An electrical equipment automatic control and fault prediction system based on digital twinning

CN122548976APending Publication Date: 2026-08-11TURUI BOWEN (BEIJING) ELECTRICAL TECHNOLOGY CO LTD
View PDF 0 Cites 0 Cited by

Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-05-13
Publication Date
2026-08-11

AI Technical Summary

Technical Problem

顶层油温监测只能反映变压器整体的热状态,无法识别绕组局部的热点温度变化

Benefits of technology

[0007]本发明的有益效果在于:本发明通过将谐波阶次平方纳入附加损耗计算,提高了电磁损耗计算的准确性,能够感知新能源波动与谐波导致的局部热点变化。通过同步重构热点温度和绝缘含水率耦合状态,实现了热湿耦合状态感知,能够识别湿迁移与热效应共同导致的泡化风险。通过构造油纸界面泡化裕度侵蚀速率,将泡化裕度的时间变化、结构空间曲率和水分迁移通量统一为同一量纲的连续状态量,实现了泡化前沿发展速度的定量表征。通过将泡化剩余时间映射为控制作用时域并自动转换为冷却和降载控制量,实现了预测结果到可执行控制量的直接映射,形成了预测控制验证的完整闭环。本发明通过基于物理机理的数字孪生模型构建方法,减少了对大量真实故障样本的依赖,适配低故障率电力设备的运行监测需求。

✦ Generated by Eureka AI based on patent content.

Smart Images

  • Figure CN122548976A_ABST
    Figure CN122548976A_ABST
Patent Text Reader

Abstract

This invention relates to the field of electrical equipment fault prediction technology, and discloses an automated control and fault prediction system for electrical equipment based on digital twins. The system includes: calculating the heat source power of each physical segment; reconstructing the hot spot temperature and insulation moisture content of each physical segment; calculating the bubbling margin; calculating the equivalent erosion rate and equivalent margin; calculating the remaining bubbling time; calculating the fan duty cycle and current limit; and executing commands. This invention achieves thermal-humidity coupling state perception by synchronously reconstructing the coupled state of hot spot temperature and insulation moisture content. It can identify the bubbling risk caused by both moisture migration and thermal effects. By constructing the bubbling margin and erosion rate of the oil-paper interface, and mapping the remaining bubbling time to the control action time domain and automatically converting it into cooling and load reduction control quantities, it achieves direct mapping from prediction results to executable control quantities, adapting to the operation monitoring needs of low-failure-rate power equipment.
Need to check novelty before this filing date? Find Prior Art

Description

Technical Field

[0001] This invention relates to the field of electrical equipment fault prediction technology, and more specifically, to an electrical equipment automation control and fault prediction system based on digital twins. Background Technology

[0002] Oil-immersed main transformers are core equipment in power systems, and their safe and stable operation directly affects the reliability of power supply. In renewable energy collection stations, main transformers need to withstand frequent load changes caused by fluctuations in output from photovoltaic, wind power, and energy storage, while also facing complex environmental conditions. Currently, condition monitoring and fault prediction of oil-immersed transformers mainly employ two techniques: dissolved gas analysis in the oil and top oil temperature monitoring. Dissolved gas analysis in the oil determines the equipment fault state by detecting the composition and content of gases produced by decomposition in the insulating oil, while top oil temperature monitoring assesses the thermal state of the equipment by measuring the temperature of the top oil layer of the transformer. Digital twin technology has been increasingly applied to the field of power equipment condition monitoring in recent years, achieving condition reconstruction and trend prediction by constructing a virtual mapping of physical equipment.

[0003] Existing technologies have certain limitations in practical applications. Dissolved gas analysis in oil reflects the results of gas generation, dissolution, diffusion, and sampling, exhibiting a significant time lag. By the time gas anomalies are detected, serious insulation defects may have already formed inside the equipment. Top-level oil temperature monitoring can only reflect the overall thermal state of the transformer and cannot identify local hot spot temperature changes in the windings. Current digital twin applications mostly focus on visualizing equipment status and providing simple trend predictions, failing to effectively integrate prediction results with automated control. Control actions are typically triggered passively after a fault alarm, making it difficult to cope with rapidly changing operating conditions.

[0004] The root cause of these shortcomings lies in the fact that existing technologies primarily focus on the characteristics of the consequences after a fault occurs, rather than the changes in physical quantities during the fault evolution process. They fail to adequately consider the coupling effects of thermal effects, moisture migration, and material aging on the insulation state. Furthermore, existing prediction methods often output discrete fault level or type labels, failing to provide quantitative indicators with control significance and hindering the direct conversion of prediction results into control commands. Therefore, a technical solution is urgently needed that can identify the insulation fault evolution process in advance and achieve a closed-loop prediction and control system. Summary of the Invention

[0005] This invention provides an electrical equipment automation control and fault prediction system based on digital twins, which solves the technical problems mentioned in the background.

[0006] This invention provides an electrical equipment automation control and fault prediction system based on digital twins, comprising: The heat source power calculation module collects the operating current, harmonic current, adjacent oil zone temperature, oil moisture and cooler operating power of each physical section, and calculates the heat source power of each physical section by combining the resistance value and harmonic loss conversion factor. The parameter reconstruction module inputs the heat source power of each physical section, the temperature of adjacent oil areas, the moisture content in the oil, and the operating power of the cooler into the digital twin model to reconstruct the hot spot temperature and insulation moisture content of each physical section. The foaming margin calculation module updates the degree of polymerization of insulation based on the hot spot temperature, calculates the critical temperature for foaming based on the moisture content of insulation, and obtains the foaming margin by subtracting the hot spot temperature from the critical temperature for foaming. The interface erosion rate calculation module calculates the interface erosion rate based on the time change of blistering margin, spatial curvature, and spatial gradient of insulation moisture content. It also performs area weighting on the positive value of the interface erosion rate and the blistering margin to obtain the equivalent erosion rate and equivalent margin. The bubbling time calculation module divides the equivalent margin by the equivalent erosion rate to obtain the bubbling time. The temperature rise reduction calculation module determines the control time domain based on the remaining time of bubbling, calculates the temperature rise to be reduced in combination with the design margin, and obtains the fan duty cycle and current limit from the temperature rise to be reduced. The parameter execution module performs cooling control according to the fan duty cycle, limits the load power according to the current limit, and recalculates the hot spot temperature, foaming margin and foaming time in the digital twin model for the next control cycle.

[0007] The beneficial effects of this invention are as follows: By incorporating the square of the harmonic order into the calculation of additional losses, this invention improves the accuracy of electromagnetic loss calculation and can detect changes in local hotspots caused by new energy fluctuations and harmonics. By synchronously reconstructing the coupling state of hotspot temperature and insulation moisture content, it achieves the perception of thermal-humid coupling state and can identify the foaming risk caused by the combined effects of moisture migration and thermal effects. By constructing the foaming margin erosion rate of the oil-paper interface, it unifies the temporal change of foaming margin, structural spatial curvature, and moisture migration flux into continuous state quantities of the same dimension, realizing a quantitative characterization of the foaming front development speed. By mapping the remaining foaming time to the control action time domain and automatically converting it into cooling and load reduction control quantities, it achieves a direct mapping from prediction results to executable control quantities, forming a complete closed loop for predictive control verification. This invention, through a digital twin model construction method based on physical mechanisms, reduces the dependence on a large number of real fault samples and adapts to the operation monitoring needs of low-failure-rate power equipment. Attached Figure Description

[0008] Figure 1 This is a calculation flowchart of an electrical equipment automation control and fault prediction system based on digital twins according to the present invention. Detailed Implementation

[0009] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, features described in some examples may be combined in other examples.

[0010] It should be noted that, unless otherwise defined, the technical or scientific terms used in one or more embodiments of the present invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in one or more embodiments of the present invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" indicate that the element or object preceding the term encompasses the elements or objects listed following the term and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0011] like Figure 1 As shown, an electrical equipment automation control and fault prediction system based on digital twins includes: The heat source power calculation module is used to collect the operating current, harmonic current, adjacent oil zone temperature, water content in the oil and cooler operating power of each physical section, and calculate the heat source power of each physical section by combining the resistance value and harmonic loss conversion factor. The parameter reconstruction module is used to input the heat source power of each physical section, the temperature of adjacent oil areas, the moisture content in the oil, and the operating power of the cooler into the digital twin model to reconstruct the hot spot temperature and insulation moisture content of each physical section. The foaming margin calculation module is used to update the degree of polymerization of insulation based on the hot spot temperature, calculate the critical temperature of foaming based on the moisture content of insulation, and obtain the foaming margin by subtracting the hot spot temperature from the critical temperature of foaming. The interface erosion rate calculation module is used to calculate the interface erosion rate based on the time change of blistering margin, spatial curvature, and spatial gradient of insulation moisture content. It also performs area weighting on the positive value of the interface erosion rate and the blistering margin to obtain the equivalent erosion rate and equivalent margin. The foaming time calculation module is used to divide the equivalent margin by the equivalent erosion rate to obtain the foaming time. The temperature rise reduction calculation module is used to determine the control time domain based on the remaining foaming time, calculate the temperature rise to be reduced in combination with the design margin, and obtain the fan duty cycle and current limit from the temperature rise to be reduced. The parameter execution module is used to perform cooling control according to the fan duty cycle, limit the load power according to the current limit, and recalculate the hot spot temperature, foaming margin and foaming time in the digital twin model for the next control cycle.

[0012] In one embodiment of the present invention, the formula for calculating the heat source loss power based on the effective value of the operating current, the winding copper resistance value, and the additional loss coefficient is as follows: in, Indicates the current time No. The heat source loss power of each physical segment Indicates the current time No. Each physical segment is affected by the hotspot temperature value. The influence of the winding copper resistance value. Indicates the current time No. Hotspot temperature values ​​for each physical segment Represents the set of harmonic orders. Indicates the harmonic order value. Indicates the current time No. The physical segment in the first Harmonic current amplitude at each order value Indicates the first Additional loss coefficient for each physical segment.

[0013] It should be noted that the structural additional loss coefficient is a user-defined parameter used to convert the additional eddy current losses and leakage magnetic structural losses caused by higher-order harmonics into equivalent ohmic dimensions. A preferred value is 0.01 to 0.05, obtained through factory testing based on the main transformer winding structure and core material characteristics. The specific calibration method involves measuring the total loss and fundamental loss under different harmonic contents during the main transformer's factory load test. The additional loss is obtained by subtracting the fundamental loss from the total loss, and then the structural additional loss coefficient is calculated based on the ratio of the additional loss to the sum of the squares of the harmonic currents. For a conventional 220kV oil-immersed main transformer, a typical value for the structural additional loss coefficient is 0.03.

[0014] The harmonic order set is the set of all harmonic orders involved in the loss calculation. The elements in this set are integers, representing harmonic components of different orders.

[0015] Specifically, the selection range of the harmonic order set should at least include the 3rd, 5th, 7th, 11th, and 13th harmonics commonly found in the operation of the main transformer of the renewable energy collection station. It should be noted that in practical applications, this set can be appropriately expanded based on on-site harmonic monitoring results, for example, by adding higher-order harmonics such as the 17th and 19th, but the aforementioned 5th harmonic is a fundamental component that must be included. Specifically, for renewable energy collection stations that primarily use photovoltaic and wind power, the 3rd and 5th harmonic content is usually high, while the 11th and 13th harmonics are mainly generated by power electronic converter equipment.

[0016] Specifically, the effective value of the operating current can be obtained by current transformers installed on the high-voltage and low-voltage sides of the main transformer. The amplitude of the harmonic current can be obtained by performing a fast Fourier transform analysis on the current signal collected by the current transformer. The winding copper resistance value can be obtained from the main transformer's factory test report and corrected according to the current hot spot temperature value.

[0017] It should be noted that incorporating the square of the harmonic order into the calculation of additional losses accurately reflects the amplification effect of higher-order harmonics on additional eddy current losses, enabling digital twins to perceive the fluctuations in new energy sources and the changes in local hotspots caused by harmonics. Specifically, as the harmonic order increases, eddy current losses increase at a rate equal to the square of the harmonic order. This characteristic is ignored in traditional calculations of total load current losses, leading to an underestimation of local hotspot temperatures. For example, when a 13th harmonic exists with an amplitude of 10% of the fundamental current, the resulting additional eddy current losses are approximately 16.9 times those generated by the fundamental current.

[0018] In one embodiment of the present invention, the calculation formula for reconstructing the hot spot temperature value based on the heat source loss power, the temperature of adjacent oil zones, and the operating power of the cooler is as follows: in, Indicates the first The equivalent heat capacity values ​​of each physical segment Indicates the current time No. The rate of change of hot spot temperature in each physical segment Indicates the first The equivalent thermal conductivity of each physical segment Indicates the current time No. Temperature of adjacent oil zones in each physical segment Indicates the current time No. The operating power of the cooler in each physical segment; Based on the hot spot temperature value, the insulation moisture content value, and the moisture content in the oil, the formula for reconstructing the insulation moisture content value is as follows: in, Indicates the current time No. The rate of change of insulation moisture in each physical segment Indicates the first Moisture diffusion coefficient of each physical segment Indicates the current time No. The moisture content value of each physical segment insulation along the axial spatial coordinate The second spatial derivative, Indicates the first The axial spatial coordinates of each physical segment Indicates the first Desorption rate coefficients of each physical segment Indicates the first The desorption activation energy of each physical segment Represents the molar gas constant. Indicates the current time No. The water content in the oil of each physical segment Indicates the first Moisture balance coefficient of each physical segment Indicates the current time No. The insulation moisture content value of each physical segment.

[0019] It should be noted that the equivalent heat capacity is a user-defined parameter, representing the equivalent heat capacity of a single physical segment. A preferred value is between 10,000 J / K and 50,000 J / K, calculated based on the volume, material density, and specific heat capacity of the physical segment. For the winding disc structure of a conventional 220kV main transformer, the typical equivalent heat capacity of a single physical segment is 25,000 J / K.

[0020] The equivalent thermal conductivity is a user-defined parameter, representing the equivalent thermal conductivity from a single physical segment hotspot to adjacent oil zones. A preferred value is 50 W / K to 200 W / K, obtained through thermal simulation calculations based on oil channel dimensions, oil flow velocity, and the thermal conductivity of the insulating paper. A typical equivalent thermal conductivity value for a conventional 220kV main transformer is 120 W / K.

[0021] The moisture diffusion coefficient is a user-defined parameter and represents the rate of moisture diffusion in paper insulation. A preferred value is [value to be filled in]. to This is determined experimentally based on the type of paper insulation material and its temperature characteristics. At 20℃, the typical value for the moisture diffusion coefficient of ordinary insulating paper is [value missing]. .

[0022] The desorption rate coefficient is a user-defined parameter, representing the rate at which moisture at the oil-paper interface desorbs from the insulating paper into the transformer oil. A preferred value is [value to be filled in]. to This is obtained through experimental determination based on the interfacial and temperature characteristics of the oil-paper mixture. At 20℃, the typical value for the desorption rate coefficient is... .

[0023] The desorption activation energy is a user-defined parameter, representing the activation energy required for moisture to desorb from the insulating paper. A preferred value is 40 kJ / mol to 60 kJ / mol, determined experimentally based on the characteristics of the paper insulation material. A typical desorption activation energy for ordinary insulating paper is 50 kJ / mol.

[0024] The moisture balance coefficient is a user-defined parameter, representing the conversion factor between the moisture content in the oil and the moisture content of the paper insulation when the oil-paper interface reaches moisture balance. A preferred value is 0.01 to 0.1, obtained experimentally based on temperature characteristics. At 20℃, a typical value for the moisture balance coefficient is 0.05.

[0025] Specifically, the principle of constructing the thermal-humidity reduced-order model is to discretize the three-dimensional heat conduction, oil flow, and moisture migration problem of the main transformer winding oil passages into multiple physical segments along the axial direction. Each segment is described by a lumped parameter model, preserving the core physical relationship of thermal-humidity coupling. It should be noted that this reduced-order model ignores the radial temperature and moisture distribution differences, considering only the axial changes. This simplification, while ensuring computational accuracy, can significantly improve the online calculation speed and meet the requirements of real-time control.

[0026] Specifically, the temperature of adjacent oil zones can be acquired using fiber optic temperature sensors installed in the oil channels. The water content in the oil can be acquired using a water content sensor installed in the oil tank. The cooler's operating power can be acquired using a cooler status acquisition unit, which can monitor the operating status and power consumption of the cooler fan and oil pump in real time.

[0027] It is important to note that simultaneously reconstructing the coupled state of hotspot temperature and insulation moisture content, rather than calculating temperature or moisture separately, can identify the foaming risk caused by the combined effects of moisture migration and thermal effects. Specifically, increased temperature accelerates the diffusion of moisture in paper insulation and its desorption from the oil-paper interface, while increased moisture content lowers the foaming initiation temperature, creating a positive feedback effect. Calculating temperature or moisture separately would not accurately assess the foaming risk resulting from this coupling effect. For example, when the hotspot temperature increases by 10°C, the moisture diffusion coefficient increases by approximately two times, while the foaming initiation temperature decreases by approximately 5K due to moisture migration.

[0028] In one embodiment of the present invention, the calculation formula for updating the degree of polymerization of insulation based on the hot spot temperature value and the aging rate coefficient is as follows: in, Indicates the current time No. The degree of polymerization decay rate of each physical segment Indicates the first The aging rate coefficient of each physical segment Indicates the first The aging activation energy of each physical segment Indicates the current time No. The degree of insulation polymerization value of each physical segment; Based on the degree of polymerization and moisture content of the insulation, the formula for calculating the critical temperature for bubbling is as follows: in, Indicates the current time No. The critical temperature for foaming in each physical segment. Indicates the first The reference foaming temperature for each physical segment Indicates the first Aggregate conversion factor for each physical segment Indicates the first The baseline degree of polymerization value for each physical segment. Indicates the first Moisture conversion factor for each physical segment; The calculation steps for the foaming margin value are as follows: subtract the hot spot temperature value from the foaming critical temperature value to obtain the foaming margin value.

[0029] It should be noted that the aging rate coefficient is a user-defined parameter, representing the rate at which the degree of polymerization of the paper insulation decreases with temperature. A preferred value is [value to be filled in]. to This is determined through accelerated aging tests based on the properties and temperature characteristics of paper insulation materials. The typical aging rate coefficient for ordinary insulating paper at 100℃ is [value missing]. .

[0030] The aging activation energy is a user-defined parameter, representing the activation energy required for the aging reaction of paper insulation. A preferred value is 80 kJ / mol to 120 kJ / mol, determined through accelerated aging tests based on the characteristics of the paper insulation material. The typical aging activation energy for ordinary insulating paper is 100 kJ / mol.

[0031] The reference bubbling temperature is a user-defined parameter, representing the initial bubbling temperature of the physical segments under baseline conditions. A preferred value is 140℃ to 160℃, determined experimentally based on the characteristics of the paper insulation material. A typical reference bubbling temperature for ordinary insulating paper is 150℃.

[0032] The baseline degree of polymerization is a user-defined parameter, representing the degree of polymerization of the paper insulation in the physical segments under baseline conditions. A preferred value is 1000 to 1200, which is the value measured during factory testing before a new transformer is put into operation. A typical baseline degree of polymerization value for a conventional new transformer is 1100.

[0033] The polymerization conversion factor is a user-defined parameter that represents the conversion factor for changes in the degree of polymerization with respect to the foaming initiation temperature. A preferred value is -10K to -5K, obtained through experimental determination of the foaming initiation temperature at different degrees of polymerization. A typical value for the polymerization conversion factor is -7K.

[0034] The moisture conversion factor is a user-defined parameter that represents the conversion factor for the foaming initiation temperature based on changes in the moisture content of the paper insulation. A preferred value is 5K / % to 10K / %, obtained through experimental determination of the foaming initiation temperature at different moisture contents. A typical value for the moisture conversion factor is 7K / %.

[0035] Specifically, the baseline state is defined as the initial state of a new transformer under standard conditions of 20℃ and 50% relative humidity before it is put into operation. It should be noted that in practical applications, for transformers already in operation, an oil sample can be taken to test the degree of polymerization of the paper insulation. The test result can be used as the current baseline degree of polymerization value, and the initial baseline degree of polymerization value can be calculated by combining it with historical operating data.

[0036] Specifically, the degree of polymerization of insulation can be obtained through periodic oil sample analysis using high-performance liquid chromatography (HPLC), or it can be calculated in real time using a digital twin model based on historical operating temperature data. In this invention, the real-time calculation results from the digital twin model are preferred, with periodic corrections made using experimental test results.

[0037] It should be noted that incorporating both aging degree and moisture content into the calculation of the foaming initiation temperature, instead of the traditional fixed temperature threshold, can reflect the changes in the critical foaming temperature under different aging and moisture content conditions. Specifically, paper insulation aging leads to the breakage of cellulose molecular chains, resulting in a decrease in mechanical strength and dielectric properties, thus lowering the foaming initiation temperature; while an increase in moisture content causes water to vaporize at high temperatures, lowering the critical temperature for bubble formation. For example, when the degree of polymerization decreases from 1100 to 500, the foaming initiation temperature decreases by approximately 5K; when the moisture content increases from 1% to 3%, the foaming initiation temperature decreases by approximately 14K.

[0038] In one embodiment of the present invention, the formula for calculating the interface erosion rate based on the bubbling margin value and the insulation moisture content value is as follows: in, Indicates the current time No. The interface erosion rate of each physical segment Indicates the current time No. The margin time decay of each physical segment Indicates the current time No. The foaming margin value for each physical segment. Indicates the first Curvature participation coefficient of each physical segment Indicates the first The insulation and thermal conductivity of each physical segment Indicates the first The insulation density values ​​of each physical segment. Indicates the first The specific heat capacity of insulation in each physical segment. Indicates the current time No. The foaming margin values ​​of each physical segment are along the axial spatial coordinate. The second margin curvature, Indicates the first The wet-flux participation coefficient of each physical segment Indicates the reference temperature scale value. Indicates the first The characteristic length value of each physical segment Indicates the current time No. The moisture content value of each physical segment insulation along the axial spatial coordinate The first-order moisture gradient; Based on the interface erosion rate, the formula for calculating the equivalent erosion rate is as follows: in, Indicates the current time The equivalent erosion rate, Indicates the first The area value of each physical segment; The formula for calculating the equivalent margin value based on the foaming margin value is as follows: in, Indicates the current time The equivalent margin value.

[0039] It should be noted that the curvature participation factor is a user-defined parameter that characterizes the strength of the influence of oil channels, winding structure, and paper insulation arrangement on the bending propagation of the foaming front in the physical segment. The preferred value is between 0.1 and 1.0, obtained through thermal simulation calculations based on the main transformer winding structure and oil channel arrangement. For a conventional disc-shaped winding structure, a typical value for the curvature participation factor is 0.5.

[0040] Thermal conductivity is the coefficient of thermal conductivity of paper insulation materials. This parameter is an inherent property of the material; the typical value for the thermal conductivity of ordinary insulating paper is 0.15. .

[0041] The insulation density value refers to the density of the paper insulation material. This parameter is an inherent property of the material; the typical insulation density value for ordinary insulating paper is 1200 kg / m³.

[0042] The specific heat capacity of paper insulation material is its specific heat capacity. This parameter is an inherent property of the material; the typical specific heat capacity of ordinary insulating paper is 1300 kJ / m³. .

[0043] The wet-through participation factor is a user-defined parameter that characterizes the degree to which moisture migration participates in the foaming margin erosion. A preferred value is 0.1 to 1.0, obtained through experimental determination based on the environmental humidity and main transformer sealing performance in coastal areas. For main transformers operating in coastal areas, a typical wet-through participation factor value is 0.8.

[0044] The reference temperature scale is a user-defined parameter used to convert the moisture migration term into an equivalent temperature erosion rate. A preferred value is 10K to 50K, obtained by experimentally determining the correlation between the moisture migration rate and the rate of decrease in foaming allowance. A typical reference temperature scale value is 20K.

[0045] The physical segment area is the area of ​​the oil-paper interface of a single physical segment. This parameter can be calculated based on the geometry of the main transformer winding. For the winding disc structure of a conventional 220kV main transformer, the typical area of ​​a single physical segment is 0.5m².

[0046] The characteristic length value is a user-defined parameter, representing the characteristic length of a single physical segment along the axial direction. A preferred value is 50mm to 150mm, which corresponds to the discrete axial length of the physical segment.

[0047] Specifically, the discretization principle for physical segments is to discretize the main transformer winding along its axial direction into multiple physical segments at equal intervals or according to the winding disc structure. The axial length of each segment does not exceed 100mm to ensure the capture of local hot spots and the bubbling front. It should be noted that discretization according to the winding disc structure is the preferred method because the winding disc is the basic structural unit of the main transformer winding, and the electromagnetic and thermal characteristics of each winding disc are relatively uniform. For example, the high-voltage winding of a 220kV main transformer typically has 20 winding discs, which can be discretized into 20 physical segments, each with an axial length of approximately 80mm.

[0048] Specifically, the physical meaning of area weighting is that the risk of foaming at the oil-paper interface is positively correlated with the interface area, and area weighting can more accurately reflect the overall foaming risk level of the structural surface. Specifically, when the area of ​​a certain physical segment is large, the probability of foaming failure and its impact range are also large; therefore, it should be assigned a greater weight when calculating the equivalent quantity of the structural surface.

[0049] It should be noted that constructing the erosion rate based on the foaming margin at the oil-paper interface unifies the temporal variation of the foaming margin, the spatial curvature of the structure, and the water migration flux into a continuous state quantity of the same dimension, thereby achieving a quantitative characterization of the foaming front development speed. Specifically, the foaming front is not a fixed point, but an interface that varies with time and space, and its development speed is influenced by multiple factors. By constructing an erosion rate with a unified dimension, these complex influencing factors can be integrated into a quantifiable index, facilitating subsequent prediction and control. For example, when a local bend occurs at the foaming front, the spatial curvature term increases, leading to a faster erosion rate and indicating a sharp increase in the risk of localized foaming.

[0050] In one embodiment of the present invention, the formula for calculating the expected remaining foaming time based on the forward interface erosion rate and the forward foaming margin value is as follows: in, Indicates the current time Calculate the determined estimated remaining foaming time. This represents a tiny positive real number that is eroded. The calculation steps for the estimated time of foaming failure, based on the current running time and the estimated remaining time of foaming, are as follows: add the current running time to the estimated remaining time of foaming to obtain the estimated time of foaming failure.

[0051] It should be noted that the erosion micro-positive real number is a user-defined parameter used to prevent oddly shaped micro-positive values ​​from occurring when calculating the remaining bubble-forming time, as the denominator is zero or close to zero. The preferred value is [value missing]. to That is, it is determined according to the system's required computational accuracy. When the system's computational accuracy is high, a smaller value can be used; when the computational accuracy is low, a larger value can be used. A typical value for the erosion of a small positive real number is... .

[0052] Specifically, the range of values ​​for the erosion of small positive real numbers is: to The specific value is determined based on the system's calculation accuracy requirements. It should be noted that this parameter should not be too large, otherwise the calculated remaining bubble time will be too low, leading to unnecessary control actions; nor should it be too small, otherwise numerical singularity problems cannot be effectively prevented. In practical applications, the optimal value can be determined through simulation testing.

[0053] Specifically, the current operating time value can be obtained through the system clock, which should be synchronized with the power dispatching system clock to ensure time accuracy.

[0054] It should be noted that the remaining foaming time is calculated by the ratio of the area-weighted sum of the positive foaming margin to the area-weighted sum of the positive erosion rate, outputting a time quantity with control significance rather than the traditional binary label of normal or abnormal. Specifically, traditional fault prediction methods usually only output two states, normal or abnormal, and cannot provide the specific time of fault occurrence, resulting in a lack of specificity and timeliness in control actions. The remaining foaming time output by this invention directly reflects the urgency of the fault occurrence, providing a quantitative basis for subsequent control action decisions. For example, when the remaining foaming time is 10 minutes, immediate emergency cooling and load reduction measures are required; when the remaining foaming time is 2 hours, conventional cooling measures can be taken.

[0055] In one embodiment of the present invention, the calculation steps for calculating the control action time domain based on the scheduling control cycle value and the expected remaining bubbling time are as follows: multiply the scheduling control cycle value by the expected remaining bubbling time and divide by the sum of the two to obtain the control action time domain; Based on the equivalent margin value and the equivalent erosion rate, the formula for calculating the required reduction in temperature rise is as follows: in, Indicates the current time The temperature rise needs to be reduced. This indicates the design margin value. Indicates the current time The control action time domain; Based on the equivalent heat capacity value, the formula for calculating the global structural equivalent heat capacity is as follows: in, Indicates the global structural equivalent heat capacity; The calculation steps for the target cooling command power are as follows, based on the required temperature rise reduction value and the current basic cooling power: multiply the global structural equivalent heat capacity by the required temperature rise reduction value, divide by the control action time domain, and add the current basic cooling power to obtain the target cooling command power. The calculation steps for the actual fan duty cycle based on the target cooling command power and the maximum fan heat dissipation power are as follows: divide the target cooling command power by the maximum fan heat dissipation power, take the maximum value of zero and the minimum value of zero to obtain the actual fan duty cycle. The formula for calculating the power loss reduction required based on the actual wind turbine duty cycle is as follows: in, Indicates the current time The need to reduce power loss Indicates the current time The actual duty cycle of the wind turbine This indicates the maximum fan cooling capacity. Indicates the current time The current base cooling power; Based on the sum of the first currents, the formula for calculating the global equivalent copper loss is as follows: in, Indicates the current time Global structural equivalent copper loss; Based on the required reduction in power loss and the equivalent copper loss of the overall structure, the formula for calculating the current operating limit is as follows: in, Indicates the current time Current operating limit value, Indicates the current time The effective value of the operating current, It represents a small positive real number representing power.

[0056] It should be noted that the dispatch control cycle value is the control cycle of the power dispatching system or automated control system. This parameter is determined according to the requirements of the power dispatching system and is usually consistent with the dispatch cycle of the new energy collection station.

[0057] The design margin value is a custom parameter, representing the desired bubble-forming safety temperature difference that the system should retain after control. A preferred value is 5K to 10K, determined based on power industry standards and equipment operating experience. A typical design margin value is 7K.

[0058] The current base cooling power is the heat dissipation power that the cooling system has been operating at the current moment. This parameter can be obtained through the cooler status acquisition unit.

[0059] The maximum fan cooling capacity is the maximum cooling capacity that the cooler or fan system can provide. This parameter can be obtained from the main transformer's factory test report.

[0060] The small positive real power value is a user-defined parameter used to prevent the denominator from being zero when calculating the current operating limit. The preferred value is between 1W and 100W, determined based on the system's calculation accuracy requirements. A typical value for the small positive real power value is 10W.

[0061] Specifically, the design margin value is determined based on power industry standards and equipment operating experience, typically ranging from 5K to 10K, to ensure sufficient safety margin for the system after control. It should be noted that the design margin value should not be too large, otherwise it will lead to unnecessary load shedding and affect the transmission of renewable energy; nor should it be too small, otherwise the safety margin after control cannot be guaranteed. In practical applications, this value can be appropriately adjusted according to the importance and service life of the main transformer.

[0062] Specifically, the typical value for the scheduling control cycle is 1 to 5 minutes, matching the scheduling cycle of the new energy aggregation station. It should be noted that the scheduling control cycle should not be too long, otherwise it will lead to lag in control actions and an inability to respond promptly to rapid changes in bubble formation risk; nor should it be too short, otherwise it will increase the system's computational and communication burden.

[0063] Specifically, the effective value of the operating current can be obtained through a current transformer. The global structural equivalent copper loss is the area-weighted average of the copper losses of each physical segment, used to characterize the average copper loss level of the entire winding.

[0064] Specifically, the system generates wind turbine duty cycles and current operating limits, which are then transmitted via the IEC 61850 standard communication interface. The wind turbine duty cycle command is sent directly to the cooler control cabinet, which adjusts the operating status of each wind turbine accordingly. The current operating limit is sent to the dispatch automation system of the renewable energy collection station, which adjusts the output of each renewable energy source based on this value to ensure that the operating current of the main transformer does not exceed the limit.

[0065] It should be noted that the remaining bubble formation time is mapped to the control action time domain, and when the cooling capacity is insufficient, the remaining risk is automatically converted into load current limiting, achieving predictive drive closed-loop control. Specifically, the control action time domain refers to the time it should take for the system to complete the cooling or load reduction action. This time is related to the remaining bubble formation time. When the remaining bubble formation time is short, the control action time domain is correspondingly shortened, requiring a rapid system response; when the remaining bubble formation time is long, the control action time domain is correspondingly extended, allowing for more gradual control measures. When the maximum heat dissipation capacity of the cooling system is insufficient to eliminate the bubble formation risk, the system automatically calculates the power loss that needs to be reduced and converts it into a current operating limit value. By limiting the load current, electromagnetic losses are reduced, thereby controlling the bubble formation risk.

[0066] In one embodiment of the present invention, the calculation formula for calculating the hot spot temperature of the next prediction cycle based on the heat source loss power and the control prediction step size is as follows: in, Indicates the number of the next forecast period The next predicted hotspot temperature for each physical segment. Indicates the control prediction step size, Indicates the first The maximum allocated heat dissipation power of each physical segment; The calculation steps for calculating the foaming margin for the next prediction cycle, based on the foaming critical temperature and the hot spot temperature of the next prediction cycle, are as follows: subtract the hot spot temperature of the next prediction cycle from the foaming critical temperature to obtain the foaming margin for the next prediction cycle. Based on the bubbling margin and interface erosion rate for the next prediction cycle, the formula for calculating the remaining bubbling time for the next prediction cycle is as follows: in, Indicates the current time Calculated remaining time for bubbling in the next forecast period. Indicates the number of the next forecast period Bubble margin for the next prediction period of each physical segment.

[0067] It should be noted that the control prediction step size is a user-defined parameter, representing the time interval between the next control or prediction operation. The preferred value is the same as the dispatch control cycle value, i.e., synchronized with the control cycle of the power dispatch system.

[0068] The maximum allocated heat dissipation power is a user-defined parameter, representing the maximum cooling capacity distributed across a single physical segment. This means it is dynamically allocated based on the hotspot temperature and foaming margin of each physical segment.

[0069] Specifically, the matching relationship between the control prediction step size and the scheduling control cycle is that the control prediction step size should be equal to the scheduling control cycle value to ensure that the prediction result is synchronized with the control action. It should be noted that when the scheduling control cycle changes, the control prediction step size should also be adjusted accordingly to maintain the synchronization between the two.

[0070] Specifically, the principle for allocating the maximum cooling power is to dynamically distribute it based on the hot spot temperature and foaming margin of each physical segment. Segments with higher hot spot temperatures and smaller foaming margins are allocated more cooling power. Specifically, a proportional allocation method can be used, meaning the cooling power allocated to each physical segment is directly proportional to the difference between its hot spot temperature and the average hot spot temperature, and inversely proportional to its foaming margin. For example, if the hot spot temperature of a physical segment is 10°C higher than the average hot spot temperature, and its foaming margin is 5K lower than the average foaming margin, its allocated cooling power will be approximately twice the average allocated power.

[0071] Specifically, when the system detects missing or out-of-range data from a sensor, it automatically uses the average value of the previous three cycles for that sensor as a substitute value for calculation. If the same sensor detects abnormal data for three consecutive cycles, the system issues a sensor fault alarm and switches to a backup calculation mode, using the interpolation result of adjacent physical segments to replace the measurement value of the segment containing the abnormal sensor.

[0072] Specifically, every 24 hours, the system automatically performs an online correction of the digital twin model's parameters using the day's actual operating data. The correction method involves comparing the actual measured top-layer oil temperature, oil moisture content, and DGA data with the model's prediction results, and adjusting the values ​​of each user-defined parameter using the least squares method to minimize the deviation between the model's prediction results and the actual measured data.

[0073] It should be noted that after executing the control command, the same digital twin model is used to predict the physical results after control, providing a state basis for the next round of control and forming a complete predictive control verification closed loop. Specifically, traditional control methods typically only execute control commands without verifying the control effect, making it impossible to adjust the control strategy in a timely manner. However, this invention, after executing the control command, immediately predicts the hotspot temperature, foaming margin, and safe operating time after control, and feeds the prediction results back to the digital twin model as input for the next round of prediction and control. This closed-loop control method can continuously optimize the control strategy and improve control performance. For example, if the predicted foaming margin after control is still lower than the design reserve margin, the system will further increase the cooling power or reduce the current limit value in the next control cycle.

[0074] Specifically, the system deployment of this invention is divided into two parts: hardware deployment and software deployment. Hardware deployment includes installing current transformers on the high-voltage and low-voltage sides of the main transformer, installing fiber optic temperature sensors in the winding oil channels, installing oil moisture sensors in the oil tank, connecting to existing DGA sampling devices and cooler status acquisition units, and deploying a digital twin server and communication gateway. Software deployment includes installing digital twin model software, data processing software, and control decision software on the digital twin server, configuring IEC61850 communication parameters, and completing communication connections with the dispatch automation system and cooler control cabinet.

[0075] After system deployment, the following steps are followed: First, the system collects real-time data from each sensor and transmits it to the digital twin server via a communication gateway. Then, the digital twin model sequentially calculates the heat source power of each physical segment, reconstructs the hotspot temperature and insulation moisture content, calculates the aging-corrected foaming initiation temperature and foaming margin, calculates the interface erosion rate and structural surface equivalents, predicts the foaming front arrival time, generates feedback control variables, and issues them for execution. Finally, the system predicts the physical results after control, providing a state basis for the next round of control.

[0076] In actual operation, the system outputs control results every minute. For example, when the system predicts a remaining foaming time of 30 minutes, the generated fan duty cycle is 0.7, and the current operating limit is 95% of the rated current. When the system predicts a remaining foaming time of 10 minutes, the generated fan duty cycle is 1.0, and the current operating limit is 80% of the rated current. The system also outputs status parameters such as hot spot temperature, insulation moisture content, foaming margin, and erosion rate for each physical segment for operators to view and analyze.

[0077] It should be noted that the interval and threshold sizes are set for ease of comparison. The size of the threshold depends on the amount of sample data and the base number set by those skilled in the art for each set of sample data, as long as it does not affect the proportional relationship between the parameter and the quantized value. Furthermore, the above formulas are all dimensionless calculations, and the formulas are derived from software simulations using a large amount of collected data to obtain a formula that is closest to the real situation. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0078] The content of this embodiment has been described above, but this embodiment is not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms based on the guidance of this embodiment, all of which are within the protection scope of this embodiment.

Claims

1. A digital-twin-based electrical equipment automation control and fault prediction system, characterized in that, include: The heat source power calculation module collects the operating current, harmonic current, adjacent oil zone temperature, water content in the oil, and cooler operating power of each physical section, and calculates the heat source power of each physical section by combining the resistance value and harmonic loss conversion factor. The parameter reconstruction module inputs the heat source power of each physical section, the temperature of adjacent oil areas, the moisture content in the oil, and the operating power of the cooler into the digital twin model to reconstruct the hot spot temperature and insulation moisture content of each physical section. The foaming margin calculation module updates the degree of polymerization of insulation based on the hot spot temperature, calculates the critical temperature for foaming based on the moisture content of insulation, and obtains the foaming margin by subtracting the hot spot temperature from the critical temperature for foaming. The interface erosion rate calculation module calculates the interface erosion rate based on the time change of blistering margin, spatial curvature, and spatial gradient of insulation moisture content. It also performs area weighting on the positive value of the interface erosion rate and the blistering margin to obtain the equivalent erosion rate and equivalent margin. The bubbling time calculation module divides the equivalent margin by the equivalent erosion rate to obtain the bubbling time. The temperature rise reduction calculation module determines the control time domain based on the remaining time of bubbling, calculates the temperature rise to be reduced in combination with the design margin, and obtains the fan duty cycle and current limit from the temperature rise to be reduced. The parameter execution module performs cooling control according to the fan duty cycle, limits the load power according to the current limit, and recalculates the hot spot temperature, foaming margin and foaming time in the digital twin model for the next control cycle.

2. The digital-twin-based electrical equipment automatic control and fault prediction system according to claim 1, wherein, Obtain the effective value of the operating current, the set of harmonic orders, the order value, the amplitude of the harmonic current, the copper resistance value of the winding, and the additional loss coefficient; after squaring the amplitude of the harmonic current, accumulate it according to the set of harmonic orders to obtain the first current sum, combine it with the hot spot temperature value to correct the copper resistance value of the winding, and multiply it by the first current sum to obtain the basic copper loss power. Multiply the square of the order value by the square of the harmonic current amplitude, and then sum them according to the set of harmonic orders to obtain the second current summation. The additional eddy current power is obtained by multiplying the additional loss coefficient by the sum of the second current; the heat source loss power is obtained by adding the basic copper loss power to the additional eddy current power.

3. The digital-twin-based electrical equipment automatic control and fault prediction system according to claim 1, wherein Obtain the equivalent heat capacity, equivalent thermal conductivity, moisture diffusion coefficient, desorption rate coefficient, desorption activation energy, molar gas constant, moisture balance coefficient, temperature of adjacent oil zones, moisture content in oil, and cooler operating power; The conductive heat dissipation power is obtained by subtracting the temperature of the adjacent oil zone from the hot spot temperature and multiplying the result by the equivalent thermal conductivity. After subtracting the heat dissipation power and the cooler operating power from the heat source loss power, divide by the equivalent heat capacity value to obtain the hot spot temperature change rate. Integrate the hot spot temperature change rate along the time axis to obtain the hot spot temperature value. The second-order partial derivative of the insulation moisture content value along the axial spatial coordinate is obtained and multiplied by the moisture diffusion coefficient to obtain the internal moisture diffusion rate. The desorption activation energy is divided by the molar gas constant and the hot spot temperature, and the negative value is used as the exponent of the natural constant. This exponent is then multiplied by the desorption rate coefficient to obtain the desorption intensity coefficient. Subtract the product of the moisture balance coefficient and the insulation moisture content from the moisture content in the oil to obtain the interfacial moisture concentration difference, and then multiply it by the desorption intensity coefficient to obtain the interfacial desorption flux. The insulation moisture change rate is obtained by adding the internal moisture diffusivity to the interfacial desorption flux, and then integrating along the time axis to obtain the insulation moisture content value.

4. The digital-twin-based electrical equipment automatic control and fault prediction system according to claim 1, wherein, Obtain the aging rate coefficient, aging activation energy, reference foaming temperature, reference degree of polymerization value, polymerization conversion factor, and moisture conversion factor; The aging activation energy is divided by the molar gas constant and the hot spot temperature, and the negative value is used as the base of the natural constant to calculate the exponent. This exponent is then multiplied by the aging rate coefficient and the degree of polymerization of the insulation to obtain the degree of polymerization decay. The degree of polymerization decay is then negative to obtain the degree of polymerization change rate. This is then integrated along the time axis to obtain the degree of polymerization of the insulation. Divide the degree of polymerization of the insulation by the reference degree of polymerization and take the natural logarithm, then multiply by the polymerization conversion factor to obtain the aging correction temperature difference; The moisture correction temperature difference is obtained by multiplying the moisture conversion factor by the insulation moisture content value. The foaming critical temperature is obtained by adding the aging correction temperature difference to the baseline foaming temperature and then subtracting the moisture correction temperature difference; the foaming margin is obtained by subtracting the hot spot temperature value from the foaming critical temperature.

5. The digital-twin-based electrical equipment automatic control and fault prediction system according to claim 1, wherein, Obtain the curvature participation factor, insulation thermal conductivity, insulation density, insulation specific heat capacity, moisture participation factor, reference temperature scale value, physical segment area value, and characteristic length value; The time decay of the bubbling margin is obtained by taking the negative first partial derivative of the bubbling margin value along the time axis; the absolute value of the second partial derivative of the bubbling margin value along the axial spatial coordinate is multiplied by the curvature participation coefficient and the thermal conductivity of the insulation, and then divided by the product of the insulation density value and the insulation specific heat capacity value to obtain the curvature erosion rate.

6. The digital-twin-based electrical equipment automatic control and fault prediction system according to claim 5, wherein, The absolute value of the insulation moisture content value along the axial spatial coordinate is obtained by taking the first partial derivative, multiplying it by the moisture diffusion coefficient, the moisture participation coefficient, and the reference temperature scale value, and dividing it by the characteristic length value to obtain the moisture migration erosion rate; the interface erosion rate is obtained by adding the margin time decay amount, the curvature erosion rate, and the moisture migration erosion rate. The positive interface erosion rate is obtained by taking the maximum value of zero for the interface erosion rate, multiplying it by the physical segment area value and summing them globally to obtain the equivalent positive erosion sum; the physical segment area value is summed globally to obtain the total area value of the global structure; the equivalent positive erosion sum is divided by the total area value of the global structure to obtain the equivalent erosion rate; the physical segment area value is multiplied by the bubbling margin value and summed globally, then divided by the total area value of the global structure to obtain the equivalent margin value.

7. The digital-twin-based electrical equipment automatic control and fault prediction system according to claim 1, wherein, Obtain the small positive real number of erosion and the value at the current running time; take the maximum value of the bubbling margin value and zero, multiply it by the physical segment area value and sum it globally to obtain the positive margin surface accumulation sum; Multiply the small positive real erosion number by the total area of ​​the global structure, and then add the equivalent positive erosion sum to obtain the safe equivalent erosion denominator. The estimated remaining time for bubbling is obtained by summing the positive margin surface and dividing by the safety equivalent erosion denominator; the estimated remaining time for bubbling is obtained by adding the current running time value to the estimated remaining time for bubbling.

8. The digital-twin-based electrical equipment automatic control and fault prediction system according to claim 6, wherein, Obtain the scheduling control cycle value, design margin value, current basic cooling power, maximum fan heat dissipation power, small positive real power value, and effective value of operating current; Multiply the scheduling control cycle value by the expected remaining bubbling time, and then divide by the sum of the two to obtain the control action time domain; multiply the equivalent erosion rate by the control action time domain to obtain the predicted equivalent margin decay during the period. The value of the required temperature rise reduction is obtained by subtracting the predicted amount of the equivalent margin decay during the period from the equivalent margin value and then subtracting it from the design retention margin value. Multiply the physical segment area value by the equivalent heat capacity value and sum them globally, then divide by the total area value of the global structure to obtain the global equivalent heat capacity of the structure. Multiply the global structural equivalent heat capacity by the required temperature rise reduction value, divide by the control action time domain, and add the current base cooling power to obtain the target cooling command power.

9. The electrical equipment automation control and fault prediction system based on digital twins according to claim 8, characterized in that, The actual fan duty cycle is obtained by dividing the target cooling command power by the maximum fan heat dissipation power and taking the maximum value of zero and the minimum value. Multiply the actual fan duty cycle by the maximum fan cooling power to obtain the expected cooling power; subtract the expected cooling power from the target cooling command power and take the maximum value of zero to obtain the power loss to be reduced. Multiply the physical segment area value by the winding copper resistance value and the sum of the first current, and then sum them globally. Finally, divide by the total area value of the global structure to obtain the global equivalent copper loss. The load loss reduction ratio is obtained by dividing the power to be reduced by the sum of the global structural equivalent copper loss and the power by a small positive real number; the load loss reduction ratio is subtracted from the constant value, and the arithmetic square root of the maximum value is multiplied by the effective value of the operating current to obtain the current operating limit value.

10. The electrical equipment automation control and fault prediction system based on digital twin according to claim 1, characterized in that, Obtain the control prediction step size and the maximum allocated heat dissipation power; Divide the current operating limit value by the effective value of the operating current and square it, then multiply it by the heat source loss power to obtain the limited predicted heat source power. The equivalent thermal conductivity is multiplied by the boundary temperature difference to obtain the constrained predicted conduction power. Multiply the actual fan duty cycle by the maximum allocated heat dissipation power to obtain the limited predicted cooling power; Subtract the limited predicted conduction power and the limited predicted cooling power from the limited predicted heat source power to obtain the predicted net heat power; Divide the predicted net heat power by the equivalent heat capacity value and multiply by the control prediction step size to obtain the predicted temperature rise change. Add the predicted temperature rise change to the hot spot temperature value to obtain the hot spot temperature for the next prediction cycle. Subtracting the hot spot temperature of the next prediction period from the critical foaming temperature yields the foaming margin for the next prediction period. The bubble margin for the next prediction period is taken as the maximum value of zero, multiplied by the physical segment area value and globally accumulated, and then divided by the safe equivalent erosion denominator to obtain the remaining bubble time for the next prediction period.