A transformer cauer thermal parameter identification method and system based on modal constraint

Abstract

The application relates to a transformer Cauer thermal parameter identification method and system based on modal constraint, which comprises the following steps: obtaining winding hot spot time sequence temperature data and shell time sequence temperature data of a transformer under a target working condition; applying a thermal circuit characteristic equation constraint, performing second-order exponential fitting on the two types of data, forcing the two fitting curves to share a system time constant, obtaining a modal matching standard temperature rise curve and a steady-state temperature rise parameter; analytically calculating two-stage thermal resistance parameters based on the steady-state temperature rise parameter; taking the standard temperature rise curve as an optimization target and the thermal resistance as a known quantity, solving two-stage thermal capacity parameters through a constrained nonlinear optimization algorithm, and completing thermal parameter identification. The application eliminates modal mismatch from the bottom layer, reduces transient error, and improves the physical consistency of parameters; adopts a step-by-step decoupling strategy to reduce the optimization dimension and improve the convergence speed; constructs an offline parameter library to support online adaptive updating, realizes low-latency reasoning; and internally builds a closed-loop verification fallback mechanism to guarantee the robustness of the identification result.

Description

Technical Field

[0001] This invention relates to the field of transformer thermal parameter identification technology, and in particular to a transformer Cauer thermal parameter identification method and system based on modal constraints. Background Technology

[0002] Power transformers are core equipment in power transmission and distribution systems, and their winding hot spot temperatures directly determine the insulation aging rate, safe operating limits, and service life. In engineering practice, the Cauer second-order thermal circuit model is commonly used to describe the dynamic process of heat conduction and storage inside the transformer. This model relies on thermal resistance and thermal capacity parameters to construct a set of differential equations for the dynamic evolution of temperature, thereby enabling long-term prediction of winding hot spot temperatures and casing temperatures, as well as overload capacity assessment. However, these thermal parameters are intrinsic physical properties of the model and cannot be directly measured. They must be indirectly obtained through parameter identification methods based on observable temperature rise time-series data. Therefore, the accuracy and rationality of thermal parameter identification directly determine the engineering practical effectiveness of the thermal circuit model.

[0003] The most similar existing technical solutions can be mainly divided into two categories. The first category is the unconstrained second-order exponential fitting direct identification scheme. This scheme is currently the most widely used basic identification method. Its core approach is to collect time-series data of winding hot spot temperature and shell temperature under multiple operating conditions, and directly use a second-order exponential function to independently fit the two sets of temperature curves. The sole optimization objective is to minimize the numerical error between the original temperature data and the fitted curve, without imposing any characteristic equation constraints from the Cauer thermal circuit system on the fitting process. The fitting processes for hot spot temperature and shell temperature independently optimize all parameters such as time constant, amplitude coefficient, and steady-state temperature rise. After the fitting is completed, the steady-state temperature rise difference is extracted to directly calculate the two-stage thermal resistance. Then, using the original measured temperature as the target, an unconstrained nonlinear least squares algorithm is used to solve for the heat capacity parameters, and finally, the complete set of thermal parameters under a single operating condition is output. This scheme has a simple process, low computational threshold, and good fitting effect in the steady-state temperature rise range. It is often used for the rough calibration of thermal parameters of traditional offline transformers.

[0004] The second category is a mode-free, single-objective least squares optimization identification scheme. This scheme introduces an iterative optimization step based on the first category. It first uses unconstrained second-order exponential fitting to obtain the temperature curve, then sets thermal resistance and heat capacity as variables to be optimized. Using the time-series error of the original measured temperature as the single optimization objective, a conventional nonlinear least squares algorithm is used for global joint optimization to solve for all thermal parameters. This scheme can reduce steady-state numerical errors to some extent through multiple iterations. However, since neither the fitting nor the optimization stage introduces the inherent modal constraints of the thermal circuit system, its improvement effect is still limited to a finite numerical correction.

[0005] However, both of the aforementioned existing schemes share a common fundamental flaw: they fail to incorporate the inherent characteristic equations of the Cauer thermal circuit system as constraints throughout the entire process, resulting in an inherent modal mismatch between the fitted temperature analytical curves and the thermal circuit differential equations. The optimization process can only compensate for numerical deviations, but cannot eliminate the systematic errors caused by modal mismatch, which are particularly significant during the transient phase of rapid winding temperature rise. Furthermore, due to the lack of physical constraints, the thermal parameters identified under different load conditions exhibit poor consistency, the model's generalization ability is insufficient, and it is difficult to meet the practical engineering requirements for accurate assessment of the transformer's thermal state under all operating conditions, nor can it provide a stable and reliable model foundation for overload capacity calculation and insulation life prediction. Summary of the Invention

[0006] This invention provides a transformer Cauer thermal parameter identification method and system based on modal constraints, which solves the technical problems of missing thermal circuit modal constraints, large transient temperature rise identification error, and poor consistency of parameters under multiple operating conditions in the prior art.

[0007] In a first aspect of the present invention, a method for identifying transformer Cauer thermal parameters based on modal constraints is provided, comprising: S1, acquire the winding hot spot time-series temperature data and the outer casing time-series temperature data of the transformer under the target operating conditions; S2, apply the characteristic equation constraint of the Cauer second-order thermal circuit system, perform second-order exponential fitting on the winding hot spot time-series temperature data and the shell time-series temperature data, force the two fitting curves to share the same set of system time constants, and obtain the standard temperature rise curve and steady-state temperature rise parameters of modal matching. S3. Based on the steady-state temperature rise parameters, the two-stage thermal resistance parameters of the Cauer second-order thermal circuit model are obtained by analytical calculation. S4. Using the standard temperature rise curve as the optimization target, and taking the two-stage thermal resistance parameters as known quantities, the two-stage thermal capacity parameters of the Cauer second-order thermal circuit model are obtained by using a constrained nonlinear optimization algorithm, thus completing the identification of the transformer thermal parameters.

[0008] Preferably, in step S1, acquiring the winding hot spot time-series temperature data and the casing time-series temperature data of the transformer under the target operating condition includes: Collect multiple sets of raw time-series temperature data under different constant load rate conditions. Each set of conditions corresponds to a fixed load rate. The raw time-series temperature data includes the raw time-series temperature data of the winding hotspots and the raw time-series temperature data of the casing. The original time-series temperature data is preprocessed to remove invalid noise points caused by abnormal sensor jumps and short-term disturbances, and the time-series sampling interval is unified and time-series alignment is completed to obtain a regular multi-condition temperature time-series dataset. The multi-condition temperature time series dataset is divided into single-condition segments according to the load rate to obtain independent winding hot spot time series temperature data and shell time series temperature data under each target condition.

[0009] Preferably, step S2 specifically includes: Establish the general solution form of the Cauer second-order thermal circuit differential equations: (1) In the formula, T h ( t Let t be the winding hot spot temperature at any time t. T k ( t Let t be the temperature of the device casing at any given time. T h,ss As the temperature rises steadily in hot spots, T k,ss For the steady-state temperature rise of the outer casing, A 1. A 2 represents the amplitude coefficient of the second-order exponential dynamic term of hotspot temperature. B 1. B 2 represents the amplitude coefficient of the second-order exponential dynamic term of the outer casing temperature. τ 1. τ 2 represents the unified first-order and second-order time constants of the Cauer second-order thermal circuit system, respectively; Based on the aforementioned general solution form, the winding hot spot temperature fitting curve and the casing temperature fitting curve are forced to share the same set of first-order time constants. τ 1 and second-order time constant τ 2. With the goal of minimizing the global error between the original temperature time series data and the fitted curve, a nonlinear fitting algorithm is used to solve the fitting parameters, and the standard temperature rise curve of the modal matching and the steady-state temperature rise parameters are output.

[0010] Preferably, in step S3, based on the steady-state temperature rise parameters, the two-stage thermal resistance parameters of the Cauer second-order thermal circuit model are analytically calculated, specifically including: Extract the hot spot steady-state temperature rise from the steady-state temperature rise parameters. T h,ss and the steady-state temperature rise of the casing T k,ss And obtain the total heat loss power of the transformer under the current operating conditions. P ; Based on the steady-state heat conduction equilibrium relationship, the two-stage thermal resistance parameters are analytically calculated using the following formula: (2) In the formula, R 1 represents the first-stage thermal resistance from the winding to the casing. R 2 represents the secondary thermal resistance from the casing to the environment.

[0011] Preferably, in step S4, using the standard temperature rise curve as the optimization objective and the two-stage thermal resistance parameters as known quantities, the two-stage heat capacity parameters of the Cauer second-order thermal circuit model are obtained by a constrained nonlinear optimization algorithm, specifically including: Construct a complete set of Cauer second-order thermal circuit differential equations, using the two-stage thermal resistance parameters as fixed input parameters and the two-stage heat capacity parameters as variables to be optimized; The optimization objective function is constructed with the goal of minimizing the sum of squared errors between the time-series temperature curve output by the simulation of the thermal differential equations and the standard temperature rise curve. Apply physical boundary constraints on heat capacity, and use the trust domain reflection algorithm to iteratively solve the optimization objective function, outputting the optimal two-stage heat capacity parameters under the current operating conditions.

[0012] Preferably, after identifying the thermal parameters of the transformer, the method further includes: Substituting the two-stage thermal resistance parameters and the two-stage heat capacity parameters into the Cauer second-order thermal circuit differential equations, the simulation outputs a complete time-series temperature curve. The complete time-series temperature curve output by the simulation is compared globally with the standard temperature rise curve to calculate the temperature rise deviation over the entire time period, and the error level of the transient range of rapid temperature rise is verified in particular. If the temperature rise deviation over the entire time period meets the preset engineering threshold, the current operating condition thermal parameter identification is deemed valid; if the temperature rise deviation over the entire time period exceeds the preset engineering threshold, the process returns to the second-order exponential fitting operation in step S2 and the constraint fitting and parameter identification process is re-executed.

[0013] Preferably, after identifying the thermal parameters of the transformer, the method further includes: Traverse all different load conditions and sequentially execute the complete thermal parameter identification process corresponding to steps S1-S4 to obtain the complete thermal parameter set corresponding to each load condition. The complete thermal parameter set includes two levels of thermal resistance parameters and two levels of thermal capacity parameters. The complete thermal parameter sets corresponding to each load condition are associated, bound, and stored one by one with the corresponding load rate to build a transformer load-related Cauer thermal circuit parameter database, so as to support online real-time retrieval of matching thermal parameters for temperature prediction.

[0014] In a second aspect of the present invention, a transformer Cauer thermal parameter identification system based on modal constraints is provided, comprising: The data acquisition module is used to acquire the winding hot spot time-series temperature data and the outer casing time-series temperature data of the transformer under the target operating conditions. The modal constraint fitting module is used to apply the characteristic equation constraint of the Cauer second-order thermal circuit system, perform second-order exponential fitting on the winding hot spot time-series temperature data and the shell time-series temperature data, force the two fitting curves to share the same set of system time constants, and obtain the standard temperature rise curve and steady-state temperature rise parameters of modal matching. The thermal resistance analytical calculation module is used to analytically calculate the two-stage thermal resistance parameters of the Cauer second-order thermal circuit model based on the steady-state temperature rise parameters. The heat capacity optimization solution module is used to obtain the two-stage heat capacity parameters of the Cauer second-order thermal circuit model by taking the standard temperature rise curve as the optimization target and the two-stage thermal resistance parameters as known quantities through a constrained nonlinear optimization algorithm, thereby completing the identification of the transformer thermal parameters. The model verification module is used to substitute the identified thermal parameters into the thermal circuit differential equations to simulate the output temperature curve, perform a global comparison and verification with the standard temperature rise curve, and return to re-execute the constraint fitting and parameter identification process when the deviation exceeds the limit. The parameter library construction module is used to traverse multiple sets of load conditions to perform the identification process, associate and bind the complete thermal parameter group corresponding to each condition with the load condition, and build a transformer load-related Cauer thermal circuit parameter database.

[0015] In a third aspect of the present invention, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable by the processor, wherein the processor executes the computer program to implement the steps of the method as described in the first aspect of the present invention.

[0016] In a fourth aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the method as described in the first aspect of the present invention.

[0017] This invention provides a transformer Cauer thermal parameter identification method and system based on modal constraints. By applying characteristic equation constraints and forcing the fitted curves to share the system time constant, modal mismatch is eliminated from the ground up, significantly reducing transient temperature rise identification errors. Using the standard temperature rise curve as the optimization target and combining it with a constrained nonlinear optimization algorithm, the identified parameters strictly conform to the physical laws of heat conduction, improving the consistency of parameters under multiple operating conditions. A step-by-step decoupling strategy is adopted, treating thermal resistance as a known quantity and optimizing only the heat capacity, effectively reducing the optimization dimensionality and improving convergence speed and computational efficiency. Attached Figure Description

[0018] Figure 1A schematic diagram of the transformer Cauer thermal parameter identification method based on modal constraints provided by the present invention; Figure 2 A flowchart of transformer Cauer thermal parameter identification based on modal constraints provided by the present invention; Figure 3 The structural block diagram of the transformer Cauer thermal parameter identification system based on modal constraints provided by the present invention; Figure 4 This is a structural block diagram of the electronic device provided by the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Figure 1 A flowchart illustrating the transformer Cauer thermal parameter identification method based on modal constraints provided by this invention. (Refer to...) Figure 1 The method includes the following steps: Step S1: Obtain the winding hot spot time-series temperature data and the outer casing time-series temperature data of the transformer under the target operating conditions.

[0021] Specifically, the winding hotspot temperature data and the casing temperature data refer to the continuous data sequences of the winding hotspot temperature and the equipment casing temperature over time, obtained by the transformer under a specific target load condition through built-in fiber optic sensors or thermal simulation. These data serve as the data foundation for subsequent thermal parameter inversion. In practice, the two types of temperature time-series data under the target operating condition are directly collected and extracted as the raw input for subsequent fitting and identification.

[0022] Step S2: Apply the characteristic equation constraint of the Cauer second-order thermal circuit system, perform second-order exponential fitting on the winding hot spot time-series temperature data and the shell time-series temperature data, force the two fitting curves to share the same set of system time constants, and obtain the standard temperature rise curve and steady-state temperature rise parameters of modal matching.

[0023] Specifically, the characteristic equation constraint of the Cauer second-order thermal circuit system refers to forcing the hot spot and shell temperature analytical models to use the same time constant based on the inherent dynamic characteristics determined by the eigenvalues ​​of the thermal circuit system matrix. In implementation, a second-order exponential general solution model containing the unified time constant is established. The two sets of temperature data are substituted into this model for joint fitting, with the goal of minimizing the global error, thereby outputting a standard temperature rise curve that strictly conforms to the physical modes of the thermal circuit and the corresponding steady-state temperature rise parameters.

[0024] Step S3: Based on the steady-state temperature rise parameters, the two-stage thermal resistance parameters of the Cauer second-order thermal circuit model are analytically calculated.

[0025] Specifically, the two-stage thermal resistance parameters include the primary thermal resistance from the winding to the casing and the secondary thermal resistance from the casing to the environment. In practice, the hot spot and casing steady-state temperature rise parameters obtained from step S2 are directly extracted. Combined with the total heat loss power of the transformer under the current operating conditions, the two-stage thermal resistance parameters are directly solved analytically through algebraic relationships by utilizing the physical law that the heat capacity energy storage effect disappears and heat conduction reaches equilibrium under steady state.

[0026] Step S4: Using the standard temperature rise curve as the optimization target, and taking the two-stage thermal resistance parameters as known quantities, the two-stage thermal capacity parameters of the Cauer second-order thermal circuit model are obtained by using a constrained nonlinear optimization algorithm, thus completing the identification of the transformer thermal parameters.

[0027] Specifically, constrained nonlinear optimization algorithms refer to numerical methods that iteratively optimize and solve for the parameters of complex nonlinear models under boundary conditions that satisfy the physical properties of energy storage elements. In practice, a set of thermal differential equations containing known thermal resistance is constructed. Using the standard temperature rise curve output in step S2 as the benchmark target, only the two-stage heat capacity is set as the variables to be optimized for iterative solution, thereby accurately reproducing the heat capacity parameters that conform to physical laws and completing the identification of the complete set of thermal parameters.

[0028] The transformer Cauer thermal parameter identification method based on modal constraints provided by this invention eliminates modal mismatch from the ground up by applying characteristic equation constraints and forcing the fitted curves to share the same system time constant, significantly reducing transient temperature rise identification errors. Using the standard temperature rise curve as the optimization target and combining it with a constrained nonlinear optimization algorithm ensures that the identified parameters strictly conform to the physical laws of heat conduction, improving the consistency of parameters under multiple operating conditions. A step-by-step decoupling strategy is adopted, treating thermal resistance as a known quantity and optimizing only the heat capacity, effectively reducing the optimization dimensionality and improving convergence speed and computational efficiency.

[0029] In some embodiments of this application, step S1, which involves obtaining the winding hot spot time-series temperature data and the casing time-series temperature data of the transformer under the target operating condition, specifically includes: Step S101: Collect multiple sets of time-series temperature data of transformers under different constant load rate conditions.

[0030] Specifically, the timing temperature data includes the timing temperature of winding hot spots. T h ( t and equipment housing time-series temperature T k ( t Each set of operating conditions corresponds to a fixed load rate. n In this embodiment, sensors or monitoring systems deployed at key parts of the transformer are used to monitor the transformer under different constant load rates. n Under stable operating conditions, the temperature of the hottest spot in the winding is recorded synchronously. T h ( t ) and equipment casing temperature T k ( t A continuous data sequence that changes over time is used to construct a raw temperature dataset covering multiple load conditions.

[0031] Step S102: Clean and organize the collected time-series temperature data.

[0032] Specifically, this step aims to remove invalid noise points in the collected data caused by abnormal sensor jumps or short-term disturbances, and to standardize the time-series sampling interval. In this embodiment, the original data sequence obtained in step S101 is traversed and detected to identify and remove abnormal jump points exceeding the preset physical threshold range and short-term disturbance data that are not physically regular. Then, interpolation or resampling algorithms are used to unify the data of all channels to the preset standard time-series sampling interval, thereby constructing a regular multi-condition temperature time-series dataset.

[0033] Step S103: Divide the single-condition independent dataset.

[0034] Specifically, based on the load factor n Based on the differences, the normalized multi-condition temperature time-series dataset is divided into multiple independent single-condition datasets, with each dataset corresponding to a specific load condition. In specific implementation, the same load rate is used... n Winding hotspot timing temperature T h ( t ) and the time-series temperature of the equipment casing T k ( t The datasets are grouped into a single data set, and each dataset will undergo separate fitting and parameter identification processes.

[0035] This embodiment obtains clean, time-series-uniform, and condition-independent raw temperature input data through abnormal data cleaning, time-series alignment, and single-condition dataset splitting. This provides a reliable data source for subsequent constraint exponent fitting, effectively ensuring the condition independence and data reliability of the overall identification process.

[0036] In some embodiments of this application, in step S2, the characteristic equation constraint of the Cauer second-order thermal circuit system is applied, and a second-order exponential fit is performed on the winding hot spot time-series temperature data and the shell time-series temperature data. The two fitted curves are forced to share the same set of system time constants to obtain the standard temperature rise curve and steady-state temperature rise parameters for modal matching. Specifically, this includes: Step S201: Establish the general solution form of the Cauer second-order thermal circuit differential equation system.

[0037] Specifically, this application defines a second-order exponential fitting method constrained by the characteristic equation of the thermal path (CECF method). The core of this method is to apply the Cauer second-order characteristic equation of the thermal path system to the hot spot and shell temperature fitting process, forcing the two temperature curves to share the same dynamic time constant and eliminating modal mismatch.

[0038] The general solution of Cauer's second-order thermal circuit differential equations is as follows: (1) In the formula, T h ( t (t) represents the winding hot spot temperature at any time t, in Kelvin. T k ( t (t) represents the equipment casing temperature at any given time t, in Kelvin (K). T h,ss For steady-state temperature rise of hotspots, in K; T k,ss This represents the steady-state temperature rise of the outer casing, in Kelvin (K). A 1. A 2 represents the amplitude coefficient of the second-order exponential dynamic term of hotspot temperature, which is dimensionless; B 1. B 2 represents the amplitude coefficient of the second-order exponential dynamic term of the outer shell temperature, which is dimensionless; τ 1. τ 2 represents the unified first-order and second-order time constants of the Cauer second-order thermal circuit system, in seconds.

[0039] Step S202: Apply the Cauer thermal path characteristic equation constraint and perform a joint fitting solution.

[0040] Specifically, the eigenvalues ​​of the second-order thermal system matrix correspond to a unified time constant, and the two temperature fitting curves for the forced hot spot and the shell share the same set of first-order time constants. τ 1 and second-order time constant τ 2. Optimize the amplitude coefficient independently. A 1. A 2. B 1. B 2. Steady-state temperature rise term. In specific implementation, the goal is to minimize the global error between the original temperature time series data and the fitted curve, and a nonlinear fitting algorithm is used to solve for all 8 fitting parameters. A 1, A 2, B 1, B 2, τ 1, τ 2, T h,ss , T k,ss This outputs a standardized second-order exponential temperature analytical expression with modal constraints (i.e., a standard temperature rise curve with modal matching) and steady-state temperature rise parameters.

[0041] This embodiment establishes a second-order exponential general solution model with a unified time constant, jointly fits the hot spot and shell temperature data, applies thermal path characteristic equation constraints, and ensures that the fitted curve strictly matches the modal characteristics of the Cauer second-order thermal path differential system. This eliminates modal mismatch defects from the source, provides a standard target curve with physical consistency for subsequent thermal parameter inversion, and effectively suppresses the identification system error of the transient temperature rise range.

[0042] In some embodiments of this application, step S3 involves analytically calculating the two-stage thermal resistance parameters of the Cauer second-order thermal circuit model based on the steady-state temperature rise parameters. Specifically, this includes: Step S301: Extract steady-state temperature rise parameters and obtain the total heat loss power under the current operating conditions.

[0043] Specifically, the steady-state temperature rise of the hot spot is directly read from the modal matching standard temperature rise curve and steady-state temperature rise parameters output in step S202. T h,ss With the steady-state temperature rise of the outer casing T k,ss At the same time, the total heat loss power P of the transformer under the current load condition is obtained, providing a data basis for subsequent analytical calculations.

[0044] Step S302: Analyze the thermal resistance parameters of the two stages based on the steady-state thermal conduction equilibrium relationship.

[0045] In this embodiment, the two-stage thermal resistance parameters are directly calculated analytically based on the steady-state heat conduction equilibrium relationship. Specifically, utilizing the physical law that the heat capacity energy storage effect disappears and heat conduction reaches equilibrium under steady state, the two-stage thermal resistance parameters are analytically calculated using the following formula: (2) In the formula, R 1 represents the first-stage thermal resistance from the winding to the casing, in K / W; R 2 represents the secondary thermal resistance from the casing to the environment, in K / W; P This represents the total heat loss power of the transformer under the current load conditions, in watts (W).

[0046] Step S303: Store the thermal resistance parameters solved under the current operating conditions as fixed known parameters for subsequent thermal capacity optimization identification.

[0047] Specifically, it stores the thermal resistance parameters solved under the current operating conditions. R 1( n ), R 2( n The two-stage thermal resistance parameters obtained from the analytical calculation are solidified as known constants and used as fixed input parameters in the subsequent step S4 for optimizing the thermal capacity parameters, and will no longer participate in the iterative optimization.

[0048] This embodiment rapidly obtains thermal resistance parameters based on the steady-state heat conduction law without dynamic energy storage, fixes the thermal resistance as a known constant, significantly reduces the dimensionality of subsequent nonlinear optimization solutions, reduces computational complexity, and improves the efficiency of batch thermal parameter identification under multiple operating conditions.

[0049] In some embodiments of this application, in step S4, using the standard temperature rise curve as the optimization objective and the two-stage thermal resistance parameters as known quantities, the two-stage heat capacity parameters of the Cauer second-order thermal circuit model are obtained by a constrained nonlinear optimization algorithm, specifically including: Step S401: Construct the complete set of Cauer second-order thermal circuit differential equations and set the variables to be optimized.

[0050] Specifically, this application defines a Modal Matching Nonlinear Least Squares (MMNLS) method for inverting thermal parameters. It constructs a complete set of Cauer second-order thermal path differential equations and applies the two-stage thermal resistance parameters obtained in step S3. R 1. R 2 is used as a fixed input parameter, and the two-stage heat capacity parameters are... C 1. C 2 is set as the variable to be optimized.

[0051] Step S402: Construct the optimization objective function.

[0052] Specifically, the optimization objective is to minimize the sum of squared errors between the time-series temperature curve output from the thermal differential equation system simulation and the standard second-order exponential curve (i.e., the standard temperature rise curve) obtained by fitting the CECF method in step S2. An optimization objective function is then constructed. By numerically solving this differential equation system, the sum of squared deviations between the simulated output temperature and the standard temperature rise curve at each time point is calculated, and this is used as the fitness function to evaluate the merits of the parameters.

[0053] Step S403: Apply physical boundary constraints for heat capacity and iteratively solve for the optimal heat capacity parameters.

[0054] Specifically, physical boundary constraints are introduced to force the heat capacity parameter to be greater than 0, in order to satisfy the physical properties of the energy storage element. The trust domain reflection algorithm is used to iteratively solve this least-squares optimization problem. Under the premise of satisfying the physical boundary conditions, a fast global optimal parameter search is performed, outputting the optimal two-stage heat capacity parameters under the current operating conditions. C 1( n ), C 2( n This allows for the identification of the transformer's thermal parameters.

[0055] This embodiment accurately inverts heat capacity parameters that conform to thermal dynamic characteristics based on the standard temperature curve after modal matching. By adopting a step-by-step strategy of combining steady-state thermal resistance analytical direct calculation with heat capacity single-variable constraint optimization, the optimization dimensions are significantly reduced, and the computational cost of batch identification is lowered; at the same time, it ensures that the heat capacity parameters have true physical meaning, effectively reducing the parameter identification error in the transient temperature rise range.

[0056] Figure 2 The overall flowchart for transformer Cauer thermal parameter identification based on modal constraints provided by this invention, in some embodiments of this application, after completing the identification of transformer thermal parameters, the method further includes: Step S5: Substitute the identified thermal parameters into the thermal circuit differential equation set to simulate the output temperature curve, perform a global comparison and verification with the standard temperature rise curve, and return to re-execute the constraint fitting and parameter identification process if the deviation exceeds the limit.

[0057] Step S5 specifically includes the following sub-steps S501-S503: Step S501: Substitute the identified complete set of thermal parameters into the Cauer second-order thermal circuit differential equations for simulation.

[0058] Specifically, the two-stage thermal resistance parameters obtained from the analytical calculation in step S3 are... R 1. R 2 and the two-stage heat capacity parameters obtained from step S4 optimization and identification. C 1. C2 is used as a known input quantity and substituted into the Cauer second-order thermal circuit differential equation system. The differential equation system is solved numerically, and the simulation output is a temperature curve covering the complete time series.

[0059] Step S502: Perform a global comparison between the complete time-series temperature curve output by the simulation and the standard temperature rise curve.

[0060] Specifically, the modal matching standard temperature rise curve obtained by fitting the CECF method in step S2 is acquired and compared with the complete time-series temperature curve output by the simulation in step S501 over all time periods. The temperature rise deviation between the two at each time point is calculated. During the comparison process, the error level in the transient region of rapid temperature rise is carefully verified to evaluate the ability of thermal parameters to reproduce dynamic thermal characteristics.

[0061] Step S503: Determine the validity of the identification based on the preset engineering threshold and execute the closed-loop rollback logic.

[0062] Specifically, if the temperature rise deviation over the entire time period meets the preset engineering threshold, the thermal parameter identification result under the current operating condition is determined to be valid and retained. If the temperature rise deviation over the entire time period exceeds the preset engineering threshold, the current identification result is determined to be invalid, and a rollback mechanism is automatically triggered to return to the second-order exponential fitting operation in step S2, and the constraint fitting and subsequent parameter identification process are re-executed until the identification error meets the requirements.

[0063] This embodiment achieves fully automated quality control of the entire process of thermal parameter identification through a built-in closed-loop verification and rollback quality control mechanism. By comparing the reproduced temperature rise curve with the standard fitted curve, unqualified thermal parameters caused by modal mismatch are automatically eliminated, avoiding the amplification of long-term prediction deviations caused by the introduction of invalid parameters into practical applications, thereby improving the robustness of the identification results and the stability of the overall operation.

[0064] In some embodiments of this application, reference is made to Figure 2 After identifying the thermal parameters of the transformer, the method further includes: Step S6: Traverse multiple sets of load conditions to execute the identification process, associate and bind the complete thermal parameter group corresponding to each condition with the load condition and store it to build a transformer load associated Cauer thermal circuit parameter database.

[0065] Specifically, all collected multi-load conditions are traversed, and the complete thermal parameter identification process corresponding to steps S1 to S5 is executed sequentially to obtain the complete thermal parameter set corresponding to each load factor n. R 1( n ), R 2( n ), C 1( n ), C 2( nFor each set of time-series temperature data under a specific load rate, the entire process from modal constraint fitting and steady-state thermal resistance analysis to dynamic heat capacity optimization is completed independently, thereby obtaining a set of off-grid parameters covering the entire operating load range.

[0066] Furthermore, the complete thermal parameter sets corresponding to each load condition are associated, bound, and stored with the corresponding load rates to construct a transformer load-related Cauer thermal circuit parameter database. In specific implementation, a mapping table between load rates and thermal parameters is established, and the identified parameters are stored in the database to support rapid retrieval of thermal models and temperature prediction under any subsequent load condition. The construction of this database eliminates the need to repeatedly execute the entire fitting and optimization process during online temperature rise simulation. Instead, it allows for rapid table lookup of matching parameters based on the rolling load time domain, enabling low-latency, second-level real-time temperature rise inference. This effectively adapts to resource-constrained engineering scenarios such as substation edge monitoring and online thermal status management.

[0067] This embodiment constructs an offline database of thermal parameters related to all load conditions, forming a complete thermal parameter dataset covering the entire operating load range. This provides comprehensive parameter support for real-time thermal state prediction and overload capacity calculation of transformers under dynamic load. Simultaneously, it avoids the high latency issues caused by repeated online calculations, improving engineering deployment performance and real-time response capabilities.

[0068] Based on the above embodiments, after the transformer load-related Cauer thermal circuit parameter database is constructed, the method further includes: The CECF fitting proxy model is periodically updated based on field measurement data.

[0069] Specifically, during the online operation of the transformer, the winding hot spot time-series temperature data and the shell time-series temperature data under the current real-time load rate are periodically collected. The newly collected measured data are used as incremental samples and input into the corresponding load rate range in the constructed transformer load-related Cauer thermal circuit parameter database. The CECF fitting proxy model established in step S2 is modified and iteratively updated using an incremental learning algorithm or a sliding window mechanism. By continuously reinjecting the field-measured temperature rise dynamic characteristic data, model drift caused by transformer insulation aging, oil quality changes, or environmental factors is eliminated, ensuring that the CECF fitting proxy model can adapt to the current physical state of the transformer in real time, thereby maintaining the long-term accuracy of low-latency, second-level temperature rise inference.

[0070] Figure 3 The structural block diagram of the transformer Cauer thermal parameter identification system based on modal constraints provided by the present invention is shown below. Figure 3 The system includes: The data acquisition module is used to acquire the winding hot spot time-series temperature data and the outer casing time-series temperature data of the transformer under the target operating conditions. The modal constraint fitting module is used to apply the characteristic equation constraint of the Cauer second-order thermal circuit system, perform second-order exponential fitting on the winding hot spot time-series temperature data and the shell time-series temperature data, force the two fitting curves to share the same set of system time constants, and obtain the standard temperature rise curve and steady-state temperature rise parameters of modal matching. The thermal resistance analytical calculation module is used to analytically calculate the two-stage thermal resistance parameters of the Cauer second-order thermal circuit model based on the steady-state temperature rise parameters. The heat capacity optimization solution module is used to obtain the two-stage heat capacity parameters of the Cauer second-order thermal circuit model by taking the standard temperature rise curve as the optimization target and the two-stage thermal resistance parameters as known quantities through a constrained nonlinear optimization algorithm, thereby completing the identification of the transformer thermal parameters. The model verification module is used to substitute the identified thermal parameters into the thermal circuit differential equations to simulate the output temperature curve, perform a global comparison and verification with the standard temperature rise curve, and return to re-execute the constraint fitting and parameter identification process when the deviation exceeds the limit. The parameter library construction module is used to traverse multiple sets of load conditions to perform the identification process, associate and bind the complete thermal parameter group corresponding to each condition with the load condition, and build a transformer load-related Cauer thermal circuit parameter database.

[0071] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the above system and modules can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0072] The transformer Cauer thermal parameter identification method and system based on modal constraints provided by this invention have the following advantages compared with the prior art: (1) The thermal circuit mode matching capability is stronger, and the transient temperature rise identification error is significantly reduced. The existing optimal scheme has no thermal circuit characteristic equation constraint, and the hot spot and shell temperature fitting curves are independently optimized for time constants. The temperature analytical model and the inherent modes of the Cauer thermal circuit differential system are mismatched, and there is a fixed system deviation in the rapid rise stage of the winding temperature. This invention uses the CECF method to force the two temperature rise curves to share a unified time constant, strictly fits the modal characteristics of the second-order thermal circuit system, eliminates the modal mismatch defect from the bottom layer of modeling, significantly suppresses the transient temperature rise interval identification error, and uniformly improves the accuracy of temperature rise fitting and parameter inversion throughout the entire time period.

[0073] (2) The optimization objective has a physical benchmark, and the physical consistency of the identified thermal parameters is better. Existing least squares optimization directly uses the original measured temperature as the optimization objective. The fitted curve has no thermal circuit mode constraints, and the obtained thermal resistance and heat capacity can only match the values. The parameters fluctuate drastically under different load conditions and do not meet the physical laws of transformer heat transfer. The MMNLS method of this invention uses the mode matching standard temperature rise curve output by CECF as the optimization benchmark, combined with integrated physical penalty constraints. The thermal parameters output by iteration completely fit the dynamic characteristics of Cauer's second-order thermal circuit differential equation. The parameter change law under different load conditions is stable and reasonable, and the generalization ability of the model is significantly improved.

[0074] (3) Step-by-step decoupled optimization architecture significantly improves optimization efficiency and convergence speed. The existing optimal solution uses thermal resistance and heat capacity as all variables to be optimized for joint global optimization. The optimization variable dimension is high, and the thermal circuit simulation model needs to be run completely in each iteration. The batch identification calculation for multiple operating conditions is time-consuming. This invention directly solves the thermal resistance by relying on the steady-state heat conduction balance relationship and solidifies it as a known constant. Only the two-stage heat capacity is used as the optimization variable, which greatly reduces the dimension of nonlinear optimization solution. With the trust domain reflection fast iteration mechanism, the number of real evaluations of thermal circuit simulation is significantly reduced, and the efficiency of batch thermal parameter identification for multiple load conditions is greatly improved.

[0075] (4) Offline parameter library + online adaptive update architecture, resulting in superior real-time engineering deployment performance. Existing identification schemes only support single-operating-condition offline calculations, lacking standardized operating condition parameter storage, rolling table lookup, and adaptive update logic. Online temperature rise inference requires complete repeated fitting and optimization of the entire process, resulting in high latency and failing to meet the real-time calculation requirements of edge monitoring equipment. This invention constructs a full-load-condition associated thermal parameter library offline, and online relies on rolling load time domain to quickly look up matching parameters. Simultaneously, it periodically recharges on-site measured temperature rise data to iteratively update the CECF fitting proxy model, enabling low-latency, second-level real-time temperature rise inference, adapting to resource-constrained engineering scenarios such as substation edge monitoring and online thermal status management.

[0076] (5) Built-in closed-loop verification and rollback quality control mechanism, resulting in higher robustness of identification results. Existing best-in-class technologies lack standardized model consistency verification processes and cannot automatically identify unqualified thermal parameters caused by modal mismatch. Invalid parameters with excessive errors are directly used in temperature prediction, which continuously amplifies prediction deviations over long-term operation. This invention sets up a complete closed-loop verification process, comparing the temperature rise curve reproduced by the thermal path with the CECF standard fitting curve. If the error exceeds the limit, it automatically rolls back and re-performs constraint fitting, forming a fully automated quality control logic that avoids unqualified thermal parameters from being used in actual applications, resulting in stronger overall system stability.

[0077] Figure 4 A structural block diagram of the electronic device provided by the present invention, such as Figure 4As shown, the present invention also provides an electronic device 400, which can be a mobile terminal, desktop computer, laptop, handheld computer, server, or other computing device. The electronic device 400 includes a processor 401 and a memory 402, wherein the memory 402 stores a transformer Cauer thermal parameter identification program 403 based on modal constraints. In one embodiment, when the transformer Cauer thermal parameter identification program 403 based on modal constraints is executed by the processor 401, it performs the following steps: Acquire the winding hot spot time-series temperature data and the outer casing time-series temperature data of the transformer under the target operating conditions; By applying the characteristic equation constraint of the Cauer second-order thermal circuit system, second-order exponential fitting is performed on the winding hot spot time-series temperature data and the shell time-series temperature data, forcing the two fitting curves to share the same set of system time constants, and obtaining the standard temperature rise curve and steady-state temperature rise parameters of modal matching. Based on the steady-state temperature rise parameters, the two-stage thermal resistance parameters of the Cauer second-order thermal circuit model are analytically calculated. Using the standard temperature rise curve as the optimization target and the two-stage thermal resistance parameters as known quantities, the two-stage thermal capacity parameters of the Cauer second-order thermal circuit model are obtained by using a constrained nonlinear optimization algorithm, thus completing the identification of the transformer thermal parameters.

[0078] This embodiment also provides a computer-readable storage medium storing a transformer Cauer thermal parameter identification program based on modal constraints. When the transformer Cauer thermal parameter identification program based on modal constraints is executed by a processor, it implements the steps of the transformer Cauer thermal parameter identification method based on modal constraints.

[0079] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

[0080] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for identifying Cauer thermal parameters of a transformer based on modal constraints, characterized in that, include: S1, acquire the winding hot spot time-series temperature data and the outer casing time-series temperature data of the transformer under the target operating conditions; S2, apply the characteristic equation constraint of the Cauer second-order thermal circuit system, perform second-order exponential fitting on the winding hot spot time-series temperature data and the shell time-series temperature data, force the two fitting curves to share the same set of system time constants, and obtain the standard temperature rise curve and steady-state temperature rise parameters of modal matching. S3. Based on the steady-state temperature rise parameters, the two-stage thermal resistance parameters of the Cauer second-order thermal circuit model are obtained by analytical calculation. S4. Using the standard temperature rise curve as the optimization target, and taking the two-stage thermal resistance parameters as known quantities, the two-stage thermal capacity parameters of the Cauer second-order thermal circuit model are obtained by using a constrained nonlinear optimization algorithm, thus completing the identification of the transformer thermal parameters.

2. The transformer Cauer thermal parameter identification method based on modal constraints according to claim 1, characterized in that, In step S1, acquiring the winding hot spot time-series temperature data and the casing time-series temperature data of the transformer under the target operating condition includes: Collect multiple sets of raw time-series temperature data under different constant load rate conditions. Each set of conditions corresponds to a fixed load rate. The raw time-series temperature data includes the raw time-series temperature data of the winding hotspots and the raw time-series temperature data of the casing. The original time-series temperature data is preprocessed to remove invalid noise points caused by abnormal sensor jumps and short-term disturbances, and the time-series sampling interval is unified and time-series alignment is completed to obtain a regular multi-condition temperature time-series dataset. The multi-condition temperature time series dataset is divided into single-condition segments according to the load rate to obtain independent winding hot spot time series temperature data and shell time series temperature data under each target condition.

3. The method for identifying transformer Cauer thermal parameters based on modal constraints according to claim 1, characterized in that, Step S2 specifically includes: Establish the general solution form of the Cauer second-order thermal circuit differential equations: （1） In the formula, T h ( t Let t be the winding hot spot temperature at any time t. T k ( t Let t be the temperature of the device casing at any given time. T h,ss As the temperature in hot spots steadily rises, T k,ss For the steady-state temperature rise of the outer casing, A 1. A 2 represents the amplitude coefficient of the second-order exponential dynamic term of hotspot temperature. B 1. B 2 represents the amplitude coefficient of the second-order exponential dynamic term of the outer casing temperature. τ 1. τ 2 represents the unified first-order and second-order time constants of the Cauer second-order thermal circuit system, respectively; Based on the aforementioned general solution form, the winding hot spot temperature fitting curve and the casing temperature fitting curve are forced to share the same set of first-order time constants. τ 1 and second-order time constant τ 2. With the goal of minimizing the global error between the original temperature time series data and the fitted curve, a nonlinear fitting algorithm is used to solve the fitting parameters, and the standard temperature rise curve of the modal matching and the steady-state temperature rise parameters are output.

4. The transformer Cauer thermal parameter identification method based on modal constraints according to claim 1, characterized in that, In step S3, based on the steady-state temperature rise parameters, the two-stage thermal resistance parameters of the Cauer second-order thermal circuit model are analytically calculated, specifically including: Extract the hot spot steady-state temperature rise from the steady-state temperature rise parameters. T h,ss and the steady-state temperature rise of the casing T k,ss And obtain the total heat loss power of the transformer under the current operating conditions. P ; Based on the steady-state heat conduction equilibrium relationship, the two-stage thermal resistance parameters are analytically calculated using the following formula: （2） In the formula, R 1 represents the first-stage thermal resistance from the winding to the casing. R 2 represents the secondary thermal resistance from the casing to the environment.

5. The transformer Cauer thermal parameter identification method based on modal constraints according to claim 1, characterized in that, In step S4, using the standard temperature rise curve as the optimization objective and the two-stage thermal resistance parameters as known quantities, the two-stage heat capacity parameters of the Cauer second-order thermal circuit model are obtained through a constrained nonlinear optimization algorithm. Specifically, this includes: Construct a complete set of Cauer second-order thermal circuit differential equations, using the two-stage thermal resistance parameters as fixed input parameters and the two-stage heat capacity parameters as variables to be optimized; The optimization objective function is constructed with the goal of minimizing the sum of squared errors between the time-series temperature curve output by the simulation of the thermal differential equations and the standard temperature rise curve. Apply physical boundary constraints on heat capacity, use the trust domain reflection algorithm to iteratively solve the optimization objective function, and output the optimal two-stage heat capacity parameters under the current operating conditions.

6. The transformer Cauer thermal parameter identification method based on modal constraints according to claim 1, characterized in that, After identifying the thermal parameters of the transformer, the method further includes: Substituting the two-stage thermal resistance parameters and the two-stage heat capacity parameters into the Cauer second-order thermal circuit differential equations, the simulation outputs a complete time-series temperature curve. The complete time-series temperature curve output by the simulation is compared globally with the standard temperature rise curve to calculate the temperature rise deviation over the entire time period, and the error level of the transient range of rapid temperature rise is verified in particular. If the temperature rise deviation over the entire time period meets the preset engineering threshold, the current operating condition thermal parameter identification is deemed valid; if the temperature rise deviation over the entire time period exceeds the preset engineering threshold, the process returns to the second-order exponential fitting operation in step S2 and the constraint fitting and parameter identification process is re-executed.

7. The transformer Cauer thermal parameter identification method based on modal constraints according to claim 1, characterized in that, After identifying the thermal parameters of the transformer, the method further includes: Traverse all different load conditions and sequentially execute the complete thermal parameter identification process corresponding to steps S1-S4 to obtain the complete thermal parameter set corresponding to each load condition. The complete thermal parameter set includes two levels of thermal resistance parameters and two levels of thermal capacity parameters. The complete thermal parameter sets corresponding to each load condition are associated, bound, and stored one by one with the corresponding load rate to build a transformer load-related Cauer thermal circuit parameter database, so as to support online real-time retrieval of matching thermal parameters for temperature prediction.

8. A transformer Cauer thermal parameter identification system based on modal constraints, the system being used to execute the transformer Cauer thermal parameter identification method based on modal constraints according to any one of claims 1-7, characterized in that, The system includes: The data acquisition module is used to acquire the winding hot spot time-series temperature data and the outer casing time-series temperature data of the transformer under the target operating conditions. The modal constraint fitting module is used to apply the characteristic equation constraint of the Cauer second-order thermal circuit system, perform second-order exponential fitting on the winding hot spot time-series temperature data and the shell time-series temperature data, force the two fitting curves to share the same set of system time constants, and obtain the standard temperature rise curve and steady-state temperature rise parameters of modal matching. The thermal resistance analytical calculation module is used to analytically calculate the two-stage thermal resistance parameters of the Cauer second-order thermal circuit model based on the steady-state temperature rise parameters. The heat capacity optimization solution module is used to obtain the two-stage heat capacity parameters of the Cauer second-order thermal circuit model by taking the standard temperature rise curve as the optimization target and the two-stage thermal resistance parameters as known quantities through a constrained nonlinear optimization algorithm, thereby completing the identification of the transformer thermal parameters. The model verification module is used to substitute the identified thermal parameters into the thermal circuit differential equations to simulate the output temperature curve, perform a global comparison and verification with the standard temperature rise curve, and return to re-execute the constraint fitting and parameter identification process when the deviation exceeds the limit. The parameter library construction module is used to traverse multiple sets of load conditions to perform the identification process, associate and bind the complete thermal parameter group corresponding to each condition with the load condition, and build a transformer load-related Cauer thermal circuit parameter database.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the transformer Cauer thermal parameter identification method based on modal constraints as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the transformer Cauer thermal parameter identification method based on modal constraints as described in any one of claims 1 to 7.

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