A Method and System for Estimating Fuel Cell Parameters Based on Adaptive Subset Simulation

Abstract

This invention discloses a method and system for estimating fuel cell parameters based on adaptive subset simulation. It transforms the updating of the posterior distribution of parameters into a structural reliability problem, constructs a limit state function using measurement data to form an intermediate failure domain, and generates conditional samples using the MCMC method to progressively approximate the target posterior probability distribution, thereby achieving parameter estimation of the fuel cell system. This method does not require a Gaussian prior assumption, can adaptively adjust algorithm parameters to ensure the reliability of the estimation results, and can comprehensively characterize the probability distribution of unknown parameters, achieving accurate estimation of fuel cell system parameters.

Description

Technical Field

[0001] This invention belongs to the technical field of power system parameter estimation, and mainly relates to a fuel cell parameter estimation method and system based on adaptive subset simulation. Background Technology

[0002] In recent years, the proportion of renewable energy generation in the power system has been continuously increasing, and its intermittency and volatility inevitably threaten the safety of power system operation and control. Fuel cells, under conditions of sufficient fuel, can reliably provide clean power, offering advantages such as high efficiency and flexible operation, making them a widely adopted choice for compensating for renewable energy fluctuations and enhancing grid resilience. Among them, solid oxide fuel cells (SOFCs) can operate at high temperatures and do not rely on precious metal catalysts, offering both performance and cost advantages. However, due to harsh operating environments, mechanical wear, and chemical corrosion, the internal components of SOFCs gradually deteriorate over time, causing parameter values ​​to deviate from initial settings. Therefore, accurate SOFC models are crucial for evaluating and optimizing energy storage system performance, but this task remains challenging due to the highly nonlinear and complex characteristics of the system.

[0003] Current research on battery parameter estimation focuses on simplified steady-state battery models and does not incorporate grid-connected control strategies, considering only independent operation. It rarely addresses the parameter estimation problem for dynamic models of grid-connected solid oxide fuel cells. Therefore, this invention focuses on parameter estimation for grid-connected solid oxide fuel cell systems. Summary of the Invention

[0004] This invention addresses the parameter estimation problem of grid-connected solid oxide fuel cells (SOCFCs) in existing technologies that do not consider the dynamic model. It proposes a fuel cell parameter estimation method and system based on adaptive subset simulation. The method transforms the updating of the posterior distribution of parameters into a structural reliability problem, constructs a limit state function using measurement data to form an intermediate failure domain, and generates conditional samples using the MCMC method to progressively approximate the target posterior probability distribution, thus achieving parameter estimation of the fuel cell system. This method does not require a Gaussian prior assumption, can adaptively adjust algorithm parameters to ensure the reliability of the estimation results, and can comprehensively characterize the probability distribution of unknown parameters, achieving accurate estimation of fuel cell system parameters.

[0005] To achieve the above objectives, the technical solution adopted by this invention is: a fuel cell parameter estimation method based on adaptive subset simulation, comprising the following steps:

[0006] S1: Establish a parameter estimation model for solid oxide fuel cells. This model is based on a solid oxide fuel cell model and establishes Bayesian inference and solid oxide fuel cell measurement equations. Bayesian inference links the posterior probability distribution of the parameters with the likelihood function and the prior distribution of the parameters. The measurement equations correlate the system measurements with the parameter values, specifically:

[0007]

[0008]

[0009]

[0010] in, It is a measurement vector containing active power measurements and reactive power measurements, defined as follows: and , Let be the parameter vector to be estimated. It is a nonlinear measurement function. Measurement noise is composed of independent random variables. Let be the likelihood function. Let be the prior probability distribution of the parameter. Let be the posterior probability distribution of the parameter. Here is the regularization constant;

[0011] S2: Decentralize and decouple the parameter estimation model of solid oxide fuel cell to reduce the parameter space dimension. Use the voltage and current phasors measured by the local PMU as input to simulate the active power and reactive power response. Based on the simulated response value and the PMU power measurement value, further obtain the likelihood function value.

[0012] S3: Construct an adaptive Bayesian update algorithm based on subset simulation to achieve parameter estimation of the decoupled solid oxide fuel cell system; the algorithm constructs an intermediate failure domain based on the limit state function, thereby gradually approximating the posterior probability distribution of the parameters, and adaptively updates the algorithm parameters to ensure the reliability of the estimation results.

[0013] As an improvement of the present invention, step S2 specifically includes the following steps:

[0014] S21: During the set measurement period, acquire the bus voltage phasor of the node where the fuel cell is located via the PMU. Current phasor ;

[0015] S22: The external power system, including generators, network topology, loads, etc., is equivalent to an infinite bus at the point of common coupling, from the parameter vector... Obtained from the prior probability distribution Each sample value is injected into the nonlinear measurement function of the solid oxide fuel cell parameter estimation model. In this process, the dynamic trajectory of the internal state variables of the fuel cell system is obtained, thereby simulating the dynamic response of active and reactive power at the point of common coupling:

[0016]

[0017]

[0018] in and These are the active power and reactive power outputs of the fuel cell, respectively. It is the equivalent line impedance. and These are the measurement noises for active power and reactive power, respectively.

[0019] S23: The joint probability density function of the measurement noise is:

[0020]

[0021] in and These are the measurement noise probability distributions for active power and reactive power, respectively.

[0022] The output power measurement value of the node where the fuel cell is located within a set time period is obtained by acquiring the PMU, and combined with the simulated active power and reactive power response values ​​obtained in step S22, the likelihood function value of the parameter sample is obtained. :

[0023] ;

[0024] ;

[0025] superscript Indicates the time within the set time period The value at that location, Indicates the total duration of the measurement. and These are the active power measurement vector and the reactive power measurement vector, respectively. and It is the corresponding measurement mapping function.

[0026] As a further improvement of the present invention, step S3 specifically includes the following steps:

[0027] S31: Set the number of iterations for subset simulation and initial intermediate threshold For fuel cell systems The parameter vector to be estimated ,according to Given the prior sample values ​​and likelihood function values ​​in the original variable space, the limiting state function value of the original variable space is obtained as follows:

[0028]

[0029] in For a standard uniform random variable, It must be a positive integer and satisfy the following conditions: ;

[0030] S32: Transform the samples to the standard normal space and generate... Initial independent samples Construct the sample set of layer 0, and its equivalent mapping formula is:

[0031]

[0032] in It is the standard normal cumulative distribution function. It is to satisfy transformation, for 3D independent standard normal random variables, superscript Indicates inverse transformation, subscript Indicates being in the first layer, ;

[0033] The limit state function value in the standard normal space is:

[0034]

[0035] in ;

[0036] Obtain the logarithmic limit state function of the sample value:

[0037]

[0038] remember To meet The initial maximum likelihood value in the standard normal space is set by combining the PMU power measurement value and the simulated power response value:

[0039] ;

[0040] S33: Determine the threshold value of the current layer Is it greater than the target threshold of 0? Execute step S34, if When the time comes, proceed to step S35;

[0041] S34: The final true posterior distribution domain of the successive approximation parameters, specifically including:

[0042] S341 updates the iteration level of the subset simulation: ;

[0043] S342: Calculate the samples from the previous layer Logarithmic limit state function Values ​​and sort them in ascending order; compare The sorted set is ranked in the th order. The percentile value is the larger of the two (0 and 0) and set as the 1st percentile. Intermediate threshold of layer ,in This is the intermediate conditional probability;

[0044] S343: In the sample set In the middle, identify and extract all that meet the requirements The samples are used to construct the current intermediate failure domain. This sample is used as a conditional seed sample and randomly arranged. The total number of samples that successfully enter the intermediate failure domain in this layer is denoted as . ;

[0045] S344: with Seed samples as A Markov chain seed, generated based on the Markov Chain Monte Carlo (MCMC) algorithm. A new conditional sample;

[0046] S345: Calculate the... Maximum log-likelihood function value of layer samples and adaptive adjustment ,in accordance with For the defined intermediate threshold Perform dynamic corrections and updates. ;

[0047] S346: From the support set Samples were drawn from a uniform distribution. and order To reduce The correlation dependence generated by the nth sample during the evolution of the Markov chain yields the nth... Layer conditional samples Proceed to step S33;

[0048] S35: When the intermediate threshold iterates to... season , No. Layer samples are the target posterior samples of the parameters to be estimated;

[0049] S36: Convert the samples back to the original variable space for storage, plot the posterior probability density function and obtain the maximum posterior probability (MAP) estimate, which is the final parameter estimation result, thus completing the parameter estimation of the fuel cell system.

[0050] As a further improvement of the present invention, the generation of MCMC conditional samples in step S344 specifically includes the following steps:

[0051] S344-1: Setting adaptive initial level parameters ;

[0052] S344-2: For dimensions From the mean The standard deviation is Proposal samples are drawn from a normal distribution. ; Calculate the proposed sample log-likelihood function value And determine whether it satisfies If the conditions are met, the proposed sample successfully falls into the intermediate failure region and is accepted. As the next state in the Markov chain, if the condition is not met, it is rejected. and the previous layer sample As the next state of the Markov chain;

[0053] S344-3: After completion In the process of building a Markov chain, the loop variable is established as The iterative loop, where For each iteration Determine the current iteration step. Has the adaptive adjustment period been reached? ,judge Is it valid?

[0054] If true, then calculate the acceptance rate of the current proposed sample that falls within the intermediate failure region. Adaptive adjustment of standard deviation parameter:

[0055]

[0056] in To determine the target acceptance rate for the sample, the adaptive hierarchical parameters are updated as follows: ;

[0057] If not true, then maintain the current state. and constant;

[0058] After completing the current step, let Proceed to the next iteration, until the loop variable... Finish Second traversal;

[0059] S344-4: Obtained through the Markov chain evolution process A new conditional sample.

[0060] To achieve the above objectives, the present invention also adopts the following technical solution: a fuel cell parameter estimation system based on adaptive subset simulation, comprising a computer program, wherein the computer program, when executed by a processor, implements the steps of any of the methods described above.

[0061] Compared with the prior art, the present invention has the following advantages: In view of the era in which energy storage devices are gradually connected to the power grid, the present invention proposes a fuel cell parameter estimation method and system based on adaptive subset simulation.

[0062] Regarding the selection of fuel cell system models, existing parameter estimation work in the field is based on simplified steady-state battery models, without incorporating grid-connected control strategies, and only considers independent operating states, rarely addressing the parameter estimation problem of grid-connected solid oxide fuel cell dynamic models. This invention, for the first time, studies the parameter estimation problem in a detailed grid-connected solid oxide fuel cell dynamic model, including the solid oxide fuel cell, boost converter, and inverter, which is beneficial for better describing the system's dynamic characteristics. Furthermore, this invention utilizes PMU measurement data to achieve decentralization, decoupling, and dynamic calibration of the grid-connected solid oxide fuel cell system model, significantly enhancing its practical application value.

[0063] Regarding parameter estimation algorithms, this technology provides an adaptive Bayesian update method based on subset simulation, which transforms the update of the posterior distribution of parameters into a structural reliability problem. It constructs an intermediate failure domain and uses the MCMC method to generate conditional samples, progressively approximating the target posterior probability distribution. This method requires no Gaussian prior assumptions or model linearization, and can adaptively adjust algorithm parameters to ensure the reliability of the estimation results. It can comprehensively characterize the probability distribution of unknown parameters, achieving accurate estimation of solid oxide fuel cell system parameters. Attached Figure Description

[0064] Figure 1 This is a flowchart of the fuel cell parameter estimation method based on adaptive subset simulation of the present invention;

[0065] Figure 2 This is a schematic diagram of the grid connection of the solid oxide fuel cell system of Embodiments 1 and 2 of the present invention;

[0066] Figure 3 This is a schematic diagram of the decentralization and decoupling of the solid oxide fuel cell system in Embodiments 1 and 2 of the present invention;

[0067] Figure 4 This is a schematic diagram of the generation of intermediate failure domains in Embodiments 1 and 2 of the present invention;

[0068] Figure 5 This is a schematic diagram of the parameter estimation results obtained in Embodiment 1 of the present invention;

[0069] Figure 6 This is a schematic diagram of the parameter estimation results obtained in Embodiment 2 of the present invention. Detailed Implementation

[0070] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0071] Example 1

[0072] This example is applied to the IEEE 39-node system connected to a solid oxide fuel cell system. A schematic diagram of the solid oxide fuel cell system connected to the grid is shown below. Figure 2 As shown, the solid oxide fuel cell system is connected to node 5. The synchronous generator model considered is a two-axis model, including an IEEE-DC1A exciter and a TGOV1 turbine governor. The simulation starts from the system steady state at t=0 seconds, and a disturbance is introduced at t=0.5 seconds, with a total simulation time of 5.5 seconds.

[0073] Fuel cell parameter estimation methods based on adaptive subset simulation, such as Figure 1 As shown, it includes the following steps:

[0074] S1: Establish a parameter estimation model for solid oxide fuel cells. This model is based on a solid oxide fuel cell system model and establishes Bayesian inference and solid oxide fuel cell measurement equations, specifically:

[0075]

[0076]

[0077]

[0078] in, It is a measurement vector containing active power measurements and reactive power measurements, defined as follows: and , Let be the parameter vector to be estimated. It is a nonlinear measurement function. Measurement noise is composed of independent random variables. Let be the likelihood function. Let be the prior probability distribution of the parameter. Let be the posterior probability distribution of the parameter. Here is the regularization constant;

[0079] The parameter estimation model for solid oxide fuel cells relies on Bayesian inference and measurement equations from the cell model. The solid oxide fuel cell system used consists of a solid oxide fuel cell dynamic model and a grid-type controller.

[0080] The dynamic model of a solid oxide fuel cell consists of the following components:

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] in, , , These represent the partial pressures of hydrogen, oxygen, and water in the reactants, respectively. , , These are the response time constants for hydrogen flow rate, oxygen flow rate, and water flow rate, respectively. , , The valve molar constants for hydrogen, oxygen, and water are respectively. This represents the load current of the fuel cell; It is the internal electromotive force of the fuel cell, derived from the Nernst equation. It is ohmic loss. It is polarization voltage loss. It is the concentration pressure drop. It is the output voltage of the fuel cell; It is the ideal standard potential for a single fuel cell. It refers to the number of fuel cell stacks. It is the universal gas constant. It is approximately the optimal operating temperature. It is Faraday's constant. It is the ohmic resistance coefficient. It is the temperature coefficient. It refers to the temperature of the fuel cell stack. It is the output current of the fuel cell. It is an alternating current. It is the current-limiting current; Since it is a constant, it can be calculated as .

[0090] A network-type controller includes a boost converter and an inverter. The boost converter consists of the following components:

[0091]

[0092]

[0093]

[0094]

[0095] in, It is the circuit inductance. It is a DC bus capacitor. It is the DC bus output current. It is the DC bus output voltage. It is a pulse width modulation (PWM) signal. This is the DC reference voltage. For reference current, , These are the proportional gain and integral gain of the voltage loop, respectively. , These are the proportional coefficient and integral coefficient of the current loop, respectively. This indicates a PWM signal.

[0096] The inverter employs a droop controller and a dual closed-loop voltage and current controller. The power droop controller provides reference voltage and frequency for the dual-loop voltage and current controller. The specific components are as follows:

[0097]

[0098]

[0099]

[0100]

[0101]

[0102] in, This represents the internal angular frequency of a solid oxide fuel cell system. As the reference angular frequency, This represents the phase difference between the solid oxide fuel cell system and the point of common coupling. For the virtual inertia of the network controller, The damping coefficient; To output electromagnetic torque, As the reference torque, it can be obtained separately through and Calculations show that , These are the reference active power and the output active power, respectively. and These are the integral coefficient and droop coefficient of the reactive power control loop, respectively. and These are the baseline reactive power and the output reactive power, respectively. This refers to the internal voltage amplitude of the solid oxide fuel cell system. This is the voltage reference value; and These represent the d-axis and q-axis components of the controller output voltage, respectively. and These represent the d-axis and q-axis components of the reference voltage value, respectively. and These are the d-axis and q-axis components of the controller output current, respectively. It is the time constant of the inner current loop control. It is a filter capacitor. and These are the proportional coefficient and integral coefficient of the external voltage loop, respectively.

[0103] S2: Decentralize and decouple the parameter estimation model for solid oxide fuel cells, such as... Figure 3 As shown, the parameter space dimension is reduced. Using the voltage and current phasors measured by the local PMU as input, the active and reactive power responses are simulated, and the likelihood function values ​​are further obtained based on the simulated response values ​​and the PMU power measurement values.

[0104] S21: During the set measurement period, acquire the bus voltage phasor of the node where the fuel cell is located via the PMU. Current phasor Due to deviations in actual measurements, the acquired data contains PMU measurement noise.

[0105] S22: The external power system, including generators, network topology, loads, etc., is equivalent to an infinite bus at the point of common coupling, from the parameter vector... Obtained from the prior probability distribution Each sample value is injected into the nonlinear measurement function of the solid oxide fuel cell parameter estimation model. In this process, the dynamic trajectory of the internal state variables of the fuel cell system is obtained, thereby simulating the dynamic response of active and reactive power at the point of common coupling:

[0106]

[0107]

[0108] in and These are the active power and reactive power outputs of the fuel cell, respectively. It is the equivalent line impedance. and These are the measurement noises for active power and reactive power, respectively.

[0109] S23: The joint probability density function of the measurement noise is:

[0110]

[0111] in and These are the measurement noise probability distributions for active power and reactive power, respectively.

[0112] The output power measurement value of the node where the fuel cell is located within a set time period is obtained by acquiring the PMU, and combined with the simulated active power and reactive power response values ​​obtained in step S22, the likelihood function value of the parameter sample is obtained. :

[0113] ;

[0114] ;

[0115] superscript Indicates the time within the set time period The value at that location, Indicates the total duration of the measurement. and These are the active power measurement vector and the reactive power measurement vector, respectively. and It is the corresponding measurement mapping function.

[0116] S3: Construct an adaptive Bayesian update algorithm based on subset simulation to estimate the parameters of the decoupled solid oxide fuel cell system. The algorithm constructs an intermediate failure domain based on the limit state function, thereby gradually approximating the posterior probability distribution of the parameters, and adaptively updates the algorithm parameters to ensure the reliability of the estimation results.

[0117] S31: Set the number of iterations for subset simulation and initial intermediate threshold For fuel cell systems The parameter vector to be estimated ,according to Given the prior sample values ​​and likelihood function values ​​in the original variable space, the limiting state function value of the original variable space is obtained as follows:

[0118]

[0119] in For a standard uniform random variable, It must be a positive integer and satisfy the following conditions: .

[0120] S32: Transform the samples to the standard normal space and generate... Initial independent samples Construct the sample set for layer 0. Its equivalent mapping formula is:

[0121]

[0122] in It is the standard normal cumulative distribution function. It is to satisfy transformation, for 3D independent standard normal random variables, superscript Indicates inverse transformation, subscript Indicates being in the first layer, .

[0123] The limit state function value in the standard normal space is:

[0124]

[0125] in .

[0126] Obtain the logarithmic limit state function of the sample value:

[0127]

[0128] remember To meet The initial maximum likelihood value in the standard normal space is set by combining the PMU power measurement value and the simulated power response value:

[0129] .

[0130] S33: Determine the threshold value of the current layer Is it greater than the target threshold of 0? Execute step S34, if At that time, proceed to step S35.

[0131] S34: The final true posterior distribution domain of the successive approximation parameters, specifically including:

[0132] S341 updates the iteration level of the subset simulation: ;

[0133] S342: Calculate the samples from the previous layer Logarithmic limit state function Values ​​and sort them in ascending order; compare The sorted set is ranked in the th order. The percentile value is the larger of the two (0 and 0) and set as the 1st percentile. Intermediate threshold of layer ,in This is the intermediate conditional probability;

[0134] S343: In the sample set In the middle, identify and extract all that meet the requirements The samples are used to construct the current intermediate failure domain. This sample is used as a conditional seed sample and randomly arranged. The total number of samples that successfully enter the intermediate failure domain in this layer is denoted as . ;

[0135] S344: with Seed samples as A Markov chain seed, generated based on the Markov Chain Monte Carlo (MCMC) algorithm. A new conditional sample;

[0136] S345: Calculate the... Maximum log-likelihood function value of layer samples and adaptive adjustment ,in accordance with For the defined intermediate threshold Perform dynamic corrections and updates. ;

[0137] S346: From the support set Samples were drawn from a uniform distribution. and order To reduce The correlation dependence generated by the nth sample during the evolution of the Markov chain yields the nth... Layer conditional samples Then proceed to step S33.

[0138] S35: When the intermediate threshold iterates to... season , No. Layer samples are the target posterior samples of the parameters to be estimated.

[0139] S36: Convert the samples back to the original variable space for storage, plot the posterior probability density function and obtain the maximum posterior probability (MAP) estimate, which is the final parameter estimation result, thus completing the parameter estimation of the fuel cell system.

[0140] The generation of MCMC conditional samples in step S344 specifically includes the following steps:

[0141] S344-1: Setting adaptive initial level parameters ;

[0142] S344-2: For dimensions From the mean The standard deviation is Proposal samples are drawn from a normal distribution. ; Calculate the proposed sample log-likelihood function value And determine whether it satisfies If the conditions are met, the proposed sample successfully falls into the intermediate failure region and is accepted. As the next state in the Markov chain, if the condition is not met, it is rejected. and the previous layer sample As the next state of the Markov chain;

[0143] S344-3: After completion In the process of building a Markov chain, the loop variable is established as The iterative loop, where For each iteration Determine the current iteration step. Has the adaptive adjustment period been reached? ,judge Is it valid?

[0144] If true, then calculate the acceptance rate of the current proposed sample that falls within the intermediate failure region. Adaptive adjustment of standard deviation parameter:

[0145]

[0146] in To determine the target acceptance rate for the sample, the adaptive hierarchical parameters are updated as follows: ;

[0147] If not true, then maintain the current state. and constant;

[0148] After completing the current step, let Proceed to the next iteration, until the loop variable... Finish Second traversal;

[0149] S344-4: Obtained through the Markov chain evolution process A new conditional sample.

[0150] In this embodiment, the disturbance is set as a tripping of the transmission line between busbar 4 and busbar 5, affecting system parameters. An estimation is performed. A 5% numerical error is set to reflect the uncertainty and prior error of the parameters. It is assumed that the prior probability of the parameters follows a uniform distribution, with its prior mean set to [16.8; 31.5; 336; 21; 0.021; 0.00315], while the actual values ​​of the parameters are [16; 30; 320; 20; 0.02; 0.003]. Measurement error. Assume the noise is independent and identically distributed Gaussian noise with a standard deviation of 0.01. Other parameters are set as follows: median probability... Number of intermediate samples in each layer Initial standard deviation of MCMC process Adaptive adjustment interval Target acceptance rate .

[0151] The schematic diagram of the intermediate failure domain formed by subset simulation in this simulation verification is shown below. Figure 4 As shown, the right side of the curve represents the intermediate failure domain, which is the limit state function. Set a series of intermediate thresholds The parameters gradually approach the target failure domain, thereby obtaining the posterior probability distribution of the parameters to be estimated.

[0152] Figure 5 The simulation results of parameter estimation obtained by the method proposed in this invention are shown. The contour plots present the two-dimensional spatial distribution of corresponding parameter pairs, with light-colored contour lines representing higher probability densities and dark-colored contour lines representing lower probability densities. The diagonal plots show the parameters sequentially from top to bottom. , , , , , The posterior probability density distribution. Figure 5 The MAP estimation results for the visible parameters are 16.068, 29.967, 320.976, 19.724, 0.01973, and 0.0030002, respectively, with calculated estimation errors of 0.43%, 0.11%, 0.31%, 1.38%, 1.35%, and 0.00667%. This demonstrates that the proposed method can accurately estimate system parameters when the system is disturbed.

[0153] Example 2

[0154] This embodiment is also applied to the IEEE 39-node system connected to a solid oxide fuel cell system. The grid connection diagram for the solid oxide fuel cell system is similarly shown below. Figure 2 As shown, the solid oxide fuel cell system is connected to node 5. A schematic diagram of the decentralized and decoupled solid oxide fuel cell system is shown below. Figure 3 As shown. The synchronous generator model considered is a two-shaft model, including an IEEE-DC1A exciter and a TGOV1 turbine governor. The simulation starts from the system steady state at t=0 seconds, and a disturbance is introduced at t=0.5 seconds. The simulation time is set to 5.5 seconds.

[0155] The parameters of a solid oxide fuel cell system are estimated according to the steps of the present invention. The disturbance is set to disconnect 30% of the load on buses 3, 4, 7, 8, 12, 15, 16, and 18, and the system parameters are then evaluated. An estimation is performed. A 5% numerical error is set to reflect the uncertainty and prior error of the parameters. It is assumed that the prior probability of the parameters follows a uniform distribution, with its prior mean set to [16.8; 31.5; 336; 21; 0.021; 0.00315], while the actual values ​​of the parameters are [16; 30; 320; 20; 0.02; 0.003]. Measurement error. Assume the noise is independent and identically distributed Gaussian noise with a standard deviation of 0.01. Other parameters are set as follows: median probability... Number of intermediate samples in each layer Initial standard deviation of MCMC process Adaptive adjustment interval Target acceptance rate .

[0156] Figure 6 The posterior distribution and contour maps of the parameters obtained by the method of this invention in this embodiment are shown. The MAP estimation results of the parameters are 15.959, 29.997, 317.842, 19.768, 0.01991, and 0.0030001, respectively, and the calculated estimation errors are 0.26%, 0.01%, 0.67%, 1.16%, 0.45%, and 0.00333%, respectively. It can be seen that even if the prior information is inaccurate, the proposed method can still accurately estimate the parameter vector. When the system is subjected to different perturbations, the method can still maintain excellent estimation performance and has robustness.

[0157] In summary, this invention provides a fuel cell parameter estimation method based on adaptive subset simulation, supporting the development of accurate solid oxide fuel cell models and the optimization of energy storage system performance. The method includes the following steps: S1, establishing a solid oxide fuel cell parameter estimation model; S2, decentralizing and decoupling the solid oxide fuel cell parameter estimation model; and S3, using an adaptive Bayesian update algorithm based on subset simulation to estimate parameters. This method does not require Gaussian prior assumptions or model linearization, and can adaptively adjust algorithm parameters to ensure the reliability of the estimation results. It can comprehensively characterize the probability distribution of unknown parameters, achieving accurate estimation of solid oxide fuel cell system parameters.

[0158] It should be noted that the above content merely illustrates the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principle of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.

Claims

1. A fuel cell parameter estimation method based on adaptive subset simulation, characterized in that: Includes the following steps: S1: Establish a parameter estimation model for solid oxide fuel cells. This estimation model is based on Bayesian inference and measurement equations from the solid oxide fuel cell model. Specifically: ； ； ； in, It is a measurement vector that includes active power measurements and reactive power measurements. Let be the parameter vector to be estimated. It is a nonlinear measurement function. To measure noise, for The joint probability density function components, Let be the likelihood function. Let be the prior probability distribution of the parameter. Let be the posterior probability distribution of the parameter. Here is the regularization constant; S2: Decentralize and decouple the solid oxide fuel cell parameter estimation model established in step S1. Use the voltage and current phasors measured by the local PMU as inputs to simulate the output active power and reactive power response. Obtain the likelihood function value based on the active power and reactive power response values ​​and the PMU power measurement values. S3: Construct an adaptive Bayesian update algorithm based on subset simulation and apply it to the solid oxide fuel cell parameter estimation model after decoupling in step S2 to achieve system parameter estimation; the algorithm constructs an intermediate failure domain based on the limit state function, thereby gradually approximating the posterior probability distribution of the parameters and adaptively updating the algorithm parameters.

2. The fuel cell parameter estimation method based on adaptive subset simulation as described in claim 1, characterized in that: The solid oxide fuel cell model in step S1 includes a solid oxide fuel cell dynamic model and a grid-type controller. The solid oxide fuel cell model is specifically as follows: ； ； ； ； ； ； ； ； in, , , These represent the partial pressures of hydrogen, oxygen, and water in the reactants, respectively. , , These are the response time constants for hydrogen flow rate, oxygen flow rate, and water flow rate, respectively. , , The valve molar constants for hydrogen, oxygen, and water are respectively. This represents the load current of the fuel cell; It is the internal electromotive force of the fuel cell. It is ohmic loss. It is polarization voltage loss. It is the concentration pressure drop. It is the output voltage of the fuel cell; It is the ideal standard potential for a single fuel cell. It refers to the number of fuel cell stacks. It is the universal gas constant. It is the optimal operating temperature. It is Faraday's constant. It is the ohmic resistance coefficient. It is the temperature coefficient. It refers to the temperature of the fuel cell stack. It is the output current of the fuel cell. It is an alternating current. It is the current-limiting current; It is a constant.

3. The fuel cell parameter estimation method based on adaptive subset simulation as described in claim 2, characterized in that: The grid-type controller in step S1 includes a boost converter and an inverter. The dynamic model of the solid oxide fuel cell is connected to the power grid through the grid-type controller. The boost converter is specifically: ； ； ； ； in, It is the circuit inductance. It is a DC bus capacitor. It is the DC bus output current. It is the DC bus output voltage. It is a pulse width modulation (PWM) signal. This is the DC reference voltage. For reference current, , These are the proportional gain and integral gain of the voltage loop, respectively. , These are the proportional coefficient and integral coefficient of the current loop, respectively. Indicates a PWM signal; The inverter employs a droop controller and a dual closed-loop voltage and current controller. The power droop controller provides reference voltage and frequency for the dual-loop voltage and current controller, specifically: ； ； ； ； ； in, This represents the internal angular frequency of a solid oxide fuel cell system. As the reference angular frequency, This represents the phase difference between the solid oxide fuel cell system and the point of common coupling. For the virtual inertia of the network controller, The damping coefficient; To output electromagnetic torque, As the reference torque, , These are the reference active power and the output active power, respectively. and These are the integral coefficient and droop coefficient of the reactive power control loop, respectively. and These are the baseline reactive power and the output reactive power, respectively. This refers to the internal voltage amplitude of the solid oxide fuel cell system. This is the voltage reference value; and These represent the d-axis and q-axis components of the controller output voltage, respectively. and These represent the d-axis and q-axis components of the reference voltage value, respectively. and These are the d-axis and q-axis components of the controller output current, respectively. It is the time constant of the inner current loop control. It is a filter capacitor. and These are the proportional coefficient and integral coefficient of the external voltage loop, respectively.

4. The fuel cell parameter estimation method based on adaptive subset simulation as described in claim 2, characterized in that: Step S2 specifically includes the following steps: S21: During the set measurement period, acquire the bus voltage phasor of the node where the fuel cell is located via the PMU. Current phasor ; S22: The external power system at the point of common coupling is equivalent to an infinite bus, from the parameter vector. Obtained from the prior probability distribution Each sample value is injected into the nonlinear measurement function of the solid oxide fuel cell parameter estimation model. In this process, the dynamic trajectory of the internal state variables of the fuel cell system is obtained, and the dynamic response of active and reactive power at the point of common coupling is simulated and output. ； ； in and These are the active power and reactive power outputs of the fuel cell, respectively. It is the equivalent line impedance. and These are the measurement noises for active power and reactive power, respectively. S23: The joint probability density function of the measurement noise is: ； in and These are the measurement noise probability distributions for active power and reactive power, respectively. The output power measurement value of the node where the fuel cell is located within a set time period is obtained by acquiring the PMU, and combined with the simulated active power and reactive power response values ​​obtained in step S22, the likelihood function value of the parameter sample is obtained. : ； ； superscript Indicates the time within the set time period The value at that location, Indicates the total duration of the measurement. and These are the active power measurement vector and the reactive power measurement vector, respectively. and It is the corresponding measurement mapping function.

5. The fuel cell parameter estimation method based on adaptive subset simulation as described in claim 2, characterized in that: Step S3 specifically includes the following steps: S31: Set the number of iterations for subset simulation and initial intermediate threshold ,for The parameter vector to be estimated ,according to Given the prior sample values ​​and likelihood function values ​​in the original variable space, the limiting state function value of the original variable space is obtained as follows: ； in For a standard uniform random variable, It must be a positive integer and satisfy the following conditions: ; S32: Transform the samples to the standard normal space and generate... Initial independent samples Construct the sample set of layer 0, and its equivalent mapping formula is: ； in It is the standard normal cumulative distribution function. It is to satisfy transformation, for 3D independent standard normal random variables, superscript Indicates inverse transformation, subscript Indicates being in the first layer, ; The limit state function value in the standard normal space is: ； in ; Obtain the logarithmic limit state function of the sample value: ； remember To meet The initial maximum likelihood value in the standard normal space is set by combining the PMU power measurement value and the simulated power response value: ； S33: Determine the threshold value of the current layer Is it greater than the target threshold of 0? Execute step S34, if When the time comes, proceed to step S35; S34: The final true posterior distribution domain of the successive approximation parameters, specifically including: S341: Update the number of iterations for the subset simulation: ; S342: Calculate the samples from the previous layer Logarithmic limit state function Values ​​and sort them in ascending order; compare The sorted set is ranked in the th order. The percentile value is the larger of the two (0 and 0) and set as the 1st percentile. Intermediate threshold of layer ,in This is the intermediate conditional probability; S343: In the sample set In the middle, identify and extract all that meet the requirements The samples are used to construct the current intermediate failure domain. This sample is used as a conditional seed sample and randomly arranged. The total number of samples that successfully enter the intermediate failure domain in this layer is denoted as . ; S344: with Seed samples as A Markov chain seed, generated based on the Markov Chain Monte Carlo (MCMC) algorithm. A new conditional sample; S345: Calculate the... Maximum log-likelihood function value of layer samples and adaptive adjustment ,in accordance with For the defined intermediate threshold Perform dynamic corrections and updates. ; S346: From the support set Samples were drawn from a uniform distribution. and order To reduce The correlation dependence generated by the nth sample during the evolution of the Markov chain yields the nth... Layer conditional samples Proceed to step S33; S35: When the intermediate threshold iterates to... season , No. Layer samples are the target posterior samples of the parameters to be estimated; S36: Convert the samples back to the original variable space for storage, plot the posterior probability density function and obtain the maximum posterior probability (MAP) estimate, which is the final parameter estimation result, thus completing the parameter estimation of the fuel cell system.

6. The fuel cell parameter estimation method based on adaptive subset simulation as described in claim 5, characterized in that: The MCMC conditional sample generation in step S344 specifically includes the following steps: S344-1: Setting adaptive initial level parameters ; S344-2: For dimensions From the mean The standard deviation is Proposal samples are drawn from a normal distribution. ; Calculate the proposed sample log-likelihood function value And determine whether it satisfies If the conditions are met, the proposed sample successfully falls into the intermediate failure region and is accepted. As the next state in the Markov chain, if the condition is not met, it is rejected. and the previous layer sample As the next state of the Markov chain; S344-3: After completion In the process of building a Markov chain, the loop variable is established as The iterative loop, where For each iteration Determine the current iteration step. Has the adaptive adjustment period been reached? ,judge Is it valid? If true, then calculate the acceptance rate of the current proposed sample that falls within the intermediate failure region. Adaptive adjustment of standard deviation parameter: ； in To determine the target acceptance rate for the sample, the adaptive hierarchical parameters are updated as follows: ; If not true, then maintain the current state. and constant; After completing the current step, let Proceed to the next iteration, until the loop variable... Finish Second traversal; S344-4: Obtained through the Markov chain evolution process A new conditional sample.

7. A fuel cell parameter estimation system based on adaptive subset simulation, comprising a computer program, characterized in that: When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1-6 above.

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