Transient stability assessment method, system, terminal equipment and storage medium for multi-machine system based on hyper-tangent plane

Abstract

The present invention discloses a method, system, terminal device and storage medium for transient stability assessment of a multi-machine system based on a hyper-tangent plane. The method constructs a differential algebraic equation group of the multi-machine system according to the state quantity of the multi-machine system, calculates the equilibrium point and Jacobian matrix of the multi-machine system according to the differential algebraic equation group of the multi-machine system, and then determines a class of unstable equilibrium points and Jacobian matrices thereof. The hyper-tangent plane equation is calculated according to the Jacobian matrix of the class of unstable equilibrium points. The nonlinear characteristics of the multi-machine system are analyzed by the hyper-tangent plane equation and the fault trajectory to calculate the critical fault removal time of the multi-machine system, and the transient stability of the multi-machine system is evaluated according to the critical fault removal time, thereby improving the accuracy of the transient stability assessment of the multi-machine system, ensuring the stable operation of the multi-machine system, and solving the problem that the transient stability assessment result of the multi-machine system is low due to the lack of analysis of the nonlinear characteristics of the multi-machine system in the time domain simulation method.

Description

Technical Field

[0001] The present invention relates to the field of transient stability assessment of multi-machine systems, and in particular to a method, system, terminal device and storage medium for transient stability assessment of multi-machine systems based on a hyper-tangent plane. Background Art

[0002] New energy equipment contains energy storage elements of varying capacities. When disturbances occur in the power system, they exhibit varying response speeds, resulting in the entire system exhibiting multi-timescale characteristics. Therefore, when the system experiences a fault, the new energy equipment is equipped with corresponding multi-timescale sequential switching control. Due to the large number of nonlinear control links within new energy equipment, it exhibits strong nonlinearity and strong coupling. Furthermore, compared to traditional synchronous machines, new energy equipment often operates faster, making relay protection based on the response speed of traditional synchronous machines unsuitable. Therefore, assessing the transient stability of multi-machine systems containing new energy equipment becomes a challenging issue.

[0003] Currently, time-domain simulation methods are commonly used to evaluate the transient stability of multi-machine systems containing new energy equipment. However, time-domain simulation methods have difficulty capturing the nonlinear characteristics of dynamic operation in multi-machine systems. Consequently, the lack of analysis of the nonlinear characteristics of multi-machine systems leads to low accuracy in the transient stability evaluation results of multi-machine systems. Summary of the Invention

[0004] The present invention provides a method and system for transient stability assessment of a multi-machine system based on a hyper-tangent plane, which can solve the problem that the time domain simulation method lacks analysis of the nonlinear characteristics of the multi-machine system, resulting in low accuracy of transient stability assessment results of the multi-machine system.

[0005] To solve the above technical problems, an embodiment of the present invention provides a method for transient stability assessment of a multi-machine system based on a hypertangent plane, comprising:

[0006] Establishing a differential equation group and an algebraic equation group of the multi-machine system according to the state quantity of the multi-machine system, and solving the differential equation group and the algebraic equation group to determine several equilibrium points of the multi-machine system;

[0007] Adding disturbances to the differential equations and the algebraic equations, and calculating the Jacobian matrix of each equilibrium point of the multi-machine system;

[0008] Decomposing the Jacobian matrix of each equilibrium point to obtain the decomposed Jacobian matrix of each equilibrium point, and determining a number of first-class unstable equilibrium points according to the decomposed Jacobian matrix of each equilibrium point;

[0009] Calculate the Jacobian matrix of each unstable equilibrium point and decompose the Jacobian matrix of each unstable equilibrium point to obtain the decomposed Jacobian matrix of each unstable equilibrium point;

[0010] Determine the hypertangent plane of each first-class unstable equilibrium point according to the Jacobian matrix after decomposition of each first-class unstable equilibrium point;

[0011] The hyper-tangent plane that first intersects the continuous fault trajectory of the multi-machine system is used as the target hyper-tangent plane, and the critical fault removal time is determined according to the time point when the target hyper-tangent plane intersects the continuous fault trajectory of the multi-machine system.

[0012] The transient stability of the multi-machine system is determined according to the duration of the critical fault clearing time.

[0013] Furthermore, establishing a differential equation group and an algebraic equation group of the multi-machine system based on the state quantities of the multi-machine system, and solving the differential equation group and the algebraic equation group to determine several equilibrium points of the multi-machine system includes:

[0014] Establish a differential equation for each device in the multi-machine system based on the state quantity of each device, and establish a differential equation group for the multi-machine system based on the differential equation of each device;

[0015] According to the output current, line reactance and line voltage of each equipment in the multi-machine system, the algebraic equations of the multi-machine system are established in combination with the coordinate transformation matrix;

[0016] The differential equations and algebraic equations of the multi-machine system are solved simultaneously to determine several equilibrium points of the multi-machine system.

[0017] Furthermore, the adding of disturbances to the differential equations and the algebraic equations, and calculating the Jacobian matrix of each equilibrium point of the multi-machine system, includes:

[0018] At several equilibrium points of the multi-machine system, perturbations are added to the differential equations and algebraic equations of the multi-machine system to obtain the differential equations and algebraic equations with added perturbations;

[0019] The Jacobian matrix of each equilibrium point of the multi-machine system is calculated based on the differential equations with added disturbances and the algebraic equations with added disturbances.

[0020] Furthermore, the Jacobian matrix of each equilibrium point is decomposed to obtain the decomposed Jacobian matrix of each equilibrium point, and a number of first-class unstable equilibrium points are determined according to the decomposed Jacobian matrix of each equilibrium point, including:

[0021] The Jacobian matrix of each equilibrium point is decomposed by the SVD method to obtain the characteristic root matrix of each equilibrium point, and several first-class unstable equilibrium points are determined according to the characteristic root matrix.

[0022] Furthermore, the calculation of the Jacobian matrix of each unstable equilibrium point of the first type and the decomposition of the Jacobian matrix of each unstable equilibrium point of the first type to obtain the decomposed Jacobian matrix of each unstable equilibrium point of the first type include:

[0023] The Jacobian matrix of each first-class unstable equilibrium point is calculated according to each first-class unstable equilibrium point, and the Jacobian matrix of each first-class unstable equilibrium point is decomposed by the SVD method to obtain the left characteristic matrix and characteristic root matrix of each first-class unstable equilibrium point.

[0024] Furthermore, determining the hypertangent plane of each first-class unstable equilibrium point according to the Jacobian matrix decomposed from each first-class unstable equilibrium point includes:

[0025] According to the unique positive eigenvalue in the eigenvalue matrix of each first-class unstable equilibrium point and the left eigenvector of the left eigenvalue matrix corresponding to the positive eigenvalue, the hypertangent plane equation of each first-class unstable equilibrium point is calculated, and then the hypertangent plane of each first-class unstable equilibrium point is determined.

[0026] Furthermore, the method of using the hyper-tangent plane that first intersects the continuous fault trajectory of the multi-machine system as the target hyper-tangent plane and determining the critical fault removal time according to the time point when the target hyper-tangent plane intersects the continuous fault trajectory of the multi-machine system includes:

[0027] The continuous fault trajectory of a multi-machine system is calculated by the classic fourth-order Runge-Kutta method. The state variables of the continuous fault trajectory are substituted into the hypertangent plane equation of each first-class unstable equilibrium point to calculate the solution of the hypertangent plane equation.

[0028] Determine the hyper-tangent plane that first intersects the continuous fault trajectory of the multi-machine system according to the solution of the hyper-tangent plane equation, and use the hyper-tangent plane that first intersects the continuous fault trajectory of the multi-machine system as the target hyper-tangent plane;

[0029] The critical fault removal time is determined based on the time point where the target hyper-cut plane intersects the continuous fault trajectory of the multi-machine system.

[0030] Based on the above method embodiment, the present invention provides a corresponding system embodiment;

[0031] An embodiment of the present invention provides a multi-machine system transient stability assessment system based on a hypertangent plane, comprising: a differential algebra and equilibrium point determination module, an equilibrium point Jacobian matrix calculation module, a type of unstable equilibrium point determination module, a type of unstable equilibrium point Jacobian matrix calculation module, a type of unstable equilibrium point hypertangent plane determination module, a fault critical removal time determination module, and a transient stability assessment module;

[0032] The differential-algebra and equilibrium point determination module is used to establish a differential equation group and an algebraic equation group of the multi-machine system according to the state quantity of the multi-machine system, and solve the differential equation group and the algebraic equation group to determine a plurality of equilibrium points of the multi-machine system;

[0033] The equilibrium point Jacobian matrix calculation module is used to add disturbances to the differential equations and the algebraic equations, and calculate the Jacobian matrix of each equilibrium point of the multi-machine system;

[0034] The first-class unstable equilibrium point determination module is used to decompose the Jacobian matrix of each equilibrium point to obtain the decomposed Jacobian matrix of each equilibrium point, and determine a plurality of first-class unstable equilibrium points according to the decomposed Jacobian matrix of each equilibrium point;

[0035] The first-class unstable equilibrium point Jacobian matrix calculation module is used to calculate the Jacobian matrix of each first-class unstable equilibrium point, and decompose the Jacobian matrix of each first-class unstable equilibrium point to obtain the decomposed Jacobian matrix of each first-class unstable equilibrium point;

[0036] The hypertangent plane determining module of the first type of unstable equilibrium point is used to determine the hypertangent plane of each first type of unstable equilibrium point according to the Jacobian matrix after decomposition of each first type of unstable equilibrium point;

[0037] The critical fault removal time determination module is used to use the hyper-tangent plane that first intersects the continuous fault trajectory of the multi-machine system as the target hyper-tangent plane, and determine the critical fault removal time according to the time point when the target hyper-tangent plane intersects the continuous fault trajectory of the multi-machine system;

[0038] The transient stability evaluation module is used to determine the transient stability of the multi-machine system according to the duration of the critical fault clearing time.

[0039] Based on the above-mentioned method embodiment, the present invention provides a corresponding terminal device embodiment, including: a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, it implements the transient stability assessment method of a multi-machine system based on a hyper-cutting plane as described in the present invention.

[0040] Based on the above-mentioned method embodiment, the present invention provides a corresponding computer-readable storage medium embodiment, including: a stored computer program, which, when the computer program is running, controls the device where the computer-readable storage medium is located to execute the multi-machine system transient stability assessment method based on the hyper-cutting plane as described in the present invention.

[0041] Compared with the prior art, the embodiments of the present invention have the following beneficial effects:

[0042] The present invention constructs a differential algebraic equation group of the multi-machine system according to the state quantity of the multi-machine system, calculates the equilibrium point and the Jacobian matrix of the multi-machine system according to the differential algebraic equation group of the multi-machine system, and then determines a class of unstable equilibrium points and their Jacobian matrices, calculates the hypertangent plane equation according to the Jacobian matrix of the class of unstable equilibrium points, analyzes the nonlinear characteristics of the multi-machine system through the hypertangent plane equation and the fault trajectory, calculates the critical fault removal time of the multi-machine system, and evaluates the transient stability of the multi-machine system according to the critical fault removal time, thereby improving the accuracy of the transient stability evaluation of the multi-machine system and ensuring the stable operation of the multi-machine system, solving the problem that the time domain simulation method is difficult to capture the nonlinear characteristics of the dynamic operation of the multi-machine system, and thus the lack of analysis of the nonlinear characteristics of the multi-machine system leads to low accuracy of the transient stability evaluation result of the multi-machine system. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 : A flowchart of the steps of a method for transient stability assessment of a multi-machine system based on a hyper-tangent plane provided by an embodiment of the present invention;

[0044] Figure 2 : A topological diagram of a three-machine, nine-node system provided by an embodiment of the present invention;

[0045] Figure 3 : A time-domain simulation diagram of system stability and instability obtained at different critical fault removal times when a fault occurs in a multi-machine system provided by an embodiment of the present invention;

[0046] Figure 4 : A system structure diagram of a multi-machine system transient stability assessment system based on a hypercut plane provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0047] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0048] In the description of the present invention, it should be understood that the term "first" is only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features.

[0049] Example 1:

[0050] Please refer to Figure 1 , is a flowchart of a method for transient stability assessment of a multi-machine system based on a hyper-tangent plane provided by an embodiment of the present invention, the method comprising at least the following steps:

[0051] Step S1: establishing a differential equation system and an algebraic equation system of the multi-machine system according to the state quantity of the multi-machine system, and solving the differential equation system and the algebraic equation system to determine several equilibrium points of the multi-machine system;

[0052] In this embodiment, the method of establishing a differential equation system and an algebraic equation system of the multi-machine system based on the state quantities of the multi-machine system, and solving the differential equation system and the algebraic equation system to determine several equilibrium points of the multi-machine system includes:

[0053] Establish a differential equation for each device in the multi-machine system based on the state quantity of each device, and establish a differential equation group for the multi-machine system based on the differential equation of each device;

[0054] In this embodiment, the state quantity of each device includes [θ plli , x plli ], where θ plli Indicates that the phase-locked loop of the i-th device provides the angle between the dq coordinate system and the common rotating xy coordinate system, x plli represents the output of the integrator of the phase-locked loop PI control of the i-th device; the differential equation of each device satisfies the following formula:

[0055] where k ipll represents the integral coefficient of the phase-locked loop PI controller of the i-th device, k ppll represents the proportional coefficient of the phase-locked loop PI controller of the i-th device;

[0056] According to the output current, line reactance and line voltage of each equipment in the multi-machine system, the algebraic equations of the multi-machine system are established in combination with the coordinate transformation matrix;

[0057] The derivative terms of the differential equations of the multi-machine system are set to zero, and the algebraic equations of the multi-machine system are solved in parallel to determine several equilibrium points of the multi-machine system;

[0058] In this embodiment, the differential equations of the multi-machine system represent the relationship between the various state quantities in the multi-machine system and time; the algebraic equations of the multi-machine system represent the balance relationship between the various state quantities in the multi-machine system.

[0059] Step S2: adding disturbances to the differential equations and the algebraic equations, and calculating the Jacobian matrix of each equilibrium point of the multi-machine system;

[0060] In this embodiment, adding disturbances to the differential equations and the algebraic equations and calculating the Jacobian matrix of each equilibrium point of the multi-machine system includes:

[0061] At several equilibrium points of the multi-machine system, perturbations are added to the differential equations and algebraic equations of the multi-machine system to obtain the differential equations and algebraic equations with added perturbations;

[0062] The Jacobian matrix of each equilibrium point of the multi-machine system is calculated based on the differential equations with added disturbances and the algebraic equations with added disturbances.

[0063] Step S3: Decomposing the Jacobian matrix of each equilibrium point to obtain the decomposed Jacobian matrix of each equilibrium point, and determining a number of first-class unstable equilibrium points according to the decomposed Jacobian matrix of each equilibrium point;

[0064] In this embodiment, the Jacobian matrix of each equilibrium point is decomposed to obtain the decomposed Jacobian matrix of each equilibrium point, and a number of first-class unstable equilibrium points are determined according to the decomposed Jacobian matrix of each equilibrium point, including:

[0065] The Jacobian matrix of each equilibrium point is decomposed by the SVD method to obtain the characteristic root matrix of each equilibrium point, and several first-class unstable equilibrium points are determined based on the characteristic root matrix;

[0066] In this embodiment, in the characteristic sum matrix of each equilibrium point of the multi-machine system, the equilibrium point is a type of unstable equilibrium point if and only if there is only one positive characteristic root and three negative characteristic roots in the characteristic sum matrix.

[0067] Step S4: Calculate the Jacobian matrix of each unstable equilibrium point, and decompose the Jacobian matrix of each unstable equilibrium point to obtain the decomposed Jacobian matrix of each unstable equilibrium point;

[0068] In this embodiment, the calculation of the Jacobian matrix of each unstable equilibrium point of the first type and the decomposition of the Jacobian matrix of each unstable equilibrium point of the first type to obtain the decomposed Jacobian matrix of each unstable equilibrium point of the first type include:

[0069] Calculate the Jacobian matrix of each unstable equilibrium point according to each unstable equilibrium point, and decompose the Jacobian matrix of each unstable equilibrium point by SVD method to obtain the left characteristic matrix and characteristic root matrix of each unstable equilibrium point;

[0070] In this embodiment, the hypertangent plane equation of each type of unstable equilibrium point is calculated based on the unique positive eigenvalue in the eigenvalue matrix of each type of unstable equilibrium point and the left eigenvector of the left eigenvalue matrix corresponding to the positive eigenvalue, and then the hypertangent plane of each type of unstable equilibrium point is determined.

[0071] Step S5: determining the hypertangent plane of each first-class unstable equilibrium point according to the Jacobian matrix after decomposition of each first-class unstable equilibrium point;

[0072] In this embodiment, determining the hypertangent plane of each first-class unstable equilibrium point according to the Jacobian matrix decomposed from each first-class unstable equilibrium point includes:

[0073] In this embodiment, the hypertangent plane equation of each first-class unstable equilibrium point is calculated based on the unique positive eigenvalue in the eigenvalue matrix of each first-class unstable equilibrium point and the left eigenvector of the left eigenvalue matrix corresponding to the positive eigenvalue, thereby determining the hypertangent plane of each first-class unstable equilibrium point.

[0074] In this embodiment, the supertangent plane equation of each type of unstable equilibrium point is Among them, x represents the state column vector of the multi-machine system, x usep represents the state column vector of a type of unstable equilibrium point, represents the transpose of the left eigenvector of this type of unstable equilibrium point.

[0075] Step S6: taking the hyper-tangent plane that first intersects the continuous fault trajectory of the multi-machine system as the target hyper-tangent plane, and determining the critical fault removal time according to the time point at which the target hyper-tangent plane intersects the continuous fault trajectory of the multi-machine system;

[0076] In this embodiment, the method of using the hyper-tangent plane that first intersects the continuous fault trajectory of the multi-machine system as the target hyper-tangent plane and determining the critical fault removal time according to the time point when the target hyper-tangent plane intersects the continuous fault trajectory of the multi-machine system includes:

[0077] The continuous fault trajectory of a multi-machine system is calculated by the classic fourth-order Runge-Kutta method. The state variables of the continuous fault trajectory are substituted into the hypertangent plane equation of each first-class unstable equilibrium point to calculate the solution of the hypertangent plane equation.

[0078] In this embodiment, the initial state value of stable operation, the time of fault occurrence, and the fault condition are set for the multi-machine system, and the classic fourth-order Runge-Kutta method is used to calculate the continuous fault trajectory when the multi-machine system fails. The state quantity of the continuous fault trajectory is substituted into the hypertangent plane equation of each first-class unstable equilibrium point to calculate the solution of the hypertangent plane equation.

[0079] Determine the hyper-tangent plane that first intersects the continuous fault trajectory of the multi-machine system according to the solution of the hyper-tangent plane equation, and use the hyper-tangent plane that first intersects the continuous fault trajectory of the multi-machine system as the target hyper-tangent plane;

[0080] In this embodiment, the state quantity of the continuous fault trajectory is substituted into the hypertangent plane equation of each first-class unstable equilibrium point to calculate the hypertangent plane equation solution. When a hypertangent plane equation solution is greater than 0 for the first time, it is considered that the continuous fault trajectory at that moment has crossed the hypertangent plane; when a hypertangent plane equation solution is less than zero, it is considered that the continuous fault trajectory at that moment does not intersect the plane equation.

[0081] Determine the critical fault removal time based on the time point where the target hyper-tangent plane intersects the continuous fault trajectory of the multi-machine system;

[0082] In this embodiment, the time point at which the target hyper-tangent plane intersects the continuous fault trajectory of the multi-machine system minus a preset step length is used as the critical fault removal time.

[0083] Step S7: determining the transient stability of the multi-machine system according to the duration of the critical fault clearing time;

[0084] In this embodiment, when the critical fault clearing time is shorter, the transient stability of the multi-machine system is worse; when the critical fault clearing time is longer, the transient stability of the multi-machine system is better.

[0085] Example 2:

[0086] Please refer to Figure 2 , is a topological structure diagram of a three-machine nine-node system provided by an embodiment of the present invention. Node 3 is a balancing node, and nodes 1 and 2 are new energy equipment. The transient stability assessment method for a multi-machine system based on a hypercut plane described in Example 1 is used to perform a transient stability assessment on the three-machine nine-node system. The steps are as follows:

[0087] Step A1: A differential equation group of the three-machine nine-node system is established based on the state quantities of node 1 and node 2 of the three-machine nine-node system. The differential equation group of the three-machine nine-node system satisfies the following formula:

[0088] The voltage vector calculation formula of the PCC node is calculated based on the line reactance of the three-machine nine-node system, the voltage vector of node 1, the voltage vector of node 2, and the voltage vector of node 3. The voltage vector calculation formula of the PCC node is: X1, X2, and X3 represent the line reactances of the three-machine nine-bus system; represents the voltage vector of node 1; represents the voltage vector of node 2; represents the voltage vector of node 3;

[0089] Under the common rotating xy coordinates, the vector equations of nodes 1, 2, and 3 are calculated according to the voltage vector calculation formula of the PCC node. The vector equations are as follows: Among them, j represents an imaginary number, is the admittance matrix. The expressions of the coefficients in the admittance matrix are as follows:

[0090] In this embodiment, a scalar equation is calculated based on the vector equation, the current vector equation, and the voltage vector equation; wherein the expressions of the current vector equation and the voltage vector equation are respectively The scalar equation is The expression of matrix Y is:

[0091] The algebraic equations of the three-machine nine-node system are calculated based on the scalar equation and the transformation matrix; wherein the transformation matrix is The algebraic equations of the three-machine nine-node system are: U gd =U g cosθ pll，1 , U gq =-U g sinθp ll，1 ;

[0092] The system of differential equations and algebraic equations of the three-machine nine-bus system is solved to determine several equilibrium points of the three-machine nine-bus system.

[0093] In this embodiment, the derivative of the differential equations of the three-machine nine-node system is set to 0, and we get The algebraic equations of the three-machine nine-bus system are solved in parallel to determine several equilibrium points of the three-machine nine-bus system.

[0094] Step A2: At several equilibrium points of the multi-machine system, perturbations are added to the differential equations and algebraic equations of the three-machine nine-bus system to obtain the perturbed differential equations and algebraic equations, and the Jacobian matrix of each equilibrium point of the three-machine nine-bus system is calculated based on the perturbed differential equations and algebraic equations.

[0095] In this embodiment, the differential equations for adding disturbance are: The algebraic equations for adding disturbances are The transformation matrix for adding perturbation is Among them, θ pll，i0 represents the phase-locked loop phase of the ith device at the equilibrium point.

[0096] Step A3: Decompose the Jacobian matrix of each equilibrium point of the three-machine nine-bus system to obtain the decomposed Jacobian matrix of each equilibrium point of the three-machine nine-bus system. Determine several first-class unstable equilibrium points based on the decomposed Jacobian matrix of each equilibrium point of the three-machine nine-bus system.

[0097] In this embodiment, the Jacobian matrix of each equilibrium point of the three-machine nine-bus system is decomposed by the SVD method to obtain the characteristic root matrix of each equilibrium point of the three-machine nine-bus system, and several first-class unstable equilibrium points are determined based on the characteristic root matrix;

[0098] In this embodiment, in the characteristic root matrix of each equilibrium point of the three-machine nine-node system, the equilibrium point is a type of unstable equilibrium point of the three-machine nine-node system if and only if there is only one positive characteristic root and three negative characteristic roots in the characteristic root matrix.

[0099] Step A4: Calculate the Jacobian matrix of each first-class unstable equilibrium point of the three-machine nine-bus system, and decompose the Jacobian matrix of each first-class unstable equilibrium point of the three-machine nine-bus system to obtain the decomposed Jacobian matrix of each first-class unstable equilibrium point of the three-machine nine-bus system;

[0100] In this embodiment, the Jacobian matrix of each first-class unstable equilibrium point of the three-machine nine-bus system is calculated based on each first-class unstable equilibrium point, and the Jacobian matrix of each first-class unstable equilibrium point of the three-machine nine-bus system is decomposed by the SVD method to obtain the left characteristic matrix and characteristic root matrix of each first-class unstable equilibrium point;

[0101] In this embodiment, based on the unique positive eigenvalue in the eigenvalue matrix of each type of unstable equilibrium point of the three-machine nine-node system and the left eigenvector of the left eigenvalue matrix corresponding to the positive eigenvalue, the hypertangent plane equation of each type of unstable equilibrium point of the three-machine nine-node system is calculated, and then the hypertangent plane of each type of unstable equilibrium point of the three-machine nine-node system is determined.

[0102] Step A5: Determine the hypertangent plane of each first-class unstable equilibrium point of the three-machine nine-bus system according to the decomposed Jacobian matrix of each first-class unstable equilibrium point of the three-machine nine-bus system;

[0103] In this embodiment, based on the unique positive eigenvalue in the eigenvalue matrix of each first-class unstable equilibrium point of the three-machine nine-node system and the left eigenvector of the left eigenvalue matrix corresponding to the positive eigenvalue, the hypertangent plane equation of each first-class unstable equilibrium point of the three-machine nine-node system is calculated, and then the hypertangent plane of each first-class unstable equilibrium point of the three-machine nine-node system is determined.

[0104] In this embodiment, the hypertangent plane equation of each first-class unstable equilibrium point of the three-machine nine-node system is Where x represents the state column vector of the three-machine nine-node system, x usep The state column vector representing a type of unstable equilibrium point of a three-machine nine-node system, The transpose of the left eigenvector representing a type of unstable equilibrium point of a three-machine, nine-node system.

[0105] Step A6: The hyper-tangent plane that first intersects the continuous fault trajectory of the three-machine nine-bus system is used as the target hyper-tangent plane. The critical fault removal time is determined based on the time point at which the target hyper-tangent plane intersects the continuous fault trajectory of the three-machine nine-bus system.

[0106] In this embodiment, the initial state values ​​of stable operation, the time of fault occurrence, and the fault conditions are set for the three-machine, nine-bus system. The classic fourth-order Runge-Kutta method is used to calculate the continuous fault trajectory when the three-machine, nine-bus system fails. The state quantities of the continuous fault trajectory are substituted into the hypertangent plane equation of each first-class unstable equilibrium point of the three-machine, nine-bus system to calculate the solution of the hypertangent plane equation.

[0107] Determine the hypertangent plane that first intersects the continuous fault trajectory of the three-machine nine-bus system based on the solution of the hypertangent plane equation, and use the hypertangent plane that first intersects the continuous fault trajectory of the three-machine nine-bus system as the target hypertangent plane;

[0108] In this embodiment, the state quantity of the continuous fault trajectory is substituted into the hypertangent plane equation of each first-class unstable equilibrium point of the three-machine nine-node system to calculate the hypertangent plane equation solution. When a hypertangent plane equation solution is greater than 0 for the first time, it is considered that the continuous fault trajectory at that moment has crossed the hypertangent plane; when a hypertangent plane equation solution is less than zero, it is considered that the continuous fault trajectory at that moment does not intersect the plane equation.

[0109] The time point where the target hyper-tangent plane intersects the continuous fault trajectory of the three-machine nine-bus system minus a preset step length is taken as the critical fault removal time of the three-machine nine-bus system.

[0110] Step A7: Determine the transient stability of the three-machine nine-bus system based on the critical fault clearing time of the three-machine nine-bus system;

[0111] In this embodiment, when the critical fault clearing time is shorter, the transient stability of the multi-machine system is worse; when the critical fault clearing time is longer, the transient stability of the multi-machine system is better.

[0112] Reference Figure 3 , which is a time domain simulation diagram of system stability and instability obtained at different critical fault removal times when a fault occurs in a multi-machine system provided by an embodiment of the present invention, according to Figure 3 It can be seen that the critical fault removal simulation time of the three-machine nine-bus system is 0.06s; when the bus voltage drops to 0.4pu at 1s, it takes 0.06s and 0.07s to recover to the initial state respectively. Figure 3 As shown in the implementation, when the fault is removed in 1.06s, the three-machine nine-bus system is transiently stable; according to Figure 3 As shown by the dotted line in , when the fault is removed at 1.07s, the three-machine nine-bus system becomes transiently unstable.

[0113] Example 3:

[0114] Please refer to Figure 4 , which is a system structure diagram of a multi-machine system transient stability assessment system based on a hypertangent plane provided by an embodiment of the present invention, the system includes: a differential algebra and equilibrium point determination module, an equilibrium point Jacobian matrix calculation module, a type of unstable equilibrium point determination module, a type of unstable equilibrium point Jacobian matrix calculation module, a type of unstable equilibrium point hypertangent plane determination module, a fault critical removal time determination module, and a transient stability assessment module;

[0115] The differential-algebra and equilibrium point determination module is used to establish a differential equation group and an algebraic equation group of the multi-machine system according to the state quantity of the multi-machine system, and solve the differential equation group and the algebraic equation group to determine a plurality of equilibrium points of the multi-machine system;

[0116] The equilibrium point Jacobian matrix calculation module is used to add disturbances to the differential equations and the algebraic equations, and calculate the Jacobian matrix of each equilibrium point of the multi-machine system;

[0117] The first-class unstable equilibrium point determination module is used to decompose the Jacobian matrix of each equilibrium point to obtain the decomposed Jacobian matrix of each equilibrium point, and determine a plurality of first-class unstable equilibrium points according to the decomposed Jacobian matrix of each equilibrium point;

[0118] The first-class unstable equilibrium point Jacobian matrix calculation module is used to calculate the Jacobian matrix of each first-class unstable equilibrium point, and decompose the Jacobian matrix of each first-class unstable equilibrium point to obtain the decomposed Jacobian matrix of each first-class unstable equilibrium point;

[0119] The hypertangent plane determining module of the first type of unstable equilibrium point is used to determine the hypertangent plane of each first type of unstable equilibrium point according to the Jacobian matrix after decomposition of each first type of unstable equilibrium point;

[0120] The critical fault removal time determination module is used to use the hyper-tangent plane that first intersects the continuous fault trajectory of the multi-machine system as the target hyper-tangent plane, and determine the critical fault removal time according to the time point when the target hyper-tangent plane intersects the continuous fault trajectory of the multi-machine system;

[0121] The transient stability evaluation module is used to determine the transient stability of the multi-machine system according to the duration of the critical fault clearing time.

[0122] Based on the above method embodiment, another embodiment is provided;

[0123] Another embodiment of the present invention provides a terminal device for transient stability assessment of a multi-machine system based on a hyper-cutting plane, comprising a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, the method for transient stability assessment of a multi-machine system based on a hyper-cutting plane described in any one of the above-mentioned method embodiments of the present invention is implemented.

[0124] Exemplarily, the computer program may be divided into one or more modules / units, which are stored in the memory and executed by the processor to implement the present invention. The one or more modules / units may be a series of computer program instruction segments capable of performing specific functions, and the instruction segments are used to describe the execution process of the computer program in the terminal device for transient stability assessment of a multi-machine system based on a hypercut plane.

[0125] The hyper-section plane-based multi-machine system transient stability assessment terminal device can be a computing device such as a desktop computer, laptop, PDA, or cloud server. The hyper-section plane-based multi-machine system transient stability assessment terminal device can include, but is not limited to, a processor and memory. Those skilled in the art will appreciate that, for example, the hyper-section plane-based multi-machine system transient stability assessment terminal device can also include input / output devices, network access devices, buses, and the like.

[0126] The processor may be a central processing unit (CPU), other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor, etc. The processor serves as the control center of the multi-machine system transient stability assessment terminal device based on the hyper-cutting plane, and utilizes various interfaces and lines to connect various parts of the multi-machine system transient stability assessment terminal device based on the hyper-cutting plane.

[0127] The memory can be used to store the computer program and / or module, and the processor implements the various functions of the terminal device for transient stability assessment of a multi-machine system based on a hypercut plane by running or executing the computer program and / or module stored in the memory and calling the data stored in the memory. The memory can mainly include a program storage area and a data storage area, wherein the program storage area can store an operating system, an application required for at least one function (such as a sound playback function, an image playback function, etc.), etc.; the data storage area can store data created based on the use of the mobile phone (such as audio data, a phone book, etc.). In addition, the memory can include a high-speed random access memory and can also include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), at least one disk storage device, a flash memory device, or other volatile solid-state storage device.

[0128] Based on the above method embodiment, another embodiment is provided;

[0129] Another embodiment of the present invention provides a storage medium, including a stored computer program, wherein, when the computer program is running, the device where the storage medium is located is controlled to execute the multi-machine system transient stability assessment method based on the hyper-cutting plane as described in any one of the above-mentioned method embodiments of the present invention.

[0130] The storage medium is a computer-readable storage medium. If the module / unit of the multi-machine system transient stability assessment system / terminal device integrated based on the hypercut plane is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present invention can implement all or part of the processes in the above-mentioned embodiment method by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, it can implement the steps of each of the above-mentioned method embodiments. The computer program includes computer program code, which can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signal, telecommunication signal and software distribution medium.

[0131] It should be noted that the above-mentioned terminal device may include, but is not limited to, a processor and a memory. Those skilled in the art will understand that the above-mentioned terminal device is merely an example and does not constitute a limitation on the terminal device. It may include more or fewer components, or a combination of certain components, or different components.

[0132] The specific embodiments described above further illustrate the objectives, technical solutions, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. In particular, it should be noted that any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included within the scope of protection of the present invention for those skilled in the art.

Claims

1. A method for transient stability assessment of a multi-machine system based on a hyper-tangent plane, characterized in that: include: Establishing a differential equation group and an algebraic equation group of the multi-machine system according to the state quantity of the multi-machine system, and solving the differential equation group and the algebraic equation group to determine several equilibrium points of the multi-machine system; Adding disturbances to the differential equations and the algebraic equations, and calculating the Jacobian matrix of each equilibrium point of the multi-machine system; Decomposing the Jacobian matrix of each equilibrium point to obtain the decomposed Jacobian matrix of each equilibrium point, and determining a number of first-class unstable equilibrium points according to the decomposed Jacobian matrix of each equilibrium point; Calculate the Jacobian matrix of each unstable equilibrium point and decompose the Jacobian matrix of each unstable equilibrium point to obtain the decomposed Jacobian matrix of each unstable equilibrium point; Determine the hypertangent plane of each first-class unstable equilibrium point according to the Jacobian matrix after decomposition of each first-class unstable equilibrium point; The hyper-tangent plane that first intersects the continuous fault trajectory of the multi-machine system is used as the target hyper-tangent plane, and the critical fault removal time is determined according to the time point when the target hyper-tangent plane intersects the continuous fault trajectory of the multi-machine system. The transient stability of the multi-machine system is determined according to the duration of the critical fault clearing time.

2. The method for transient stability assessment of a multi-machine system based on a hypercut plane according to claim 1, characterized in that: The step of establishing a differential equation group and an algebraic equation group of the multi-machine system according to the state quantity of the multi-machine system, and solving the differential equation group and the algebraic equation group to determine a plurality of equilibrium points of the multi-machine system includes: Establish a differential equation for each device in the multi-machine system based on the state quantity of each device, and establish a differential equation group for the multi-machine system based on the differential equation of each device; According to the output current, line reactance and line voltage of each equipment in the multi-machine system, the algebraic equations of the multi-machine system are established in combination with the coordinate transformation matrix; The differential equations and algebraic equations of the multi-machine system are solved simultaneously to determine several equilibrium points of the multi-machine system.

3. The method for transient stability assessment of a multi-machine system based on a hypercut plane according to claim 2, characterized in that: Adding disturbances to the differential equations and the algebraic equations, and calculating the Jacobian matrix of each equilibrium point of the multi-machine system, includes: At several equilibrium points of the multi-machine system, perturbations are added to the differential equations and algebraic equations of the multi-machine system to obtain the differential equations and algebraic equations with added perturbations; The Jacobian matrix of each equilibrium point of the multi-machine system is calculated based on the differential equations with added disturbances and the algebraic equations with added disturbances.

4. The method for transient stability assessment of a multi-machine system based on a hyper-tangent plane according to claim 1, characterized in that: The Jacobian matrix of each equilibrium point is decomposed to obtain the decomposed Jacobian matrix of each equilibrium point, and a plurality of first-class unstable equilibrium points are determined according to the decomposed Jacobian matrix of each equilibrium point, including: The Jacobian matrix of each equilibrium point is decomposed by the SVD method to obtain the characteristic root matrix of each equilibrium point, and several first-class unstable equilibrium points are determined according to the characteristic root matrix.

5. The method for transient stability assessment of a multi-machine system based on a hypercut plane according to claim 1, characterized in that: The calculating of the Jacobian matrix of each unstable equilibrium point of the first class and decomposing the Jacobian matrix of each unstable equilibrium point of the first class to obtain the decomposed Jacobian matrix of each unstable equilibrium point of the first class includes: The Jacobian matrix of each first-class unstable equilibrium point is calculated according to each first-class unstable equilibrium point, and the Jacobian matrix of each first-class unstable equilibrium point is decomposed by the SVD method to obtain the left characteristic matrix and characteristic root matrix of each first-class unstable equilibrium point.

6. The method for transient stability assessment of a multi-machine system based on a hypercut plane according to claim 2, characterized in that: Determining the hypertangent plane of each first-class unstable equilibrium point according to the Jacobian matrix decomposed from each first-class unstable equilibrium point includes: According to the unique positive eigenvalue in the eigenvalue matrix of each first-class unstable equilibrium point and the left eigenvector of the left eigenvalue matrix corresponding to the positive eigenvalue, the hypertangent plane equation of each first-class unstable equilibrium point is calculated, and then the hypertangent plane of each first-class unstable equilibrium point is determined.

7. The method for transient stability assessment of a multi-machine system based on a hyper-tangent plane according to claim 6, characterized in that: The method of using the hyper-tangent plane that first intersects the continuous fault trajectory of the multi-machine system as the target hyper-tangent plane and determining the critical fault removal time according to the time point when the target hyper-tangent plane intersects the continuous fault trajectory of the multi-machine system includes: The continuous fault trajectory of a multi-machine system is calculated by the classic fourth-order Runge-Kutta method. The state variables of the continuous fault trajectory are substituted into the hypertangent plane equation of each first-class unstable equilibrium point to calculate the solution of the hypertangent plane equation. Determine the hyper-tangent plane that first intersects the continuous fault trajectory of the multi-machine system according to the solution of the hyper-tangent plane equation, and use the hyper-tangent plane that first intersects the continuous fault trajectory of the multi-machine system as the target hyper-tangent plane; The critical fault removal time is determined based on the time point where the target hyper-cut plane intersects the continuous fault trajectory of the multi-machine system.

8. The multi-machine system transient stability assessment system based on the hyper-cutting plane is characterized by: include: Differential algebra and equilibrium point determination module, equilibrium point Jacobian matrix calculation module, a type of unstable equilibrium point determination module, a type of unstable equilibrium point Jacobian matrix calculation module, a type of unstable equilibrium point hypertangent plane determination module, a fault critical removal time determination module and a transient stability assessment module; The differential-algebra and equilibrium point determination module is used to establish a differential equation group and an algebraic equation group of the multi-machine system according to the state quantity of the multi-machine system, and solve the differential equation group and the algebraic equation group to determine a plurality of equilibrium points of the multi-machine system; The equilibrium point Jacobian matrix calculation module is used to add disturbances to the differential equations and the algebraic equations, and calculate the Jacobian matrix of each equilibrium point of the multi-machine system; The first-class unstable equilibrium point determination module is used to decompose the Jacobian matrix of each equilibrium point to obtain the decomposed Jacobian matrix of each equilibrium point, and determine a plurality of first-class unstable equilibrium points according to the decomposed Jacobian matrix of each equilibrium point; The first-class unstable equilibrium point Jacobian matrix calculation module is used to calculate the Jacobian matrix of each first-class unstable equilibrium point, and decompose the Jacobian matrix of each first-class unstable equilibrium point to obtain the decomposed Jacobian matrix of each first-class unstable equilibrium point; The hypertangent plane determining module of the first type of unstable equilibrium point is used to determine the hypertangent plane of each first type of unstable equilibrium point according to the Jacobian matrix after decomposition of each first type of unstable equilibrium point; The critical fault removal time determination module is used to use the hyper-tangent plane that first intersects the continuous fault trajectory of the multi-machine system as the target hyper-tangent plane, and determine the critical fault removal time according to the time point when the target hyper-tangent plane intersects the continuous fault trajectory of the multi-machine system; The transient stability evaluation module is used to determine the transient stability of the multi-machine system according to the duration of the critical fault clearing time.

9. A terminal device for transient stability assessment of a multi-machine system based on a hyper-cutting plane, comprising a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein when the processor executes the computer program, the method for transient stability assessment of a multi-machine system based on a hyper-cutting plane as described in any one of claims 1 to 7 is implemented.

10. A storage medium, characterized in that: The storage medium includes a stored computer program, wherein when the computer program is running, the device where the storage medium is located is controlled to execute the method for transient stability assessment of a multi-machine system based on a hyper-cutting plane according to any one of claims 1 to 7.

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