Distributed parallel modeling method for small signal state space of power system

Abstract

The invention relates to the technical field of electric power system modeling, in particular to an electric power system small signal state space distributed parallel modeling method, which comprises the following steps of: constructing a topological structure of an electric power system, identifying a boundary topological structure of each subsystem, and determining a transmission relationship among the subsystems according to a control mode; a mathematical model of each subsystem is determined, a parallel computing thread pool is created, and a two-dimensional index is generated to be associated with the number of equations and the number of variables in the mathematical models respectively; carrying out parallel linearization on the mathematical model by taking the mapping relation of the two-dimensional index as a constraint; based on a parallel linearization result, a linearization state space model of the subsystem is automatically constructed, and remainder term verification is carried out; and according to the transmission relation and the boundary topology structure, interconnection is carried out on the linearized state space models to generate a power system small signal state space model. Through the method, the problem of modeling calculation infeasibility of a large-scale power system caused by state matrix dimension upgrading is effectively solved.

Description

Technical Field

[0001] This invention relates to the field of power system modeling technology, and in particular to a distributed parallel modeling method for small-signal state space of power systems. Background Technology

[0002] Within my country's "West-to-East Power Transmission" strategy, projects such as the ±800kV Wudongde DC transmission project and the ±800kV Baihetan-Jiangsu UHV hybrid cascaded DC transmission system have adopted multi-terminal DC architectures, with some individual projects featuring converter station clusters ranging from 6 to 12 units. These projects, through the large-scale deployment of modular multilevel converters, have achieved a technological breakthrough in cross-regional, high-capacity power transmission.

[0003] However, a single converter integrates 200 to 400 sub-modules, leading to a significant increase in the number of system state variables. The prominent high-dimensional state space problem not only greatly increases the difficulty of extracting key modes of the system but also poses a severe challenge to the efficiency of full-order small-signal modeling. Current research on power system state-space modeling uses a traditional centralized modeling strategy that treats the entire system as a single entity. This involves establishing a unified system of differential-algebraic equations and performing global linearization to achieve synchronous observation and control of all state variables. However, when the system contains multiple converter stations, the number of state variables and computational complexity increase exponentially with the model dimension, significantly increasing computation time and difficulty, resulting in low modeling efficiency. Furthermore, when the system topology is adjusted or the operating mode changes, the centralized modeling method requires re-establishing the global Jacobian matrix, lacking applicability under complex and variable operating conditions and lacking error verification, making it difficult to guarantee the accuracy of linearized modeling.

[0004] The information disclosed in this background section is intended only to enhance the understanding of the general background of this disclosure and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0005] This invention provides a distributed parallel modeling method for small-signal state space of power systems, which can effectively solve the problems in the background technology.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A distributed parallel modeling method for small-signal state space of a power system, the method comprising:

[0008] Construct the topology of the power system, identify the boundary topology of each subsystem, and determine the transmission relationships between the subsystems;

[0009] A mathematical model for each subsystem is determined and a parallel computing thread pool is created. A two-dimensional index is generated in the parallel computing thread pool, and the mathematical model is linearized in parallel based on the two-dimensional index.

[0010] Based on the results of the parallel linearization, the linearized state-space model of the subsystem is automatically constructed according to the hierarchical parallel strategy, and the remainder term is verified.

[0011] Based on the transmission relationship and the boundary topology, the linearized state-space models of each subsystem are interconnected to generate a small-signal state-space model of the power system.

[0012] Furthermore, parallel computing and two-dimensional indexing include:

[0013] The number of threads N for parallel computing must satisfy:

[0014] N = min(k, number of CPU cores);

[0015] In the formula, k represents a constant, k∈[1,m×p], and m and p represent the dimensions of the equation f to be linearized and the linearized variable x, respectively;

[0016] The two-dimensional index mapping should be configured as follows to ensure that each parallel task processes a unique combination of equations or variables:

[0017]

[0018] In the formula, i and j are respectively associated with the number of equations to be linearized f and the number of linearized variables x.

[0019] Furthermore, a multi-core parallel differentiation algorithm based on two-dimensional index mapping includes:

[0020] The execution tasks are divided into m × p independent tasks, and the partial derivative calculations of m equations with respect to p variables are decomposed into m × p independent tasks. The rounding up and modulo operations are used to ensure that each kernel obtains an approximate number of index coordinate combinations.

[0021] Pre-allocate memory space for the steady-state value vector to avoid repeatedly performing symbol substitution in m×p iterations. The core formula for parallel speedup is:

[0022]

[0023] In the formula, S is the speedup ratio, and a and N represent the proportion of parallel computing and the number of processor threads, respectively.

[0024] After parallel computation is completed, the Jacobian matrix of the subsystem is reconstructed through a reshaping operation and stored in a sparse matrix format, the expression of which is:

[0025]

[0026] In the formula, f i For the i-th system of equations to be linearized, x j Let J(i,j) be the j-th linearized variable, i = 1, 2, ..., m, j = 1, 2, ..., p, and J(i,j) represent the i-th nonlinear equation f. i x for the j-th variable j Partial derivatives.

[0027] Furthermore, based on the power flow of the power system, the voltage, current, and power are substituted into the Jacobian matrix of the subsystem to obtain the linearized equation of the subsystem near the current steady-state point.

[0028] Furthermore, the linearized state-space model includes:

[0029] The linearized state-space model expression is as follows:

[0030]

[0031] In the formula, the subscript k represents the kth subsystem, ΔX, ΔU, and ΔY are the state variable, input variable, and input variable, respectively; A, B, C, and D are the state matrix, input matrix, output matrix, and direct transfer matrix, respectively. This represents the set of state variables after the subsystems are interconnected in series.

[0032] Furthermore, the method for automatically obtaining linearized matrices based on a hierarchical parallel strategy includes:

[0033] ΔX, ΔU, and ΔY are determined from the m×1-dimensional linearized equation and the p×1-dimensional linearized variables, where m and p represent the dimensions of the linearized equation and the linearized variables, respectively.

[0034] Memory space is allocated for the linearization matrix based on the linearization equation and the dimension of the linearization variables;

[0035] The calculation of the state matrix and the output matrix is ​​split into multiple independent rows, and the partial derivative calculations are performed in parallel by different working processes;

[0036] Based on the result of the partial derivative calculation, determine whether the remainder term is zero to determine whether the linearization process is complete. If it is zero, calculate the input matrix and the direct transfer matrix in parallel. If it is not zero, immediately interrupt the calculation and redetermine the mathematical model, input variables, and state variables of the subsystem.

[0037] Furthermore, the topology of each transmission line in the power system is traversed and topology segmentation is performed based on the boundary topology of the subsystem to ensure that there is a complete electrical path between nodes within the subsystem, and the segmented subsystems are connected in series to construct a complete transmission line.

[0038] Furthermore, based on the control mode, the complete transmission relationship of the subsystem is generated by combining the input and output variables of the controller of each subsystem.

[0039] Furthermore, the mathematical model of the subsystem is established based on the logic of the control mode, and the input and output variables of the subsystem are controlled according to the physical constraints of the electrical ports and control ports.

[0040] Furthermore, a small-signal state-space model of the power system is generated, including:

[0041] When the subsystems are connected in series, the interconnected state-space model is as follows:

[0042]

[0043]

[0044] In the formula, the subscripts j & k represent any two subsystems j and k connected in series, k and j represent the labels of any subsystem, ΔX, ΔU, and ΔY are the state variable, input variable, and input variable, respectively; A, B, C, and D are the state matrix, input matrix, output matrix, and direct transfer matrix, respectively.

[0045] If the subsystems are connected in parallel, the interconnected state-space model is as follows:

[0046]

[0047] In the formula, the subscript j||k represents that the subsystem j and the subsystem k are connected in parallel;

[0048] When the subsystems are interconnected via feedback, that is, when a portion of the output of any subsystem j is the input of any subsystem k, and the output of any subsystem k is a portion of the input of any subsystem j, the state-space model after interconnection is:

[0049]

[0050] ΔU j,k =[ΔV j ΔV k ] T ;

[0051]

[0052] C jk =[M jj C j M jk C k ];

[0053] C kj =[M kj C j M kk C k ];

[0054] D jk =[M jj D j M jk D k ];

[0055] D kj =[M kj D j M kk D k ];

[0056]

[0057] In the formula, subscripts j and k represent feedback interconnection between subsystems j and k; subscript jk represents transmission from subsystem j to subsystem k, and subscript kj represents the reverse; subscript jj represents self-mapping within subsystem j, and subscript kk represents the same; ΔV j With ΔV k These are the external input parts of subsystems j and k, respectively; B j B′ is the transfer matrix where a portion of the output of subsystem k acts on a portion of the input of subsystem j. k The reverse is also true; D j D′ is the transfer matrix where a portion of the output of subsystem k directly affects the output of subsystem j. k The reverse is also true; I is the identity matrix.

[0058] The technical solution of this invention can achieve the following technical effects:

[0059] While ensuring the accuracy of small-signal stability analysis, the computational efficiency and operating condition adaptability of large-scale power grids have been improved, and accurate and efficient modeling of high-dimensional state matrices of large-scale power systems has been achieved.

[0060] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0061] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0062] Figure 1 Flowchart of a distributed parallel modeling method for small-signal state space in power systems;

[0063] Figure 2 Equivalent circuit diagram for flexible DC transmission project;

[0064] Figure 3 Comparison results of the time-domain responses of the small-signal state-space model and the electromagnetic transient model;

[0065] Figure 4 Comparison results of the time-domain responses of the small-signal state-space model and the electromagnetic transient model;

[0066] Figure 5 Equivalent circuit diagram for a hybrid cascaded DC transmission project;

[0067] Figure 6 This is a schematic diagram illustrating the interconnection relationship between subsystems.

[0068] Figure 7 Comparison results of the time-domain responses of the small-signal state-space model and the electromagnetic transient model;

[0069] Figure 8 Comparison results of the time-domain responses of the small-signal state-space model and the electromagnetic transient model;

[0070] Figure 9 The results show a comparison of the time-domain responses of the small-signal state-space model and the electromagnetic transient model. Detailed Implementation

[0071] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0072] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which this invention pertains. The terms used in this specification are for the purpose of describing specific embodiments only and are not intended to limit the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0073] Example 1;

[0074] like Figure 1 , Figure 3 and Figure 4 As shown in the figure, the white dashed line represents the actual effect of the present invention in simulation testing. This application provides a distributed parallel modeling method for small-signal state space of power systems, the method comprising:

[0075] A distributed parallel modeling method for small-signal state space of power systems, the method comprising:

[0076] Construct the topology of the power system, identify the boundary topology of each subsystem, and determine the transmission relationships between the subsystems;

[0077] A mathematical model for each subsystem is determined and a parallel computing thread pool is created. A two-dimensional index is generated in the parallel computing thread pool, and the mathematical model is linearized in parallel based on the two-dimensional index.

[0078] Based on the results of the parallel linearization, the linearized state-space model of the subsystem is automatically constructed according to the hierarchical parallel strategy, and the remainder term is verified.

[0079] Based on the transmission relationship and the boundary topology, the linearized state-space models of each subsystem are interconnected to generate a small-signal state-space model of the power system.

[0080] Specifically, the first step is to perform topology analysis on the large-scale power system. This step primarily involves identifying the boundaries and topological relationships of each subsystem within the system, as well as the transmission relationships between subsystems under different control modes. By using efficient graph theory methods and node-edge relationship analysis techniques, the boundary topology of each subsystem can be accurately defined, and the transmission relationships between subsystems under different control modes can be effectively modeled. For example, in the topology of a transmission network, by identifying the connection relationships between substations and lines, an independent mathematical model can be constructed for each subsystem, providing a foundation for subsequent calculations. The mathematical model of each subsystem typically consists of a system of equations. The process group includes the system's state variables, input and output variables, and their inter-constraint relationships. Based on the physical characteristics and control logic of each subsystem, a corresponding mathematical model is constructed. This mathematical model is typically in the form of a system of linear equations. To achieve efficient computation, a parallel computing thread pool is created. Each thread is responsible for calculating the mathematical model of one subsystem. The thread pool is created based on the complexity of the subsystem and its computational requirements, employing a load balancing algorithm to optimize thread allocation and ensure the efficiency of each thread's computation. The mathematical model of each subsystem is mapped using a two-dimensional index, which associates each equation with the number of variables. This index mapping not only optimizes memory usage but also facilitates subsequent parallel computation. The algorithm provides clear task partitioning and scheduling rules. After modeling the mathematical model of each subsystem, the next step is to linearize the model using a multi-core parallel differentiation algorithm. Multi-core parallel processing can improve the speed of differentiation calculations, especially in large-scale power systems where multi-core processing can effectively distribute computational tasks and shorten the time required for linearization. In implementation, for each subsystem model, the Jacobian matrix is ​​calculated in parallel, and an optimized parallel linearization algorithm is used to solve for the partial derivatives of each variable. In this process, each computational core only needs to calculate a portion of the partial derivatives, thus avoiding redundant calculations and improving efficiency. Based on the results of parallel linearization, further... The linearized state-space model of each subsystem is constructed step by step. For the state-space model of each subsystem, the construction is automated through a hierarchical parallel strategy. Specifically, all subsystems are first divided into different computational levels. Then, the computational tasks of each level are relatively independent through hierarchical processing. During the computation process, memory sharing and communication mechanisms are used to ensure data consistency between different levels. After the linearized state-space model of each subsystem is completed, residual verification is required. This verification process checks the error of the linearized model to ensure that the error between it and the original nonlinear model is within an acceptable range. The verification results are fed back into the parallel computing process to further optimize the model.Finally, based on the transmission relationships and topology between subsystems, the linearized state-space models of each subsystem are interconnected to form a complete small-signal state-space model of a large-scale power system. The interconnection method between the state-space models of different subsystems is flexibly selected according to the different system topologies. For example, when there is a series relationship between subsystems, the system combines the state-space models of each subsystem through matrix operation rules; when there is a parallel relationship between subsystems, the system combines their state-space models according to parallel rules; for subsystems with feedback, feedback rules are used for model construction. Through this precise combination of state-space models, an overall model that accurately reflects the dynamic characteristics of the system can be obtained.

[0081] The technical solution of this invention improves the computational efficiency and operating condition adaptability of large-scale power grids while ensuring the accuracy of small-signal stability analysis, and realizes accurate and efficient modeling of high-dimensional state matrices of large-scale power systems.

[0082] Furthermore, parallel computing thread pools and two-dimensional indexes include:

[0083] The number of threads N for parallel computing must satisfy:

[0084] N = min(k, number of CPU cores);

[0085] In the formula, k represents a constant, k∈[1,m×p], and m and p represent the dimensions of the equation f to be linearized and the linearized variable x, respectively;

[0086] The two-dimensional index mapping should be configured as follows to ensure that each parallel task processes a unique combination of equations or variables:

[0087]

[0088] In the formula, i and j are associated with the number of equations to be linearized f and the number of linearized variables x, respectively.

[0089] As a preferred embodiment of the above, in the process of parallel linearization of the subsystem mathematical model, it is first necessary to reasonably set the number of parallel threads to fully utilize computing resources and avoid thread redundancy or uneven load. This embodiment adopts the following thread configuration strategy: Suppose that the mathematical model before linearization contains a function f(x) composed of m nonlinear differential algebraic equations (DAEs), and the dimension of the variable x is p. In the linearization process, it is necessary to process each variable x separately. j In each equation f iThe partial derivatives in the equation are used to calculate the total number of computational tasks, which is m×p. To ensure that the granularity of each thread task is appropriate and to avoid the thread scheduling overhead caused by excessive fine-grained granularity, while also considering parallel performance, the number of parallel threads N is set to satisfy the constraint that the number of threads N≥k√(m×p), where the constant k is a coefficient optimized according to the performance of the computing platform. When the number of available physical cores in the system is greater than this estimated value, the estimated value is used as the upper limit; when the number of cores is insufficient, the number of physical cores is used as the upper limit. Unassigned tasks are handled by a task queue round-robin method. The number of threads set in this way can cover all tasks while ensuring the efficiency of high-performance parallel computing, and is suitable for large-scale power system modeling tasks containing hundreds to tens of thousands of variables and equations. To achieve accurate task partitioning and thread allocation, a two-dimensional index mapping mechanism is constructed. This mechanism maps each computational task to a function f. i With variable x j The derivative relationship between them is mapped to a unique two-dimensional index pair (i,j), where index i corresponds to the i-th nonlinear equation and index j corresponds to the j-th variable. Each parallel task corresponds to a unique index pair (i,j) and needs to process the corresponding function f. i For variable x j The partial derivative calculation expands these two-dimensional indices into a linear queue (task pool) in row-major or column-major order, and distributes them through a thread scheduling mechanism. When the number of threads is less than the total number of tasks, a round-robin scheduling or a dynamic allocation mechanism based on a hash function is used to achieve a uniform distribution of tasks among multiple threads. During the linearization differentiation process, each thread independently processes its assigned set of two-dimensional index pairs and executes the corresponding function f. i and its input variable x j Based on numerical differentiation or symbolic differentiation strategies, calculate The results are filled into the corresponding Jacobian matrix elements. Since each thread only processes a unique (i,j) combination, there is no data write conflict, which greatly simplifies the complexity of the synchronization mechanism. In addition, threads can pass commonly used intermediate results (such as initial values ​​of variables) through shared memory or caching mechanisms, which improves computational efficiency.

[0090] Furthermore, multi-core parallel differentiation algorithms based on two-dimensional index mapping include:

[0091] The execution tasks are divided into m × p independent tasks, and the partial derivative calculations of m equations with respect to p variables are decomposed into m × p independent tasks. The rounding up and modulo operations are used to ensure that each kernel obtains an approximate number of index coordinate combinations.

[0092] Pre-allocate memory space for the steady-state value vector to avoid repeatedly performing symbol substitution in m×p iterations. The core formula for parallel speedup is:

[0093]

[0094] In the formula, S is the speedup ratio, and a and N represent the proportion of parallel computing and the number of processor threads, respectively.

[0095] After parallel computation is completed, the Jacobian matrix of the subsystem is reconstructed through a reshaping operation and stored in a sparse matrix format, the expression of which is:

[0096]

[0097] In the formula, f i For the i-th system of equations to be linearized, x j Let J(i,j) be the j-th linearized variable, i = 1, 2, ..., m, j = 1, 2, ..., p, and J(i,j) represent the i-th nonlinear equation f. i x for the j-th variable j Partial derivatives.

[0098] As a preferred embodiment of the above, in the small-signal analysis of the power system, in order to achieve efficient parallel computing, the linearization calculation task is first divided into independent subtasks. Assuming the mathematical model of the system contains m nonlinear equations, and each equation has p state variables, it is necessary to calculate the partial derivative of each equation with respect to each variable. Therefore, the total computational workload is m×p. Each partial derivative calculation task can be independently performed in parallel. To ensure that the computational tasks are evenly distributed on the multi-core computing platform, a rounding-up and modulo operation strategy is adopted to distribute the m×p tasks across N cores. Specifically, the total number of tasks is first divided by the number of cores N and then rounded up. The number of tasks allocated to each core is obtained. Modulo operations are used to ensure that the number of tasks is distributed as evenly as possible among the cores, avoiding overloading of some cores and ensuring load balancing and efficient utilization of computing resources. Before parallel computation, memory space is pre-allocated for the steady-state value vector to avoid repeatedly performing sign substitution operations in each computation loop. The steady-state value vector refers to the voltage, frequency, and other values ​​of the system in steady state. This vector is usually the starting point for model linearization calculations. Avoiding repeated substitution in each partial derivative calculation helps reduce unnecessary computational overhead. During this process, sign substitution optimization techniques are used to ensure that each parallel task independently reads the steady-state data. The value of 'a' is determined without interfering with the execution of other computational tasks. This not only accelerates the computation process but also avoids memory bottlenecks, ensuring efficient parallel computing for large-scale power systems. Furthermore, the efficiency of parallel computing is further optimized through a parallel speedup formula, which describes the acceleration effect as the number of threads increases. By reasonably adjusting the value of 'a' (i.e., the proportion of parallel computation), the acceleration effect can be maximized while maintaining computational accuracy. For example, when the proportion of parallel tasks is high, a larger speedup can be obtained by increasing the number of threads, thus improving computational performance. After completing all parallel computation tasks, the final generated Jacobian matrix needs to be reconstructed and stored. In the computation process, since many partial derivatives are zero, the generated Jacobian matrix is ​​usually a sparse matrix. To save memory and improve storage efficiency, a sparse matrix format is used for storage. The Jacobian matrix J(i,j) is an important matrix describing the dynamic characteristics of the system. It records the partial derivative of the i-th nonlinear equation with respect to the j-th variable. In the final reconstruction of the Jacobian matrix, all non-zero elements will be stored in the sparse matrix for fast access in subsequent calculations. Using sparse matrix storage not only greatly reduces the storage space requirement but also improves the calculation speed, which is especially important when dealing with large-scale power systems.

[0099] Furthermore, based on the power flow of the power system, the voltage, current, and power are substituted into the Jacobian matrix of the subsystem to obtain the linearized equation of the subsystem near the current steady-state point.

[0100] As a preferred embodiment of the above, in the dynamic analysis of power systems, the steady-state point usually refers to the state in which the physical quantities such as voltage, current, and power of each system component reach their steady-state values ​​during system operation. Therefore, power flow analysis is required first to calculate the physical quantities such as voltage, current, and power of the system under steady-state conditions. Power flow analysis is based on the topology of the power system and the rated parameters of the equipment. Through numerical calculation, the voltage amplitude and phase of each node in the system, as well as the power flow of each transmission line, are determined. Power flow analysis is generally solved using the Newton-Raphson method or the Gauss-Seidel method. By modeling the topology of the power system, the steady-state value is first calculated. Under steady-state conditions, the voltage (amplitude and phase) of each bus and the power flow of each transmission line in the system should satisfy the corresponding power balance equations. The voltage amplitude and phase of each bus and the current and power flow of each transmission line obtained after power flow calculation are the steady-state operating points of the system. These steady-state quantities serve as the starting point for the subsequent linearization processing of the state-space model. The steady-state voltage, current, and power values ​​obtained through power flow analysis are substituted into the Jacobian matrix as the operating points of the system. These physical quantities serve as the basis for the small-signal analysis of the system and can help establish the system's operating points. The small-disturbance dynamic equations of the system are derived by substituting the steady-state voltage, current, and power into the system's nonlinear equations. The Jacobian matrix represents the system's response to small disturbances near the steady-state point. These nonlinear equations describe the interrelationships of various components in the power system and how they respond to external inputs or state changes under small disturbances. In the Jacobian matrix, voltage is modeled through the relationship between the partial derivative of the bus voltage and other variables; current is calculated in the Jacobian matrix through its relationship with voltage changes; and power changes directly affect the system's dynamic behavior. When voltage, current, and power are substituted as representative values ​​of the system's steady-state point into the system's nonlinear equations... In linear mathematical models, the Jacobian matrix describes the linearized relationship between the system's state variables and the input. Each element in the Jacobian matrix is ​​a partial derivative of each system state variable with respect to its respective variable. Substituting these partial derivatives into the steady-state values, the results will provide the basis for the linearized equations of the system near that steady-state point. After substituting voltage, current, and power into the Jacobian matrix, the behavior of the system near the current steady-state point can be obtained based on these linearized equations. By calculating the elements of the Jacobian matrix, small-signal equations describing the dynamic characteristics of the system can be constructed. These equations will be used for further stability analysis, frequency response analysis, and system optimization design.

[0101] Furthermore, linearized state-space models include:

[0102] The linearized state-space model expression is:

[0103]

[0104] In the formula, the subscript k represents the k-th subsystem, ΔX, ΔU, and ΔY are the state variable, input variable, and input variable, respectively; A, B, C, and D are the state matrix, input matrix, output matrix, and direct transfer matrix, respectively. This represents the set of state variables after the subsystems are interconnected in series.

[0105] As a preferred embodiment of the above, in the small-signal analysis of the power system, the dynamic behavior of the system can be described by a state-space model. By linearizing the nonlinear system, a linearized state-space model is obtained. The linearization process transforms the original nonlinear equations into approximate linear equations, thereby approximately describing the dynamic response of the system under small disturbances. In the expression, ΔX represents the change in system state variables, typically including voltage, frequency, generator output power, etc.; ΔU represents the change in system input variables, typically control signals (such as power setpoints, voltage regulation signals, etc.); ΔY represents the change in system output variables, typically the system output signals (such as generator output power, bus voltage, etc.); A is the state matrix, describing the dynamic relationship between internal states of the system; B is the input matrix, describing the influence of input signals on state variables; C is the output matrix, describing the influence of state variables on system output; and D is the direct transfer matrix, describing the direct transfer of input signals to output variables. Impact: By linearizing the nonlinear mathematical model of the power system, the aforementioned state-space form can be obtained. The linearization process generally involves Taylor expansion of the original system equations, retaining first-order derivative terms and ignoring higher-order terms. Specifically, the nonlinear equations of the power system typically involve the nonlinear relationships between state variables such as voltage, frequency, and power of each bus and their control inputs. Through linearization, these relationships are transformed into linear equations, allowing the system to be described by a linear model under small disturbances. Before linearization, the steady-state operating point of the power system needs to be calculated through power flow analysis. This steady-state point is typically the operating state of the system without external disturbances. Based on the steady-state point, partial derivatives are calculated for each equation of the system for the state variables and input variables to obtain the Jacobian matrix. These partial derivatives constitute the core of the linearized equations. By substituting the calculated Jacobian matrix into the standard form of the state-space model, the linearized state-space equations of the system can be obtained.

[0106] Furthermore, the automatic linearized matrix acquisition method based on a hierarchical parallel strategy includes:

[0107] Determine ΔX, ΔU, and ΔY from the m×1-dimensional linearized equation and the p×1-dimensional linearized variables, where m and p represent the dimensions of the linearized equation and the linearized variables, respectively.

[0108] Allocate memory space for the linearization matrix based on the linearization equation and the dimension of the linearization variables;

[0109] The calculation of the state matrix and the output matrix is ​​split into multiple independent rows, and the partial derivative calculations are performed in parallel by different working processes;

[0110] The linearization process is determined by checking whether the remainder is zero based on the result of the partial derivative calculation. If it is zero, the input matrix and the direct transfer matrix are calculated in parallel. If it is not zero, the calculation is immediately interrupted, and the mathematical model, input variables, and state variables of the subsystem are redefined.

[0111] As a preferred embodiment of the above, it is necessary to clearly define the state variables, input variables, and output variables from the linearized mathematical model of each subsystem, thereby determining the dimensions of the linearized equation set and the variable set. Specifically, the linearized equation set of the system is represented as an m×1 vector, where m represents the number of equations, reflecting the internal and external state constraints of the system; the linearized variables of the system are represented as a p×1 vector, where p represents the number of variables, typically including state variables, control inputs, and possible external disturbance variables; based on the distribution of variables and equations in the linearized model, the system automatically extracts the corresponding ΔX (state variable offset), ΔU (input variable offset), and ΔY (output variable offset), laying the foundation for constructing the state-space model. Basic; After defining the variable dimensions, the system automatically pre-allocates memory space for the state matrix A, input matrix B, output matrix C, and direct transfer matrix D based on the values ​​of m and p. Since these matrices often exhibit sparse structures, a sparse matrix format is preferred for memory pre-allocation to reduce storage pressure and improve read / write efficiency. The state matrix A, with a size of m×p, stores the linearized response of each state variable to itself or other variables; the input matrix B, with a size of m×q, describes the effect of the input variable ΔU on the system state; the output matrix C, with a size of r×p, describes the influence of the state variables on the system output; and the direct transfer matrix D, with a size of r×q, records the proportional relationship between the input variables and the output variables; where q and r are the input and output variables, respectively. The system automatically identifies the dimensions of the output variables when constructing the state-space model. During the linearization of partial derivative calculations, a hierarchical parallel strategy is adopted: first, large-scale computational tasks are logically divided, and then tasks within the same level are allocated to different threads / processes for parallel execution, ensuring computational efficiency and task independence. Each row of the state matrix A and output matrix C is considered an independent computational task, and each task involves calculating the partial derivatives of a certain equation with respect to all state variables (or output variables). The system creates a task scheduler, allocating these row tasks to different computing cores according to the number of cores or thread pool size for parallel execution. In a distributed computing environment, tasks from different subsystems can be further allocated to independent nodes, improving the overall system parallelism level. This strategy offers several advantages. The key feature is that each computational task is independent and there are no data dependency conflicts, making it suitable for efficient parallel processing in multi-core and multi-node architectures. To ensure the accuracy and completeness of linearization calculations, a remainder judgment mechanism is introduced. This mechanism checks the error terms in the linearization results to determine whether they are acceptable or if there are any model settings errors. During the linearization process, after each partial derivative is calculated, the error between the original nonlinear equation and the linear approximation is automatically compared. If the error (i.e., higher-order remainder terms) is within the set tolerance range, the linearization is considered successful, and the process proceeds to the next stage of matrix construction. If the remainder terms are significantly non-zero, it indicates that the linearization accuracy is insufficient or the model settings are incorrect. In this case, the current round of calculation will be immediately interrupted, and the following dynamic adjustment operation will be triggered: re-check the mathematical model definition of the subsystem.The system re-evaluates the rationality of the selection of input and state variables; provides diagnostic prompts for non-analytical expressions, strongly coupled links, or missing control logic in the model; users can choose to adjust the model structure, or the system can automatically perform variable substitution and model simplification operations before re-performing linearization; if the remaining terms pass verification, the system will continue to calculate the input matrix B and direct transfer matrix D in parallel based on the existing state and output matrices. The calculation method of the input matrix is ​​consistent with that of the state matrix, assigning each row as a parallel task; if there is a direct linear relationship between the input and output, the terms of matrix D are directly obtained through derivatives; after all matrix calculations are completed, a unified convergence test is performed to construct the final state-space model of the subsystem.

[0112] Furthermore, such as Figure 2 and Figure 5 As shown, the topology of each transmission line in the power system is traversed and topology segmentation is performed based on the boundary topology of the subsystem to ensure that there is a complete electrical path between nodes within the subsystem. The segmented subsystems are then connected in series to construct a complete transmission line.

[0113] As a preferred embodiment of the above, the identification and partitioning of the power system topology employs a depth-first search (DFS) algorithm to identify and partition the electrical topology of the power system. Specifically, the power system is first modeled as a graph structure, where each node represents a bus, transformer station, or other key equipment in the power system, and each edge represents a closed transmission line, switch, or circuit breaker. The connection relationships between nodes are described using an adjacency list or adjacency matrix. This graph structure model simplifies the topological relationships of the power system and provides a clear view for subsequent topology partitioning. The implementation process of the DFS algorithm is as follows: In the graph structure initialization phase, the power system is first... All key equipment and transmission lines in the system are treated as nodes and edges in a graph, forming a complete power system topology network. The connections between nodes (i.e., edge relationships) can be represented by an adjacency matrix or an adjacency list, depending on the system size and computational requirements. Before the Depth-First Search (DFS) algorithm begins, to ensure that each node is traversed only once, a marker array needs to be maintained for each node. Initially, the visit status of all nodes is set to "unvisited". Starting from any node, the DFS algorithm marks that node as "visited" and recursively traverses all its adjacent nodes (i.e., nodes connected through closed transmission lines or switches). When the algorithm backtracks to the starting node and there are no unvisited adjacent nodes, it indicates that the current connected region has been divided, and this region is an independent topological subnet. If there are unvisited nodes, the algorithm will select an unvisited node and continue performing a depth-first traversal until all nodes have been visited, thus completing the topological division of the entire power system. Through the above steps, the DFS algorithm can efficiently divide the power system into several independent topological subnets, each representing a subsystem. These subsystems will be processed as independent units in subsequent calculations. Based on the system's control mode, the control links of each subsystem are further determined. Input-output relationships: Power systems typically involve multiple control levels, including control links such as generation, dispatch, and transmission. The input-output relationships of each control link are different. By analyzing the system's control mode, the control links of each subsystem are identified and divided. In specific implementation, each subsystem is first divided according to the system's operational requirements and control methods. For each subsystem, the system determines its main control variables (such as voltage, frequency, etc.) and completes the division of control subsystems by analyzing their input-output relationships. For example, for some power generation systems, the input may be the power regulation signal of the generator, and the output may be the power or voltage on the transmission line.For some dispatching subsystems, the input may be instructions from the superior dispatching system, and the output may be dispatching information provided to downstream subsystems. This process involves analyzing the feedback and constraint relationships between subsystems in the power system and constructing an input-output model with practical control significance. This approach ensures the integrity of the electrical paths within each subsystem and effectively guarantees the stability and accuracy of each subsystem's control links. After identifying and dividing the subsystem topology, further ensuring the integrity of the electrical paths within each subsystem is crucial; that is, during topology partitioning, ensuring connectivity between all nodes within each subsystem is essential. Electrical paths, especially when performing series partitioning of subsystems, require ensuring that the electrical connections between subsystems do not compromise the electrical performance of the original system. For example, when partitioning the topology among multiple transmission lines, it is essential to ensure that the partitioned subsystems can operate independently without causing the loss of power system functionality due to path breaks. During topology partitioning, for each transmission line, the presence of circuit breakers or switches is checked to determine if it is being cut off, and the partitioning boundaries are adjusted based on electrical connectivity. Finally, by connecting the partitioned subsystems in series according to the topological relationships, a complete transmission line model can be obtained, ensuring the stable operation of the system. This method can also be applied to other systems. Figure 2 and Figure 5 In the two circuits shown.

[0114] Furthermore, such as Figure 6 The diagram showing the interconnection of subsystems illustrates the transmission relationships of the complete subsystems based on the control mode and the input and output variables of the controllers of each subsystem.

[0115] As a preferred embodiment of the above, it is first necessary to identify and determine the control mode of the power system. The control modes in the power system may include, but are not limited to, generation control, frequency regulation, load distribution, generator excitation control, and automatic voltage regulation. Under each control mode, the input and output variables of different subsystems have specific correlations. These control modes reflect the system's stability requirements, power dispatch needs, and response mechanisms. Depending on the control mode, the input and output variables and control methods of the controller in each subsystem also differ. Analyzing the input and output variables of the controller in each subsystem is a crucial step. In each subsystem, the controller's input and output variables are affected by other components in the power system. For example, the generator's input power regulation signal may affect the power flow direction or voltage value of the transmission line. Therefore, the relationship between input and output variables determines the dynamic characteristics of the system. In specific implementation, for each subsystem, the controller's input and output variables must first be identified, and the interaction between these variables must be further analyzed based on the identified control mode. After identifying and analyzing the input and output variables of each subsystem... After the initial measurement, the next step is to generate complete subsystem transfer relationships based on the control model. The transfer relationships of each subsystem can be described by mathematical models, including linear or nonlinear relationships between input and output signals. By establishing a state-space model of the subsystem, the input-output relationship is transformed into a mathematical expression between state variables. Specifically, the transfer relationships of a subsystem typically involve its state equations and output equations. In the state-space model, the input signal acts on the system's state variables through the controller, while the system's state variables affect the output signal through the corresponding output equations. Combining the relationship between input and output variables, this association can be described using an appropriate transfer function or transfer matrix. The transfer relationships of each subsystem can be realized by constructing a transfer function or transfer matrix. Transfer functions are commonly used tools for describing the dynamic relationship between input and output, especially important in small-signal analysis. By analyzing the state-space model of each subsystem, the linear relationship between its input and output variables is determined, and the corresponding transfer function is constructed. When constructing the transfer function, the coupling effects between multiple control loops may be involved. To facilitate calculation and analysis, these transfer relationships can be combined into a transfer matrix, which describes the interactions between the subsystems. After generating the subsystem transfer relationships, the relationships are verified and optimized. To ensure the accuracy of the transfer relationships of each subsystem, small-signal stability analysis can be used to verify the rationality and stability of the subsystem transfer functions. If there are deviations in the construction of the transfer functions, it may affect the overall stability of the system. Therefore, it is necessary to optimize these transfer relationships by adjusting the control parameters or model structure to ensure the stability and dynamic response capability of the system under different operating conditions.

[0116] Furthermore, a mathematical model of the subsystem is established based on Kirchhoff's theorem and the logic of the control mode, and the input and output variables of the subsystem are controlled according to the physical constraints of the electrical ports and control ports.

[0117] As a preferred embodiment of the above, Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL) are the most fundamental and indispensable electrical laws in power system modeling. In actual modeling, each subsystem is used as the basic modeling unit. Starting from its electrical topology, its internal electrical connection structure is extracted. KCL is applied to all electrical nodes for current balance analysis, and KVL is applied to all electrical loops for voltage balance analysis. For example, in a substation subsystem, current constraint equations are listed for all connected busbars, transformers, and switchgear nodes; in a generator or motor subsystem, loop voltage constraint equations are listed, including those formed by the excitation winding and armature winding. Through the above process, an electrical equivalent model of the subsystem can be established to obtain accurate electrical constraint relationships. In addition to electrical constraints, the dynamic behavior of the subsystem is also affected by its control logic. Therefore, the role of the controller needs to be considered simultaneously during the modeling process. By analyzing the control mode logic, various control... This study defines the position and function of the controller in the electrical process and incorporates the controller's dynamic equations into the subsystem model. The modeling of the control logic includes not only the dynamic characteristics of the controller itself but also its response to physical system variables. Determining the input and output variables of each subsystem is crucial in constructing the state-space model. To ensure physical consistency in modeling and compatibility with subsequent system interconnections, input and output variables are systematically selected based on the physical constraints between electrical and control ports. Electrical ports are often used as boundary variables connecting the subsystem to other systems, and their input and output selection must satisfy constraints under Kirchhoff's theorems. For control ports, variables that directly interact with the controller should be selected. Furthermore, a variable mapping matrix is ​​established to bind input and output variables to model state variables, achieving unified modeling and interface coordination. In this way, each subsystem can achieve model coupling through defined standard interfaces during subsequent interconnections, avoiding the risk of variable duplication or omission.

[0118] Furthermore, such as Figure 7 , Figure 8 and Figure 9 As shown in the figure, the white dashed line represents the actual effect of this invention in simulation testing, generating a small-signal state-space model of the power system, including:

[0119] When subsystems are connected in series, the state-space model after interconnection is as follows:

[0120]

[0121]

[0122] In the formula, the subscripts j & k represent any two subsystems j and k connected in series, k and j represent the labels of any subsystem, ΔX, ΔU, and ΔY are the state variable, input variable, and input variable, respectively; A, B, C, and D are the state matrix, input matrix, output matrix, and direct transfer matrix, respectively.

[0123] If the subsystems are connected in parallel, the state-space model after interconnection is as follows:

[0124]

[0125] In the formula, the subscript j||k represents that subsystem j and subsystem k are connected in parallel;

[0126] When the subsystems are interconnected via feedback, that is, when a portion of the output of any subsystem j is the input of any subsystem k, and the output of any subsystem k is a portion of the input of any subsystem j, the state-space model after interconnection is:

[0127]

[0128] ΔU j,k =[ΔV j ΔV k ] T ;

[0129]

[0130] C jk =[M jj C j M jk C k ];

[0131] C kj =[M kj C j M kk C k ];

[0132] D jk =[M jj D j M jk D k ];

[0133] D kj =[M kj D j M kk D k ];

[0134]

[0135] In the formula, subscripts j and k represent feedback interconnection between subsystems j and k; subscript jk represents transmission from subsystem j to subsystem k, and subscript kj represents the reverse; subscript jj represents self-mapping within subsystem j, and subscript kk represents the same; ΔV j With ΔV k These are the external input parts of subsystems j and k, respectively; B j B′ is the transfer matrix where the partial output of subsystem k acts on the partial input of subsystem j. k The reverse is also true; D j j is the transfer matrix where part of the output of subsystem k directly affects the output of subsystem j, D′ k The reverse is also true; I is the identity matrix.

[0136] As a preferred embodiment of the above, when two subsystems j and k are connected in series, the relationship between their input, state, and output variables needs to be described in a series manner. Series connection means that the output of one subsystem is the input of another. This connection method can be used to construct the overall state-space model in the following way: each subsystem remains independent when connected in series, but their inputs and outputs are intertwined in the overall system. When generating the state-space model, the state matrix, input matrix, output matrix, and direct transfer matrix are concatenated according to the series connection rules. For example, the state matrix reflects the interrelationships between subsystems, the input matrix merges the inputs of two subsystems, and the output matrix is ​​concatenated according to the series connection rules. In a parallel system, the direct transfer matrix of the overall system is usually zero, meaning that the direct influence of the input on the output is indirectly transmitted by other matrices. When subsystems j and k are connected in parallel, their input signals are the same, but their output signals remain independent. The parallel relationship means that the two subsystems perform independent functions, but they share the same input source. The output variables are formed independently. In the parallel model, the state and output matrices of each subsystem remain independent. The input matrix combines the inputs of both subsystems. The state and input matrices merge the calculations of the two subsystems, and the output matrix directly reflects the output variables of the two subsystems. The direct transfer matrix is ​​usually still zero because the direct transfer matrix of the parallel subsystems is zero. There is no direct input-output transmission between the two subsystems; when the two subsystems j and k are in a feedback interconnection state, it means that the output of one subsystem becomes the input of the other subsystem, and vice versa. This feedback relationship leads to complex interactions between the two subsystems, which need to be described by a complex state-space model. In the feedback interconnection model, the input and output variables of each subsystem are intertwined, producing bidirectional effects. The input and output variables of subsystem j and subsystem k are coupled through a feedback mechanism, forming bidirectional feedback. The state matrix, input matrix, output matrix, and direct transmission matrix need to be generated through different feedback connection methods. In this model, in addition to the state matrix of the subsystem itself... In addition to the matrix, the feedback transfer matrix and the impact of feedback to the input also need to be considered. Feedback interconnection models usually include additional matrices, such as the feedback transfer matrix, which reflects how the output of one subsystem affects the input of another subsystem, or how feedback occurs in reverse. In the case of feedback interconnection, in addition to the coupling between the matrices mentioned above, the system also needs to determine whether the transfer matrix meets the stability requirements. If some matrix terms are zero during the feedback process, it indicates that the linearization result has fully met the requirements, and the system can continue to calculate the input matrix and the direct transfer matrix to construct a complete state-space model. If some matrix terms are not zero, the mathematical model of the subsystem, the selection of input and output variables, and the adjustment of state variables need to be re-examined.

[0137] Although this application has been described in conjunction with specific features and embodiments, it is obvious that various modifications and combinations can be made thereto without departing from the spirit and scope of this application. Accordingly, this specification and drawings are merely exemplary illustrations of the application as defined herein, and are to be considered as covering any and all modifications, variations, combinations, or equivalents within the scope of this application. Clearly, those skilled in the art can make various alterations and modifications to this application without departing from its scope. Thus, if such modifications and modifications fall within the scope of this application and its equivalents, this application intends to include such modifications and modifications.

Claims

1. A distributed parallel modeling method for small-signal state space of a power system, characterized in that, The method includes: Construct the topology of the power system, identify the boundary topology of each subsystem, and determine the transmission relationships between the subsystems; A mathematical model for each subsystem is determined and a parallel computing thread pool is created. A two-dimensional index is generated in the parallel computing thread pool, and the mathematical model is linearized in parallel based on the two-dimensional index. Based on the results of the parallel linearization, the linearized state-space model of the subsystem is automatically constructed according to the hierarchical parallel strategy, and the remainder term is verified. Based on the transmission relationship and the boundary topology, the linearized state-space models of each subsystem are interconnected to generate a small-signal state-space model of the power system.

2. The small-signal state-space distributed parallel modeling method for power systems according to claim 1, characterized in that, Parallel computing thread pools and two-dimensional indexes, including: The number of threads N for parallel computing must satisfy: N = min(k, number of CPU cores); In the formula, k represents a constant, k∈[1,m×p], and m and p represent the dimensions of the equation f to be linearized and the linearized variable x, respectively; The two-dimensional indexes are associated with the number of equations and the number of variables in the mathematical model, respectively. The two-dimensional indexes should be configured as follows to ensure that each parallel task processes a unique combination of equations or variables: In the formula, i and j are respectively associated with the number of equations to be linearized f and the number of linearized variables x.

3. The small-signal state-space distributed parallel modeling method for power systems according to claim 2, characterized in that, Multi-core parallel differentiation algorithms based on two-dimensional index mapping include: The execution tasks are divided into m × p independent tasks, and the partial derivative calculations of m equations with respect to p variables are decomposed into m × p independent tasks. The rounding up and modulo operations are used to ensure that each kernel obtains an approximate number of index coordinate combinations. Pre-allocate memory space for the steady-state value vector to avoid repeatedly performing symbol substitution in m×p iterations. The core formula for parallel speedup is: In the formula, S is the speedup ratio, and a and N represent the proportion of parallel computing and the number of processor threads, respectively. After parallel computation is completed, the Jacobian matrix of the subsystem is reconstructed through a reshaping operation and stored in a sparse matrix format, the expression of which is: In the formula, f i For the i-th system of equations to be linearized, x j Let J(i,j) be the j-th linearized variable, i = 1, 2, ..., m, j = 1, 2, ..., p, and J(i,j) represent the i-th nonlinear equation f. i x for the j-th variable j Partial derivatives.

4. The small-signal state-space distributed parallel modeling method for power systems according to claim 3, characterized in that, Based on the power flow of the power system, the voltage, current, and power are substituted into the Jacobian matrix of the subsystem to obtain the linearized equation of the subsystem near the current steady-state point.

5. The small-signal state-space distributed parallel modeling method for power systems according to claim 1, characterized in that, The linearized state-space model includes: The linearized state-space model expression is as follows: In the formula, the subscript k represents the kth subsystem, ΔX, ΔU, and ΔY are the state variable, input variable, and input variable, respectively; A, B, C, and D are the state matrix, input matrix, output matrix, and direct transfer matrix, respectively. This represents the set of state variables after the subsystems are interconnected in series.

6. The small-signal state-space distributed parallel modeling method for power systems according to claim 5, characterized in that, A method for automatically obtaining linearized matrices based on a hierarchical parallel strategy includes: ΔX, ΔU, and ΔY are determined from the m×1-dimensional linearized equation and the p×1-dimensional linearized variables, where m and p represent the dimensions of the linearized equation and the linearized variables, respectively. Memory space is allocated for the linearization matrix based on the linearization equation and the dimension of the linearization variables; The calculation of the state matrix and the output matrix is ​​split into multiple independent rows, and the partial derivative calculations are performed in parallel by different working processes; Based on the result of the partial derivative calculation, determine whether the remainder term is zero to determine whether the linearization process is complete. If it is zero, calculate the input matrix and the direct transfer matrix in parallel. If it is not zero, immediately interrupt the calculation and redetermine the mathematical model, input variables, and state variables of the subsystem.

7. The small-signal state-space distributed parallel modeling method for power systems according to claim 1, characterized in that, The topology of each transmission line in the power system is traversed and topology segmentation is performed based on the boundary topology of the subsystem to ensure that there is a complete electrical path between nodes within the subsystem. The series segmented subsystems are then used to construct a complete transmission line.

8. The small-signal state-space distributed parallel modeling method for power systems according to claim 1, characterized in that, Based on the control mode, the complete transmission relationship of the subsystems is established by combining the input and output variables of the controllers of each subsystem.

9. The small-signal state-space distributed parallel modeling method for power systems according to claim 1, characterized in that, The mathematical model of the subsystem is established based on the logic of the control mode, and the input and output variables of the subsystem are controlled according to the physical constraints of the electrical ports and control ports.

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