Multi-stage PMU optimal configuration method, system, equipment and medium

Abstract

The invention relates to a multi-stage PMU (Phasor Measurement Unit) optimal configuration method, system, equipment and medium, the method adopts a multi-stage serial method, and the PMU optimal configuration is divided into a plurality of stages by defining the unobservable depth of the system; and in the case of incomplete observability, the unobservable depth constraint is considered in the critical observability optimization model to carry out optimal configuration, and in the case of redundancy complete observability, the limited number constraint is considered in the critical observability optimization model to carry out optimal configuration, so that a PMU observability improvement optimal configuration scheme from incomplete observability to critical observability to redundancy complete observability is obtained. Compared with the prior art, PMU optimal configuration capable of gradually improving observability under the condition that the system is not completely observable can be realized.

Description

Technical Field

[0001] This invention relates to the field of PMU optimization configuration technology, and in particular to a multi-stage PMU optimization configuration method, system, device and medium. Background Technology

[0002] Phasor measurement units (PMUs) greatly assist in distribution network state estimation, fault location, and optimized control. If synchronized phasor measurement units were installed at all nodes of the distribution network, global observability could obviously be achieved. However, in actual production, economic and spatial factors must be considered, and configuring PMUs at every node of the distribution network is not practical. Therefore, it is necessary to study the optimal placement of synchronized phasor measurement units in the distribution network, i.e., to achieve global observability of the distribution network with the fewest possible synchronized phasor measurement units.

[0003] In practical distribution network PMU configuration, due to technical and cost limitations, it is difficult to configure all PMUs on all nodes at once, which is uneconomical and infeasible. Furthermore, distribution networks are undergoing multi-stage dynamic development and upgrades, and existing PMU configurations may become unpredictable due to changes in network topology. Therefore, determining the minimum number of PMUs required for multi-stage configuration and specifying their locations is of significant research importance.

[0004] A Power Measure (PMU) can measure the voltage and current phasors of a configured node, and indirectly calculate the voltage and current vectors of its neighboring nodes. Therefore, a PMU can make the configured node and its neighbors observable. Related research shows that when the system's unobservability is low, the state estimation results are not significantly different from the actual values. However, when the unobservability depth is large, according to the error propagation principle, the error of the pseudo-measurements constructed for state estimation increases, and the state estimation error also increases accordingly. With the increasing unobservability, the state estimation results become essentially unusable. Therefore, a PMU optimization configuration method that considers the usability of state estimation results and improves observability is needed to ensure an effective PMU configuration scheme even under unobservable system conditions. Summary of the Invention

[0005] The purpose of this invention is to overcome the defects of the prior art by providing a multi-stage PMU optimization configuration method, system, device and medium.

[0006] The objective of this invention can be achieved through the following technical solutions: According to a first aspect of the present invention, a multi-stage PMU optimization configuration method based on observability improvement is provided. This method adopts a multi-stage serial approach, which divides the PMU optimization configuration into multiple stages by defining the unobservable depth of the system: when the system is critically observable, optimization configuration is performed based on the critical observable optimization model; when the system is not fully observable, optimization configuration is performed considering the unobservable depth constraint in the critical observable optimization model; and when the system is redundantly fully observable, optimization configuration is performed considering the limited number constraint in the critical observable optimization model. This results in a PMU observability improvement optimization configuration scheme that progresses from incomplete observability to critical observability and then to redundantly fully observable.

[0007] As a preferred technical solution, the method includes the following steps: Define the unobservable depth of the system; Based on the depth of unobservability, the system is divided into three states: incomplete observability, critical observability, and redundant complete observability. Construct a critical observable optimization model, which includes inequality constraints and equality constraints; When the system is not fully observable, add unobservable depth constraints to the inequality constraints of the critical observable optimization model for optimization configuration; When the system is critically observable, optimize the configuration based on the critically observable optimization model; When the system redundancy is fully observable, a limited number of constraints are added to the equality constraints of the critical observable optimization model to optimize the configuration.

[0008] As a preferred technical solution, the unobservable depth is defined as the number of edges traversed by a node to reach an adjacent observable node, and the maximum value of all nodes in the system is taken as the unobservable depth of the system.

[0009] As a preferred technical solution, the PMU optimization configuration objective of the critical observable optimization model is to minimize the number of PMU configurations, maximize the node comprehensive measurement index, and maximize the system measurement redundancy.

[0010] As a preferred technical solution, the critical observable optimization model is as follows: , , In the formula: N is the total number of system nodes; r i Let w represent the redundancy of node i, defined as the number of times it can be directly measured by the PMU. i Let be the comprehensive metric value for node i. b is a unit column vector. ;x i This indicates the PMU installation status of node i. .

[0011] As a preferred technical solution, the constraints of the critical observable optimization model include zero-injection node constraints: , In the formula: y ij The 0-1 phasor indicates that node i becomes observable from its neighboring zero-injection node j, and for non-zero-injection node y... ij =0; a ij x is a 0-1 phasor representing the association between node i and node j; j This indicates the PMU installation status of node j; I represents the set of all nodes in the network, n is the total number of nodes, and Z represents the PMU installation status of node j. j The phasor is 0-1, indicating whether it is a zero-injection node.

[0012] .

[0013] As a preferred technical solution, when the system is critically observable, the hybrid constraint variable X is composed of the state phasor x and the zero-injection node decision phasor y. , Among them, x i Indicates the PMU installation status of node i, y ij A 0-1 phasor indicates that node i becomes observable from its neighboring zero-injection node j; The critical observable mixed constraint conditions are as follows: , Where A is an n-order node association matrix, representing the degree of association between nodes in the system, and the element a ij The definition is as follows: , Both matrices B and C are obtained from the node connection matrix: , Z i The phasor is 0-1, indicating whether it is a zero-injection node.

[0014] As a preferred technical solution, when the system is not fully observable, a generalized connectivity matrix is ​​constructed based on the unobservable depth constraint, and the node incidence matrix in the inequality constraint of the critical observable optimization model is replaced with the generalized connectivity matrix. The method for constructing the generalized connectivity matrix is ​​as follows: Let the unobservable depth of the system be d. Find a node that is connected to a certain node at a distance of d+1, and connect the two to form a virtual connection relationship. Based on the node relationship after the virtual connection, construct a generalized connection matrix. The element a in the generalized connection matrix is...ij Redefining: .

[0015] As a preferred technical solution, when the system is not fully observable, the constraints of the critical observable optimization model are modified as follows: , Among them, A d Let represent the generalized connectivity matrix at an unobservable depth of d.

[0016] As a preferred technical solution, when the system redundancy is fully observable, the constraints of the critical observable optimization model are modified as follows: , In the formula: b set The number of PMU configurations can be set according to the actual needs of power grid construction or economic conditions. ones(1,n) is a row vector of length n, in which all elements are 1. zeros(1,n*n) represents a row vector of length n×n, in which all elements are 0.

[0017] As a preferred technical solution, the critical observable optimization model is a linear model, and the optimization configuration itself is a 0-1 programming problem, which is solved by a 0-1 integer programming algorithm.

[0018] According to a second aspect of the present invention, a multi-stage PMU optimization configuration system based on observability improvement is provided, the system comprising, based on the aforementioned PMU optimization configuration method: Phase partitioning module: Divides the PMU optimization configuration into multiple phases by defining the unobservable depth of the system; Critical observable optimization model construction module: Constructs a critical observable optimization model; The PMU optimization configuration module employs a multi-stage serial approach. When the PMU is critically observable, it performs optimization configuration based on the critically observable optimization model. When the PMU is not fully observable, it performs optimization configuration by considering the unobservable depth constraint in the critically observable optimization model. When the PMU is redundantly fully observable, it performs optimization configuration by considering the limited number constraint in the critically observable optimization model. This results in an optimization configuration scheme for improving the observability of the PMU from incomplete observability to critical observability and then to redundantly fully observable.

[0019] According to a third aspect of the present invention, an electronic device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the program to implement the method described thereon.

[0020] According to a fourth aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the method described thereon.

[0021] Compared with the prior art, the present invention has the following beneficial effects: This invention employs a multi-stage serial approach, considering the node comprehensive evaluation index to divide the PMU optimization configuration into multiple stages: when the system is not fully observable, the unobservable depth constraint is considered; when the system is redundantly fully observable, a limited number of optimization configurations are performed; and finally, a PMU observability improvement configuration scheme is obtained from incomplete observability to critical observability and then to redundantly fully observable. This can achieve effective PMU optimization configuration when the system has a high degree of unobservability. Attached Figure Description

[0022] Figure 1 is a flow chart of the method of the present invention; Figure 2 This is a schematic diagram illustrating the impact of zero-injection nodes on observability in one embodiment; Figure 3 This is a schematic diagram of the construction process of the generalized connectivity matrix when the unobservable depth is 1 in one embodiment. Figure 4 This is a topology diagram of an IEEE 33 system in one embodiment; Figure 5 This is a comprehensive evaluation index of IEEE 33 system nodes in one embodiment. Figure 6 This is an example of an actual power distribution network topology diagram for a certain region. Figure 7 This is a comprehensive node measurement index for a certain region in one embodiment; Figure 8 This is a PMU configuration scheme for a certain region when d=2 in one embodiment; Figure 9 This is a PMU configuration scheme for a certain region when d=1 in one embodiment; Figure 10 This is a PMU configuration scheme for a certain region when d=0 in one embodiment; Figure 11 This is a PMU configuration scheme in one embodiment when the redundancy in a certain region is completely observable. Figure 12 This is a PMU configuration scheme in one embodiment where the node comprehensive measurement index d=1 is not considered. Detailed Implementation

[0023] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0024] Unless otherwise defined, the technical or scientific terms used in this application shall have the ordinary meaning understood by one of ordinary skill in the art to which this application pertains. The terms “a,” “an,” “an,” “the,” and similar words used in this application do not indicate quantity limitation and may indicate singular or plural. The terms “comprising,” “including,” “having,” and any variations thereof used in this application are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or device that includes a series of steps or modules (units) is not limited to the listed steps or units, but may also include steps or units not listed, or may include other steps or units inherent to these processes, methods, products, or devices. The terms “connected,” “linked,” “coupled,” and similar words used in this application are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. “Multiple” used in this application refers to two or more. “And / or” describes the relationship between related objects, indicating that three relationships may exist; for example, “A and / or B” can represent: A alone, A and B simultaneously, and B alone. The character " / " generally indicates that the preceding and following objects are in an "or" relationship. The terms "first," "second," and "third" used in this application are merely to distinguish similar objects and do not represent a specific ordering of the objects.

[0025] Example 1 This embodiment provides a multi-stage PMU optimization configuration method based on observability improvement. The method adopts a multi-stage serial approach, which divides the PMU optimization configuration into multiple stages by defining the unobservable depth of the system: when the system is critically observable, optimization configuration is performed based on the critical observable optimization model; when the system is not fully observable, optimization configuration is performed by considering the unobservable depth constraint in the critical observable optimization model; and when the system is redundantly fully observable, optimization configuration is performed by considering the limited number constraint in the critical observable optimization model. This results in a PMU observability improvement optimization configuration scheme that progresses from incomplete observability to critical observability and then to redundantly fully observable.

[0026] Specifically, such as Figure 1 As shown, the following steps are included: S1 defines the unobservable depth of the system.

[0027] Unobservable depth is defined as the number of edges traversed by a node to reach its adjacent observable nodes. The maximum value of this unobservable depth across all nodes in the system is taken as the unobservable depth d. A value of d=0 indicates critical observability.

[0028] When the unobservable depth d=2, the state estimation result is not significantly different from the actual value. When the unobservable depth exceeds 3, according to the error propagation principle, the error of the pseudo-measurement constructed for state estimation increases, and the state estimation error also increases accordingly. When d=4 or 5, the state estimation result is basically unusable.

[0029] S2 divides the system into three states based on the depth of unobservability: incompletely observable, critically observable, and redundantly completely observable.

[0030] S3, construct a critically observable optimization model, which includes inequality constraints and equality constraints.

[0031] For a plant with PMU installation, the voltage phasors of its equivalent topology nodes and the current phasors of all outgoing lines are directly observable, and the voltage measurement information of the nodes connected to the installation site can be obtained through circuit laws. Therefore, the nodes connected to the PMU installation node can be considered indirectly observable.

[0032] Based on the above analysis, an observability analysis is performed on a power system with a total of n nodes. First, an n-order node correlation matrix A is defined to represent the correlation degree between the nodes in the system, where the element a... ij The definition is as follows:

[0033] (1) It can be seen that the node association matrix is ​​a sparse matrix composed of 0s and 1s, and the 0 and 1 elements in the matrix reflect the interconnection between the nodes in the system.

[0034] Then, define an n-dimensional column vector X to represent the PMU installation status of each node in the system, where the element x is defined as follows: (2) In this embodiment, the PMU optimization configuration objective of the critical observable optimization model is to minimize the number of PMU configurations, maximize the node comprehensive metric index, and maximize the system measurement redundancy. The determination of the node comprehensive metric index can be found in the content disclosed in patent CN115906353A, and will not be repeated here.

[0035] The critical observable optimization model is shown below: (3) (4) In the formula: N is the total number of system nodes; r i Let w represent the redundancy of node i, defined as the number of times it can be directly measured by the PMU. i Let be the comprehensive metric value for node i. b is a unit column vector. ;x i This indicates the PMU installation status of node i.

[0036] A zero-injection node is a node in the power grid where no additional power flow is injected or emanated; it typically refers to a node without load or generators. Zero-injection nodes are common in systems. Considering the constraints of zero-injection nodes can reduce the number of power management units (PMUs) required and lower their configuration costs.

[0037] like Figure 2 As shown, white represents nodes that can be directly observed, and black represents nodes that cannot be directly observed. Figure 2 In (a) of the above, when only one of the nodes adjacent to node 5, node 3, is unobservable, node 3 can be made observable according to Kirchhoff's Current Law (KCL). Similarly, Figure 2 The 5 nodes in (b) can also become observable.

[0038] Representing the zero-injection node and its neighboring nodes as a set, when all nodes in the set are observable except for one, the only unobservable node can become observable through KCL. Modifying the constraints of equation (4), the constraints for the zero-injection node are as follows:

[0039] (5) In the formula: y ij The 0-1 phasor indicates that node i becomes observable from its neighboring zero-injection node j, and for non-zero-injection node y... ij =0; a ij x is a 0-1 phasor representing the association between node i and node j; j Z represents the PMU installation status of node j; I is the set of all nodes in the network, and n is the total number of nodes. j The phasor is 0-1, indicating whether it is a zero-injection node.

[0040] (6) 1) For non-zero injection nodes ( ), ,For example .

[0041] 2) For zero-injection nodes ( For example, each zero-injection node has a set with an equation, such as .

[0042] When the system is critically observable, the hybrid constraint variable X consists of the state phasor x and the zero-injection node decision phasor y. ij Only elements in the set of zero-injection nodes can be 1, while the vast majority of element values ​​can be determined to be 0, thus the size of the mixed constraint variables becomes very small.

[0043] (7) Among them, x i Indicates the PMU installation status of node i, y ij A 0-1 phasor indicates that node i becomes observable from its neighboring zero-injection node j; The critical observable mixed constraint conditions are as follows: (8) Where A is an n-order node association matrix, representing the degree of association between nodes in the system, and the element a ij The definition is as follows: Both matrices B and C are obtained from the node connection matrix: (9) Z i The phasor is 0-1, indicating whether it is a zero-injection node.

[0044] S4. When the system is critically observable, optimize the configuration based on the critically observable optimization model.

[0045] The critical observable optimization model is a linear model, and the optimization configuration itself is a 0-1 programming problem, which is solved using a 0-1 integer programming algorithm. The solution process is common knowledge in the field, and to avoid ambiguity of the purpose of this application, it will not be described in detail here.

[0046] S5. When the system is not fully observable, add unobservable depth constraints to the inequality constraints of the critical observable optimization model and perform optimization configuration.

[0047] In order to combine unobservable depth with 0-1 integer programming algorithms, it is necessary to represent unobservable depth and use it as a constraint on the optimization model.

[0048] Specifically, a generalized connectivity matrix is ​​constructed based on the unobservable depth constraint, and this generalized connectivity matrix replaces the node incidence matrix in the inequality constraints of the critical observable optimization model. The method for constructing the generalized connectivity matrix is ​​as follows: Let the unobservable depth of the system be d. Find nodes connected to a given node at a distance of d+1, and connect them to form a virtual connection. Construct a generalized connectivity matrix based on these virtual connections. Since the variables in the 0-1 integer programming algorithm can only be 0 or 1, when using the generalized connectivity matrix for incomplete observability optimization, the elements in the generalized connectivity matrix can also only be 0 or 1. Therefore, in the generalized connectivity matrix, nodes at a distance of d+1 are represented as 1, and the original network topology is also represented as a 0-1 relationship. The element a in the generalized connectivity matrix... ij Redefining:

[0049] (10) Figure 3 This diagram illustrates the state when d=1, with solid lines representing the actual connections between nodes. Nodes 2, 3, 4, 6, 7, and 8 are observable nodes, while nodes 1 and 5 are unobservable nodes with an unobservable depth of 1. Therefore, the unobservable depth of the system is d=1. When d=1, it is necessary to find nodes that are 2 units away from a given node and connect them to form a virtual connection. Assume the goal is to handle the unobservable state of node 3:

[0050] 1. Directly connected nodes (connection distance is 1): Nodes 2, 4, and 6.

[0051] 2. Nodes with a connection distance of 2: Find the adjacent nodes of these directly connected nodes (2, 4, 6), exclude the nodes that have already been processed (i.e., 3 itself), and find the new nodes: For node 2: it is directly connected to node 1. Here, node 1 is the node that is 2 units away from node 3.

[0052] For node 4: it is directly connected to node 5. Node 5 is a node that is 2 units away from node 3.

[0053] For node 6: it is directly connected to node 7. Node 7 is a node that is 2 units away from node 3.

[0054] After merging, the nodes that are 2 units away from node 3 are: 1, 5, and 7.

[0055] 3. Construct a virtual connection: Establish a virtual connection (dashed line) between node 3 and nodes 1, 5, and 7, as shown below. Figure 3 As shown.

[0056] The processing method for other nodes is similar: find nodes with a distance of 2 from the original node and establish virtual connections. Through this process, the previously unobservable nodes at depth d=1 have their connectivity expanded due to the introduction of virtual connections, thereby improving the observability of the system. After establishing the virtual connections, construct the generalized connectivity matrix A1. Similarly, construct matrix A2.

[0057] When the system is not fully observable, the matrix A in the inequality constraints of the critical observable optimization model is modified to a generalized connectivity matrix: (11) Among them, A d Let represent the generalized connectivity matrix at an unobservable depth of d.

[0058] That is, by changing the A matrix in the inequality constraint of equation (8) to the generalized connectivity matrix A2 with an unobservable depth of 2, and adding constraints to solve, the optimal configuration with an unobservable depth of 2 can be obtained. Similarly, for an unobservable depth of 1, the A matrix is ​​changed to the generalized connectivity matrix A1 with an unobservable depth of 1.

[0059] S6. When the system redundancy is fully observable, add a limited number of constraints to the equality constraints of the critical observable optimization model to perform optimization configuration.

[0060] When the system redundancy is completely observable, a row of constraints with a limited number of conditions is added to the A matrix in equation (8), modifying the constraints of the critical observable optimization model as follows: (12) In the formula: b set The number of PMUs can be set according to the actual needs or economic conditions of power grid construction; ones(1,n) represents a row vector of length n, where all elements are 1, used to represent the upper limit constraint on the total number of PMUs, which can be multiplied by variables to form a sum; zeros(1,n*n) represents a row vector of length n×n, where all elements are 0, representing variables or system states that are not subject to constraints, ensuring the correct mathematical form of the model. These parameters, combined with A in the formula... eq and A ineq The matrices together construct the optimization constraints, which are used to describe the number of PMU configurations (by b). set (Limitations) and the observability and redundancy of the power grid.

[0061] Example 2 To verify this algorithm, this embodiment uses the IEEE 33 system and a real distribution network in a certain region as simulation objects. The specific simulation steps are as follows: (1) Calculate the node metric index for each node: Based on the network topology and power flow distribution, calculate the node metric index consisting of distribution network node degree, distribution network spatiotemporal correlation and node power proportion.

[0062] (2) Determine the comprehensive evaluation index of the node.

[0063] (3) Construct a multi-stage PMU configuration model with improved observability: By adding different mixed constraints to the objective function, an optimization configuration model is established with the goal of minimizing the number of optimized configurations, maximizing the node metric index, and maximizing the system redundancy.

[0064] (4) The optimal configuration scheme is obtained by solving the model based on the 0-1 integer programming algorithm.

[0065] According to Figure 4 The IEEE 33 system topology, node impedance matrix and system power flow distribution are used to calculate the distribution network node degree, distribution network spatiotemporal correlation and node power ratio index.

[0066] The subjective weights of each indicator are obtained based on the analytic hierarchy process (AHP), and the subjective judgment matrix is ​​established as follows: (13) The calculation steps based on the analytic hierarchy process (AHP) are as follows: The largest eigenvalue and its corresponding eigenphasor of the subjective judgment matrix *mat* are calculated. The eigenphasors are normalized, and a consistency test is performed to determine whether the subjective judgment matrix is ​​contradictory. The consistency ratio CR = 0.037 < 0.1, indicating acceptable consistency. Objective weights are calculated using the improved entropy weight method, resulting in the comprehensive subjective-objective weight *k* for the three indicators. The weights are shown in Table 1 below.

[0067] Table 1. Weights of IEEE 33 System Indicators

[0068] Since this paper focuses on optimizing configuration to improve observability, the importance of network topology is considered greater than that of network parameters and operating mode in the setting of subjective weights.

[0069] Multiplying the normalized standard matrix P by the corresponding node comprehensive evaluation index k yields the node comprehensive evaluation index w, as shown below. Figure 5 As shown.

[0070] The node comprehensive evaluation index reflects the importance of each node. For example, nodes 2, 3, 6, 14, and 23 have relatively high comprehensive evaluation indexes and can be considered as more important nodes in the system. By using the node comprehensive evaluation index, the importance of different nodes can be better distinguished, allowing for the priority allocation of PMUs to important nodes.

[0071] By adding observability enhancement hybrid constraints to the model, a multi-stage PMU configuration scheme is obtained based on the 0-1 integer programming algorithm, progressing from incomplete observability to critical observability and then to redundant complete observability, as shown in Table 2. Due to the high cost of PMU configuration, the optimal number of PMUs is typically limited to about half the total number of system nodes. Exceeding this number, while achieving further measurement redundancy, limits the configuration to 15 PMUs for redundant observability. This paper also compares the impact of considering node comprehensive performance metrics on PMU optimal configuration; the unobservable depth is represented by d.

[0072] Table 2 PMU Configuration Scheme for IEEE 33 System

[0073] As shown in Table 2, the optimized PMU configuration considering the node comprehensive evaluation index did not increase the number of PMUs. When the observability is critical, nodes with higher comprehensive evaluation indices (2, 3, 6, 14, and 23) were prioritized. This ensured that PMUs were configured at critical nodes while further improving system redundancy and maximizing the observable area.

[0074] Furthermore, the multi-stage PMU optimization configuration considered in this embodiment is not a staged optimization configuration of the global optimal solution of the PMU. For example, the optimal configuration positions at unobservable depths of 2 and 1 are not completely inclusive. Since the distribution network is closely related to the electricity consumption behavior of users, and the monitoring needs of different distribution networks are different, this embodiment provides phased solutions for PMU configurations of distribution networks with different observability requirements.

[0075] To further verify the effectiveness of the proposed method in a real power grid, a simulation was conducted using a real distribution network system in a certain region. The power grid topology is as follows: Figure 6 As shown, the black nodes are nodes with zero injection.

[0076] Based on the actual distribution network system topology, node impedance matrix, and system power flow distribution in a certain region, the distribution network nodality, spatiotemporal correlation, and node power proportion indices are calculated. The subjective and objective comprehensive weights k of the three indices are calculated, as shown in Table 3 below.

[0077] Table 3. Indicator Weights of a Regional Distribution Network System

[0078] Multiplying the normalized standard matrix P by the corresponding comprehensive weight k yields the node comprehensive measurement index w, as shown below. Figure 7 As shown.

[0079] Add observability enhancement hybrid constraints to the model, and solve the multi-stage PMU configuration scheme from incomplete observability to critical observability and then to redundant complete observability based on the 0-1 integer programming algorithm, as shown in Table 4. Among them, the number of redundant observable PMUs is limited to 30.

[0080] Table 4. Multi-stage PMU configuration scheme for a case study of Feeder 11 in a certain region

[0081] Figure 8 This is a schematic diagram of the multi-stage PMU configuration locations based on the observability improvement of the Qi11 power distribution system in a certain region. In this diagram, gray nodes are PMU configuration nodes, black nodes are zero-injection nodes, and nodes with dashed borders are zero-injection nodes with PMU configuration.

[0082] The comparison of the optimized configuration schemes considering and not considering the node comprehensive measurement index in the above figure shows that when d=1, without considering the node comprehensive measurement index, the system end nodes 12, 16, 55, and 57 with smaller index values ​​were selected. This resulted in insufficient utilization of PMU measurement data, leading to lower system redundancy compared to the scheme considering the node comprehensive measurement index. However, by considering the node comprehensive measurement index, nodes such as 14 and 31 with larger index values ​​can be selected, achieving greater observability without increasing the number of PMUs. Furthermore, compared with the configuration results of the IEEE 33 system, for nodes with many branches in the distribution network, the optimization configuration considering the node comprehensive measurement index shows a more significant improvement in system redundancy observability compared to the scheme without considering the index.

[0083] The actual distribution network system has 10 zero-injection nodes, which are considered as general transmission nodes. The monitoring requirements for PMUs at these zero-injection nodes are not as high as those at other nodes. The proposed method optimizes the PMU configuration to approximately one-third of the total number of nodes based on the network's critical observability requirement. With the same number of PMUs, considering the node comprehensive evaluation index, optimizing the configuration at critical observability requires only 20 PMUs to achieve the system redundancy of 30 PMUs without considering the node comprehensive evaluation index. Therefore, considering the node comprehensive evaluation index further optimizes the PMU configuration location at each stage, achieving greater redundancy observability for the distribution network.

[0084] Example 3 The above is an introduction to the method embodiments. The following system embodiments will further illustrate the solution of the present invention.

[0085] A multi-stage PMU optimization configuration system based on observability improvement, based on the PMU optimization configuration method described in Example 1, the system includes: Phase partitioning module: Divides the PMU optimization configuration into multiple phases by defining the unobservable depth of the system; Critical observable optimization model construction module: Constructs a critical observable optimization model; The PMU optimization configuration module employs a multi-stage serial approach. When the PMU is critically observable, it performs optimization configuration based on the critically observable optimization model. When the PMU is not fully observable, it performs optimization configuration by considering the unobservable depth constraint in the critically observable optimization model. When the PMU is redundantly fully observable, it performs optimization configuration by considering the limited number constraint in the critically observable optimization model. This results in an optimization configuration scheme for improving the observability of the PMU from incomplete observability to critical observability and then to redundantly fully observable.

[0086] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the described module can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0087] Example 4 The electronic device of this invention includes a central processing unit (CPU), which can perform various appropriate actions and processes according to computer program instructions stored in read-only memory (ROM) or loaded from a storage unit into random access memory (RAM). The RAM may also store various programs and data required for device operation. The CPU, ROM, and RAM are interconnected via a bus. Input / output (I / O) interfaces are also connected to the bus.

[0088] Multiple components in the device are connected to the I / O interface, including: input units such as keyboards and mice; output units such as various types of displays and speakers; storage units such as disks and optical discs; and communication units such as network interface cards (NICs), modems, and wireless transceivers. The communication unit allows the device to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0089] The processing unit executes the various methods and processes described above, such as methods S1 to S6. For example, in some embodiments, methods S1 to S6 may be implemented as computer software programs tangibly contained in a machine-readable medium, such as a storage unit. In some embodiments, part or all of the computer program may be loaded and / or installed on the device via ROM and / or a communication unit. When the computer program is loaded into RAM and executed by the CPU, one or more steps of methods S1 to S6 described above may be performed. Alternatively, in other embodiments, the CPU may be configured to execute methods S1 to S6 by any other suitable means (e.g., by means of firmware).

[0090] The functions described above in this document can be performed, at least in part, by one or more hardware logic components. For example, exemplary types of hardware logic components that can be used, without limitation, include: Field Programmable Gate Arrays (FPGAs), Application-Specific Integrated Circuits (ASICs), Application Standard Products (ASSPs), System-on-Chip (SoCs), Complex Programmable Logic Devices (CPLDs), and so on.

[0091] The program code used to implement the methods of the present invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code can be executed entirely on the machine, partially on the machine, as a standalone software package partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0092] In the context of this invention, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable media can include, but are not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0093] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and such modifications or substitutions are intended to be within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection of the claims.

Claims

1. A multi-stage PMU optimization configuration method based on observability improvement, characterized in that: This method adopts a multi-stage serial method and divides the PMU optimization configuration into multiple stages by defining the unobservable depth of the system: when it is critically observable, the optimization configuration is performed based on the critically observable optimization model; when it is not completely observable, the optimization configuration is performed by considering the unobservable depth constraint in the critically observable optimization model; when the redundancy is fully observable, the optimization configuration is performed by considering the limited number constraint in the critically observable optimization model. The result is an optimization configuration scheme for improving the observability of PMU from incompletely observable to critically observable and then to redundantly fully observable.

2. The multi-stage PMU optimization configuration method based on observability improvement according to claim 1 is characterized in that: The method comprises the following steps: Define the unobservable depth of the system; According to the unobservable depth, the system is divided into three states: incomplete observability, critical observability and redundant complete observability; Constructing a critical observable optimization model, wherein the critical observable optimization model includes an inequality constraint and an equality constraint; When the system is not completely observable, unobservable depth constraints are added to the inequality constraints of the critical observable optimization model to perform the optimization configuration; When the system is critically observable, the optimal configuration is performed based on the critically observable optimization model; When the system redundancy is completely observable, a limited number of constraints are added to the equality constraints of the critical observable optimization model to perform the optimization configuration.

3. The multi-stage PMU optimization configuration method based on observability improvement according to claim 1 is characterized in that: The unobservable depth is defined as the number of edges that a node passes through to reach an adjacent observable node, and the maximum value of all nodes in the system is taken as the unobservable depth of the system.

4. The multi-stage PMU optimization configuration method based on observability improvement according to claim 1 is characterized in that: The PMU optimization configuration objectives of the critical observable optimization model are to minimize the number of PMU configurations, maximize the node comprehensive measurement index, and maximize the system measurement redundancy.

5. The multi-stage PMU optimization configuration method based on observability improvement according to claim 1 is characterized in that: The critical observable optimization model is as follows: ， ， Where: N is the total number of system nodes; r i is the redundancy of node i, which is defined as the number of times it can be directly measured by the PMU, and w i is the comprehensive measurement index value of node i, ; b is the unit column vector, ;x i Indicates the PMU installation status of node i, 。 6. The multi-stage PMU optimization configuration method based on observability improvement according to claim 1 is characterized in that: The constraints of the critical observable optimization model include zero injection node constraints: ， Where: y ij is a 0-1 judgment phasor, indicating that node i becomes observable by the adjacent zero injection node j, and for non-zero injection node y ij =0; a ij is a 0-1 phasor, indicating the relationship between node i and node j; j represents the PMU installation status of node j; I is the set of all nodes in the network, n is the total number of nodes, Z j It is a 0-1 judgment phase quantity, indicating whether it is a zero injection node. .

7. The multi-stage PMU optimization configuration method based on observability improvement according to claim 1 is characterized in that: When the system is critical, the hybrid constraint variable X is composed of the state phasor x and the zero injection node judgment phasor y. ， Among them, x i Indicates the PMU installation status of node i, y ij It is a 0-1 judgment phasor, indicating that node i becomes observable by injecting adjacent zeros into node j; The critical observable mixing constraints are as follows: ， Among them, A is an n-order node association matrix, which represents the degree of association between each node in the system, and the element a ij The definition is as follows: ， Both B and C matrices are obtained from the node connection relationship matrix: ， Z i It is a 0-1 judgment phase quantity, indicating whether it is a zero injection node.

8. The multi-stage PMU optimization configuration method based on observability improvement according to claim 1 is characterized in that: When the system is not completely observable, a generalized connection matrix is ​​constructed according to the unobservable depth constraint, and the generalized connection matrix is ​​used to replace the node association matrix in the inequality constraint of the critical observable optimization model, wherein the construction method of the generalized connection matrix is: Assume that the unobservable depth of the system is d, find a node that is connected to a certain node at a distance of d+1, connect the two to form a virtual connection relationship, and construct a generalized connection matrix based on the node relationship after virtual connection. The element a in the generalized connection matrix is ij Redefine as: 。 9. The multi-stage PMU optimization configuration method based on observability improvement according to claim 7 is characterized in that: When the system is not completely observable, the constraints of the critical observable optimization model are modified as follows: ， Among them, A d represents the generalized connectivity matrix when the unobservable depth is d.

10. The multi-stage PMU optimization configuration method based on observability improvement according to claim 7, characterized in that: When the system redundancy is fully observable, the constraints of the critical observable optimization model are modified as follows: ， Where: b set is the number of PMU configurations that can be set according to the actual needs of power grid construction or economic conditions. ones(1,n) is a row vector of length n, all elements in the vector are 1, and zeros(1,n*n) represents a row vector of length n×n, all elements in the vector are 0.

11. The multi-stage PMU optimization configuration method based on observability improvement according to claim 1, characterized in that: The critical observable optimization model is a linear model, and the optimization configuration itself is a 0-1 programming problem, and the model is solved using a 0-1 integer programming algorithm.

12. A multi-stage PMU optimization configuration system based on observability improvement, characterized in that: Based on the PMU optimization configuration method according to any one of claims 1 to 11, the system comprises: Phase division module: divides the PMU optimization configuration into multiple stages by defining the unobservable depth of the system; Critical observable optimization model construction module: construct critical observable optimization model; PMU optimization configuration module: adopts a multi-stage serial method. When it is critically observable, it is optimized based on the critically observable optimization model. When it is not completely observable, it is optimized by considering the unobservable depth constraints in the critically observable optimization model. When it is redundantly fully observable, it is optimized by considering the limited number constraints in the critically observable optimization model. The optimal configuration scheme for improving the observability of PMU from incompletely observable to critically observable and then to redundantly fully observable is obtained.

13. An electronic device comprising a memory and a processor, wherein a computer program is stored in the memory, wherein: When the processor executes the program, the method according to any one of claims 1 to 11 is implemented.

14. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the method according to any one of claims 1 to 11 is implemented.

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