Probability determination of transformer end of life

Abstract

A method of estimating future aging of a transformer includes generating a probability model of factors affecting effective aging of the transformer, generating a probability curve of factors affecting effective aging of the transformer based on the probability model, generating an expected hotspot curve from the probability curve, simulating a plurality of aging scenarios of the transformer based on the expected hotspot curve and an ambient temperature curve, and estimating future aging of the transformer from the plurality of aging scenarios.

Description

Technical Field

[0001] The present disclosure relates to analysis of high voltage transformers. Specifically, the present disclosure relates to systems and methods for estimating future aging of high voltage transformers. Background Art

[0002] High-voltage transformers, such as those used in substations, are complex and expensive items. The ability to accurately estimate the transformer's remaining operating life is of great concern to manufacturers and owners of such transformers. Transformer manufacturers typically specify the nominal expected operating life of a new transformer. For example, a typical new high-voltage transformer may be rated by its manufacturer as having a nominal life of 180,000 hours, or approximately 20 years. Such ratings are based on use at nominal ambient temperature and nominal operating load, and are typically calculated using a formula based on the IEC 60076-7 standard, which takes into account the nominal ambient temperature and the transformer's top oil temperature at nominal load.

[0003] However, the actual ambient temperature and operating load in which a transformer operates vary from day to day and from season to season, and both quantities may frequently exceed their nominal values, depending on how and where the transformer is operated. Therefore, the ratings provided by the manufacturer are at best a rough estimate of the actual lifespan of the transformer.

[0004] Furthermore, the actual lifespan of a transformer is affected by other factors, the most significant of which are the moisture and oxygen levels within the transformer. High-voltage transformers are filled with oil, such as mineral oil, which acts as a coolant and / or insulator, and protects the solid insulation within the transformer (e.g., cellulose or paper) from chemical attack. The presence of moisture and / or oxygen in the oil impairs these functions, resulting in a shortened transformer lifespan.

[0005] Other factors that may affect transformer life include maintenance, oil leaks, internal oil line blockages, environmental influences (lightning, storms, etc.), physical location changes, and other factors. Summary of the Invention

[0006] A method for estimating future aging of a transformer includes: generating a probability model of factors affecting effective aging of the transformer; generating multiple probability curves of the factors affecting effective aging of the transformer based on the probability model; generating an expected hot spot curve based on the probability curve; simulating multiple future aging scenarios of the transformer based on the expected hot spot curve; and estimating the expected remaining life of the transformer based on the multiple future aging scenarios.

[0007] In some embodiments, the plurality of probability curves are generated for a first time period, and the future aging scenario is generated within a second time period different from the first time period. The first time period may be a 24-hour time period, and the second time period may be a one-year time period.

[0008] In some embodiments, factors affecting the effective aging of the transformer may include load conditions, ambient temperature, humidity levels within the transformer, and oxygen levels within the transformer.

[0009] In some embodiments, simulating the plurality of future aging scenarios includes performing a Monte Carlo simulation on the future aging scenarios.

[0010] In some embodiments, simulating the plurality of aging scenarios comprises: generating a plurality of aging curves simulating aging of the transformer during the first time period; for each of the plurality of aging curves, estimating an effective aging amount of the transformer to provide a plurality of effective aging amounts; and summing the plurality of effective aging amounts to provide an estimated effective aging amount during the second time period.

[0011] In some embodiments, generating the probability curve of factors affecting the effective aging of the transformer includes generating a plurality of ambient temperature curves based on historical changes in ambient temperature.

[0012] In some embodiments, the ambient temperature profile describes an expected ambient temperature over a predetermined period of time.

[0013] Some embodiments further comprise generating an ambient temperature profile based on a probability distribution at a plurality of time intervals within the predetermined time period. In some embodiments, the probability distribution comprises a uniform probability distribution.

[0014] In some embodiments, generating a probability curve of factors affecting the effective aging of the transformer includes generating a plurality of expected load curves based on a predicted load of the transformer.

[0015] In some embodiments, the expected load profile describes an expected load over a predetermined time period.

[0016] In some embodiments, the method further comprises generating the expected load profile based on a probability distribution at a plurality of time intervals within the predetermined time period. In some embodiments, the probability distribution comprises a uniform probability distribution.

[0017] In some embodiments, estimating the remaining life of the transformer according to the plurality of future life scenarios includes generating a histogram of expected aging scenarios, and generating a confidence interval of the expected remaining life of the transformer based on the histogram of expected aging scenarios.

[0018] In some embodiments, the aging scenario includes an expected annual aging scenario, and the expected remaining life of the transformer is estimated based on the nominal expected life of the transformer and the expected annual aging scenario.

[0019] In some embodiments, the method includes collecting operational data representing factors affecting effective aging of the transformer during operation of the transformer, and updating a probabilistic model of factors affecting effective aging of the transformer.

[0020] In some embodiments, the method includes determining an effective current age of the transformer based on the operating data, wherein the expected remaining lifetime of the transformer is estimated based on the multiple future aging scenarios, based on the effective current age of the transformer and the nominal expected lifetime of the transformer.

[0021] In some embodiments, the method further includes maintaining the transformer and / or adjusting a load on the transformer based on the estimated future aging of the transformer.

[0022] According to some embodiments, a method for operating a transformer based on a probabilistic model of factors affecting transformer aging includes: collecting operational data indicating factors affecting effective aging of the transformer during operation of the transformer; updating the probabilistic model of factors affecting effective aging of the transformer based on the operational data; and determining an effective current age of the transformer based on the operational data. The expected remaining life of the transformer is estimated based on a plurality of future aging scenarios generated based on the probabilistic factors, based on the effective current age of the transformer, and based on the nominal expected life of the transformer.

[0023] In some embodiments, collecting the operational data includes collecting the operational data from sensors in the transformer.

[0024] A device for generating an expected remaining life of a transformer includes a processing circuit and a memory coupled to the processing circuit. The memory stores computer program instructions that, when executed by the processing circuit, cause the device to perform operations including: generating a probabilistic model of factors affecting effective aging of the transformer; generating an expected hot spot curve based on the probabilistic model; simulating multiple future aging scenarios of the transformer based on the expected hot spot curve; and estimating the expected remaining life of the transformer based on the multiple future aging scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The accompanying drawings illustrate certain non-limiting embodiments of the inventive concept and are included to provide a further understanding of the disclosure, and are incorporated in and constitute a part of this application. In the drawings:

[0026] Figure 1 is a graph illustrating the effect of hot spot temperature variation on the aging acceleration factor of a transformer including thermally stable paper.

[0027] Figure 2 is a graph illustrating the effect of a + / - 2% error in ambient temperature on transformer aging hours.

[0028] Figures 3A to 3C is a graph illustrating the calculation of equivalent aging hours for a transformer over a 24 hour period using load and ambient temperature data.

[0029] Figure 4 is a graph illustrating an example of hourly variations in temperature (402) and load (404) profiles for a representative transformer.

[0030] Figure 5 The graph illustrates probability distributions of ambient temperature changes and load changes, which can be used to estimate the remaining life of a transformer in some embodiments.

[0031] Figure 6 is the three-dimensional probability density function of the combination of load and ambient temperature in a given time period.

[0032] Figure 7A is a graph of the transformer load curve generated by Monte Carlo simulation.

[0033] Figure 7B It is a graph of the transformer ambient temperature curve generated by Monte Carlo simulation.

[0034] Figure 8A Illustrated using Figure 7A and Figure 7B The probability hot spot curve is generated based on the load curve and ambient temperature curve.

[0035] Figure 8B Illustrated using Figure 8A The probabilistic aging curve is generated from the probabilistic hot spot curve.

[0036] Figure 9 The cumulative aging for three separate 365-day aging simulations is shown.

[0037] Figure 10 A histogram showing the one-year aging curve is shown.

[0038] Figure 11 The graph shows the probability distribution of annual transformer life consumption.

[0039] Figure 12 An example of simulation results as the sample size (n) increases is shown.

[0040] Figure 13A The graph shows the expected life of a transformer as a function of hotspot temperature at different humidity and oxygen levels on heat-stabilized paper according to IEC 60076-7.

[0041] Figure 13B is a graph showing the environmental factor (A) as a function of the humidity level in the transformer.

[0042] Figure 14A is a graph illustrating the dependence of expected transformer life on the humidity level in the transformer.

[0043] Figure 14B The figure shows the probabilistic aging curve generated using probabilistic hotspot data in combination with probabilistic humidity data.

[0044] Figure 15 The figure shows a histogram of the one-year aging curves at different moisture contents.

[0045] Figure 16 is a flowchart of operations according to some embodiments.

[0046] Figure 17 is the functional block diagram of the transformer aging estimator.

[0047] Figure 18 The figure shows the estimation of the remaining life of the transformer.

[0048] Figure 19 is a flowchart of operations according to some embodiments.

[0049] Figure 20A is a block diagram illustrating a system for performing dissolved gas analysis according to some embodiments.

[0050] Figure 20B is a block diagram illustrating functional modules of a system for performing dissolved gas analysis according to some embodiments. DETAILED DESCRIPTION

[0051] The present invention will now be described more fully below with reference to the accompanying drawings, in which examples of embodiments of the present invention are shown. However, the present invention can be implemented in many different forms and should not be construed as being limited to the embodiments set forth herein. On the contrary, these embodiments are provided to make this disclosure more complete and comprehensive and to fully convey the scope of the present invention to those skilled in the art. It should also be noted that these embodiments are not mutually exclusive. Components in one embodiment may be assumed to be present in / used in another embodiment.

[0052] The following description presents various embodiments of the disclosed subject matter. The embodiments are presented as illustrative examples and should not be construed as limiting the scope of the disclosed subject matter. For example, certain details of the described embodiments can be modified, omitted, or extended without departing from the scope of the described subject matter.

[0053] It is generally accepted that the hot-spot temperature of a transformer is the main factor influencing the aging of the transformer. The hot-spot temperature refers to the highest temperature in the transformer. Typically, the hot-spot temperature of a transformer is not measured directly, but is estimated using a thermal model adapted to the design of the transformer (e.g., the insulation material used, the cooling arrangement of the transformer, etc.) and environmental temperature and power load data. The hot-spot temperature and its variation over time depend on the on-site geographical location (environmental temperature) of the transformer and the power load on the transformer. Thus, the hot-spot temperature value is a transformer characteristic value that depends on the environmental conditions (temperature and load) and the transformer design. The nominal operating life of a transformer is typically calculated using the hot-spot temperature value according to the formula set forth in IEC 60076-7 IEEE C57.19 Load Guide. As an example, for a constant hot-spot temperature of 110 °C, the unit life termination of a transformer can be estimated according to equation [1] as:

[0054]

[0055] where θH is the hot-spot temperature of the transformer. Thus, for a constant hot-spot temperature of 110 °C, using thermal stabilized paper as the insulation material in the transformer (e.g., according to the design of the transformer), the transformer has an estimated unit (standard) life of 1.0. For a transformer with a rated operating time of 180,000 hours, this means that if the transformer is operated at a constant hot-spot temperature of 110 °C at the rated load, the expected life of the transformer is 180,000 hours.

[0056] The aging of a transformer can be accelerated or delayed depending on whether the transformer is operated at a temperature higher or lower than the nominal hot-spot temperature. With this in mind, the IEC 60076-7 and IEEE C57.91 standards also specify a formula for estimating the aging acceleration factor F AA based on the estimated hot-spot temperature, as shown in equation [2]:

[0057]

[0058] As can be seen in equation [2], when the transformer is operated at a hot-spot temperature higher than 110 °C, the argument of the exponential function is positive, meaning that the aging acceleration factor F AA is greater than one (indicating accelerated aging), while when the transformer is operated at a hot-spot temperature lower than 110 °C, the argument of the exponential function is negative, meaning that the aging acceleration factor F AALess than one (indicating delayed aging). The actual aging can then be estimated by multiplying the unit life of the transformer by the aging acceleration factor. The hot spot temperature change of the transformer including the thermally stabilized paper is proportional to the aging acceleration factor F. AA The impact of Figure 1 As can be seen in the figure, the increase in hotspot temperature from 110°C to 116°C results in an aging acceleration factor F AA Doubling this, from 1 to about 2, means that when the transformer is operated at a hotspot temperature of 116°C, its expected life is about twice as long as when it is operated at a hotspot temperature of 110°C.

[0059] from Figure 1 As can be seen from the curve, a hotspot temperature change of + / -6°C can lead to an aging acceleration factor F AA Varying from about 0.5 to about 2, this means that the actual aging rate of the transformer can vary from about 50% of the nominal rate to about 200% of the nominal rate based on a fairly small change in hot spot temperature.

[0060] Hotspot temperature estimates can be subject to various inaccuracies. For example, the estimated hotspot location may be inaccurate, leading to an inaccurate hotspot estimate. The sensor used to measure the temperature within the transformer (e.g., top oil temperature) may have some inaccuracies, and whether the hotspot is estimated continuously or intermittently can affect the measurement results. These inaccuracies can affect transformer aging estimates.

[0061] According to IEC 60076-7 and IEEE C57.91 standards, it is assumed that the hotspot temperature consists of three components, as shown in equation [3]:

[0062] Θ H =Θ A +ΔΘ TO +ΔΘ H [3]

[0064] Among them, θ H is the hottest temperature of the winding, θ A is the average ambient temperature during the load cycle to be studied, Δθ TO is the top oil temperature rise relative to the ambient temperature, and Δθ H is the temperature rise of the hottest point relative to the top oil temperature. The top oil temperature is given by equation [4]:

[0065] Θ TO =Θ A +ΔΘ TO [4]

[0067] The transient hottest winding temperature is given by equation [5]:

[0068]

[0069] Where t is the load duration, Δθ H，U is the final winding hottest point temperature rise relative to the top oil temperature for load L, Δθ H，i is the initial winding hottest point temperature rise relative to the top oil temperature at t = 0, and τ w is the winding time constant at the hotspot position h.

[0070] In this model, errors in ambient temperature measurement / estimation may affect the hotspot temperature calculation, which in turn affects the transformer aging acceleration factor. For example, Figure 2 The graph shows the effect of a + / - 2% error in ambient temperature on the transformer aging hours for a given operating load curve as shown. Figure 2 In the example shown, the aging of the transformer over a single 2 hour period may vary by up to approximately + / - 2.5 hours based on changes in ambient temperature.

[0071] As mentioned above, in addition to hotspot temperature, a transformer's actual aging can be affected by many factors, including ambient temperature, moisture content, oxygen content, operating load, and other factors. This complexity limits the accuracy of industry-accepted aging models based on thermal performance, which use deterministic load and ambient temperature factors. Consequently, current challenges in the field include accurately estimating the transformer's future aging so that its expected end of life can be accurately determined. A related issue is how to incorporate these multiple factors influencing transformer aging into future aging estimates.

[0072] Some embodiments described herein provide systems and methods for estimating the expected future aging of a transformer based on probabilistic models of various factors that influence transformer aging, including the transformer's operating load and ambient temperature. In addition to the transformer's operating load and ambient temperature, other embodiments provide systems and methods for estimating the expected future aging of a transformer based on probabilistic models of moisture and oxygen content within the transformer. Still other embodiments adapt transformer aging estimation based on specific characteristics of the transformer (e.g., design characteristics, geographic location characteristics, historical data related to transformer usage, etc.).

[0073] Some embodiments incorporate probabilistic models of factors influencing transformer aging, rather than relying on previously used deterministic models. The probabilistic models can be adapted using actual historical operating data from the transformer. For a given transformer, these methods can provide more accurate remaining life estimates than deterministic models.

[0074] The probabilistic approach described in this paper accounts for the fact that the actual loads and ambient temperatures to which the transformer will be subjected in the future are unknown. The probabilistic approach replaces the "unknown" deterministic values ​​of the load and environment (past and future) with their most likely probabilistic values ​​(based on probability distribution functions that better represent probabilistic variations) and applies Monte Carlo simulation to simulate a large number of these scenarios. Based on the simulation results, an estimate of the cumulative aging (past and future) can be obtained, which is represented by the resulting "normal distribution" of aging hours.

[0075] Figures 3A to 3C The figure illustrates the calculation of equivalent aging hours for a transformer over an exemplary 24-hour period (first period) using load and ambient temperature data. In particular, Figure 3A is a graph of transformer hourly load 302 and ambient temperature 304 data. It should be noted that Figure 3A The load curves shown in are given in terms per unit or normalized so that the nominal load is represented as load 1.0. Figure 3B is a graph of the hot spot temperature (curve 306) calculated according to the temperature model of the transformer in question, which is based on Figure 3A Load and ambient temperature data shown.

[0076] Figure 3C is based on Figure 3B The hot spot temperature curve shown is used to calculate the aging acceleration factor F of the transformer within a 24-hour period. AA (curve 308) is a graph showing the aging acceleration factor F. AA The curve is integrated to obtain the equivalent aging hours of the transformer in a 24-hour period, as shown in curve 310. Figure 3C As shown, given Figure 3B The hot spot temperature curve shown is based on Figure 3A The ambient temperature curve and load curve shown, the estimated transformer cumulative 'aging' over a 24 hour period is approximately 35 hours of aging (also known as effective aging).

[0077] It will be appreciated that the load and ambient temperature profile of a given transformer is variable. Figure 4 An example of an hourly temperature variation curve 402 and an hourly load variation curve 404 for a representative transformer over a 24-hour period is shown, these curves being generated by accumulating data collected over a long period of time (e.g., several years). The temperature variation for each time interval can be bounded by an upper bound 402H and a lower bound 402L for each time interval, and the load variation for each time interval can be bounded by an upper bound 404H and a lower bound 404L for each time interval. Thus, for example, Figure 4As shown in the temperature curve 402, at the 10th hour, the temperature may drop to somewhere between about 10°C and 25°C. Similarly, for Figure 4 As shown in the load curve 404 , at hour 10, the temperature may drop to somewhere between approximately 0.6 and 0.8.

[0078] exist Figure 4 In the illustrative example shown, the ambient temperature varies by up to 50%, and the load varies by up to 30%. For analysis purposes, it is assumed that the ambient temperature profile and the load profile of the transformer are known and / or can be estimated by considering appropriate lower and upper bounds (limits) at each moment in time within the first time period. For example, the first time period data can be an hourly, daily, weekly, monthly, quarterly, or yearly time period and can be used accordingly with changes observed over a long period of time at similar / corresponding moments. It will be understood that Figure 4 The curve shown in is for a given 24-hour period and will typically vary over a given year due to seasonal variations in ambient temperature and / or load demand, resulting in variations in ambient temperature / load values ​​at specific moments in the organization data within the first period (a 24-hour period in this example).

[0079] In some embodiments, a transformer monitoring system can be used to collect transformer load, ambient temperature, and / or other data. The transformer monitoring system can be used to detect transformer faults and provide data collection capabilities for transformer condition assessment. The transformer monitoring system can monitor temperature and current in the transformer to determine hot spot temperatures and electrical load on the transformer for transformer aging and life assessment. The transformer monitoring system can calculate hot spot temperatures according to IEC and / or IEEE standards and use this data to model thermal behavior, allowing comparisons between measured and expected readings and providing prognostic services, such as estimating the future life of the transformer. Services from the transformer monitoring system can be provided as part of the transformer or as advanced transformer services supported by a remote transformer monitoring system (which can be provided as a device or as a software solution provided on a digital system). The remote transformer monitoring system monitors the transformer using sensors within and around the transformer to measure transformer and environmental parameters and also provides information used to adapt probabilistic models to represent the monitored transformer (including its environment). The output of the transformer monitoring system can be monitored locally (at the transformer site) and / or remotely (at locations other than the transformer site) via a network interface. The transformer monitoring system can be used to monitor several transformers and assess the aging / remaining life of these transformers using the methods described herein. Some embodiments described herein can be performed by the transformer monitoring system.

[0080] In particular, the transformer monitoring system according to some embodiments can generate predictions of future transformer aging, including predictions of transformer end of life, based on various transformer-related parameters (e.g., ambient temperature, load on the transformer, moisture content, oxygen content, etc.). The predicted aging and / or end of life of the transformer can be used to schedule transformer maintenance, plan / adjust transformer loads, provide early warning of faults, and / or for other purposes related to asset management. Figure 20A and Figure 20B A transformer monitoring system according to some embodiments is described in further detail.

[0081] Transformer-related parameters (e.g., the load on the transformer) and the transformer's ambient temperature data can be obtained by the transformer monitoring system from measurements within / at the transformer site. Transformer-related parameters, including moisture content, dissolved oxygen content, and other parameters that aid in transformer diagnosis / transformer life assessment, can be measured using sensors installed in the transformer. This data can be stored by the transformer monitoring system (historical data for the monitored transformer) and used to generate predictions of transformer-related parameters, such as the transformer's future load and ambient temperature. Ambient temperature data can also be collected by the transformer monitoring system from meteorological tools in a given geographic location based on field information associated with the transformer and used in assessments when environmental data is not collected through field measurements of the transformer. As discussed in more detail below, to effectively capture observable variations in the data, daily probability curves for load / ambient temperature can be generated using Monte Carlo simulation or other statistical techniques, and such curves can be used to calculate annual aging estimates and life assessments. Multiple annual aging estimates can be generated using Monte Carlo simulations. These estimates can be analyzed to determine the expected annual aging of the transformer.

[0082] Figure 5 The figure shows a uniform probability distribution of ambient temperature variation (502) and load variation (504), which can be used in some embodiments to predict the future aging / estimated remaining life of the transformer. Figure 5 As shown, for estimation purposes, in some embodiments, it can be assumed that the load and ambient temperature variations within any given time interval are uniformly distributed between upper and lower bounds. It will be appreciated that in some embodiments, a different daily temperature distribution can be used. For a given geographic location, daily maximum and minimum temperatures are readily available. This information can be used to model daily temperature variations using a uniform probability distribution.

[0083] However, a transformer monitoring system can monitor ambient temperature and generate a more accurate probability distribution of the transformer's daily temperature. Specifically, the system can use ambient temperature data acquired from on-site transformers as historical data and generate a probability distribution of ambient temperature based on historical data collected over a specific duration (day / month / year). Consequently, this probability distribution of ambient temperature may better represent actual temperature conditions and temperature variations based on time of day and season than a uniform probability distribution.

[0084] For example, the actual probability distribution of daily temperature variations may be found to follow a normal distribution, a lognormal distribution, or other probability distributions, and these may be used in further evaluation in lieu of a uniform distribution. It is currently believed that a uniform distribution is a conservative choice for temperature variation modeling for the purposes of predicting / estimating transformer aging, and in some embodiments, the method is illustrated using a uniform probability distribution within measured / expected limits (bounds) of transformer parameters (e.g., ambient temperature and load).

[0085] Based on these assumptions, a probability model of load and ambient temperature can be generated for a given time period. The probability model can provide a three-dimensional probability density function for the combination of load and ambient temperature in a given time period, such as Figure 6 A three-dimensional probability density function 602 is shown.

[0086] In some embodiments, it is assumed that oil temperature is the main aging factor of the transformer, ie, moisture and oxygen content do not have a substantial impact on aging, and the transformer uses thermally stable paper.

[0087] Based on these assumptions, for a given time period (first time period), such as a 24-hour time period, multiple potential load-ambient temperature curves can be generated, and Monte Carlo simulation can be used to capture possible changes in the load-ambient temperature curves. Figure 7A and Figure 7B Examples of the resulting load and ambient temperature curves 702, 704, respectively, are illustrated in The load and ambient temperature curves are examples of curves (also called probability curves) of factors influencing aging generated based on a probabilistic model (a probability density function created from available measured / obtained data). Figure 7A and Figure 7B Many different possible curves for load and ambient temperature are shown.

[0088] Figure 7A and Figure 7BThe load and ambient temperature curves shown in are generated based on the following assumptions: at any given hour, the load can vary with a probability based on the load probability distribution observed at the given hour, and the ambient temperature can vary with a probability based on the ambient temperature probability distribution observed at the given hour. That is, as an example of a uniform load probability distribution (assumption), at any given hour, any load value within the range (from minimum to maximum) is equally likely to occur. Similarly, for a uniform temperature probability distribution, at any given hour, any ambient temperature within the range is equally likely to occur. As previously described, the transformer monitoring system can calculate the load and temperature probability distributions observed at any given hour (time) using the stored historical data. Figure 7A and Figure 7B The load and ambient temperature curves shown are taken into account and Monte Carlo simulation techniques are used to consider the statistical variations of future load and ambient temperatures to provide a more robust and accurate prediction of the remaining life of the transformer.

[0089] Next, for Figure 7A and Figure 7B For each probability scenario shown, calculate the corresponding hot spot curve and get Figure 8A A plurality of probabilistic hot spot curves 802 are shown. That is, for each load and ambient temperature profile generated by the Monte Carlo simulation, a probabilistic hot spot curve is generated containing the hot spot value at each instant. The probabilistic hot spot curve is calculated based on temperature measurements in the transformer (ambient temperature, top oil temperature, etc.) and using a hot spot model, which may be unique to the transformer or transformer design in question (a modification of a general model). This uniqueness is captured by various constants, such as the oil temperature constant, the winding temperature constant, the rated hot spot gradient, the rated oil temperature rise, and other parameters that constitute the hot spot temperature characteristics of the transformer in question.

[0090] Next, for each probability hot spot curve, the corresponding aging acceleration F is obtained for one day (24-hour period) AA The calculation and integration of the curves generate a corresponding probability aging hour curve for each day of the year (365 days). The resulting probability aging hour curve 806 (also called the effective aging curve) is displayed together with the histogram 808 of the total effective aging hour values ​​for the 24-hour period. Figure 8B As shown in Figure 8B As can be seen in FIG, in this example, based on the probabilistically generated temperature and load profiles, the effective aging hours of the transformer over a 24-hour period vary from approximately 5 hours to approximately 31 hours.

[0091] Therefore, these estimated aging hours for multiple simulated 24-hour periods can be summed to determine the total effective aging hours over a year, thereby estimating the cumulative aging of the transformer. For example, in one simulation, the total aging hours predicted for the transformer over a one-year period were 5785. This means that over a one-year period (equal to 8760 hours), the transformer was expected to be effective for only 5785 hours.

[0092] Figure 9 The figure shows three separate 365-day aging hour simulations for the future aging scenario of 902. Figure 9 As can be seen in Figure 2, the simulation estimated similar cumulative aging hours of approximately 5,700 hours in a year, thus constituting the annual aging scenario. Therefore, future aging scenarios are probabilistic scenarios that estimate the future aging of the transformer over a given time period based on randomly selected transformer aging factors, such as ambient temperature and load.

[0093] Figure 10 The histogram 1002 shown illustrates Figure 8B The expected effective aging over one year is shown in the multiple probabilistic aging hour curves. Figure 10 As shown, the distribution can be approximated as a normal distribution with a peak just above 5700 hours. Based on this data, the mean and standard deviation of the expected effective annual aging hours of the transformer can be calculated. The normal distribution is approximated according to the central limit theorem so that the sum of the distributions of multiple aging time periods (i.e., 365×24h periods) forms a normal distribution, and the mean and standard deviation of the normal distribution can be calculated without considering the original probability density function representing the components that cause the calculated aging (i.e., the statistical distribution of hourly load and the statistical distribution of hourly ambient temperature). Therefore, due to the central limit theorem, calculations associated with the normal distribution can be used to determine a 95% confidence interval for the expected effective aging hours in a year based on this information. Specifically, the 95% confidence interval is calculated according to equation [6] as:

[0094]

[0095] where n is the number of samples, mean is the sample mean, and σ is the sample standard deviation.

[0096] For example, Figure 11 As shown, in one example, for 100 samples, the mean is 5738 hours, and the standard deviation (σ) is 110 hours. Therefore, the 95% confidence interval for aging in this case is 5738 ± 21.6 effective aging hours or 239 ± 0.9 effective aging days. Considering a nominal life expectancy of 180,000 hours, this means that the transformer in question is expected to have an actual operating life of 180,000 / 5738 = 31.4 years.

[0097] Figure 12 The figure shows an example as the sample size (n) increases, that is, as the number of simulations increases. Figure 12 (a) shows the effective annual aging hours distribution for n=100 simulations, Figure 12 (b) shows the effective annual aging hours distribution for n=500 simulations, and Figure 12 (c) shows the effective annual aging hour distribution for the simulation with n = 1000. It can be seen that the mean and standard deviation change very little as the number of simulations increases.

[0098] As mentioned above, the effective aging of a transformer may also be affected by the presence of humidity and / or oxygen within the transformer, as the presence of oxygen and / or humidity may affect the performance of the solid insulation in the transformer. Figure 13A The following is a graph showing the expected life of a transformer as a function of hotspot temperature at different moisture and oxygen levels in heat-stabilized paper according to IEC 60076-7. Figure 13A As can be seen in the graph, as the oxygen and moisture content increases, the life expectancy curve shifts downward, resulting in a shorter lifespan, and the presence of oxygen has a stronger negative impact on lifespan. Figure 13A The graph in the figure is generated by applying the Arrhenius equation, where the environmental factor (A) and the activation energy E A The parameters of are selected based on the humidity and oxygen levels. The equation used to generate the graph in Figure 13 is shown in equation [7] according to IEC 60076-7, and Table 1 shows the parameters used.

[0099]

[0100] Table 1 - Activation energy of oxidation and hydrolysis (E A ) and environmental factors (A)

[0101]

[0102] In equation [7], the following quantities are used: DP end is the degree of polymerization of the insulation paper at the end of transformer life (estimated to be 200), DP start is the initial degree of polymerization of the transformer insulation paper (estimated to be 1100), A is the environmental factor in 1 / h, EA is the activation energy in KJ / mol, t is the transformer life in hours, R is the gas constant in J / (K-mol), and θ h is the hot spot temperature.

[0103] It will be understood that Figure 13AThe curves shown in are only for discrete humidity levels. According to some embodiments, these curves can be interpolated to obtain a continuous relationship between the moisture content of the insulation paper and the environmental factor A, such as Figure 13B As shown. That is, the curve can be interpolated to obtain A as a function of moisture in the insulation paper. From this data, a series of curves can be generated to show the expected transformer life as a function of moisture. Transformer monitoring systems can use measurements of moisture and dissolved oxygen in the oil to estimate the moisture in the paper insulation, or use the range of data reported in the literature to probabilistically account for the presence of moisture and oxygen in the paper and create the appropriate curves mentioned above, thereby accounting for these factors (humidity, oxygen) in the assessment of the transformer's remaining life.

[0104] exist Figure 14A The dependence of the life expectancy on the humidity in the transformer can be seen in the graph of , which shows the life expectancy as a function of the humidity level in the transformer solid insulation for various hotspot temperatures of the thermally stable paper.

[0105] refer to Figure 14B The probability model of humidity in the transformer can be generated by assuming that the probability of humidity is uniformly distributed within limits obtained from measurements of the transformer or limits that may be observed for a particular type of transformer. By simulating multiple probabilistic aging curves based on the probabilistic hot spot curves and probabilistic humidity levels shown in Figure 8, a transformer aging histogram 1402 that takes into account the humidity in the transformer can be generated, as shown in Figure 8. Figure 14B It will be appreciated that if the actual distribution of humidity probabilities is known, such a distribution may be used instead of a uniform distribution.

[0106] Therefore, the relationship between moisture and oxygen content can be added to the above expected life estimation process to produce different expected effective aging curves. The results of simulating 1000 365-day scenarios are shown in Figure 2. Figure 15 As shown there, different effective aging curves result for different levels of humidity and oxygen in the transformer.

[0107] Figure 16 The operation of a system / method according to some embodiments is illustrated. As shown therein, a method for estimating future aging of a transformer includes generating a probability model of factors affecting effective aging of the transformer (block 1602), generating a probability curve of the factors affecting aging of the transformer (block 1604), generating an expected hot spot curve based on the probability curve (block 1606), simulating multiple future life scenarios of the transformer based on the expected hot spot curve (block 1608), and estimating the effective aging of the transformer based on the multiple future life scenarios (block 1610).

[0108] Factors that influence the effective aging of a transformer include one or more factors such as load conditions, ambient temperature, humidity levels within the transformer, and oxygen levels within the transformer. Monte Carlo simulation of future life scenarios can be used to simulate multiple future life scenarios. Monte Carlo simulation is a technique used to model the probabilities of different outcomes in a process that can be predicted by considering observable statistical variations in the variables involved in the system. In a Monte Carlo simulation, random samples of system parameters are generated and provided as inputs to a complex system or process, or its model, and the final outcomes are measured / determined. This process is repeated multiple times by randomly selecting different inputs, and information about the system or process can be gathered by examining the statistical parameters of the outputs. In various embodiments, Monte Carlo simulation is used to perform a large number of simulations to consider a large number of possible conditions (e.g., seasonal / environmental variations) and possible factor values ​​(e.g., power load, humidity levels, oxygen levels) that may affect the transformer's life (transformer condition), and to account for these variations when estimating transformer aging factors and remaining life. Probabilistic models derived from historical data (collected from one or more devices, such as transformer measurements, behavioral curves / data ranges available in the literature, and established mathematical formulas) are used to simulate various environmental and transformer conditions. These simulated conditions, known as future life scenarios, are used to estimate the transformer's aging factors and remaining life (remnant / remaining life) with greater statistical confidence.

[0109] Figure 17 A system for generating an estimate of the remaining life of a transformer is illustrated. According to some embodiments, this estimate, referred to as an end-of-life (EOL) estimate, can be generated at the beginning of the transformer's life based on predicted / expected aging factors (such as expected changes in ambient temperature and / or operating load) or at any time during the transformer's operating life. For example, Figure 18 As shown, the transformer EOL can be estimated at the beginning of its life (t=0) or at time t1 between t=0 and the transformer's EOL. At any given time t, the estimate of the transformer's remaining life is based on a combination of the estimated effective aging as of time t and a prediction of the transformer's future effective aging between time t and the transformer's EOL. The estimated effective aging of the transformer as of time t can be based on known or estimated aging factors, such as known load and ambient temperature variations as of time t. The prediction of the transformer's future effective aging between time t and EOL is based on predicted / expected aging factors.

[0110] The predicted / estimated aging factors can be based on known past aging factor values. For example, at the beginning of the life of a transformer, the EOL estimate is based on a model of expected ambient temperature and operating load variations, consisting entirely of future effective aging predictions for the transformer. As the transformer operates, data reflecting the actual ambient temperature and operating load variations experienced by the transformer can be recorded. The model of expected ambient temperature and operating load variations used to estimate future effective aging can be updated using the recorded data, which can improve the accuracy of the EOL estimate over time.

[0111] Referring again to Figure 17 , the transformer aging estimator 200 includes a past effective aging estimator 230 that generates a past effective aging estimate for the transformer based on an actual or estimated aging factor history for the transformer (e.g., actual or estimated ambient temperature and operating load experienced by the transformer up to that point). The transformer aging estimator 200 also includes a future effective aging predictor 220 that generates a remaining life prediction for the transformer based on the transformer past aging estimate and a future aging prediction for the transformer. The transformer future aging prediction is based on an aging factor model that can take into account a predicted aging factor profile (e.g., a historical or average ambient temperature and / or operating load profile) as well as actual aging factor data for the transformer in question.

[0112] For example, at the beginning of the life of a transformer with a rated life of 180,000 hours, the past effective aging estimator 230 will generate a 0 hour past effective age. The future effective aging predictor 220 will produce an EOL estimate based only on an aging factor model that takes into account only a predicted aging factor profile.

[0113] At some later time in the life of the transformer (e.g., at t = ti), the past effective aging estimator 230 will generate a past effective age estimate for the transformer, e.g., based on the actual ambient temperature and load experienced by the transformer. In one example, the past effective aging estimator 230 can generate a 100,000 hour past effective age for the transformer. To determine an EOL estimate, the future effective aging predictor 220 generates a prediction of the number of effective aging hours per year that the transformer will experience based on a predicted aging factor profile. Continuing the example, the future effective aging predictor 220 can determine that the transformer will age at a rate of 6,000 effective aging hours per year (within a predetermined confidence) based on a predicted aging factor (ambient temperature, load, moisture content, oxygen content, etc.). The transformer remaining expected life is calculated as 180,000 - 100,000 = 80,000 hours. This quantity is divided by the effective aging rate determined by the future effective aging predictor 220 to generate a value for EOL (80,000 (hours) / 6,000 (hours / year) = 13.33 years).

[0114] Figure 19 is a flow chart of the operation of the transformer aging estimator 200 according to some embodiments. The method includes collecting (block 1902) operational data representing factors affecting effective aging of the transformer during operation of the transformer, and updating (block 1904) a probabilistic model of factors affecting effective aging of the transformer.

[0115] The method further includes determining (block 1906) the effective current age of the transformer based on the operational data. The expected remaining life of the transformer is estimated based on a plurality of future aging scenarios, the effective current age of the transformer, and the nominal expected life of the transformer. Thus, the method includes determining (block 1908) the remaining life of the transformer based on the effective current age and the future aging scenarios.

[0116] Figure 20A FIG1 is a block diagram of a transformer monitoring system 30 for estimating the end of life (EOL) of transformers 10A and 10B. The transformer monitoring system 30 according to some embodiments can monitor one or more transformers 10A, 10B. In some embodiments, the transformer monitoring system 30 is integrated into the transformer 10A provided as a device for monitoring and life assessment, while in other embodiments, the transformer monitoring system 30 is separate from the monitored transformers 10A, 10B.

[0117] The transformer monitoring system 30 includes a processor circuit 34, a communication interface 32 coupled to the processor circuit, and a memory 36 coupled to the processor circuit 34. The memory 36 includes machine-readable computer program instructions that, when executed by the processor circuit, cause the processor circuit to perform some of the operations described herein. For example, the transformer monitoring system 30 may perform the operations of the transformer aging estimator 200.

[0118] As shown, the transformer monitoring system 30 includes a communication interface 32 (also referred to as a network interface) configured to provide communication with other devices, such as sensors 20 in the transformers 10A, 10B, via a wired or wireless communication channel 14 .

[0119] Transformer monitoring system 30 also includes processing circuitry 34 (also referred to as a processor) and memory 36 (also referred to as memory) coupled to processing circuitry 34. According to other embodiments, processing circuitry 34 may be defined to include memory, such that separate memory circuitry is not required.

[0120] As discussed herein, operations of the transformer monitoring system 30 may be performed by the processing circuitry 34 and / or the communication interface 32. For example, the processing circuitry 34 may control the communication interface 32 to transmit communications to one or more other devices via the communication interface 32 and / or to receive communications from one or more other devices via the network interface. Furthermore, modules may be stored in the memory 36, and these modules may provide instructions such that, when the instructions of the modules are executed by the processing circuitry 34, the processing circuitry 34 performs corresponding operations (e.g., the operations discussed herein with respect to the example embodiments).

[0121] Transformers 10A, 10B (which may be, for example, high-voltage transformers) include an oil-filled chamber 12. Sensors 20 are disposed within or adjacent to the oil-filled chamber 12. Sensors 20 measure various quantities associated with transformers 10A, 10B, such as operating load, ambient temperature, moisture, and / or oxygen content, and transmit the measurements to a transformer monitoring system 30 via a communication channel 14. Communication channel 14 may include a wired or wireless link, and in some embodiments may include a wireless local area network (WLAN) or a cellular communication network, such as a 4G or 5G communication network.

[0122] The transformer monitoring system 30 receives online or offline measurements of operating load, temperature, moisture, and / or oxygen content from the transformers 10A, 10B and processes these measurements to determine the expected end-of-life (EOL) of the transformers 10A, 10B. Although depicted as a standalone device, the transformer monitoring system 30 can be implemented in a server, a server cluster, and / or a cloud-based remote server system that provides asset monitoring. The transformer monitoring system 30 can obtain measurement data from one transformer and / or multiple transformers.

[0123] The transformer monitoring system 30 described herein can be implemented in many different ways. For example, according to some embodiments, the transformer monitoring system 30 can receive online and offline data, and the received data can be used by machine learning techniques configured in the device for learning and classification to identify different behavioral patterns (e.g., transformer parameters related to season, electrical load, or time of day), which can be considered for estimation / simulation described in various embodiments. The device can be connected to one or more transformers 10 to receive measurement data.

[0124] In some embodiments, the transformer monitoring system 30 may be connectable to receive measurement data associated with a number of transformers 10 .

[0125] Figure 20BThe diagram illustrates various functional modules that may be stored in the memory 36 of the transformer monitoring system 30. The modules may include an aging factor measurement module 36A for obtaining measurements from the sensors 20 in the transformer 10 via the communication interface 32, a future aging prediction module 36B for generating an estimate of the effective future aging of the transformer, a past aging estimation module 36C for generating an estimate of the past aging of the transformer based on, for example, actual aging factors experienced by the transformer, and an aging factor model 36D for estimating a future aging factor curve.

[0126] In the above description of various embodiments of the present invention, it should be understood that the terms used herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention. Unless otherwise defined, all terms used herein (including technical terms and scientific terms) have the same meaning as those commonly understood by those skilled in the art to which the present invention belongs. It should be further understood that the terms as defined in commonly used dictionaries should be interpreted as having a meaning consistent with their meaning in the context of this specification and in the relevant field.

[0127] When an element is referred to as being "connected to," "coupled to," "responsive to" (or variations thereof) another element, it may be directly connected to, coupled to, or responsive to another element, or there may be intermediate elements. In contrast, when an element is referred to as being "directly connected to," "directly coupled to," "directly responsive to" (or variations thereof) another element, there are no intermediate elements. Throughout the text, the same numbers refer to the same elements. In addition, "coupling," "connecting," "responsiveness" or variations thereof used herein may include wireless coupling, connection or response. Unless the context clearly indicates otherwise, as used herein, the singular forms "one," "a," and "said" are intended to include plural forms. For the sake of brevity and / or clarity, well-known functions or configurations may not be described in detail. The term "and / or" includes any and all combinations of one or more of the associated listed items.

[0128] It should be understood that although the terms first, second, third, etc. can be used herein to describe various elements / operations, these elements / operations should not be limited by these terms. These terms are only used to distinguish one element / operation from another element / operation. Therefore, without departing from the teachings of the present invention, the first element / operation in some embodiments can be referred to as the second element / operation in other embodiments. Throughout this specification, the same reference numerals or the same figure indicators represent the same or similar elements.

[0129] As used herein, the terms "comprises," "includes," "has," or variations thereof are open ended and include one or more stated features, integers, elements, steps, parts, or functions, but do not preclude the presence or addition of one or more other features, integers, elements, steps, parts, functions, or combinations thereof.

[0130] This article describes example embodiments with reference to block diagrams and / or flow charts of computer-implemented methods, devices (systems and / or equipment) and / or computer program products. It should be understood that the blocks of the block diagrams and / or flow charts and the combination of blocks in the block diagrams and / or flow charts can be implemented by computer program instructions executed by one or more computer circuits. These computer program instructions can be provided to a processor circuit of a general-purpose computer circuit, a special-purpose computer circuit and / or other programmable data processing circuit to produce a machine so that the instructions executed by the processor of the computer and / or other programmable data processing device convert and control transistors, values ​​stored in memory locations, and other hardware components within such circuits to implement the functions / actions specified in the block diagrams and / or one or more flow chart blocks, and thereby create a device (function) and / or structure for implementing the functions / actions specified in the block diagrams and / or (multiple) flow chart blocks.

[0131] These computer program instructions may also be stored in a tangible computer-readable medium that can direct a computer or other programmable data processing apparatus to function in a particular manner such that the instructions stored in the computer-readable medium produce an article of manufacture comprising instructions that implement the functions / actions specified in the block diagram and / or one or more flowchart blocks. Thus, embodiments of the present inventive concept may be embodied in hardware and / or software (including firmware, resident software, microcode, etc.) that runs on a processor such as a digital signal processor, which may be collectively referred to as a "circuit," "module," or variations thereof.

[0132] It should also be noted that, in some alternative embodiments, the function / action annotated in the frame may not occur in the order annotated in the flow chart. For example, depending on the function / action involved, the two frames shown in succession may actually be performed substantially simultaneously, or these frames may sometimes be performed in reverse order. In addition, the function of a given frame of a flow chart and / or block diagram may be divided into multiple frames, and / or the function of two or more frames of a flow chart and / or block diagram may be at least partially integrated. Finally, without departing from the scope of the present invention, other frames may be added / inserted between the frames shown, and / or frames / operations may be omitted. In addition, although some of the figures in the figure include arrows on the communication paths to illustrate the main direction of communication, it should be understood that communication may occur in the direction opposite to the arrows depicted.

[0133] Without actually departing from the principles of the present invention, many changes and modifications can be made to the embodiments. All of these changes and modifications are intended to be included within the scope of the present invention. Therefore, the subject matter disclosed above should be considered illustrative rather than restrictive, and the examples of the embodiments are intended to cover all such modifications, enhancements, and other embodiments that fall within the spirit and scope of the present invention. Therefore, in order to obtain legal permission to the greatest extent, the scope of the present invention will be determined by the most widely allowed interpretation of the present disclosure, which includes examples of embodiments and their equivalents, and should not be limited to or restricted to the aforementioned specific detailed description.

Claims

1. A method for generating an expected remaining life of a transformer, the method comprising: generating a probabilistic model of factors affecting effective aging of the transformer; generating a plurality of probability curves of factors affecting the effective aging of the transformer based on the probability model; generating a plurality of probabilistic hot spot curves from the plurality of probability curves and a hot spot temperature characteristic of the transformer; simulating a plurality of future aging scenarios of the transformer based on the probabilistic hot spot curve; as well as An expected remaining lifetime of the transformer is estimated from the plurality of future aging scenarios.

2. The method according to claim 1, wherein The plurality of probability curves are generated for a first time period, and wherein the future aging scenario is generated within a second time period different from the first time period.

3. The method according to claim 2, wherein: Simulating the multiple future aging scenarios includes: generating a plurality of aging curves simulating aging of the transformer during the first time period; For each aging curve in the plurality of aging curves, estimating an effective aging amount of the transformer to provide a plurality of effective aging amounts; and The plurality of effective aging amounts are summed to provide an estimated effective aging amount during the second time period.

4. The method according to claim 3, wherein: The first time period comprises a 24-hour time period, and the second time period comprises a one-year time period.

5. The method according to any one of claims 1 to 4, wherein Factors that affect the effective aging of the transformer include: load conditions, ambient temperature, humidity levels within the transformer, and / or oxygen levels within the transformer.

6. The method according to any one of claims 1 to 4, wherein Simulating the plurality of future aging scenarios includes performing a Monte Carlo simulation of the future aging scenarios based on the plurality of probabilistic hot spot curves.

7. The method according to any one of claims 1 to 4, wherein Generating a probability curve of factors affecting the effective aging of the transformer includes generating a plurality of ambient temperature curves based on historical changes in ambient temperature.

8. The method of claim 7, wherein: The ambient temperature profile describes the expected ambient temperature over a predetermined period of time.

9. The method of claim 8, wherein: The method further includes generating the ambient temperature profile based on a probability distribution of ambient temperatures at a plurality of intervals within the predetermined time period.

10. The method of claim 9, wherein: The probability distribution includes a uniform probability distribution.

11. The method of claim 9, wherein: The probability distribution includes a probability distribution generated based on actual ambient temperature data.

12. The method according to any one of claims 1 to 4, wherein Generating a probability curve of factors affecting the effective aging of the transformer includes generating a plurality of expected load curves based on a predicted load of the transformer.

13. The method of claim 12, wherein: The expected load profile describes the expected load over a predetermined time period.

14. The method of claim 13, wherein: The method further includes generating the expected load profile based on a probability distribution at a plurality of time intervals within the predetermined time period.

15. The method of claim 14, wherein: The probability distribution includes a uniform probability distribution.

16. The method of claim 14, wherein: The probability distribution includes an estimate of the actual probability distribution of the expected load.

17. The method according to any one of claims 1 to 4, wherein Estimating the future aging of the transformer from the plurality of future aging scenarios includes generating a histogram of simulated future aging scenarios; as well as A confidence interval for the expected remaining lifetime of the transformer is generated based on a histogram of the simulated future aging scenarios and an associated mean and standard deviation of a distribution of the simulated future aging scenarios.

18. The method of claim 17, wherein: The future aging scenarios include expected annual aging scenarios, and the method further includes generating an estimate of the expected remaining lifetime of the transformer based on the nominal expected lifetime of the transformer and the expected annual aging scenarios.

19. The method according to any one of claims 1 to 4, wherein The method further comprises: collecting operational data indicative of factors affecting effective aging of the transformer during operation of the transformer; and A probabilistic model of factors affecting the effective aging of the transformer is updated.

20. The method of claim 19, wherein: The method further comprises: determining a current effective age of the transformer based on the operating data; The expected remaining life of the transformer is estimated based on the multiple future aging scenarios, the effective current age of the transformer, and the nominal expected life of the transformer.

21. The method according to any one of claims 1 to 4, wherein The probability model includes probability distributions of factors affecting the transformer aging.

22. The method of any one of claims 1 to 4, wherein: Factors affecting the transformer aging include ambient temperature and load, and wherein the probability model includes a uniform probability distribution.

23. The method of any one of claims 1 to 4, wherein: The method further includes performing maintenance on the transformer and / or adjusting a load on the transformer based on the estimated future aging of the transformer.

24. A method for estimating the expected remaining life of a transformer based on a probabilistic model of factors affecting transformer aging, the method comprising: collecting operational data indicative of factors affecting effective aging of the transformer during operation of the transformer; updating a probabilistic model of factors affecting effective aging of the transformer based on the operating data; and determining a current effective age of the transformer based on the operating data; The expected remaining life of the transformer is estimated from a plurality of future aging scenarios generated based on a probabilistic model of the factors, the effective current age of the transformer, and the nominal expected life of the transformer.

25. The method of claim 24, wherein: Collecting the operating data includes collecting the operating data from sensors in the transformer.

26. The method of claim 24 or 25, wherein: Factors that affect the effective aging of the transformer include: load conditions, ambient temperature, humidity levels within the transformer, and / or oxygen levels within the transformer.

27. A device for estimating future aging of a transformer, the device comprising: processing circuit; as well as a memory coupled to the processing circuit, wherein the memory stores computer program instructions that, when executed by the processing circuit, cause the apparatus to perform operations comprising: generating a probabilistic model of factors affecting effective aging of the transformer; generating a plurality of probability curves of factors affecting effective aging of the transformer within a first time period based on the probability model; generating an expected hot spot curve from the probability curve and the hot spot temperature characteristic of the transformer; simulating a plurality of future aging scenarios for the transformer based on the expected hot spot curves during a second time period; and The future aging of the transformer is estimated from the plurality of future aging scenarios.

28. The apparatus of claim 27, wherein: Factors that affect the effective aging of the transformer include: load conditions, ambient temperature, humidity levels within the transformer, and / or oxygen levels within the transformer.

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