Parameter correction method of digital twin of power electronic converter based on uncertainty quantification

Abstract

The present invention belongs to, but is not limited to, the field of power electronic simulation technology, and discloses a parameter correction method for a digital twin of a power electronic converter based on uncertainty quantification. Based on uncertainty quantification, the method sequentially performs parameter uncertainty characterization of a power electronic converter simulation model, parameter sensitivity analysis based on forward uncertainty propagation, and parameter correction based on reverse uncertainty propagation. Within this framework, the parameters of the power electronic converter simulation model are no longer regarded as fixed unknowns, but as probability distributions with statistical characteristics such as mean and variance. The correction results of the simulation model parameters can more accurately and comprehensively represent the parameters of the power electronic converter device, thereby improving the accuracy of the simulation model prediction. The steps of the present invention are simple and clear, and easy to implement. The present invention aims to make the model response and experimental data consistent, quantify the random uncertainty of the simulation model parameters, and reduce the cognitive uncertainty of the simulation model parameters.

Description

Technical Field

[0001] The present invention belongs to but is not limited to the field of power electronic simulation technology, and in particular relates to a method for correcting parameters of a digital twin of a power electronic converter based on uncertainty quantification. Background Art

[0002] Controller Hardware-in-the-Loop (CHIL), a key simulation technology in the development of power electronic converters, combines numerical simulation with hardware testing, significantly advancing the entire R&D process. CHIL simulation technology enables detailed testing and verification of controllers using a hardware-in-the-loop testbed. This allows developers to debug code in a safe and controllable environment, simulate various fault scenarios, and deeply explore the performance and limitations of control strategies, significantly improving overall controller development efficiency.

[0003] The accuracy of simulation models is crucial to the performance of CHIL simulation technology. Inadequate model accuracy directly leads to performance degradation. However, when faced with complex power electronic converters, building a high-fidelity simulation model in one go is a challenging task. Therefore, model correction is essential.

[0004] Model correction refers to the process of continuously revising simulation model parameters to align the model response with experimental data. Traditional model correction, or deterministic model correction methods, aim to minimize the gap between the model response and experimental data. This process is typically achieved through intelligent optimization algorithms such as particle swarm optimization, genetic algorithms, and simulated annealing. These algorithms can search for the optimal set of parameters to ensure that the model response matches the experimental data.

[0005] However, a significant amount of uncertainty exists in physical modeling, numerical simulation, and experimentation. The physical modeling process inevitably involves simplifications and approximations; the limitations of knowledge prevent the precise characterization of the inherent parameters of physical systems in numerical simulations; and the acquisition of experimental data, the basis for model modification, is subject to random factors (such as environmental noise, systematic errors, and subjective judgment). Models modified using deterministic model modification methods are highly likely to produce significant prediction bias.

[0006] Currently, existing methods for correcting power electronic converter simulation model parameters fail to consider the uncertainty of these parameters. These methods are known as deterministic correction methods. These methods treat simulation model parameters as fixed, unknown physical quantities and use intelligent optimization algorithms to find a set of parameters that minimizes the discrepancy between the simulation model response and experimental data. However, uncertainty is ubiquitous in the construction of physical models, numerical simulations, and experiments for power electronic converters. During the construction of physical models, simplifications and approximations are necessary, making it impossible to fully capture all details. In numerical simulations, limitations in our understanding of power electronic converters prevent the precise characterization of their intrinsic parameters. Experimental data, a key reference for correcting simulation model parameters, is susceptible to interference from various random factors, including environmental noise, systematic errors, and subjective evaluations. If these uncertainties from physical modeling, numerical simulations, and experiments are not considered, the results of simulation model parameter corrections can lead to fluctuations in the power electronic converter simulation model response, potentially leading to design failures and potentially catastrophic consequences.

[0007] In view of the above analysis, the technical problems that need to be solved urgently in the existing technology are:

[0008] In summary, current power electronic converter simulation model parameter correction methods are all performed without considering parameter uncertainty. Due to the influence of parameter uncertainty, correction deviations may occur. Therefore, it is particularly important to perform simulation model parameter correction under the condition of considering parameter uncertainty. Summary of the Invention

[0009] In response to the problems existing in the prior art, the present invention provides a digital twin parameter correction method for a power electronic converter based on uncertainty quantification.

[0010] The present invention is implemented as follows: a method for correcting parameters of a digital twin of a power electronic converter based on uncertainty quantification, comprising the following steps:

[0011] Step 1: Characterize the parameter uncertainty of the power electronic converter simulation model;

[0012] Step 2: Parameter sensitivity analysis based on forward uncertainty propagation;

[0013] Step 3: Parameter correction based on reverse uncertainty propagation.

[0014] Furthermore, in step 1, the parameter uncertainty of the power electronic converter simulation model is expressed in the form of probability distribution; the device parameters are assumed to obey a normal distribution with a mean of the device parameter rated value and a standard deviation of half the device parameter tolerance.

[0015] Furthermore, in step 2, based on the forward parameter uncertainty propagation, the influence of different uncertain input parameters on the response of the power electronic converter simulation model is explored to evaluate the sensitivity of the simulation model response to changes in the input parameters, find the uncertain input parameters with less impact on the simulation model response, and assign them fixed and known values, thereby effectively reducing the computational complexity of simulation model parameter correction.

[0016] Furthermore, based on the effective characterization of parameter uncertainty, the parameter uncertainty is transferred through the power electronic converter simulation model, and then its impact on the simulation model response is analyzed and the simulation model parameter uncertainty is quantified.

[0017] Furthermore, in step 2, the cumulative probability density function is used to quantify the parameter uncertainty of the power electronic converter simulation model, that is, a suitable sampling method is selected according to the distribution of the input parameters to sample the input parameters to obtain several groups of different input parameter combinations, and then each group of input parameters is input into the simulation model to simulate and obtain the simulation model response, and then the cumulative probability density function of the simulation model response is obtained. At this time, the parameter uncertainty can be represented by the cumulative probability density function.

[0018] Furthermore, in step three, based on the power electronic converter test data and the initial uncertainty representation of the simulation model parameters (prior probability distribution), the optimal uncertainty representation of the simulation model parameters (posterior probability distribution) is reversely calculated; during the reverse calculation, Bayesian reasoning forward calculation is used to solve the optimal uncertainty representation problem of the power electronic converter simulation model parameters.

[0019] Another object of the present invention is to provide a power electronic converter simulation model parameter correction system based on uncertainty quantification and a power electronic converter digital twin parameter correction method based on uncertainty quantification, comprising:

[0020] Parameter uncertainty characterization module, parameter uncertainty characterization of power electronic converter simulation model;

[0021] Parameter sensitivity analysis module, parameter sensitivity analysis based on forward uncertainty propagation;

[0022] Parameter correction module, parameter correction based on reverse uncertainty propagation.

[0023] Another object of the present invention is to provide a computer device, which includes a memory and a processor, wherein the memory stores a computer program. When the computer program is executed by the processor, the processor executes the steps of the method for correcting parameters of a digital twin of a power electronic converter based on uncertainty quantification.

[0024] Another object of the present invention is to provide a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the processor executes the steps of the method for correcting parameters of a digital twin of a power electronic converter based on uncertainty quantification.

[0025] Another object of the present invention is to provide an information data processing terminal, which includes the power electronic converter simulation model parameter correction system based on uncertainty quantification.

[0026] In combination with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are as follows:

[0027] First, the disclosed method for modifying power electronic converter digital twin parameters based on uncertainty quantification fully accounts for the uncertainty of simulation model parameters. By incorporating simulation model parameter uncertainty, simulation model parameters are no longer considered fixed unknowns, but rather probability distributions with statistical characteristics such as mean and variance. The resulting simulation model parameter modification provides a more accurate and comprehensive representation of power electronic converter device parameters, thereby improving the accuracy of simulation model predictions.

[0028] Second, the technical problems solved by the technical solution of the present invention in industrial applications.

[0029] Traditional simulation models for power electronic converters typically treat parameters as fixed values, ignoring the randomness and uncertainty of actual component parameters due to factors such as manufacturing tolerances and environmental influences. This leads to deviations between simulation results and experimental data, reducing the accuracy and practicality of the models.

[0030] Existing technologies lack systematicity when facing random uncertainties, making it difficult to fully quantify and correct the uncertainty of model parameters, which affects the reliability of simulation models in complex application scenarios.

[0031] The parameter optimization process lacks effective screening methods and cannot distinguish between high-sensitivity and low-sensitivity parameters, resulting in a significant increase in the amount of optimization calculations and a reduction in the efficiency of parameter correction.

[0032] Existing model calibration methods are usually based on fixed parameters for adjustment, ignoring the parameter distribution characteristics brought about by randomness, resulting in the calibrated model still unable to effectively reflect the dynamic characteristics of the real circuit.

[0033] The lack of methods to deal with epistemic uncertainty (such as the lack of accurate distribution description of certain parameters) leads to insufficient reliability of model modification results.

[0034] The present invention regards the parameters of the power electronic converter simulation model as probability distribution, and comprehensively characterizes the uncertainty of the parameters, including random uncertainty and epistemic uncertainty.

[0035] Use probability distributions (such as normal distribution) to accurately describe the mean and variance of device parameters and quantify the random characteristics of model parameters, thereby significantly improving the practical adaptability of simulation models.

[0036] Through forward uncertainty propagation analysis, the impact of input parameters on the simulation model response is systematically evaluated to provide data support for sensitivity analysis.

[0037] Combined with reverse uncertainty propagation, model parameters are adjusted according to experimental data feedback to make the simulation model response closer to the actual system performance, thereby effectively reducing epistemic uncertainty.

[0038] Sensitivity analysis optimizes model updating efficiency

[0039] The present invention adopts advanced methods such as Sobol's sensitivity index to quickly identify high-sensitivity parameters that have a greater impact on the response of the simulation model and low-sensitivity parameters that have a smaller impact.

[0040] By fixing low-sensitivity parameters to reduce the amount of calculation and focusing on correcting high-sensitivity parameters, the efficiency of simulation model correction is greatly improved.

[0041] The present invention iteratively corrects the simulation model parameters so that the simulation response and experimental results tend to be consistent in statistical characteristics, thereby greatly improving the accuracy of the model.

[0042] By reducing the epistemic uncertainty of the model and quantifying the random uncertainty of the model, the reliability of the simulation model in industrial applications can be significantly improved.

[0043] The technical solution of the present invention is applicable to various types of power electronic converters, including DC-DC converters, inverters, AC-DC rectifiers, etc., and can effectively deal with the impact of different circuit parameter uncertainties on simulation models.

[0044] By improving model accuracy and correction efficiency, it can be widely used in new energy, electric vehicles, industrial automation and other fields, providing strong support for the optimal design of complex power electronic systems.

[0045] By integrating uncertainty quantification, forward and backward uncertainty propagation, and sensitivity analysis, this method effectively addresses the existing challenges of fixed simulation model parameters, low calibration efficiency, and an inability to quantify parameter randomness. This significant technological advancement is reflected in improved simulation model accuracy, enhanced consistency between the model and experimental data, and optimized correction efficiency, providing more reliable and efficient technical support for the simulation modeling and application of power electronic converters. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a flow chart of a method for correcting parameters of a digital twin of a power electronic converter based on uncertainty quantification provided by an embodiment of the present invention;

[0047] Figure 2 Schematic diagram of forward parameter uncertainty propagation provided by an embodiment of the present invention;

[0048] Figure 3 Schematic diagram of reverse parameter sensitivity analysis (parameter correction) provided by an embodiment of the present invention;

[0049] Figure 4 This is a structural diagram of a power electronic converter simulation model parameter correction system based on uncertainty quantification provided by an embodiment of the present invention;

[0050] Figure 5 This is a physical diagram of a buck converter provided by an embodiment of the present invention;

[0051] Figure 6 is a topology diagram of a buck converter circuit provided by an embodiment of the present invention;

[0052] Figure 7 is a discrete circuit topology diagram of a buck converter provided by an embodiment of the present invention;

[0053] Figure 8 Schematic diagram of the MH sampling process provided by an embodiment of the present invention;

[0054] Figure 9 Schematic diagram of a Markov chain of a traditional MCMC algorithm provided by an embodiment of the present invention;

[0055] Figure 10 Schematic diagram of a CDF curve provided by an embodiment of the present invention;

[0056] Figure 11 1 is a schematic diagram of quantifying uncertainty of simulation model parameters before correction provided by an embodiment of the present invention;

[0057] Figure 12 1 is a schematic diagram of the total uncertainty probability box of the simulation model before correction provided by an embodiment of the present invention;

[0058] Figure 13 1 is a schematic diagram of quantifying uncertainty of simulation model parameters after correction provided by an embodiment of the present invention;

[0059] Figure 14 3. It is a schematic diagram of the total uncertainty probability box of the corrected simulation model provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0060] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0061] like Figure 1 As shown, an embodiment of the present invention provides a method for correcting parameters of a digital twin of a power electronic converter based on uncertainty quantification. The method for correcting parameters of a digital twin of a power electronic converter based on uncertainty quantification is a comprehensive technical framework. Based on uncertainty quantification, it sequentially performs parameter uncertainty characterization of a power electronic converter simulation model, parameter sensitivity analysis based on forward uncertainty propagation, and parameter correction based on reverse uncertainty propagation. Under this framework, the parameters of the power electronic converter simulation model are no longer regarded as fixed unknowns, but as probability distributions with statistical characteristics such as mean and variance. The present invention aims to make the response of the power electronic converter simulation model and the test data consistent, quantify the random uncertainty of the simulation model parameters, and reduce the cognitive uncertainty of the simulation model parameters.

[0062] 1 Characterization of parameter uncertainty

[0063] Uncertainty quantification consists of uncertainty characterization and uncertainty propagation. Before modifying the simulation model parameters, the present invention first characterizes the parameter uncertainty of the power electronic converter simulation model.

[0064] Uncertainty can be categorized into aleatory uncertainty and epistemic uncertainty based on its properties. Aleatory uncertainty refers to the randomness inherent in nature or physical phenomena, which cannot be controlled or reduced. Epistemic uncertainty arises from insufficient subjective understanding, knowledge, and data, leading to the inability to accurately construct physical models or accurately describe the uncertainty of certain factors or parameters using precise probability distributions.

[0065] The uncertainty of the parameters in the simulation model of power electronic converters is caused by the fact that the input parameters of the simulation model are not uniquely determined but rather have a range of values. This uncertainty includes both random uncertainty and epistemic uncertainty. The uncertainty of the input parameters is transmitted through the simulation model, resulting in uncertainty in the simulation model response.

[0066] This invention uses probability distributions to represent parameter uncertainty in power electronic converter simulation models. When purchasing components such as resistors, inductors, and capacitors, they are given rated values ​​and tolerances. According to the law of large numbers and the central limit theorem, if a sufficient number of device samples are collected, the distribution of device parameters approaches a normal distribution. Therefore, this invention assumes that device parameters follow a normal distribution with a mean equal to the rated value and a standard deviation equal to half the tolerance.

[0067] 2 Parameter sensitivity analysis

[0068] The parameter uncertainty propagation of power electronic converter simulation model includes two aspects: (1) forward parameter uncertainty propagation, such as Figure 2 As shown; (2) Reverse parameter uncertainty propagation. Forward parameter uncertainty propagation is based on the effective characterization of parameter uncertainty, which is then transferred through the power electronic converter simulation model. The influence of the parameter uncertainty on the simulation model response is then analyzed and the simulation model parameter uncertainty is quantified. The present invention uses the cumulative probability density function to quantify the simulation model parameter uncertainty.

[0069] The present invention performs input parameter sensitivity analysis based on the forward propagation of parameter uncertainty in the power electronic converter simulation model, and deeply explores the influence of different uncertain input parameters on the response of the power electronic converter simulation model. The purpose is to evaluate the sensitivity of the simulation model response to changes in input parameters, find the uncertain input parameters with less impact on the simulation model response, and assign them fixed and known values, thereby effectively reducing the computational complexity of simulation model parameter correction.

[0070] Traditional global sensitivity analysis methods for dealing with random uncertainty can be roughly divided into regression-based methods and variance-based methods. Among them, the variance analysis method based on Sobol's sensitivity index has been widely used due to its simplicity and effectiveness.

[0071] 3 Parameter correction

[0072] like Figure 3 As shown in the figure, as a part of the parameter uncertainty propagation of the power electronic converter simulation model, the reverse parameter uncertainty propagation (parameter correction) is based on the power electronic converter test data and the initial representation of the simulation model parameter uncertainty (prior probability distribution), and the optimal uncertainty representation of the simulation model parameters (posterior probability distribution) is calculated in reverse, thereby reducing the epistemic uncertainty of the simulation model parameters and quantifying the random uncertainty of the simulation model parameters.

[0073] As can be seen from the above, the key to correcting the parameters of a power electronic converter simulation model lies in inversely calculating the posterior distribution of the simulation model parameters. Bayesian reasoning, a mature technology, solves the complex mathematical model of uncertainty propagation in reverse simulation model parameters through forward calculation. This method can derive the prior distribution of simulation model parameters and the posterior distribution of simulation model parameters under given experimental data.

[0074] The parameter correction of the power electronic converter simulation model using Bayesian reasoning can be expressed as:

[0075] (1);

[0076] in, is the simulation model parameter Prior distribution, when obtaining experimental data Previously obtained by collecting expert information and historical data; is the simulation model parameter The likelihood function can be understood as the simulation model parameters Under the conditions of degree of fit; Is the evidence function, which serves as a normalization constant to ensure that the posterior distribution integral is always 1. Its value is fixed and is consistent with the simulation model parameters. Therefore, the following proportional relationship can be obtained:

[0077] (2);

[0078] From formula (2), we can see that the simulation model parameters The posterior distribution of is only implicitly known. When using Bayesian reasoning to modify simulation model parameters, the key is to understand the simulation model parameters. and test data Therefore, the present invention has a Ignore.

[0079] The prior distribution of the simulation model parameters is determined before obtaining the test data. It combines the prior information and initial assumptions of the simulation model parameters. Although any type of distribution can be used as the prior distribution in theory, in practice, uniform distribution and normal distribution are the most commonly used types. According to the parameter uncertainty characterization described above, the present invention knows the mean and standard deviation of the simulation model parameters, so its prior distribution is set to normal distribution. Dimensional parameters to be corrected The probability density function can be expressed as:

[0080] (3);

[0081] in, yes The mean of yes The standard deviation of .

[0082] set up are independent of each other, the prior distribution can be expressed as:

[0083] (4);

[0084] When constructing the likelihood function, two elements must be included: the difference between the experimental data and the simulation model response, and the simulation model parameters. After that, it is assumed that each dimension of the test data is independent of each other and each dimension obeys the same distribution, then the likelihood function can be expressed as follows:

[0085] (5);

[0086] Set test data and simulation model response results The error between them obeys a zero-mean normal distribution with a fixed variance and a mean of zero, then the likelihood function obeys the following normal distribution:

[0087] (6);

[0088] in, Represents the error between the j-th dimension test data and the model output result The standard deviation of Represents the output result of the j-th dimension model.

[0089] The Markov Chain Monte Carlo (MCMC) algorithm is a commonly used algorithm for solving the posterior distribution of Bayesian inference. Its idea is to obtain a sample sequence, namely a Markov chain, by sampling the posterior distribution of the simulation model parameters. The chain will eventually converge and the posterior distribution of the simulation model parameters can be estimated using the Markov chain without the burning period.

[0090] The most widely used sampling methods in MCMC algorithms are Metropolis-Hastings (MH) sampling and Gibbs sampling. In Gibbs sampling, choosing an appropriate conditional probability distribution to represent the posterior distribution of the parameter to be corrected is more difficult for high-dimensional and complex posterior distributions, which limits the applicability of Gibbs sampling. However, MH sampling can sample from any probability distribution as long as the function is proportional to its normalized probability density function and the value of the function can be calculated.

[0091] like Figure 4 As shown, an embodiment of the present invention provides a power electronic converter simulation model parameter correction system based on uncertainty quantification, comprising:

[0092] Parameter uncertainty characterization module, parameter uncertainty characterization of power electronic converter simulation model;

[0093] Parameter sensitivity analysis module, parameter sensitivity analysis based on forward uncertainty propagation;

[0094] Parameter correction module, parameter correction based on reverse uncertainty propagation.

[0095] This invention takes the buck converter as an example to introduce the whole process of power electronic converter model parameter uncertainty correction. Figure 5 As shown in the figure, the operating frequency of the buck converter is 200kHz. When the inductor current is steady at 4A in closed-loop control, the peak-to-peak value of the inductor current and the output voltage are selected as the steady-state response of the buck converter. The response time (rise time) of the inductor current stepping from 1A to 4A and the response time (fall time) of the inductor current stepping from 4A to 1A in closed-loop control are selected as the transient response of the buck converter.

[0096] 1 Converter Modeling

[0097] Buck converter circuit topology Figure 6 As shown, the present invention uses the node voltage method to construct the BUCK mathematical model, which is divided into the following three steps:

[0098] (1) Use the binary resistance method to model the switching device in the circuit. When the switching device is turned on, a small resistor is used as the equivalent, and when the switching device is turned off, a large resistor is used as the equivalent.

[0099] (2) The implicit Euler method is used to discretize the continuous model of the nonlinear devices in the circuit. The discretization results of the inductor and capacitor are as follows:

[0100] (7);

[0101] in, is the simulation time step, Respectively Hedi Step inductor current, For the Step inductor voltage, For the The capacitor current of the step, Respectively Hedi The capacitor voltage of the step, and:

[0102] (8);

[0103] get Figure 7 The discrete circuit topology diagram of the buck converter.

[0104] (3) The node voltage method is used to establish the node voltage equation of the discrete circuit. The node voltage equation is expressed as follows:

[0105] (9);

[0106] in, represents the admittance matrix, as shown in formula (10); represents the node voltage vector, as shown in formula (11); represents the vector of the current source injected into the node, as shown in equation (12).

[0107] (10);

[0108] in, For the switch tube The equivalent conductance, For the switch tube The equivalent conductance, is the input resistance The equivalent conductance, is the input capacitance The equivalent conductance, Capacitor The equivalent conductance, It is an inductor The equivalent conductance, is a resistor The equivalent conductance, is the output capacitor The equivalent conductance, is the output resistance The equivalent conductance, is the load resistance The equivalent conductance.

[0109] (11);

[0110] (12);

[0111] in, is the input voltage, are equivalent model parameters of inductance and capacitance.

[0112] The node voltage is obtained by solving equation (9) and is used to update the entire network.

[0113] 2 Parameter sensitivity analysis

[0114] The present invention uses a variance analysis method based on the Sobol's sensitivity index to perform sensitivity analysis on the parameters of a power electronic converter simulation model. This method expands the variance of the simulation model response through the power electronic converter simulation model, and then uses the ratio of the local variance to the total variance of the simulation model response as the Sobol's sensitivity index, thereby quantifying the contribution of each uncertainty parameter to the global sensitivity of the simulation model response and evaluating its relative importance in affecting the uncertainty of the simulation model response. Monte Carlo simulation is a commonly used method for calculating the Sobol's sensitivity index. The method is carried out in three steps: the first step is to characterize the uncertainty of the power electronic converter simulation model parameters in the form of a probability distribution; the second step is to generate a set of parameter samples using the distribution of the simulation model uncertainty parameters; the third step is to input the parameter samples into the power electronic converter simulation model for simulation, and then calculate the variance of the simulation model response, and finally obtain the Sobol's sensitivity index.

[0115] The present invention briefly introduces the Sobol' sensitivity index. dimensional uncertainty parameter The power electronic converter simulation model response , which can be expressed as:

[0116] (13);

[0117] in, represents the mean of the system response y, Representation and parameters and Related simulation model responses.

[0118] (14);

[0119] in, yes The domain of yes The joint probability density function of . If the simulation model responds If the square is integrable, the uncertainty parameters are independent and the mean of each term in the expansion (14) is 0, then all terms in the expansion (13) are orthogonal to each other, and each term can be uniquely determined.

[0120] Simulation model response The total variance of can be expressed as:

[0121] (15);

[0122] According to formula (13) and the orthogonality between its components, the total variance D of the simulation model response can be decomposed into the sum of the variances:

[0123] (16);

[0124] Among them, the variance can be expressed as follows:

[0125] (17);

[0126] In formula (16), A single parameter representing the corresponding dimension Response to simulation model the impact of; Represents multiple parameters The interaction between the two has an impact on the simulation model response The impact of Represents multiple parameters The interaction between the two has an impact on the simulation model response The impact of Represents multiple parameters The interaction between the two has an impact on the simulation model response impact.

[0127] It can be seen from equations (13) and (16) that when the input parameters are independent of each other, the variance decomposition formula can reflect the structure of the power electronic converter simulation model. The variance of can be decomposed into: the variance term related to a single input parameter, the variance term related to two input parameters, and the variance term related to multiple input parameters, so that the simulation model response The uncertainty (variance) of the model is distributed among the various input parameters and the interaction terms between different input parameters.

[0128] The total variance of the simulation model response and the local variance of each simulation model uncertainty parameter alone or when they interact with each other can be obtained through equations (16) and (17). Then, the influence of each simulation model uncertainty parameter on the simulation model response can be quantified by the ratio of the local variance to the total variance, which is the Sobol' global sensitivity index:

[0129] (18);

[0130] in, is the uncertainty parameter of the simulation model The global sensitivity index of the uncertainty parameter of the simulation model can be used as a key indicator to judge the sensitivity of the power electronic converter simulation model response to the change of the uncertainty parameter.

[0131] The present invention uses the variance analysis method based on Sobol's sensitivity index to analyze the inductance of the BUCK converter. , load resistance and output capacitors Sensitivity analysis was performed. The parameters of the inductor, resistor, and capacitor selected in the present invention are shown in Table 1. Based on the parameter uncertainty characterization described above, the present invention assumes that the inductor, resistor, and capacitor obey a normal distribution, and their distribution parameters are given below:

[0132] (19);

[0133] (20);

[0134] (twenty one);

[0135] Table 1 Main device parameters

[0136] components code name Rating Tolerance inductance L 15 15% Output capacitor <![CDATA[C out ]]> 242 20% load resistance <![CDATA[R load ]]> 2.5Ω 5%

[0137] A key issue in sampling parameter distributions is sampling error. The greater the number of sample groups, the smaller the sampling error, and the more representative the sample groups are of the parameter probability distribution. However, model execution requires a certain amount of time. After weighing sampling error and time cost, it was decided to take 400 samples per sampling. Table 2 shows the sensitivity calculated for each 400-sample period. It can be seen that the output capacitance C out The uncertainty of the inductor L and the load resistance R has little effect on the responses of the four simulation models. load The influence on the response of the four simulation models is significant. Therefore, it is concluded that the inductor L and the load resistance R load Make corrections.

[0138] Table 2 Parameter sensitivity analysis results

[0139] Sensitivity index Inductor current peak-to-peak Output voltage Rise time Fall time <![CDATA[ S L ]]> 0.238460692 0.002641453 0.162603572 0.092090224 <![CDATA[ S R ]]> 0.002865478 0.248218852 0.167870139 0.185932278 <![CDATA[ S C ]]> 7.36716E-09 1.54267E-10 9.16689E-06 2.21501E-05 <![CDATA[ S LR ]]> 0.250428747 0.244766835 0.176450132 0.184493712 <![CDATA[ S LC ]]> 0.267255999 0.002107876 0.146028017 0.098062024 <![CDATA[ S RC ]]> 0.002785802 0.252367927 0.174542059 0.178423477 <![CDATA[ S LRC ]]> 0.238203275 0.249897057 0.172496914 0.260976135

[0140] 3 Model parameter uncertainty correction

[0141] The present invention uses the MCMC algorithm to solve the posterior distribution of the simulation model parameters. The present invention uses the Metropolis-Hastings (MH) sampling method to obtain the Markov chain, which is a random walk algorithm that proposes a distribution. Generate candidate samples for the Markov chain , and the candidate samples The acceptance or rejection is determined by the acceptance probability function, which is defined as follows:

[0142] (twenty two);

[0143] in, Represents candidate samples The estimated value on the posterior distribution, Indicates the current sample The estimated value on the posterior distribution, Indicates that in the candidate sample Under the condition of The probability of Indicates that in the current sample Under the condition of probability.

[0144] In order to reduce the amount of calculation, the present invention recommends using a symmetrical distribution. , so formula (22) can be simplified as:

[0145] (twenty three);

[0146] Substituting formula (1) into formula (23) yields:

[0147] (twenty four);

[0148] in, Is a candidate sample The value of the likelihood function, Is the current sample The value of the likelihood function, Is a candidate sample The value on the prior distribution, Is the current sample in the prior distribution The value on .

[0149] The present invention selects the normal distribution, a symmetrical distribution, as the recommended distribution for generating candidate samples, whose mean is the current sample , the standard deviation is used as a regulating parameter for MH sampling and can be adjusted accordingly according to the specific situation. The standard deviation of the proposed distribution affects the sampling efficiency of the MCMC algorithm. If the standard deviation of the proposed distribution is small, the difference between adjacent samples in the Markov chain will be small, and more iterations will be required to achieve convergence. If the standard deviation is large, the generated candidate samples may exceed the range of the posterior distribution, making it impossible to effectively search the entire posterior distribution space, which will result in a higher candidate sample rejection rate. Therefore, setting the standard deviation of the proposed distribution too large or too small will lead to low sampling efficiency.

[0150] Figure 8 The MH sampling process is shown. Combined with formula (23), it can be seen that when the proposed distribution Generated candidate samples When it moves toward the high probability density of the posterior distribution, it is always accepted, otherwise the candidate sample Substitute into formula (23) to calculate the reception probability , then with uniform distribution Generated random values Compare, if , then accept the candidate sample ,if , then reject the candidate sample .

[0151] The present invention uses 300 inductors with the same parameters and 300 resistors with given distribution and implemented by electronic load to connect to a real buck converter, measures test data, and uses the test data to verify the power electronic converter simulation model correction method proposed above.

[0152] After 914 iterations, we get Figure 9 It can be seen from the traditional MCMC algorithm Markov chain that the Markov chain gradually converges after about 300 iterations.

[0153] The present invention uses the form of cumulative probability density function to quantify the parameter uncertainty of the power electronic converter simulation model, that is, according to the distribution of the input parameters, a suitable sampling method is selected to sample the input parameters to obtain several groups of different input parameter combinations, and then each group of input parameters is input into the simulation model to simulate and obtain the simulation model response, and then the cumulative probability density function of the simulation model response is obtained. At this time, the parameter uncertainty can be represented by the cumulative probability density function. Figure 10 A cumulative probability density function curve is given, which is a plot of the simulation model response based on the experimental data, prior distribution, and posterior distribution. It can be seen that the method proposed in the present invention effectively corrects the simulation model parameters, making the simulation model response more consistent with the experimental data.

[0154] 4 Quantification of total uncertainty before and after parameter correction of the BUCK converter simulation model

[0155] The uncertainty of power electronic converter simulation model parameters can be measured using a cumulative probability density function, and the uncertainty of the power electronic converter simulation model form can be measured using an improved area metric verification method. To combine the uncertainty of simulation model parameters and the uncertainty of simulation model form to obtain the total uncertainty of the simulation model, the present invention adopts a probability box. In the probability box, the uncertainty of simulation model parameters is represented as a probability distribution, and the uncertainty of simulation model form is represented as an interval.

[0156] (1) Before amendment:

[0157] Figure 11 The uncertainty quantification CDF curve of the simulation model parameters before correction is given.

[0158] According to the improved area measurement verification method, the peak-to-peak value of the inductor current, the output voltage value, the rise time of the inductor current from 1A to 4A, and the fall time of the inductor current from 4A to 1A are obtained. and As shown in Table 3.

[0159] Table 3 Before correction and calculate

[0160] Output Response <![CDATA[d - ]]> <![CDATA[ d + ]]> Steady State Inductor current peak-to-peak value / A 0.0241 0.0323 Steady State Output voltage / V 2.1221 0 transient Rise time / s 5.11051e-3 0 transient Fall time / s 8.9025e-3 0

[0161] Safety factor of the present invention The formal uncertainty of the simulation model before correction of the four groups of response quantities, namely, the peak-to-peak value of the inductor current, the output voltage value, the rise time of the inductor current from 1A to 4A, and the fall time of the inductor current from 4A to 1A, are shown in Table 4.

[0162] Table 4 Formal uncertainty of simulation model before correction

[0163] Target response <![CDATA[Model form uncertainty F(x) - F S d - , F(x)+F S d + > Steady State Inductor current peak-to-peak value / A [-0.042005，+0.056297] Steady State Output voltage / V [-3.698714，] transient Rise time / s [-8.9074-3，] transient Fall time / s [-15.5166-3，]

[0164] The two forms of simulation uncertainty are combined into one diagram in the form of probability boxes to represent the total simulation uncertainty. The probability boxes of the total simulation uncertainty before correction of the four system response quantities are as follows: Figure 12 shown.

[0165] (2) After correction:

[0166] Figure 13 The modified CDF curve of simulation model parameter uncertainty quantification is given.

[0167] Table 5 shows the corrected and calculate

[0168] Output Response <![CDATA[ d - ]]> <![CDATA[ d + ]]> Steady State Inductor current peak-to-peak value / A 0.00879 0.0132 Steady State Output voltage / V 0.04039 0.0184 transient Rise time / s 3.0759e-5 0.0013 transient Fall time / s 6e-4 0

[0169] Safety factor of the present invention The formal uncertainty of the corrected simulation model for the four groups of response quantities, namely, the peak-to-peak value of the inductor current, the output voltage value, the rise time when the inductor current steps from 1A to 4A, and the fall time when the inductor current steps from 4A to 1A, are shown in Table 6.

[0170] Table 6 Formal uncertainty of the corrected simulation model

[0171] Target response <![CDATA[Model form uncertainty F(x) - F S d - , F(x)+F S d + > Steady State Inductor current peak-to-peak value / A [-0.015321，+0.023007] Steady State Output voltage / V [-0.070398，0.03207] transient Rise time / s [-5.3611-5，0.002266] transient Fall time / s [-1.04577-3，]

[0172] The two forms of simulation uncertainty are combined into one diagram in the form of probability boxes to represent the total simulation uncertainty. The probability boxes of the corrected total simulation uncertainty of the four system response quantities are as follows: Figure 14 shown.

[0173] Table 7 shows the comparison of the total uncertainty of the simulation before and after parameter correction at a confidence level of 95.45%. It can be seen that after applying the parameter correction method for the power electronic converter simulation model described in the present invention, the total uncertainty of the simulation is significantly reduced for the BUCK converter simulation model.

[0174] Table 7 Comparison of total uncertainty of simulation before and after parameter correction at 95.45% confidence level

[0175] Target response Total uncertainty before correction Corrected total uncertainty Steady State Inductor current peak-to-peak value / A 1.97923-1.42957=0.54966 1.83479-1.55513=0.27966 Steady State Output voltage / V 10.3941-5.89555=4.49855 8.50652-7.36426=1.14226 transient Rise time / s 0.0399775-0.0279551=0.0120225 0.0359635-0.0303789=0.0055846 transient Fall time / s 0.0434275-0.0245159=0.0189116 0.0358775-0.0304617=0.0054158

[0176] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware portion can be implemented using dedicated logic; the software portion can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. Those skilled in the art will appreciate that the above-mentioned devices and methods can be implemented using computer-executable instructions and / or contained in processor control code, for example, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, or can be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0177] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with this technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered by the scope of protection of the present invention.

Claims

1. A method for correcting parameters of digital twins of power electronic converters based on uncertainty quantification, characterized in that: The following steps are involved: Step 1: Characterize the parameter uncertainty of the power electronic converter twin model; Step 2: Parameter sensitivity analysis based on forward uncertainty propagation; Step 3: Parameter correction based on reverse uncertainty propagation; In step 1, the parameter uncertainty of the power electronic converter twin model is represented by using a probability distribution to represent the parameter uncertainty of the power electronic converter twin model; the device parameters are assumed to obey a normal distribution with a mean of the device parameter rated value and a standard deviation of half the device parameter tolerance; In step 2, based on forward parameter uncertainty propagation, the degree of influence of different uncertain input parameters on the response of the power electronic converter twin model is determined. This is used to evaluate the sensitivity of the twin model response to changes in input parameters, identify uncertain input parameters with minimal impact on the twin model response, and assign them fixed and known values, thereby effectively reducing the computational complexity of twin model parameter correction. Based on the effective characterization of parameter uncertainty, the parameter uncertainty is transferred through the twin model of the power electronic converter, and then its impact on the twin model response is analyzed and the twin model parameter uncertainty is quantified; In step 2, the parameter sensitivity analysis based on forward uncertainty propagation uses a cumulative probability density function curve to quantify the parameter uncertainty of the power electronic converter twin model. That is, according to the distribution of the input parameters, a suitable sampling method is selected to sample the input parameters to obtain several groups of different input parameter combinations. Each group of input parameters is then input into the twin model to simulate the twin model response. The twin model response is then plotted as a cumulative probability density function curve. At this time, the parameter uncertainty is represented by the cumulative probability density function curve. The parameter correction based on reverse uncertainty propagation in step three is based on the power electronic converter test data and the initial characterization of the twin model parameter uncertainty, that is, the prior probability distribution, and the optimal uncertainty characterization of the twin model parameters, that is, the posterior probability distribution, is calculated in reverse. During the reverse calculation, Bayesian reasoning is used to forwardly calculate and solve the optimal uncertainty characterization problem of the power electronic converter twin model parameters.

2. A power electronic converter digital twin parameter correction system based on uncertainty quantification, which adopts the method described in claim 1, characterized in that: include: Parameter uncertainty characterization module, parameter uncertainty characterization of the power electronic converter twin model; Parameter sensitivity analysis module, parameter sensitivity analysis based on forward uncertainty propagation; Parameter correction module, parameter correction based on reverse uncertainty propagation.

3. A computer device, characterized in that: The computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the power electronic converter digital twin parameter correction method based on uncertainty quantification as claimed in claim 1.

4. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the processor performs the steps of the power electronic converter digital twin parameter correction method based on uncertainty quantification as claimed in claim 1.

5. An information data processing terminal, characterized in that: The information data processing terminal includes the power electronic converter digital twin parameter correction system based on uncertainty quantification as described in claim 2.

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