Distribution network distinguishing research method for reactive equipment configuration
By using the Newton-Ravson method and the improved AP clustering algorithm in the grid partitioning method, the problems of staticity and lack of flexibility in the traditional grid partitioning method are solved, and the efficient, stable operation and adaptability of the power grid are achieved.
Patent Information
- Application Number
- CN202411713976.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-27
- Publication Date
- 2025-03-04
AI Technical Summary
Traditional grid partitioning methods are static, lack flexibility and automation, and are difficult to adapt to dynamic load changes and new energy access, resulting in insufficient voltage stability and reactive power management.
A distribution network partitioning method for reactive equipment configuration is proposed. By reading the power grid data, a node admission matrix is formed, a Newton-Ravson normal linearized flow equation is used to calculate the Jacqueline matrix and sensitivity matrix, a partition optimization model is established, and a network node clustering analysis and partition optimization are carried out through the improved AP clustering algorithm.
It realizes fast and effective grid partitioning, improves the operating efficiency and stability of the power grid, can adapt to dynamic load changes and new energy access, and meets the efficient operation and expansion needs of the power grid.
Smart Images
Figure CN119561171A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of power systems, and in particular relates to a distribution network partitioning method for reactive equipment configuration. Background Art
[0002] With the rapid development of social economy and the continuous improvement of people's living standards, the rapid growth of power grid load and the continuous expansion of scale have put forward higher requirements for the stability, reliability and economy of the power system. As an important infrastructure for power transmission and distribution, the optimization management of the power grid is the key to ensure the efficient operation of the power system, and the optimization of power grid zoning is an important task in the planning and operation of the power system.
[0003] Traditional grid zoning methods have the disadvantages of being static, lacking flexibility and automation, and are difficult to adapt to dynamic changes in loads and the access of new energy sources, resulting in insufficient voltage stability and reactive power management, complex calculations and reliance on experience, which limits the efficient operation and expansion of the grid. Therefore, it is necessary to explore more intelligent and flexible zoning methods to improve the operating efficiency and stability of the power system and meet the ever-changing needs and challenges. Summary of the invention
[0004] In order to solve the above problems, the present invention proposes a distribution network partitioning method for reactive equipment configuration, which can quickly and effectively solve the above problems.
[0005] To achieve the above object, the technical solution adopted by the present invention is: a distribution network partitioning method for reactive equipment configuration, comprising the steps of:
[0006] S10: Read the power grid data, obtain the node and branch information to form a node admittance matrix;
[0007] S20: Linearize the power flow equation using the Newton-Raphson method to obtain the Jacobian matrix;
[0008] S30: The sensitivity matrix is obtained through the Jacobian matrix to calculate the electrical distance between each node and establish a partition optimization model;
[0009] S40: performing cluster analysis of network nodes based on electrical distances using an improved AP clustering algorithm to perform preliminary partitioning of PQ nodes;
[0010] S50: Calculate the electrical distances between the isolated node and the nodes adjacent to the PV node, and merge them into the area with the strongest electrical coupling with them;
[0011] S60: Determine whether the partition satisfies reactive power balance, constraint conditions and network loss reduction. If so, the partition ends. Otherwise, the critical point of the adjustment area continues to be optimized.
[0012] Furthermore, the grid data is obtained to obtain the corresponding branch and node information to form a node admittance matrix, and the power flow equation is linearized using the Newton-Raphson method to obtain the Jacobian matrix. Including: The power flow equation of N nodes is converted into polar coordinate form:
[0013] In the above formula, i∈[1,N],P i and Q i are the active and reactive power injected into the node respectively; V i is the voltage amplitude of node i; θ ij is the phase angle difference between node i and node j; G ij and B ij are the real and imaginary parts of the node admittance matrix respectively; j∈i means that node j is connected to node i.
[0014] Furthermore, the formula (1) is transformed into:
[0015] In the above formula, ΔP i and ΔQ i are the changes of active power and reactive power injected into node i respectively; P Gi and Q Gi are the active and reactive power of generator node i, respectively, P Li and Q Li are the active and reactive powers of load node i respectively.
[0016] Furthermore, by transforming formula (2), we can obtain:
[0017] In the above formula, ΔP and ΔQ are the changes in active and reactive power injected into the node; Δθ and ΔV are the changes in the node voltage phase angle and amplitude. J is the Jacobian matrix used by the Newton-Raphson method to solve the power flow.
[0018] Furthermore, by setting the change in active power ΔP=0 in equation (3), eliminating Δθ in equation (3), we can obtain the relationship between ΔQ and ΔV.
[0019] In the above formula, M VQ It is the sensitivity matrix obtained by the Jacobian matrix; J Pθ , J PV , J Qθ , J QV This is the submodule of the Jacobian matrix.
[0020] Furthermore, from the reactive power equation in equation (2), we can directly derive ΔQ with respect to ΔV. M qv =(M vq ) -1 (7)
[0021] In the above formula, M qv is the voltage amplitude change of node j ΔV j Reactive power change ΔQ for node i i The sensitivity matrix.
[0022] Furthermore, considering that the electrical distance between two nodes in the electrical distance matrix is symmetrical, the electrical distance between node i and node j is defined as:
[0022] Furthermore, a partition optimization model is established, including constraints and objective functions.
[0023] U imin <U i <U imax (9)
[0024] I i <I imax (10)
[0025]
[0026] Furthermore, equation (9) is the node voltage constraint; equation (10) is the branch current constraint; and equation (11) is the objective function optimized with network loss.
[0027] Furthermore, in formula (9), U i , U imin , U imax are the actual voltage, lower limit and upper limit of the voltage at node i respectively; in formula (10), I i is the actual current of the ith line; I imax is the maximum current allowed by the i-th line; in formula (11), k is the number of branches, V is the node voltage, and θ is the phase angle; G ij ,θ ij are the conductance and phase difference between node i and node j respectively.
[0028] Furthermore, the AP clustering algorithm is improved and a bias parameter is introduced to adjust the convergence system, which can effectively make dynamic adjustments along with the algorithm, accelerate the convergence process of the algorithm, and ensure the convergence of the algorithm.
[0029] Furthermore, the bias parameter is defined as follows:
[0030] Furthermore, the formulas for updating Responsibility and Availability are as follows:
[0031] In the above formula, R new (i, k) represents the attraction, which is used to describe the degree to which point k is suitable as the cluster center of data point i. new (i,k) represents the degree of belonging, which is used to describe the suitability of point i to select point k as its cluster center. ρ represents the bias parameter and λ represents the damping factor.
[0032] Furthermore, the AP clustering algorithm is improved, and an adaptive optimization method is introduced to adaptively optimize the bias parameters and damping factors, which can automate the selection of parameters, increase the flexibility and adaptability of the clustering algorithm, and improve the optimization efficiency.
[0033] Furthermore, the specific process is as follows: bias parameter ρ is adaptive: first, the bias parameter ρ is taken as half of the original one, and the number of clusters γ1 is obtained through iterative convergence, and the bias parameter is gradually reduced by step size l to obtain all γ 1,2,3,...l The number of clusters,
[0034] Furthermore, the step size formula is as follows:
[0035] In the above formula, N is the total number of data points, The number of samples added, N υ is the number of data point changes.
[0036] Furthermore, the Davidson-Boulding Index (DBI) was used to determine the optimal number of clusters.
[0037] Furthermore, the damping factor λ is adaptive: R new (i,k) and A new Each time (i, k) is updated, the oscillation index OI is used to detect whether the algorithm is oscillating.
[0038] Furthermore, the formula for the oscillation OI is:
[0039] In the above formula, δ is the number of times the number of iterative clustering is greater than zero, and T is the number of iterations.
[0040] Furthermore, the greater the oscillation degree, the more violent the oscillation is, and vice versa. If oscillation occurs, the value of the damping factor λ is increased in steps of 0.1*OI.
[0041] Furthermore, it is determined whether there are isolated nodes, and if so, the isolated nodes are merged. After the PQ nodes are initially partitioned by improved AP clustering, it is first determined whether there are isolated nodes, that is, single nodes that do not contain PV nodes. If there are isolated nodes, the electrical distance between the partition nodes connected to the isolated nodes is calculated. The electrical distance represents the coupling strength between nodes, and the isolated nodes are merged into the partition with the strongest coupling strength.
[0042] Furthermore, for a PV node connected to only one PQ node, the PV node is directly merged into the partition where the PQ node is located.
[0043] Furthermore, if there are multiple PQ nodes connected to the PV node, the electrical distances between the PV node and each PQ node are calculated and merged into the partition where the PQ node with the strongest electrical coupling is located.
[0044] Furthermore, it is determined whether all conditions are met, including reactive power balance conditions, objective functions and constraints. If not, the boundaries of the partitions are adjusted and the optimization is continued until all conditions are met, which is the optimal partition result. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 It is a flow chart of a distribution network partitioning method for reactive equipment configuration. Figure 2 Improved AP clustering algorithm flow chart Figure 3 This is a schematic diagram of the AP clustering model. Specific implementation plan
[0001] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention is further described below in conjunction with the accompanying drawings.
[0002] In this embodiment, the present invention proposes a distribution network partitioning method for reactive equipment configuration, comprising the steps of:
[0003] S10: Read the power grid data, obtain the node and branch information to form a node admittance matrix;
[0004] S20: Linearize the power flow equation using the Newton-Raphson method to obtain the Jacobian matrix;
[0005] S30: The sensitivity matrix is obtained through the Jacobian matrix to calculate the electrical distance between each node and establish a partition optimization model;
[0006] S40: performing cluster analysis of network nodes based on electrical distances using an improved AP clustering algorithm to perform preliminary partitioning of PQ nodes;
[0007] S50: Calculate the electrical distances between the isolated node and the nodes adjacent to the PV node, and merge them into the area with the strongest electrical coupling with them;
[0008] S60: Determine whether the partition satisfies reactive power balance, constraint conditions and network loss reduction. If so, the partition ends. Otherwise, the critical point of the adjustment area continues to be optimized.
[0009] As an optimization solution for the above embodiment, the grid data is obtained to obtain the corresponding branch and node information to form a node admittance matrix, and the power flow equation is linearized using the Newton-Raphson method to obtain the Jacobian matrix. include: The power flow equation of N nodes is converted into polar coordinate form:
[0010] In the above formula, i∈[1,N],P i and Q i are the active and reactive power injected into the node respectively; V i is the voltage amplitude of node i; θ ij is the phase angle difference between node i and node j; G ij and B ij are the real and imaginary parts of the node admittance matrix respectively; j∈i means that node j is connected to node i.
[0011] As an optimization solution of the above embodiment, formula (1) is transformed to obtain:
[0012] In the above formula, ΔP i and ΔQ i are the changes of active power and reactive power injected into node i respectively; P Gi and Q Gi are the active and reactive power of generator node i, respectively, P Li and Q Li are the active and reactive powers of load node i respectively.
[0013] As an optimization solution of the above embodiment, formula (2) is transformed to obtain:
[0014] In the above formula, ΔP and ΔQ are the changes in active and reactive power injected into the node; Δθ and ΔV are the changes in the node voltage phase angle and amplitude. J is the Jacobian matrix used by the Newton-Raphson method to solve the power flow.
[0015] As an optimization solution of the above embodiment, let the change of active power ΔP in equation (3) = 0, eliminate Δθ in equation (3), and obtain the relationship between ΔQ and ΔV.
[0016] In the above formula, M VQ It is the sensitivity matrix obtained by the Jacobian matrix; J Pθ , J PV , J Qθ , J QV This is the submodule of the Jacobian matrix.
[0020] As an optimization solution of the above embodiment, the derivative of ΔQ with respect to ΔV is directly obtained from the reactive power equation in equation (2). M qv =(M vq ) -1 (7)
[0017] In the above formula, M qv is the voltage amplitude change of node j ΔV j Reactive power change ΔQ for node i i The sensitivity matrix.
[0016] As an optimization solution of the above embodiment, considering that the electrical distance between two nodes in the electrical distance matrix is symmetrical, the electrical distance between node i and node j is defined as:
[0018] As an optimization solution of the above embodiment, a partition optimization model is established, including constraint conditions and objective functions.
[0019] U imin <U i <U imax (9)
[0020] I i <I imax (10)
[0021]
[0022] As an optimization scheme for the above embodiment, equation (9) is the node voltage constraint; equation (10) is the branch current constraint; and equation (11) is the objective function for optimizing network loss.
[0023] As an optimization solution of the above embodiment, in formula (9), U i , U imin , U imaxare the actual voltage, lower limit and upper limit of the voltage at node i respectively; in formula (10), I i is the actual current of the ith line; I imax is the maximum current allowed by the i-th line; in formula (11), k is the number of branches, V is the node voltage, and θ is the phase angle; G ij ,θ ij are the conductance and phase difference between node i and node j respectively.
[0024] As an optimization solution for the above embodiment, the AP clustering algorithm is improved and a bias parameter is introduced to adjust the convergence system, which can effectively make dynamic adjustments along with the algorithm, accelerate the convergence process of the algorithm, and ensure the convergence of the algorithm.
[0025] As an optimization solution of the above embodiment, the bias parameter is defined as follows:
[0026] As an optimization solution of the above embodiment, the formula for updating Responsibility and Availability is as follows:
[0027] In the above formula, R new (i, k) represents the attraction, which is used to describe the degree to which point k is suitable as the cluster center of data point i. new (i,k) represents the degree of belonging, which is used to describe the suitability of point i to select point k as its cluster center. ρ represents the bias parameter and λ represents the damping factor.
[0028] As an optimization solution for the above embodiment, the AP clustering algorithm is improved, and an adaptive optimization method is introduced to adaptively optimize the bias parameters and damping factors, which can automate the selection of parameters, increase the flexibility and adaptability of the clustering algorithm, and improve the optimization efficiency.
[0029] As an optimization scheme of the above embodiment, the specific process is as follows: bias parameter ρ is adaptive: first, the bias parameter ρ is taken as half of the original one, and the number of clusters γ1 is obtained through iterative convergence, and the bias parameter is gradually reduced by step size l to obtain all γ 1,2,3,...l The number of clusters,
[0030] As an optimization solution of the above embodiment, the step length formula is as follows:
[0031] In the above formula, N is the total number of data points, The number of samples added, N υ is the number of data point changes.
[0032] As an optimization solution of the above embodiment, the Davidson-Boulding Index (DBI) is used to determine the optimal number of clusters.
[0033] As an optimization solution of the above embodiment, the damping factor λ is adaptive: R new (i,k) and A new Each time (i, k) is updated, the oscillation index OI is used to detect whether the algorithm is oscillating.
[0034] As an optimization solution of the above embodiment, the formula of the oscillation degree OI is:
[0035] In the above formula, δ is the number of times the number of iterative clustering is greater than zero, and T is the number of iterations.
[0036] As an optimization solution of the above embodiment, the larger the oscillation degree, the more violent the oscillation, and vice versa. If oscillation occurs, the value of the damping factor λ is increased in steps of 0.1*OI.
[0037] As an optimization solution of the above embodiment, it is determined whether there are isolated nodes, and if so, the isolated nodes are merged. After the PQ nodes are preliminarily partitioned by improved AP clustering, it is first determined whether there are isolated nodes, that is, single nodes that do not contain PV nodes. If there are isolated nodes, the electrical distance between the partition nodes connected to the isolated nodes is calculated. The electrical distance represents the coupling strength between the nodes, and the isolated nodes are merged into the partition with the strongest coupling strength.
[0038] As an optimization solution of the above embodiment, for a PV node connected to only one PQ node, the PV node is directly merged into the partition where the PQ node is located.
[0039] As an optimization solution of the above embodiment, if multiple PQ nodes are connected to a PV node, the electrical distance between the PV node and each PQ node is calculated and the PV node is merged into the partition where the PQ node with the strongest electrical coupling is located.
[0040] As an optimization scheme of the above embodiment, it is determined whether all conditions are met, including reactive power balance conditions, objective functions and constraints. If not all conditions are met, the boundaries of the partitions are adjusted and the optimization is continued until all conditions are met, which is the optimal partition result.
[0041] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.
Claims
1. A distribution network partitioning method for reactive equipment configuration, characterized in that: Includes steps: S10: Read the power grid data, obtain the node and branch information to form a node admittance matrix; S20: Linearize the power flow equation using the Newton-Raphson method to obtain the Jacobian matrix; S30: The sensitivity matrix is obtained through the Jacobian matrix to calculate the electrical distance between each node and establish a partition optimization model; S40: performing cluster analysis of network nodes based on electrical distances using an improved AP clustering algorithm to perform preliminary partitioning of PQ nodes; S50: Calculate the electrical distances between the isolated node and the nodes adjacent to the PV node, and merge them into the area with the strongest electrical coupling with them; S60: Determine whether the partition satisfies reactive power balance, constraint conditions and network loss reduction. If so, the partition ends. Otherwise, the critical point of the adjustment area continues to be optimized.
2. A distribution network partitioning method for reactive equipment configuration according to claim 1, characterized in that: Read the grid data, obtain the corresponding branch and node information to form the node admittance matrix, and use the Newton-Raphson method to linearize the power flow equation to obtain the Jacobian matrix. Including: The power flow equation of N nodes is converted into polar coordinate form: Where i∈[1,N],P i and Q i are the active and reactive power injected into the node respectively; V i is the voltage amplitude of node i; θ ij is the phase angle difference between node i and node j; G ij and B ij are the real and imaginary parts of the node admittance matrix respectively; j∈i means that node j is connected to node i. Transforming formula (1) yields: In the formula, ΔP i and ΔQ i are the changes of active power and reactive power injected into node i respectively; P Gi and Q Gi are the active and reactive power of generator node i, respectively, P Li and Q Li are the active and reactive power of load node i respectively. Transforming equation (2) yields: Where ΔP and ΔQ are the changes in active and reactive power injected into the node; Δθ and ΔV are the changes in the node voltage phase angle and amplitude. J is the Jacobian matrix used by the Newton-Raphson method to solve the power flow.
3. A distribution network partitioning method for reactive equipment configuration according to claim 1, characterized in that: The sensitivity matrix is obtained through the Jacobian matrix to calculate the electrical distance between each node. Including: Let the change in active power ΔP=0 in equation (3), eliminate Δθ in equation (3), and obtain the relationship between ΔQ and ΔV. Where M VQ It is the sensitivity matrix obtained by the Jacobian matrix; J Pθ , J PV , J Qθ , J QV This is the submodule of the Jacobian matrix. From the reactive power equation in equation (2), we can directly derive ΔQ with respect to ΔV. M qv =(M vq ) -1 (7) Where M qv is the voltage amplitude change of node j ΔV j Reactive power change ΔQ for node i i Considering that the electrical distance between two nodes in the electrical distance matrix is symmetrical, the electrical distance between node i and node j is defined as:
4. A distribution network partitioning method for reactive equipment configuration according to claim 1, characterized in that: Establish a partition optimization model. Including: Constraints: (1) Node voltage constraints IN imin <In i <In imax (9) Where: U i , U imin , U imax are the actual voltage, lower limit and upper limit of the voltage at node i respectively. (2) Branch current constraints I i <I imax (10) Where: I i is the actual current of the ith line; I imax The maximum current allowed for the i-th circuit. Objective function: Select the minimum network loss as the objective function: Where k is the number of branches, V is the node voltage, and θ is the phase angle; G ij ,θ ij are the conductance and phase difference between node i and node j respectively.
5. A distribution network partitioning method for reactive equipment configuration according to claim 1, characterized in that: Improve AP clustering algorithm, including: (1) Introducing bias parameters to adjust the convergence coefficient The introduction of bias parameters can effectively adjust dynamically with the algorithm, which can accelerate the convergence process of the algorithm and ensure the convergence of the algorithm. The bias parameters are defined as follows: The formulas for updating Responsibility and Availability are as follows: In the formula, R new (i, k) represents the attraction, which is used to describe the degree to which point k is suitable as the cluster center of data point i. new (i,k) represents the degree of belonging, which is used to describe the suitability of point i to select point k as its cluster center. ρ represents the bias parameter and λ represents the damping factor. (2) Introducing adaptive optimization methods The introduction of adaptive optimization method to adaptively optimize the bias parameters and damping factors can automate the selection of parameters, increase the flexibility and adaptability of the clustering algorithm, and improve the optimization efficiency. The specific process is as follows: Bias parameter ρ is adaptive: first, the bias parameter ρ is taken as half of the original one, and the number of clusters γ1 is obtained through iterative convergence. The bias parameter is gradually reduced by the step size l to obtain all γ 1,2,3,...l The number of clusters, the step size formula is as follows: Where N is the total number of data points, The number of samples added, N υ is the number of data point changes. The Davidson-Boulding Index (DBI) was used to determine the optimal number of clusters. Damping factor λ adaptive: R new (i,k) and A new Every time (i, k) is updated, the oscillation OI is used to detect whether the algorithm is oscillating. The formula of oscillation OI is: Where δ is the number of times the number of iterative clustering is greater than zero, and T is the number of iterations. The larger the oscillation degree, the more violent the oscillation, and vice versa. If oscillation occurs, the value of the damping factor λ is increased by a step size of 0.1*OI.
6. A distribution network partitioning method for reactive equipment configuration according to claim 1, characterized in that: Merge isolated nodes and PV nodes, including: After the PQ nodes are initially partitioned by improved AP clustering, first determine whether there is an isolated node, that is, a single node that does not contain a PV node. If there is an isolated node, calculate the electrical distance between the partition nodes connected to the isolated node. The electrical distance represents the coupling strength between nodes, and the isolated node is merged into the partition with the strongest coupling strength. If there is no isolated node, for a PV node that is only connected to one PQ node, directly merge this PV node into the partition where the PQ node is located. If there are multiple PQ nodes connected to the PV node, calculate the electrical distance between this PV node and each PQ node, and merge it into the partition where the PQ node with the strongest electrical coupling is located.
7. A distribution network partitioning method for reactive equipment configuration according to claim 1, characterized in that: Determine whether the conditions are met, otherwise continue to optimize the critical points of the adjustment area, including: The reactive power balance means that the reactive power output in each partition is greater than the reactive power of the load and satisfies the objective function and constraint conditions. If not, the boundary of the partition is adjusted and the optimization is continued until all conditions are met.