Power feasible region fast estimation method for distribution network based on physical information neural network

Abstract

The application discloses a power distribution network power feasible region fast estimation method based on a physical information neural network, relates to the technical field of power system optimization operation and artificial intelligence, and comprises the following steps: establishing a parameterized real power feasible region and a neural network mapping of operation parameters to estimated polygon parameters, and calculating a directional geometric error according to directional support points of the real power feasible region and the estimated polygon in corresponding directions to obtain an explicit physical information loss function, and training the parameter mapping neural network by using automatic differentiation and back propagation; obtaining a current operation parameter vector of the power distribution network and inputting the trained parameter mapping neural network to directly obtain a normal vector matrix and an offset vector corresponding to a current operation state through one-time neural network forward propagation, so as to form an estimated power feasible region at a power transmission and distribution network interface. The application realizes fast online estimation of the power feasible region under the condition of operation parameter change.

Description

Technical Field

[0001] This invention belongs to the field of power system optimization operation and artificial intelligence technology, specifically involving a fast estimation method for the feasible power domain of distribution networks based on physical information neural networks. Background Technology

[0002] The integration of massive adjustable resources such as distributed photovoltaics, energy storage, electric vehicles, and flexible loads enables distribution networks to proactively regulate their operations. These resources can exchange active and reactive power with the upstream transmission network through transmission and distribution interfaces. To ensure the safe implementation of upstream dispatch commands, it is necessary to determine the active-reactive power range of the distribution network's transmission and distribution interfaces under internal power flow security and flexible resource regulation constraints—this is the feasible power region of the distribution network. This feasible region is the projection of the high-dimensional feasible operating space within the distribution network onto the two-dimensional plane of active and reactive power at the transmission and distribution interfaces, and it dynamically changes with node loads, distributed power output, and energy storage operating conditions. Currently, constructing the feasible region mainly involves analytical calculation methods and machine learning methods. The former requires repeatedly solving boundary optimization problems with nonlinear power flow constraints in multiple directions, and repeated searches after changes in operating conditions lead to high online computational pressure. The latter relies on offline training to build a mapping between operating parameters and feasible region features, and online estimation is faster, but it depends on massive amounts of data. The limitations of labeled samples and training data in fully covering complex operating conditions and the lack of sufficient embedding of physical information can lead to reliability risks under incomplete coverage. Furthermore, existing research on related physical information neural networks primarily focuses on specific physical variables such as state variables, trajectories, or control variables, relying on residual training from physical equations. This approach cannot directly address the geometric deviation between the power feasible region and the estimation region, which is a multi-constraint geometric set. This geometric deviation requires directional search and set projection solutions, and the optimal solution is deeply coupled with the polygon parameters output by the neural network. Directly taking implicit derivatives of the nested optimization process is not only computationally complex but also prone to numerical instability. Therefore, there is an urgent need for a fast method for estimating the power feasible region of a distribution network that can directly construct the mapping relationship between the operating state and power feasible region parameters of the distribution network, embed the nonlinear physical constraints of the distribution network for neural network training, and transform the geometric deviation into an explicit differentiable loss. Summary of the Invention

[0003] To address the aforementioned issues, the present invention aims to provide a fast estimation method for the power feasible region of a distribution network based on a physical information neural network. This method aims to establish a mapping between the operating parameters of the distribution network and the polygonal parameters of the power feasible region, transforming the physical operating constraints of the distribution network into explicit geometric losses for neural network training. By combining two-stage training and dynamic loss weight adjustment, the method achieves rapid online estimation of the power feasible region under varying operating parameters.

[0004] To achieve the above technical objectives, this application provides a fast method for estimating the feasible power domain of a distribution network based on a physical information neural network, comprising the following steps: Establish a parameterized real power feasible region and a neural network mapping from running parameters to estimated polygon parameters. Based on the real power feasible region and the directional support points of the estimated polygon in the corresponding direction, calculate the directional geometric error to obtain an explicit physical information loss function. Then, use automatic differentiation and backpropagation to train the parameter mapping neural network. The current operating parameter vector of the distribution network is obtained and input into the trained parameter mapping neural network. The normal vector matrix and offset vector corresponding to the current operating state are directly obtained through one forward propagation of the neural network to form the estimated power feasible region at the transmission and distribution network interface.

[0005] Preferably, when establishing the parameterized real power feasible region, the distribution network topology, branch parameters and node flexible resource configuration are obtained, a distribution network physical operation model is established, and the set of power of the transmission and distribution network interfaces that satisfy the constraints of the physical operation model is determined according to the distribution network operation parameters, thus forming the real power feasible region corresponding to the operation parameters.

[0006] Preferably, when constructing the real power feasible region, the operating parameter vector is composed of the reference active power and reference reactive power of each non-root node of the distribution network; The physical operation model of the distribution network adopts the radial distribution network DistFlow model, and the actual power feasible region is jointly determined by DistFlow power flow constraints, node voltage constraints, and node power regulation constraints.

[0007] Preferably, when mapping the running parameters to the estimated polygon parameters in a neural network, the intersection of multiple linear half-spaces is used to represent the feasible region of the estimated polygon, and a parameter mapping neural network is constructed with the running parameter vector as input and the normal vector matrix and offset vector as output.

[0008] Preferably, when constructing the parameter mapping neural network, the original normal vectors generated inside the parameter mapping neural network and their corresponding original offsets are normalized to the same scale to reduce the impact of half-space parameter scale differences on loss calculation and network training.

[0009] Preferably, when calculating the directional geometric error, multiple two-dimensional direction vectors are randomly sampled for the running parameter samples, and the directional support points of the real power feasible region and the estimated polygon in the corresponding directions are obtained respectively. The two types of directional support points are then projected onto another set to obtain the feasibility error and optimality error that characterize the degree of boundary crossing and the degree of conservatism of the estimated region.

[0010] Preferably, when obtaining the explicit physical information loss function, the activation constraints at the corresponding boundary points of the estimated polygon are identified, and explicit feasibility residuals and explicit optimality residuals are constructed based on the directional support points, projection points, and activation constraints, and feasibility loss and optimality loss are formed respectively; the total loss function is constructed by weighted combination, and the parameter mapping neural network is trained using automatic differentiation and backpropagation.

[0011] Preferably, when training the parameter mapping neural network, after obtaining the basic polygons through pre-training under the baseline operating state, the complete parameter mapping neural network is initialized using the basic polygons, and different operating states are sampled from the operating parameter distribution to carry out complete parameterized training.

[0012] Preferably, when training the parameter mapping neural network, a two-stage training method of pre-training and full training is adopted. In the pre-training stage, the initial polygonal approximation is constructed by using the initial normal vector with uniformly distributed direction angle and the maximum projection value of the reference true power feasible domain in the corresponding direction, and the basic polygonal parameters are obtained by optimization. During the full training initialization, the weights of the output layer of the parameter mapping neural network are set to zero, and the corresponding output layer bias is initialized to the basic polygonal parameters.

[0013] Preferably, when performing full training, the full training includes a balanced training phase and a feasibility reinforcement phase; in the balanced training phase, a first optimality loss weight is used so that the feasibility loss and the optimality loss participate in the training together; in the feasibility reinforcement phase, a second optimality loss weight that is smaller than the first optimality loss weight is used.

[0014] The present invention discloses the following technical effects: (1) This invention establishes a direct mapping between the operating parameters of the power distribution network and the polygonal parameters of the power feasible region, and places the main calculation processes such as direction search, projection calculation and loss assessment in the offline training stage. In the online stage, only one neural network forward propagation needs to be performed, thereby realizing the rapid update of the power feasible region.

[0015] (2) This invention does not require pre-generating complete power feasible domain labels for different operating states. Instead, it dynamically generates directional boundary points and projection information during the training process using the physical operating constraints of the power distribution network, thereby reducing the dependence on large-scale complete feasible domain labeling data.

[0016] (3) The present invention characterizes the degree of boundary crossing and the degree of conservatism of the estimated polygon by feasibility error and optimality error respectively, thereby taking into account both the physical feasibility and boundary compactness of the estimated region.

[0017] (4) This invention utilizes the activation constraints at the estimated polygon boundary points to transform the set geometric deviation obtained through direction search and projection optimization into a residual loss that explicitly depends on the normal vector matrix and the offset vector, which facilitates the use of automatic differentiation and backpropagation to train the parameter mapping neural network.

[0018] (5) The present invention adopts basic polygon pre-training, complete parameterized training and dynamic loss weight adjustment strategy to improve the stability of parameter mapping neural network training and further reduce the risk of estimated polygons going out of bounds in the later stage of training. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart illustrating the overall process of the method described in this invention. Figure 2 This is a schematic diagram illustrating the mapping from the power distribution network operating parameters to the estimated polygon feasible region as described in this invention.

[0021] Figure 3 This is a schematic diagram illustrating the construction principle of feasibility error, optimality error, and explicit physical information loss as described in this invention.

[0022] Figure 4 This is the flowchart of the pre-training-complete training and dynamic loss weight adjustment described in this invention. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0024] like Figure 1As shown, this invention provides a fast estimation method for the power feasible region of a distribution network based on a physical information neural network. This method establishes a mapping between the operating parameters of the distribution network and the polygonal parameters of the power feasible region, transforms the physical operating constraints of the distribution network into explicit geometric losses for neural network training, and combines two-stage training and dynamic loss weight adjustment to achieve fast online estimation of the power feasible region under changing operating parameters.

[0025] Step S100 establishes the parameterized real power feasible region.

[0026] In one embodiment, the distribution network topology, branch parameters, and node flexible resource configuration are obtained, and an operating parameter vector is constructed based on the node reference active power and reference reactive power. Based on nonlinear power flow constraints, node voltage constraints, and node flexible resource adjustment constraints, the true power feasible region corresponding to the operating parameters is established. .

[0027] For example, the operating parameter vector consists of the reference active power and reference reactive power of each non-root node in the distribution network.

[0028] For example, the runtime parameter vector is represented as: in, This represents the number of non-root nodes in the distribution network. and The first The reference active power and reference reactive power of each non-root node.

[0029] For example, given a vector of runtime parameters The feasible region of true power is represented as: in, and These are the active power and reactive power at the power transmission and distribution network interface, respectively.

[0030] For example, the actual power feasible region is determined by the DistFlow power flow equations of the radial distribution network, the node voltage constraints, and the node power regulation constraints.

[0031] For example, the physical operation model of the distribution network adopts the DistFlow model of the radial distribution network, which includes the power relationship of the transmission and distribution network interface, active power balance constraints of branches, reactive power balance constraints of branches, voltage drop constraints of nodes, nonlinear constraints of power-current-voltage of branches, voltage constraints of root nodes, and upper and lower limits of node voltage.

[0032] For example, the node power regulation constraints include at least: fixed power node constraints; node constraints in which active power and reactive power are regulated in independent intervals; and coupled regulation node constraints in which active power and reactive power satisfy apparent power capacity constraints.

[0033] Step S200 establishes a neural network mapping from running parameters to estimated polygon parameters.

[0034] In one implementation, the intersection of multiple linear half-spaces is used to estimate the feasible region of the polygon. Construct a runtime parameter vector As input, with normal vector matrix and offset vector The parameters of the output are mapped to the neural network.

[0035] For example, the feasible region of the estimated polygon is represented by the intersection of multiple linear half-spaces, and the parameter mapping neural network directly takes the power distribution network operation parameter vector as input and outputs the normal vector matrix and offset vector of the estimated polygon.

[0036] For example, the estimated feasible region of the polygon is represented as: in, To estimate the normal vector matrix of the polygon, For offset vectors, The preset number of sides for the polygon; For example, the parameter mapping neural network generates the normal vector matrix and offset vector based on the running parameter vector: in, The trainable parameters of the parameter mapping neural network are given.

[0037] For example, the original normal vectors generated inside the parameter mapping neural network and their corresponding original offsets are normalized to the same scale to reduce the impact of half-space parameter scale differences on loss calculation and network training.

[0038] For example, for the parameter mapping neural network internally generated by the first... The original normal vectors and the corresponding original offset Normalize to the same scale according to the following formula: in, This is a preset positive number used to prevent the denominator from being zero.

[0039] Step S300 calculates the directional geometric error.

[0040] In one embodiment, multiple two-dimensional direction vectors are randomly sampled for the operating parameter samples, and the directional support points of the real power feasible region and the estimated polygon in the corresponding directions are obtained respectively. The two types of directional support points are then projected onto another set to obtain the feasibility error and optimality error that characterize the degree of boundary crossing and the degree of conservatism of the estimated region.

[0041] For example, for a given direction vector The directional support points of the estimated feasible region of the polygon are represented as follows: ; Projecting the directional support points onto the real power feasible region yields: .

[0042] For example, the directional support points of the true power feasible region are represented as: ; Projecting the directional support points of the true power feasible region onto the estimated polygon feasible region, we obtain: ; The objective function values ​​corresponding to the projection problem are used to characterize the feasibility error and optimality error of estimating the feasible region of the polygon, respectively.

[0043] Step S400: Construct an explicit physical information loss function.

[0044] In one embodiment, activation constraints at corresponding boundary points of the estimated polygon are identified, explicit feasibility residuals and explicit optimality residuals are constructed based on directional support points, projection points and activation constraints, and feasibility loss and optimality loss are formed respectively; a total loss function is constructed by weighted combination, and a parameter mapping neural network is trained using automatic differentiation and backpropagation.

[0045] For example, for estimating polygonal orientation support points Its activation constraint set is represented as: ; Construct a feasibility residual based on the projection points on the actual power feasible region: ; And construct a one-way feasibility loss: .

[0046] For the projection points of the support points in the true power feasible region onto the estimated polygon, the set of activation constraints is expressed as: ; Constructing optimal residuals: ; And unidirectional optimality loss: .

[0047] For example, during offline training, multiple two-dimensional direction vectors are randomly sampled. Based on the projection points of the estimated polygon direction support points and the true power feasible domain direction support points onto the estimated polygon, corresponding activation constraints are identified. Single-direction feasibility loss and optimality loss are constructed, and the losses of multiple directions are averaged to form a total loss function composed of feasibility loss and optimality loss weighted by weight coefficients.

[0048] For example, random sampling is performed in each training iteration. Given several directional vectors, calculate the corresponding single-directional feasibility loss and single-directional optimality loss respectively, and obtain: The total loss function is expressed as: in, The optimality loss weight coefficient; For example, in each gradient calculation process, the boundary points, projection points and activation constraint set obtained by the current iteration through direction search and projection calculation are regarded as determined geometric information, so that the total loss function explicitly depends on the normal vector matrix and the offset vector, and the parameter mapping neural network is updated using automatic differentiation and backpropagation.

[0049] Step S500 employs a two-stage training and dynamic weight scheduling strategy.

[0050] In one embodiment, a base polygon is first pre-trained under a baseline operating state; then, the base polygon is used to initialize a complete parameter mapping neural network, and different operating states are sampled from the operating parameter distribution to conduct complete parameterized training. The complete training further includes a balanced training phase and a feasibility enhancement phase, in which the optimality loss weight is reduced in the later stage of training, so that the final estimation result focuses more on physical feasibility.

[0051] For example, the parameter mapping neural network adopts a two-stage training method of pre-training and full training. In the pre-training stage, the initial polygonal approximation is constructed by using the initial normal vector with uniformly distributed direction angle and the maximum projection value of the reference true power feasible domain in the corresponding direction, and the basic polygonal parameters are obtained by optimization. During the full training initialization, the weights of the output layer of the parameter mapping neural network are set to zero, and the corresponding output layer bias is initialized to the basic polygonal parameters.

[0052] For example, the parameter mapping neural network adopts a two-stage training method of pre-training-full training; During the pre-training phase, the fixed running parameter vector is used as the baseline running parameter vector. Directly optimize the basic polygon parameters under the baseline operating state. ; The complete training phase samples the running parameter vector from the running parameter distribution. The input parameters are mapped to a neural network, and the normal vector matrix and offset vector corresponding to the operating state are output to learn the mapping relationship between the changes in the operating state and the changes in the parameters of the power feasible region polygon.

[0053] For example, the baseline polygon is initialized during the pre-training phase as follows: in: The initial offset is determined based on the actual power feasible region under the baseline operating conditions: An initial polygonal approximation of the true power feasible region is formed by the initial normal vector and the initial offset, and the basic polygonal parameters are obtained by optimization through the total loss function.

[0054] For example, during the full training initialization, the weights of the parameter-mapped neural network output layer are initialized to zero, and the output layer biases used for the output normal vector matrix and offset vector are initialized to the pre-trained basic normal vector matrix and basic offset vector, respectively, so that the following conditions are met during the full training initialization: This holds true for any input parameter vector.

[0055] For example, the complete training includes a balancing training phase and a feasibility enhancement phase; in the balancing training phase, a first optimality loss weight is used so that the feasibility loss and the optimality loss participate in the training together; in the feasibility enhancement phase, a second optimality loss weight, which is smaller than the first optimality loss weight, is used so that the training objective focuses more on reducing the infeasible parts in the estimated polygon.

[0056] Step S600: Online rapid estimation.

[0057] In one embodiment, the current operating parameter vector of the distribution network is obtained and input into the trained parameter mapping neural network. The normal vector matrix and offset vector corresponding to the current operating state are directly obtained through one forward propagation of the neural network, and the estimated power feasible region at the transmission and distribution network interface is formed accordingly.

[0058] Example 1: As Figure 1As shown, the method in this embodiment includes parameterized real power feasible domain modeling, polygon parameterized representation, parameter mapping neural network construction, directional geometric error calculation, explicit physical information loss construction, two-stage offline training, and online fast estimation.

[0059] Step 1: Establish the parameterized power feasible region. Assume the distribution network includes... There are nodes, and the node set is: Among them, node 0 is the root node connected to the upper-level transmission network, and the set of non-root nodes is: The set of branches is represented as .

[0060] The active power and reactive power at the transmission and distribution network interface are respectively expressed as: and .

[0061] The power requirements of the transmission and distribution network interface must be met: For branch roads The DistFlow model is used to describe the power flow relationships in the distribution network: in, and These are the active power and reactive power of the branch circuit, respectively. The square of the branch current amplitude, The square of the node voltage magnitude, and These are the branch resistance and reactance, respectively.

[0062] The root node voltage and other node voltages satisfy: Based on the node power regulation characteristics, non-root nodes are divided into fixed power nodes, active and reactive power independently regulated nodes, and active and reactive power coupled regulated nodes.

[0063] in, , and Let these represent the set of fixed power nodes, the set of independently regulated nodes, and the set of coupled regulated nodes, respectively. These three sets are mutually exclusive and satisfy the following conditions: . and They represent the first The reference active power and reference reactive power of each node.

[0064] Define the runtime parameter vector: Given a vector of runtime parameters At that time, the real power feasible domain It consists of active and reactive power operating points of the transmission and distribution network interfaces that satisfy all the above-mentioned physical operation constraints of the distribution network.

[0065] Step 2: Establish a parameter mapping neural network. Although the high-dimensional feasible operating space of the distribution network may be non-convex, its projection onto the active-reactive two-dimensional space of the transmission and distribution network interface usually exhibits an approximately convex characteristic. Therefore, this embodiment uses a convex polygon formed by the intersection of multiple linear half-spaces for approximation. For scenarios with obvious non-convex boundaries, the radial boundary search method described later can be used for expansion.

[0066] like Figure 2 As shown, the parameter mapping neural network uses the distribution network operating parameter vector. As input, output the estimated normal vector matrix of the polygon. and offset vector Based on this, an estimated polygon feasible region is constructed for the corresponding operating state. The estimated polygon feasible region is expressed as: in: Parameter mapping neural networks to run parameter vectors The input is used to generate the original normal vector matrix within the network. and the original offset vector For the first Each half-space constraint is normalized to the same scale according to the following formula: in, The default value is a positive number. The normalized normal vector matrix. and offset vector Used to construct the estimated polygon, and subsequently for orientation search, projection, and loss calculation. Same-scale normalization does not change the geometric region represented by the corresponding linear half-space and can reduce the impact of half-space parameter scale differences on the training process.

[0067] Step 3: Calculate the directional geometric error. For example... Figure 3 As shown, for each sample of operating parameters, multiple two-dimensional direction vectors are randomly sampled from a two-dimensional standard Gaussian distribution. .

[0068] Estimate the polygon in direction The upward support point is represented as: Projecting the directional support point onto the real power feasible region: The directional support points in the same direction within the true feasible power region are represented as follows: Project it onto the estimated polygon: The objective function values ​​for the two projection problems mentioned above are defined as feasibility error and optimality error, respectively. Feasibility error is used to characterize the degree of boundary violation of the estimated polygon, while optimality error is used to characterize the degree of conservatism of the estimated polygon.

[0069] Step 4: Construct explicit physical information loss. For estimating polygonal orientation support points... Identify the set of activation constraints: Substituting its projection point on the real power feasible region into the corresponding activation constraints, we construct: The unidirectional feasibility loss is: For the projection points of the support points in the true power feasible region onto the estimated polygon, identify: And construct: The unidirectional optimality loss is: For each training random sampling Averaging in each of the following directions: The total loss function is expressed as: in, The optimality loss weights.

[0070] During gradient calculation in each training iteration, the boundary points, projection points, and activation constraint sets obtained from the current direction search and projection calculation are treated as predetermined geometric information, making the loss function explicitly dependent on... and This allows for the use of automatic differentiation and backpropagation to update the parameter mapping neural network.

[0071] Step 5: Employ two-stage training and dynamic weight adjustment. For example... Figure 4 As shown, the baseline operating parameter vector is first selected: Pre-training phase fixed: It also directly optimizes the static base polygon parameters.

[0072] No. The initial normal vector of the edge is set as follows: in: The corresponding initial offset is: This leads to the construction of an initial polygonal out-of-polygon approximation covering the feasible region of the baseline true power, which is then optimized using the total loss function to obtain the basic polygonal parameters: .

[0073] During complete training initialization, the parameter mapping neural network output layer weights are initialized to zero, and the corresponding output layer biases are initialized to... and To make the complete training start at the beginning: Subsequently, from the distribution of operating parameters We conduct complete parameterized training by sampling different operating states.

[0074] The complete training process further includes a balanced training phase and a feasibility enhancement phase. The balanced training phase uses a relatively large optimality loss weight, allowing both feasibility loss and optimality loss to participate in the training. The feasibility enhancement phase reduces the optimality loss weight, making the training objective more focused on reducing the risk of the estimated polygon going out of bounds.

[0075] Step Six: Online Rapid Estimation. After completing offline training, obtain the reference active power and reference reactive power of each non-root node in the current distribution network online, and construct the current operating parameter vector: Then, directly input it into the trained parameter mapping neural network: This allows us to obtain the estimated power feasible region corresponding to the current operating state: During the online application phase, there is no need to re-execute the search for support points in the direction of the real power feasible domain, set projection, or loss calculation.

[0076] When the feasible region of true power exhibits significant non-convexity, the power of each non-root node is fixed to its reference value. , Solve for the power flow of the distribution network that satisfies the voltage constraints, and denote the corresponding operating point of the transmission and distribution network interface as . and along the direction Structural rays: Solve for the feasible region of the true power and estimate the radial boundary points of the polygon along the ray direction to construct the corresponding radial boundary error.

[0077] The radial search method can be used as an extended boundary error metric when the real power feasible region has strong non-convexity; this embodiment mainly uses the aforementioned error based on directional support points for training.

[0078] Example 2: This example uses an IEEE-33 node radial distribution system for verification, where the root node serves as the interface node for the transmission and distribution network. The system base capacity is 10 MVA, and the node voltage operating range is 0.90–1.10 pu.

[0079] To characterize the power regulation capabilities of different nodes, the 32 non-root nodes (excluding the root node) are divided into three categories: fixed power nodes, nodes with independent active and reactive power regulation, and nodes with coupled active and reactive power regulation, with 15, 15, and 2 nodes respectively. Fixed power nodes maintain constant reference active and reactive power; nodes with independent active and reactive power regulation can adjust both active and reactive power within ±30% of the reference operating point; and nodes with coupled active and reactive power regulation satisfy the apparent power regulation capacity constraint.

[0080] For nodes with independent active and reactive power regulation: For active and reactive power coupled regulation nodes: The node voltage amplitude is limited to: The dimensions of the runtime parameter vector are: The baseline operating parameter vector is constructed using the active and reactive power data of the original nodes in the IEEE-33 Node system. The training parameters are as follows: This generates a parameter mapping neural network that learns the mapping relationship between operating parameters and the corresponding power feasible region within a ±20% variation range around the baseline operating state.

[0081] In the IEEE-33 node master case, the estimated number of polygon sides is set to The corresponding polygon parameter output dimension is In subsequent comparisons of computational efficiency and approximation results across different systems, further settings will be implemented. and Two polygon sizes.

[0082] The parameter mapping neural network uses a single hidden layer structure, with 128 neurons in the hidden layer.

[0083] The SGD optimizer is used in the pre-training phase, with an initial learning rate of: in, The per-unit value of the total active load of the system under the baseline operating condition is calculated as the ratio of the sum of the baseline active loads of each node to the baseline capacity of the system: in, For the first The baseline active load of each node This is the system baseline capacity. (Using...) The learning rate is scale-normalized to reduce the impact of power magnitude differences between systems of different sizes on the training parameter settings.

[0084] During the pre-training phase, the StepLR learning rate scheduling strategy is adopted. Every 100 iterations, the current learning rate is adjusted to 0.99 times the original value. The optimality loss weight in the total loss function is set to 0.6. A total of 2000 iterations are trained, with 5 directions sampled in each iteration step, and the batch size is set to 1.

[0085] After pre-training, the obtained basic polygon parameters are used to initialize the complete parameter mapping neural network. Following the method described in Example 1, the weights of the output layer of the parameter mapping neural network are initialized to zero, and the output layer biases corresponding to the normal vector matrix and the offset vector are initialized to the basic normal vector matrix and the basic offset vector, respectively, so that the different running parameter inputs at the beginning of the complete training correspond to the basic polygons in the baseline running state.

[0086] The full training phase uses the Adam optimizer and sets the running parameter vector. The input parameters are mapped to a neural network, and the output is the polygon normal vector matrix corresponding to the running state. and offset vector The complete training program further includes a balance training phase and a feasibility enhancement phase.

[0087] During the balancing training phase, the learning rate is set as follows: The optimality loss weight was set to 0.6, and a total of 1600 iterations were trained. After completing the balanced training, the feasibility enhancement phase began, with the learning rate set to: And reduce the optimality loss weight to Continue training for 800 iterations. During the balancing training phase and the feasibility enhancement phase, each running parameter sample is sampled in two directions, and the batch size is set to 5.

[0088] The node configuration, operating parameter perturbation range, network structure, and training parameters described above are all specific settings used in this embodiment to illustrate the specific implementation process of the method of the present invention, and do not constitute a limitation on the scope of protection of the present invention.

[0089] After offline training is completed, the current running parameter vector is directly input into the trained parameter mapping neural network. The corresponding normal vector matrix and offset vector can be obtained through one forward propagation, forming the estimated P-Q power feasible region under the current running state.

[0090] To verify the applicability and online computation efficiency of this invention under different system scales and distribution network models, further extended tests were conducted using an IEEE-118-bus system, an IEEE-533-bus system, and a real 36-bus unbalanced three-phase distribution system. and A comparison is made with the vertex-based inscribed polygon method at two polygon scales. The method sets up in the P–Q plane. Uniformly distributed directions: in: For each direction, the boundary optimization problem of the true power feasible region is solved separately to obtain the corresponding boundary points. A convex hull is then calculated for each boundary point to form a polygon approximation. When the original power feasible region is a convex set, the convex hull constitutes its interior approximation. The online computation time for different methods is shown in Table 1.

[0091] Table 1 As can be seen from the above results, under the test system and polygon side number settings, the online calculation time of the method of the present invention is about 28 to 31 ms, which can achieve a calculation speedup of about 13 to 800 times compared with the vertex-based inscribed polygon method.

[0092] To evaluate the conservatism of the estimated power feasible region, a reference operating point is used. Starting from the ray, the maximum radial distance is calculated along a given direction for both the actual power feasible region and the estimated polygon, denoted as . and The directional coverage is defined as: The higher the coverage, the lower the conservatism of the estimated polygons.

[0093] Test results further demonstrate that the estimated power feasible region generated by this invention has a small feasibility error and an average coverage rate of over 80%, which can significantly improve online computing efficiency while maintaining a moderate power feasible region coverage capability.

[0094] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0095] In the description of this invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0096] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A fast method for estimating the feasible power region of a distribution network based on a physical information neural network, characterized in that, Includes the following steps: Establish a parameterized real power feasible region and a neural network mapping from running parameters to estimated polygon parameters. Based on the real power feasible region and the directional support points of the estimated polygon in the corresponding direction, calculate the directional geometric error to obtain an explicit physical information loss function. Then, use automatic differentiation and backpropagation to train the parameter mapping neural network. The current operating parameter vector of the distribution network is obtained and input into the trained parameter mapping neural network. The normal vector matrix and offset vector corresponding to the current operating state are directly obtained through one forward propagation of the neural network to form the estimated power feasible region at the transmission and distribution network interface.

2. The fast estimation method for the feasible power region of a distribution network based on a physical information neural network according to claim 1, characterized in that: When establishing the parameterized real power feasible region, the distribution network topology, branch parameters and node flexible resource configuration are obtained, a distribution network physical operation model is established, and the set of power of the transmission and distribution network interfaces that satisfy the constraints of the physical operation model is determined according to the distribution network operation parameters, thus forming the real power feasible region corresponding to the operation parameters.

3. The fast estimation method for the feasible power region of a distribution network based on a physical information neural network according to claim 2, characterized in that: When constructing the real power feasible region, the operating parameter vector is composed of the reference active power and reference reactive power of each non-root node of the distribution network. The physical operation model of the distribution network adopts the radial distribution network DistFlow model, and the real power feasible region is jointly determined by DistFlow power flow constraints, node voltage constraints, and node power regulation constraints.

4. The fast estimation method for the feasible power region of a distribution network based on a physical information neural network according to claim 1, characterized in that: When mapping the running parameters to the estimated polygon parameters in a neural network, the intersection of multiple linear half-spaces is used to represent the feasible region of the estimated polygon. A parameter mapping neural network is constructed with the running parameter vector as input and the normal vector matrix and offset vector as output.

5. The fast estimation method for the feasible power region of a distribution network based on a physical information neural network according to claim 4, characterized in that: When generating polygon parameters in a parameter mapping neural network, the original normal vectors generated inside the parameter mapping neural network and their corresponding original offsets are normalized to the same scale to reduce the impact of half-space parameter scale differences on loss calculation and network training.

6. The fast estimation method for the feasible power region of a distribution network based on a physical information neural network according to claim 1, characterized in that: When calculating the directional geometric error, multiple two-dimensional direction vectors are randomly sampled for the running parameter samples. The directional support points of the real power feasible region and the estimated polygon in the corresponding directions are obtained respectively. The two types of directional support points are then projected onto another set to obtain the feasibility error and optimality error, which characterize the degree of boundary crossing and the degree of conservatism of the estimated region.

7. The fast estimation method for the feasible power region of a distribution network based on a physical information neural network according to claim 6, characterized in that: When obtaining the explicit physical information loss function, the activation constraints at the corresponding boundary points of the estimated polygon are identified. Explicit feasibility residuals and explicit optimality residuals are constructed based on the directional support points, projection points, and activation constraints, and feasibility loss and optimality loss are formed respectively. The total loss function is constructed by weighted combination, and the parameter mapping neural network is trained using automatic differentiation and backpropagation.

8. The fast estimation method for the feasible power region of a distribution network based on a physical information neural network according to claim 1, characterized in that: When training the parameter mapping neural network, after obtaining the basic polygons in the baseline operating state through pre-training, the complete parameter mapping neural network is initialized using the basic polygons, and different operating states are sampled from the operating parameter distribution to carry out complete parameterized training.

9. The fast estimation method for the feasible power region of a distribution network based on a physical information neural network according to claim 8, characterized in that: When training the parameter mapping neural network, a two-stage training method of pre-training and full training is adopted. In the pre-training stage, the initial polygonal approximation is constructed by using the initial normal vector with uniformly distributed direction angle and the maximum projection value of the reference true power feasible domain in the corresponding direction, and the basic polygonal parameters are obtained by optimization. During the full training initialization, the weights of the output layer of the parameter mapping neural network are set to zero, and the corresponding output layer bias is initialized to the basic polygonal parameters.

10. The fast estimation method for the feasible power region of a distribution network based on a physical information neural network according to claim 9, characterized in that: When performing full training, the full training includes a balanced training phase and a feasibility reinforcement phase; in the balanced training phase, a first optimality loss weight is used so that the feasibility loss and the optimality loss participate in the training together; in the feasibility reinforcement phase, a second optimality loss weight that is smaller than the first optimality loss weight is used.

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