Double-high-characteristic electric power transient stability analysis method, system, equipment and medium

Abstract

The invention relates to the technical field of electric power system transient state analysis, in particular to a double-high-characteristic electric power transient state stability analysis method, system and device and a medium. The nonlinear part of the model is limited in an adjustable neighborhood of a given balance point so as to construct a Lyapunov function; the estimation of a Lyapunov function time derivative is improved by introducing a non-uniform limiting condition, and the conservative property is reduced; meanwhile, the construction of the Lyapunov function and the lower limit estimation of the fault clearing time are subjected to collaborative optimization, so that more accurate fault clearing time estimation is obtained; according to the method, the optimal Lyapunov function and parameters are solved by using the semi-definite programming problem, the method effectively adapts to the complex dynamic characteristics of high-proportion renewable energy and power electronic equipment, and the transient stability analysis precision and reliability of a power system are improved.

Description

Technical Field

[0001] This invention relates to the field of power system transient analysis technology, and in particular to a method, system, equipment and medium for power transient stability analysis with dual high characteristics. Background Technology

[0002] With the continuous expansion and increasing complexity of power systems, the integration of high proportions of renewable energy (such as wind and solar power) and power electronic equipment has given power systems a "dual-high" characteristic, posing new challenges to their stable operation. Transient stability, a key performance indicator of power systems, reflects the system's ability to maintain synchronous operation and recover to a stable state after being subjected to large disturbances. With the large-scale integration of renewable energy (such as wind and solar power), the dynamic characteristics of power systems have become more complex, and existing analysis methods and control systems are no longer sufficient to meet practical needs.

[0003] Traditional transient stability analysis methods mainly include time-domain simulation and direct methods. Time-domain simulation simulates the dynamic behavior of a system through numerical integration and can handle complex system models, but it requires a large amount of computation and is difficult to meet real-time requirements. Direct methods, on the other hand, are based on energy functions or topological properties, avoid numerical integration, and can quickly screen faults and provide stability information, but they are more conservative and have more restrictions on the system model.

[0004] Therefore, researching new methods and systems for transient stability analysis applicable to power systems with "high energy consumption and high emissions" characteristics is of great significance for improving the transient stability of power systems, promoting the efficient utilization of renewable energy, and ensuring the safe and stable operation of power systems. Summary of the Invention

[0005] In view of the aforementioned existing problems, the present invention is proposed.

[0006] Therefore, this invention provides a dual-high characteristic power transient stability analysis method and system to solve the technical problems of inaccurate transient stability analysis, high conservatism, and low precision in existing technologies when analyzing high-proportion renewable energy and high-proportion power electronic equipment connected to the grid, due to their complex and variable dynamic characteristics. This invention proposes an adaptive Lyapunov function (ALF) method for systematically performing transient stability analysis, significantly reducing conservatism. By proposing an adaptive sector condition within the adjustable neighborhood of the post-fault stable equilibrium point (SEP), the nonlinearity of the power system model is constrained, providing additional degrees of freedom for the construction of the Lyapunov function. Simultaneously, an improved simulation-free boundary technique is introduced to more accurately estimate the time derivative of the Lyapunov function during fault dynamics. Finally, this invention innovatively co-optimizes the parameters in the candidate Lyapunov function with the parameters in the sector condition to obtain the tightest possible critical clearance time estimate, significantly reducing conservatism and improving the accuracy of transient stability analysis.

[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0008] In a first aspect, the present invention provides a method for analyzing the transient stability of electricity with dual high characteristics, comprising:

[0009] A model is used to describe the electromechanical transient process, which is represented by first-order and second-order equations.

[0010] Within the adjustable neighborhood of a given equilibrium point, the nonlinear part of the model is constrained, and a new constructor is constructed.

[0011] By introducing constraints, the time derivative of the function during the fault period is obtained;

[0012] The fault clearing time is obtained by co-optimizing the function construction and the lower bound of the fault clearing time.

[0013] By solving the problem, the optimal function and parameters are obtained, and the fault clearing time is calculated.

[0014] The fault information is used to determine the fault clearing time through calculation.

[0015] As a preferred embodiment of the dual-high characteristic power transient stability analysis method described in this invention, the electromechanical transient process is described by a model and represented by first-order and second-order equations, including:

[0016] Model is constructed based on node type;

[0017] The load nodes and generator nodes are represented by first-order and second-order equations.

[0018] As a preferred embodiment of the dual-high characteristic power transient stability analysis method described in this invention, wherein: within the adjustable neighborhood of a given equilibrium point, the nonlinear part of the model is restricted, and a constructor is constructed, including:

[0019] A parameterized framework based on dynamic equilibrium neighborhood is used to construct nonlinear constraint boundaries;

[0020] A multi-dimensional constraint framework is formed by using nonlinear constraint boundaries;

[0021] By combining the parameters within the adjustable neighborhood, a function is constructed.

[0022] As a preferred embodiment of the dual-high characteristic power transient stability analysis method described in this invention, the following is included: Introducing constraints to obtain the time derivative of the function during the fault period, including:

[0023] Based on the dynamic process, the evolution boundary of the function derivative is quantized by nonlinear constraint boundary.

[0024] By optimizing the mechanism, the relationship between functions and derivatives can be mapped.

[0025] As a preferred embodiment of the dual-high characteristic power transient stability analysis method described in this invention, the fault clearing time is obtained by co-optimizing the function construction and the lower limit of the fault clearing time, including:

[0026] Based on the collaborative optimization framework, a correlation model between function construction and time threshold is constructed;

[0027] Joint optimization is achieved by integrating constraints and time boundary conditions through mathematical programming.

[0028] As a preferred embodiment of the dual-high characteristic power transient stability analysis method described in this invention, the optimal function and parameters are obtained through solving to determine the fault clearing time, including:

[0029] A global optimization is constructed based on mathematical programming to achieve the joint solution of function parameters and constraints;

[0030] Through iterative optimization, the multi-objective constraints are analyzed to obtain the optimal parameter combination;

[0031] Based on the optimized result mapping mechanism, the fault clearing time is quantitatively output.

[0032] As a preferred embodiment of the dual-high characteristic power transient stability analysis method of the present invention, the method includes: utilizing fault information and determining the fault clearing time through calculation, including:

[0033] Based on the correlation mapping between fault information and function characteristics, and through constraints and iterative optimization using real-time dynamic data, the matching of fault characteristics and functions is achieved;

[0034] By combining the boundary mapping of the optimal parameters, an adaptive correction of the fault clearing time and stability boundary is obtained.

[0035] Secondly, the present invention provides a dual-high characteristic power transient stability analysis system, comprising:

[0036] The system modeling module uses a model that preserves the system structure to describe the electromechanical transient processes of the power system, and represents the generator and the load as second-order and first-order differential equations, respectively.

[0037] The Lyapunov function construction module restricts the nonlinear part of the power system model within an adjustable neighborhood of a given equilibrium point, providing additional degrees of freedom to construct Lyapunov functions.

[0038] The non-uniform constraint module introduces non-uniform constraints to more tightly estimate the time derivative of the Lyapunov function during the fault, reducing conservatism.

[0039] The parameter optimization module co-optimizes the construction of the Lyapunov function and the lower bound estimation of the fault clearing time to obtain a compact fault clearing time estimate.

[0040] The algorithm solution module solves semidefinite programming problems, obtains the optimal Lyapunov function and parameters, and estimates the fault clearing time.

[0041] Thirdly, the present invention provides an electronic device, comprising:

[0042] memory and processor;

[0043] The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions, which, when executed by the processor, implement the steps of the dual-high characteristic power transient stability analysis method.

[0044] Fourthly, the present invention provides a computer-readable storage medium storing computer-executable instructions that, when executed by a processor, implement the steps of the dual-high characteristic power transient stability analysis method.

[0045] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention constructs a multi-dimensional degree-of-freedom foundation for stability analysis through flexible handling of nonlinear constraints within a dynamic neighborhood and an adaptive parameter framework; it significantly reduces the conservatism of time derivative estimation and improves parameter tightness by combining non-uniform boundary optimization and multi-objective collaborative solution mechanisms; it achieves optimal mapping of fault clearing time threshold and adaptive boundary correction through the fusion and iteration of global mathematical programming and dynamic data; and it ultimately forms a systematic and high-precision transient stability analysis method that effectively adapts to the complex dynamic characteristics of high-proportion renewable energy and power electronic equipment, comprehensively improving the safety assessment capability and operational reliability of power systems. Attached Figure Description

[0046] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 This is a schematic diagram of the overall process of the power transient stability analysis method with dual high characteristics according to an embodiment of the present invention.

[0048] Figure 2 This is a time-varying diagram illustrating the uniformity and non-uniformity of the time derivative of the Lyapunov function in the dual-high characteristic power transient stability analysis method described in an embodiment of the present invention.

[0049] Figure 3 This is a schematic diagram of the nonlinear adaptive sector boundary of the dual-high characteristic power transient stability analysis method according to an embodiment of the present invention.

[0050] Figure 4 This is a comparison chart of the CCTs calculated by the dual-high characteristic power transient stability analysis method described in one embodiment of the present invention and the traditional LLF method under the NE 39-bus system.

[0051] Figure 5 This is a comparison chart of the CCTs calculated by the dual-high characteristic power transient stability analysis method described in one embodiment of the present invention and the traditional LLF method under the IEEE 68-bus system.

[0052] Figure 6 This is a comparison chart of the CCTs calculated by the dual-high characteristic power transient stability analysis method described in one embodiment of the present invention and the traditional LLF method under the IEEE 118-bus system.

[0053] Figure 7This is a schematic diagram of the structure of a dual-high characteristic power transient stability analysis system according to an embodiment of the present invention.

[0054] Figure 8 This is a schematic diagram of an electronic device according to an embodiment of the dual-high characteristic power transient stability analysis method of the present invention. Detailed Implementation

[0055] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0056] Example 1, referring to Figure 1 As an embodiment of the present invention, a method for analyzing the transient stability of electricity with dual high characteristics is provided, comprising:

[0057] S1: The electromechanical transient process is described by a model, using first-order and second-order equations;

[0058] S2: Within the adjustable neighborhood of a given equilibrium point, restrict the nonlinear part of the model and construct a new function;

[0059] S3: Introducing constraints, we obtain the time derivative of the function during the fault period;

[0060] S4: Co-optimize the function construction and the lower bound of the fault clearing time to obtain the fault clearing time;

[0061] S5: By solving the problem, the optimal function and parameters are obtained, and the fault clearing time is obtained;

[0062] S6: Utilize fault information and determine the fault clearing time through calculation.

[0063] It should be noted that existing transient stability analysis methods often face core problems when dealing with complex systems with a high proportion of power electronic devices connected, such as strong conservatism in model nonlinear processing, significant isolation in parameter optimization, and insufficient coupling between dynamic characteristics and time thresholds. This results in limited accuracy in estimating critical clearing time and excessive redundancy in safety boundaries.

[0064] Therefore, to address the aforementioned issues of insufficient model adaptability, redundant conservative constraints, and lack of multi-objective collaborative optimization, a systematic analysis framework based on dynamic neighborhood parameterized modeling and non-uniform boundary optimization is established through steps S1-S6. This framework achieves dynamic decoupling between nonlinear constraints and Lyapunov function construction. Furthermore, by employing multi-dimensional parameter collaborative optimization and fault data fusion mechanisms, it overcomes the accuracy bottleneck of traditional methods in the stability analysis of complex systems, forming a transient stability evaluation system that balances computational efficiency and compactness assurance.

[0065] Example 2, refer to Figure 2-Figure 3 As an embodiment of the present invention, based on the above embodiment, a method for analyzing the transient stability of electric power with dual high characteristics is provided.

[0066] In this embodiment of the application, step S1 uses a model to describe the electromechanical transient process. First-order and second-order equations are used to represent the dynamic modeling of pure load nodes as having a frequency coefficient r, based on system node type classification. i The first-order differential equation describes the transient response of its power consumption and line coupling; the generator node dynamics are modeled as having an inertia coefficient m. i and damping coefficient d i The second-order differential equation characterizes the dynamic process of its mechanical power input and electromechanical oscillation; combined with the transmission line admittance matrix and the node coupling strength vector σ k Construct a global dynamic equation system containing nonlinear sine terms, and at the steady-state equilibrium point δ * The balance between power input and load consumption is ensured through power flow equation constraints.

[0067] In an optional implementation, step S1 uses a model to describe the electromechanical transient process. This can be represented by first-order and second-order equations, or by introducing the dynamic variation characteristics of node voltage amplitude. The pure load node is dynamically modeled as a first-order differential equation containing frequency coefficients and voltage sensitivity, describing its power consumption and the transient response of line coupling. The generator node is dynamically modeled as a second-order differential equation containing inertia coefficients, damping coefficients, and excitation regulation, characterizing its mechanical power input and the dynamic process of electromechanical oscillations. Combining the transmission line admittance matrix, node coupling strength vector, and node voltage amplitude deviation, a global dynamic equation set containing nonlinear sinusoidal terms and voltage dynamic characteristics is constructed. At the steady-state equilibrium point, power flow equation constraints ensure the balance between power input and load consumption, while also considering the stability constraints of node voltage amplitude.

[0068] In another optional implementation, step S1 uses a model to describe the electromechanical transient process. This can be represented by first-order and second-order equations, taking into account the characteristics of distributed energy access. The pure load node is dynamically modeled as a first-order differential equation containing frequency coefficients, voltage sensitivity, and distributed energy output fluctuations, describing its power consumption and the transient response of line coupling. The generator node is dynamically modeled as a second-order differential equation containing inertia coefficients, damping coefficients, excitation regulation, and speed control system dynamics, characterizing its mechanical power input and electromechanical oscillation dynamics. Combining the transmission line admittance matrix, node coupling strength vector, node voltage amplitude deviation, and the dynamic characteristics of the distributed energy access point, a global dynamic equation set is constructed, including nonlinear sinusoidal terms, voltage dynamic characteristics, and distributed energy fluctuation characteristics. At the steady-state equilibrium point, power flow equation constraints ensure the balance between power input and load consumption, while also considering the impact of distributed energy access on system stability.

[0069] In this embodiment of the application, step S1 uses a model to describe the electromechanical transient process, represented by first-order and second-order equations, including:

[0070] A model that preserves the system structure is used to describe the electromechanical transient processes of the power system, and the generator and load are represented as second-order and first-order differential equations, respectively.

[0071] Specifically, consider a nonlinear function:

[0072]

[0073] in, It is a state vector; Represents the linear part of the system's dynamics; It is a nonlinear function that captures all the nonlinearities of the system; and The coupling between nonlinearity and system state is encoded; assuming x = 0 is the system equilibrium point relevant to engineering applications, the stability of the equilibrium point under transient structural changes is considered; it is assumed that the system remains at the equilibrium point x(t) = 0 when t ≤ 0; starting from t = 0, a structural change (e.g., a fault) forces matrix B to switch to a different matrix B', causing the system state to enter a transient state; after the event ends (e.g., fault clearing), matrix B' switches back to B at t = τ; the problem addressed by TSA is whether the system state will return to the equilibrium point x = 0 after the transient state, and how stability depends on the clearing time τ; the maximum clearing time τ for the system to remain stable. m It is called CCT.

[0074] In this embodiment, step S2 restricts the nonlinear part of the model. The constructor constructs a polyhedral region Ω(γ) that satisfies the constraint -γ≤Cx≤γ by using an adjustable neighborhood parameterization framework of the steady-state equilibrium point. The nonlinear term φ(Cx) is bounded by an adaptive sector condition to construct a model that satisfies (φ(Cx)-H'(γ)Cx). T E k The constraint relationship (φ(Cx)-H""γ)Cx)≤0 is established; by combining S-Lemma and Schur complement, the nonlinear constraint is transformed into a robust linear matrix inequality (LMI), and by adaptively adjusting the parameter matrices H'(γ) and H""γ", a Lyapunov function V(x) = x that satisfies the local stability condition is constructed. T Px, while ensuring Intra-domain validity.

[0075] In one alternative implementation, the nonlinear part of the model is restricted in step S2, and the constructor can also fit the nonlinear characteristics of the system through a combination of polynomial basis functions. Specifically, the nonlinear function is decomposed into a weighted sum of multiple polynomial terms, each polynomial term corresponding to a different dynamic characteristic of the system.

[0076] In another alternative implementation, the nonlinear portion of the model is constrained in step S2, and the constructor can also perform nonlinear approximation by introducing a radial basis function (RBF) network. The RBF network can efficiently capture the local nonlinear characteristics of the system by selecting appropriate center points and width parameters.

[0077] In this embodiment of the application, step S2, which restricts the nonlinear part of the model within the adjustable neighborhood of a given equilibrium point and constructs a constructor, includes:

[0078] Introducing adaptive sector conditions: Within an adjustable neighborhood of a given equilibrium point, the nonlinear portion of the power system model is constrained, providing additional degrees of freedom to construct the Lyapunov function. The ALF method aims to provide additional degrees of freedom for any τ < τ m A rigorous mathematical representation is established, given system information (A, B, B', C, φ(·)), to further derive the algorithm for calculating the CCT. To this end, a parameter set is first constructed. The neighborhood of the equilibrium point x = 0 is considered. The size of the neighborhood Ω(γ) is adjustable by changing the parameter γ; based on Ω(γ), the local Lyapunov function V(x) of formula (1) can be constructed, expressed as:

[0079]

[0080] In this embodiment, a constraint is introduced in step S3. The time derivative of the function during the fault period is obtained by constructing a non-uniform upper bound condition based on the changes in the system structure during the dynamic period of the fault. To constrain the evolution boundary of the time derivative of the Lyapunov function; the following is derived using the comparison principle. The exponential growth frontier, combined with level sets The inclusion relationship is established at the critical clearing time τ m The lower bound is obtained; nonlinear dynamic constraints (such as the adaptive sector condition of φ(Cx)) are transformed into linear matrix inequalities (LMI) using S-Lemma, and the compactness of the Lyapunov function time derivative estimation during the fault period is improved by co-optimizing the parameters η, α and the neighborhood parameter γ, which significantly reduces the conservatism introduced by the traditional uniform boundary method.

[0081] In an alternative implementation, the constraints introduced in step S3 allow the time derivative of the function during the fault period to be obtained further by using machine learning algorithms to predict the dynamic changes of the system during the fault. The machine learning model can be trained based on historical fault data and system operating characteristics, thereby predicting the possible dynamic behavior of the system when a fault occurs. Based on this predictive information, the constraints on the time derivative of the Lyapunov function can be dynamically adjusted to better adapt to the actual fault dynamic process, thereby further improving the accuracy and reliability of transient stability analysis.

[0082] In another optional implementation, the constraints introduced in step S3 allow the time derivative of the function during the fault period to be obtained by combining real-time monitoring data. By deploying sensor networks at key nodes of the power system, real-time system operating data, such as voltage, current, and frequency, can be collected. When a fault occurs, this real-time data is used to quickly assess changes in the system state, and the constraints on the time derivative of the Lyapunov function are dynamically adjusted accordingly. This method can promptly capture the actual dynamic characteristics of the system during a fault, making the time derivative constraints of the Lyapunov function more consistent with reality, thereby improving the accuracy and real-time performance of transient stability analysis.

[0083] In this embodiment of the application, a constraint is introduced in step S3 to obtain the time derivative of the function during the fault period, including:

[0084] Improved constraint technique for the time derivative of Lyapunov functions: Introduce non-uniform constraints to more tightly estimate the time derivative of Lyapunov functions during faults and reduce conservatism.

[0085] Using information from Ω(γ) and structural change B', the upper bound of the time derivative of the Lyapunov function is derived, expressed as:

[0086]

[0087] During structural changes, when inequality (3) holds for certain parameters η and α, according to the comparison principle, we obtain:

[0088]

[0089] Where, V0 = V(x(0)); V0 = 0 when the equilibrium point before the fault is the same as the equilibrium point after the fault; V0 = 0 is assumed to simplify the problem; given the Lyapunov function V(x), any level set in the neighborhood Ω(γ) is represented as:

[0090]

[0091] It is a subset of the attraction region of the equilibrium point x = 0. Therefore, the clearing time τ is less than τ. m , represented as:

[0092]

[0093] therefore, It is the critical purge time τ m The lower approximation is introduced by a non-uniform upper bound (3) to limit the value. This results in a tighter upper bound on the Lyapunov function value during fault dynamics; such as Figure 2 As shown, given the same critical Lyapunov function value ρ, a tighter upper bound leads to lower conservatism in the CCT estimate;

[0094] In this embodiment of the application, step S4 involves co-optimizing the function construction and the lower limit of the fault clearing time to obtain the fault clearing time, including:

[0095] Parameter optimization: The construction of the Lyapunov function and the lower bound estimation of the fault clearing time are co-optimized to obtain the tightest possible fault clearing time estimate, expressed as:

[0096]

[0097] in, yes The goal is to find the optimal Lyapunov function V(·), the adjustable neighborhood parameter γ, the level set parameter ρ, and the time derivative boundary parameters η and α in the space of continuous functions to jointly realize CCTτ. m The minimum conservative estimate.

[0098] In this embodiment of the application, step S5 involves solving for the optimal function and parameters to obtain the fault clearing time, including:

[0099] Solving the semidefinite programming problem: By solving the semidefinite programming (SDP) problem, the optimal Lyapunov function and parameters are obtained, thereby estimating the fault clearing time;

[0100] The candidate Lyapunov function is parameterized as V(x) = x. T Px, where P∈S n S n Represents the set of n×n real symmetric matrices;

[0101] There are two parameter matrices and The following adaptive sector condition holds:

[0102]

[0103] Among them, E k Let (k,k) be a matrix with elements 1 and all other elements 0; from an optimization perspective, condition (8) can be considered as a robust constraint on state x, and its uncertainty set Ω(γ) is adjustable; an ideal trade-off between conservatism and effective region is achieved by optimizing parameter γ; assuming the form of structural change is B'=B+SΔ, where S and Δ are two matrices of appropriate dimensions, and matrix Δ satisfies φ T Δ T Δφ≤1; using S-Lemma and Schur complement, the Lyapunov function condition (2), boundary inequality (3) and adaptive sector condition (8) simultaneously hold, if the robust linear matrix inequality (9) is satisfied, where:

[0104]

[0105] And λ=(λ i ), 1≤i≤l, are auxiliary variables introduced by S-Lemma.

[0106] To restate condition (5), we further assume that the parameter neighborhood Ω(γ) is a polyhedron, expressed as:

[0107]

[0108] Among them, the lower boundary and the Upper Realm It is a linear function of parameter γ; by further using S-Lemma, condition (5) holds if an auxiliary variable exists. and Make:

[0109]

[0110] Based on the above analysis, the function optimization problem (7) can be transformed into the following semidefinite programming problem (SDP), expressed as:

[0111]

[0112] To model the electromechanical dynamics of the power system in the form of equation (1), a structure-preserving model is adopted, where the load and generator are represented by first-order and second-order differential equations, respectively; it is assumed that the network has a total of n b There are n nodes, of which the first n are nodes. c One node is a pure load node, and the remaining n nodes are pure load nodes. g Each node is a generator node; n b =n c +n g Let n l Let n be the number of transmission lines; define n as... l \n b A matrix F, whose (k,i) elements are all 1, is defined if the k-th transmission line has node i as its "starting" end; similarly, n is defined... l \n b A matrix T, where the (k,i) elements are all 1s, is defined if the k-th transmission line terminates at node i; all other unspecified elements of F and T are zero. Also defined... Using vectors Representation matrix In the k-th row, use the scalar f ki and t ki Let (k,i) represent the (k,i) elements of matrices F and T respectively; furthermore, n l The complex vector y represents the admittance of the transmission line, i.e., ×1. It is the admittance of the k-th line (with an amplitude of |y) k |, phase is Define the coupling strength vector. Its k-th element σ k =V i Vj | y k |, where V i and V j These are the voltage amplitudes at the starting and ending points of the k-th transmission line, respectively.

[0113] The dynamics of a power system are described by the following equations:

[0114]

[0115] Where, m i and d i Let P represent the inertia coefficient and damping coefficient of the generator at node i, respectively. mi Its mechanical power input; constant r iIt is the frequency coefficient, P di This represents the power consumption of the load at node i; in steady state, the system operates at a given equilibrium point δ that satisfies the power flow equations. * :

[0116]

[0117] By subtracting equation (16) from equation (15) and redefining the state variable x = [x1, x2, x3] T ,in The dynamic system (15) can be rewritten in the form of equation (1), where:

[0118]

[0119] Among them, the diagonal matrix The sin(·) function applies element-wise to the vector parameters;

[0120] Consider a symmetrical tripping fault on the k-th transmission line. After the fault is cleared, the line successfully recloses after a certain period of time. Based on the framework described above, the fault is modeled as a matrix B switching to B' = B + SΔ, expressed as:

[0121]

[0122] and Where E k is n l \n l A matrix with (k,k) elements being 1 and the rest being zero; the structural changes are illustrated using a line tripping fault as an example.

[0123] The nonlinearity of the model defined by equations (1), (17) and (20) is completely captured by the nonlinear function φ(Cx); the sector condition of the nonlinear term φ(Cx) is derived by specifying the structure of the neighborhood Ω(γ) and the matrices H'(γ) and H""γ".

[0124] Given the steady-state power flow solution δ * The neighborhood Ω(γ) is constructed as a polyhedron with the following parameters, denoted as:

[0125]

[0126] in, It is a non-negative vector, and the k-th element is γ. k The rotor angle difference δ was encoded. i -δ j and The allowable deviation, where node i and node j are the starting and ending points of the k-th transmission line, respectively; through this simple Ω(γ) structure, the sector boundary of the nonlinear term φ(Cx) in equation (20) is derived, considering the k-th element of φ, expressed as:

[0127]

[0128] For some 1≤k≤n l Within the neighborhood Ω(γ) defined by equation (22), Seeking to find two parameter scalars h' k and h” k Dependent on γ k , so that:

[0129]

[0130] For all satisfying δ holds true;

[0131] Determine the scalar h' k and h” k Methods such as Figure 3 As shown; by assuming Begin analysis; in With φ k On a plane, the scalar h' k You can choose to cross the balance point. and with function graphics ( Figure 3 The straight line tangent to the sine curve in the middle ( Figure 3 The slope of the oblique line in the diagram; the point of tangency is always located at φ. k In the quadrant where x ≤ 0, its z coordinate is... k satisfy:

[0132]

[0133] The solution yields:

[0134]

[0135] Through this selection h' k ,have for and for

[0136] In order to derive the scalar h” k Introducing a quadratic function, which is a nonlinear function. exist Provides the tightest lower bound within the region, such as Figure 3 The dashed curve in the image shows the quadratic function passing through the point. and Represented as:

[0137]

[0138] For a certain scalar a k >0; in order to make It becomes the tightest second lower bound. The curve must be at the equilibrium point Nonlinear functions The optimal selection of parameters is obtained by finding the curve tangent to it, which is expressed as:

[0139]

[0140] Due to the function The concavity, given any scalar pass and The secant is also a function In the interval The inner bound provides a lower bound; the same secant line in the interval The inner part is a function An upper bound is provided; by selecting h” k Let be the slope of the secant, i.e.:

[0141]

[0142] have for and for The above h' k and h” k The choice ensures that the sector condition (24) is satisfied for all of Established;

[0143] The above analysis is similarly extended to The only difference is that:

[0144]

[0145] Combining the formulas for these two cases, we can conclude that the scalar... Given by equation (26), where z k The solution from equation (25), scalar Calculated by the following formula:

[0146]

[0147] The function sgn(z) returns the sign of its parameter z; h'k and h” k All are based on steady-state power flow solutions Adaptive selection, h” k The adjustable parameter γ is linearly dependent on the neighborhood Ω(γ). k Therefore, equation (24) and h' k and h” k The choice provides additional degrees of freedom in the adaptive sector condition for constructing the Lyapunov function and proving transient stability.

[0148] In this embodiment of the application, step S6 utilizes fault information and calculates to determine the fault clearing time, including:

[0149] Trajectory Utilization: If fault trajectory information is available, this information can be used to further reduce conservatism by calculating the Lyapunov function values ​​at each point on the trajectory to determine the fault clearance time; if the fault trajectory is available, as assumed by the previous direct energy function method, the proposed method is flexible and can utilize trajectory information to further reduce conservatism; examine each point on the trajectory until at some point x F (t cl The Lyapunov function value reaches the critical level V(x) at point ). F (t cl ))=ρ;Corresponding fault clearing time t cl This is the estimated CCT.

[0150] In summary, this invention provides a transient stability analysis method and system for power systems with "high" and "high" characteristics. By introducing an adaptive Lyapunov function method, it effectively solves the problems of inaccuracy, high conservatism, and low precision in existing technologies when analyzing transient stability with high proportions of renewable energy and power electronic equipment connected to the grid. This invention proposes innovative technical solutions in system modeling, nonlinear constraint handling, Lyapunov function construction, and parameter optimization, which can significantly reduce the conservatism of transient stability analysis, improve analysis accuracy, and expand the applicability of the method to large and complex power systems.

[0151] Example 3, referring to Figures 4-8 As one embodiment of the invention, a method for analyzing the transient stability of electricity with dual high characteristics is provided. To verify the beneficial effects of the invention, scientific demonstration is carried out through economic benefit calculations and simulation experiments.

[0152] To demonstrate the effectiveness of the proposed TSA method in multi-machine systems, extensive numerical studies were conducted on three benchmark systems: the New England 10-machine 39-node system (NE 39-node system), the IEEE 68-node system, and the IEEE 118-node system. For each test system, the damping coefficient d... i Set to min{m i}, inertial parameter m i The data is obtained directly from the dataset. In the implementation of the proposed method, the initial values ​​of parameters α = 10 and κ = 0.1 are set. The fault considered in this experiment is the tripping of a transmission line, which is then automatically reclosed by the protection system. When the reclosing is successful, the post-fault SEP of the system is the same as the pre-fault SEP. Under this setting, the CCT of each line is the maximum time between the transmission line tripping and reclosing, ensuring system stability.

[0153] The proposed simulation-free method and the LLF method were used to estimate the CCT corresponding to each line, and the two methods were compared on three benchmark systems. The results are as follows: Figure 4 , 5 As shown in Figure 6. For the NE 39-node system, as... Figure 4 As shown, compared with the traditional LLF method, the proposed method improves the CCT estimate by an average of approximately 21 times. Among the 46 lines in the system, line 14 (between nodes 7 and 8) shows the smallest CCT improvement, approximately 2.84 times, while line 46 (between nodes 31 and 6) shows the largest improvement, approximately 97 times. For the IEEE 68-node system, the proposed method improves the CCT estimate by an average of approximately 26 times, such as... Figure 5 As shown. It should be noted that with the current algorithm parameter α = 10, the CCT estimate for one line (i.e., line 83) is slightly lower than that of the traditional LLF method. However, if the parameter α is reduced from 10 to 1, the proposed method's CCT estimate is 5.77 seconds, approximately four times higher than the LLF method (1.18 seconds). For the IEEE 118-bus system, the proposed method still performs well and provides CCT estimates for each transmission line. In contrast, the traditional LLF method fails to find a feasible solution to the Lyapunov function construction problem, resulting in zero CCT estimates for all transmission lines. The results are as follows... Figure 6 As shown in the comparison above, it can be seen that, compared with the previous LLF method, the proposed ALF method significantly reduces the conservatism of stability proof and CCT estimation, and extends the applicability of the LLF method to large systems that were originally difficult to handle.

[0154] To comprehensively compare the results obtained through different methods, some quantitative results are presented in Table 1. Clearly, due to the three main techniques introduced in this invention—adaptive sector boundary for the nonlinear term, non-uniform upper bound of the Lyapunov function's time derivative along the fault trajectory, and co-optimization of Lyapunov function construction and CCT lower bound estimation—the proposed simulation-free method is less conservative than the traditional LLF method. The simulation-free ALF method does not assume the availability of fault trajectory information. If the fault trajectory is available, the value of the Lyapunov function along the trajectory can be accurately calculated. Then, by locating the time when the Lyapunov function value equals the critical value ρ, a less conservative trajectory-based CCT estimate can be obtained, as shown in column 5 of Table 1.

[0155] Table 1 Comparison of CCTs data calculated by different methods under line tripping faults

[0156]

[0157] It is worth noting that the proposed ALF method can also be used to analyze the stability of systems subjected to short-circuit faults. In this invention, a large load P connected at node i is used. s =10 2 PU is used to simulate short-circuit faults. When considering short-circuit faults in the ALF method, the matrix S needs to be modified to have a dimension of (n). b +n g A column vector of size 1. It can be obtained in the following ways:

[0158]

[0159] in, It is (n b +n g A square matrix of dimension 1, where (i,i) elements are 1 and the rest are zero; 1 is a column vector of appropriate dimension, where all elements are 1. In addition, the third column and the third row in LMI(9) should be modified to an appropriate dimension. After these modifications, the short-circuit fault TSA results of different benchmark systems can be obtained by iteratively solving SDPs(37) and (38). The results of the NE 39-node system, the IEEE 68-node system and the IEEE 118-node system are listed in Table 2. It can be found that the CCT estimate obtained by the proposed ALF method is less conservative than that of the traditional LLF method. In addition, the use of fault trajectory information helps to further reduce the conservatism.

[0160] Table 2 Comparison of CCTs data calculated by different methods under short-circuit faults.

[0161]

[0162] Example 4 illustrates a schematic scheme for a method for analyzing transient stability of electricity with dual high characteristics. It should be noted that the technical solution of this system for analyzing transient stability of electricity with dual high characteristics is based on the same concept as the technical solution of the method described above. Details not described in detail in this embodiment can be found in the description of the technical solution of the method described above.

[0163] like Figure 7 As shown, this embodiment also provides a dual-high characteristic power transient stability analysis system, including:

[0164] The system modeling module 100 uses a model that preserves the system structure to describe the electromechanical transient process of the power system, and represents the generator and the load as second-order and first-order differential equations, respectively.

[0165] Lyapunov function construction module 200 restricts the nonlinear part of the power system model within an adjustable neighborhood of a given equilibrium point, providing additional degrees of freedom to construct Lyapunov functions.

[0166] Non-uniform constraint module 300 introduces non-uniform constraints to more tightly estimate the time derivative of the Lyapunov function during the fault, reducing conservatism;

[0167] The parameter optimization module 400 performs co-optimization on the construction of the Lyapunov function and the lower bound estimation of the fault clearing time to obtain a compact fault clearing time estimate.

[0168] The algorithm solution module 500 solves semidefinite programming problems, obtains the optimal Lyapunov function and parameters, and estimates the fault clearing time.

[0169] like Figure 8 As shown, this embodiment also provides an electronic device 10, which is suitable for the case of power transient stability analysis with dual high characteristics, including: a memory 20 and a processor 30; the memory 20 is used to store computer-executable instructions, and the processor 30 is used to execute computer-executable instructions to implement the power transient stability analysis method with dual high characteristics as proposed in the above embodiment.

[0170] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements the method for analyzing the transient stability of high-voltage power characteristics as proposed in the above embodiments.

[0171] The storage medium proposed in this embodiment and the method for realizing the transient stability analysis of high-voltage power characteristics proposed in the above embodiments belong to the same inventive concept. Technical details not described in detail in this embodiment can be found in the above embodiments, and this embodiment has the same beneficial effects as the above embodiments.

[0172] Based on the above description of the implementation methods, those skilled in the art will clearly understand that the present invention can be implemented using software and necessary general-purpose hardware, and of course, it can also be implemented using hardware. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as a computer floppy disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk, or optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of the various embodiments of the present invention.

[0173] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for analyzing transient stability of electricity with dual high characteristics, characterized in that, include: A model is used to describe the electromechanical transient process, which is represented by first-order and second-order equations. Within the adjustable neighborhood of a given equilibrium point, the nonlinear part of the model is constrained, and a new constructor is constructed. By introducing constraints, the time derivative of the function during the fault period is obtained; The fault clearing time is obtained by co-optimizing the function construction and the lower bound of the fault clearing time. By solving the problem, the optimal function and parameters are obtained, and the fault clearing time is calculated. The fault information is used to determine the fault clearing time through calculation.

2. The method for analyzing the transient stability of electricity with dual high characteristics as described in claim 1, characterized in that, The electromechanical transient process is described by a model, represented by first-order and second-order equations, including: Model is constructed based on node type; The load nodes and generator nodes are represented by first-order and second-order equations.

3. The method for analyzing the transient stability of electricity with dual high characteristics as described in claim 2, characterized in that, Within the adjustable neighborhood of a given equilibrium point, the nonlinear part of the model is constrained, and a constructor is constructed, including: A parameterized framework based on dynamic equilibrium neighborhood is used to construct nonlinear constraint boundaries; A multi-dimensional constraint framework is formed by using nonlinear constraint boundaries; By combining the parameters within the adjustable neighborhood, a function is constructed.

4. The method for analyzing the transient stability of electricity with dual high characteristics as described in claim 3, characterized in that, By introducing constraints, we obtain the time derivative of the function during the fault period, including: Based on the dynamic process, the evolution boundary of the function derivative is quantized by nonlinear constraint boundary. By optimizing the mechanism, the relationship between functions and derivatives can be mapped.

5. The method for analyzing the transient stability of electricity with dual high characteristics as described in claim 4, characterized in that, By co-optimizing the function construction and the lower bound of the fault clearing time, the fault clearing time is obtained, including: Based on the collaborative optimization framework, a correlation model between function construction and time threshold is constructed; Joint optimization is achieved by integrating constraints and time boundary conditions through mathematical programming.

6. The method for analyzing the transient stability of electricity with dual high characteristics as described in claim 5, characterized in that, By solving the problem, the optimal function and parameters are obtained, and the fault clearing time is calculated, including: A global optimization is constructed based on mathematical programming to achieve the joint solution of function parameters and constraints; Through iterative optimization, the multi-objective constraints are analyzed to obtain the optimal parameter combination; Based on the optimized result mapping mechanism, the fault clearing time is quantitatively output.

7. The method for analyzing the transient stability of electricity with dual high characteristics as described in claim 6, characterized in that, Using fault information and calculating to determine the fault clearing time, including: Based on the correlation mapping between fault information and function characteristics, and through constraints and iterative optimization using real-time dynamic data, the matching of fault characteristics and functions is achieved; By combining the boundary mapping of the optimal parameters, an adaptive correction of the fault clearing time and stability boundary is obtained.

8. A power transient stability analysis system with dual high characteristics, using the method described in any one of claims 1-7, characterized in that, include: The system modeling module uses a model that preserves the system structure to describe the electromechanical transient processes of the power system, and represents the generator and the load as second-order and first-order differential equations, respectively. The Lyapunov function construction module restricts the nonlinear part of the power system model within an adjustable neighborhood of a given equilibrium point, providing additional degrees of freedom to construct Lyapunov functions. The non-uniform constraint module introduces non-uniform constraints to more tightly estimate the time derivative of the Lyapunov function during the fault, reducing conservatism. The parameter optimization module co-optimizes the construction of the Lyapunov function and the lower bound estimation of the fault clearing time to obtain a compact fault clearing time estimate. The algorithm solution module solves semidefinite programming problems, obtains the optimal Lyapunov function and parameters, and estimates the fault clearing time.

9. An electronic device, comprising: memory and processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the computer-executable instructions are executed by the processor, they implement the steps of the dual-high characteristic power transient stability analysis method according to any one of claims 1 to 7.

10. A computer-readable storage medium storing computer-executable instructions that, when executed by a processor, implement the steps of the dual-high characteristic power transient stability analysis method according to any one of claims 1 to 7.

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