Method and system for computing voltage-active power sensitivity at power system nodes

Abstract

A method and system for computing voltage-active power sensitivity at power system nodes. The method comprises: constructing an admittance matrix of nonlinear nodes in a power system (101); inverting the admittance matrix of the nonlinear nodes to obtain an impedance matrix of the nonlinear nodes in the power system (102); determining a reactance matrix of the nonlinear nodes in the power system on the basis of the impedance matrix of the nonlinear nodes, to serve as a first reactance matrix (103); constructing an approximate reactance matrix of the nonlinear nodes in the power system, to serve as a second reactance matrix (104); and on the basis of the first reactance matrix and the second reactance matrix, determining the relationship between variation of active power injected at each nonlinear node in the power system and variation of the voltage at any nonlinear node, so as to determine the voltage sensitivity of each nonlinear node (105).

Description

Methods and systems for calculating voltage-active power sensitivity at power system nodes

[0001] This application claims priority to Chinese Patent Application No. 202510180740.6, filed with the Chinese Patent Office on February 19, 2025, the entire contents of which are incorporated herein by reference. Technical Field

[0002] This application belongs to the field of power system operation and control technology, and for example relates to a method and system for calculating the voltage-active power sensitivity of power system nodes. Background Technology

[0003] Voltage-active power sensitivity refers to the degree of change in voltage at a node or other nodes in a power system when the injected active power changes. It quantitatively describes the sensitivity of voltage to changes in a certain amount of active power. Voltage-active power sensitivity plays a crucial role in the planning, operation, and control of power systems. It can help analyze the voltage stability of the power system, determine the installation location and capacity of reactive power compensation equipment, and assess the impact of changes in different operating parameters on voltage, thereby achieving optimized operation of the power system and effective voltage control.

[0004] Compared to traditional power systems dominated by synchronous generators, high-penetration renewable energy power systems exhibit more complex dynamic characteristics, particularly in terms of primary energy characteristics, component quantity and type, and time scale. During the transition from traditional power systems to modern power systems with high-penetration renewable energy, various dynamic characteristics interact, making the dynamic process exceptionally complex. One of the main reasons why renewable energy generation and grid connection have a significant impact on the short-term voltage stability of the grid is that, as an active power injection source, it typically does not provide voltage support. Therefore, exploring the impact of changes in active power injection at renewable energy nodes on voltage amplitude and short-term voltage stability is of great significance.

[0005] However, there is very little research on how to calculate voltage-active power sensitivity in power systems, and the impact of changes in active power injection on voltage amplitude and short-term voltage stability remains unclear. Therefore, there is an urgent need for an analyzable method for calculating the voltage-active power sensitivity of power system nodes, suitable for voltage stability analysis. Summary of the Invention

[0006] This application provides a method and system for calculating the voltage-active power sensitivity of power system nodes.

[0007] In a first aspect, this application provides a method for calculating the node voltage-active power sensitivity of a power system, including:

[0008] Construct the admittance matrix of nonlinear nodes in the power system;

[0009] By inverting the admittance matrix of the nonlinear node, the impedance matrix of the nonlinear node in the power system can be obtained.

[0010] The reactance matrix of the nonlinear node in the power system is determined based on the impedance matrix of the nonlinear node, and is used as the first reactance matrix.

[0011] Construct an approximate reactance matrix for nonlinear nodes in the power system, which serves as the second reactance matrix;

[0012] The relationship between the active power injected into each nonlinear node in the power system and the voltage change of any nonlinear node is determined based on the first reactance matrix and the second reactance matrix, so as to determine the voltage sensitivity of each nonlinear node.

[0013] Optionally, constructing the admittance matrix of nonlinear nodes in the power system includes:

[0014] Construct the admittance matrix Y of the nonlinear node CC The expression:

[0015] ;

[0016] in, is the initial admittance matrix of the nonlinear node; This is the initial mutual admittance matrix between nonlinear nodes and passive nodes; Let be the initial admittance matrix of the passive node; This is the initial mutual admittance matrix between passive nodes and nonlinear nodes.

[0017] Optionally, determining the reactance matrix of the nonlinear node in the power system based on the impedance matrix of the nonlinear node, as the first reactance matrix, includes:

[0018] Construct the first reactance matrix X CC The expression:

[0019] X CC =Im(Z CC );

[0020] Where Im(·) represents the operation of taking the imaginary part of a complex number; Z CC The impedance matrix of the nonlinear node; Y CC is the admittance matrix of the nonlinear node.

[0021] Optionally, constructing the reactance matrix of an approximate nonlinear node in the power system as a second reactance matrix includes:

[0022] Construct the second reactance matrix The expression:

[0023] ;

[0024] Where Im(·) represents the operation of taking the imaginary part of a complex number; diag -1 (·) indicates that the vector is converted into a diagonal matrix and then inverted; The voltage vector V of the nonlinear node C The conjugate; The impedance matrix Z of the nonlinear node CC . conjugate.

[0025] Optionally, determining the relationship between the active power injected into each nonlinear node in the power system and the voltage change of any nonlinear node based on the first reactance matrix and the second reactance matrix, in order to determine the voltage sensitivity of each nonlinear node, includes:

[0026] Obtain the voltage V of the t-th nonlinear node in the power system Ct and injected active power P Ct ;

[0027] Obtain the voltage V of the p-th nonlinear node in the power system Cp ;

[0028] Construct an expression relating the active power injected at each nonlinear node to the voltage change at any nonlinear node:

[0029] ;

[0030] in, This represents the relationship between the active power injected at the p-th nonlinear node and the voltage at the q-th nonlinear node; n is the total number of nonlinear nodes in the power system; x pt Let be the mutual reactance between the p-th nonlinear node and the t-th nonlinear node; For the second reactance matrix The element in the t-th row and q-th column of the complex number; Re(·) represents the operation on the real part of the complex number; Im(·) represents the operation on the imaginary part of the complex number; |·| represents the modulo operation.

[0031] Secondly, this application provides a power system node voltage-active power sensitivity calculation system, comprising:

[0032] The first construction module is set up to construct the admittance matrix of nonlinear nodes in the power system;

[0033] The inversion module is configured to invert the admittance matrix of the nonlinear node to obtain the impedance matrix of the nonlinear node in the power system.

[0034] The first determining module is configured to determine the reactance matrix of the nonlinear node in the power system based on the impedance matrix of the nonlinear node, and use it as the first reactance matrix.

[0035] The second construction module is configured to construct the reactance matrix of an approximate nonlinear node in the power system, which serves as the second reactance matrix.

[0036] The second determining module is configured to determine the relationship between the active power injected into each nonlinear node in the power system and the voltage change of any nonlinear node based on the first reactance matrix and the second reactance matrix, so as to determine the voltage sensitivity of each nonlinear node.

[0037] Optionally, the first building module includes:

[0038] The first building unit is set to construct the admittance matrix Y of the nonlinear node. CC The expression:

[0039] ;

[0040] in, is the initial admittance matrix of the nonlinear node; This is the initial mutual admittance matrix between nonlinear nodes and passive nodes; Let be the initial admittance matrix of the passive node; This is the initial mutual admittance matrix between passive nodes and nonlinear nodes.

[0041] Optionally, the first determining module includes:

[0042] The second building unit is configured to construct the first reactance matrix X. CC The expression:

[0043] X CC =Im(Z CC );

[0044] Where Im(·) represents the operation of taking the imaginary part of a complex number; Z CC The impedance matrix of the nonlinear node; Y CC is the admittance matrix of the nonlinear node.

[0045] Optionally, the second building module includes:

[0046] The third building unit is set to construct the second reactance matrix. The expression:

[0047] ;

[0048] Where Im(·) represents the operation of taking the imaginary part of a complex number; diag-1 (·) indicates that the vector is converted into a diagonal matrix and then inverted; The voltage vector V of the nonlinear node C The conjugate; The impedance matrix Z of the nonlinear node CC . conjugate.

[0049] Optionally, the second determining module includes:

[0050] The first acquisition unit is configured to acquire the voltage V of the t-th nonlinear node in the power system. Ct and injected active power P Ct ;

[0051] The second acquisition unit is configured to acquire the voltage V of the p-th nonlinear node in the power system. Cp ;

[0052] The fourth building unit is configured to construct an expression relating the active power injected at each nonlinear node to the voltage change at any nonlinear node:

[0053] ;

[0054] in, This represents the relationship between the active power injected at the p-th nonlinear node and the voltage at the q-th nonlinear node; n is the total number of nonlinear nodes in the power system; x pt Let be the mutual reactance between the p-th nonlinear node and the t-th nonlinear node; For the second reactance matrix The element in the t-th row and q-th column of the complex number; Re(·) represents the operation on the real part of the complex number; Im(·) represents the operation on the imaginary part of the complex number; |·| represents the modulo operation. Attached Figure Description

[0055] Figure 1 is a flowchart illustrating a method for calculating the node voltage-active power sensitivity of a power system according to an embodiment of this application;

[0056] Figure 2 shows the voltage collapse calculation example from the standard calculation example provided by the China Electric Power Research Institute in this application. Heat map;

[0057] Figure 3 is a heat map of the sending and receiving end voltage-active power sensitivity of the IEEE 4-machine 11-node system example provided in the embodiments of this application;

[0058] Figure 4 is a thermogram of nonlinear power supply voltage-active power sensitivity provided in an embodiment of this application;

[0059] Figure 5 is a thermogram of nonlinear load voltage-active power sensitivity provided in an embodiment of this application;

[0060] Figure 6 is a schematic diagram of a power system node voltage-active power sensitivity calculation system provided in an embodiment of this application. Detailed Implementation

[0061] The technical solutions of the embodiments of this application will be described below with reference to the accompanying drawings. The described embodiments are only some embodiments of this application, and not all embodiments.

[0062] Example 1

[0063] As shown in Figure 1, this embodiment provides a method for calculating the node voltage-active power sensitivity of a power system, including:

[0064] Step 101: Construct the admittance matrix of nonlinear nodes in the power system.

[0065] In this embodiment, nodes in the power system are divided into passive nodes (no injected current at this type of node), linear nodes (the injected current expression of this type of node does not affect the original network equation and has an explicit solution), and nonlinear nodes (the injected current expression of this type of node affects the network equation and has an explicit solution).

[0066] The constructed network equations are as follows:

[0067] .

[0068] in, Let be the initial admittance matrix of the linear nodes; Let be the initial mutual admittance matrix between linear nodes and passive nodes; This is the initial mutual admittance matrix between linear and nonlinear nodes; This is the initial mutual admittance matrix between passive nodes and linear nodes; Let be the initial admittance matrix of the passive node; This is the initial mutual admittance matrix between passive nodes and nonlinear nodes; This is the initial mutual admittance matrix between nonlinear and linear nodes; This is the initial mutual admittance matrix between nonlinear nodes and passive nodes; V is the initial admittance matrix of the nonlinear node; S V is the voltage vector of a linear node; N V is the voltage vector of the passive node; C I is the voltage vector of the nonlinear node; S This represents the injected current vector at a linear node; . / indicates element-wise division. The voltage vector V of the linear node S The conjugate; The voltage vector V of the nonlinear node C The conjugate of. In this embodiment, This indicates the conjugate of y.

[0069] by and For example, if If the dimension is n×m, then The dimension is m×n.

[0070] By performing Cronbach's alpha reduction on the network equations to eliminate passive nodes, we obtain the reduced network equations:

[0071] .

[0072] Among them, Y SS for Reduced admittance matrix; ; Indicates to The inverse of Y; SC for Reduced admittance matrix; ; Indicates to Inverse; Y CS for Reduced admittance matrix; ;Y CC for Reduced admittance matrix; .

[0073] Construct the admittance matrix Y of the nonlinear node CC The expression:

[0074] ;

[0075] in, is the initial admittance matrix of the nonlinear node; This is the initial mutual admittance matrix between nonlinear nodes and passive nodes; Let be the initial admittance matrix of the passive node; This is the initial mutual admittance matrix between passive nodes and nonlinear nodes.

[0076] Step 102: Invert the admittance matrix of the nonlinear node to obtain the impedance matrix of the nonlinear node in the power system.

[0077] In this embodiment, the impedance matrix of the nonlinear node in the power system Y CC is the admittance matrix of the nonlinear node.

[0078] Step 103: Determine the reactance matrix of the nonlinear node in the power system based on the impedance matrix of the nonlinear node, and use it as the first reactance matrix.

[0079] In this embodiment, the first reactance matrix X is constructed. CC The expression is:

[0080] X CC =Im(Z CC ).

[0081] Where Im(·) represents the operation of taking the imaginary part of a complex number.

[0082] Step 104: Construct an approximate reactance matrix of nonlinear nodes in the power system as the second reactance matrix.

[0083] For example, the constructed second reactance matrix The expression is:

[0084] .

[0085] Where Im(·) represents the operation of taking the imaginary part of a complex number; diag -1 (·) indicates that the vector is converted into a diagonal matrix and then inverted; The voltage vector V of the nonlinear node C The conjugate; The impedance matrix Z of the nonlinear node CC . conjugate.

[0086] Step 105: Determine the relationship between the active power injected into each nonlinear node in the power system and the voltage change of any nonlinear node based on the first reactance matrix and the second reactance matrix, so as to determine the voltage sensitivity of each nonlinear node.

[0087] From the reduced network equations, we can obtain:

[0088] ;

[0089] .

[0090] Linearize the above equation in this step:

[0091] Assume the node power is determined by S C Change to S C +ΔS C Then the voltage will be changed from V C The change is V C +ΔV C ,get:

[0092] .

[0093] Further ignoring the quadratic term, we get:

[0094] .

[0095] In this embodiment, M is used to replace , use I C Replace Y CC V C +Y CS V S We can obtain:

[0096] .

[0097] For any two complex numbers z and w, the following equation holds:

[0098] .

[0099] Therefore, we can conclude that:

[0100] .

[0101] Furthermore, we can obtain:

[0102] .

[0103] Let ΔS C =ΔP C ,So:

[0104] .

[0105] Generally due to Y CC The order of magnitude is generally 10 2 Then we get:

[0106] ;

[0107] .

[0108] Where I is the identity matrix.

[0109] Neglecting resistance further, we can obtain:

[0110] .

[0111] And because , Indicates "much greater than", resulting in:

[0112] .

[0113] Where j represents the imaginary unit.

[0114] It is known that for any two complex numbers z and w, the following equation holds:

[0115] .

[0116] get:

[0117] .

[0118] Here, Re(·) represents the operation on the real part of a complex number; .* represents element-wise multiplication, following MATLAB rules.

[0119] Therefore, the expression Substitution From this, we can obtain:

[0120] .

[0121] For example, this step includes:

[0122] Obtain the voltage V of the t-th nonlinear node in the power system Ct and injected active power P Ct .

[0123] Obtain the voltage V of the p-th nonlinear node in the power system Cp .

[0124] Construct an expression relating the active power injected at each nonlinear node to the voltage change at any nonlinear node:

[0125] .

[0126] in, This represents the relationship between the active power injected at the p-th nonlinear node and the voltage at the q-th nonlinear node, i.e., the sensitivity of the voltage at the q-th nonlinear node to the active power injected at the p-th nonlinear node; n is the total number of nonlinear nodes in the power system; x pt X is the mutual reactance between the p-th nonlinear node and the t-th nonlinear node, i.e., the first reactance matrix X. CC The element in the p-th row and t-th column of the array; For the second reactance matrix The element in the t-th row and q-th column of the complex number; Re(·) represents the operation on the real part of the complex number; Im(·) represents the operation on the imaginary part of the complex number; |·| represents the modulo operation.

[0127] In verification For characteristic calculations, the voltage collapse calculation example from the China Electric Power Research Institute is used. The synchronous machine adopts a constant transient potential model, with transient reactances all at 0.1, and the load is of constant power type. The expression for Calculations were performed, and a heat map was plotted, as shown in Figure 2. Figure 2 illustrates... It has the property that it is a square matrix with diagonal dominance in its partitions.

[0128] When verifying this embodiment using the IEEE 4-machine 11-node system example shown in Figure 3, the synchronous machine adopts a constant transient potential model, with transient reactances all at 0.3. The load is of constant power type, and the photovoltaic outer loop uses constant active power and constant reactive power control, ignoring line resistance. Based on the original example, the synchronous generator at node 1 is replaced with a 300MW photovoltaic power station; a 100MW photovoltaic power station is added at node 5; the original load at node 7 is removed; and the output of the synchronous generator at node 2 is changed to 300MW. The calculation of this sending-receiving system is performed according to the calculation method provided in this embodiment, and the results are shown in Figure 3. The voltage-active power sensitivity matrix of this sending-receiving system is a block diagonally dominated matrix, and the voltage-active power sensitivity of the corresponding node in the sending system is negative, while the voltage-active power sensitivity of the corresponding node in the receiving system is positive.

[0129] When this embodiment was verified using the voltage collapse calculation example from the China Electric Power Research Institute as shown in Figure 4, the synchronous machine adopted a constant transient potential model, the transient reactance was 0.1, the load was of constant power and constant impedance type, the photovoltaic outer loop adopted constant active power and constant reactive power control, and the line resistance was ignored.

[0130] Figure 4 shows the voltage-active power sensitivity heatmap of the standard voltage collapse calculation case of the China Electric Power Research Institute without nonlinearity. In this case, all 13 generators are set as synchronous generators, the constant power load penetration rate is 40%, and the constant impedance penetration rate is 60%. The voltage collapse calculation case of the China Electric Power Research Institute standard calculation case is calculated according to the calculation method provided in this embodiment. The result is shown in Figure 4. The voltage-active power sensitivity matrix of this voltage collapse calculation case of the China Electric Power Research Institute standard calculation case is a block diagonally dominant matrix, and the voltage-active power sensitivity is all positive.

[0131] Figure 5 shows the voltage-active power sensitivity thermogram of the standard voltage collapse calculation from the China Electric Power Research Institute (CEPRI) without nonlinearity. In this case, 9 generators are configured as synchronous generators, and 4 are configured as photovoltaic generators, with a load type of constant impedance. Following the calculation method provided in this implementation, the voltage collapse calculation for this CEPRI standard voltage collapse calculation is performed, and the results are shown in Figure 5. The voltage-active power sensitivity matrix of this CEPRI standard voltage collapse calculation is a block-diagonally dominant matrix, and the voltage-active power sensitivity is entirely negative.

[0132] In summary, the power system node voltage-active power sensitivity calculation method provided in this embodiment focuses on the relationship between active power injection changes and voltage. Based on network equations, it can be used for transient voltage stability analysis. Furthermore, the voltage-active power sensitivity calculation method in this embodiment is not limited to traditional power grids, but can also be used in power grids with a high proportion of new energy sources, demonstrating good adaptability and robustness. Finally, its effectiveness was verified through MATLAB simulation.

[0133] Example 2

[0134] Based on the same concept as Embodiment 1, this embodiment provides a power system node voltage-active power sensitivity calculation system. Since the principle of this system in solving the problem is similar to the power system node voltage-active power sensitivity calculation method provided in Embodiment 1, the implementation of this system can refer to the implementation of the power system node voltage-active power sensitivity calculation method provided in Embodiment 1.

[0135] As shown in Figure 6, the power system node voltage-active power sensitivity calculation system includes:

[0136] The first construction module 10 is configured to construct the admittance matrix of nonlinear nodes in the power system.

[0137] The inversion module 20 is configured to invert the admittance matrix of the nonlinear node to obtain the impedance matrix of the nonlinear node in the power system.

[0138] The first determining module 30 is configured to determine the reactance matrix of the nonlinear node in the power system based on the impedance matrix of the nonlinear node, and use it as the first reactance matrix.

[0139] The second construction module 40 is configured to construct the reactance matrix of an approximate nonlinear node in the power system, which serves as the second reactance matrix.

[0140] The second determining module 50 is configured to determine the relationship between the active power injected into each nonlinear node in the power system and the voltage change of any nonlinear node based on the first reactance matrix and the second reactance matrix, so as to determine the voltage sensitivity of each nonlinear node.

[0141] For example, the first building module 10 includes:

[0142] The first building unit is set to construct the admittance matrix Y of the nonlinear node. CC The expression:

[0143] .

[0144] in, is the initial admittance matrix of the nonlinear node; This is the initial mutual admittance matrix between nonlinear nodes and passive nodes; Let be the initial admittance matrix of the passive node; This is the initial mutual admittance matrix between passive nodes and nonlinear nodes.

[0145] For example, the first determining module 30 includes:

[0146] The second building unit is configured to construct the first reactance matrix X. CC The expression:

[0147] X CC =Im(Z CC ).

[0148] Where Im(·) represents the operation of taking the imaginary part of a complex number; Z CC The impedance matrix of the nonlinear node; Y CC is the admittance matrix of the nonlinear node.

[0149] For example, the second building module 40 includes:

[0150] The third building unit is set to construct the second reactance matrix. The expression:

[0151] .

[0152] Where Im(·) represents the operation of taking the imaginary part of a complex number; diag -1 (·) indicates that the vector is converted into a diagonal matrix and then inverted; The voltage vector V of the nonlinear node C The conjugate; The impedance matrix Z of the nonlinear node CC . conjugate.

[0153] For example, the second determining module 50 includes:

[0154] The first acquisition unit is configured to acquire the voltage V of the t-th nonlinear node in the power system. Ct and injected active power P Ct .

[0155] The second acquisition unit is configured to acquire the voltage V of the p-th nonlinear node in the power system. Cp .

[0156] The fourth building unit is configured to construct an expression relating the active power injected at each nonlinear node to the voltage change at any nonlinear node:

[0157] .

[0158] in, This represents the relationship between the active power injected at the p-th nonlinear node and the voltage at the q-th nonlinear node; n is the total number of nonlinear nodes in the power system; x pt Let be the mutual reactance between the p-th nonlinear node and the t-th nonlinear node; For the second reactance matrix The element in the t-th row and q-th column of the complex number; Re(·) represents the operation on the real part of the complex number; Im(·) represents the operation on the imaginary part of the complex number; |·| represents the modulo operation.

[0159] For a more detailed description of the working process of the above modules, please refer to the relevant content disclosed in Example 1, which will not be repeated here.

[0160] This application provides a method and system for calculating the voltage-active power sensitivity of power system nodes. The method focuses on the relationship between changes in active power injection and voltage, and can be used for transient voltage stability analysis. Furthermore, the voltage-active power sensitivity calculation method in this application is not limited to traditional power grids, but can also be applied to power grids with a high proportion of renewable energy, demonstrating good adaptability and robustness.

[0161] Example 3

[0162] This embodiment provides a computer device, including a processor and a memory; wherein, when the processor executes the computer program stored in the memory, it implements the power system node voltage-active power sensitivity calculation method described in Embodiment 1 above.

[0163] For a more detailed explanation of the above method, please refer to the relevant content disclosed in Embodiment 1 above, which will not be repeated here.

[0164] Example 4

[0165] This embodiment provides a computer-readable storage medium for storing a computer program; when the computer program is executed by a processor, it implements the power system node voltage-active power sensitivity calculation method described in Embodiment 1. The storage medium can be a non-transitory storage medium.

[0166] For a more detailed explanation of the above method, please refer to the relevant content disclosed in Example 1, which will not be repeated here.

[0167] Example 5

[0168] This embodiment provides a computer program product, including computer-executable instructions or a computer program. When the computer-executable instructions or the computer program are executed by a processor, they implement the power system node voltage-active power sensitivity calculation method described in Embodiment 1.

[0169] For a more detailed explanation of the above method, please refer to the relevant content disclosed in Example 1, which will not be repeated here.

[0170] This specification describes multiple embodiments in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems, devices, storage media, and computer program products disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant details can be found in the method section.

[0171] The technologies in the embodiments of this application can be implemented using a combination of software and general-purpose hardware platforms. The technical solutions in the embodiments of this application can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as a read-only memory / random access memory (ROM / RAM), a magnetic disk, an optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the methods described in multiple embodiments or certain parts of the embodiments of this application.

[0172] In some embodiments, computer-executable instructions may take the form of programs, software, software modules, scripts, or code, written in any form of programming language (including compiled or interpreted languages, or declarative or procedural languages), and may be deployed in any form, including as stand-alone programs or as modules, components, subroutines, or other units suitable for use in a computing environment.

[0173] As an example, computer-executable instructions may, but do not necessarily, correspond to files in a file system. They may be stored as part of a file that holds other programs or data, for example, in one or more scripts in a Hyper Text Markup Language (HTML) document, in a single file dedicated to the program in question, or in multiple co-located files (e.g., files that store one or more modules, subroutines, or code sections).

[0174] As an example, computer-executable instructions can be deployed to execute on a single electronic device, or on multiple electronic devices located in one location, or on multiple electronic devices distributed across multiple locations and interconnected via a communication network.

Claims

1. A method for calculating the voltage-active power sensitivity of power system nodes, comprising: Construct the admittance matrix of nonlinear nodes in the power system; Inverting the admittance matrix of the nonlinear node yields the impedance matrix of the nonlinear node in the power system. The reactance matrix of the nonlinear node in the power system is determined based on the impedance matrix of the nonlinear node, and used as the first reactance matrix. Constructing the reactance matrix of an approximate nonlinear node in the power system, as a second reactance matrix, includes: constructing the second reactance matrix The expression: ； where Im(·) denotes taking the imaginary part of a complex number; diag -1 (·) denotes taking the inverse of a vector converted to a diagonal matrix; for the voltage vector V of the non-linear node C of the conjugate; the impedance matrix Z of the non-linear node CC the conjugate of the impedance matrix Z of the non-linear node Based on the first reactance matrix and the second reactance matrix, the relationship between the active power injected into each nonlinear node in the power system and the voltage change of any nonlinear node is determined to determine the voltage sensitivity of each nonlinear node, including: obtaining a voltage V of a tth non-linear node in the power system Ct and an injected active power P Ct ; obtaining a voltage Vp of a pth non-linear node in the power system Cp ; Construct an expression relating the active power injected at each nonlinear node to the voltage change at any nonlinear node: ； wherein, represents the variation relationship between the active power injected by the pthnonlinear node and the qthnonlinear node voltage; n is the total number of the nonlinear nodes in the power system; x pt is the mutual admittance between the pthnonlinear node and the tthnonlinear node; The second reactance matrix The element in the t-th row and q-th column of the complex number; Re(·) represents the operation on the real part of the complex number; |·| represents the modulo operation.

2. The method according to claim 1, wherein, The construction of the admittance matrix of nonlinear nodes in the power system includes: constructing a mobility matrix Y of the non-linear node CC the expression: ； in, Let be the initial admittance matrix of the nonlinear node; This is the initial mutual admittance matrix between the nonlinear node and the passive node; Let be the initial admittance matrix of the passive node; Let be the initial mutual admittance matrix between the passive node and the nonlinear node.

3. The method according to claim 1, wherein, Determining the reactance matrix of the nonlinear node in the power system based on the impedance matrix of the nonlinear node, as the first reactance matrix, includes: constructing the first reactance matrix X CC the expression: X CC = Im(Z CC ) Where Im(·) represents the operation of taking the imaginary part of a complex number; Z CC Let be the impedance matrix of the nonlinear node; , Y CC is the admittance matrix of the nonlinear node.

4. A power system node voltage-active power sensitivity calculation system, comprising: The first construction module is set up to construct the admittance matrix of nonlinear nodes in the power system; The inversion module is configured to invert the admittance matrix of the nonlinear node to obtain the impedance matrix of the nonlinear node in the power system. The first determining module is configured to determine the reactance matrix of the nonlinear node in the power system based on the impedance matrix of the nonlinear node, and use it as the first reactance matrix; The second construction module is configured to construct the reactance matrix of an approximate nonlinear node in the power system, as the second reactance matrix; The second building module includes: The third building unit is configured to build the second reactance matrix. The expression: ； Where Im(·) represents the operation of taking the imaginary part of a complex number; diag -1 (·) indicates that the vector is converted into a diagonal matrix and then inverted; The voltage vector V of the nonlinear node C The conjugate; the impedance matrix Z of the non-linear node CC the conjugate of the impedance matrix Z of the non-linear node The second determining module is configured to determine the relationship between the active power injected into each nonlinear node in the power system and the voltage change of any nonlinear node based on the first reactance matrix and the second reactance matrix, so as to determine the voltage sensitivity of each nonlinear node. The second determining module includes: The first acquisition unit is configured to acquire the voltage V of the tth nonlinear node in the power system Ct and the injected active power P Ct ; a second acquisition unit, configured to acquire a voltage V of a pth non-linear node in the power system Cp ; The fourth construction unit is configured to construct an expression relating the active power injected by each nonlinear node to the voltage change of any nonlinear node: ； in, This represents the relationship between the active power injected by the p-th nonlinear node and the voltage of the q-th nonlinear node; n is the total number of nonlinear nodes in the power system; x pt The mutual reactance between the p-th nonlinear node and the t-th nonlinear node; The second reactance matrix The element in the t-th row and q-th column of the complex number; Re(·) represents the operation on the real part of the complex number; |·| represents the modulo operation.

5. The system according to claim 4, wherein, The first building module includes: a first building unit configured to build an admittance matrix Y of the nonlinear node CC the expression: ； in, Let be the initial admittance matrix of the nonlinear node; This is the initial mutual admittance matrix between the nonlinear node and the passive node; Let be the initial admittance matrix of the passive node; Let be the initial mutual admittance matrix between the passive node and the nonlinear node.

6. The system according to claim 4, wherein, The first determining module includes: a second building unit configured to build the first reactance matrix X CC the expression: X CC = Im(Z CC ) Where Im(·) represents the operation of taking the imaginary part of a complex number; Z CC Let be the impedance matrix of the nonlinear node; , Y CC is the admittance matrix of the nonlinear node.

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