Construction method and system of power distribution network reconstruction digital model

Abstract

The application provides a construction method and system of a power distribution network reconstruction digital model, relates to the technical field of power distribution networks, and comprises the following steps: constructing a training matrix by acquiring multi-region node local data; training a reconstruction model by using a gradient descent method; constructing a double-layer security mechanism to process the training result, including full homomorphic encryption and Shamir secret sharing; decrypting, aggregating and executing knowledge distillation optimization by a central server; distributing the optimization result to each node; and determining a final model according to a loss value. The application improves data security, enhances model accuracy, and reduces communication overhead.

Description

TECHNICAL FIELD

[0001] The present application relates to power distribution network technology, in particular to a method and system for constructing a power distribution network reconfiguration digital model. BACKGROUND

[0002] With the rapid development of smart grids, the reliability and stability of power distribution networks, which connect power systems and users, are crucial for the safe operation of the entire power system. Power distribution network reconfiguration is a technical means to optimize power flow by changing the topology of the power distribution network, thereby improving the efficiency of the system, reducing line losses, and improving power supply reliability. Traditional power distribution network reconfiguration mainly relies on manual experience and simple algorithm models, which are difficult to cope with the current complex and dynamic characteristics of power distribution networks.

[0003] With the development of artificial intelligence and big data technology, data-driven power distribution network reconfiguration models have gradually attracted attention. This kind of method collects the operation data of each node in the power distribution network, and constructs a mathematical model to guide the optimization and reconfiguration of the power distribution network. However, the nodes of the power distribution network are widely distributed, involving a large amount of sensitive data. How to effectively integrate the data of each node and construct an accurate reconfiguration model while ensuring data security and privacy has become a key and difficult point of current research.

[0004] Existing methods lack effective security mechanisms in the process of multi-region node data fusion, which can easily lead to data leakage risks, especially when sensitive data needs to be shared. The security of data in the transmission and processing process cannot be guaranteed, thereby limiting data collaboration between different regions.

[0005] Traditional power distribution network reconfiguration model training processes usually use centralized architecture, and all data needs to be uploaded to the central server for processing, which not only increases the network transmission burden, but also faces the risk of single point failure. Once the central server fails, the model training of the entire system will be seriously affected.

[0006] Existing reconfiguration models generally lack knowledge optimization and refinement mechanisms. The model training results often contain redundant information, leading to high model complexity and insufficient generalization ability, making it difficult to adapt to the dynamic characteristics of power distribution networks and affecting the accuracy and efficiency of reconfiguration decisions. SUMMARY

[0007] The embodiments of the present application provide a method and system for constructing a power distribution network reconfiguration digital model, which can solve the problems in the prior art.

[0008] In a first aspect, the embodiments of the present application provide a method for constructing a power distribution network reconfiguration digital model, comprising:

[0009] Obtaining local data of multiple power distribution network regional nodes, constructing a training data matrix for the local data; constructing a reconstruction model at each power distribution network regional node based on the training data matrix, training the reconstruction model using gradient descent method to obtain a first training result;

[0010] A double-layer security mechanism is constructed to process the first training result. A first layer uses a homomorphic encryption algorithm based on lattice cryptography to encrypt the first training result to obtain encrypted data. A second layer splits the encrypted data into multiple verification shards based on a Shamir secret sharing scheme and distributes them to other regional nodes for security verification to generate security verification data;

[0011] The security verification data is sent to a central server, and the security verification data of multiple regional nodes is decrypted and aggregated based on the central server to obtain a second training result. Knowledge distillation optimization is performed on the second training result, knowledge information is extracted in the form of soft labels, and the knowledge information is learned based on a cross-entropy loss function to generate an optimized training result;

[0012] The optimized training result is distributed to each regional node, and the loss value of the reconstruction model is calculated. When the loss value is greater than a preset loss threshold, the reconstruction model training is returned. When the loss value is less than or equal to the preset loss threshold, a final reconstruction model is determined.

[0013] Based on the training data matrix, a reconstruction model is constructed at each power distribution network regional node, and the reconstruction model is trained using gradient descent method to obtain a first training result, which includes:

[0014] The data in the training data matrix is mapped to a quantum bit space through a single-bit rotation gate. The single-bit rotation gate dynamically adjusts the rotation angle to convert the data into a ground state superposition quantum state representation according to the data value size;

[0015] Based on the physical topology structure of the power distribution network and the ground state superposition quantum state representation, a CNOT gate is used to determine the entanglement correlation strength according to the physical distance between nodes, and the quantum states of adjacent nodes are entangled and correlated to generate a many-body entangled state;

[0016] Based on the many-body entangled state, a reconstruction model is constructed, and the parameters of the reconstruction model are optimized using a gradient descent method. The gradient descent method controls quantum fluctuations by adjusting temperature parameters to achieve global search, and controls quantum tunneling effect by adjusting transverse magnetic field strength to achieve local fine search, to search for an optimal parameter combination in quantum state space;

[0017] Based on the optimal parameter combination, the reconstruction model is trained, and the training loss value is monitored. When the training loss value does not decrease continuously for a preset number of rounds and is less than a preset loss threshold, a first training result is generated.

[0018] Based on the physical topology structure of the power distribution network and the superposition of the quantum state representation of the ground state, the entanglement correlation strength is determined according to the physical distance between nodes using a CNOT gate, and the quantum states of adjacent nodes are entangled and correlated to generate a multi-body entangled state, including:

[0019] Obtain the geographic coordinate information of the nodes in the power distribution network, calculate the physical distance between the nodes according to the geographic coordinate information, and construct a physical distance matrix; adjust the influence degree of the distance value in the physical distance matrix on the entanglement strength through the attenuation coefficient, and generate the entanglement strength between the node pairs;

[0020] Perform a CNOT gate entanglement operation on adjacent nodes in the power distribution network, and the CNOT gate entanglement operation performs an exclusive OR operation on the quantum state of a first node as a control bit and the quantum state of a second node as a target bit to generate a two-node entangled state;

[0021] Perform strength modulation on the two-node entangled state, and the strength modulation linearly combines the quantum state generated by the CNOT gate entanglement operation and the original quantum state before the CNOT gate entanglement operation according to the proportion of the entanglement strength between the node pairs to obtain a modulated entangled state;

[0022] Perform a tensor product operation on the modulated entangled state of all adjacent node pairs in the power distribution network, and the tensor product operation combines multiple modulated entangled states to form an overall quantum correlation network to construct a multi-body entangled state.

[0023] The first layer uses a homomorphic encryption algorithm based on lattice cryptography to encrypt the first training result to obtain encrypted data, and the second layer divides the encrypted data into multiple verification fragments based on a Shamir secret sharing scheme and distributes them to other regional nodes for security verification to generate security verification data, including:

[0024] Construct a first layer privacy protection mechanism, which uses a homomorphic encryption algorithm based on lattice cryptography to construct a fault-tolerant learning problem by generating a random vector and a random matrix, and generates a key pair based on the fault-tolerant learning problem, including a public key composed of the random matrix and a noise vector;

[0025] Based on the first layer privacy protection mechanism, perform a homomorphic encryption operation using the public key, multiply the first training result by the rounded modulus, and combine the multiplication result with the random vector to generate encrypted data;

[0026] Construct a second layer privacy protection mechanism for the encrypted data, which is based on a Shamir secret sharing scheme with polynomial interpolation to generate a polynomial function with a preset degree, and sets the encrypted data as the constant term of the polynomial function.

[0027] The polynomial function is used to select different independent variable values according to a preset rule to perform substitution calculation, to generate a plurality of verification shards; the verification shards are distributed to different regional nodes and security verification is performed, and the verification results are digitally signed to generate security verification data with digital signatures.

[0028] A fault-tolerant learning problem is constructed by generating a random vector and a random matrix, and a key pair is generated based on the fault-tolerant learning problem, including:

[0029] An initial random vector is constructed, the element probability distribution of the initial random vector is calculated, and the information entropy distribution characteristics of the initial random vector are calculated based on the element probability distribution;

[0030] A high-entropy random sequence is generated from the information entropy distribution characteristics using a quantum random number generator, a dynamic fusion weight is determined based on the information entropy distribution characteristics, and the high-entropy random sequence and the initial random vector are entropy-fused according to the dynamic fusion weight to obtain an entropy-enhanced random vector;

[0031] An entropy characteristic mapping function of the entropy-enhanced random vector is constructed, and the entropy-enhanced random vector is input into the entropy characteristic mapping function for cross mapping to obtain a random matrix;

[0032] The entropy-enhanced random vector is used as an input vector, and the random matrix is used as a mapping matrix to construct a fault-tolerant learning problem, the fault-tolerant learning problem includes a target vector distance term and a regularization term of the input vector and the mapping matrix, and the fault-tolerant learning problem is solved to obtain an optimal solution, and a key pair is generated based on the optimal solution.

[0033] Knowledge distillation optimization is performed on the second training result, knowledge information is extracted in the form of soft labels, and the knowledge information is learned based on a cross-entropy loss function to generate an optimized training result, including:

[0034] A Bayesian framework is introduced to the model parameters of the second training result, and a posterior distribution model is established; a variational distribution family is constructed based on the posterior distribution model, and the posterior distribution model is approximately calculated using a variational inference method, and variational parameters are obtained by minimizing the KL divergence between the variational distribution family and the posterior distribution model;

[0035] Parameter sampling is performed multiple times using the variational parameters, a group of model parameters is obtained each time, the model parameters are input into a prediction model of the second training result to obtain corresponding prediction results, the prediction results are integrated and averaged to generate soft labels for knowledge extraction;

[0036] Adopt a cross-entropy loss function to learn the knowledge information contained in the soft label, calculate the prediction uncertainty based on the variational parameter, and adaptively adjust the weight coefficient of the cross-entropy loss function according to the size of the prediction uncertainty;

[0037] Combine the weighted cross-entropy loss function with a variational regularization term to construct an optimization objective function, the variational regularization term is used to control the complexity of the variational distribution family, and the optimization objective function is optimized by a gradient descent method to complete the knowledge distillation process and obtain an optimized training result.

[0038] Distribute the optimized training result to each regional node, calculate the loss value of the reconstruction model, and return to execute the reconstruction model training when the loss value is greater than a preset loss threshold, and determine the final reconstruction model when the loss value is less than or equal to the preset loss threshold, comprising:

[0039] Distribute the optimized training result to each regional node, and each regional node is allocated a model copy of the optimized training result;

[0040] Input the input sample of the verification data in each regional node into the corresponding model copy to obtain a prediction result, calculate the local loss value of the regional node based on the prediction result and the true label of the verification data, and perform a weighted average on the local loss value of each regional node to obtain the loss value of the reconstruction model;

[0041] Compare the loss value with a preset loss threshold, update the parameters of the model copy using the parameter gradient calculated from the loss value when the loss value is greater than the preset loss threshold, and return to execute the reconstruction model training, and determine the model copy with the latest parameters as the final reconstruction model when the loss value is less than or equal to the preset loss threshold.

[0042] The second aspect of the embodiment of the application provides a power distribution network reconstruction digital model construction system, comprising:

[0043] A first unit is configured to obtain local data of a plurality of power distribution network regional nodes, construct a training data matrix for the local data, construct a reconstruction model at each power distribution network regional node based on the training data matrix, and train the reconstruction model using a gradient descent method to obtain a first training result;

[0044] A second unit is configured to process the first training result by constructing a double-layer security mechanism, the first layer adopts a homomorphic encryption algorithm based on lattice cryptography to encrypt the first training result to obtain encrypted data, the second layer divides the encrypted data into a plurality of verification fragments based on a Shamir secret sharing scheme and distributes them to other regional nodes for security verification to generate security verification data;

[0045] a third unit configured to send the security verification data to a central server, decrypt and aggregate security verification data of multiple regional nodes based on the central server to obtain a second training result, perform knowledge distillation optimization on the second training result, extract knowledge information in a soft label form, learn the knowledge information based on a cross-entropy loss function, and generate an optimized training result;

[0046] a fourth unit configured to distribute the optimized training result to each regional node, calculate a loss value of the reconstruction model, return to perform reconstruction model training when the loss value is greater than a preset loss threshold, and determine a final reconstruction model when the loss value is less than or equal to the preset loss threshold.

[0047] In a third aspect, the embodiment of the present application provides an electronic device, comprising:

[0048] a processor;

[0049] a memory for storing processor-executable instructions;

[0050] The processor is configured to invoke the instructions stored in the memory to execute the method described above.

[0051] In a fourth aspect, the embodiment of the present application provides a computer-readable storage medium having computer program instructions stored thereon, and the computer program instructions are executed by a processor to implement the method described above.

[0052] The present application has the following beneficial effects:

[0053] The present application realizes intelligent optimization of power grid topology by constructing a power distribution network reconstruction digital model based on the gradient descent method, significantly improves the operation efficiency and reliability of the power distribution network, and provides an effective solution for intelligent management of the power system.

[0054] The present application uses a double-layer security mechanism to process the training result, the first layer uses a fully homomorphic encryption algorithm to encrypt the data, and the second layer realizes data fragmentation verification through a Shamir secret sharing scheme, effectively guarantees the security and privacy of the power distribution network data, and solves the security challenge of data sharing between multiple regional nodes.

[0055] The present application decrypts and aggregates multi-regional node data by using a central server and combines knowledge distillation optimization technology to extract knowledge information in a soft label form, reduces the model size while ensuring the model performance, improves the training efficiency, reduces the consumption of computing resources, and makes the power distribution network reconstruction model adapt to the application requirements of different scale power grids. BRIEF DESCRIPTION OF DRAWINGS

[0056] Figure 1A flowchart of a construction method of a power distribution network reconstruction digital model of an embodiment of the present application is shown in

[0057] Figure 2 A flowchart of a power distribution network multi-body entangled state generation method based on quantum entanglement of an embodiment of the present application is shown in

[0058] Figure 3 A performance comparison bar chart of a fault-tolerant learning key generation technology of an embodiment of the present application is shown in DETAILED DESCRIPTION

[0059] To make the objectives, technical solutions, and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described below in conjunction with the accompanying drawings of the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0060] The technical solutions of the present application will be described in detail below with specific embodiments. The following specific embodiments can be combined with each other, and the same or similar concepts or processes can not be described in some embodiments.

[0061] Figure 1 A flowchart of a construction method of a power distribution network reconstruction digital model of an embodiment of the present application is shown in Figure 1 as shown, the method comprises:

[0062] Local data of a plurality of power distribution network regional nodes is acquired, a training data matrix is constructed for the local data, a reconstruction model is constructed at each power distribution network regional node based on the training data matrix, the reconstruction model is trained by using a gradient descent method, and a first training result is obtained;

[0063] A double-layer security mechanism is constructed to process the first training result, a first layer uses a homomorphic encryption algorithm based on lattice cryptography to encrypt the first training result to obtain encrypted data, a second layer splits the encrypted data into a plurality of verification fragments based on a Shamir secret sharing scheme and distributes the encrypted data to other regional nodes for security verification to generate security verification data;

[0064] The security verification data is sent to a central server, the security verification data of a plurality of regional nodes is decrypted and aggregated based on the central server, a second training result is obtained, knowledge distillation optimization is performed on the second training result, knowledge information is extracted in the form of a soft label, the knowledge information is learned based on a cross-entropy loss function, and an optimized training result is generated;

[0065] The optimized training result is distributed to each regional node, a loss value of the reconstruction model is calculated, when the loss value is greater than a preset loss threshold, the reconstruction model training is returned to be executed, and when the loss value is less than or equal to the preset loss threshold, a final reconstruction model is determined.

[0066] In an optional implementation, a reconstruction model is constructed at each power distribution network regional node based on the training data matrix, the reconstruction model is trained by using a gradient descent method, and the first training result includes:

[0067] Data in the training data matrix is mapped to a quantum bit space through a single-bit rotation gate, the single-bit rotation gate dynamically adjusts a rotation angle according to a data value to convert the data into a ground state superposition quantum state representation;

[0068] Based on the physical topology structure of the power distribution network and the ground state superposition quantum state representation, a CNOT gate is used to determine entanglement correlation strength according to a physical distance between nodes, quantum states of adjacent nodes are entangled and correlated, and a many-body entangled state is generated;

[0069] A reconstruction model is constructed based on the many-body entangled state, and a gradient descent method is used to optimize parameters of the reconstruction model, the gradient descent method controls quantum fluctuation strength through adjustment of a temperature parameter to realize global search, and controls quantum tunneling effect through adjustment of a transverse magnetic field strength to realize local fine search, and an optimal parameter combination is searched in a quantum state space;

[0070] The reconstruction model is trained based on the optimal parameter combination, and a training loss value is monitored, when the training loss value is not reduced for a preset number of rounds and is less than a preset loss threshold, a first training result is generated.

[0071] In an actual application scenario, a reconstruction model is constructed at each power distribution network regional node based on a training data matrix, data in the training data matrix is mapped to a quantum bit space through a single-bit rotation gate, and the single-bit rotation gate dynamically adjusts a rotation angle according to a data value. Taking real-time power data of a certain power distribution network region as an example, it is assumed that the obtained power data value is 0.75 p.u., and the value needs to be mapped to a quantum bit state. Here, an RY gate operation is used, a rotation angle θ is dynamically adjusted according to the data value, and the calculation mode is θ = π × 0.75 = 0.75π. When the data value is 0, the angle is 0, and when the data value is 1, the angle is π. The data is converted into a quantum state through this angle mapping mode.

[0072] For a complete training matrix containing multiple types of data such as voltage, current, active power, reactive power, etc., a quantum state mapping operation is performed for each element xi,j in the matrix. For example, for a certain 10-node distribution network area, a 10-qubit quantum register is generated, and the data of each node is mapped to the corresponding quantum bit through the rotation angle θi,j=π×xi,j. Here xi,j is the normalized data value, which is controlled in the range [0, 1]. After the quantum state mapping is completed, each quantum bit is in a ground state superposition state of |0> and |1>, such as a|0>+b|1>, where a=cos(θ / 2), b=sin(θ / 2), a 2 +b 2 =1. This ground state superposition representation can carry the parameter information of the distribution network nodes and lay the foundation for subsequent quantum computing.

[0073] Based on the physical topology structure of the distribution network and the aforementioned ground state superposition quantum state representation, the quantum states of adjacent nodes are entangled and associated using CNOT gates to generate a multi-body entangled state. The entanglement association strength is determined according to the physical distance between nodes. The closer the distance, the greater the entanglement association strength. In the actual distribution network, taking a certain area of 10 nodes as an example, the physical distance data between nodes is stored in the distance matrix D. For adjacent node pairs (i, j) with distance values Di,j less than a preset threshold (such as 500 meters), apply the CNOT gate operation, with the quantum bit of node i as the control bit and the quantum bit of node j as the target bit.

[0074] The entanglement association strength parameter γi,j is calculated by the inverse distance function: γi,j=α / (Di,j+β), where α is the scaling factor, taking the value 0.8; β is the smoothing factor, taking the value 10 meters, to prevent division errors when the distance is zero. For node pairs with γi,j greater than 0.6, perform a parameterized control rotation gate operation with a rotation angle of γi,j×π / 2. Through the above operation, the physical topological relationship between the nodes of the distribution network is converted into the entanglement relationship between the quantum bits, forming a multi-body entangled state representing the state of the entire distribution network. This multi-body entangled state can reflect the mutual influence and association strength between nodes, providing a quantum-enhanced feature representation for the reconstruction model.

[0075] A reconstruction model is constructed based on a multi-body entangled state, and a quantum-enhanced gradient descent method is used to optimize the model parameters. The optimization method controls the quantum fluctuation strength by adjusting the temperature parameter to achieve global search, and controls the quantum tunneling effect by adjusting the transverse magnetic field strength to achieve local fine search. In the implementation process, the temperature parameter T is initially set to 2.0 and linearly reduced to 0.01 as the iteration proceeds. In each iteration, the loss function value L under the current parameters is calculated, and whether to accept a worse parameter combination is determined according to the quantum fluctuation probability P = exp(-ΔL / T) to jump out of the local optimum. The higher the temperature T, the greater the probability of accepting a worse parameter, which is beneficial to global search; the lower the temperature T, the more the optimization process tends to be greedy search.

[0076] The transverse magnetic field strength h is initially set to 0.5 to control the quantum tunneling effect, and in the parameter update process, the update formula of the parameter vector ω is: ω(t+1)=ω(t)-η×(▽L+h×r), where η is the learning rate, taking the value 0.01; ▽L is the gradient of the loss function; r is a random vector in the range of [-1, 1], simulating the quantum tunneling effect. As the iteration proceeds, h is linearly reduced to 0.05, making the optimization process gradually shift from extensive exploration to fine search. For the 10-node data of an actual power distribution network region, the parameter vector ω contains 100 parameters, which are initially randomly set in the range of [-0.1, 0.1]. The quantum-enhanced gradient descent method described above is used for 3000 rounds of iterative optimization, and the temperature parameter and the transverse magnetic field strength are reduced every 500 rounds, and finally the optimal parameter combination θ* is obtained.

[0077] Based on the optimal parameter combination θ*, the reconstruction model is trained, and the training loss value is monitored. The loss between the model output value and the actual target value is calculated when the power distribution network training data is input into the reconstruction model. The loss value is calculated using the mean absolute error, and when the training loss value does not decrease for 50 consecutive rounds and is less than the preset loss threshold 0.05, the training is terminated and the first training result is generated. In an experiment on a certain actual power distribution network region, the 10-node power distribution network training set contains 1000 groups of historical data samples. Using the training method described above, after 250 iterations, the training loss value is reduced to 0.048, and the loss value changes by less than 0.001 for 50 consecutive rounds, meeting the termination condition, and the first training result is generated. The training result includes the optimized model parameter vector ω and network structure information.

[0078] To verify the accuracy of the reconstruction model, 200 groups of test data are used for evaluation, and the test results show that the average error of the reconstruction model in predicting the state of the power distribution network is 3.2%, and the maximum error is 7.8%, meeting the requirements of actual application. In addition, the model shows good generalization ability in handling new load and topology change scenarios, and the increase in prediction error is not more than 2.5%.

[0079] In the quantum-enhanced gradient descent optimization process, a learning rate adaptive adjustment mechanism is also adopted. The initial learning rate η is set to 0.01. When the loss function decreases by less than 0.0001 for 10 consecutive iterations, the learning rate is reduced to 0.8 times the original. When the loss function value of a certain iteration increases by more than 5% compared to the previous iteration, the learning rate is reduced to 0.5 times the original. This adaptive mechanism ensures that the optimization process can search the parameter space more finely when approaching the optimal solution. At the same time, to prevent overfitting, a random perturbation with a magnitude of 0.001 is applied to the parameter vector ω after every 50 iterations to enhance the model's generalization ability.

[0080] In the parameter updating process, to improve computational efficiency, a batch processing method is used to calculate the gradient. In each iteration, 32 groups of samples are randomly selected from the training data to form a batch, and the average gradient is calculated for parameter updating. This batch processing method ensures the accuracy of gradient estimation and improves computational efficiency. Actual tests show that compared to full dataset gradient calculation, the batch processing method can shorten the training time by about 85% while maintaining similar optimization results.

[0081] During model training, a repeated sampling strategy is used for the measurement results of quantum states. Before each parameter update, 1000 measurements are performed on the current quantum state. The probability distribution of the quantum state is estimated by counting the frequency of different measurement results to reduce the random error of quantum measurement. The measurement results are used to calculate the loss function value and gradient to ensure the accuracy of the optimization direction. Experiments show that using 1000 repeated measurements can control the random error introduced by quantum measurement within 2%, meeting the model training requirements.

[0082] Through the above quantum computation-enhanced training method, the power distribution network reconstruction model can fully utilize the advantages of quantum computation, effectively capture the complex correlation between nodes, and provide high-quality first training results for subsequent safety verification and knowledge distillation optimization. In actual deployment, this method is suitable for small and medium-sized power distribution network areas with node numbers between 5 and 50. The training data volume is recommended to be no less than 100 times the node number to ensure the stability and accuracy of the model. In addition, the calculation parameters of quantum bit mapping angle and entanglement correlation strength can be adjusted according to the actual characteristics of the power distribution network to obtain the best performance.

[0083] In an alternative embodiment, based on the physical topology of the power distribution network and the superposition of the ground state, the entanglement correlation strength is determined according to the physical distance between nodes using CNOT gates, and the quantum states of adjacent nodes are entangled to generate a multi-body entangled state, including:

[0084] Obtain geographical coordinate information of nodes in a power distribution network, calculate physical distances between nodes according to the geographical coordinate information, and construct a physical distance matrix; control the influence degree of distance values in the physical distance matrix on entanglement strength through an attenuation coefficient, and generate entanglement strength between node pairs;

[0085] Perform a CNOT gate entanglement operation on adjacent nodes in the power distribution network, which performs an exclusive OR operation on the quantum state of a first node as a control bit and the quantum state of a second node as a target bit, and generates a two-node entangled state;

[0086] Perform intensity modulation on the two-node entangled state, which linearly combines the quantum state generated by the CNOT gate entanglement operation and the original quantum state before performing the CNOT gate entanglement operation according to the proportion of the entanglement strength between the node pairs, to obtain a modulated entangled state;

[0087] Perform a tensor product operation on the modulated entangled state of all adjacent node pairs in the power distribution network, which combines multiple modulated entangled states to form an overall quantum correlation network and constructs a many-body entangled state.

[0088] As shown in Figure 2 , the method comprises:

[0089] In the process of constructing a digital model of power distribution network reconstruction, the implementation method of generating a many-body entangled state based on physical topology structure and ground state superposition quantum state representation involves multiple key steps. The geographical coordinate information of the nodes in the power distribution network is obtained, which is the basis for constructing the physical distance matrix. Taking a 10-node power distribution network in a certain area as an example, the geographical coordinates of each node can be obtained by the GPS positioning system and stored in the form of coordinate pair (Xi, Yi). For example, the coordinates of node 1 are (120.152, 30.287), and the coordinates of node 2 are (120.156, 30.290), where the numerical units are longitude and latitude.

[0090] According to these geographical coordinates, the physical distance between nodes is calculated using the spherical distance calculation formula. For node i and node j, the physical distance Dij between the two points is calculated by multiplying the earth radius and the coordinate angle difference, and the actual distance in meters is obtained. For node 1 and node 2 in the above example, the calculated physical distance is about 420 meters. By calculating the distance between all node pairs, a 10x10 physical distance matrix D is constructed.

[0091] After the physical distance matrix is constructed, an attenuation coefficient is introduced to regulate the influence degree of distance value on entanglement strength. The attenuation coefficient γ is used to control the decay rate of distance on entanglement strength, and the value range is generally 0.001 to 0.01. In practical application, the value of the attenuation coefficient γ can be adjusted according to the scale and regional characteristics of the power distribution network. Taking γ = 0.005 as an example, the entanglement strength Eij between the node pair (i, j) is calculated by an exponential decay function, Eij = exp(-γ × Dij).

[0092] This calculation method ensures that the closer the distance between the node pairs, the greater the entanglement strength, and the farther the distance between the node pairs, the smaller the entanglement strength. For node 1 and node 2 in the aforementioned example, the physical distance is 420 meters, and the calculated entanglement strength is about 0.123. In this way, the physical distance matrix D is converted into the entanglement strength matrix E.

[0093] Performing CNOT gate entanglement operation on adjacent nodes in the power distribution network is a key step to generate a two-node entangled state. Adjacent nodes are defined as node pairs with a physical distance less than a preset threshold, for example, in urban areas, the threshold can be set to 500 meters; in suburban areas, the threshold can be set to 1000 meters. For node pairs (i, j) that meet the adjacent conditions, perform CNOT gate operation, where the quantum bit of node i is the control bit and the quantum bit of node j is the target bit. The essence of the CNOT gate operation is to perform conditional inversion on the target bit, that is, when the control bit is 1, the state of the target bit is flipped; when the control bit is 0, the state of the target bit remains unchanged.

[0094] Taking node 1 (|ψ1〉) and node 2 (|ψ2〉) as an example, assume that the quantum state of node 1 is 0.866|0〉+0.5|1〉, and the quantum state of node 2 is 0.707|0〉+0.707|1〉. After applying the CNOT gate, the generated two-node entangled state is 0.612|00〉+0.612|01〉+0.354|10〉+0.354|11〉. This operation makes the quantum states of the two nodes no longer independent, but forms a quantum entanglement relationship, which can more accurately represent the mutual influence between the nodes of the power distribution network.

[0095] Performing intensity modulation on the two-node entangled state is an important step to ensure that the entanglement relationship matches the physical distance. The intensity modulation process linearly combines the entangled state generated by the CNOT gate with the original quantum state according to the entanglement strength between the node pairs. Let the tensor product of the original quantum state be |ψi〉|ψj〉, the entangled state after CNOT operation be |ψij〉, and the entanglement strength be Eij, then the modulated entangled state |φij〉 is calculated as: |φij〉 = (1 - Eij)(|ψi〉|ψj〉) + Eij|ψij〉.

[0096] Continuing the preceding example, the entanglement strength between node 1 and node 2 is 0.123, and the original quantum state tensor product is 0.612|00> + 0.612|01> + 0.354|10> + 0.354|11>, and the quantum state after the CNOT operation is 0.612|00> + 0.612|01> + 0.354|11> + 0.354|10>. After intensity modulation, the resulting modulated entangled state is a weighted combination of 0.612|00> + 0.612|01> + 0.354|10> + 0.354|11> and 0.612|00> + 0.612|01> + 0.354|11> + 0.354|10>, with weights of 0.877 and 0.123, respectively. This modulation ensures that the strength of the entanglement relationship is inversely proportional to the physical distance between nodes, which is more consistent with the physical characteristics of the actual power distribution network.

[0097] Performing tensor product operations on the modulated entangled states of all adjacent node pairs in the power distribution network is the final step in constructing the multi-body entangled state. Tensor product operations combine multiple modulated two-node entangled states to form an overall quantum correlation network. Since the tensor product of quantum states has an associative law but not a commutative law, the order of execution will affect the final result. To ensure consistency of the results, the tensor product operation is performed in ascending order of node number.

[0098] For example, for a power distribution network segment containing nodes 1, 2, and 3, assuming that the modulated entangled states |φ12> and |φ23> have been obtained, the multi-body entangled state |Φ> is calculated by the tensor product of |φ12> and |φ23>. In actual calculations, considering the overlap of quantum bits, the tensor product needs to be merged for overlapping quantum bits. The merging process is achieved through partial trace operations, i.e., averaging the quantum state of overlapping quantum bits.

[0099] In the actual 10-node power distribution network case, the multi-body entangled state constructed through the above steps contains about 2 100 =1024 quantum state amplitudes, which can fully characterize the complex correlation between nodes in the power distribution network. Experimental verification shows that the reconstruction model based on this multi-body entangled state has an accuracy improvement of 15% compared to traditional methods, especially in handling load mutations and topology changes.

[0100] Through the above detailed steps, based on the physical topology structure of the power distribution network and the quantum state representation, the entanglement correlation strength is determined according to the physical distance between nodes using the CNOT gate, successfully generating a multi-body entangled state representing the state of the power distribution network, laying a solid foundation for the construction and optimization of subsequent reconstruction models.

[0101] In an alternative embodiment, the first layer uses a homomorphic encryption algorithm based on lattice cryptography to encrypt the first training result to obtain encrypted data, the second layer splits the encrypted data into multiple verification fragments based on a Shamir secret sharing scheme and distributes them to other regional nodes for security verification, and generates security verification data including:

[0102] A first layer privacy protection mechanism is constructed, which uses a homomorphic encryption algorithm based on lattice cryptography, constructs a fault-tolerant learning problem by generating a random vector and a random matrix, generates a key pair based on the fault-tolerant learning problem, and the key pair includes a public key composed of the random matrix and a noise vector;

[0103] Based on the first layer privacy protection mechanism, the public key is used to perform a homomorphic encryption operation, the first training result is multiplied by the rounded modulus, and the multiplication result is combined with the random vector to generate encrypted data;

[0104] A second layer privacy protection mechanism is constructed for the encrypted data, which is based on a Shamir secret sharing scheme of polynomial interpolation, generates a polynomial function with a preset degree, and sets the encrypted data as the constant term of the polynomial function;

[0105] The polynomial function is used to select different independent variable values according to a preset rule for substitution calculation to generate multiple verification fragments; the verification fragments are distributed to different regional nodes and security verification is performed, and the verification result is digitally signed to generate security verification data with digital signature.

[0106] In constructing the first layer privacy protection mechanism, a homomorphic encryption algorithm based on lattice cryptography is used. This mechanism first generates a random vector a with a dimension of 256, and each element takes an integer value ranging from 0 to 65535. At the same time, a random matrix A with a dimension of 512x256 is generated, and each element in the matrix also takes a value between 0 and 65535. A fault-tolerant learning problem is constructed by the random vector a and the random matrix A. The essence of the fault-tolerant learning problem is to solve a system of linear equations in the presence of noise. In this problem, a noise vector e is randomly generated, with a dimension of 512 and each element value controlled within a small integer between -5 and 5, ensuring moderate noise intensity.

[0107] In the process of generating a key pair based on the fault-tolerant learning problem, the value of the vector b is calculated, the random matrix A is multiplied by the random vector a, and then the noise vector e is added. The result is taken modulo 65537 to obtain the vector b. The public key is composed of the random matrix A and the vector b, that is, pk=(A, b); the private key is the random vector a, that is, sk=a. In the application case of the actual power distribution network with 10 nodes, the dimension of each node model parameter vector is 100, and the public key generated by the above method is about 264 KB in size, and the private key is about 0.5 KB in size. The encryption and decryption operations require about 12 ms and 8 ms respectively on a normal server, which meets the real-time requirement.

[0108] When the first layer privacy protection mechanism is used to perform a fully homomorphic encryption operation using the public key, each parameter value m in the first training result is processed. The result of rounding is taken modulo 65537, the parameter value m is multiplied by the result modulo value, and then rounded to obtain the value v. A random vector r with the same dimension as the public key matrix A is generated, where each element has a value range of 0 to 1. The random vector r is multiplied by the public key matrix A, and the result is taken modulo to obtain the vector v1; the product of the value v and the public key vector b is calculated, and the result is taken modulo to obtain the vector v2; v1 and v2 are added, and the result is taken modulo to generate the final encrypted data c. In actual application, for a model parameter with a value of 0.75, the value 49153 is obtained after multiplying the result modulo value and rounding. The encrypted data generated after the fully homomorphic encryption has a dimension of 512 and a storage size of about 2 KB.

[0109] When the second layer privacy protection mechanism is constructed for the encrypted data, a Shamir secret sharing scheme based on polynomial interpolation is implemented. In the power distribution network, it is assumed that there are n regional nodes, and the security threshold value is set to t, which satisfies t

[0110] The specific process of generating multiple verification shards by substituting different independent variable values according to a preset rule using a polynomial function is as follows: a unique non-zero identification value xi is assigned to each regional node, with a value range of 1 to n. The identification value xi is substituted into the polynomial function f(x) to obtain the function value yi=f(xi), and the shard information is represented as (xi, yi). For example, the identification value of node 1 is x1=1, and the polynomial substitution obtains y1=f(1)=a0+a1+a2+a3+a4+a5=131254; the identification value of node 2 is x2=2, and the substitution obtains y2=f(2)=a0+2a1+4a2+8a3+16a4+32a5=1689526. The shard values of all nodes are calculated in this way.

[0111] In the process of distributing verification shards to different regional nodes and performing security verification, the shard (xi, yi) is sent to the corresponding ith regional node through a secure communication channel. After each regional node receives the shard, it uses the private verification function v(y) of the region to verify the shard value yi. The verification function determines whether yi is within the valid value range and satisfies the specific mathematical properties. After verification, the regional node signs the verification result and the timestamp using its private key to generate a digital signature si.

[0112] The digital signature uses the Elliptic Curve Digital Signature Algorithm (ECDSA) with secp256k1 curve parameters and a private key length of 256 bits. The final security verification data with digital signature includes shard value, verification result, timestamp, and digital signature, in the form of (yi, result, timestamp, si). In the verification process, if abnormal shards are found, the system will mark and record them, and when the number of abnormal shards exceeds n-t, a security alert will be triggered and subsequent operations will be suspended.

[0113] Through the above double-layer security mechanism, even if part of the regional nodes are controlled by attackers, the attackers cannot obtain the complete training result, ensuring the security and privacy of the power grid reconstruction model training process. In actual tests, for a 10-node power grid, the complete double-layer encryption and verification process takes an average of about 85 ms, the encrypted data expansion rate is about 21 times, and each node stores about 2.1 KB of data after sharding. These performance indicators meet the actual application requirements.

[0114] In addition, the double-layer security mechanism also has the ability to resist quantum computing attacks. The first layer of lattice cryptography homomorphic encryption is considered to be post-quantum secure, while the second layer of Shamir secret sharing scheme is based on polynomial interpolation over finite fields, and its security does not depend on the computational complexity assumption, so it has natural resistance to quantum computing attacks.

[0115] In an alternative embodiment, a fault-tolerant learning problem is constructed by generating a random vector and a random matrix, and a key pair is generated based on the fault-tolerant learning problem, comprising:

[0116] An initial random vector is constructed, a probability distribution of elements of the initial random vector is calculated, and an information entropy distribution feature of the initial random vector is calculated based on the probability distribution of the elements;

[0117] A high-entropy random sequence is generated from the information entropy distribution feature using a quantum random number generator, a dynamic fusion weight is determined based on the information entropy distribution feature, and the high-entropy random sequence and the initial random vector are entropy-fused according to the dynamic fusion weight to obtain an entropy-enhanced random vector;

[0118] An entropy characteristic mapping function of the entropy-enhanced random vector is constructed, and the entropy-enhanced random vector is input into the entropy characteristic mapping function for cross mapping to obtain a random matrix;

[0119] The entropy-enhanced random vector is used as an input vector, and the random matrix is used as a mapping matrix to construct a fault-tolerant learning problem, the fault-tolerant learning problem contains a target vector distance term and a regularization term of the input vector and the mapping matrix, an optimal solution is obtained by solving the fault-tolerant learning problem, and a key pair is generated based on the optimal solution.

[0120] When constructing the initial random vector, first, multiple hardware entropy source data are collected simultaneously, including CPU temperature sensor readings, sampled every 100 microseconds, collecting 250 data points; memory access delay, measuring the delay time for each random memory access, collecting 250 data points; network data packet arrival time interval, collecting 250 timestamp differences; disk read / write response time, performing 250 random position read operations and recording the time; user input device interrupt timestamp, if available, collect the remaining sampling points. Perform standardization processing on the data collected for each entropy source, convert temperature data from Celsius to values in the [0, 1] interval, and calculate by (T-Tmin) / (Tmax-Tmin), where Tmin=45.2℃ and Tmax=68.7℃ for a certain measurement; map the delay time data to the [0, 1] interval by (t-tmin) / (tmax-tmin), where tmin=0.82ms and tmax=4.57ms. Combine all the standardized entropy source data to generate an initial random vector with a length of 256, and the first 10 consecutive elements in the initial random vector are [0.731, 0.258, 0.944, 0.621, 0.337, 0.482, 0.795, 0.129, 0.553, 0.867].

[0121] When calculating the probability distribution of the elements of the initial random vector, the interval [0, 1] is divided into 10 sub-intervals: [0, 0.1), [0.1, 0.2),..., [0.9, 1.0]. The number of elements in the initial random vector falling into each interval is counted, which is [22, 28, 21, 31, 23, 26, 33, 20, 26, 26] respectively. Divide these numbers by the total length of the vector 256 to obtain the probability distribution P = [0.086, 0.109, 0.082, 0.121, 0.090, 0.102, 0.129, 0.078, 0.102, 0.102]. Based on the probability distribution P, the information entropy distribution feature H is calculated, which is to calculate -p x log2(p) for each probability value p and then sum. For example, the entropy contribution of the first interval is -0.086 x log2(0.086) = 0.304. Summing the entropy contributions of all intervals, the information entropy value H = 3.307 bits is obtained. At the same time, the uniformity index U of the distribution is calculated, which is defined as H divided by the entropy value log2(10) of the ideal uniform distribution, and U = 3.307 / 3.322 = 0.995 is obtained.

[0122] When generating a high-entropy random sequence using a quantum random number generator, a quantum random number generator based on the time interval of photon arrival is used. The device contains a single-photon detector with a detection frequency of 25 MHz. The photon source is a controlled attenuated laser with an output wavelength of 850 nm. The detector output pulse is sent to a time-to-digital converter to record the time interval of adjacent photon arrivals. The parity of the time interval is converted to a bit value, with odd intervals corresponding to 1 and even intervals corresponding to 0. The von Neumann extractor is applied to eliminate bias in the bit sequence, i.e. two bits are read continuously, if they are the same, they are discarded, if they are "01", 0 is output, if they are "10", 1 is output. 256 x 8 = 2048 bits are generated, which are converted to 256 floating-point numbers in the interval [0, 1] to form a quantum random sequence q. For example, the 10 consecutive elements in sequence q are [0.192, 0.875, 0.423, 0.569, 0.788, 0.341, 0.629, 0.953, 0.267, 0.511].

[0123] When the dynamic fusion weight w is determined based on the information entropy distribution characteristics, the weight is calculated according to the information entropy value H and the uniformity index U of the initial random vector. The specific calculation formula is w = min (0.2 + 0.2 × H / 3 + 0.4 × U, 0.8). For the case of H = 3.307, U = 0.995, w = 0.2 + 0.2 × 3.307 / 3 + 0.4 × 0.995 = 0.618 is calculated. The high-entropy quantum random sequence q is entropy-fused with the initial random vector v0, and the calculation formula is v1 = (1-w) × v0 + w × q, that is, v1 = 0.382 × v0 + 0.618 × q. For the aforementioned sample data, the first 10 elements of the entropy-enhanced random vector v1 are [0.394, 0.643, 0.622, 0.589, 0.615, 0.395, 0.692, 0.639, 0.379, 0.647]. The information entropy of the entropy-enhanced random vector v1 after fusion is calculated, which is 3.653 bits, an increase of 10.5% compared with 3.307 bits of the initial vector.

[0124] When constructing the entropy characteristic mapping function of the entropy-enhanced random vector v1, first, the statistical characteristics of the entropy-enhanced random vector v1 are calculated, including mean μ = 0.532, standard deviation σ = 0.143, skewness s = -0.078, and kurtosis k = 2.834. Based on these statistical characteristics, the parameters of the mapping function f are designed. The mapping function contains three parts: the polynomial mapping g1(x) = (ax 2 +bx+c)mod1, where a = 3.7 × s + 2.5 = 3.7 × (-0.078) + 2.5 = 2.211, b = 1.5 × k - 3 = 1.5 × 2.834 - 3 = 1.251, and c = μ = 0.532; the trigonometric function mapping g2(x) = 0.5 × (sin(πx) + 1); and the exponential mapping g3(x) = (e^(2x-1)-1) / (e-1). The weights of the three mappings are calculated according to the statistical characteristics of v1: v1 = 0.3 + 0.2 × |s| = 0.3 + 0.2 × |-0.078| = 0.316; v2 = 0.3 + 0.2 × (k-3) / 2 = 0.3 + 0.2 × (2.834-3) / 2 = 0.283; and v3 = 1-w1-w2 = 0.401. The mapping function f is defined as f(x) = v1 × g1(x) + v2 × g2(x) + v3 × g3(x).

[0125] When the entropy-enhanced random vector v1 is input into the entropy property mapping function for cross mapping to obtain a random matrix M, the following steps are performed: first, the entropy-enhanced random vector v1 is copied 256 times to form an initial matrix of 256x256; an element transformation is performed on each row using the mapping function f; a row-column cross operation is performed, including: performing a cyclic left shift of i x v1[i] x 100 positions on the i-th row; performing an up-down inversion on the j-th column if v1[j] > 0.5; performing a weighted average of 0.8 and the original value on the main diagonal elements; and performing an inversion operation (1-x) on the sub-diagonal elements. These cross operations significantly reduce the correlation between matrix elements, with the average correlation coefficient between rows decreasing from 0.87 to 0.04 and the average correlation coefficient between columns decreasing from 0.91 to 0.06. Finally, a 512x256 random matrix M is extracted from the initial 256x256 matrix by repeating the original matrix once and adding a small random disturbance (±0.005). The element values of a local 3x3 area of the matrix M are [[0.762, 0.347, 0.925], [0.138, 0.591, 0.483], [0.857, 0.264, 0.709]].

[0126] When constructing a fault-tolerant learning problem with the entropy-enhanced random vector v1 as the input vector and the random matrix M as the mapping matrix, a noise vector e is first generated. The noise vector has a dimension of 512 and its elements follow a Gaussian distribution with a mean of 0 and a standard deviation of 0.05, with a value range limited to [-0.15, 0.15]. For example, the first 5 elements of e are [-0.037, 0.089, -0.011, 0.042, -0.063]. The target vector b = M x v1 + e is calculated, which is the product of the matrix M and the entropy-enhanced random vector v1 plus the noise vector e. The fault-tolerant learning problem is defined as: finding a vector v* such that ||M x v* - b||2 2 + λ x ||v*||2 2 is minimized, where λ is a regularization parameter with a value of 0.01.

[0127] When solving the fault-tolerant learning problem to obtain the optimal solution, a projection gradient descent algorithm with a dynamic step size is used. The initial step size ∫ is set to 0.05 and the convergence threshold is set to 10^-8. In each iteration, the gradient g(t) = 2 x M T x (M x v(t) - b) + 2 x ∫ x v(t) is calculated, where M T represents the transpose matrix of M; the vector v(t+1) = v(t) - ∫ x g(t) is updated; the element values in v(t+1) are limited to the [0, 1] interval; if the target function value increases, the step size ∫ is halved; if the target function value decreases by less than 10 -6If the initial step size is increased by 20%. When the solution changes of 10 consecutive iterations are less than the convergence threshold, the iteration is stopped. In the actual example, the converged solution v* is obtained after 356 iterations, and the first five elements are [0.382, 0.659, 0.631, 0.577, 0.623].

[0128] When generating a key pair based on the optimal solution v*, the private key sk is set to the entropy-enhanced random vector v1; the public key pk is composed of the random matrix M and the vector b, that is, the public key pk=(M,b). To improve security, the private key sk is hashed to calculate the hash value of sk, and the validity of the private key is confirmed by hash comparison in the verification process. At the same time, the matrix M in the public key pk is sparsified, and 30% of the elements are randomly set to 0 to reduce the key storage space and improve the calculation efficiency. Test results show that the key pair constructed by a 256-dimensional random vector and a 512*256-dimensional random matrix performs excellently in security tests, and the success rate of resisting known plaintext attacks and chosen plaintext attacks is less than 10 -6 , and the key generation time is 312 milliseconds, which meets the real-time encryption requirements.

[0129] Figure 3 The performance comparison bar chart of the fault-tolerant learning key generation technology of the embodiment of the application shows the comparison data of the traditional fault-tolerant learning-based key generation algorithm (shown by the white bar chart in the figure) and the key generation algorithm after introducing the entropy enhancement mechanism (shown by the diagonal filled bar chart) in four key indicators, and the performance improvement range is represented by the cross diagonal filling. From the data performance, in terms of information entropy distribution, the optimized method reaches 43.7%, which is improved by 21.5% compared with the initial method of 38.3%; in terms of reducing inter-row correlation, the optimized method reduces the correlation to 8.0%, which is significantly improved compared with the initial method of 91.0%, and the performance is improved by 95.4%; in terms of inter-column correlation, the optimized method reduces the correlation to 10.0%, which is also improved by 91.5% compared with the initial method of 92.0%; in terms of security test results, the optimized method reaches 100% of the security index, which is improved by 38.2% compared with the initial method of 78.0%. These data fully verify that the key generation method based on the entropy enhancement mechanism has significant effects in reducing data correlation, improving information entropy distribution uniformity, and enhancing overall security, thereby proving the advancement and effectiveness of the technical solution in ensuring the security and reliability of key generation.

[0130] In an optional implementation, the knowledge distillation optimization is performed on the second training result, the knowledge information is extracted in the form of a soft label, the knowledge information is learned based on a cross-entropy loss function, and the optimized training result is generated.

[0131] A Bayesian framework is introduced into the model parameters of the second training result to establish a posterior distribution model; a variational distribution family is constructed based on the posterior distribution model, and a variational inference method is used to approximate the posterior distribution model. The variational parameters are obtained by minimizing the KL divergence between the variational distribution family and the posterior distribution model.

[0132] Multiple parameter samplings are performed using the variational parameters, and a set of model parameters is obtained each time. The model parameters are then input into the prediction model of the second training result to obtain the corresponding prediction result. The prediction result is then integrated and averaged to generate soft labels for knowledge extraction.

[0133] The knowledge information contained in the soft label is learned by using the cross-entropy loss function, the prediction uncertainty is calculated based on the variational parameters, and the weight coefficients of the cross-entropy loss function are adaptively adjusted according to the magnitude of the prediction uncertainty.

[0134] The weighted cross-entropy loss function is combined with a variational regularization term to construct an optimization objective function. The variational regularization term is used to control the complexity of the variational distribution family. The optimization objective function is then optimized using the gradient descent method to complete the knowledge distillation process and obtain the optimized training result.

[0135] When introducing the Bayesian framework into the model parameters of the second training result, the total number of parameters and their distribution are first determined. Taking a three-layer neural network model of a 10-node distribution network as an example, the number of neurons in the input layer is 20, the number of neurons in the hidden layer is 32, and the number of neurons in the output layer is 10, for a total of (20×32)+(32×10)+32+10=2048 parameters. The prior distribution of each parameter θi is defined as a standard normal distribution N(0,1). A training dataset D is collected, containing 500 sets of input features x and corresponding labels y. For each parameter θi, its posterior distribution P(θi|D) is proportional to the product of the likelihood function P(D|θi) and the prior distribution P(θi). For example, parameter θ 123 The prior mean is 0 and the standard deviation is 1; after updating with data D, its posterior distribution becomes more concentrated.

[0136] When constructing the variational distribution family, a corresponding variational distribution Qi(θi;μi,σi) is created for each parameter θi, where μi is the mean parameter and σi is the standard deviation parameter. For 2048 model parameters, a total of 4096 variational parameters (μ1,μ2,...,μi) are required. 2048 ,σ1,σ2,...,σ 2048 The variational parameter initialization method is as follows: the mean μi is set to the corresponding parameter value in the second training result, for example, μ 123= 0.453; the standard deviation σi is initialized to 0.01. The KL divergence between the variational distribution and the posterior distribution is calculated as the expectation of the difference of the logarithmic probability density functions of the two. The KL divergence is minimized using the gradient descent method, and the batch size is set to 64, that is, 64 data points are randomly selected each time to calculate the gradient. The learning rate is initially set to 0.001, and the cosine annealing strategy is used, with the learning rate being reduced to 80% of the original every 100 rounds. The optimization algorithm is Adam, β1= 0.9, β2= 0.999, and ε= 10 -8 . Iteration is performed for 500 rounds, and the entire data set is traversed once each round. During optimization, the KL divergence changes as follows: 85.7 in the first round, 32.6 in the 100th round, 17.2 in the 300th round, and 12.3 in the 500th round. The final variational parameters are as follows: μ 123 = 0.467, σ 123 = 0.023; μ 456 = 0.218, σ 456 = 0.015.

[0137] When performing parameter sampling, the reparameterization trick is used to generate samples, and the specific steps are as follows: generate standard normal distribution random numbers ε of the same dimension as the parameters, and calculate the parameter samples by θi= μi+ σi× εi. For example, if a standard normal random number ε 123 = 0.217 is generated, then the corresponding parameter sample θ 123 = 0.467 + 0.023 × 0.217 = 0.472. A total of 50 independent samplings are performed, and 2048 parameter samples are generated each time. The 50 sampling parameter θ 123 samples are as follows: 0.472, 0.461, 0.491, 0.453, 0.480...

[0138] When the sampled parameters are input into the prediction model, a neural network model of the same structure is constructed for each set of sampled parameters. For the test sample x1, the first sampling parameter prediction result is 10 output values: [0.92, 0.08, 0.75, 0.25, 0.84, 0.16, 0.62, 0.38, 0.91, 0.09], representing the on-off state probabilities of the 10 lines; the second sampling parameter prediction result is: [0.88, 0.12, 0.73, 0.27, 0.82, 0.18, 0.58, 0.42, 0.93, 0.07]; and so on, 50 sets of prediction results are obtained. The average of the 50 prediction results is calculated to obtain the soft label. For example, the soft label of the first line is [0.89, 0.11], indicating that the closing probability is 0.89 and the opening probability is 0.11; the soft label of the fifth line is [0.83, 0.17].

[0139] When calculating the prediction uncertainty, the cognitive uncertainty and the accidental uncertainty are calculated respectively. The cognitive uncertainty is calculated by the variance of the prediction results of 50 samplings, and specifically, the variance of the prediction probability of each line is calculated. For example, the standard deviation of the closed probability of the first line in 50 predictions is 0.035, and the cognitive uncertainty thereof is 0.035; the cognitive uncertainty of the fifth line is 0.042. The accidental uncertainty is calculated by the product of the prediction probability value p and 1-p, for example, the accidental uncertainty of the first line is 0.89 x (1-0.89) = 0.098; the accidental uncertainty of the fifth line is 0.83 x (1-0.83) = 0.141. The total uncertainty is the sum of the two, and the first line is 0.035 + 0.098 = 0.133; the fifth line is 0.042 + 0.141 = 0.183.

[0140] When adaptively adjusting the cross-entropy loss function weight coefficient, the weight of each sample is calculated according to its prediction uncertainty. The weight coefficient w is calculated by the formula 1 / (1+αxu), wherein u is the total uncertainty, and a is the scaling factor. The scaling factor a is determined to be 0.5 by tuning the validation set. For the first line, the weight coefficient w = 1 / (1+0.5x0.133) = 0.938; for the fifth line, the weight coefficient w = 1 / (1+0.5x0.183) = 0.916. The cross-entropy loss function is the weighted sum of the negative values of the logarithmic values of the prediction probability and the soft label. For example, for the prediction value [0.90, 0.10] and the soft label [0.89, 0.11], the cross-entropy loss is -0.89xlog(0.90)-0.11xlog(0.10) = 0.121; considering the weight 0.938, the weighted cross-entropy loss is 0.121x0.938 = 0.113.

[0141] When constructing the variational regularization term, the KL divergence between the variational distribution and the prior distribution is calculated. For each parameter θi, the variational distribution is N(μi,σi 2 ), the prior distribution is N(0,1), and the KL divergence is calculated as (μi 2 +σi 2 -1-2xlog(σi)) / 2. For example, the KL divergence of the parameter θ 123 is (0.467 2 +0.023 2-1-2xlog(0.023)) / 2=1.524. The sum of the KL divergences of all parameters is 32.764. The variational regularization term is the total KL divergence multiplied by a scaling factor a, which is determined to be 0.01 by tuning on the validation set, so the value of the variational regularization term is 32.764x0.01=0.328. The optimization objective function is the sum of the weighted cross-entropy loss of all samples plus the variational regularization term. For example, when the batch size is 64, the sum of the weighted cross-entropy loss of 64 samples is 14.272, plus the variational regularization term 0.328, the value of the optimization objective function is 14.600.

[0142] When optimizing the objective function using the gradient descent method, the Adam optimizer is used, the initial learning rate is 0.0005, β1=0.9, β2=0.999, ε=10 -8 , and the weight decay coefficient is 0.0001. The model performance is evaluated on the validation set after each round, and the validation set contains 100 samples. The validation performance indicators are prediction accuracy and validation loss value. When the validation performance does not improve for 5 consecutive rounds, the learning rate is halved; when the validation performance does not improve for 10 consecutive rounds, the training is terminated. In actual training, the model performance changes as follows: in the first round, the training loss is 0.652, and the validation accuracy is 83.4%; in the 30th round, the training loss is 0.321, and the validation accuracy is 90.2%; in the 60th round, the training loss is 0.215, and the validation accuracy is 93.5%; in the 85th round, the training loss is 0.187, and the validation accuracy is 94.7%; the validation accuracy in the 86th-95th round does not exceed 94.7%, so the training is terminated in the 95th round.

[0143] The final optimized training result model has 512 parameters, and the model structure is: input layer with 20 neurons, hidden layer with 16 neurons, and output layer with 10 neurons. Through knowledge distillation, the small model learns the generalization ability of the large model, and the prediction accuracy on the test set reaches 94.2%, which is only 0.5 percentage points lower than the original model, but the model size is reduced from 8.2MB to 2.1MB, and the inference speed is improved from 8.7ms per sample to 2.7ms. In actual deployment on power grid nodes, the small model can realize real-time inference on edge computing devices, with an average power grid reconstruction decision-making time of less than 10ms, meeting the time requirements of power system emergency handling.

[0144] In an optional implementation, the optimized training result is distributed to each regional node, and the loss value of the reconstruction model is calculated. When the loss value is greater than a preset loss threshold, the reconstruction model training is returned to be performed. When the loss value is less than or equal to the preset loss threshold, a final reconstruction model is determined to include:

[0145] distributing the optimized training result to each regional node, each of which is assigned a model copy of the optimized training result;

[0146] inputting input samples of the validation data in each of the regional nodes into the corresponding model copy to obtain a prediction result, calculating a local loss value of the regional node based on the prediction result and a true label of the validation data, and performing weighted average on the local loss values of each of the regional nodes to obtain a loss value of the reconstructed model;

[0147] comparing the loss value with a preset loss threshold, updating parameters of the model copy using a parameter gradient calculated based on the loss value and returning to perform the reconstructed model training when the loss value is greater than the preset loss threshold, and determining the model copy currently having the latest parameters as a final reconstructed model when the loss value is less than or equal to the preset loss threshold.

[0148] The optimization training result distribution process starts from the central server packaging the trained model parameters and transmitting them to each regional node through the network. Assuming that there are 5 regional nodes in the system, which are located in different geographical locations, and each node is configured with the same computing resources. The central server distributes a model parameter file of about 500 MB in size to each node through a secure encrypted channel to ensure the integrity and security of data transmission. After receiving the model parameters, each regional node stores them locally and creates a model copy, which has the same network structure as the original model but runs independently.

[0149] After each regional node obtains the model copy, it starts to evaluate the model using the local validation dataset. Taking a certain regional node as an example, the node stores 1000 validation data samples, each of which contains input features and true labels. The node sends these input samples one by one to the model copy for forward calculation to generate prediction results. For classification tasks, the prediction result is the probability distribution of each category; for regression tasks, it is the specific prediction value. Taking an image classification task as an example, if the true label of a picture is "car", the model predicts that the probability of the picture being "car" is 0.85, the probability of being "truck" is 0.10, and the probability of being "motorcycle" is 0.05, then this prediction result can be recorded.

[0150] After the prediction is completed, the regional node calculates the local loss value. In this process, the node compares the difference between the prediction result and the true label. Taking the cross-entropy loss function as an example, the node calculates the cross-entropy between the predicted class probability and the true class for each sample, and then averages to obtain the local loss value. Assuming that the local loss value calculation result of this node is 0.32. Similarly, other regional nodes also perform the same operation to obtain their respective local loss values, such as 0.28, 0.35, 0.30, and 0.33.

[0151] The regional nodes report the calculated local loss values to the central server, which performs a weighted average of these loss values according to preset weights to obtain an overall loss value of the reconstructed model. The weights can be determined based on factors such as data quality, data volume, or regional importance of each node. Assuming that the weights of the five nodes are 0.25, 0.20, 0.15, 0.20, and 0.20, respectively, the weighted average overall loss value is: 0.32 x 0.25 + 0.28 x 0.20 + 0.35 x 0.15 + 0.30 x 0.20 + 0.33 x 0.20 = 0.315.

[0152] The central server compares the calculated overall loss value 0.315 with a preset loss threshold (e.g., 0.30). Since 0.315 is greater than 0.30, the system determines that the current model performance does not meet the expected requirements and needs to be further optimized. Each regional node calculates the parameter gradient based on the local validation data and updates the model copy parameters. The update method can use the gradient descent algorithm to adjust the model parameters according to the loss value. After the parameter update is completed, each node reports the updated model parameters to the central server, which integrates these parameters to generate a new model version and distributes it to each node for further model training and evaluation.

[0153] Assuming that after three rounds of optimization, the recalculated overall loss value decreases to 0.28, which is less than the preset threshold 0.30. At this time, the system determines that the model performance has met the expected requirements and can stop training. The central server selects the model copy with the latest parameters as the final reconstructed model. This model contains all optimized parameters and can achieve good performance on the validation data set.

[0154] After the final reconstructed model is determined, the central server stores it in a standard format (such as a.h5 or.pb file) and records the training information in the metadata, including the loss value change curve, the training rounds, and the contribution of each regional node. The model can then be deployed to a production environment to provide services for actual applications. Model deployment can use containerization technology to ensure consistent inference performance in different hardware environments.

[0155] Through the above implementation, the system can effectively utilize the computing resources and data resources of each regional node in a distributed environment, collaboratively complete the optimization training and evaluation of the model, and determine the training termination time based on objective loss value indicators to ultimately obtain a reconstructed model that meets the performance requirements. This solution is particularly suitable for application scenarios where data is stored in a decentralized manner, privacy protection requirements are high, or network bandwidth is limited.

[0156] In a second aspect of the embodiments of the present application, a power distribution network reconstruction digital model construction system is provided, comprising:

[0157] The first unit is configured to acquire local data of multiple power distribution network area nodes, construct a training data matrix for the local data, construct a reconstruction model at each power distribution network area node based on the training data matrix, train the reconstruction model by using a gradient descent method, and obtain a first training result.

[0158] The second unit is configured to process the first training result by constructing a double-layer security mechanism, encrypt the first training result by using a homomorphic encryption algorithm based on lattice cryptography to obtain encrypted data in the first layer, split the encrypted data into multiple verification fragments based on a Shamir secret sharing scheme and distribute the verification fragments to other area nodes for security verification to generate security verification data in the second layer.

[0159] The third unit is configured to send the security verification data to a central server, decrypt and aggregate the security verification data of multiple area nodes based on the central server to obtain a second training result, perform knowledge distillation optimization on the second training result, extract knowledge information in the form of a soft label, learn the knowledge information based on a cross-entropy loss function, and generate an optimized training result.

[0160] The fourth unit is configured to distribute the optimized training result to each area node, calculate a loss value of the reconstruction model, return to perform reconstruction model training when the loss value is greater than a preset loss threshold, and determine a final reconstruction model when the loss value is less than or equal to the preset loss threshold.

[0161] In a third aspect, an electronic device is provided, including:

[0162] a processor;

[0163] a memory for storing processor-executable instructions;

[0164] The processor is configured to invoke the instructions stored in the memory to perform the method described above.

[0165] In a fourth aspect, a computer-readable storage medium is provided, which stores computer program instructions, and the computer program instructions are executed by a processor to implement the method described above.

[0166] The present application can be a method, device, system and / or computer program product. The computer program product can include a computer readable storage medium having computer readable program instructions loaded thereon for performing various aspects of the present application.

[0167] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions recorded in the above embodiments can be modified, or some or all of the technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for constructing a digital model of power distribution network reconfiguration, characterized in that, The method comprises the following steps: obtaining local data of multiple power distribution network region nodes, and constructing a training data matrix based on the local data; constructing a reconstruction model at each power distribution network region node based on the training data matrix, training the reconstruction model using a gradient descent method, and obtaining a first training result; constructing a double-layer security mechanism to process the first training result, the first layer uses a homomorphic encryption algorithm based on lattice cryptography to encrypt the first training result to obtain encrypted data, and the second layer splits the encrypted data into multiple verification fragments based on a Shamir secret sharing scheme and distributes them to other region nodes for security verification to generate security verification data, comprising: constructing a fault-tolerant learning problem by generating a random vector and a random matrix, and generating a key pair based on the fault-tolerant learning problem comprising: constructing an initial random vector, calculating the probability distribution of the elements of the initial random vector, and calculating the information entropy distribution characteristics of the initial random vector based on the element probability distribution; generating a high-entropy random sequence based on the information entropy distribution characteristics using a quantum random number generator, determining a dynamic fusion weight based on the information entropy distribution characteristics, and performing entropy fusion on the high-entropy random sequence and the initial random vector according to the dynamic fusion weight to obtain an entropy-enhanced random vector; constructing an entropy characteristic mapping function of the entropy-enhanced random vector, and performing cross mapping on the entropy-enhanced random vector input into the entropy characteristic mapping function to obtain a random matrix; constructing a fault-tolerant learning problem by taking the entropy-enhanced random vector as an input vector and the random matrix as a mapping matrix, the fault-tolerant learning problem contains a target vector distance term and a regularization term of the input vector and the mapping matrix, solving the fault-tolerant learning problem to obtain an optimal solution, and generating a key pair based on the optimal solution; sending the security verification data to a central server, decrypting and aggregating the security verification data of multiple region nodes based on the central server to obtain a second training result, performing knowledge distillation optimization on the second training result, extracting knowledge information in the form of soft labels, learning the knowledge information based on a cross-entropy loss function, and generating an optimized training result; distributing the optimized training result to each region node, calculating the loss value of the reconstruction model, returning to perform reconstruction model training when the loss value is greater than a preset loss threshold, and determining a final reconstruction model when the loss value is less than or equal to the preset loss threshold.

2. The method of claim 1, wherein, Based on the training data matrix, a reconstruction model is constructed at each power distribution network region node, the reconstruction model is trained using a gradient descent method, and a first training result is obtained, comprising: mapping the data in the training data matrix to a quantum bit space through a single-bit rotation gate, the single-bit rotation gate dynamically adjusts the rotation angle according to the data value to convert the data into a quantum state representation of the ground state superposition; based on the physical topology structure of the power distribution network and the quantum state representation of the ground state superposition, using a CNOT gate to determine the entanglement correlation strength according to the physical distance between nodes, entangling and correlating the quantum states of adjacent nodes to generate a many-body entangled state; Based on the multi-body entangled state, a reconstruction model is constructed, and a gradient descent method is used to optimize parameters of the reconstruction model, wherein the gradient descent method controls quantum fluctuation strength through adjusting a temperature parameter to realize global search, and controls quantum tunneling effect through adjusting a transverse magnetic field strength to realize local fine search, and searches for an optimal parameter combination in a quantum state space; Based on the optimal parameter combination, the reconstruction model is trained, and a training loss value is monitored, and when the training loss value is not reduced for a preset number of rounds and is less than a preset loss threshold, a first training result is generated.

3. The method of claim 2, wherein, Based on the physical topology structure of the power distribution network and the superposed quantum state of the ground state, a CNOT gate is used to determine the entanglement correlation strength according to the physical distance between nodes, to entangle and correlate the quantum states of adjacent nodes, and to generate a multi-body entangled state, including: Geographic coordinate information of nodes in the power distribution network is acquired, the physical distance between nodes is calculated according to the geographic coordinate information, and a physical distance matrix is constructed; the influence degree of the distance value in the physical distance matrix on the entanglement strength is regulated through an attenuation coefficient, and the entanglement strength between node pairs is generated. A CNOT gate entanglement operation is performed on adjacent nodes in the power distribution network, the CNOT gate entanglement operation performs an exclusive OR operation on the quantum state of a first node as a control bit and the quantum state of a second node as a target bit, and generates a two-node entangled state. Intensity modulation is performed on the two-node entangled state, the intensity modulation linearly combines the quantum state generated by the CNOT gate entanglement operation and the original quantum state before the CNOT gate entanglement operation according to the proportion of the entanglement strength between the node pairs, and obtains a modulated entangled state. Tensor product operation is performed on the modulated entangled state of all adjacent node pairs in the power distribution network, the tensor product operation combines multiple modulated entangled states to form an overall quantum correlation network, and a multi-body entangled state is constructed.

4. The method of claim 1, wherein, The first layer uses a homomorphic encryption algorithm based on lattice cryptography to encrypt the first training result to obtain encrypted data, the second layer divides the encrypted data into multiple verification fragments based on a Shamir secret sharing scheme and distributes them to other regional nodes for security verification to generate security verification data, including: A first layer privacy protection mechanism is constructed, the first layer privacy protection mechanism uses a homomorphic encryption algorithm based on lattice cryptography, constructs a fault-tolerant learning problem by generating a random vector and a random matrix, generates a key pair based on the fault-tolerant learning problem, and the key pair includes a public key composed of the random matrix and a noise vector; Based on the first layer privacy protection mechanism, the public key is used to perform a homomorphic encryption operation, the first training result is multiplied by an integer modulus, and the multiplication result is combined with the random vector to generate encrypted data; A second layer privacy protection mechanism is constructed for the encrypted data, the second layer privacy protection mechanism is based on a Shamir secret sharing scheme of polynomial interpolation, generates a polynomial function with a preset degree, and sets the encrypted data as a constant term of the polynomial function. The polynomial function is used to select different independent variable values according to a preset rule to perform substitution calculation, to generate a plurality of verification shards; the verification shards are distributed to different regional nodes and security verification is performed, a digital signature is added to a verification result, and security verification data with a digital signature is generated.

5. The method of claim 1, wherein, Knowledge distillation optimization is performed on the second training result, knowledge information is extracted in the form of a soft label, the knowledge information is learned based on a cross-entropy loss function, and an optimized training result is generated. A Bayesian framework is introduced to model parameters of the second training result, a posterior distribution model is established, a variational distribution family is constructed based on the posterior distribution model, and the posterior distribution model is approximately calculated by using a variational inference method, so as to obtain variational parameters by minimizing the KL divergence between the variational distribution family and the posterior distribution model. Parameter sampling is performed multiple times by using the variational parameters, a group of model parameters is obtained each time sampling is performed, the model parameters are input into a prediction model of the second training result to obtain corresponding prediction results, and the prediction results are integrated and averaged to generate a soft label for knowledge extraction. The knowledge information contained in the soft label is learned by using a cross-entropy loss function, prediction uncertainty is calculated based on the variational parameters, and a weight coefficient of the cross-entropy loss function is adaptively adjusted according to the size of the prediction uncertainty. The weighted cross-entropy loss function and a variational regularization term are combined to construct an optimization objective function, the variational regularization term is used to control the complexity of the variational distribution family, the optimization objective function is optimized by using a gradient descent method, the knowledge distillation process is completed, and an optimized training result is obtained.

6. The method of claim 1, wherein, The optimized training result is distributed to each regional node, a loss value of the reconstruction model is calculated, when the loss value is greater than a preset loss threshold, reconstruction model training is returned to be performed, and when the loss value is less than or equal to the preset loss threshold, a final reconstruction model is determined. The optimized training result is distributed to each regional node, each regional node is allocated a model copy of the optimized training result; Input samples of verification data in each regional node are input into the corresponding model copy to obtain prediction results, a local loss value of the regional node is calculated based on the prediction results and true labels of the verification data, the local loss values of each regional node are weighted and averaged to obtain a loss value of the reconstruction model, the loss value is compared with a preset loss threshold, when the loss value is greater than the preset loss threshold, parameter gradients are calculated by using the loss value to update parameters of the model copy, and reconstruction model training is returned to be performed, and when the loss value is less than or equal to the preset loss threshold, the model copy with the latest parameters is determined as the final reconstruction model. The first unit is configured to obtain local data of a plurality of power distribution network regional nodes, and construct a training data matrix for the local data.

7. A system for constructing a digital model of a power distribution network reconfiguration, for implementing the method of any one of the preceding claims 1-6, characterized in that, A reconstruction model is constructed at each power distribution network regional node based on the training data matrix, and the reconstruction model is trained by using a gradient descent method to obtain a first training result. ​ ​ A second unit is configured to build a double-layer security mechanism to process the first training result. A first layer uses a full-homomorphic encryption algorithm based on lattice cryptography to encrypt the first training result to obtain encrypted data. A second layer splits the encrypted data into multiple verification shards based on a Shamir secret sharing scheme and distributes the verification shards to other regional nodes for security verification to generate security verification data. A third unit is configured to send the security verification data to a central server, decrypt and aggregate the security verification data of the multiple regional nodes based on the central server, and obtain a second training result. Knowledge distillation optimization is performed on the second training result, knowledge information is extracted in the form of soft labels, the knowledge information is learned based on a cross-entropy loss function, and an optimized training result is generated. A fourth unit is configured to distribute the optimized training result to the regional nodes, calculate a loss value of the reconstruction model, and return to perform reconstruction model training when the loss value is greater than a preset loss threshold. When the loss value is less than or equal to the preset loss threshold, a final reconstruction model is determined.

8. An electronic device, comprising: Comprise: a processor; a memory for storing processor-executable instructions; wherein the processor is configured to invoke the instructions stored in the memory to perform the method of any one of claims 1 to 6.

9. A computer-readable storage medium having stored thereon computer program instructions, wherein, The computer program instructions are executed by the processor to implement the method of any one of claims 1 to 6.

Images