Thermo-chemical digital twinning of power transformers

Abstract

Currently, it is not possible to install sensors within power transformers to directly measure water content in the solid insulation of the windings. As a result, the extent of the degradation of the insulation is typically not known without maintenance intervention. Accordingly, the disclosed embodiments model the thermo-chemical degradation in the digital twin of the transformer based on the water content in the insulation liquid and the load on the transformer to continuously estimate the water content in segments of the insulation. This estimated water content can take into account the diffusion between the insulation liquid and the insulation, as well as the water generated in the insulation material by cellulose degradation. The estimated water content can be used to estimate other parameters, such as the total water content in the transformer, a measure of the aging of the transformer, etc., as well as inform the maintenance schedule of the transformer.

Description

[0001] Cross-reference to related applications

[0002] This application claims priority to U.S. Provisional Patent Application No. 63 / 440,843, filed January 24, 2023, which is incorporated herein by reference in its entirety. Background Technology

[0003] Invention Field

[0004] The embodiments described herein generally relate to digital twins of power transformers, and more specifically, to modeling thermochemical degradation in digital twins of power transformers.

[0005] BACKGROUND

[0006] The remaining life of a power transformer is typically associated with the life of its internal solid insulation. While temperature is the most relevant parameter in calculating the lifespan of a power transformer, the influence of water and oxygen content cannot be ignored, especially under partial load conditions. For example, water negatively impacts dielectric capacitance and degrades insulation. However, water is a natural byproduct of the aging of solid insulators (e.g., paper or other cellulose-based materials) and insulating liquids (e.g., mineral oil, liquid esters, etc.). In fact, water removal is one of the most common reasons for maintenance interventions in power transformers.

[0007] One challenge in evaluating power transformers within a power grid is the inability to measure many parameters related to their performance and health. Sensors can interfere with field distribution and output biased measurements. Therefore, sensors cannot be used to measure the water content in the solid insulation inside a power transformer. Furthermore, even if a sample is removed from a critical location within the insulation, it will no longer represent the same conditions after being cooled to ambient temperature and / or immersed in any liquid other than the insulating fluid found inside the power transformer.

[0008] Therefore, directly measuring the water content in the solid insulation of a power transformer is not feasible. Therefore, this disclosure relates to thermochemical degradation modeling in a digital twin of a power transformer, enabling the estimation of the water content in the solid insulation. This disclosure also relates to one or more other problems identified by the inventors. Summary of the Invention

[0009] Systems, methods, and non-transitory computer-readable media for modeling thermo-chemical degradation in a digital twin of a power transformer are disclosed. One aspect of one or more disclosed embodiments is estimation of total water content in an insulating body of a power transformer based on both diffusion between an insulating liquid and the insulating body and degradation of the insulating body. Another aspect is logically dividing the power transformer into a plurality of sections such that total water content in the insulating body of each section can be estimated. Yet another aspect is utilizing artificial intelligence to adjust the total water content in the power transformer in order to account for leaks, hydrolysis, and / or other chemical processes.

[0010] In one embodiment, a method for modeling thermo-chemical degradation in a digital twin of a power transformer includes, using at least one hardware processor, for each of one or more time intervals: determining a total water content in an insulating liquid of the power transformer; for each of a plurality of sections of at least one winding of the power transformer logically divided along at least one axis of the at least one winding, estimating a temperature of the section based on a load of the power transformer and a temperature gradient along the at least one axis, estimating a diffusion-related water content in an insulating body of the at least one winding in the section caused by diffusion based on the estimated temperature and the total water content in the insulating liquid, estimating a degradation-related water content based on degradation of a material of the insulating body, and estimating a total water content within the insulating body of the at least one winding in the section based on the diffusion-related water content and the degradation-related water content; and estimating a total water content in the power transformer based on the total water content in the insulating liquid and the total water content within the insulating body of the at least one winding in all of the plurality of sections.

[0011] The method can further include determining, using the at least one hardware processor, for each of the one or more time intervals, an average temperature of the insulating liquid for each of a plurality of time instants spanning the time interval. The plurality of sections can include at least one lower stack representing a first assembly element at a first end of the at least one winding along the longitudinal axis, at least one upper stack representing a second assembly element at a second end of the at least one winding opposite the first end of the at least one winding along the longitudinal axis, and one or more coil sections each representing at least a portion of at least one coil between the first end and the second end of the at least one winding. The temperature gradient can include an axial temperature gradient along the axial axis and a radial temperature gradient along the radial axis, and estimating the temperature of each of the plurality of sections can include, for each of the plurality of time instants: calculating a localized temperature of the at least one lower stack based on the axial temperature gradient calculated for the time instant and the average temperature of the insulating liquid; calculating a localized temperature of the at least one upper stack based on the axial temperature gradient calculated for the time instant and the average temperature of the insulating liquid; and calculating a localized temperature for each of the one or more coil sections based on the temperature of the at least one lower stack or the at least one upper stack, the load, and the radial temperature gradient and the axial temperature gradient. The one or more coil sections can be a plurality of coil sections, and the temperature of one of the plurality of coil sections closest to the second end can be further calculated based on a hot spot coefficient or a heat dissipation coefficient associated with the power transformer.

[0012] Estimating the diffusion-related water content can include, for each of the plurality of time instants spanning the time interval, calculating a water content diffused into the insulation based on a time constant for diffusion of water into a material of the insulation. For each of the plurality of time instants, the water content diffused into the insulation can be calculated as:

[0013]

[0014] where W diffusion is the water content diffused into the insulation at time instant t, W equilibrium is the water content in the insulation at equilibrium conditions, W initial is the water content in the insulation at a time instant immediately preceding time instant t, e is Euler’s number, and τ p is a time constant.

[0015] The material of the insulation can be cellulose-based. The degradation-related water content in the insulation can be estimated based on a water generation rate from a breakage of cellulose chains in the cellulose-based material. The water generation rate can be calculated as:

[0016]

[0017] where W rate is the amount of water generated per hour, k is the number of breaks, Mol water is the molar mass of water, DP is the degree of polymerization of the material of the insulator, and Mol glucose is the molar mass of the monomer of glucose.

[0018] The method can further include, using the at least one hardware processor, for each of one or more time intervals, for each of a plurality of sections of the at least one winding in the power transformer, calculating a measure of aging for the section based on the total water content in the insulator; and determining an overall measure of aging of the power transformer based on the measures of aging for the plurality of sections. The measure of aging for each of the plurality of sections can be further based on one or both of an oxygen content in the insulator or an acidity of the insulating liquid. Calculating the measure of aging for each of the plurality of sections can include determining a nominal aging parameter associated with a material of the insulator; interpolating an aging parameter for the section based on the total water content in the insulator of the at least one winding in the section; and calculating an aging ratio between the nominal aging parameter and the interpolated aging parameter. Calculating the measure of aging for each of the plurality of sections can also include determining an activation energy under a nominal condition associated with the material of the insulator; interpolating the activation energy of the material of the insulator; calculating an exponential coefficient based on the activation energy under the nominal condition and the interpolated activation energy; and determining the measure of aging for the section based on the aging ratio and the exponential coefficient. The measure of aging for each of the plurality of sections can be calculated as:

[0019]

[0020] where V is the measure of aging, A is the interpolated aging parameter, A r is the nominal aging parameter, e is Euler’s number, R is the molar gas constant, E r is the activation energy under the nominal condition, E is the interpolated activation energy, Q h,r is the hot spot to top oil temperature under a nominal load, and Q h is the hot spot temperature.

[0021] Determining the total water content in the insulating liquid can include deriving the total water content in the insulating liquid from an output of at least one sensor in the power transformer, and the method can further include, using the at least one hardware processor, for each of one or more time intervals at least once: calculating a deviation between an actual value of the total water content in the insulating liquid derived from the output of the at least one sensor and one or more estimated values of the total water content in the insulating liquid output by the digital twin artificial intelligence (AI) model; and determining an adjustment parameter based on the deviation, wherein the estimation of the total water content in the transformer is further based on the adjustment parameter.

[0022] The method can further include estimating, using the at least one hardware processor, a risk of dielectric failure of the insulation of the at least one winding based on the estimated total water content within the insulation.

[0023] The method can further include estimating, using the at least one hardware processor, a likelihood of microbubbles on a surface of the insulation of the at least one winding based on the estimated total water content within the insulation.

[0024] The method can further include using the at least one hardware processor to: estimate a breakdown voltage of the insulating liquid based on the total water content within the insulating liquid; and generate an alert when the estimated breakdown voltage satisfies a threshold.

[0025] It will be appreciated that any of the features in the above-described methods can be implemented alone, or in any combination with any subset of the other features. Accordingly, to the extent that the appended claims suggest particular combinations of features, the disclosed embodiments are not limited to these particular claim combinations. Rather, any of the features described herein can be combined with any other feature described herein, or implemented in any combination of features without requiring any one or more of the other features described herein.

[0026] Further, any of the methods described above and elsewhere herein can be embodied in an executable software module of a processor-based system (such as a server), and / or in executable instructions stored in a non-transitory computer-readable medium. BRIEF DESCRIPTION OF DRAWINGS

[0027] The details of the application, both as to its structure and operation, can be gleaned in part by study of the accompanying figures, in which like reference numerals refer to like parts, and in which:

[0028] FIG. 1 An example infrastructure according to an embodiment is shown, in which one or more of the processes described herein can be implemented;

[0029] FIG. 2 An example processing system according to an embodiment is shown, through which one or more of the processes described herein can be executed;

[0030] FIG. 3 A schematic illustration of a discretized power transformer according to an embodiment is shown;

[0031] FIG. 4 A process for modeling thermal-chemical degradation in a digital twin of a power transformer according to an embodiment is shown;

[0032] FIG. 5 Chemical illustrations of two monomers of glucose according to an example are shown;

[0033] FIG. 6 Water content of the insulating liquid and the insulator in a simulated power transformer is shown for tested implementations according to embodiments;

[0034] FIG. 7 Water generation from cellulose degradation in a simulated power transformer is shown for tested implementations according to embodiments;

[0035] FIG. 8 Measurements of aging for a simulated power transformer are shown for tested implementations according to embodiments. DETAILED DESCRIPTION

[0036] In embodiments, systems, methods, and non-transitory computer-readable media for modeling thermal-chemical degradation in a digital twin of a power transformer are disclosed. Upon reading this specification, those skilled in the art will appreciate various alternative embodiments and obvious modifications to the embodiments described herein. However, it is to be understood that the embodiments described herein are merely exemplary and illustrative, and are not restrictive in terms of the scope of the disclosure. Accordingly, the detailed description of various embodiments should not be construed as limiting the scope or breadth of the disclosure as set forth in the appended claims.

[0037] Conventional methods of estimating thermal-chemical degradation of a power transformer include measuring water content in the insulating liquid (e.g., by a sensor or manual sampling), testing the power transformer during a planned outage (e.g., measuring power factor, insulation resistance, dielectric frequency response, etc.), or draining the insulating liquid and measuring the dew point of the insulator after twenty-four hours of contact with dry air.

[0038] The least invasive of these methods is monitoring water content in the insulating liquid via a sensor. However, this monitoring is not trivial. Neither the load nor the ambient temperature remains stable for long enough for the system to reach equilibrium conditions. Therefore, any measurement is only a snapshot of a transient condition. Conventional procedures “correct” the water content to conditions at a reference temperature of 20 degrees Celsius (°C). Above a temperature reference of 20 °C, the water saturation in mineral oil approximately doubles for every 40 °C increase in temperature. Therefore, a reading in parts per million (ppm) has a completely different meaning when the temperature of the mineral oil is 20 °C than when the temperature of the mineral oil is 100 °C. In response to this, a typical approach is to check the water content relative to saturation at the sampling temperature under different load conditions and ambient temperatures in an effort to identify a model.

[0039] In a second conventional method, the average water content in a power transformer can be estimated by measuring the dielectric loss factor between terminals over a range of frequencies. However, this only gives an average measurement of the water content for the entire power transformer. It cannot estimate the water content at a specific location within the power transformer.

[0040] A third conventional method is to measure the dew point. However, this method is very labor intensive. It requires draining the insulating liquid from the power transformer, evacuating the surroundings of the insulation, filling the vacuum with dry air, and waiting for a certain equilibrium between the surface of the insulation and the air. The change in water content in the air, measured by the change in its dew point, provides a good estimate of the average water content at the surface of the insulation. Again, this method cannot estimate the water content at a specific location within the power transformer, such as the hottest spot (i.e., hot spot) of the power transformer during operation.

[0041] In contrast to these conventional methods, the disclosed embodiments implement a thermo-chemical digital twin of a power transformer. This thermo-chemical digital twin represents a mathematical model of the conditions experienced by the real physical power transformer. The parameters estimated by the digital twin accurately correspond to the parameters of the real power transformer, given that both start under the same conditions and are subjected to the same loads and temperatures.

[0042] Furthermore, no system is completely sealed, and chemical reactions that generate and / or consume water can occur inside the real power transformer. Therefore, in embodiments, the digital twin can utilize artificial intelligence (AI) to continuously correct the total water content inside the power transformer based on the measurements of water in the insulating liquid output by the moisture sensors in the monitoring system of the power transformer. For example, the water content estimated by the digital twin can be continuously or continuously compared to the water content derived from the moisture sensors, and the deviation between the two values of water content can be used to correct the total water content in the power transformer estimated by the digital twin. This keeps the calculations in the digital twin meaningful and technically reasonable.

[0043] FIG. 1 An example infrastructure according to embodiments is shown in which one or more of the disclosed processes can be implemented. The infrastructure can include a platform 110 (e.g., one or more servers) that hosts and / or executes one or more of the various processes, methods, functions, and / or software modules described herein, including, for example, a thermo-chemical digital twin. The platform 110 can include dedicated servers, or can alternatively be implemented in a computing cloud in which resources of one or more servers are dynamically and elastically allocated to multiple tenants based on demand. In either case, the servers can be co-located and / or distributed by geographic location. The platform 110 can execute a server application 112 that can utilize a database 114.

[0044] The platform 110 can be communicatively connected to one or more user systems 130 via one or more networks 120. The platform 110 can also be communicatively connected to one or more monitoring systems 140 via one or more networks 120. Each monitoring system 140 can monitor one or more parameters in one or more power transformers 150.

[0045] The network(s) 120 can include the Internet, and the platform 110 can communicate with the user system(s) 130 and / or the monitoring system(s) 140 over the Internet using standard transmission protocols (such as Hypertext Transfer Protocol (HTTP), HTTP Secure (HTTPS), File Transfer Protocol (FTP), FTP Secure (FTPS), Secure Shell FTP (SFTP), and the like, as well as proprietary protocols). While the platform 110 is shown as being connected to each system through a single group of network(s) 120, it should be understood that the platform 110 can be connected to each system via different groups of one or more networks. For example, the platform 110 can be connected to a subset of the user systems 130 and / or the monitoring systems 140 via the Internet, but can be connected to one or more other user systems 130 and / or monitoring systems 140 via an intranet. Furthermore, while only a single platform 110, user system 130, and monitoring system 140 are shown, it should be understood that this infrastructure can include any number of platforms 110, user systems 130, and monitoring systems 140.

[0046] The user systems 130 can include any type of computing device capable of wired and / or wireless communication, including but not limited to a desktop computer, a laptop computer, a tablet computer, a smartphone or other mobile phone, a server, a game console, a television, a set-top box, an electronic kiosk, or the like. However, it is generally expected that the user systems 130 will include a workstation or personal computing device of a user responsible for operating and / or maintaining the power transformers 150. Each user system 130 can execute a client application 132, which can utilize a local database 134.

[0047] The monitoring system(s) 140 can include any type of device capable of wired and / or wireless communication. In the simplest form, the monitoring system 140 can be a sensor configured to measure a parameter of the power transformer 150 and output a signal to the platform 110 representing a value of the measured parameter. In a more complex form, the monitoring system 140 can include a computing device that receives signals output by one or more sensors configured to measure one or more parameters of the power transformer 150. In this case, the monitoring system 140 can relay raw data represented by the output signal(s) from the sensor(s) to the platform 110 or pre-process the raw data and send the pre-processed data to the platform 110. In any case, the sensor(s) can include a moisture sensor that measures a water content of an insulating liquid inside the power transformer 150.

[0048] The platform 110 can include a web server hosting one or more websites and / or web services. In embodiments in which a website is provided, the website can include a graphical user interface, e.g., including one or more screens (e.g., web pages) generated in hypertext markup language (HTML) or other languages. The platform 110 can transmit or serve one or more screens of the graphical user interface in response to requests from the user system(s) 130. In some embodiments, the screens can be provided in the form of a wizard, in which case two or more screens can be provided in a sequential manner, and one or more of the sequential screens can depend on the user or user system 130’s interaction with one or more prior screens. The requests to the platform 110 and responses from the platform 110, including screens of the graphical user interface, can be communicated using standard communication protocols (e.g., HTTP, HTTPS, etc.) over the network(s) 120, which can include the Internet. The screens (e.g., web pages) can include a combination of content and elements, such as text, images, video, animation, references (e.g., hyperlinks), frames, inputs (e.g., text boxes, text areas, checkboxes, radio buttons, drop-down menus, buttons, forms, etc.), scripts (e.g., JavaScript), etc., including elements that include or are derived from data stored in the database 114. It will be appreciated that the platform 110 can also respond to other requests (e.g., unrelated to the graphical user interface) from the user system(s) 130.

[0049] The platform 110 can include a database 114 that is communicatively coupled with, or otherwise has access to, the platform 110. For example, the platform 110 can include a database server that manages the database 114. The server applications 112 executing on the platform 110 and / or the client applications 132 executing on the user systems 130 can submit data (e.g., user data, form data, etc.) to be stored in the database 114 and / or request access to data stored in the database 114. Any suitable database can be utilized, including but not limited to MySQL TM , Oracle TM , IBM TM , Microsoft SQL TM , Access TM , PostgreSQL TM , MongoDB TM , and the like, including cloud-based databases and proprietary databases. For example, data can be sent to the platform 110 using well-known POST requests supported by HTTP, via FTP, and the like. This data, as well as other requests, can be handled by server-side web technologies (e.g., a servlet or other software module (e.g., included in the server applications 112)) executed by the platform 110.

[0050] In embodiments in which a web service is provided, the platform 110 can receive requests from the user system(s) 130 and / or other external system(s) (e.g., which can themselves be servers) and provide responses in an extensible markup language (XML), JavaScript Object Notation (JSON), and / or any other suitable or desired format. In such embodiments, the platform 110 can provide an application programming interface (API) that defines the manner in which the user system(s) 130 and / or other external system(s) 140 can interact with the web service. Thus, the user system(s) 130 and / or other external system(s) 140 can define their own user interfaces and rely on the web service to implement or otherwise provide the backend processes, methods, functionality, storage, and the like described herein. For example, in such embodiments, the client applications 132 executing on one or more user systems 130 can interact with the server applications 112 executing on the platform 110 to perform one or more or portions of one or more of the various functionalities, processes, methods, and / or software modules described herein.

[0051] Client application 132 can be "thin," in which case processing is primarily performed on the server side by server application 112 on platform 110. A basic example of a thin client application 132 is a browser application that simply requests, receives, and renders web pages on user system(s) 130, while server application 112 on platform 110 is responsible for generating web pages and managing database functions. Alternatively, client application 132 can be "thick," in which case processing is primarily performed on the client side by user system(s) 130. It should be understood that, depending on the design goals of the specific implementation, client application 132 can perform a certain amount of processing relative to server application 112 on platform 110 at any point between the "thin" and "thick" spectrum. In any case, the software described herein may reside entirely on one of platform 110 (e.g., in this case, server application 112 performs all processing) or one or more user systems 130 (e.g., in this case, client application 132 performs all processing), or may be distributed between platform 110 and one or more user systems 130 (e.g., in this case, both server application 112 and client application 132 perform processing). The software may include one or more executable software modules, which include instructions for implementing one or more of the processes, methods, or functions described herein.

[0052] FIG. 2 An example wired or wireless system 200 is illustrated, which can be used in conjunction with various embodiments described herein. For example, system 200 can be used in conjunction with one or more of the processes, methods, or functions described herein (e.g., storing and / or executing software), and can represent components of platform 110, user system 130, monitoring system 140, and / or other processing devices described herein. System 200 can be any processor-enabled device (e.g., a server, personal computer, etc.) capable of wired or wireless data communication. Other processing systems and / or architectures may also be used, as will be apparent to those skilled in the art.

[0053] System 200 may include one or more processors 210. The processors 210 may include a central processing unit (CPU) or a main processor. Additional processors may also be provided, such as a graphics processing unit (GPU), an auxiliary processor for managing input / output, an auxiliary processor for performing floating-point mathematical operations, a special-purpose microprocessor (e.g., a digital signal processor) with a fast execution architecture suitable for signal processing algorithms, a slave processor (e.g., a back-end processor), an additional microprocessor or controller for a dual-processor or multi-processor system, and / or a coprocessor. Such auxiliary processors may be discrete processors or may be integrated with the main processor. Examples of processors 210 that may be used with system 200 include, but are not limited to, any processor supplied by Intel Corporation (Santa Clara, California) (e.g., a Pentium). TM Core i7 TM Core i9 TM Supreme TM Any processor supplied by AMD (Santa Clara, California), Apple (Cupertino), or Samsung Electronics (Seoul, South Korea) (e.g., Exynos processors). TM Any processor and / or similar processor supplied by NXP Semiconductors (Eindhoven, Netherlands).

[0054] One or more processors 210 may be connected to a communication bus 205. The communication bus 205 may include a data channel to facilitate information transfer between the system 200's memory and other peripheral components. Furthermore, the communication bus 205 may provide a set of signals for communicating with the processors 210, including a data bus, an address bus, and / or a control bus (not shown). The communication bus 205 may include any standard or non-standard bus architecture, such as, for example, Industry Standard Architecture (ISA), Extended Industry Standard Architecture (EISA), Micro Channel Architecture (MCA), Peripheral Component Interconnect (PCI) local bus, IEEE standards (including IEEE 488 Universal Interface Bus (GPIB), IEEE 696 / S-100), and / or similar bus architectures.

[0055] The system 200 can include a main memory 215. The main memory 215 provides storage of instructions and data for programs (such as any of the software disclosed herein) executing on the processor 210. It will be appreciated that programs stored in memory and executed by the processor 210 can be written and / or compiled according to any suitable language, including but not limited to C / C++, Java, JavaScript, Perl, Python, Visual Basic,.NET, and the like. The main memory 215 is typically a semiconductor-based memory, such as a dynamic random access memory (DRAM) and / or a static random access memory (SRAM). Other semiconductor-based memory types include, for example, synchronous dynamic random access memory (SDRAM), Rambus dynamic random access memory (RDRAM), ferroelectric random access memory (FRAM), and the like, including read only memory (ROM).

[0056] The system 200 can include a secondary memory 220. The secondary memory 220 is a non-transitory computer-readable medium on which is stored computer-executable code and / or other data (e.g., any of the software disclosed herein). As used herein, the term “computer- readable medium” refers to any non-transitory computer-readable storage media used to provide computer-executable code and / or other data to and / or within the system 200. Computer software stored on the secondary memory 220 is read into the main memory 215 for execution by the processor 210. The secondary memory 220 can include, for example, semiconductor-based memory, such as programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), and flash memory (block-oriented memory like EEPROM).

[0057] The secondary memory 220 can include an internal medium 225 and / or a removable medium 230. The removable medium 230 is read and / or written in any known manner. The removable storage medium 230 can be, for example, a magnetic tape drive, an optical disk (CD) drive, a digital versatile disk (DVD) drive, other optical drive, a flash memory drive, and / or the like.

[0058] The system 200 can include an input / output (I / O) interface 235. The I / O interface 235 provides an interface between one or more components of the system 200 and one or more input and / or output devices. Example input devices include, without limitation, sensors, keyboards, touch screens or other touch-sensitive devices, cameras, biometric sensing devices, computer mice, trackballs, pen-based pointing devices, and / or the like. Example output devices include, without limitation, other processing systems, cathode ray tubes (CRTs), plasma displays, light-emitting diode (LED) displays, liquid crystal displays (LCDs), printers, vacuum florescent displays (VFDs), surface-conduction electron-emitter displays (SEDs), field emission displays (FEDs), and / or the like. In some cases, input and output devices can be combined, such as in the case of a touch screen display (e.g., in a smartphone, tablet, or other mobile device).

[0059] The system 200 can include a communication interface 240. The communication interface 240 allows data to be transferred between the system 200 and external devices (e.g., printers), networks, or other information sources. For example, computer-executable code and / or other data can be transferred to the system 200 from a network server (e.g., the platform 110) via the communication interface 240. Examples of communication interface 240 include a built-in network adapter, network interface card (NIC), Personal Computer Memory Card International Association (PCMCIA) network card, card bus network adapter, wireless network adapter, Universal Serial Bus (USB) network adapter, modem, wireless data card, communication port, infrared interface, IEEE 1394 Fire Wire, and any other device capable of connecting the system 200 to a network (e.g., the network(s) 120) or another computing device. The communication interface 240 preferably implements industry- promulgated protocols, such as the Ethernet IEEE 802 standards, Fiber Channel, Digital Subscriber Line (DSL), Asymmetric Digital Subscriber Line (ADSL), Frame Relay, Asynchronous Transfer Mode (ATM), Integrated Digital Services Network (ISDN), Personal Communications Service (PCS), Transmission Control Protocol / Internet Protocol (TCP / IP), Serial Line Internet Protocol / Point-to-Point Protocol (SLIP / PPP), and / or the like, but can also implement customized or non-standard interface protocols, as well.

[0060] Data transmitted via the communications interface 240 is typically in the form of electrical communication signals 255. These signals 255 can be provided to the communications interface 240 via a communications channel 250 between the communications interface 240 and an external system 245 (e.g., which can correspond to a sensor of the power transformer 150, an external computer-readable medium, and / or the like). In embodiments, the communications channel 250 can be a wired or wireless network (e.g., the network(s) 120), or any of various other communication links. The communications channel 250 carries the signals 255 and can be implemented using a variety of wired or wireless communication means including wire or cable, fiber optics, conventional phone line, cellular phone link, wireless data communication link, radio frequency ("RF") link, or infrared link, etc.

[0061] Computer-executable code is stored in the primary memory 215 and / or the secondary memory 220. Computer-executable code can also be received from the external system 245 via the communications interface 240 and stored in the primary memory 215 and / or the secondary memory 220. Such computer-executable code, when executed by the processor 210, enables the system 200 to perform various functions of the disclosed embodiments.

[0062] In embodiments in which software is used, the software can be stored on a computer-readable medium and initially loaded into the system 200 via the removable storage 230, the I / O interface 235, or the communications interface 240. In such embodiments, the software is initially loaded into the system 200 in the form of electrical communication signals 255. The software, when executed by the processor 210, preferably causes the processor 210 to perform one or more of the processes and functions described elsewhere herein.

[0063] The system 200 can include wireless communication components that facilitate wireless communications over a voice network and / or a data network (e.g., in the case of the user system 130). The wireless communication components include an antenna system 270, a radio system 265, and a baseband system 260. In the system 200, radio frequency (RF) signals are transmitted and received over the air by the antenna system 270 under the management of the radio system 265.

[0064] In embodiments, the antenna system 270 can include one or more antennas and one or more multiplexers (not shown) that perform a switching function to provide transmit and receive signal paths to the antenna system 270. In the receive path, received RF signals can be coupled from the multiplexer to a low noise amplifier (not shown) that amplifies the received RF signals and sends the amplified signals to the radio system 265.

[0065] In alternative embodiments, the radio system 265 can include one or more radios configured to communicate at various frequencies. In embodiments, the radio system 265 can combine a demodulator (not shown) and a modulator (not shown) in one integrated circuit (IC). The demodulator and modulator can also be separate components. In the incoming path, the demodulator strips the RF carrier signal, leaving the baseband receive audio signal, which is sent from the radio system 265 to the baseband system 260.

[0066] The baseband system 260 is communicatively coupled to the processor(s) 210, which can access the memory 215 and 220. Accordingly, software can be received from the baseband processor 260 and stored in the main memory 210 or the secondary memory 220, or executed immediately upon being received. Such software, when executed, enables the system 200 to perform various functions of the disclosed embodiments.

[0067] FIG. 3 A schematic illustration of a discretized power transformer 150 according to an embodiment is shown. It should be understood that the actual structure and dimensions of the power transformer 150 do not limit any embodiment. Rather, the disclosed embodiments can be utilized or adapted with any type, size, or model of power transformer 150.

[0068] The power transformer 150 can include a housing 300 that encloses one or more windings around a core 310. The winding(s) can include one or more lower laminations 320, one or more upper laminations 330, one or more leads 340, and one or more coils 350. In the illustrated embodiment, the power transformer 150 has two coils 350A and 350B. However, it should be understood that the power transformer 150 can include any number of coils 350, including one coil 350 or three or more coils 350. The lower lamination(s) 320, the upper lamination(s) 330, and the coil(s) 350 can each be annular, substantially symmetrical about the core 310, and concentric about a longitudinal Z-axis L of the core 310. Each lower lamination 320 represents a first assembly element at a bottom end of the winding(s) along the longitudinal axis L, and each upper lamination 330 represents a second assembly element at an opposite top end of the winding(s) along the longitudinal axis L. The leads 340 provide electrical connections between the windings and terminals of the power transformer 150. The lead(s) 340 and the coil(s) 350 can be formed of any suitable electrically conductive material, such as copper, brass, bronze, aluminum, and / or the like. The lower lamination(s) 320, the upper lamination(s) 330, the lead(s) 340, and the coil(s) 350 can also include an insulator, which can be formed of a cellulose-based material and is commonly referred to as "paper."

[0069] The housing 300 is filled with an insulating liquid 360 that surrounds the internal components of the power transformer 150, including the core 310, the lower lamination(s) 320, the upper lamination(s) 330, the lead(s) 340, and the coil(s) 350. The insulating liquid can include, or consist of, mineral oil, liquid ester, or another substance suitable for insulating the internal components of the power transformer 150. Regardless of the particular substance, the water content of the insulating liquid will vary over time and operating conditions (e.g., load and temperature).

[0070] The interior of power transformer 150 can be logically divided into a plurality of sections along one or more axes. For example, each coil 350 is divided into a plurality of sections 355 along the Z-axis. In particular, coil 350A is divided into sections 355A1, 355A2, 355A3, 355A4, and 355A5 along the Z-axis from the bottom end to the top end of the winding. Similarly, coil 350B is divided into sections 355B1, 355B2, 355B3, 355B4, and 355B5 along the Z-axis from the bottom end to the top end of the winding. It will be appreciated that each coil 350 can be divided into any number of sections, including fewer than five sections (and potentially only a single section) or more than five sections. The plurality of sections for the entire power transformer 150 can include each of the coil sections 355, as well as at least one section representing the lower laminate(s) 320, at least one section representing the upper laminate(s) 330, and / or at least one section representing the lead wire 340. Thus, the insulated interior components of power transformer 150 can be logically divided along the Z-axis and the radial X-axis. It will be appreciated that the sections representing the lower laminate(s) 320, the upper laminate(s) 330, and the coil(s) 350 can be annular about the longitudinal axis L, or each can be further divided into annular sectors about the longitudinal axis L. Each of the plurality of sections can be associated with a mass and thickness of insulation in that section based on proportional values of the total mass and total thickness of insulation in the entire power transformer 150.

[0071] Power transformer 150 can also include one or more sensors 370. The sensor(s) 370 can include a moisture sensor that senses the water content in the insulating liquid 360. The moisture sensor 370 can output a signal indicative of the water content in the insulating liquid 360 to the monitoring system 140 or directly to the platform 110 for use as an input to the thermo-chemical digital twin described herein. In embodiments, it is assumed that the water content in the insulating liquid 360 is uniform throughout the interior of the power transformer 150.

[0072] FIG. 4 A process 400 for modeling thermo-chemical degradation in a digital twin of a power transformer 150 is shown in accordance with an embodiment. While process 400 is shown in a certain arrangement and ordering of sub-processes, process 400 can be implemented with fewer, more, or different sub-processes, and in a different arrangement and / or ordering of sub-processes. Moreover, it will be appreciated that any sub-process that is not dependent on the completion of another sub-process can be performed prior to, after, or in parallel with other independent sub-processes, even if those sub-processes are described or illustrated in a particular order.

[0073] The process 400 can be embodied in one or more software modules executed by one or more hardware processors (e.g., the processor 210) on the system 200, e.g., as a software application (e.g., the server application 112, the client application 132, and / or a distributed application including both the server application 112 and the client application 132), which can be executed in whole by the processor(s) of the platform 110, in whole by the processor(s) of the user system(s) 130, or can be distributed across the platform 110 and the user system(s) 130 such that some modules of the software application are executed by the platform 110 and other modules of the software application are executed by the user system(s) 130. The process 400 can be implemented as instructions in source code, object code, and / or machine code. These instructions can be executed directly by the hardware processor(s) 210 or, alternatively, can be executed by a virtual machine operating between the object code and the hardware processor(s) 210. Alternatively, the process 400 can be implemented as a hardware component (e.g., a general-purpose processor, an integrated circuit (IC), an application-specific integrated circuit (ASIC), a digital signal processor (DSP), a field programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, etc.), a combination of hardware components, or a combination of hardware and software components.

[0074] The process 400 can iterate for one or more time intervals. When there are remaining time intervals (i.e., “Yes” in sub-process 410), the process 400 can perform an iteration of the outer loop including sub-processes 420-480. Otherwise, when there are no remaining time intervals (i.e., “No” in sub-process 410), the process 400 can end. In embodiments, the process 400 can perform an iteration of the outer loop at a plurality of fixed time intervals (e.g., a number of milliseconds, seconds, minutes, hours, days, etc.) as long as the power transformer 150 modeled by the digital twin is operational. In other words, the determination in sub-process 410 can be “Yes” as long as the power transformer 150 is operational and being monitored. Thus, for each power transformer 150 being monitored and in operation, the digital twin of the power transformer 150 can perform the process 400 in real-time based on input data acquired for the current time interval. As used herein, the terms “real-time” or “immediate” are to be understood to include events (e.g., the iteration of the outer loop in the process 400) that are delayed from another event (the acquisition of data into the iteration of the outer loop in the process 400) by ordinary delays of computer processing, network communications, data storage and retrieval, and / or the like, as well as events that occur simultaneously with one another. Once the power transformer 150 becomes inoperable or monitoring of the power transformer 150 is terminated for some reason, the determination in sub-process 410 can be “No”.

[0075] In sub-process 420, the total water content in the insulating liquid 360 of the power transformer 150 is determined. In embodiments, sub-process 420 includes deriving the total water content in the insulating liquid 360 from the output of at least one sensor 370, which can include a moisture sensor in the power transformer 150. In alternative embodiments, the total water content in the insulating liquid 360 can be determined manually, using an estimation algorithm, retrieving a value from a lookup table based on one or more other parameter values, or any other suitable manner.

[0076] As mentioned above, in embodiments, the power transformer 150 is logically divided into a plurality of sections along at least one axis of the winding(s) in the power transformer 150. When another of the plurality of sections is still to be considered (i.e., “yes” in sub-process 430), the process 400 can perform an iteration of the inner loop including sub-processes 440-470 for that section. Otherwise, when no more of the plurality of sections are to be considered (i.e., “no” in sub-process 430), the process 400 can proceed to sub-process 480. It will be appreciated that, during each iteration of the outer loop for a given time interval, each and every one of the plurality of sections will be considered exactly once. While it is generally contemplated that there will be a plurality of sections, in alternative embodiments, there can be only a single section (e.g., encompassing the entire insulation of the power transformer 150). In this case, the inner loop iteration will only be performed once for each iteration of the outer loop.

[0077] It will be appreciated that each iteration of the inner loop including sub-processes 440-470 need not be performed individually and sequentially for each of the sections. While it can be the case that the iterations of the inner loop are performed individually for each section (whether serially or in parallel), this is not a requirement of any embodiment. Rather, in alternative embodiments, each of sub-processes 440-470 can be performed simultaneously for all of the sections in a block of combined calculations.

[0078] Sub-process 440 represents a thermal model of the thermo-chemical digital twin. In sub-process 440, the temperature of the section currently under consideration in the inner loop is estimated based on the load of the power transformer 150 and the temperature gradient along the at least one axis. To account for transient conditions in the power transformer 150, the temperature of the section can be calculated for each of a plurality of time instants spanning the current time interval under consideration. Alternatively, the time interval can contain only a single time instant.

[0079] For each time interval, the process 400 can include determining an average temperature of the insulating liquid 360 for each time instant in the time interval. The average temperature of the insulating liquid 360 can be calculated based on the load conditions from IEEE C57.91-2011, Article 7, which is incorporated herein by reference in its entirety, using equations for transient calculation of temperature. Specifically, the equations are:

[0080]

[0081] where Δθ TO is the average temperature rise of the insulating liquid 360 relative to ambient temperature, Δθ TO,U is the limiting temperature rise of the insulating liquid 360 relative to ambient temperature for the current load of the power transformer 150, Δθ TO,i is the initial temperature rise of the insulating liquid 360 relative to ambient temperature for the preceding load, e is Euler's number, t is the time instant, and τ TO is the time constant of the insulating liquid 360 for any particular temperature difference between the limiting temperature rise Δθ TO,U and the initial temperature rise Δθ TO,i .

[0082]

[0083] where Δθ TO,R is the temperature rise of the insulating liquid 360 relative to ambient temperature at rated load at the tap location, K i is the ratio of the preceding load to the per unit rated load, n is an empirically derived exponent for calculating the change in temperature rise of the insulating liquid 360 with load changes (e.g., defined in a table), and R is the ratio of the load loss to the no-load loss at rated load at the tap location.

[0084]

[0085] where τ TO,R is the time constant for the rated load starting from an initial top oil temperature rise of 0°C, C is the initial temperature rise of the insulating liquid 360 relative to ambient temperature for the preceding load, and P T,R is the total loss at rated load.

[0086]

[0087] The above equations can be applied to the values of the load and ambient temperature for each time instant to calculate the average temperature of the insulating liquid 360 at each time instant. It should be understood that this is just one example of calculating the average temperature of the insulating liquid 360. In alternative embodiments, the average temperature of the insulating liquid 360 can be determined in any other suitable manner.

[0088] In addition to the average temperature of the insulating liquid 360, a vertical temperature gradient for the load can also be calculated for each instant. The vertical temperature gradient represents the temperature difference of the insulating liquid 360 between the bottom end and the top end of the winding(s) along the Z-axis. The vertical temperature gradient is directly proportional to the current load.

[0089] Similarly, an axial temperature gradient for the load can also be calculated for each instant. The axial temperature gradient represents the temperature difference of the insulating liquid 360 from the center of the housing 300 to the outer circumference along the radial X-axis. The axial temperature gradient can also be directly proportional to the current load.

[0090] In one embodiment, a winding-to-oil temperature gradient can also be calculated or otherwise determined. The winding-to-oil temperature gradient takes into account the temperature between the conductor and the insulating liquid 360, which can vary across the segments along the Z-axis and / or the radial X-axis.

[0091] The localized temperature of each segment of the winding(s) can be calculated based on the average temperature of the insulating liquid 360, the vertical temperature gradient, the axial temperature gradient, and / or the winding-to-oil temperature gradient. For example, the sub-process 440 can include estimating the temperature of each segment for each instant by: calculating a localized temperature of the lower laminate(s) 320 based on the average temperature of the insulating liquid 360 and the axial temperature gradient calculated for that instant; calculating a localized temperature of the upper laminate(s) 330 based on the average temperature of the insulating liquid and the axial temperature gradient calculated for that instant; and calculating a localized temperature for each coil segment 355 based on the temperature of the lower laminate(s) 320 or the upper laminate(s) 330, the load, and the radial temperature gradient and the axial temperature gradient.

[0092] As an example, the localized temperature of the lower laminate(s) 320 can be calculated as (or based on) the difference between the average temperature of the insulating liquid 360 and half of the vertical temperature gradient for the current load. The value of this difference represents the bottom temperature of the insulating liquid 360 at the bottom end of the winding(s). In embodiments where there are multiple lower laminates 320 along the radial X-axis, the localized temperature of each lower laminate 320 can be further determined based on the axial temperature gradient.

[0093] As an example, the localized temperature of the upper tier(s) 330 can be calculated as (or based on) the average temperature of the insulating liquid 360 summed with half of the vertical temperature gradient for that load. The value of this sum represents the top temperature of the insulating liquid 360 at the top end of the winding(s). In embodiments where there are multiple upper tiers 330 along the radial X-axis, the localized temperature of each upper tier 330 can be further determined based on an axial temperature gradient.

[0094] As an example, the localized temperature of each coil section 355 can be calculated as (or based on) the sum of the bottom temperature (e.g., the localized temperature of the lower tier(s) 320), a percentage of the vertical temperature gradient, and half of the winding-to-oil temperature gradient. Alternatively, the localized temperature of each coil section 355 can be calculated as (or based on) the sum of the top temperature (e.g., the localized temperature of the upper tier(s) 330) and half of the winding-to-oil temperature gradient, minus the percentage of the vertical temperature gradient. In either case, the percentage of the vertical temperature gradient used for a particular coil section 355 can be proportional to the height range of that coil section 355 along the Z-axis of the power transformer 150. For example, using coil 350A as an example, if there are five coil sections 355A1-355A5, the percentage of the vertical temperature gradient for the bottom-most first coil section 355A1 can be 10%, the vertical temperature gradient percentage for the second coil section 355A2 can be 30%, the vertical temperature gradient percentage for the third coil section 355A3 can be 50%, the vertical temperature gradient percentage for the fourth coil section 355A4 can be 70%, and the vertical temperature gradient percentage for the top-most fifth coil section 355A5 can be 100%. More generally, the percentage of the vertical temperature gradient for each coil section 355 can be determined as the middle value of the height range represented by that coil section 355 (e.g., 30% for the third coil section 355A3 because the third coil section 355A3 represents a range of 20-40% of the total height of the coil 350A). In embodiments where there are multiple coils 350 along the radial X-axis, the localized temperature of each coil section 355 can be further determined based on an axial temperature gradient. For example, the localized temperature of each coil section 355A1-355A5 of coil 350A can be determined using a different percentage of the axial temperature gradient than each coil section 355B1-355B1 of coil 350B.

[0095] In embodiments, in each coil 350, the localized temperature of the one coil section 355 closest to the top end of the power transformer 150 can be further based on a hot spot factor or a heat sink factor associated with the power transformer 150. In other words, the localized temperature of the topmost coil section 355 of each coil 350 can be adjusted based on this factor to account for the fact that the topmost coil section 355 is the hottest region in each coil 350. The hot spot factor or heat sink factor can be calculated or otherwise determined in any suitable manner (e.g., retrieved as a predefined constant).

[0096] If the sub-process 440 represents a thermal model, then the sub-processes 450-470 represent a chemical model of the thermal-chemical digital twin. In the sub-process 450, a diffusion-related water content in the insulation of the winding(s) in the currently considered section in the inner ring caused by diffusion is estimated based on the localized temperature for that section determined in the sub-process 440 and the total water content in the insulating liquid 360.

[0097] The load conditions of the power transformer 150 typically do not remain stable for a sufficient length of time to reach equilibrium conditions. Therefore, in embodiments, the diffusion process is modeled for transient conditions. In particular, the sub-process 450 can include, for each of a plurality of time instants spanning a time interval, calculating a water content in the insulation diffused into the insulation based on a time constant for water diffusion into the material of the insulation.

[0098] The diffusion process during transient conditions can be modeled as an exponential process controlled by a time constant calculated based on the temperature, the water content in the insulating liquid 360, the thickness of the insulation, and / or the geometry of the insulation. For example, for each time instant t, the water content in the insulation diffused into the insulation can be calculated in the sub-process 450 as:

[0099]

[0100] where W diffusion is the water content in the insulation diffused into the insulation at the time instant t, W equilibrium is the water content in the insulation at equilibrium conditions, W initial is the water content in the insulation at a time instant immediately preceding the time instant t (i.e., at the time instant t-1), e is Euler’s number, and e is the time constant.

[0101] In embodiments in which the insulating liquid 360 is mineral oil and the insulation is cellulose-based, W equilibriumThe value can be derived from the water equilibrium shown by a set of equilibrium curves plotted by Oomen in "Moisture Equilibrium in Paper-Oil Systems," (Proceedings of the IEEE Electrical Insulation Conference, Chicago, IL, pp. 162-166, October 1983) (incorporated hereby by reference in its entirety). For example, the water content in an insulator under equilibrium conditions can be calculated as follows:

[0102] W equilibrium =Me K*T

[0103] M = M slope ·RS oil +M intercept

[0104] K = K slope ·RS oil +K intercept

[0105]

[0106] Among them, W equilibrium W is the water content in the insulator due to diffusion under equilibrium conditions. oil It is the water content in the insulating liquid 360, T is the equilibrium temperature, and RS oil M is the relative saturation of water content in the insulating liquid 360 (i.e., the ratio between water content and saturation content), and M slope M intercept ,K slope , and K intercept These are coefficients defined by linear segments, whose slope and intercept can be defined with respect to RS. oil The given values ​​are as follows:

[0107] RS oil (%)]] M slope ]]> M intercept ]]> K slope ]]> K intercept ]]> 0 48.055 0 0 -0.01155245 5 14.411 1.6822 0.051383 -0.014122 10 12.179 1.9055 0.0095265 -0.0099359 20 12.358 1.8696 0.0019723 -0.0084251 30 9.5961 2.6982 0.0059252 -0.009611 40 11.168 2.0696 0.0034817 -0.0086336 50 12.061 1.623 0.0041801 -0.0089828 60 13.053 1.0276 0.0034595 -0.0085504 70 14.065 0.3191 0.01389 -0.015851 80 32.112 -14.118 0.0095796 -0.012403 90 83.494 -60.362 -0.011016 0.0061326 95 217.31 -187.48 -0.022849 0.017374 100 217.31 -187.48 -0.022849 0.017374

[0108] In the embodiment, the time constant τ pmay be calculated based on the disclosure of Du et al. in "Moisture Equilibrium in Transformer Paper-Oil Systems," Dielectrics and Electrical Insulation Society (DEIS) Electrical Insulation Magazine, Featured Article, vol. 15, no. 1, Jan. / Feb. 1999 (incorporated by reference in its entirety). For example, the time constant τ p may be calculated as:

[0109] When moisture intrusion occurs through both surfaces of the insulation

[0110] When moisture intrusion occurs through only one surface of the insulation

[0111] where d is the thickness of the insulation material, and D is a coefficient. In an embodiment, the coefficient D is calculated as:

[0112]

[0113] where D0= 1.34 x 10- 13 m 2 / s, C is the moisture concentration in weight percent, E a = 8074 K, T0= 298 K, and T is the temperature of the segment (in Kelvin) determined in sub-process 440.

[0114] In sub-process 460, the degradation-related water content is estimated based on the degradation of the material of the insulation of the winding(s) in the segment currently considered in the inner loop. If the insulation of the winding(s) is cellulose-based, then the stoichiometry of cellulose degradation can be used to estimate the degradation-related water content. In particular, the degradation-related water content in the insulation can be estimated based on the water generation rate from the breakage of cellulose chains in the cellulose-based material.

[0115] As discussed by Lundgaard et al. in “Aging of Oil-Impregnated Paper in Power Transformers,” (IEEE Transactions on Power Delivery, vol. 19, no. 1, Jan. 2004) (hereinafter “Lundgaard”) (incorporated by reference in its entirety), there is a net production of two molecules of water for each glucose monomer. Considering that each break in the cellulose degradation results in the reaction of two glucose monomers, there will be a net production of four molecules of water for each break.

[0116] FIG. 5 A chemical representation of two glucose monomers (C6H 10 O5) n is shown, with the hydroxyl groups that result in the production of water circled. Of the six circled hydroxyl groups, two will be consumed in the chain of reactions. The complete degradation of a certain mass of cellulose requires approximately 8 to 10 breaks in the cellulose chain.

[0117] Lundgaard plots a relatively linear trend for the number of molecules of water produced in successive breaks in the cellulose degradation. However, the rate of production should follow an exponential curve. Therefore, in embodiments, the water production from cellulose degradation is modeled to have exponential behavior. The decay of the viscosity of the polymerization accounts for this exponential behavior, which justifies the adoption of a rate of water production per unit of consumed lifetime that is constant.

[0118] The break of a cellulose molecule can occur at any point in the cellulose chain, which results in the production of 4 molecules of water, and, on average, results in a halving of the molecular weight of the cellulose chain. Therefore, the number of molecules of water produced from successive breaks in the cellulose chain can be represented as a geometric series, starting with 4, doubling for each new break. The integral of this curve can then be divided by the molecular weight of the cellulose (e.g., which starts with the number of glucose monomers defined by the degree of polymerization), and multiplied by the molecular weight of water. In this case, the rate of water production from cellulose degradation can be modeled as:

[0119]

[0120] where W rate is the rate of water production from cellulose degradation, k is the number of breaks in the cellulose chain (e.g., k = 8), Mol water is the molar mass of water (e.g., Mol water= 18.01528 grams per mole), DP is the degree of polymerization of the insulating cellulose-based material (defined as the number of monomer units, e.g., DP = 1200 monomers), Mol glucose is the molar mass of the monomer of glucose (e.g., Mol glucose = 162.1406 grams per mole), and UoL is the unit life of the power transformer 150. Based on the results of the Lockie Test and employing a safety factor of 5, IEEE defines the unit life for power transformers to be UoL = 180,000 hours. It should be understood, however, that other values can be used for the unit life UoL. Moreover, it should be understood that W rate will be defined as: W water = (Mol glucose (e.g., grams) per unit of monomer mass (defined by DP • Mol rate (e.g., grams) per unit of time (defined by UoL (e.g., hours)). If the insulator has a degree of polymerization DP = 1200, and experiences k = 8 breaks (which results in a lower average DP value), and the unit life UoL = 180,000 hours, then the rate of water generation W rate calculated according to the above formula is 68.4 milligrams of water per hour per gram of insulation. Notably, this model for the rate of water generation is highly consistent with the empirical observations in Lundgaard.

[0121] It should be understood that the degradation-related water content for a time period (such as the current time interval) can be calculated by multiplying the rate of water generation W rate by the length of the time period. For example, if W rate is in units of hours, and the time interval is one minute, then the degradation-related water content generated during the time interval can be calculated as W rate / 60.

[0122] In sub-process 470, the total water content in the insulation of the winding(s) in the segment currently under consideration in the inner ring is estimated based on the diffusion-related water content estimated in sub-process 450 and the degradation-related water content estimated in sub-process 460. For example, the total water content in the insulation of the winding(s) in the segment can be estimated as the sum of the diffusion-related water content and the degradation-related water content.

[0123] In sub-process 480, at least one parameter of power transformer 150 can be estimated based on the total water content in insulating liquid 360 determined in sub-process 420, and / or the total water content in the insulation of the winding(s) determined in the iteration(s) of sub-process 470. The at least one parameter can include the total water content in power transformer 150, a measure of the aging of power transformer 150, a risk of dielectric failure, a likelihood of microbubbles appearing on the surface of the insulation, a breakdown voltage, and / or the like.

[0124] In an embodiment of sub-process 480, the at least one parameter includes the total water content in power transformer 150. In this case, the total water content in power transformer 150 can be estimated based on the total water content in insulating liquid 360 and the total water content in the insulation of all of the winding(s) of the plurality of sections. The total water content in the insulation of all of the winding(s) of the plurality of sections can be determined as a sum of the estimated total water content in the insulation of each section across all of the plurality of sections (as determined in each iteration of sub-process 470 in the inner loop).

[0125] In this embodiment of sub-process 480, the total water content in the power transformer can be further estimated based on an adjustment parameter determined using artificial intelligence (AI). Power transformer 150 can not be a perfectly sealed system, and can involve complex chemical processes and reactions that can lead to hydrolysis and / or pyrolysis. This adjustment parameter serves as a leakage factor that can account for water entering power transformer 150, water exiting power transformer 150, and / or any chemical reactions that generate and / or consume water that occur inside the actual power transformer 150 and are not accounted for by other components of the thermo-chemical digital twin discussed herein.

[0126] The artificial intelligence can include an AI model of a thermal-chemical digital twin of the power transformer 150 that outputs an estimate of the total water content in the insulating liquid 360. In each time interval, the sub-process 480 can include calculating a deviation between an actual value of the total water content in the insulating liquid 360 derived from the output of the sensor 370 and one or more estimates of the total water content in the insulating liquid 360 output by the AI model. The deviation can vary with the temperature of the insulating liquid 360 and the rate of change over time in the load in addition to changes in the water content in the power transformer 150. The sub-process 480 can determine an adjustment parameter based on the calculated deviation and utilize the adjustment parameter in the estimation of the total water content in the power transformer 150. For example, the adjustment parameter, which can be a positive or negative value, can be added to the total water content in the power transformer 150, thereby adjusting the estimate of the total water content in the power transformer 150. Thus, the AI model is able to track deviations from the measured value of the water content in the insulating liquid 360 and continuously adjust the adjustment parameter as a correction to keep the thermal-chemical digital twin of the power transformer 150 in line with the actual physical power transformer 150.

[0127] The AI model can include a recurrent neural network (RNN) or other artificial neural network that can utilize long short-term memory (LSTM). Alternatively, the AI model can include a K- nearest neighbor (KNN) algorithm. The AI model can be trained using supervised learning or unsupervised learning. In supervised learning, the AI model can be trained using a labeled dataset that includes one or more features (e.g., temperature) labeled with one or more target values (e.g., total water content in the insulating liquid 360).

[0128] As an example, the KNN algorithm operates by finding the k-nearest neighbors of a set of feature(s), and then estimates the target value based on the average of the k-nearest neighbors. A history set of measured features (e.g., temperature and water content in the insulating liquid 360 measured by the sensor 370) for each of a plurality of past time intervals can be retained, as well as a corresponding estimated water content in the insulating liquid 360 for each of the plurality of past time intervals. The history set of measured and estimated features can be retained as a sliding window (e.g., representing the most recent 48 hours). The bias can be computed by finding the k-nearest neighbors of the current measured features (e.g., the current temperature and current water content in the insulating liquid 360 measured by the sensor 370), and computing the average bias between the measured water content in the insulating liquid 360 and the estimate of the water content in the insulating liquid 360 for these k-nearest neighbors. This average bias is used to determine an adjustment parameter (e.g., by converting the average bias to units of water content). Furthermore, if the value of the average bias exceeds a pre-defined tolerance value (e.g., 0.5%), the AI model can increase the number of k-nearest neighbors used in order to use more neighbors to compute the average bias until the average bias is minimized and the average bias falls below the pre-defined tolerance value. By optimizing the number of k-nearest neighbors, this process will minimize the error between the calculated and measured values of the water content in the insulating liquid 360.

[0129] In alternative or additional embodiments of the sub-process 480, the at least one parameter includes an overall measure of aging of the power transformer 150. In this case, the process 400 can further include, for each of the time interval(s), computing, for each of the segment(s) of winding(s) in the power transformer 150, a measure of aging for the segment based on the total water content in the insulation of the winding(s) in the segment. An overall measure of aging can be determined based on these measures of aging for the segment(s). For example, the overall measure of aging can be determined as the maximum of the measures of aging for the segment(s).

[0130] In this embodiment of the sub-process 480, the measure of aging for each segment can be computed as:

[0131]

[0132] where V is a measure of aging, A is an interpolated aging parameter associated with the material of the insulation, A r is a nominal aging parameter associated with the material of the insulation, e is Euler’s number, R is the molar gas constant (e.g., R = 8.31446261815324 J K -1 mol -1 ), Er is the activation energy (e.g., Arrhenius activation energy) of the material of the insulator under rated conditions, E is the interpolated activation energy (e.g., Arrhenius activation energy) of the insulator material, and θ h,r is the hotspot to top oil temperature under rated load, and θ h is the hotspot temperature. The rated aging parameter A r and the rated activation energy E r may be pre-defined constants.

[0133] The value of the measure of aging V is an aging acceleration factor that indicates how many equivalent units (e.g., hours) of the life of the power transformer 150 have been consumed. A value of V > 1 indicates that the power transformer 150 is aging faster than expected under rated conditions, and a value of V < 1 indicates that the power transformer 150 is aging slower than expected under rated conditions. A value of V = 1 indicates that the power transformer 150 is aging exactly as expected under rated conditions.

[0134] The values of A and E can be determined from a look-up table, for example, based on the water content of the insulator, the oxygen content, the acidity in the insulating fluid 360, and / or the like to retrieve the values thereof. One possible example of a look-up table is given in International Electrotechnical Commission (IEC) 60076-7 Appendix A, Table Al, which is reproduced below for a thermal class paper insulator:

[0135]

[0136] Alternatively, A and E can be retrieved from different look-up tables, or determined in other suitable manners. If the values of A and / or E are not included in the look-up table for a particular humidity (i.e., water content of the insulator), the values of the parameters can be interpolated from the values of the parameters for the surrounding humidities included in the look-up table. For example, if the paper insulator material does not contain air and has 0.9% moisture, the value of A can be interpolated to be a value between 1.6 x 10 4 and 3.0 x 10 4 for 1.5% moisture (e.g., A = 2.16 x 10 4 ). Subsequently, the ratio between the rated aging parameter A r and the interpolated aging parameter A can be calculated as The ratio represents an aging ratio. The value of activation energy E can similarly be interpolated. It will be appreciated that the water content in the insulation used for the lookup is the total water content in the insulation in the winding(s) in each section estimated in sub-process 470. Notably, the values of A and E are based on the oxygen content in the insulation (i.e., air-free vs. air-containing), such that the measure of aging is based on the oxygen content in the insulation. Additionally or alternatively, the values of A and / or E and / or the values of other parameters can be based on the acidity of the insulating liquid 360, such that the measure of aging is based on the acidity of the insulating liquid 360.

[0137] The value of the exponent coefficient represents an exponential coefficient. The measure of aging is computed based on the aging ratio and the exponential coefficient, e.g., as the product of the aging ratio and the exponential coefficient. Hot-spot-to-top-oil temperature θ h,r and hot-spot temperature θ h The value of the hot-spot-to-top-oil temperature ratio can be a predefined constant, can be computed based on one or more other parameters, or determined in any other suitable manner.

[0138] In alternative or additional embodiments of sub-process 480, the at least one parameter includes a risk of dielectric failure in the insulation of the winding(s). The risk of dielectric failure can be estimated based on the total water content in the insulation, which can be estimated as described above. For example, based on the relationship described in Balma et al., “The Effects of Long Term Operation and System Conditions on the Dielectric Capability and Insulation Coordination of Large Power Transformers,” (IEEE Transactions on Power Delivery, vol. 14, no. 3, July 1999) (hereinafter “Balma”), which is incorporated by reference herein in its entirety, the risk of dielectric failure is determined as a function of the water content in the insulation.

[0139] In alternative or additional embodiments of sub-process 480, the at least one parameter includes a likelihood of micro-bubble formation on the surface of the insulation of the winding(s). The likelihood of micro-bubble formation can be estimated based on the total water content in the insulation, which can be estimated as described above. For example, based on the relationship described in Oommen et al., “Bubble Evolution from Transformer Overload,” doi: 10.1109 / TDC.2001.971223, which is incorporated by reference herein in its entirety, the likelihood of micro-bubble formation is determined as a function of the water content in the insulation.

[0140] In alternative or additional embodiments of sub-process 480, the at least one parameter includes a breakdown voltage of the insulating liquid 360. The breakdown voltage can be estimated based on the total water content in the insulating liquid 360 determined by measurement (e.g., by the sensor 370) and / or based on the total water content in the power transformer 150 as can be estimated as described above. For example, the breakdown voltage can be determined as a function of the water content in the insulating liquid 360 based on the relationship described in Balma.

[0141] Regardless of which parameter(s) are estimated in sub-process 480, the parameter(s) estimated in sub-process 480 can be used in any beneficial way. For example, the parameter(s) are provided in a report (e.g., in a graphical user interface on a display of the user system 130). The report can display any of the above-described parameters (e.g., the estimated water content in the insulating liquid 360, the estimated water content in the insulation, the estimated total water content in the power transformer 150, the measure of aging, the risk of dielectric failure, the likelihood of microbubbles, the breakdown voltage, etc.), as well as any parameters derived from these indicated parameters, which can be indicative of a risk of operation, an estimated lifetime, and / or the like. Such a report can be used by an operator of the power transformer 150 to schedule or otherwise plan for maintenance of the power transformer 150, replacement of the power transformer 150, increased or decreased load on the power transformer 150, and / or the like.

[0142] Alternatively or additionally, the parameter(s) can be used to generate one or more alerts. For example, when a parameter such as the risk of dielectric failure, the likelihood of microbubbles, or the breakdown voltage satisfies a threshold (e.g., the risk of dielectric failure exceeds a predefined threshold, the likelihood of microbubbles exceeds a predefined threshold, or the breakdown voltage falls below a predefined threshold), the platform 110 can issue an alert to at least one recipient (possibly a responsible person or other system). The alert can include, for example, a communication (e.g., an email message, a pre-recorded or synthesized telephone message, a short message service (SMS) or multimedia message service (MMS) message, an in-application message within the server application 112, an inter-application message via an API, etc.) to one or more user accounts, the user system(s) 130, or other systems.

[0143] Alternatively or additionally, the parameter(s) can be used to trigger one or more physical controls. For example, when a parameter such as the risk of dielectric failure, the likelihood of microbubbles, or the breakdown voltage meets a threshold (e.g., the risk of dielectric failure exceeds a predefined threshold, the likelihood of microbubbles exceeds a predefined threshold, or the breakdown voltage falls below a predefined threshold), indicating unsafe operation, the platform 110 can automatically trip the power transformer 150, limit the load capacity of the power transformer, or control other relevant components of the power network. However, it should be understood that such an approach can not be desirable or permissible in scenarios where control has significant consequences (e.g., a severe power outage). In such cases, the platform 110 can generate an alert as described previously, allowing an operator to decide whether to implement control.

[0144] To validate the disclosed embodiments, an implementation of the process 400 was performed on a simulated power transformer 150. In the implementation tested, the process 400 was performed for a plurality of time intervals, with only the water content in the insulating liquid 360 as an independent variable. At each iteration of the outer loop of the process 400, a solver was used to find a water content in the insulating liquid 360 that resulted in a total water content inside the power transformer 150 that matched the value at the previous iteration of the outer loop of the process 400, plus or minus the value of the adjustment parameter. Specifically, for each time interval, the solver calculated a new transient condition for the distribution of temperature and water content that satisfied the equations described herein and produced a total water content inside the power transformer 150 that was within the error tolerance. At the end of each time interval, the water content inside the power transformer 150 had to match the water content at the beginning of the time interval plus the water content generated by degradation of the insulation. In other words, the non-linear, interconnected equations described herein were integrated into a single objective function that was optimized by the solver using the water content in the insulating liquid 360 as an independent variable.

[0145] The simulated power transformer 150 was a 25 megavolt ampere (MVA) transformer with a single winding 350 and was under rated conditions. The simulated power transformer 150 had a hot spot temperature rise of 80 °C, which reached 110 °C at a flat ambient temperature of 30 °C. The initial conditions for the simulated power transformer 150 were set to a water content of 0.5% in the insulation and 10 ppm of water in the insulating liquid 360. The simulated power transformer 150 was assumed to be completely sealed. After a stabilization time of 168 hours (7 days) at the ambient temperature, the simulated power transformer 150 was energized and continuously maintained at rated capacity. The ambient temperature was set to 30 °C constant to provide rated life conditions for the insulation degradation. The parameters used were as follows: Δθ TO,R= 49°C; vertical temperature gradient = 20°C; winding-to-oil temperature gradient = 20°C; hot spot factor = 1.4; n = 0.8; R = 9.5; core and coil weight = 50,000 kilograms (kg); oil tank and accessories weight = 15,000 kg; volume of mineral oil as insulating liquid 360 = 70,000 liters; and total losses = 277.423 kilowatts (kW).

[0146] Notably, during the stabilization time, the simulated power transformer 150 is de-energized, such that the temperature is relatively low at or near ambient temperature. This results in an initial, sharp migration of water from the insulating liquid 360 toward the insulation, as the relative saturation of the insulation with a water content of 0.5% is lower than the relative saturation of the mineral oil with 10 ppm of water. In particular, the water content in the insulating liquid 360 decreases from 10 ppm to below 2 ppm. But this only increases the water content in the insulation from 0.5% to 0.54%, as the water absorption capacity of the insulation far exceeds that of the insulating liquid 360. However, this trend reverses when the simulated power transformer 150 is energized and the temperature increases.

[0147] FIG. 6 The water content in the insulating liquid 360 and the insulation is shown for the tested implementation according to the embodiment over the full simulation time of 87,600 hours (10 years). The water generated by the aging of the insulation remains in the system, accumulating in both the insulating liquid 360 and the insulation. The components exposed to lower temperatures (e.g., the lower laminations 320 and the lower coil section 355) reach a significantly higher water content than the hot spots (e.g., the upper laminations 330 and the upper coil section 355). The driest region is the hot spot region (e.g., the top-most coil section 355, which is coil section 5 in FIG. 6 the insulating liquid 360 and the insulation is shown for the tested implementation according to the embodiment over the full simulation time of 87,600 hours (10 years). The water generated by the aging of the insulation remains in the system, accumulating in both the insulating liquid 360 and the insulation. The components exposed to lower temperatures (e.g., the lower laminations 320 and the lower coil section 355) reach a significantly higher water content than the hot spots (e.g., the upper laminations 330 and the upper coil section 355). The driest region is the hot spot region (e.g., the top-most coil section 355, which is coil section 5 in

[0148] FIG. 7 The water generation from cellulose degradation over the entire simulation time for the tested implementation according to the embodiment is shown. As shown, during the full simulation time of 10 years, cellulose degradation generated 10.39 kg of water from the 1100 kg of insulation. Notably, as the water content increases, the rate of water generation (i.e., cellulose degradation) accelerates.

[0149] FIG. 8 Measurements of aging throughout the simulated time period for the tested implementation according to the embodiments are shown. Both the instantaneous aging factor (i.e., A / A r ) and the cumulative aging (i.e., V) for the hot spot section (e.g., the topmost coil section 355) are shown. Despite being the driest region, the hot spot section reaches the highest value of cumulative aging due to the higher temperature. After 87,600 hours (10 years) of operation at rated conditions, the cumulative life consumption of the simulated power transformer 150 reaches 83,670 hours, or 95.51% of the rated life. The calculated aging factor starts at 0.8x and ends up slightly over 1.2x.

[0150] Although not shown, during the second decade of the simulation, the water content in the hot spot section reaches 1.4%. As a result, the equivalent aging of 180,000 hours is reached after 154,828 hours of operation. In other words, when accounting for water generation from cellulose degradation in the insulator, the effective life of the simulated power transformer 150 is 14% lower than the unit life. This demonstrates that the effective life of a power transformer 150 operating continuously at rated capacity will be shorter than the rated life when no drying intervention is performed. Based on the simulation, a maintenance intervention should be triggered when the water content in the insulating liquid 360 exceeds 25 ppm, around the 12th year of operation. Drying the power transformer 150 at this time will prevent life reduction and ensure that the rated life is exceeded. In a similar manner, the disclosed embodiments can be used to schedule or otherwise plan maintenance interventions for any power transformer 150.

[0151] As previously described, it is not possible to place sensors within the power transformer 150 to measure the degradation of the insulator during operation of the power transformer 150. Therefore, conventionally the power transformer 150 must be shut down and opened to determine the degradation of the insulator, which results in an operational disruption. The process 400 avoids such disruptions by continuously and iteratively estimating the water content in various sections of the power transformer 150 based on known initial conditions and the output of the moisture and temperature sensors (e.g., 370). Therefore, the disclosed embodiments are able to simulate sensors within the power transformer 150 without the need for destructive testing. It should be appreciated that the disclosed embodiments can be incorporated into a larger digital twin of the power transformer 150 that models one or more other aspects of the power transformer 150.

[0152] Example embodiments include, but are not limited to:

[0153] Example 1 : A method for modeling thermo-chemical degradation in a digital twin of a power transformer, comprising using at least one hardware processor to, for each of one or more time intervals: determine a total water content in an insulating liquid of the power transformer; for each of a plurality of sections of at least one winding of the power transformer logically partitioned along at least one axis of the at least one winding, estimate a temperature of the section based on a load of the power transformer and a temperature gradient along the at least one axis, estimate a diffusion-related water content in an insulation of the at least one winding in the section caused by diffusion based on the estimated temperature and the total water content in the insulating liquid, estimate a degradation-related water content based on a degradation of a material of the insulation, and estimate a total water content within the insulation of the at least one winding in the section based on the diffusion-related water content and the degradation-related water content; and estimate a total water content in the power transformer based on the total water content in the insulating liquid and the total water content within the insulation of the at least one winding in all of the plurality of sections.

[0154] Example 2: The method of example 1, further comprising using the at least one hardware processor to, for each of the one or more time intervals, determine an average temperature of the insulating liquid for each of a plurality of time instants spanning the time interval.

[0155] Example 3: The method of any one of examples 1 or 2, wherein the plurality of sections comprises: at least one lower stack representing a first assembly element at a first end of the at least one winding along a longitudinal axis; at least one upper stack representing a second assembly element at a second end of the at least one winding opposite the first end of the at least one winding along the longitudinal axis; and one or more coil sections each representing at least a portion of at least one coil of the at least one winding between the first end and the second end.

[0156] Example 4: The method of examples 2 and 3, wherein the temperature gradient comprises an axial temperature gradient along an axial axis and a radial temperature gradient along a radial axis, and wherein estimating the temperature of each of the plurality of sections comprises, for each of the plurality of time instants: computing a localized temperature of the at least one lower stack based on the axial temperature gradient computed for the time instant and the average temperature of the insulating liquid; computing a localized temperature of the at least one upper stack based on the axial temperature gradient computed for the time instant and the average temperature of the insulating liquid; and computing a localized temperature for each of the one or more coil sections based on the temperature of the at least one lower stack or the at least one upper stack, the load, and the radial temperature gradient and the axial temperature gradient.

[0157] Example 5: According to the method of Example 4, one or more coil segments are multiple coil segments, and the temperature of one of the multiple coil segments closest to the second end is further calculated based on the hot spot coefficient or heat dissipation coefficient associated with the power transformer.

[0158] Example 6: According to any of the methods in the foregoing embodiments, wherein estimating the diffusion-related water content includes, for each of a plurality of moments spanning a time interval, calculating the water content diffused into the insulator based on the time constant of water diffusion into the material of the insulator.

[0159] Example 7: According to the method of Example 6, wherein, for each of the plurality of time points, the water content diffused into the insulator is calculated as follows:

[0160]

[0161] Among them, W diffusion W is the water content that diffuses into the insulator at time t. equilibrium W is the water content in an insulator under equilibrium conditions. initial τ is the water content in the insulator at a time immediately preceding time t, e is the Euler number, and τ p It is a time constant.

[0162] Example 8: According to any of the methods in the foregoing examples, wherein the material of the insulator is cellulose-based.

[0163] Example 9: According to the method of Example 8, the degradation-related water content in the insulator is estimated based on the water generation rate from the breakage of cellulose chains in the cellulose-based material.

[0164] Example 10: According to the method of Example 9, the water generation rate is calculated as follows:

[0165]

[0166] Among them, W rate It is the amount of water generated per hour, k is the number of breaks, and Mol water It is the molar mass of water, DP is the degree of polymerization of the insulating material, and Mol glucose It is the molar mass of glucose monomers.

[0167] Embodiment 11 : The method of any of the preceding embodiments, further comprising, using the at least one hardware processor, for each of the one or more time intervals, for each of the plurality of sections of the at least one winding, calculating a measure of aging for the section based on the total water content in the insulation; and determining an overall measure of aging of the power transformer based on the measures of aging for the plurality of sections.

[0168] Embodiment 12: The method of Embodiment 11, wherein the measure of aging for each of the plurality of sections is further based on one or both of an oxygen content in the insulation or an acidity of the insulating liquid.

[0169] Embodiment 13: The method of any of Embodiments 11 or 12, wherein calculating the measure of aging for each of the plurality of sections comprises: determining a nominal aging parameter associated with a material of the insulation; interpolating an aging parameter for the section based on the total water content in the insulation of the at least one winding in the section; and calculating an aging ratio between the nominal aging parameter and the interpolated aging parameter.

[0170] Embodiment 14: The method of Embodiment 13, wherein calculating the measure of aging for each of the plurality of sections further comprises: determining an activation energy under a nominal condition associated with the material of the insulation; interpolating the activation energy of the material of the insulation; calculating an exponential coefficient based on the activation energy under the nominal condition and the interpolated activation energy; and determining the measure of aging for the section based on the aging ratio and the exponential coefficient.

[0171] Embodiment 15: The method of Embodiment 14, wherein the measure of aging for each of the plurality of sections is calculated as:

[0172]

[0173] where V is the measure of aging, A is the interpolated aging parameter, A r is the nominal aging parameter, e is Euler’s number, R is the molar gas constant, E r is the activation energy under the nominal condition, E is the interpolated activation energy, 0 h,r is the hot spot to top oil temperature under the nominal load, and 0 h is the hot spot temperature.

[0174] Example 16: The method of any one of the preceding examples, wherein determining the total water content in the insulating liquid comprises deriving the total water content in the insulating liquid from an output of the at least one sensor in the power transformer, and wherein the method further comprises using the at least one hardware processor to, for each of one or more time intervals at least once: calculate a deviation between an actual value of the total water content in the insulating liquid derived from the output of the at least one sensor and one or more estimated values of the total water content in the insulating liquid output by the digital twin artificial intelligence (AI) model; and determine an adjustment parameter based on the deviation, wherein the estimate of the total water content in the transformer is further based on the adjustment parameter.

[0175] Example 17: The method of any one of the preceding examples, further comprising using the at least one hardware processor to estimate a risk of dielectric failure of the insulation of the at least one winding based on the estimated total water content within the insulation.

[0176] Example 18: The method of any one of the preceding examples, further comprising using the at least one hardware processor to estimate a likelihood of microbubbles on a surface of the insulation of the at least one winding based on the estimated total water content within the insulation.

[0177] Example 19: The method of any one of the preceding examples, further comprising using the at least one hardware processor to: estimate a breakdown voltage of the insulating liquid based on the total water content in the insulating liquid; and generate an alert when the estimated breakdown voltage satisfies a threshold value.

[0178] Example 20: A system comprising: at least one hardware processor; and software configured so as when executed by the at least one hardware processor to perform the method of any one of the preceding examples.

[0179] Example 21: A non-transitory computer-readable medium having instructions stored thereon, wherein the instructions, when executed by a processor, cause the processor to perform the method of any one of examples 1-19.

[0180] The foregoing description of the disclosed embodiments is presented for purposes of illustration and description. Various modifications to the embodiments will be readily apparent to those skilled in the art, and the general principles defined herein can be applied to other embodiments without departing from the spirit or scope of the disclosure. Therefore, it is to be understood that the description and drawings presented herein represent the present preferred embodiments of the disclosure and are therefore to be regarded as merely illustrative. Furthermore, it is to be understood that the disclosure is broadly applicable to other embodiments not explicitly described herein. Accordingly, the scope of the disclosure is to be interpreted in the broadest manner consistent with the principles and spirit of the disclosure.

[0181] As used herein, the terms "comprising", "comprise", and "comprises" are open- ended. For example, "A comprises B" means A can include any one of the following: (i) only B; (ii) B in combination with one or more (and possibly any number of) other components. In contrast, the terms "consisting of", "consists of", and "consists" are closed. For example, "A consists of B" means, in the same context, A includes only B, and no other components.

[0182] Combinations described herein, such as "at least one of A, B, or C", "one or more of A, B, or C", "at least one of A, B, and C", "one or more of A, B, and C", and "A, B, C, or any combination thereof", include any combination of A, B, and / or C, and can include multiples of A, multiples of B, or multiples of C. Specifically, combinations such as "at least one of A, B, or C", "one or more of A, B, or C", "at least one of A, B, and C", "one or more of A, B, and C", and "A, B, C, or any combination thereof", can be A only, B only, C only, A and B, A and C, B and C, or A and B and C, and any such combination can include any number of members of A, B, and / or C. For example, a combination of A and B can include one A and one B, one A and two B, two A and one B, or two A and two B.

Claims

1. A method for modeling thermo-chemical degradation in a digital twin of a power transformer, the method comprising using at least one hardware processor to, for each of one or more time intervals: determine a total water content in an insulating liquid of the power transformer; for each of a plurality of sections of at least one winding of the power transformer logically partitioned along at least one axis of the at least one winding, estimate a temperature of the section based on a load of the power transformer and a temperature gradient along at least the one axis, estimate a diffusion-related water content in an insulation of the at least one winding in the section caused by diffusion based on the estimated temperature and the total water content in the insulating liquid, estimate a degradation-related water content based on a degradation of a material of the insulation, and estimate a total water content within the insulation of the at least one winding in the section based on the diffusion-related water content and the degradation-related water content; and estimate a total water content in the power transformer based on the total water content in the insulating liquid and the total water content within the insulation of the at least one winding in all of the plurality of sections.

2. The method of claim 1, further comprising using the at least one hardware processor to, for each of the one or more time intervals, determine an average temperature of the insulating liquid for each of a plurality of time instants spanning the time interval.

3. The method of claim 2, wherein, the plurality of sections comprising: at least one lower laminate representing a first assembly element at a first end of the at least one winding along a longitudinal axis; at least one upper laminate representing a second assembly element at a second end of the at least one winding opposite the first end of the at least one winding along the longitudinal axis; and one or more coil sections each representing at least a portion of at least one coil between the first end and the second end of the at least one winding.

4. The method of claim 3, wherein, the temperature gradient comprising an axial temperature gradient along an axial axis and a radial temperature gradient along a radial axis, and wherein estimating the temperature of each of the plurality of sections comprises, for each of the plurality of time instants: computing a localized temperature of the at least one lower laminate based on the axial temperature gradient computed for the time instant and the average temperature of the insulating liquid; computing a localized temperature of the at least one upper laminate based on the axial temperature gradient computed for the time instant and the average temperature of the insulating liquid; and computing a localized temperature for each of the one or more coil sections based on the temperature, load, and the radial temperature gradient and the axial temperature gradient of the at least one lower laminate or the at least one upper laminate.

5. The method of claim 4, wherein, the one or more coil sections are a plurality of coil sections, and wherein the temperature for one of the plurality of coil sections closest to the second end is further computed based on a hot spot coefficient or a heat dissipation coefficient associated with the power transformer.

6. The method of claim 1, wherein, Estimating the diffusion-related water content includes, for each of a plurality of time instants spanning the time interval, calculating a water content diffused into the insulator based on a time constant for diffusion of water into the material of the insulator.

7. The method of claim 6, wherein, The water content diffused into the insulator is calculated for each of the plurality of time instants as: where W diffusion is the water content diffused into the insulation at time t, W equilibrium is the water content in the insulation at equilibrium, W initial is the water content in the insulation at a time immediately preceding time t, e is Euler's number, and τ p is the time constant.

8. The method of claim 1, wherein, The material of the insulator is cellulose-based.

9. The method of claim 8, wherein, The degradation-related water content in the insulator is estimated based on a water generation rate from breakage of cellulose chains in the cellulose-based material.

10. The method of claim 9, wherein, The water generation rate is calculated as: wherein W rate is the amount of water generated per hour, k is the number of breaks, Mol water is the molar mass of water, DP is the degree of polymerization of the material of the insulator, and Mol glucose is the molar mass of the monomer of glucose.

11. The method of claim 1, further comprising using the at least one hardware processor, for each of the one or more time intervals, calculating, for each of the plurality of segments of the at least one winding in the power transformer, a measure of aging for the segment based on a total water content in the insulator; and determining an overall measure of aging of the power transformer based on the measures of aging for the plurality of segments.

12. The method of claim 11, wherein, The measure of aging for each of the plurality of segments is further based on one or both of an oxygen content in the insulator or an acidity of the insulating liquid.

13. The method of claim 11, wherein, Calculating the measure of aging for each of the plurality of segments includes: determining a nominal aging parameter associated with the material of the insulator; interpolating an aging parameter for the segment based on a total water content in the insulator of the at least one winding in the segment; and calculating an aging ratio between the nominal aging parameter and the interpolated aging parameter.

14. The method of claim 13, wherein, Calculating the measure of aging for each of the plurality of segments further includes: determining an activation energy under nominal conditions associated with the material of the insulator; interpolating an activation energy of the material of the insulator; calculating an exponential coefficient based on the activation energy under nominal conditions and the interpolated activation energy; and determining the measure of aging for the segment based on the aging ratio and the exponential coefficient.

15. The method of claim 14, wherein, The measure of aging for each of the plurality of segments is calculated as: where V is the measured value of the aging, A is the interpolated aging parameter, A r is the nominal aging parameter, e is Euler's number, R is the molar gas constant, E r is the activation energy under nominal conditions, E is the interpolated activation energy, θ h,r is the hot spot to top oil temperature at nominal load, and θ h is the hot spot temperature.

16. The method of claim 1, wherein, Determining the total water content in the insulating liquid includes deriving the total water content in the insulating liquid from an output of at least one sensor in the power transformer, and wherein the method further comprises using the at least one hardware processor, for each of the one or more time intervals at least once: calculating a deviation between an actual value of the total water content in the insulating liquid derived from the output of the at least one sensor and one or more estimated values of the total water content in the insulating liquid output by the artificial intelligence (AI) model of the digital twin; and determining an adjustment parameter based on the deviation, wherein the estimation of the total water content in the transformer is further based on the adjustment parameter.

17. The method of claim 1, further comprising using the at least one hardware processor, based on the estimated total water content within the insulator, estimating a risk of dielectric failure of the insulator of the at least one winding.

18. The method of claim 1, further comprising estimating, using the at least one hardware processor, a likelihood of microbubbles on a surface of the insulation of the at least one winding based on the estimated total water content within the insulating fluid.

19. The method of claim 1, further comprising using the at least one hardware processor to: estimate a breakdown voltage of the insulating fluid based on a total water content in the insulating fluid; and generate an alert when the estimated breakdown voltage meets a threshold value.

20. A system comprising: at least one hardware processor; and software configured so as when executed by the at least one hardware processor to model thermal-chemical degradation in a digital twin of a power transformer by, for each of one or more time intervals: determining a total water content in an insulating fluid of the power transformer; for each of a plurality of sections of at least one winding of the power transformer logically divided along at least one axis of the at least one winding: estimating a temperature of the section based on a load of the power transformer and a temperature gradient along the at least one axis; estimating a diffusion-related water content in an insulation of the at least one winding in the section resulting from diffusion based on the estimated temperature and the total water content in the insulating fluid, estimating a degradation-related water content based on a degradation of a material of the insulation, and estimating a total water content within the insulation of the at least one winding in the section based on the diffusion-related water content and the degradation-related water content; and estimating a total water content in the power transformer based on the total water content in the insulating fluid and the total water content within the insulation of the at least one winding in all of the plurality of sections. ​

Images