Power system power angle stability evaluation method and system based on modal information

Abstract

The invention discloses an electric power system power angle stability evaluation method and system based on modal information, and belongs to the technical field of electric power system operation. The method comprises the following steps: determining and solving a system vibration kinetic equation of a power system to extract system modal information; on the basis of the system modal information, calculating modal parameters under each modal, and calculating a modal vulnerability index according to the modal parameters; and based on the modal parameters, calculating the weighted power angle difference of the generator group, determining the initial weighted power angle difference of the generator group in the most fragile modal, and evaluating the stability of the power angle of the power system. According to the method, system dynamic analysis is converted into modal parameter calculation through modal decoupling, full-time-domain simulation is avoided, and the evaluation speed is increased. The most fragile mode is focused, the stability risk is quantified through the mode fragility index and the machine group power angle difference, the mode parameters are directly associated with the system inertia, the disturbance intensity and other physical quantities, the evaluation result is easy to explain, and a clear basis is provided for scheduling decision making.

Description

Technical Field

[0001] This invention relates to the field of power system operation technology, and more specifically, to a power system power angle stability assessment method and system based on modal information. Background Technology

[0002] In power systems, when subjected to large disturbances, the relative angles between generator rotors can rapidly diverge due to dynamic synchronism loss, leading to system disconnection or even collapse and causing major blackouts. Transient power angle stability assessment is crucial for maintaining the safe operation of large power grids. Traditional methods for transient power angle stability assessment mainly include time-domain simulation and direct methods. However, methods relying on time-domain simulation have high computational complexity and are time-consuming, making them unsuitable for real-time analysis. Direct methods, such as the Lyapunov energy function method, determine stability by constructing an energy function threshold, but they have poor adaptability to complex system models and their accuracy significantly decreases in scenarios with a high proportion of renewable energy integration.

[0003] With the integration of high proportions of renewable energy and the widespread application of power electronic equipment, the dynamic characteristics of the system exhibit new features such as strong nonlinearity and multi-timescale coupling. Traditional methods have poor calculation accuracy and suffer from problems such as low discrimination efficiency and insufficient robustness when facing new power systems. Summary of the Invention

[0004] To address the above problems, this invention proposes a power system power angle stability assessment method based on modal information, comprising:

[0005] The system vibration dynamics equations of the power system are determined and solved to extract system modal information;

[0006] Based on the system modal information, modal parameters under each mode are calculated, and modal vulnerability index is calculated based on the modal parameters;

[0007] Based on modal parameters, the weighted power angle difference of the generator group is calculated, and the initial weighted power angle difference of the group with the most vulnerable mode is determined, thereby evaluating the stability of the power angle of the power system.

[0008] Optional, the system's dynamic equations include:

[0009] After the disturbance occurs, the generator rotor motion equation is as follows:

[0010]

[0011] Where Δω is the change in the generator rotor angular velocity, Δδ is the change in the phase angle of the generator internal electromotive force, and ΔP m Let ΔP be the change in the mechanical power of the generator. g T represents the change in the electromagnetic power of the generator. JLet be the generator's inertial time constant, and D be the damping coefficient;

[0012] After the disturbance occurs, assuming the generator mechanical power is constant during the inertial response phase, the network equations are as follows:

[0013]

[0014] Among them, B K To represent the stiffness matrix of the interaction between the generator rotors, B F The distribution coefficient matrix for allocating system disturbance power to each generator rotor, i.e., the synchronization power coefficient, ΔP L The disturbance power;

[0015] Furthermore, the second-order vibration dynamics equation, obtained by simultaneously solving the generator rotor motion equation and the network equation, is as follows:

[0016]

[0017] Optionally, the system vibration dynamics equations are solved to extract system modal information, including:

[0018] The eigenvalues ​​and eigenvectors of the system's vibration dynamics equations are solved, and coordinate transformation and modal decoupling are performed to obtain the dynamic equations in the transformed modal coordinates, as shown in the following formulas:

[0019]

[0020] Among them, M p For T J The quality matrix after feature transformation, D p Let K be the damping matrix of D after eigenvalue transformation. p For B K The stiffness matrix after eigenvalue transformation, x p F is the state variable that δ maps to in modal coordinates. p The transformed disturbance power state quantity is the original disturbance power allocation -B. F ΔP L B is a transpose of an eigenmatrix Φ multiplied on the left. F To represent the stiffness matrix of the interaction between the generator rotors, ΔP L The disturbance power;

[0021] By using the characteristic matrix, the variables are transformed into modal coordinates, and the modal parameters are calculated, including the disturbance power and the equivalent inertia of each mode.

[0022] The formulas for calculating the disturbance power in each mode are as follows:

[0023] ΔP eP (i) =Φ i ΔP

[0024] The formulas for calculating the equivalent inertia in each mode are as follows:

[0025]

[0026] Where, Φ i The i-th column of the eigenvalue matrix represents the eigenvector of the i-th mode, ΔP is the perturbation power, and T... j This is the quality matrix.

[0027] Optionally, the modal vulnerability index can be calculated using the following formula:

[0028]

[0029] Where k is a constant coefficient, T jP Let ΔP be the equivalent inertia in modal coordinates. P This represents the perturbation power under different modes.

[0030] Optionally, based on modal parameters, the weighted power angle difference of the generator group is calculated, including:

[0031] For a cluster of generators operating in a single mode, the generators are grouped according to the sign of the generator weighting factor in that single mode, and the sum of generator inertia for each group is calculated. and These represent the sum of the generator inertia of the positive and negative generator groups, respectively;

[0032] In mode i, the weighted power angle difference based on inertia is calculated for each generator in both groups. The weighted initial power angle difference of the k-th generator in the i-th mode is calculated according to the following formula:

[0033]

[0034] The total weighted power angle difference between the two generator groups is used as the generator group weighted power angle difference. That is, first sum the weighted power angle differences of the two generator groups, and then subtract the sum of the power angle differences of the two generator groups. The formula is as follows:

[0035]

[0036] Among them, T jP,k Let T be the equivalent inertia of the k-th generator in modal coordinates. jP,l Let δ be the equivalent inertia of the k-th generator in modal coordinates, and let δ be the generator inertia belonging to the positive and negative generator groups respectively. 0,k Let δ be the initial power angle difference of the k-th generator. 0,l Let be the initial power angle difference of the l-th generator.

[0037] Optionally, a stability criterion for evaluating the stability of the power system's power angle is as follows:

[0038] δ′=aδ0′+bΔδ

[0039] Where δ′ is the modal power angle difference, δ0′ is the modal weighted initial power angle difference, Δδ is the change in modal power angle difference, i.e. the modal vulnerability defined above, and a and b are constant coefficients of the two respectively;

[0040] If δ′>180°, the system is determined to be unstable in terms of power angle; if δ′<180°, the system is determined to be stable in terms of power angle.

[0041] Furthermore, this invention also proposes a power system power angle stability assessment system based on modal information, comprising:

[0042] An information extraction unit is used to determine the system vibration dynamics equation of the power system and solve the system vibration dynamics equation to extract system modal information;

[0043] The calculation unit is used to calculate the modal parameters under each mode based on the system modal information, and to calculate the modal vulnerability index based on the modal parameters;

[0044] The evaluation unit is used to calculate the weighted power angle difference of the generator group based on modal parameters, determine the initial weighted power angle difference of the group with the most vulnerable mode, and evaluate the stability of the power angle of the power system.

[0045] Optional, the system's dynamic equations include:

[0046] After the disturbance occurs, the generator rotor motion equation is as follows:

[0047]

[0048] Where Δω is the change in the generator rotor angular velocity, Δδ is the change in the phase angle of the generator internal electromotive force, and ΔP m Let ΔP be the change in the mechanical power of the generator. g T represents the change in the electromagnetic power of the generator. J Let be the generator's inertial time constant, and D be the damping coefficient;

[0049] After the disturbance occurs, assuming the generator mechanical power is constant during the inertial response phase, the network equations are as follows:

[0050]

[0051] Among them, B K To represent the stiffness matrix of the interaction between the generator rotors, B FThe distribution coefficient matrix for allocating system disturbance power to each generator rotor, i.e., the synchronization power coefficient, ΔP L The disturbance power;

[0052] Furthermore, the second-order vibration dynamics equation, obtained by simultaneously solving the generator rotor motion equation and the network equation, is as follows:

[0053]

[0054] Optionally, the system vibration dynamics equations are solved to extract system modal information, including:

[0055] The eigenvalues ​​and eigenvectors of the system's vibration dynamics equations are solved, and coordinate transformation and modal decoupling are performed to obtain the dynamic equations in the transformed modal coordinates, as shown in the following formulas:

[0056]

[0057] Among them, M p For T J The quality matrix after feature transformation, D p Let K be the damping matrix of D after eigenvalue transformation. p For B K The stiffness matrix after eigenvalue transformation, x p F is the state variable that δ maps to in modal coordinates. p The transformed disturbance power state quantity is the original disturbance power allocation -B. F ΔP L B is a transpose of an eigenmatrix Φ multiplied on the left. F To represent the stiffness matrix of the interaction between the generator rotors, ΔP L The disturbance power;

[0058] By using the characteristic matrix, the variables are transformed into modal coordinates, and the modal parameters are calculated, including the disturbance power and the equivalent inertia of each mode.

[0059] The formulas for calculating the disturbance power in each mode are as follows:

[0060] ΔP eP (i) =Φ i ΔP

[0061] The formulas for calculating the equivalent inertia in each mode are as follows:

[0062]

[0063] Where, Φ iThe i-th column of the eigenvalue matrix represents the eigenvector of the i-th mode, ΔP is the perturbation power, and T... j This is the quality matrix.

[0064] Optionally, the modal vulnerability index can be calculated using the following formula:

[0065]

[0066] Where k is a constant coefficient, T jP Let ΔP be the equivalent inertia in modal coordinates. P This represents the perturbation power under different modes.

[0067] Optionally, based on modal parameters, the weighted power angle difference of the generator group is calculated, including:

[0068] For a cluster of generators operating in a single mode, the generators are grouped according to the sign of the generator weighting factor in that single mode, and the sum of generator inertia for each group is calculated. and These represent the sum of the generator inertia of the positive and negative generator groups, respectively;

[0069] In mode i, the weighted power angle difference based on inertia is calculated for each generator in both groups. The weighted initial power angle difference of the k-th generator in the i-th mode is calculated according to the following formula:

[0070]

[0071] The total weighted power angle difference between the two generator groups is used as the generator group weighted power angle difference. That is, first sum the weighted power angle differences of the two generator groups, and then subtract the sum of the power angle differences of the two generator groups. The formula is as follows:

[0072]

[0073] Among them, T jP,k Let T be the equivalent inertia of the k-th generator in modal coordinates. jP,l Let δ be the equivalent inertia of the k-th generator in modal coordinates, and let δ be the generator inertia belonging to the positive and negative generator groups respectively. 0,k Let δ be the initial power angle difference of the k-th generator. 0,l Let be the initial power angle difference of the l-th generator.

[0074] Optionally, a stability criterion for evaluating the stability of the power system's power angle is as follows:

[0075] δ′=aδ0′+bΔδ

[0076] Where δ′ is the modal power angle difference, δ0′ is the modal weighted initial power angle difference, Δδ is the change in modal power angle difference, i.e. the modal vulnerability defined above, and a and b are constant coefficients of the two respectively;

[0077] If δ′>180°, the system is determined to be unstable in terms of power angle; if δ′<180°, the system is determined to be stable in terms of power angle.

[0078] In another aspect, the present invention also provides a computing device, comprising: one or more processors;

[0079] A processor is used to execute one or more programs;

[0080] When the one or more programs are executed by the one or more processors, the method described above is implemented.

[0081] In another aspect, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed, implements the method described above.

[0082] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0083] This invention provides a power system power angle stability assessment method based on modal information, comprising: determining the system vibration dynamics equation of the power system; solving the system vibration dynamics equation to extract system modal information; calculating modal parameters for each mode based on the system modal information; calculating modal vulnerability indices based on the modal parameters; calculating the weighted power angle difference of the generator group based on the modal parameters; determining the initial weighted power angle difference of the generator group for the most vulnerable mode; and assessing the power system power angle stability. This invention transforms system dynamic analysis into modal parameter calculation through modal decoupling, avoiding full-time-domain simulation and improving assessment speed. Focusing on the most vulnerable mode, it quantifies stability risk through modal vulnerability indices and generator group power angle differences. Modal parameters are directly related to physical quantities such as system inertia and disturbance intensity, making the assessment results easy to interpret and providing a clear basis for scheduling decisions. Attached Figure Description

[0084] Figure 1 This is a flowchart of an embodiment of the method of the present invention;

[0085] Figure 2 This is a geographical wiring diagram of the IEEE 68 nodes in an embodiment of the method of the present invention;

[0086] Figure 3 This is a schematic diagram illustrating the feature importance assessment in an embodiment of the method of the present invention. Detailed Implementation

[0087] Exemplary embodiments of the invention will now be described with reference to the accompanying drawings. However, the invention may be embodied in many different forms and is not limited to the embodiments described herein. These embodiments are provided to fully and completely disclose the invention and to fully convey its scope to those skilled in the art. The terminology used in the exemplary embodiments illustrated in the drawings is not intended to limit the invention. In the drawings, the same units / elements are referred to by the same reference numerals.

[0088] Unless otherwise stated, the terms used herein (including technical terms) have their common meaning as understood by one of ordinary skill in the art. Furthermore, it is understood that terms defined in commonly used dictionaries should be understood to have a meaning consistent with the context of their relevant field, and not to be interpreted as having an idealized or overly formal meaning.

[0089] Example 1:

[0090] This invention proposes a power system power angle stability assessment method S100 based on modal information, comprising:

[0091] S101, Determine the system vibration dynamics equation of the power system, solve the system vibration dynamics equation to extract system modal information;

[0092] S102, Based on the system modal information, calculate the modal parameters under each mode, and calculate the modal vulnerability index according to the modal parameters;

[0093] S103, based on modal parameters, calculates the weighted power angle difference of the generator group, determines the initial weighted power angle difference of the group with the most vulnerable mode, and evaluates the stability of the power angle of the power system.

[0094] The following is combined Figure 1 Further explanation of steps S101-S103, including their specific implementation process, is provided below. Figure 1 As shown, it includes:

[0095] Write the system vibration dynamics equations. Based on the system state, basic generator parameters, disturbance location and magnitude, write the rotor motion equations, network equations and synchronous power coefficient matrix, and transform the dynamic expression of the rotor motion equations into vibration dynamics equations.

[0096] 1) After the disturbance occurs, the generator rotor motion equation is:

[0097]

[0098] Where Λω is the change in the generator rotor angular velocity (rad / s), Δδ is the change in the phase angle of the generator internal electromotive force (rad), and ΔP mLet ΔP be the change in the mechanical power of the generator. g T represents the change in the electromagnetic power of the generator. J Let be the generator inertial time constant (s), and D be the damping coefficient.

[0099] 2) After the disturbance occurs, it is assumed that the generator mechanical power remains constant during the inertial response phase (i.e., ΔP). m If (=0), then the network equation can be expressed as:

[0100]

[0101] Among them, B K To represent the stiffness matrix of the interaction between the generator rotors, B F The distribution coefficient matrix is ​​used to allocate the system disturbance power to each generator rotor, i.e., the synchronization power coefficient.

[0102] 3) Combining the above equations, we can transform it into a second-order vibration dynamics equation:

[0103]

[0104] Where δ is the power angle of the generator, and ΔP L For the disturbance power, T J Let be the generator's moment of inertia, i.e., the mass matrix.

[0105] Solving the dynamic characteristic equations of power system vibration dynamics. The vibration dynamic equations are decoupled through eigenvalue decomposition to extract system modal information. The specific process can be divided into the following steps.

[0106] 1) Solving for the eigenvalues ​​of the matrix. Find the eigenvalues ​​of the above quadratic equation, that is, for |T... J Ω 2 -B K Solving for |=0 can be transformed into solving for |Ω. 2 IT J -1 B K | = 0, that is, to find T J -1 B K λ is an eigenvalue. i =Ω i 2 (i = 1, 2, ..., n) are used to find eigenvalues ​​to characterize modal vibration properties.

[0107] 2) Find the eigenvectors and convert the eigenvalues... Substitute into the characteristic equation:

[0108]

[0109] Obtain the corresponding eigenvector Φ i =[φi1 ,…,φ in ] T , where φ ij Let be the participation degree of the j-th generator in the i-th mode, i.e., the weighting factor. Each eigenvalue... Each has a corresponding eigenvector Φ i Both of these characteristics define a mode. A system with n generators has a total of n vibration modes.

[0110] 3) Coordinate Transformation and Modal Decoupling. Coordinate transformation is performed using the orthogonality of eigenvectors. Considering the orthogonality of eigenvectors with respect to the inertia matrix and the network matrix, the off-diagonal matrix B... K Transform into a diagonal matrix K p To achieve decoupling between different vibration modes:

[0111]

[0112] The dynamic equations in the transformed modal coordinates can be obtained, namely:

[0113]

[0114] The characteristic matrix can be used to transform variables into modal coordinates;

[0115] Based on the characteristic matrix obtained after solving the characteristic equation, the disturbance power and generator initial power angle difference under each mode are calculated, and the modal vulnerability index is calculated.

[0116] 1) Calculation of key parameters. Calculate the modal disturbance power ΔP distributed to each mode. eP (i) , where i represents the modal disturbance power after conversion in the i-th mode;

[0117] ΔP eP (i) =Φ i ΔP

[0118] 2) Calculate the reduced inertia T for each mode. jP (i) .

[0119] T jP (i) =Φ T T j Φ

[0120] 3) Calculate the modal vulnerability index. This invention defines a modal vulnerability index to assess the stability level of the system. For a generator, the change in power angle difference is positively correlated with the magnitude of the disturbance power and negatively correlated with the system inertia level. Therefore, the modal vulnerability index is defined based on modal disturbance power and modal equivalent inertia as follows:

[0121]

[0122] Where k is a constant coefficient, in order to control the ratio of modal disturbance power to modal equivalent inertia within a reasonable and visually acceptable range.

[0123] Based on modal parameters, the weighted power angle difference of the generator group is calculated. The initial power angle differences of the generators (compared to the reference unit) after grouping under each mode are weighted and summed.

[0124] 1) For a cluster of generators operating in a single mode, group them according to the sign of the generator weighting factor in that mode and calculate the sum of generator inertia for each group, i.e. and These represent the generator inertia of the positive and negative generator groups, respectively.

[0125] 2) In mode i, calculate the weighted power angle difference (relative to the reference unit) based on inertia for each generator in both groups. The weighted initial power angle difference (relative to the reference unit) of the k-th generator in mode i is:

[0126]

[0127] 3) The total weighted power angle difference between the two machine groups is used as the weighted power angle difference of the machine groups. That is, first sum the weighted power angle differences of the two machine groups, and then subtract the sum of the power angle differences of the two machine groups.

[0128]

[0129] 4) Repeat the above process for each mode to obtain the initial weighted power angle difference of the cluster for all modes.

[0130] Find the initial weighted power angle difference of the cluster with the most vulnerable mode and evaluate the system's power angle stability. Based on the modal vulnerability index calculated in step three, identify the most vulnerable mode. Combine this with the initial weighted power angle differences of the cluster for each mode calculated in step four to evaluate the system's power angle stability.

[0131] After a disturbance occurs, the system power angle can be considered as the effect of the initial power angle plus a power angle change. From a modal perspective, this invention uses the initial weighted power angle difference of the cluster as the initial power angle and modal vulnerability as the power angle change, arguing that the system power angle stability criterion is formed by the combined effect of these two parts.

[0132] δ′=aδ0′+bΔδ

[0133] Where a and b are the influence coefficients of two indicators, and appropriate parameters are selected according to the actual power grid topology.

[0134] The above method was verified through simulation in a case study. Specifically, a fault simulation was performed based on the standard IEEE 68-node example.

[0135] The geographical wiring diagram of the IEEE 68-node case is as follows: Figure 2 As shown, a load disturbance of 1000MW is set at node 23.

[0136] The following section assesses the power angle stability based on modal information.

[0137] Based on the power grid topology, write the system vibration dynamics equations;

[0138] Solving the equation yields the eigenvectors and eigenmatrix.

[0139] Based on the characteristic matrix, calculate the disturbance power and generator initial power angle difference, and other modal parameters under each mode, and calculate the modal vulnerability index.

[0140] The weighted power angle difference of the generator group is calculated based on modal parameters.

[0141] Feature importance analysis was performed on the modal vulnerability index and the initial weighted power angle difference index of the generator group.

[0142] like Figure 3 As shown, the influence of parameters such as the power angle difference of the most vulnerable mode group, modal vulnerability, modal disturbance power, and modal equivalent inertia on power angle stability was analyzed. The power angle difference of the most vulnerable mode group proposed in this invention has the greatest impact on power angle stability. It can be seen that the proposed modal vulnerability index has the second greatest impact on the system's power angle stability, after the power angle difference of the most vulnerable mode group.

[0143] For multiple samples with different outputs generated based on the IEEE68 standard, the power angle stability is judged based on the above indicators, and the accuracy rate can reach 97%.

[0144] Example 2:

[0145] This invention also proposes a power system power angle stability assessment system 200 based on modal information, comprising:

[0146] The information extraction unit 201 is used to determine the system vibration dynamics equation of the power system and solve the system vibration dynamics equation to extract system modal information;

[0147] The calculation unit 202 is used to calculate the modal parameters under each mode based on the system modal information, and to calculate the modal vulnerability index based on the modal parameters;

[0148] Evaluation unit 203 is used to calculate the weighted power angle difference of the generator group based on modal parameters, determine the initial weighted power angle difference of the generator group with the most vulnerable mode, and evaluate the stability of the power angle of the power system.

[0149] The system's vibration dynamics equations include:

[0150] After the disturbance occurs, the generator rotor motion equation is as follows:

[0151]

[0152] Where Δω is the change in the generator rotor angular velocity, Δδ is the change in the phase angle of the generator internal electromotive force, and ΔP m Let ΔP be the change in the mechanical power of the generator. g T represents the change in the electromagnetic power of the generator. J Let be the generator's inertial time constant, and D be the damping coefficient;

[0153] After the disturbance occurs, assuming the generator mechanical power is constant during the inertial response phase, the network equations are as follows:

[0154]

[0155] Among them, B K To represent the stiffness matrix of the interaction between the generator rotors, B F The distribution coefficient matrix for allocating system disturbance power to each generator rotor, i.e., the synchronization power coefficient, ΔP L The disturbance power;

[0156] Furthermore, the second-order vibration dynamics equation, obtained by simultaneously solving the generator rotor motion equation and the network equation, is as follows:

[0157]

[0158] Solving the system's vibration dynamics equations to extract system modal information includes:

[0159] The eigenvalues ​​and eigenvectors of the system's vibration dynamics equations are solved, and coordinate transformation and modal decoupling are performed to obtain the dynamic equations in the transformed modal coordinates, as shown in the following formulas:

[0160]

[0161] Among them, M p For T J The quality matrix after feature transformation, D p Let K be the damping matrix of D after eigenvalue transformation. p For B K The stiffness matrix after eigenvalue transformation, x p F is the state variable that δ maps to in modal coordinates. pThe transformed disturbance power state quantity is the original disturbance power allocation -B. F ΔP L B is a transpose of an eigenmatrix Φ multiplied on the left. F To represent the stiffness matrix of the interaction between the generator rotors, ΔP L The disturbance power;

[0162] By using the characteristic matrix, the variables are transformed into modal coordinates, and the modal parameters are calculated, including the disturbance power and the equivalent inertia of each mode.

[0163] The formulas for calculating the disturbance power in each mode are as follows:

[0164] ΔP eP (i) =Φ i ΔP

[0165] The formulas for calculating the equivalent inertia in each mode are as follows:

[0166]

[0167] Where, Φ i The i-th column of the eigenvalue matrix represents the eigenvector of the i-th mode, ΔP is the perturbation power, and T... j This is the quality matrix.

[0168] The formula for calculating the modal vulnerability index is as follows:

[0169]

[0170] Where k is a constant coefficient, T jP Let ΔP be the equivalent inertia in modal coordinates. P This represents the perturbation power under different modes.

[0171] Among them, the weighted power angle difference of the generator group is calculated based on modal parameters, including:

[0172] For a cluster of generators operating in a single mode, the generators are grouped according to the sign of the generator weighting factor in that single mode, and the sum of generator inertia for each group is calculated. and These represent the sum of the generator inertia of the positive and negative generator groups, respectively;

[0173] In mode i, the weighted power angle difference based on inertia is calculated for each generator in both groups. The weighted initial power angle difference of the k-th generator in the i-th mode is calculated according to the following formula:

[0174]

[0175] The total weighted power angle difference between the two generator groups is used as the generator group weighted power angle difference. That is, first sum the weighted power angle differences of the two generator groups, and then subtract the sum of the power angle differences of the two generator groups. The formula is as follows:

[0176]

[0177] Among them, T jP,k Let T be the equivalent inertia of the k-th generator in modal coordinates. jP,l Let δ be the equivalent inertia of the k-th generator in modal coordinates, and let δ be the generator inertia belonging to the positive and negative generator groups respectively. 0,k Let δ be the initial power angle difference of the k-th generator. 0,l Let be the initial power angle difference of the l-th generator.

[0178] The stability criterion for evaluating the stability of the power system's power angle is as follows:

[0179] δ′=aδ0′+bΔδ

[0180] Where δ′ is the modal power angle difference, δ0′ is the modal weighted initial power angle difference, Δδ is the change in modal power angle difference, i.e. the modal vulnerability defined above, and a and b are constant coefficients of the two respectively;

[0181] If δ′>180°, the system is determined to be unstable in terms of power angle; if δ′<180°, the system is determined to be stable in terms of power angle.

[0182] This invention transforms system dynamic analysis into modal parameter calculation through modal decoupling, avoiding full-time-domain simulation and improving evaluation speed. Focusing on the most vulnerable modes, it quantifies stability risk through modal vulnerability indices and cluster power angle differences. Modal parameters are directly related to physical quantities such as system inertia and disturbance intensity, making the evaluation results easy to interpret and providing a clear basis for scheduling decisions.

[0183] Example 3:

[0184] Based on the same inventive concept, this invention also provides a computer device, which includes a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions in the computer storage medium to implement corresponding method flows or corresponding functions, thereby implementing the steps of the methods in the above embodiments.

[0185] Example 4:

[0186] Based on the same inventive concept, this invention also provides a storage medium, specifically a computer-readable storage medium (Memory), which is a memory device in a computer device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the computer device and extended storage media supported by the computer device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, this storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device. The processor can load and execute one or more instructions stored in the computer-readable storage medium to implement the steps of the method in the above embodiments.

[0187] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention can be implemented using various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0188] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0189] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0190] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0191] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0192] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for power system angle stability assessment based on modal information, characterized in that, The method comprises the following steps: determining a system vibration equation of the power system, solving the system vibration equation to extract system modal information; calculating modal parameters under each mode based on the system modal information, and calculating a modal vulnerability index according to the modal parameters; calculating a generator group weighted power angle difference based on the modal parameters, and determining an initial weighted power angle difference of the group of the most vulnerable mode to evaluate the stability of the power system power angle.

2. The power system angle stability assessment method of claim 1, wherein, The system vibration equation comprises: a generator rotor motion equation after the disturbance occurs, and the equation is as follows: where Δω is the generator rotor angular speed variation, Δδ is the generator internal voltage phase angle variation, ΔP m is the generator mechanical power variation, ΔP g is the generator electromagnetic power variation, T J is the generator inertia time constant, and D is the damping coefficient. a network equation after the disturbance occurs, assuming that the generator mechanical power is constant during the inertia response stage, and the equation is as follows: where B K is the stiffness matrix representing the interaction between the rotors of the generators, B F is the distribution coefficient matrix of the system disturbance power to each generator rotor, i.e. the synchronous power coefficient, ΔP L is the disturbance power; and a second-order vibration equation after the generator rotor motion equation and the network equation are combined and transformed, and the equation is as follows:

3. The method of power system angle stability assessment according to claim 1, wherein, Solving the system vibration equation to extract system modal information comprises: performing eigenvalue solving, eigenvector solving, coordinate transformation and modal decoupling on the system vibration equation to obtain a dynamic equation in the transformed modal coordinates, and the equation is as follows: where M p is the mass matrix of the system J D p is the damping matrix of the system after eigen-transformation, K p is the stiffness matrix of the system after eigen-transformation, x K is the state variable of the system after eigen-transformation, F p is the state variable of the system after eigen-transformation, F p is the state variable of the system after eigen-transformation, F F ΔP L is the disturbance power after eigen-transformation, B F is the stiffness matrix of the system after eigen-transformation, ΔP L is the disturbance power transforming variables into modal coordinates through an eigenmatrix to calculate modal parameters, including disturbance power under each mode and equivalent inertia under each mode; the calculation formula of the disturbance power under each mode is as follows: ΔP eP (i) = Φ i ΔP the calculation formula of the equivalent inertia under each mode is as follows: where Φ i is the i-th column of the feature matrix, representing the eigenvector of the i-th modality, ΔΡ is the perturbation power, T j is the mass matrix.

4. The method of power system angle stability assessment of claim 1, wherein, the calculation formula of the modal vulnerability index is as follows: where k is a constant coefficient, T jP is the equivalent inertia in modal coordinates, ΔP P is the disturbance power in modal coordinates.

5. The method of power system angle stability assessment of claim 1, wherein, The calculation of the generator group weighted power angle difference based on the modal parameters comprises: For the fleet under a single mode, the fleet is divided into two groups according to the positive and negative of the generator weight factor under the single mode, and the generator inertia of each group is calculated, i.e. and respectively represent the generator inertia of the positive and negative two groups. calculating the inertia-based weighted power angle difference of each generator of the two groups under the mode i according to the following formula to calculate the weighted initial power angle difference of the kth generator under the i th mode: taking the total weighted power angle difference between the two groups as the group weighted power angle difference, that is, summing the weighted power angle differences of the two groups first, and then subtracting the sum of the power angle differences of the two groups, and the formula is as follows: where T jP,k is the equivalent inertia of the kth generator in modal coordinates, T jP,l is the equivalent inertia of the kth generator in modal coordinates, T 0,k is the initial angle difference of the kth generator, and δ 0,l is the initial angle difference of the lth generator.

6. The method of power system angle stability assessment of claim 1, wherein, The stability criterion for evaluating the stability of the power system power angle is as follows: δ' = aδ0' + bΔδ wherein δ' is a modal power angle difference, δ0' is a modal weighted initial power angle difference, Δδ is a modal power angle difference change, that is, the modal vulnerability defined above, and a and b are constant coefficients of the two; wherein if δ' > 180°, it is determined that the system power angle is unstable; and if δ' < 180°, it is determined that the system power angle is stable.

7. A modal information based power system angle stability assessment system, characterized in that, The method comprises the following steps: an information extraction unit configured to determine a system vibration equation of the power system, and solve the system vibration equation to extract system modal information; a calculation unit configured to calculate modal parameters under each mode based on the system modal information, and calculate a modal vulnerability index according to the modal parameters; an evaluation unit configured to calculate a generator group weighted power angle difference based on the modal parameters, and determine an initial weighted power angle difference of the group of the most vulnerable mode to evaluate the stability of the power system power angle.

8. The power system angle stability assessment system of claim 7, wherein, The system vibration equation comprises: a generator rotor motion equation after the disturbance occurs, and the equation is as follows: where Δω is the generator rotor angular speed variation, Δδ is the generator internal voltage phase angle variation, ΔP m is the generator mechanical power variation, ΔP g is the generator electromagnetic power variation, T J is the generator inertia time constant, and D is the damping coefficient. a network equation after the disturbance occurs, assuming that the generator mechanical power is constant during the inertia response stage, and the equation is as follows: where B K is a stiffness matrix representing the interaction between the rotors of the generators, B F is a distribution coefficient matrix of the system disturbance power to each rotor of the generators, i.e., a synchronous power coefficient, ΔP L is a disturbance power; And, the generator rotor motion equation and the network equation are combined to transform the second-order vibration dynamics equation, and the formula is as follows:

9. The power system angle stability assessment system of claim 7, wherein, Solving the system vibration dynamics equation to extract system modal information, including: The system vibration dynamics equation is subjected to eigenvalue solving of a matrix, eigenvector solving, and coordinate transformation and modal decoupling to obtain a dynamics equation in the converted modal coordinates, and the formula is as follows: where M p is the mass matrix of the system J D p is the damping matrix of the system after eigen-transformation, K p is the stiffness matrix of the system after eigen-transformation, x K is the state variable of the system after eigen-transformation, F p is the state variable of the system after eigen-transformation, F p is the state variable of the system after eigen-transformation, F F ΔP L is the state variable of the system after eigen-transformation, F F is the state variable of the system after eigen-transformation, F L is the state variable of the system after eigen-transformation, F Through the characteristic matrix, the variables are converted to the modal coordinates, and the modal parameters are calculated, including disturbance power in each mode and equivalent inertia in each mode; The formula for calculating the disturbance power in each mode is as follows: ΔP eP (i) = Φ i ΔP The formula for calculating the equivalent inertia in each mode is as follows: where Φ i is the i-th column of the feature matrix, representing the eigenvector of the i-th modality, ΔΡ is the perturbation power, T j is the mass matrix.

10. The power system angle stability assessment system of claim 7, wherein, The formula for calculating the modal vulnerability index is as follows: where k is a constant coefficient, T jP is the equivalent inertia in modal coordinates, ΔP P is the disturbance power in modal coordinates.

11. The power system angle stability assessment system of claim 7, wherein, Based on the modal parameters, the generator group weighted power angle difference is calculated, including: For the fleet under a single mode, the fleet is divided into two groups according to the positive and negative of the generator weight factor under the single mode, and the generator inertia of each group is calculated, i.e. and respectively represent the generator inertia of the positive and negative two groups. In the modal i, the weighted power angle difference based on inertia is calculated for each generator of the two groups, and the weighted initial power angle difference of the kth generator in the ith mode is calculated according to the following formula: The total weighted power angle difference between the two groups is taken as the group weighted power angle difference, that is, the weighted power angle differences of the two groups are summed up, and the sum of the power angle differences of the two groups is subtracted, and the formula is as follows: where T jP,k is the equivalent inertia of the kth generator in modal coordinates, T jP,l is the equivalent inertia of the kth generator in modal coordinates, T 0,k is the initial angle difference of the kth generator, and δ 0,l is the initial angle difference of the lth generator.

12. The power system angle stability assessment system of claim 7, wherein, The stability criterion for evaluating the stability of the power system power angle is as follows: δ'=aδ0'+bΔδ Where δ' is the modal power angle difference, δ0' is the modal weighted initial power angle difference, Δδ is the modal power angle difference change, that is, the modal vulnerability defined above, and a and b are the constant coefficients of the two. Wherein, if δ'>180°, it is determined that the system power angle is unstable; if δ'<180°, it is determined that the system power angle is stable.

13. A computer device, comprising: Including: One or more processors; A processor for executing one or more programs; When the one or more programs are executed by the one or more processors, the method of any one of claims 1-6 is implemented.

14. A computer-readable storage medium, characterized in that, The computer program is stored thereon, and when the computer program is executed, the method of any one of claims 1-6 is implemented.

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