High-order direct-current micro-grid system multi-loss synchronous convergence modeling method based on improved physical information neural network

Abstract

The invention discloses a high-order direct-current micro-grid system multi-loss synchronous convergence modeling method based on an improved physical information neural network. The method comprises the steps that S1, a physical information neural network model is initialized; s2, calculating physical loss and updating parameters of the physical information neural network model; s3, reflecting parameters of the physical information neural network model around physical optimization result points; s4, calculating data loss by using the reflected parameters and updating parameters of the physical information neural network model; s5, using the parameters obtained in S2 and S4 to update the parameters of the physical information neural network model through the iterative operation of Douglas-Rachford splitting; and S6, iterating the parameter updating process to solve the physical information neural network model. Different from a traditional physical information neural network which is difficult to converge for high-order system training, the method can realize synchronous convergence of physical loss and data loss in high-order direct-current micro-grid system fitting, and has important significance for mastering an internal operation rule of a direct-current micro-grid system in real time and establishing a physically interpretable data driving model.

Description

Technical Field

[0001] This invention belongs to the field of physical information neural network modeling technology for DC microgrid systems, and specifically relates to a high-order DC microgrid system multi-loss synchronous convergence modeling method based on an improved physical information neural network. Background Technology

[0002] Physical information neural networks (PINs) endow traditional data-driven models with physical interpretability, proving highly effective for solving partial differential equations (PDEs) and demonstrating great potential for fitting various PDEs that cannot be solved analytically. Therefore, PINs are a promising technical solution for modeling DC microgrid systems. However, DC microgrids exhibit high-order and nonlinear characteristics. Traditional PINs are constrained by non-convex optimization problems, and when dealing with high-order PDEs, physical loss and data loss often fail to converge simultaneously. Consequently, it is difficult to establish accurate models for high-order DC microgrid systems. Therefore, improving traditional PIN algorithms to ensure simultaneous convergence of multiple losses is crucial. Current improved algorithms for PINs have resolved the gradient conflict problem between the two losses in low-order systems, but they still cannot guarantee simultaneous convergence to the optimal solution for high-order DC microgrid systems. Therefore, there is an urgent need for an improved PIN method for modeling high-order DC microgrid systems.

[0003] Patent application CN202411433945.2 discloses a method for predicting the internal magnetic field of an aluminum electrolytic cell based on a Physical Information Network (PINN). The method includes inputting relevant data of the magnetic field to be predicted into a trained PINN model and outputting predicted data. The specific steps for constructing the trained PINN model include: S1. Constructing a physical model of the internal magnetic field of the target aluminum electrolytic cell; S2. Constructing the PINN model, building a loss function based on the physical model, calculating the physical loss during backpropagation through iterative training and backpropagation, and completing training if preset conditions are met, thus obtaining a PINN model for predicting the target's internal magnetic field; S3. Verifying the PINN model to obtain the trained PINN model. However, this method, using PINN, only models low-order systems, making it difficult to solve high-order system models. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, the present invention aims to propose a multi-loss synchronous convergence modeling method for high-order DC microgrid systems based on an improved physical information neural network. The present invention integrates the traditional physical information neural network with the Douglas-Rachford splitting algorithm to achieve synchronous convergence of physical loss and data loss when the physical information neural network fits non-convex optimization problems such as high-order DC microgrid systems, and ensures the modeling accuracy of high-order DC microgrid systems.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A multi-loss synchronous convergence modeling method for high-order DC microgrid systems based on an improved physical information neural network includes the following steps:

[0007] Step 1: Construct the state-space equations of the high-order DC microgrid system and embed them into the neural network as physical constraints to obtain the untrained physical information neural network model of the high-order DC microgrid system;

[0008] Step 2: Initialize the constructed physical information neural network model;

[0009] Step 3: Calculate the physical loss of the physical information neural network and update the physical information neural network model parameters using the gradient descent algorithm;

[0010] Step 4: Perform the reflection process in the Douglas-Rachford split algorithm on the physical information neural network model parameters around the physical constraint optimization result points;

[0011] Step 5: Calculate the data loss using the parameters of the reflected physical information neural network model, and update the parameters of the physical information neural network model again using the gradient descent algorithm;

[0012] Step 6: Combining the parameters obtained in Step 3 and Step 5, update the physical information neural network model parameters through the iterative process of the Douglas-Rachford splitting algorithm;

[0013] Step 7: Proceed to Step 3 and iterate through the above parameter update process to solve the physical information neural network model. The physical information neural network model is the data-driven model of the constructed high-order DC microgrid system.

[0014] In step 1, based on the structure of the high-order DC microgrid system, the input and state variables of the high-order DC microgrid system are determined, and the state-space equation of the DC microgrid system is constructed.

[0015] In step 2, the weights of the physical information neural network are initialized using Xavier, the weight variance is controlled, and the physical information neural network model parameters θ are saved.

[0016] In step 3, the formula for calculating the physical loss of the physical information neural network model is as follows:

[0017]

[0018] Among them, L phys The physical loss of the physical information neural network model is represented by u, where u is the input of the high-order DC microgrid system. These are estimates of the state variables of a high-order DC microgrid system. Let A be the derivative of the state variable estimate of the high-order DC microgrid system, and A and B be the system matrix and input matrix of the high-order DC microgrid, respectively.

[0019] Based on the physical loss of the physical information neural network model, a gradient descent process is performed to simulate the physical projection operator, and the parameters θ of the physical information neural network model after physical loss optimization are saved. phys .

[0020] In step 4, the physical information neural network model parameters are reflected back to the optimal point of the physical constraint optimization subproblem, and the calculation formula for the reflection operation of the Douglas-Rachford splitting algorithm is as follows:

[0021] θ ref =2θ phys -θ (2)

[0022] Where θ ref θ represents the parameters of the physical information neural network model used for data loss optimization. phys θ represents the physical information neural network model parameters after physical loss optimization, while θ represents the physical information neural network model parameters before physical loss optimization.

[0023] In step 5, the updated parameter θ is used with the physical information neural network model. ref The data loss is calculated using the following formula:

[0024]

[0025] Among them, L data For data loss, x ref These are the actual values ​​of the state variables of a high-order DC microgrid system. To estimate the state variables of a high-order DC microgrid system, gradient descent is performed based on the data loss of the physical information neural network model, and the parameters θ of the physical information neural network model after data loss optimization are saved. data .

[0026] In step 6, the parameters of the physical information neural network model are updated using the iterative formula in the Douglas-Rachford splitting algorithm. The iterative formula is as follows:

[0027] θ=θ+α(θ data -θ phys (4)

[0028] Where θ represents the parameters of the current physical information neural network model, and α∈[0,1] are weight parameters used to balance the influence of data terms and physical terms. data θ represents the parameters of the physical information neural network model optimized for data loss.phys The parameters of the physical information neural network model are optimized for physical loss.

[0029] In step 7, steps 3-6 are iterated repeatedly to solve the physical information neural network model until both the data loss and physical loss converge to below the corresponding thresholds. The output of the physical information neural network model is then the predicted value of the state variables of the high-order DC microgrid system. Compared with the prior art, this invention has the following advantages:

[0030] 1. Decoupling physical constraints and data constraints: The multi-loss coupling problem in traditional physical information neural networks is decoupled into two sub-problems, and optimization is performed on the two sub-problems separately. This avoids the competition between the two during gradient descent and significantly improves the stability and convergence of physical information neural network training when modeling high-order DC microgrid systems.

[0031] 2. High accuracy: Compared with traditional physical information neural network methods, the improved physical information neural network method of this invention, which integrates the Douglas-Rachford splitting algorithm, can still guarantee the fitting accuracy of high-order DC microgrid systems.

[0032] 3. Strong applicability: This method can escape the local optimum in DC microgrid modeling by performing reflection iteration between the two sub-objectives of physical constraints and data constraints, effectively improving the optimization effect in non-convex scenarios.

[0033] In summary, this invention achieves simultaneous convergence of physical and data losses when physical information neural networks are used to fit non-convex optimization problems such as high-order DC microgrid systems by integrating traditional physical information neural networks with the Douglas-Rachford splitting algorithm, and ensures the modeling accuracy of high-order DC microgrid systems. Attached Figure Description

[0034] Figure 1 This is a flowchart of the method of the present invention.

[0035] Figure 2 This is a diagram of the improved physical information neural network architecture described in this invention.

[0036] Figure 3 This is a structural diagram of a DC microgrid system.

[0037] Figure 4(a) is a graph showing the physical loss curve during training of the improved physical information neural network described in this invention.

[0038] Figure 4(b) is a training data loss curve of the improved physical information neural network described in this invention.

[0039] Figure 5(a) is a graph showing the physical loss curve during training of a traditional physical information neural network.

[0040] Figure 5(b) is a curve showing the training data loss of a traditional physical information neural network.

[0041] Figure 6(a) is a fitting curve of the improved physical information neural network described in this invention.

[0042] Figure 6(b) is a fitting curve of the traditional physical information neural network model. Detailed Implementation

[0043] The present invention will now be described in detail with reference to the accompanying drawings.

[0044] like Figure 1 As shown, the present invention provides a multi-loss synchronous convergence modeling method for high-order DC microgrid systems based on an improved physical information neural network, comprising the following steps:

[0045] Step 1: Construct the state-space equations of the high-order DC microgrid system and embed them into the neural network as physical constraints to obtain the untrained physical information neural network model of the high-order DC microgrid system;

[0046] Step 2: Initialize the constructed physical information neural network model;

[0047] Step 3: Calculate the physical loss of the physical information neural network model and update the parameters of the physical information neural network model using the gradient descent algorithm;

[0048] Step 4: Perform the reflection process in the Douglas-Rachford split algorithm on the physical information neural network model parameters around the physical constraint optimization result points;

[0049] Step 5: Calculate the data loss using the parameters of the reflected physical information neural network model, and update the parameters of the physical information neural network model again using the gradient descent algorithm;

[0050] Step 6: Combining the parameters obtained in Step 3 and Step 5, update the physical information neural network model parameters through the iterative process of the Douglas-Rachford splitting algorithm;

[0051] Step 7: Proceed to Step 3 and iterate through the above parameter update process to solve the physical information neural network model. The physical information neural network model is the data-driven model of the constructed high-order DC microgrid system.

[0052] The flowchart of the improved physical information neural network algorithm incorporating the Douglas-Rachford splitting algorithm is as follows: Figure 1 As shown in the diagram, the architecture is as follows: Figure 2 As shown, Figure 2The intermediate linear combiner module includes the reflection operation in the Douglas-Rachford split algorithm required for physical loss, as well as the iterative operation in the Douglas-Rachford split algorithm performed jointly by physical loss and data loss.

[0053] In step 1, the scenario for verifying the high-order physical information neural network method that integrates the Douglas-Rachford splitting algorithm is as follows: Figure 3 As shown, the input u and state x of this high-order DC microgrid system are given by equations (5) and (6).

[0054] u = [v in i L d bo d bu1 d bu2 v bus ] T (5)

[0055] x = [i L,bo v C,bo i L,bu1 v C,bu1 v in,bu1 i L,bu2 v C,bu2 v in,bu2 i 1a i 1b i 2a i 2b i 3a i 3b ] T (6)

[0056] Where u is the input of the high-order DC microgrid system, v in For the input voltage of a high-order DC microgrid system, i L For the load current of the battery load in a high-order DC microgrid system, d bo d bu1 d bu2 These represent the duty cycles of the boost, buck1, and buck2 converters, respectively. bus Let be the bus voltage of the high-order DC microgrid system, x be the state variable of the high-order DC microgrid system, and i be the bus voltage. L,bo V is the inductor current of the boost converter. C,bo i is the capacitor voltage of the boost converter. L,bu1 V is the inductor current of the Buck 1 converter. C,bu1 V is the voltage across the filter capacitor of the Buck 1 converter. in,bu1 i is the input capacitor voltage of the Buck 1 converter. L,bu2V is the inductor current of the Buck 2 converter. C,bu2 V is the voltage across the filter capacitor of the Buck2 converter. in,bu2 i is the input capacitor voltage of the Buck 2 converter. 1a Let i be the inductance current at the left end of cable 1. 1b Let i be the inductance current at the right end of cable 1. 2a Let i be the inductance current at the left end of cable 2. 2b Let i be the inductance current at the right end of cable 2. 3a The inductance current at the left end of cable 3 is i. 3b This represents the inductance current at the right end of cable 3.

[0057] The constructed state-space equations are shown in equation (7).

[0058]

[0059] Where x represents the state variables of the high-order DC microgrid system. Let A and B be the derivatives of the state variables of the high-order DC microgrid system, respectively. Equations (8) and (9) are the specific expressions of matrices A and B.

[0060]

[0061]

[0062] Where A1, A2, A3, and A4 are all submatrices of matrix A, L bo C is the inductance of the boost converter. bu2 L is the filter capacitor for the Buck 2 converter. 1b For the inductance at the right end of cable 1, L 2a For the inductance at the left end of cable 2, L 3a Let A1 be the inductance at the left end of cable 3. The specific expressions for A1, A2, A3, and A4 are shown in equations (10) to (13).

[0063]

[0064]

[0065] Among them, R bo L is the resistance of the boost converter. bo C1 is the inductor of the boost converter, C2 is the capacitor of the boost converter, and d bo R is the duty cycle of the boost converter. bu1For the resistance of the Buck 1 converter, L bu1 For the inductance of the Buck 1 converter, C bu1 C1 is the filter capacitor of the Buck 1 converter, C2 is the input capacitor of the Buck 1 converter, and R... L d is the load resistance of the Buck 1 converter. bu1 R is the duty cycle of the Buck 1 converter. bu2 For the resistance of the Buck 2 converter, L bu2 For the inductance of the buck 2 converter, C bu2 C3 is the filter capacitor of the Buck 2 converter, C4 is the input capacitor of the Buck 2 converter, and d is the input capacitor. bu2 R is the duty cycle of the buck 2 converter. 1a R is the resistance at the left end of cable 1. 1b For the resistance at the right end of cable 1, L 1a For the inductance at the left end of cable 1, L 1b R is the inductance at the right end of cable1. 1f For cable 1, the fault grounding resistance, R 2a R is the resistance at the left end of cable 2. 2b For the resistance at the right end of cable 2, L 2a For the inductance at the left end of cable 2, L 2b For the inductance at the right end of cable 2, R 2f R is the fault grounding resistance of cable 2. 3a R is the resistance at the left end of cable 3. 3b For the resistance at the right end of cable 3, L 3a For the inductance at the left end of cable 3, L 3b For the inductance at the right end of cable 3, R 3f For cable 3, the fault grounding resistance.

[0066] In step 2, the weights of the physical information neural network model are initialized using Xavier, ensuring that the variance of the weights conforms to a Gaussian distribution with a mean of 0.

[0067] W~Normal(0,σ 2 (14)

[0068]

[0069] Where W represents the weights of the physical information neural network model, σ 2 Let n be the variance. in n represents the number of inputs to the current layer of the physical information neural network model.out Set the number of outputs for the current layer of the physical information neural network model and save the physical information neural network model parameters θ.

[0070] In step 3, the physical information neural network model is input with u, and the predictions of the physical information neural network model are obtained through forward propagation. The physical loss of the physical information neural network model is calculated using equation (1).

[0071]

[0072] Among them, L phys The physical loss of the physical information neural network model is represented by u, where u is the input of the high-order DC microgrid system. These are estimates of the state variables of a high-order DC microgrid system. It is the derivative of the state quantity estimate of the high-order DC microgrid system.

[0073] The Adam optimizer is selected, and the gradient descent update process based on the physical loss of the physical information neural network model is simulated to represent the physical projection operator. The physical loss and data loss are decoupled into two sub-problems, which are then optimized alternately. The physical information neural network model parameters θ after physical loss optimization are saved. phys .

[0074] In step 4, the reflection operation of the Douglas-Rachford splitting algorithm shown in equation (2) is performed to construct a reflection point centered on the physical optimal parameters for the next data fitting step. During this operation, the physical information neural network model is not only constrained by the data but also retains the physical information direction when optimizing data items.

[0075] θ ref =2θ phys -θ (2)

[0076] Where θ ref θ represents the parameters of the physical information neural network model used for data loss optimization. phys θ represents the physical information neural network model parameters after physical loss optimization, while θ represents the physical information neural network model parameters before physical loss optimization.

[0077] In step 5, θ is used ref Initialize the parameters of the physical information neural network model, and obtain the state prediction by forward propagation of the input u. Calculate the data loss according to equation (3).

[0078]

[0079] Among them, L phys For data loss, x refThese are the actual values ​​of the state variables of a high-order DC microgrid system. These are estimates of the state variables of a high-order DC microgrid system.

[0080] The Adam optimizer is selected, and gradient descent is performed again based on the data loss of the physical information neural network to approximate the data projection. The parameters θ of the physical information neural network model after data loss optimization are then saved. data .

[0081] In step 6, the parameters of the physical information neural network model are updated using the iterative formula (4) in the Douglas-Rachford splitting algorithm. The optimal results of fusing physical loss and data loss are then used to update the true parameters θ of the physical information neural network model.

[0082] θ=θ+α(θ data -θ phys (4)

[0083] Where θ represents the parameters of the current physical information neural network model, and α∈[0,1] are weight parameters used to balance the influence of data terms and physical terms. data θ represents the parameters of the physical information neural network model optimized for data loss. phys The parameters of the physical information neural network model are optimized for physical loss.

[0084] In step 7, steps 3-6 are repeated iteratively until the data loss and physical loss converge to below the corresponding threshold. By iteratively approximating the optimal solution that simultaneously satisfies physical laws and data fitting, the output of the physical information neural network model is the predicted value of the state variables of the high-order DC microgrid system.

[0085] Comparative experiment:

[0086] use Figure 3 The operating data of the medium DC microgrid system was used to train and improve the physical information neural network model. The system simulation time was 0.02s, and Buck 2 connected a new battery load within 0.01s.

[0087] To verify the convergence of the method of this invention, this experiment used operating data from a 14th-order DC microgrid system to train an improved physical information neural network model incorporating the Douglas-Rachford splitting algorithm and a traditional physical information neural network model, respectively. The training loss curves of the improved physical information neural network are shown in Figures 4(a) and 4(b), and the training loss curve of the traditional physical information neural network is shown in Figure 4(b). Figure 5(a) and 5(b)As shown, it can be seen that the physical loss and data loss of the improved physical information neural network model can converge to below 0.001, while the physical loss of the traditional physical information neural network model continues to oscillate and cannot converge. Therefore, the improved physical information neural network method of this invention, which integrates the Douglas-Rachford splitting algorithm, can accurately establish the DC microgrid system model and has robustness and adaptability in solving non-convex optimization problems.

[0088] To evaluate the impact of the method of this invention on model accuracy, this experiment used DC microgrid operating data to train and fit an improved physical information neural network model of a 14th-order DC microgrid system, and used Boost partial operating data to train and fit a traditional physical information neural network model of a 2nd-order DC microgrid system, using the Boost inductor current i... L,bo For example, the comparison between the predicted curve and the actual operating curve is shown in Figures 6(a) and 6(b). It can be seen that before and after the load change of 0.01s, the model proposed in this invention can accurately predict the dynamic response of the state variable, and the fitting accuracy is not reduced compared with the traditional physical information neural network model. Table 1 uses mean squared error to show the relative error of the fitting results of the model proposed in this invention.

[0089] Table 1. Modeling error of the improved physical information neural network incorporating the Douglas-Rachford splitting algorithm.

[0090]

[0091] As can be seen, the errors of all state variables are less than 2%, indicating that the modeling method proposed in this invention has good accuracy. Therefore, the proposed model has the ability to accurately predict the dynamic changes of the system.

Claims

1. A multi-loss synchronous convergence modeling method for high-order DC microgrid systems based on an improved physical information neural network, characterized in that, Includes the following steps: Step 1: Construct the state-space equations of the high-order DC microgrid system and embed them into the neural network as physical constraints to obtain the untrained physical information neural network model of the high-order DC microgrid system; Step 2: Initialize the constructed physical information neural network model; Step 3: Calculate the physical loss of the physical information neural network and update the physical information neural network model parameters using the gradient descent algorithm; Step 4: Perform the reflection process in the Douglas-Rachford split algorithm on the physical information neural network model parameters around the physical constraint optimization result points; Step 5: Calculate the data loss using the parameters of the reflected physical information neural network model, and update the parameters of the physical information neural network model again using the gradient descent algorithm; Step 6: Combining the parameters obtained in Step 3 and Step 5, update the physical information neural network model parameters through the iterative process of the Douglas-Rachford splitting algorithm; Step 7: Proceed to Step 3 and iterate through the above parameter update process to solve the physical information neural network model. The physical information neural network model is the data-driven model of the constructed high-order DC microgrid system.

2. The multi-loss synchronous convergence modeling method for high-order DC microgrid systems based on an improved physical information neural network as described in claim 1, characterized in that, In step 1, based on the structure of the high-order DC microgrid system, the input and state variables of the high-order DC microgrid system are determined, and the state-space equation of the DC microgrid system is constructed.

3. The multi-loss synchronous convergence modeling method for high-order DC microgrid systems based on an improved physical information neural network as described in claim 1, characterized in that, In step 2, the weights of the physical information neural network model are initialized using Xavier, the weight variance is controlled, and the physical information neural network model parameters θ are saved.

4. The multi-loss synchronous convergence modeling method for high-order DC microgrid systems based on an improved physical information neural network as described in claim 1, characterized in that, In step 3, the formula for calculating the physical loss of the physical information neural network model is as follows: Among them, L phys The physical loss of the physical information neural network model is represented by u, where u is the input of the high-order DC microgrid system. These are estimates of the state variables of a high-order DC microgrid system. Let A be the derivative of the state variable estimate of the high-order DC microgrid system, and A and B be the system matrix and input matrix of the high-order DC microgrid, respectively. Based on the physical loss of the physical information neural network model, a gradient descent process is performed to simulate the physical projection operator, and the parameters θ of the physical information neural network model after physical loss optimization are saved. phys .

5. The multi-loss synchronous convergence modeling method for high-order DC microgrid systems based on an improved physical information neural network as described in claim 1, characterized in that, In step 4, the physical information neural network model parameters are reflected back to the optimal point of the physical constraint optimization subproblem, and the calculation formula for the reflection operation of the Douglas-Rachford splitting algorithm is as follows: i ref =2θ phys -θ (2) Where θ ref θ represents the parameters of the physical information neural network model used for data loss optimization. phys θ represents the physical information neural network model parameters after physical loss optimization, while θ represents the physical information neural network model parameters before physical loss optimization.

6. The multi-loss synchronous convergence modeling method for high-order DC microgrid systems based on an improved physical information neural network as described in claim 1, characterized in that, In step 5, the updated parameter θ is used with the physical information neural network model. ref The data loss is calculated using the following formula: Among them, L data For data loss, x ref These are the actual values ​​of the state variables of a high-order DC microgrid system. To estimate the state variables of a high-order DC microgrid system, gradient descent is performed based on the data loss of the physical information neural network model, and the parameters θ of the physical information neural network model after data loss optimization are saved. data .

7. The multi-loss synchronous convergence modeling method for high-order DC microgrid systems based on an improved physical information neural network as described in claim 1, characterized in that, In step 6, the parameters of the physical information neural network model are updated using the iterative formula in the Douglas-Rachford splitting algorithm. The iterative formula is as follows: θ=θ+α(θ data -θ phys ) (4) Where θ represents the parameters of the current physical information neural network model, and α∈[0,1] are weight parameters used to balance the influence of data terms and physical terms. data θ represents the parameters of the physical information neural network model optimized for data loss. phys The parameters of the physical information neural network model are optimized for physical loss.

8. The multi-loss synchronous convergence modeling method for high-order DC microgrid systems based on an improved physical information neural network as described in claim 1, characterized in that, In step 7, steps 3-6 are iterated repeatedly to solve the physical information neural network model until the data loss and physical loss converge to the corresponding thresholds. The output of the physical information neural network model is the predicted value of the state variables of the high-order DC microgrid system.

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