Online estimation method and system for hot-spot temperature of electrolytic cell based on fractional calculus

Abstract

The invention discloses an electrolytic bath hot spot temperature online estimation method and system based on fractional calculus, and belongs to the technical field of energy equipment state monitoring. The invention aims to solve the technical problem that a temperature estimation model in the prior art is large in calculation amount or insufficient in precision. According to the technical scheme, the method is characterized by comprising the steps that a multi-input single-output observer model is established, and the model takes the total input power and the outer surface temperature of the electrolytic cell as input and takes an estimated value of the internal hot spot temperature as output; decoupling the model into a heat production fast dynamic channel and a heat transfer slow dynamic channel; and mathematical description is carried out on the one or two channels by adopting a fractional order transfer function so as to accurately describe the memory effect of the heat transfer process. The method further comprises the steps that model parameters are determined through system identification, and temperature estimation is conducted on line through the model. The method gives consideration to calculation efficiency and estimation precision, and can be used for guaranteeing safe and efficient operation of the electrolytic cell.

Description

Technical Field

[0001] This invention relates to the field of energy equipment condition monitoring technology, and more specifically, to a method and system for online estimation of hot spot temperature in electrolytic cells based on fractional calculus. Background Technology

[0002] Proton exchange membrane (PEM) electrolyzers are key equipment for achieving electro-hydrogen conversion. When operating under dynamic conditions such as grid frequency regulation, rapid power changes can cause localized overheating inside the electrolyzer, creating safety hazards and affecting the operational stability and service life of the equipment.

[0003] Due to physical space limitations, these localized hot spots located inside the electrolytic cell cannot be directly measured by sensors. Therefore, model-based indirect estimation methods have become the technical approach to obtain their temperature information.

[0004] In existing technologies, there are methods for temperature estimation using multiphysics models based on computational fluid dynamics (CFD). These models can provide relatively accurate information on the internal temperature field distribution, but they involve huge computational demands and require high computing resources, making them unsuitable for applications requiring real-time online estimation.

[0005] Another type of existing technology employs lumped parameter models. These models have the advantage of computational efficiency, but due to their relatively simplified structure, their estimation accuracy is limited when describing the dynamics of non-uniform internal hotspots.

[0006] Furthermore, heat transfer within the electrolyzer (especially in porous media) is a complex physical process exhibiting both "memory" and "hereditary" characteristics. Traditional integer-order calculus theory struggles to accurately describe the properties of this "anomalous diffusion" phenomenon. Consequently, state estimation methods based on traditional integer-order theory are hampered in their ability to accurately capture system dynamics when applied to such systems.

[0007] In view of this, how to provide a method that is computationally efficient and can accurately characterize complex heat transfer dynamics in order to achieve online estimation of hot spot temperatures inside an electrolytic cell is a current technical problem in this field. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide an online estimation method and system for hot spot temperature of electrolytic cells based on fractional calculus, so as to overcome the problems of large computational load or insufficient accuracy in the prior art.

[0009] To address the aforementioned technical problems, this invention provides a method and system for online estimation of hotspot temperature in electrolytic cells based on fractional calculus. The specific technical solution is as follows:

[0010] An online method for estimating the hot spot temperature of an electrolyzer based on fractional calculus includes the following steps:

[0011] (a) Establish a multi-input single-output observer model, wherein the model takes the total input power of the electrolytic cell and the external surface temperature as inputs and outputs an estimated value of the internal hot spot temperature, wherein the model decouples the hot spot temperature formation process into a fast dynamic channel for heat generation driven by the total input power and a slow dynamic channel for heat transfer affected by the external surface temperature.

[0012] (b) The dynamic characteristics of the heat generation fast dynamic channel and the heat transfer slow dynamic channel are mathematically described using a fractional transfer function;

[0013] (c) Based on the acquired system identification data, determine the model parameters in the fractional transfer function to obtain a parameterized observer model;

[0014] (d) During online operation, the total input power and external surface temperature measured in real time are input into the parameterized observer model to calculate and output an estimate of the internal hot spot temperature.

[0015] An online hotspot temperature estimation system for electrolytic cells based on fractional calculus includes:

[0016] The model building unit is used to establish a multi-input single-output observer model. The model takes the total input power and external surface temperature of the electrolytic cell as inputs and outputs an estimated value of the internal hot spot temperature. The model decouples the hot spot temperature formation process into a fast heat generation dynamic channel and a slow heat transfer dynamic channel, and uses a fractional transfer function to mathematically describe at least one of the channels.

[0017] The parameter determination unit is used to determine the model parameters in the fractional-order transfer function based on the acquired system identification data, so as to obtain a parameterized observer model.

[0018] The online estimation unit is used to receive real-time measurements of the total input power and the outer surface temperature during the online operation of the electrolyzer, and to calculate and output an estimated value of the internal hot spot temperature through the parameterized observer model.

[0019] Compared with the prior art, the present invention has the following beneficial effects:

[0020] 1. Clear physical meaning: By decoupling the heat transfer process into two physical channels, heat generation and heat transfer, the model structure corresponds to physical reality.

[0021] 2. Computationally efficient and applicable online: The gray box model of this invention has a simple structure and low computational cost, which can meet the needs of online real-time estimation.

[0022] 3. High estimation accuracy: By introducing fractional operators, the memory effect in the heat transfer process can be characterized more accurately, improving the ability to capture the dynamics of hot spot temperature and the estimation accuracy. Attached Figure Description

[0023] Figure 1 : Schematic diagram of the MISO fractional-order observer framework proposed in this invention.

[0024] Figure 2 The flowchart for parameter identification based on simulation data in this invention.

[0025] Figure 3 : A schematic diagram of the functional modules of the online estimation system described in this invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of the present invention clearer, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0027] This invention provides an online estimation method for hotspot temperature in electrolytic cells based on fractional calculus. Its core lies in constructing and applying a multi-input single-output (MISO) observer based on fractional calculus. For example... Figure 1 As shown in the figure, this diagram illustrates the MISO fractional-order observer framework proposed in this invention. The model incorporates the total power input from an externally measurable electrolyzer. and external surface temperature As input, the internal, unmeasurable hot spot temperature As output, the model decouples the complex heat transfer process into two parallel physical channels: one describing the heat transfer process caused by the input power. Thermodynamic channel for direct heat generation process ( ), and the slow dynamic heat transfer channel that describes the process by which internal heat is ultimately transferred to the outer surface of the device ( ), and the heat transfer slow dynamic channel. The core relationship of the MISO observer model in the frequency domain can be expressed by the following equation:

[0028] (1)

[0029] The model parameters need to be determined through system identification methods. To accurately characterize the inherent memory effect in the above physical channels, the transfer functions of both channels can be represented by a general fractional transfer function, the general form of which is shown in equation (2):

[0030] (2)

[0031] in, For the complex frequency variable of the Laplace transform, and The coefficients of the polynomial in the transfer function. and It is any real number of orders.

[0032] To determine the unknown parameters in the model, system identification is required. Please refer to [link / reference]. Figure 2 The figure illustrates a flowchart of parameter identification in this invention. This process first requires acquiring time-series data reflecting the dynamic characteristics of the electrolyzer, including the total input power. Surface temperature And the internal hotspot temperature as a reference true value. This data can be derived from simulations of high-fidelity finite element (FEM) models or tests on physical experimental platforms. To fully excite the system dynamics, excitation signals such as pseudo-random binary sequences (PRBS) can be applied to the system. Subsequently, an optimization problem is constructed, the goal of which is to find a set of optimal model parameters. This makes the model's predicted values With reference truth value Minimize the difference between them. Define the prediction error. for:

[0033] (3)

[0034] And construct the following mean squared error (MSE) cost function. :

[0035] (4)

[0036] in, For the first The input time point or input variable for each data sample Given the total number of data samples, parameter identification is equivalent to solving for the cost function. Minimum optimal parameter vector This is a nonlinear minimization problem. To solve this minimization problem, efficient iterative optimization algorithms can be used, such as the Levenberg-Marquardt (LM) algorithm or the Sequential Quadratic Programming (SQP) algorithm. After determining the model parameters through the above identification methods, a complete observer model can be obtained. In practical applications, the real-time collected total input power... and external surface temperature The measured values ​​are input into the identified observer model, allowing for the real-time calculation of estimated internal hotspot temperatures. .

[0037] like Figure 3As shown, the present invention also provides an online estimation system for implementing the aforementioned method. This system can be implemented based on a general-purpose computer hardware platform, such as an industrial control computer, embedded system, or server. Logically, the system includes a model building unit, a parameter determination unit, and an online estimation unit. The model building unit is used to establish the MISO observer model structure and mathematically describe at least one of the channels using fractional-order functions. The parameter determination unit is used to execute the aforementioned parameter identification process, determining the unknown parameters in the model based on system identification data. The online estimation unit is used to receive real-time sensor data during online operation and calculate and output estimated values ​​of hotspot temperatures using the parameterized observer model.

[0038] In a preferred embodiment, a PEM electrolytic cell multiphysics finite element model is first established in the COMSOL Multiphysics simulation environment. Then, a PRBS signal is applied to the model as the input power excitation, and the required time series data is recorded. Subsequently, in the MATLAB environment, the lsqnonlin or fmincon solver in its optimization toolbox is called to optimize the cost function constructed according to equation (4), thereby identifying the specific parameters of the fractional-order transfer function and completing the construction of the observer.

[0039] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for online estimation of hotspot temperature in an electrolytic cell based on fractional calculus, characterized in that, Includes the following steps: (a) Establish a multi-input single-output observer model, wherein the model takes the total input power of the electrolytic cell and the external surface temperature as inputs and outputs an estimated value of the internal hot spot temperature, wherein the model decouples the hot spot temperature formation process into a fast dynamic channel for heat generation driven by the total input power and a slow dynamic channel for heat transfer affected by the external surface temperature. (b) The dynamic characteristics of the heat generation fast dynamic channel and the heat transfer slow dynamic channel are mathematically described using a fractional transfer function; (c) Based on the acquired system identification data, determine the model parameters in the fractional-order transfer function to obtain a parameterized observer model; (d) During online operation, the total input power and external surface temperature measured in real time are input into the parameterized observer model to calculate and output an estimate of the internal hot spot temperature.

2. The method according to claim 1, characterized in that, The observer model is expressed by the following equation: （1） The total power input to the electrolytic cell, The outer surface temperature. This is an estimate of the hotspot temperature. For rapid heat generation dynamic channels, and This is a slow-dynamic heat transfer channel.

3. The method according to claim 1 or 2, characterized in that, The fractional transfer function is used to represent this, as shown in equation (2): （2） in, For the complex frequency variable of the Laplace transform, and The coefficients of the polynomial in the transfer function. and It is any real number of orders.

4. The method according to claim 1, characterized in that, The step of determining the model parameters described in step (c) specifically includes: i. Acquire the system identification data, which includes a time series of total input power, external surface temperature, and internal hotspot temperature as a reference true value; ii. Based on the identified data, construct a cost function with the objective of minimizing the error between the model's predicted output and the reference true value; iii. Solve the cost function minimization problem using an iterative optimization algorithm to determine the model parameters.

5. The method according to claim 4, characterized in that, The system identification data in step i is generated by simulating a high-fidelity multiphysics finite element model.

6. The method according to claim 5, characterized in that, The excitation signal applied during the simulation is a pseudo-random binary sequence signal.

7. The method according to claim 4, characterized in that, The cost function mentioned in step ii is the mean squared error function.

8. The method according to claim 4, characterized in that, The iterative optimization algorithm described in step iii is selected from the Levenberg-Marquardt algorithm or the sequential quadratic programming algorithm.

9. An online estimation system for hot spot temperature of an electrolytic cell based on fractional calculus, characterized in that, include: The model building unit is used to establish a multi-input single-output observer model. The model takes the total input power and external surface temperature of the electrolytic cell as inputs and outputs an estimated value of the internal hot spot temperature. The model decouples the hot spot temperature formation process into a fast heat generation dynamic channel and a slow heat transfer dynamic channel, and uses a fractional transfer function to mathematically describe at least one of the channels. The parameter determination unit is used to determine the model parameters in the fractional-order transfer function based on the acquired system identification data, so as to obtain a parameterized observer model. The online estimation unit is used to receive real-time measurements of the total input power and the outer surface temperature during the online operation of the electrolyzer, and to calculate and output an estimated value of the internal hot spot temperature through the parameterized observer model.

10. The system according to claim 9, characterized in that, The parameter determination unit is specifically used to: construct a cost function based on time series identification data containing input, output and reference true values, with the goal of minimizing the error between the model prediction and the reference true values, and solve it using an iterative optimization algorithm to determine the model parameters.

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