical state variable (x) of the power grid (1) on the basis of a measurement distribution (p(z|x)) for at least one measurement variable (z) which correlates to the state variable (x), and b) carrying out a computer-aided modeling of the aging of the electrical operating means (4) during an operation of the power grid (1) using the probabilistic distribution (p(x|z)) for the state variable (x) as the basis for an input (IN) for an aging model (MOD), by means of which the aging state (A, AHI) of the respective operating means (4) is at least approximately determined. The invention further relates to a corresponding method for operating a power grid (1) and to a corresponding computer program product.

Description

[0001] Description

[0002] Determination of the aging state of electrical equipment

[0003] The present invention relates to a method for determining the aging state of at least one piece of electrical equipment in a power grid by means of computer-aided modeling. The invention further relates to a method for operating a power grid depending on the obtained result, as well as a corresponding computer program.

[0004] The operation of conventional power grids is becoming increasingly challenging due to the changes resulting from the energy transition. On the one hand, there is a rise in electrical consumers such as electrically powered heat pumps and electric vehicles. On the other hand, more and more decentralized power generators, such as photovoltaic and wind power plants, are being added. Unlike conventional power plants, these fluctuate more in their feed-in power and are more difficult to plan. Both of these effects lead to more difficult load flows to plan and control, particularly in medium- and low-voltage distribution networks, and result in an increase in critical operating conditions. Such critical operating conditions can be characterized, for example, by a violation of a permissible voltage band, the tripping of a fuse, or an exceedance of a maximum load in a section of the power grid.To limit such situations, in addition to complex and costly grid expansion, operational approaches are also planned that selectively control consumers in critical grid situations to prevent overloads within the power grid. Nevertheless, managing the risks of such critical grid conditions remains an increasing challenge in operating power grids. One of the undesirable consequences of such critical grid conditions is the overloading of the operating resources and the associated premature aging.

[0005] Determining or estimating the aging state of an asset in a power grid, depending on the grid conditions it experiences, is a crucial task in the operation of such grids. This is partly due to the fact that there is typically little measurement infrastructure in the vicinity of individual assets (e.g., at the connection points of individual transformers, lines, and switchgear). It is very rare to find a measuring device installed directly at the asset in question that would allow for local monitoring of the electrical load. Instead, usually only a few measuring devices are installed at higher-level grid nodes, meaning that the measurement results obtained only allow for imprecise conclusions about the load on individual assets.

[0006] In the operation of an electricity grid, a so-called "asset manager" is typically responsible for the upkeep and maintenance of the individual assets relevant to maintaining grid operation. The tasks of such an asset manager include assessing the aging condition of the assets as cost-effectively as possible, using as few measuring devices as possible, and then taking the necessary measures to ensure reliable operation. For planning such measures, such as the maintenance or replacement of assets affected by aging, state-of-the-art approaches like "risk-based maintenance," and in particular "reliability-centered maintenance," are used.Key aspects here are considering the potential hazards in the event of a fault occurring within the equipment under consideration and estimating the probability of such a fault occurring. To estimate the probability of a fault condition, it is typically necessary to determine or estimate the operational aging state of the equipment in question.

[0007] In a known method for estimating a network state, the weighted least squares method is applied to account for the influence of inaccuracies in the available measurements on the network state to be determined. This is achieved by assigning weights to a quadratic objective function to be minimized. This method yields a probable state vector, for example, with the expected values ​​of the individual relevant state variables. From a temporal sequence of such state vectors, an aging state can be estimated using a deterministic aging model adapted to the equipment. The aging model used depends, for example, on the design, materials, operating principle, and other properties of the equipment under consideration.The aging state determined with such a model is often represented in the form of a so-called aging indicator (AHI, short for "Asset Health Indicator" or "Asset Health Index"). However, the results obtained in this way are comparatively imprecise, mainly due to the usually small number of available measuring devices and the inaccuracy of the available measurement data, so that the network states experienced and thus the stresses occurring on the equipment are only inadequately estimated.

[0008] The object of the invention is therefore to provide a method for determining the aging state of equipment in a power grid that overcomes the aforementioned disadvantages. In particular, a method should be provided that enables a comparatively accurate estimation of the aging state even with imprecise measurement data and / or a small number of measurement data points. A further object is to provide a method for operating a power grid depending on the aging state thus determined. Furthermore, a corresponding computer program should be provided that enables such determination and operation.

[0009] These tasks are solved by the determination method described in claim 1, the operating method described in claim 12, and the computer program product described in claim 15.

[0010] The method according to the invention serves to determine the aging states of a number n of electrical equipment in a power grid, wherein the method comprises the following steps: a) computer-aided calculation of a probabilistic distribution for at least one physical state variable of the power grid, based on a measurement distribution for at least one measured variable which has a correlation with the state variable, b) computer-aided modeling of the aging of the electrical equipment during operation of the power grid using the probabilistic distribution for the state variable as the basis of an input for an aging model, by means of which an aging state of the respective equipment is determined at least approximately.

[0011] In other words, the method uses a computer-aided aging model to determine the aging state of at least one piece of equipment within the power grid, and especially for several such pieces of equipment. An "electrical piece of equipment" is generally defined as an electrical component relevant to the operation of the power grid, such as a transformer, a line, a switch, or a switchgear assembly. "Determining the aging state" here refers to calculating a quantity that is characteristic of the aging of the respective piece of equipment. This quantity can be, for example, a physical parameter that changes due to aging. It can also be a function of one or more such physical quantities, specifically a characteristic index or indicator.The characteristic parameter for aging can vary depending on the type of equipment, as different parameters change due to aging in a transformer than in an electrical conductor, for example. The aforementioned "determination" of the aging state can be carried out, in particular, by approximating a value. In other words, a parameter characteristic of aging is determined or estimated, at least approximately. Generally, nonlinear effects can be advantageously considered when determining the aging state, since in many cases the change in the parameters affected by aging follows the Arrhenius equation, resulting in a nonlinear dependence on time and / or temperature.

[0012] Within a power grid, there is typically a plurality m of electrical equipment. The inventive method determines the corresponding state of aging for a number n of this equipment. The number n can be 1 or greater than 1. In particular, the number n can be only a subset of the number m. Therefore, it is not necessary to apply the method to all existing equipment. Rather, it is sufficient to determine the state of aging for one of the existing equipment using the described method. When determining the state of aging for a plurality of equipment, this can generally be done simultaneously and / or sequentially.

[0013] The determination of the aging state is based on a probabilistic distribution for at least one state variable of the power grid. In particular, corresponding distributions for several such state variables can also be used for this determination. A "probabilistic distribution" is generally understood to be a probability distribution of the state variable under consideration. In principle, it can be represented either as a continuous or as a discretized distribution. This distribution is calculated based on a measurement distribution for at least one measured variable and, in particular, also based on multiple measurement distributions for multiple measured variables. Such a measurement distribution can be generated based on measured values ​​obtained by measuring devices available within the power grid.For example, a measurement distribution can be obtained from a single or multiple measured values, taking into account the associated measurement uncertainty. It is not necessary for the measuring instruments to be connected to the same network nodes as the equipment under consideration. Rather, the measuring instruments used in these measurements (or at least a subset thereof) can be located away from the network nodes of the modeled equipment, or they can be connected to network nodes different from those of the equipment.

[0014] It is essential that the measured quantity and the considered physical state variable exhibit a correlation. This allows information about the distribution of the considered state variable to be derived from the information contained in the measurement distribution. In other words, the information gained in this way can be used to "narrow down" the probabilistic distribution calculated in step a). Generally, the correlation used here can be caused by a physical relationship between the measured quantity and the considered state variable. In other words, the measured quantity and the state variable can be linked by a physical law. It is generally advantageous that the measured quantity and the considered physical state variable differ from each other. In particular, they can be fundamentally different physical quantities (e.g.,Active power and current) or a corresponding physical quantity (e.g., a current in each case) can be considered in different areas of the power grid (e.g., in different line sections). For example, the current in one line section can represent the measured quantity and the current in another line section the state variable under consideration, if the two current flows are related by a physical law and thus also correlate with each other within the framework of a statistical evaluation.

[0015] The aging model used in step b) can, for example, be a physical model that describes the essential aging mechanisms and thus the influence of aging on one or more key parameters of the equipment under consideration. Alternatively, it can be a data-driven model that predicts aging, for example, based on a dataset of empirical data. In particular, it can also be an artificial intelligence model, which, for example, is implemented in a neural network and has been trained on a dataset of such empirical data. Numerous approaches for predicting the aging of various pieces of equipment using a model are known in the prior art.Essential to the inventive method is that the input for the aging model is based on the probabilistic distribution for the state variable(s) under consideration obtained in step a). This can mean either that the probabilistic distribution is used directly as input, or that the input is generated from the probabilistic distribution in a further intermediate step. In both cases, it is essential that not only a mean or expected value of the state variable is used as input, but that (alternatively or additionally) information about the width of the distribution and / or about a boundary region of the distribution is used as input for the aging model.This leads to a significant improvement in the accuracy of modeling the aging of the relevant equipment, since critical operating conditions are relatively rare and thus usually found at the extremes of the distribution, yet are nevertheless responsible for a substantial portion of the aging processes. In other words, considering the probabilistic distribution of the state variable under consideration and / or a derived parameter characteristic of an extreme area of ​​the distribution leads to improved modeling of an aging-related condition. The resulting more precise determination of aging states can serve as a basis for improved operating procedures and, in particular, more resource-efficient maintenance management. Thus, a failure or fault probability for the relevant equipment can be derived from the approximately calculated aging state.Depending on this probability and, if applicable, taking into account the extent of damage in the event of such an occurrence, measures can be initiated to rectify and / or prevent such events. Overall, a more precise assessment of the effects of aging can reduce the frequency of faulty operating conditions and / or save resources that would otherwise be spent on rectifying or preventing errors that are not yet anticipated.

[0016] Accordingly, the operating method according to the invention serves to operate a power grid with a number m of electrical equipment. The operating method comprises the following steps: i) determining the aging state of a number n of the equipment according to the method according to one of the preceding claims, ii) operating the power grid, wherein at least one operating parameter is selected depending on the determined aging state.

[0017] In other words, the aging state of at least one of the existing operating resources is determined using the determination method according to the invention. The operation of the power grid depends on the result obtained. The operating parameter dependent on this result can, for example, be an operating parameter of the modeled operating resource, or it can be a higher-level operating parameter (for example, an operating parameter of a hierarchically superior operating resource) which has a particular influence on the operation of the operating resource under consideration.

[0018] The computer program product according to the invention comprises instructions, wherein, when the computer program product is executed on a computer, the instructions cause the computer to execute at least one of the methods according to the invention. This can, in principle, be the determination method and / or the operating method. The advantages of the operating method and the computer program product according to the invention are analogous to the advantages of the determination method according to the invention described above.

[0019] Advantageous embodiments and further developments of the invention will become apparent from the claims dependent on claims 1 and 12, as well as from the following description. The described embodiments of the determination method can also be implemented in the operating process or the computer program product, and vice versa.

[0020] According to a generally advantageous embodiment, the probabilistic distribution of at least one state variable can be time-dependent. In other words, a time-dependent profile can be calculated for this distribution in step a). Based on such a time-dependent profile, the aging state can also be calculated as a time-dependent function in step b). Such a time-dependent calculation is advantageous because the aging of a piece of equipment is generally influenced not only by an operating state at a discrete point in time, but by a temporal sequence of operating states. However, it is not necessary to calculate a time profile over the entire operating period of the equipment under consideration. While this can be useful in some cases, it is typically sufficient to calculate a time profile following a previous point in time.Such a reference point could, for example, be a point in time for which an experimental determination of the aging state (a so-called validation) has been carried out. For example, for a transformer, such validation could consist of an analysis of the transformer oil used and / or measuring an output current or other electrical parameter directly at the transformer. Such measurements could, for example, be carried out as part of maintenance of the equipment, which corresponds to an experimental determination of the aging state. In such a case, it is advantageous if the modeling according to the invention covers a period following this validation (e.g., in the form of a plurality of discrete journals).

[0021] To calculate a time-dependent probabilistic distribution, a separate probabilistic distribution can be calculated for multiple journals. Specifically, a probabilistic distribution can be calculated for each journal under consideration, based on a measurement distribution obtained for that journal. This calculation can be performed separately for each journal, independent of the result of the previous time step. Optionally, however, results for one or more previous journals can be taken into account when calculating the probabilistic distribution for the currently considered journal.

[0022] In general, the state variables considered in the procedure can include a current for at least one line section of the power grid and / or a voltage, voltage magnitude, and / or voltage angle for at least one network node of the power grid. Alternatively or additionally, a state variable under consideration can be one or more power flows in one or more sub-areas of the power grid. Advantageously, several such state variables can also be considered; that is, probabilistic distributions for several state variables can be calculated in step a) and used as a basis for the modeling in step b). The aforementioned variables have a significant influence on the aging of equipment during the operation of a power grid. In particular, distributions for the aforementioned physical quantities can be calculated for a plurality of line sections and / or network nodes.The aforementioned physical quantities can be calculated particularly advantageously for those line sections or network nodes that correspond to the positions of the equipment under consideration.

[0023] In general, the power grid can be a multi-phase system. The voltage for each phase can be specified as a complex-valued voltage. The state variable under consideration can also be given by the derived voltage magnitude and / or the voltage angle. Similarly, the current under consideration can be a complex-valued current.

[0024] Generally advantageously, the measurement distribution can be determined and provided based on one or more measured values ​​for active power, reactive power, voltage, and / or current within the power grid. For current and voltage, a magnitude and / or angle can be considered, as these quantities can be described as complex values ​​in an AC network. This can be done, in particular, taking into account any associated measurement error. The respective measured value can be provided, in particular, by a measuring device located in the vicinity of a selected network node or line section. The aforementioned quantities are typical measured values ​​available during the operation of a power grid through appropriate measuring devices, although usually only for a few selected network nodes or line sections.

[0025] The measurement distribution can advantageously be determined approximately by using a one- or multi-dimensional Gaussian distribution, whereby the corresponding expected values ​​and variances are determined from the available measured values ​​and the associated measurement errors. A measurement error is generally understood to be the deviation between the measured value and the actual value of the measured quantity due to the inaccuracy of the measurement. The determination of the measurement distribution can advantageously be carried out as described in European patent application EP 4312329 A1, i.e., using the measurement function described therein, which maps the expected values ​​to the measured values. In this way, the required measurement distribution can be approximately determined from the measured values ​​and the measurement function.

[0026] Generally, and regardless of the underlying measurement distribution method, at least one measured value can be provided by a so-called RTU (Remote Terminal Unit) and / or a so-called PMU (Phasor Measurement Unit). Multiple such measuring devices can also be used at various locations (network nodes and / or lines) within the power grid.

[0027] According to a particularly preferred embodiment, calculating the probabilistic distribution for the state variable can comprise the following steps: a1) providing an a priori distribution for the state variable, a2) providing the measurement distribution for the measured variable, a3) determining an a posteriori distribution for the state variable based on the a priori distribution and the measurement distribution.

[0028] In step a3), the determination of the a posterior distribution is carried out, in particular, by applying Bayes' theorem. According to Bayes' theorem, applied to a state variable x and a correlated measured variable z, the following relationship holds for the a posterior distribution p(x|z) of the state variable x, given a measured variable z, to the a priori distribution p(x) of the state variable x and the measured distribution p(z|x): p(z|x) p(x) p( |z) = p(z)

[0029] The measurement distribution p(z|x) is the probability distribution of the measured quantity z for the given state variable x. p(z) is the prior distribution of the measured quantity z. In general, p denotes the probability distribution of the quantity in parentheses. The line between two quantities describes a conditional probability, so that, for example, p(x|z) gives the probability of the event x, given that the event z has occurred. In contrast, a prior probability is an original probability for a quantity without considering such a condition. Due to the proportionality p(x|z) ∧ p(z|x) p(x), the posterior distribution p(x|z) of the state variable x can be determined based on the product of the measurement distribution p(z|x) and the prior distribution p(x) of the state variable x.The application of the Bayesian approach to determine the a posteriori distribution of such a state variable of an electrical network is described in detail in patent application EP 4312329A1. This patent application is therefore to be included in the disclosure of the present application.

[0030] If a time-dependent trend is determined for the probabilistic distribution of at least one state variable, then the described Bayesian approach can be applied separately for each journal under consideration, requiring a separate measurement distribution for each journal. If multiple state variables are used as the basis for aging modeling, the approach can again be applied separately for each state variable. Ideally, a plurality of measurements are then available from which the corresponding statistical information about several state variables can be derived.

[0031] According to an advantageous further development of this embodiment, the a priori distribution for the state variable x can be determined and provided based on measured values ​​for active power, reactive power, voltages, and / or currents in at least one power grid using load flow analysis. This can be done, in particular, taking into account the associated measurement uncertainties and / or their temporal variability (for example, within a year). In other words, an a priori distribution of the respective state variable x is determined for each network node or line section under consideration by means of measurements. In principle, the state variable x can be identical to the measured variable z on which the measurements are based. Typically, however, this is not the case. For example,From a measured distribution of active and reactive power, an a priori distribution for complex-valued voltages at specific, selected network nodes can be determined. The determination of the a priori distribution of the state variable(s), in particular the complex-valued voltages, from the available measurement data can advantageously be carried out using a load flow analysis. Information about the topology of the power grid can be used as input parameters for this analysis. In particular, it can be a linear load flow analysis, which may be implemented using an affine transformation.

[0032] The measurements used to determine the prior distribution can, in principle, be obtained from the same power grid (the one considered in the model) or from other, similar power grids. The essential requirement is that information about a typical origin probability of the respective quantity is obtained. Generally, the measurement can also be frequency-dependent, if necessary. This applies both to the measurement(s) for determining the prior distribution and to determining the measurement distribution.

[0033] According to an advantageous further development of this embodiment, the a priori distribution can also be determined approximately by using a one- or multi-dimensional Gaussian distribution, whereby the associated expected values ​​and variances are determined from the available measured values ​​and the associated measurement errors.

[0034] Alternatively, the prior distribution can be approximated by a so-called Gaussian mixture distribution, such that the prior distribution (in at least one of the dimensions under consideration) is composed of a sum of several Gaussian functions. For each of the Gaussian functions contained therein, three parameters are then determined that characterize its peak height, its peak position on the abscissa, and its width. The posterior distribution determined by the Bayesian approach then also results, in particular, as a Gaussian mixture distribution.

[0035] In general, however, the invention is not limited to approximating the a priori distributions as normal distributions or Gaussian mixture distributions. While the composition of the distributions from Gaussian functions generally allows for an analytical calculation of the a posteriori distribution, a numerical calculation can alternatively be used when employing differently composed distributions (e.g., when approximating with polynomials). For example, Monte Carlo sampling can be used in this context.

[0036] According to a first advantageous implementation variant for modeling aging, the aging model can be a deterministic model. In other words, it can be a model that generates one or more output variables not based on probability distributions, but rather based on one or more fixed input variables. In this case, the at least one input for the aging model is a fixed variable determined based on a probabilistic distribution. Thus, a characteristic value is selected based on a stochastic analysis, and a prediction for the aging state is then generated for this value in the subsequent model run.Such a fixed quantity derived from a distribution can, for example, be an expected value, median value and / or mean of the distribution, or a so-called maximum a posteriori estimate, which is given by the mode of an a posteriori distribution.

[0037] Generally, a fixed value derived from the distribution is particularly preferred for a boundary region of the distribution. This contrasts with the expected value, median, or mean of a distribution, which are characteristic of the middle region of the distribution and thus reflect the typical values ​​of the state variable under consideration. Here, the "boundary region" of the distribution is generally understood to be a region separated from the middle region of the distribution by a quantile of order 0.75 or higher. In other words, an event lies within such a boundary region of the distribution with a probability of at most 25%. The boundary region under consideration can, in particular, be one where the associated values ​​of the state variable under consideration can lead to a comparatively high risk for the aging of the asset in question. Such a boundary region is subsequently also referred to as the "risk region" of the distribution.This risk area can be particularly advantageous if it is separated from the center of the distribution by a quantile of at least 0.9 or even at least 0.95. Generally, such a risk area within the determined distribution is particularly relevant for deriving a forecast of the aging state of a piece of equipment. It should not be excluded that, in addition to a defined parameter for the risk area, a defined parameter for the middle range (e.g., an expected value, a mean, and / or a median) is also used as input for the deterministic aging model.

[0038] According to a generally advantageous further development of the first implementation variant, the defined input variable can be a characteristic value of the state variable, which is determined depending on a predefined risk level. Here, the "risk level" is understood as a predetermined threshold for a probability integrated over the distribution. This threshold corresponds to the order of a quantile in the distribution. Thus, the defined variable used in the modeling can, in particular, be the position of a quantile with a predefined order. This predefined order can, for example, lie in a range between 0.75 and 0.99, and especially preferably in a range between 0.9 and 0.99. For example, with an order of 0.97, the stress level that is undershot with a probability of 97% can be specified.Conversely, this stress level is exceeded with a probability of 3%, so the position of the associated stress value is characteristic of this 3% risk level. The risk level used can be individually defined by an asset manager for each asset under consideration. Preferably, such a definition takes into account the damage expected in the event of a failure of the respective asset. In other words, the quantile order considered allows for a differentiation between more and less critical assets as early as the input stage into the aging model (consideration of criticality).

[0039] According to a second advantageous implementation variant for modeling aging, the aging model can be a probabilistic model. In particular, the probabilistic distribution of the at least one state variable calculated in step a) is then used as input for the aging model. This variant is particularly preferred because considering the entire distribution of the respective state variable leads to a particularly accurate prediction of the aging effects. However, this modeling is more resource-intensive compared to the first implementation variant. Such a stochastic aging model can, for example, be implemented using a Monte Carlo simulation. In other words, random samples for the at least one state variable can be determined using random experiments based on the available distribution(s), and predictions for the aging of the equipment considered in the model can be derived from these samples.Alternatively or additionally to such a Monte Carlo simulation, probabilistic modeling can also be achieved through linearization in the critical region and / or by weighted sampling of a number k of points. This can be done, for example, by applying so-called sigma-point Kalman filters or analogous methods. In total, numerous methods are known from the state of the art for such stochastic modeling of aging.

[0040] Generally, it is advantageous for the number n of assets considered in the model to be greater than 1. This means that the aging state is determined for a plurality of assets. In such cases, it is particularly useful to assign a scalar aging indicator (AHI) to each asset. Determining such a scalar indicator is advantageous because it allows for the creation of a ranking of the aging status of the assets under consideration. Such a ranking can significantly facilitate decisions regarding the prioritization of measures for individual assets (such as maintenance, replacement, curtailment, or the addition of measuring devices).

[0041] In general, however, the state of aging can also be described (at least in an intermediate step) by a vector with several parameters, whereby a scalar aging indicator can be determined, if necessary, by a defined function of these individual vector elements.

[0042] According to a preferred embodiment, at least one of the equipment considered in the modeling can be a transformer, a line (e.g., an overhead line), and / or a switch or switchgear. This equipment is particularly relevant for maintaining the operation of a power grid. However, the invention is applicable in principle to all types of equipment and is therefore not limited to the examples mentioned. The power grid can preferably be a medium-voltage or low-voltage distribution network.

[0043] According to an advantageous embodiment of the operating procedure, the power grid can comprise a plurality of electrical equipment, and several of these devices can be modeled with respect to their aging. Advantageously, in step i), a scalar aging indicator (AHI) is assigned to each device, and in step ii), at least one additional measure can then be implemented, particularly if a predefined threshold for the aging indicator is exceeded. Such an additional measure can, in particular, be specific to the device most affected by aging.

[0044] This additional measure can, in particular, be one of the following: - a replacement of the respective operating equipment,

[0045] - maintenance of the respective equipment,

[0046] - an adjustment of at least one operating parameter of the respective equipment,

[0047] - the addition of a measuring device in the area of ​​the respective equipment.

[0048] The aforementioned adjustment of an operating parameter could, for example, involve reducing power and / or voltage in the respective section of the power grid. The added measuring device could be, for instance, an RTU meter or a PMU meter. Overall, the calculated aging index can help an asset manager prioritize potential measures for preventing and / or resolving fault conditions, ensuring that available resources are allocated to assets most likely to be affected by operational aging. Optionally, the criticality of the respective asset (e.g., the extent of the damage, the expected duration of the failure, and / or the size of the affected section of the power grid) can be incorporated into this prioritization in addition to the aging indicator.Overall, this allows for particularly resource-efficient asset management and high reliability with low resource consumption.

[0049] The invention is described below with reference to some preferred embodiments and the attached drawings, in which:

[0050] Figure 1 shows a schematic flowchart with exemplary steps of the operating procedure,

[0051] Figure 2 shows a sketch for determining the state of aging according to a first implementation variant of the determination method,

[0052] Figure 3 shows a sketch for determining the state of aging according to a second variant of the determination method and

[0053] Figure 4 shows a schematic representation of a section of a power grid.

[0054] In the figures, identical or functionally equivalent elements are provided with the same reference symbols.

[0055] Figure 2 shows a schematic flowchart for a method for operating a power grid according to a first example of the invention. This operating method comprises steps i) and ii). In step i), the aging state of one or more components within the power grid is determined according to an example of the determination method according to the invention. In this example, the aging state is characterized by a so-called aging indicator AHI, which is a scalar parameter. In step ii), the actual operation of the power grid takes place, e.g., by means of a control unit. Here, at least one operating parameter P is selected depending on the determined aging indicator AHI. Optionally (as indicated by the dashed arrow), one or more additional measures M can be taken depending on the aging indicator AHI.These can include, for example, measures taken by an asset manager to prevent and / or rectify fault conditions. These measures can be implemented in particular when the AHI (Aging Health Index) of an asset exceeds a predetermined threshold. Overall, the determination procedure in step i) can be used to ascertain the aging states of several assets in the power grid, and, for example, a ranking of the predicted asset aging can be derived using the respective AHI indicators.

[0056] Step i) thus comprises the individual steps of the procedure for the computer-aided determination of the aging state of one or more pieces of equipment. The underlying process is shown here only once, but the principle is analogous to the (simultaneous and / or sequential) determination of the aging states of multiple pieces of equipment. The determination procedure comprises individual steps a) and b), as well as, optionally, the intermediate step z), shown with a dashed line. In step a), a probabilistic distribution p is calculated computer-aided for at least one physical state variable of the power grid. This state variable is denoted by x for illustrative purposes. Analogously, corresponding distributions for several such state variables can also be determined here.In this example, the determined distribution is a conditional probability distribution p(x\z), i.e., the probability distribution of the state variable x for a given measured quantity z. This is an a posteriori distribution, which is determined using a Bayesian approach.

[0057] Based on the distribution p(x\z), an optional intermediate step z) can generate a defined (deterministic) input parameter IN for an aging model MOD. Alternatively, intermediate step z) can be omitted, and the calculated distribution p(x\z) can be used directly as input for an aging model MOD. The first option with intermediate step z) is appropriate if the aging model MOD is deterministic. The second option without intermediate step z) is appropriate if the aging model MOD is probabilistic. Generally, and regardless of the chosen option, step b) involves computer-aided modeling of aging based on an aging model MOD. The output of this modeling is a calculated aging state, which in this example is a scalar aging indicator AHI.In general, however, it can also be a composite of several aging parameters, i.e., in particular a vectorial aging parameter.

[0058] In the example shown in Figure 1, step a) of the determination procedure comprises several sub-steps a1) to a3). The calculation of the probabilistic distribution p(x|z) for the state variable x is based on a Bayesian approach. In sub-step a1), an a priori distribution p(x) for the state variable x is determined and provided. This a priori distribution p(x) is determined based on one or more measurements m0, which can, in principle, be performed within and / or outside the actual determination procedure. These measurements can be carried out either on the same (the one used here) power grid or on another, similar power grid. In sub-step a2), a measurement distribution for a measured variable z is provided, which is specifically treated as a measurement distribution p(z|x) for a given state variable x. In this example, this measurement distribution is determined based on a measurement m. tFor each journal t under consideration, in step a3), the a posterior distribution p(x|z) is determined by applying Bayes' theorem based on the product of the a priori distribution p(x) and the measurement distribution p(z|x). Although the procedure is shown here as an example only for one state variable x, one measurement variable z, and one journal t, the method can be particularly advantageously carried out analogously for multiple state variables, multiple measurement variables, and / or multiple time steps. This results, for example, in an overall time course of a multidimensional probability distribution for multiple state variables of the power grid. In this way, aging states for multiple pieces of equipment can also be determined particularly advantageously, especially if distributions for state variables are determined at the network nodes or line sections that are assigned to the individual pieces of equipment.

[0059] During the measurements m0 and / or m tFor example, active power, reactive power, voltages, and / or currents can be measured for selected network nodes or lines. These physical quantities thus represent preferred measured variables z. In contrast, the considered state variables x can include, for example, a (complex-valued) current for one or more line sections, a (complex-valued) voltage, a voltage magnitude, and / or a voltage angle for one or more network nodes of the power grid. For further details on the application of the Bayesian approach to determine the distribution p(x|z), reference is made to patent application EP 4312329 A1. Figure 2 schematically outlines the determination of the aging state according to a first embodiment of the determination method. In this embodiment, the aging model MOD is a deterministic model.Accordingly, in an intermediate step z), a defined quantity IN is generated from the probability distribution p(x|z) as an input for the deterministic aging model MOD. This can generally be advantageously done using information from a boundary region of the probability distribution p(x|z). In the example shown here, the probability distribution p(x|z) is approximated as a Gaussian function of a state variable x. By using the information from the obtained measurement distribution p(z|x), this a posterior distribution p(x|z) is narrower than the a priori distribution p(x) of the state variable x. With several such state variables, a multidimensional Gaussian distribution can be used.This example illustrates how a defined input variable IN can be generated based on a boundary region of the distribution: Specifically, the value of the state variable x can be used for a predefined risk level (order of a quantile). Two example x-values ​​for two risk levels are shown here: x(R1) and x(R2). The first risk level, R1, could be a quantile where the state variable has an 80% probability of being below position x(R1) and a 20% probability of being above position x(R1). The second risk level, R2, could be a quantile where the state variable has a 90% probability of being below position x(R2) and a 10% probability of being above position x(R2). Depending on the criticality of the asset under consideration, a relevant risk level can be defined.Similarly, the value of the state variable x, which results from the predefined probability threshold, can be used as the input variable IN for the aging model MOD.

[0060] Figure 3 schematically outlines the determination of the aging state according to a second implementation variant of the determination procedure. In this implementation variant, the aging model MOD is a probabilistic (stochastic) model. Accordingly, the probability distribution p(x|z) can be used directly as input IN for this model MOD. The output of this aging model MOD is also a probability distribution, specifically a probability distribution p(A) of an aging variable A. When considering multiple aging variables A, a multidimensional probability distribution can again be output. Similar to the example in Figure 2, a characteristic (fixed) value A(R1) can be determined from the distribution p(A) by considering a predefined risk level R1, specifically a scalar aging indicator AHI.When considering multiple aging parameters, the aging indicator AHI can, for example, be obtained through a predefined function of the characteristic values ​​from the individual dimensions of the distribution.

[0061] Figure 4 shows a schematic representation of a section of an exemplary power grid 1. The power grid comprises a plurality of lines 3 and network nodes 2, of which five network nodes are shown here by way of example. It further comprises a plurality of electrical equipment 4, of which only one is shown here by way of example. The equipment 4 can be, for example, a transformer, a line, or a switch. In particular, it can be assigned to a line or to one or more network nodes. In particular, if a comparatively high aging parameter A or a comparatively high aging indicator AHI is determined for such equipment 4 using the method according to the invention, then the responsible asset manager can implement additional measures M.One such additional measure could be to add an additional measuring device at an additional measuring position to enable more precise recording of the operating states of this equipment during future operation. In the power grid 1 of Figure 4, a measuring device is already present at a first measuring position P1. For the installation of an additional measuring device, the second measuring position P2 or the alternative second measuring position P2' could be considered. Various methods for determining suitable measuring positions for a limited number of measuring devices are already known in the art. These methods are summarized under the English term "Optimum Meter Placement." For example, P2 designates a measuring position that would result from a conventional Optimum Meter Placement.However, the alternative second measurement position P2' may prove to be more suitable overall if, in addition to conventional optimization criteria such as reducing the general measurement uncertainty, the aging parameter predicted by the determination method according to the invention and the associated risk of error are also taken into account. Thus, within the framework of the aforementioned additional measures, the present invention can also contribute to improved positioning of the available measurement resources.

[0062] The applicant points out at this point that, regardless of the grammatical gender of a particular personal term, it should always include persons of male, female, and other gender identities. Reference list

[0063] 1 Power grid

[0064] 2 network nodes

[0065] 3 lines

[0066] 4. Equipment a)-b) Process steps

[0067] A Aging state (age magnitude)

[0068] AHI Aging Indicator a1)-a3) Sub-steps i)-ii) Procedural steps

[0069] IN input into the aging model

[0070] M measure mo measurement to determine the a priori distribution m t Measurement to generate the measurement distribution for magazine t

[0071] MOD aging model

[0072] P Operating parameters

[0073] P1 first measuring position

[0074] P2 second measuring position

[0075] P2' alternative second measurement position p(A) probability distribution of the aging variable A p(x) prior distribution for state variable x p(z\x) measurement distribution for the measured variable z (given state variable x) p(x|z) posterior distribution for state variable x (given measured variable z)

[0076] R1,R2 risk levels (quantiles) t journal x state variable z) optional intermediate step z measured variable

Claims

Patent claims 1. A method for determining the aging states (A, AHI) of a number of electrical equipment (4) in a power grid (1), wherein the method comprises the following steps: a) computer-aided calculation of a probabilistic distribution (p(x|z)) for at least one physical state variable (x) of the power grid (1), based on a measurement distribution (p(z|x)) for at least one measurement variable (z) which has a correlation with the state variable (x), b) computer-aided modeling of the aging of the electrical equipment (4) during operation of the power grid (1) using the probabilistic distribution (p(x|z)) for the state variable (x) as the basis of an input (IN) for an aging model (MOD), by means of which an aging state (A, AHI) of the respective equipment (4) is determined at least approximately.

2. Method according to claim 1, wherein in step a) a time-dependent curve is calculated for the probabilistic distribution (p(x|z)) of the at least one state variable (x).

3. Method according to one of claims 1 or 2, wherein the considered state variables (x) comprise a current for at least one line section (3) of the power grid (1) and / or a voltage, a voltage magnitude and / or a voltage angle for at least one network node (2) of the power grid (1).

4. Method according to one of the preceding claims, wherein the measurement distribution (p(z|x)) is determined and provided based on at least one measured value for an active power, a reactive power, a voltage and / or a current within the power grid, in particular taking into account an associated measurement error.

5. A method according to any of the preceding claims, wherein the calculation of the probabilistic distribution (p(x|z)) for the state variable (x) comprises the following steps: a1) providing an a priori distribution (p(x)) for the state variable (x), a2) providing the measurement distribution (p(z|x)) for the measured variable (z), a3) determining an a posteriori distribution (p(x|z)) for the state variable (x) based on the a priori distribution (p(x)) and the measurement distribution (p(z|x)), in particular by applying Bayes' theorem.

6. Method according to claim 5, wherein the a priori distribution (p(x)) is determined and provided on the basis of measured values ​​(mo) for active power, reactive power, voltages and / or currents in at least one power grid (1) using a load flow calculation.

7. Method according to any one of claims 1 to 6, wherein the aging model (MOD) is a deterministic model, wherein the input (IN) for the aging model is a fixed quantity which is determined on the basis of the probabilistic distribution (p(x|z)).

8. Method according to claim 7, wherein the specified quantity (IN) is a characteristic value (%(R1)) of the state variable (x) which is determined as a function of a predefined risk level (R1).

9. Method according to any one of claims 1 to 6, wherein the aging model (MOD) is a probabilistic model, wherein the probabilistic distribution (p(x|z)) of the at least one state variable is used as input (IN) for the aging model (MOD).

10. Method according to any of the preceding claims, wherein the number of electrical equipment (4) is greater than 1, wherein a scalar aging indicator (AHI) is assigned to each piece of equipment (4).

11. Method according to any of the preceding claims, wherein at least one of the electrical equipment (4) is a transformer, a line and / or a switchgear.

12. Method for operating a power grid (1) with a number of electrical equipment (1), comprising the following steps: i) determining the aging state (A, AHI) of at least one of the equipment (4) according to the method according to one of the preceding claims, ii) operating the power grid (1), wherein at least one operating parameter (P) is selected depending on the determined aging state (A, AHI).

13. Method according to claim 12, wherein the power grid (1) comprises a plurality of electrical equipment (4), wherein in step i) a scalar aging indicator (AHI) is assigned to the respective equipment (4), wherein in step ii) if a predetermined threshold for the aging indicator (AHI) is exceeded, at least one additional measure (M) is implemented.

14. The method of claim 13, wherein at least one additional measure (M) is a measure from the following list: - an exchange of the respective operating equipment (4), - maintenance of the respective equipment (4), - an adjustment of at least one operating parameter of the respective equipment and - an addition of a measuring device in the area of ​​the respective equipment (4).

15. Computer program product comprising instructions, wherein the instructions, when the computer program product is executed on a computer, cause the computer to execute a method according to any one of claims 1 to 14.

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