Regional power distribution network model order reduction method and system based on Krylov subspace

Abstract

The invention discloses a regional power distribution network model order reduction method and system based on a Krylov subspace, and the method comprises the steps: collecting the operation data of a regional power distribution network, and carrying out the preprocessing; describing dynamic behaviors and electrical characteristics of the power system through a differential equation and an algebraic equation, and establishing a dynamic model for dynamic simulation of the power system; performing linearization processing on the differential algebraic equation of the power system to generate a linearized small signal model, and extracting a state variable, an algebraic variable and an input and output relationship of the system; a Krylov subspace method is applied, dimension of an order reduction system is selected, an Arnoldi algorithm is used to construct a projection space, and a matrix of the order reduction system is calculated. By adopting the Krylov subspace method, the calculation efficiency and simulation speed of regional power distribution network model order reduction are remarkably improved, the key dynamic characteristics of the model are kept, consumption of calculation resources is reduced, simulation is more flexible and reliable under complex operation conditions, the method adapts to different operation scenes, and a more accurate simulation result is provided.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and in particular to a method and system for reducing the order of a regional distribution network model based on Krylov subspace. Background Art

[0002] With the rapid economic growth and increasing demand for energy in China, regional distribution networks are facing major challenges in terms of resources and environment. In order to adapt to this change, it is essential to optimize the operation and management of regional distribution networks. Thanks to China's abundant solar thermal resources and the government's strong support for the photovoltaic power generation industry, photovoltaic power generation is increasingly used in regional distribution networks. By the end of 2019, China accounted for a significant proportion of the global photovoltaic power generation installed capacity, which provided strong support for improving the efficiency and reliability of regional distribution networks. However, with the widespread application of new energy in regional distribution networks, especially photovoltaic power generation, distribution networks are becoming more and more complex, especially with the increasing proportion of power electronics in power systems, resulting in distribution networks becoming a complex dynamic system. This leads to the high-order and complex mathematical models describing the dynamic behavior of distribution networks becoming more complex, the calculation difficulty increases, and sometimes it is even difficult to find a stable solution. In order to effectively meet these challenges and ensure the safe and stable operation of regional distribution networks, we need to reduce the order of these complex models to simplify the system simulation calculation process and ensure the efficiency and accuracy of operation.

[0003] Model order reduction is a powerful tool that has been applied in multiple disciplines, including control, dynamics, and structural dynamics. In many cases, while high-order, complex numerical models can accurately represent a problem, they perform poorly in terms of computational efficiency and are not suitable for subsequent analysis and control design, such as optimization or control design. Ideally, we would like to develop a model with low state dimensionality that can accurately capture the dynamic behavior of the system over a certain frequency and input range, thereby reducing the time for subsequent optimization and control design. Through model order reduction methods, high-order, complex mathematical models can be projected onto a reduced order space. If appropriate transformations are chosen, these models can maintain a large number of dynamic states, thereby improving computational efficiency while ensuring accuracy.

[0004] At present, the most commonly used practical method for model reduction technology for regional distribution networks is the equivalent aggregation method based on coherence. This method uses the inherent characteristics of the power system, such as line current, load characteristics and generator inertia, to derive a reduced-order external system while retaining the relevant dynamic characteristics. This method mainly includes two steps: one is to identify coherent units, and the other is to aggregate each coherent unit into a single equivalent power device. This method is widely used in model reduction of regional power grids, among which the reduction method based on linear input-output model is the most mature and widely used one.

[0005] Going deeper, the Krylov subspace method shows its wide applicability in iterative solution of high-dimensional linear equations, calculation of high-dimensional matrix eigenvalues, dimensionality reduction and simplification of large-scale linear systems, etc. The core of this method is to find a reduced-order system model by constructing a spatial projection matrix so that the moments of its transfer function match the moments of the transfer function of the original system model. Among them, the Lanczos method and the Arnoldi method are all based on the Krylov subspace. Their common feature is that at a certain frequency or frequencies, they ensure that the several order moments of the transfer function of the low-dimensional simplified system are completely consistent with those of the original system.

[0006] Based on these methods and principles, the present invention proposes a model reduction technology for regional distribution networks. First, the power system of the target area is taken as an external system and represented by a linear model. Then, the Krylov subspace method is used to reduce the overall order of the system. Finally, by using the reduced-order model for verification, it is confirmed that the model can effectively fit the original system while simplifying the model and reducing the amount of calculation. In this way, we can effectively reduce the amount of calculation in the simulation calculation process while ensuring the accuracy and efficiency of the analysis. Summary of the invention

[0007] In view of the above-mentioned problems, the present invention is proposed.

[0008] Therefore, the technical problem solved by the present invention is that in regional distribution networks, due to the large and complex calculation amount of high-order and complex mathematical models of power systems, it is difficult to perform efficient simulation and analysis, and traditional methods are insufficient in calculation efficiency and accuracy.

[0009] In order to solve the above technical problems, the present invention provides the following technical solutions: a regional distribution network model reduction method based on Krylov subspace, comprising: collecting operating data of the regional distribution network and performing preprocessing;

[0010] Describe the dynamic behavior and electrical characteristics of the power system through differential equations and algebraic equations, and establish a dynamic model for dynamic simulation of the power system;

[0011] Linearize the differential algebraic equations of the power system, generate a linearized small signal model, and extract the system's state variables, algebraic variables, and input-output relationships;

[0012] The Krylov subspace method is applied to select the dimension of the reduced-order system, the Arnoldi algorithm is used to construct the projection space, and the matrix of the reduced-order system is calculated.

[0013] As a preferred solution of the regional distribution network model reduction method based on Krylov subspace described in the present invention, the operating data of the collected regional distribution network includes power angle, speed, mechanical torque, input voltage of the excitation system, machine terminal voltage, bus voltage, active power and reactive power of the load.

[0014] As a preferred solution of the regional distribution network model reduction method based on Krylov subspace described in the present invention, wherein: the establishment of a dynamic model for dynamic simulation of the power system includes establishing a differential equation of the dynamic simulation model of the power system, the formula is:

[0015]

[0016] Among them, δ i is the power angle of the synchronous generator, ω s and ω i Respectively represent the rated speed and speed of the synchronous generator, M i represents the inertia constant of the synchronous generator, T Mi Denotes the mechanical torque of the synchronous generator, D i represents the damping of the synchronous generator, e qi ' represents the quadrature axis transient potential of the synchronous generator, e di ' represents the direct axis transient potential of the synchronous generator, I qi and I di They represent the quadrature-axis current and direct-axis current of the synchronous generator, respectively, and K Ei represents the amplification constant of the excitation system, S E Indicates the saturation coefficient of the excitation system, T Ei Represents the time constant of the excitation system, V Ri Represents the input voltage of the excitation system, E fdi represents the excitation voltage, R Fi Represents the control signal, T Fi represents the time constant of the control system, K Ai Represents the amplification constant of the excitation system, V i Represents the terminal voltage of the synchronous generator, V refi Indicates the reference voltage of the excitation system, K Fi represents the constant of the excitation system, X di represents the direct-axis reactance of the synchronous generator, X di ' represents the direct-axis transient reactance of the synchronous generator, X qi represents the quadrature-axis reactance of the synchronous generator, X qi ' represents the quadrature-axis transient reactance of the synchronous generator, T qi ' represents the quadrature axis transient time constant of the synchronous generator, T di' represents the direct-axis transient time constant of the synchronous generator, and m represents the number of synchronous generators.

[0017] As a preferred solution of the regional distribution network model reduction method based on Krylov subspace described in the present invention, wherein: the establishment of a dynamic model for dynamic simulation of the power system also includes establishing an algebraic equation of the dynamic simulation model of the power system, the formula is:

[0018]

[0019] Among them, v i represents the voltage amplitude of bus i, Y ik and α ik Respectively represent the amplitude and phase angle of the node admittance matrix, P Li and Q Li Respectively represent the active power and reactive power of the load, R si represents the internal impedance of the synchronous generator, θ i represents the bus voltage phase angle, and n represents the number of system nodes.

[0020] As a preferred solution of the regional distribution network model reduction method based on Krylov subspace described in the present invention, wherein: the generation of the linearized small signal model includes calculating the input and output model of the differential algebraic equation of the power system, and the general form of the power system dynamic model is expressed as:

[0021]

[0022] Where x represents the system state variables, including the power angle δ of the synchronous generator i , speed ω i , the quadrature axis transient potential e of the synchronous generator qi ', the direct axis transient potential of the synchronous generator e di ', Excitation voltage e fdi , input voltage V of the excitation system Ri , control signal R Fi ; y represents the system algebraic variables, including the direct-axis current I of the synchronous generator di and the quadrature axis current I qi , bus voltage amplitude V i and phase angle θ i ; u represents the system input, including the excitation reference voltage of the excitation system and the mechanical torque T of the synchronous generator Mi ;

[0023] Linearize equation (3) to get equation (4):

[0024]

[0025] Eliminating the algebraic variable y, we obtain:

[0026]

[0027] Among them, A sys The conditions are:

[0028] A sys =A-BD -1 C (6)

[0029] Linearize the differential equation (1):

[0030]

[0031] The state matrix A is obtained, which is expressed as:

[0032]

[0033] Among them, bloockdiag means block diagonal operation;

[0034] make Where T represents the transposed symbol; the matrix B is shown in formula (9):

[0035]

[0036] The matrix E is shown in formula (10):

[0037] Linearizing (2) can also get matrix C and matrix D. From formula (5), we can get matrix A sys .

[0038] As a preferred solution of the regional distribution network model reduction method based on Krylov subspace described in the present invention, wherein: the matrix of the calculation reduction system includes representing the input-output model of the power system differential algebraic equation, as shown in formula (11):

[0039]

[0040] Among them, A=A sys , B = E, the output matrix C depends on the variable to be observed. When the observed variable is the power angle δ of the synchronous generator i , speed ω i and excitation voltage e fd When , V is as shown in formula (12):

[0041]

[0042] C=blockdiag(C1,C2,…,C m ) (12)

[0043] After the dynamic simulation model of the power system is established, the model is reduced based on the Krylov subspace method.

[0044] As a preferred solution of the regional distribution network model reduction method based on Krylov subspace described in the present invention, wherein: the model reduction based on the Krylov subspace method includes selecting the dimension k of the reduced-order system, applying the Arnoldi algorithm to equation (10) to construct the projection space V t , and we get the matrix of the reduced-order system:

[0045]

[0046] The k-dimensional reduced-order system is expressed as:

[0047]

[0048] The k-dimensional reduced-order system is used as the final reduced-order system.

[0049] A regional distribution network model reduction system based on Krylov subspace, characterized by: comprising:

[0050] Data collection and preprocessing module: collects the operating data of the regional distribution network and performs preprocessing;

[0051] Dynamic model building module: describes the dynamic behavior and electrical characteristics of the power system through differential equations and algebraic equations, and builds a dynamic model for dynamic simulation of the power system;

[0052] Small signal model generation module: linearizes the differential algebraic equations of the power system, generates a linearized small signal model, and extracts the system's state variables, algebraic variables, and input-output relationships;

[0053] Model reduction module: Apply the Krylov subspace method, select the dimension of the reduced-order system, use the Arnoldi algorithm to construct the projection space, and calculate the matrix of the reduced-order system.

[0054] The beneficial effects of the present invention are as follows: (1) Traditional order reduction methods generally use simplified models to model external systems. In large systems such as regional distribution networks, the Krylov subspace method exhibits excellent computational efficiency. It can efficiently process complex distribution network models, and is particularly suitable for high-dimensional systems with a large number of nodes and connections; at the same time, for the analysis and simulation of distribution network models, the Krylov subspace method provides stable algorithm performance. It is particularly effective in solving high-dimensional linear equations involving a wide range of grid nodes and calculating eigenvalues ​​of large networks; finally, by constructing an accurate spatial projection matrix, the Krylov subspace method ensures that the transfer function of the reduced-order distribution network model at key frequency points is highly consistent with the original model, thereby ensuring that the dynamic characteristics of the model are not lost at key operating frequencies.

[0055] (2) The present invention has the following advantages during simulation: model reduction can significantly speed up the simulation process. For large-scale distribution network models, this method can significantly reduce simulation time by reducing the number of variables that need to be calculated; when dealing with complex distribution network models, the Krylov subspace method optimizes the calculation process, thereby improving the computational efficiency of the overall simulation, especially in scenarios involving large amounts of data and complex interactions; in reduced-order models, the Krylov subspace method can still ensure that key dynamic characteristics are accurately simulated. This is particularly important when performing simulation tasks such as fault analysis, stability studies, and power flow simulation, and the adaptability of this method allows the model to be flexibly adjusted under different operating conditions and scenarios, thereby providing more accurate results. Due to the reduced complexity and computational burden of the simulation, the Krylov subspace method helps to reduce the required computing resources, such as memory and processing power. Under complex operating conditions, such as variable loads or multi-source interactions, the Krylov subspace method makes the simulation more flexible and reliable by providing a more efficient model. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the figures required for use in the description of the embodiments will be briefly introduced below. Obviously, the figures described below are only some embodiments of the present invention. For ordinary technicians in this field, other figures can be obtained based on these figures without paying creative work.

[0057] Figure 1 A flow chart of a regional distribution network model reduction method based on Krylov subspace provided in the first embodiment of the present invention;

[0058] Figure 2 A model order reduction flow chart of a regional distribution network model order reduction method based on Krylov subspace provided in a second embodiment of the present invention;

[0059] Figure 3 Arnoldi algorithm flow chart for implementing a method for reducing the order system of a regional distribution network model based on Krylov subspace provided in a second embodiment of the present invention;

[0060] Figure 4 A schematic diagram of a research system and external system division of a method for reducing the order of a regional distribution network model based on Krylov subspace provided in a second embodiment of the present invention;

[0061] Figure 5 A schematic diagram of an excitation system model of a method for reducing the order system of a regional distribution network model based on Krylov subspace provided in a second embodiment of the present invention;

[0062] Figure 6 A system schematic diagram of a selected example of a method for reducing the order system of a regional distribution network model based on Krylov subspace provided in a second embodiment of the present invention;

[0063] Figure 7 Eigenvalue distribution diagram of the original system and the reduced-order system (16 dimensions) of the method for reducing the order system of the regional distribution network model based on Krylov subspace provided by the second embodiment of the present invention;

[0064] Figure 8 Eigenvalue distribution diagram of the original system and the reduced-order system (24 dimensions) of the method for reducing the order system of a regional distribution network model based on Krylov subspace provided in the second embodiment of the present invention. DETAILED DESCRIPTION

[0065] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the specification drawings. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0066] Example 1, reference Figure 1 , is an embodiment of the present invention, and provides a regional distribution network model reduction method based on Krylov subspace, comprising:

[0067] S1: Collect the operating data of the regional distribution network and perform preprocessing.

[0068] The operating data of the regional distribution network collected include power angle, speed, mechanical torque, input voltage of the excitation system, machine terminal voltage, bus voltage, active power and reactive power of the load and other data parameters.

[0069] By real-time acquisition and preprocessing of regional distribution network operation data, a reliable data foundation is provided for subsequent dynamic model establishment and simulation analysis. The preprocessing steps include data filtering, calibration and standardization to ensure data accuracy and consistency.

[0070] S2: Describe the dynamic behavior and electrical characteristics of the power system through differential equations and algebraic equations, and establish a dynamic model for dynamic simulation of the power system.

[0071] The differential equation for establishing the dynamic simulation model of the power system is as follows:

[0072]

[0073] Among them, δ i is the power angle of the synchronous generator, ω s and ω i Respectively represent the rated speed and speed of the synchronous generator, M i represents the inertia constant of the synchronous generator, T Mi Denotes the mechanical torque of the synchronous generator, D i represents the damping of the synchronous generator, e qi ' represents the quadrature axis transient potential of the synchronous generator, e di ' represents the direct axis transient potential of the synchronous generator, I qi and I di They represent the quadrature-axis current and direct-axis current of the synchronous generator, respectively, and K Ei represents the amplification constant of the excitation system, S E Indicates the saturation coefficient of the excitation system, T Ei Represents the time constant of the excitation system, V Ri Represents the input voltage of the excitation system, E fdi represents the excitation voltage, R Fi Represents the control signal, T Fi represents the time constant of the control system, K Ai Represents the amplification constant of the excitation system, V i Represents the terminal voltage of the synchronous generator, V refi Indicates the reference voltage of the excitation system, K Fi represents the constant of the excitation system, X di represents the direct-axis reactance of the synchronous generator, X di ' represents the direct-axis transient reactance of the synchronous generator, X qi represents the quadrature-axis reactance of the synchronous generator, X qi ' represents the quadrature-axis transient reactance of the synchronous generator, T qi ' represents the quadrature axis transient time constant of the synchronous generator, T di ' represents the direct-axis transient time constant of the synchronous generator, and m represents the number of synchronous generators.

[0074] The algebraic equation for establishing the dynamic simulation model of the power system is as follows:

[0075]

[0076] Among them, v i represents the voltage amplitude of bus i, Y ik and α ik Respectively represent the amplitude and phase angle of the node admittance matrix, P Li and Q Li Respectively represent the active power and reactive power of the load, R si represents the internal impedance of the synchronous generator, θ i represents the bus voltage phase angle, and n represents the number of system nodes.

[0077] Furthermore, describing the dynamic behavior and electrical characteristics of the power system through differential equations and algebraic equations is the basis for establishing dynamic simulation of the power system. Specifically, differential equations are used to describe the dynamic characteristics of synchronous generators, covering key parameters such as power angle, speed, inertia constant, mechanical torque, damping, potential and current. Algebraic equations are used to describe the static characteristics of the power system, especially the relationship between parameters such as bus voltage, load power and node admittance matrix. It provides the necessary electrical characteristics description for the dynamic simulation model. By combining differential equations and algebraic equations, the dynamic and static behavior of the power system can be fully and accurately described, providing a solid foundation for the dynamic simulation of the model. The use of these equations not only solves the shortcomings of traditional methods in accurately describing the dynamic behavior of the system, but also significantly improves the accuracy and reliability of the simulation model, providing high-quality input data and initial models for subsequent linearization and order reduction analysis.

[0078] S3: Linearize the differential algebraic equations of the power system, generate a linearized small signal model, and extract the system's state variables, algebraic variables, and input-output relationships.

[0079] The input-output model of the differential algebraic equations of the power system is calculated. The general form of the power system dynamic model is expressed as:

[0080]

[0081] Where x represents the system state variables, including the power angle δ of the synchronous generator i , speed ω i , the quadrature axis transient potential e of the synchronous generator qi ', the direct axis transient potential of the synchronous generator e di ', Excitation voltage e fdi , input voltage V of the excitation system Ri , control signal RFi ; y represents the system algebraic variables, including the direct-axis current I of the synchronous generator di and the quadrature axis current I qi , bus voltage amplitude V i and phase angle θ i ; u represents the system input, including the excitation reference voltage of the excitation system and the mechanical torque T of the synchronous generator Mi ;

[0082] Linearize equation (3) to get equation (4):

[0083]

[0084] Eliminating the algebraic variable y, we obtain:

[0085]

[0086] Among them, A sys The conditions are:

[0087] A sys =A-BD -1 C (6)

[0088] Linearize the differential equation (1):

[0089]

[0090]

[0091] The state matrix A is obtained, which is expressed as:

[0092]

[0093] Among them, bloockdiag means block diagonal operation;

[0094] make Wherein, T represents the transposition symbol.

[0095] The matrix B is obtained as shown in formula (9):

[0096]

[0097] The matrix E is shown in formula (10):

[0098]

[0099] Similarly, by linearizing (2), we can also get matrix C and matrix D, and then get matrix A from formula (5): sys .

[0100] It should be noted that by linearizing the differential algebraic equations of the power system and generating a linearized small signal model, the transformation from a complex nonlinear system to a linear system is achieved. The rationality and beneficial effects of this process can be explained in detail from the following aspects:

[0101] First, the key step of linearization is to convert nonlinear dynamic equations into linear equations, which is of great significance for dynamic simulation of large-scale power systems. Power systems contain a large number of nonlinear factors, such as the dynamic characteristics of synchronous generators and the nonlinear response of excitation systems. These complex nonlinear behaviors make direct solution and simulation extremely difficult. Through linearization, these nonlinear equations are linearly approximated near the operating point, so that complex nonlinear problems can be solved by linear system methods, which greatly simplifies the calculation difficulty. Specifically, the extraction of state variables (such as the power angle and speed of synchronous generators), algebraic variables (such as current and voltage amplitudes) and input-output relationships enables the dynamic behavior of the system to be described by a set of linear equations, thereby greatly improving the efficiency of simulation and analysis.

[0102] Secondly, the calculation of the linearized state matrix A, input matrix B, output matrix C and D has important application value. These matrices describe the dynamic response characteristics of the power system under small disturbances and can be used in system stability analysis, controller design and fault diagnosis. For example, the state matrix A reflects the dynamic relationship between the state variables of the system. By analyzing the eigenvalues ​​and eigenvectors of the A matrix, the stability and dynamic response characteristics of the system can be judged. The input matrix B and the output matrix C respectively describe the influence of the system input on the state variables and the influence of the state variables on the system output, which is crucial for designing effective control strategies. The matrix D takes into account the direct input-output relationship, which is particularly important in some special cases, such as high-frequency dynamic response.

[0103] Furthermore, although linearization is a common mathematical method, it is optimized in the present invention specifically for the complexity of the power system. For example, the introduction of the blockdiag operation effectively handles the block diagonal matrix operations in the system, making the matrix calculations of large-scale systems more efficient and stable. This processing method not only improves the computational efficiency, but also ensures that the reduced-order model can achieve fast and stable solutions while maintaining the dynamic characteristics of the original system. In addition, by introducing standard linearization methods, the present invention ensures that the generated small signal model has high accuracy in the local area, thereby providing a basis for subsequent reduced-order processing and simulation analysis.

[0104] S4: Apply the Krylov subspace method, select the dimension of the reduced-order system, construct the projection space using the Arnoldi algorithm, and calculate the matrix of the reduced-order system.

[0105] The input-output model of the power system differential algebraic equation is expressed as shown in formula (11):

[0106]

[0107] Among them, A=A sys , B = E, the output matrix C depends on the variable to be observed. When the observed variable is the power angle δ of the synchronous generator i , speed ω i and excitation voltage e fd When , C is as shown in formula (12):

[0108]

[0109] C=blockdiag(C1,C2,…,C m ) (12)

[0110] After the dynamic simulation model of the power system is established, the model is reduced based on the Krylov subspace method.

[0111] Select an appropriate reduced-order system dimension k and apply the Arnoldi algorithm to construct the projection space V for equation (10): t , and we get the matrix of the reduced-order system:

[0112]

[0113] The k-dimensional reduced-order system is expressed as:

[0114]

[0115] The k-dimensional reduced-order system is used as the final reduced-order system.

[0116] It should be noted that the Krylov subspace method is used for model reduction, and the differential algebraic equations of the power system are effectively simplified by selecting an appropriate reduced-order system dimension and using the Arnoldi algorithm to construct a projection space. This step has significant advantages in solving the high computational complexity problem of large-scale power systems. The application of the Krylov subspace method maps the high-dimensional system state space to a low-dimensional space by constructing a projection space, significantly reducing the dimensionality of the system. This process not only retains the main dynamic characteristics of the original system, but also greatly reduces the computational complexity. Specifically, by selecting an appropriate reduced-order system dimension, it can be ensured that the reduced-order system is highly consistent with the original system in terms of key performance indicators.

[0117] Furthermore, when constructing the projection space, the Arnoldi algorithm gradually approximates the eigenvalues ​​and eigenvectors of the target matrix through an iterative method, so that the projection space has good approximation and numerical stability. The specific formulas are shown in Equations (11) and (12). By processing the state matrix A, input matrix B and output matrix C of the original system, the state matrix of the reduced-order system is generated. This method not only improves the computational efficiency, but also avoids the numerical instability problem that may occur in the traditional method. After applying the Arnoldi algorithm to construct the projection space, the reduced-order system matrix is ​​shown in Equation (13), which can effectively describe the main dynamic characteristics of the system.

[0118] The above embodiments also include a regional distribution network model reduction system based on Krylov subspace, specifically:

[0119] Data collection and preprocessing module: collects the operating data of the regional distribution network and performs preprocessing;

[0120] Dynamic model building module: describes the dynamic behavior and electrical characteristics of the power system through differential equations and algebraic equations, and builds a dynamic model for dynamic simulation of the power system;

[0121] Small signal model generation module: linearizes the differential algebraic equations of the power system, generates a linearized small signal model, and extracts the system's state variables, algebraic variables, and input-output relationships;

[0122] Model reduction module: Apply the Krylov subspace method, select the dimension of the reduced-order system, use the Arnoldi algorithm to construct the projection space, and calculate the matrix of the reduced-order system.

[0123] The computer device may be a server. The computer device includes a processor, a memory, an input / output interface (I / O for short) and a communication interface. The processor, the memory and the input / output interface are connected via a system bus, and the communication interface is connected to the system bus via the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store data cluster data of a power monitoring system. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal via a network connection. When the computer program is executed by the processor, a regional distribution network model reduction method based on Krylov subspace is implemented.

[0124] A person of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory may include random access memory (RAM) or external cache memory, etc. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. Non-relational databases may include distributed databases based on blockchains, etc., but are not limited to this. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but are not limited to this.

[0125] Example 2, reference Figures 2 to 8 , which is an embodiment of the present invention, provides a regional distribution network model reduction method based on Krylov subspace. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through economic benefit calculation and simulation / comparative experiments.

[0126] The present invention discloses a model reduction method suitable for regional distribution networks. The method is implemented by two algorithms: Lanczos algorithm and Arnoldi algorithm. Figure 2 As shown, the system is first divided into the research system and the external system, as shown in Figure 4The Lanczos algorithm has the advantages of simplicity, efficiency, and speed, but it has poor numerical stability. It uses the A, B, and C matrices of the original system as input and generates a projection matrix V t and W t As output. The Arnoldi algorithm is not as fast as the Lanczos algorithm, but this algorithm is much more stable. It uses the A and B matrices of the original system as input and produces a projection matrix V t as output.

[0127] The algorithm flow chart for Arnoldi (when the pole is close to infinity) is as follows Figure 3 As shown, after this process, that is, after applying the Lanczos or Arnoldi algorithm, the state transfer matrix and other correlation matrices of the reduced-order system can be obtained. In the Lanczos algorithm, the correlation matrix of the reduced-order system is:

[0128]

[0129]

[0130] For the Arnoldi algorithm:

[0131]

[0132] In general, the problem of model order reduction using the Krylov method can be stated as follows. Given a high-dimensional original system, find a k-dimensional reduced-order system (where k is significantly smaller than the dimension n of the original system):

[0133]

[0134] In this way, the moments of the original system and the reduced-order system satisfy the equality of the first k terms (for the Arnoldi algorithm) or the equality of the first 2k terms (for the Lanczos algorithm).

[0135]

[0136] Therefore, the Krylov-based model reduction method is sometimes also called the moment matching method. Finally, it is worth noting that the model reduction method can be completed using only the state space matrix (i.e., there is no need to explicitly calculate the system moments), and the model reduction method does not modify the input and output relationship of the original system.

[0137] The following is an example of the improved IEEE 33-node power distribution system, and the Krylov subspace method is applied to the power system model reduction for simulation analysis. The original system model dimension is 28 dimensions. The IEEE 33-node power distribution system structure diagram is as follows: Figure 6As shown in FIG. 1 , a dynamic model for dynamic simulation of power system is established, including a 4th-order model of synchronous generator, and the excitation system adopts IEEE-type 1. Figure 5 shown.

[0138] Under the initial load conditions, the dimensions of the Krylov subspace reduced-order system are set to 16 and 24 dimensions respectively. The eigenvalue distributions of the original system and the reduced-order system (16 dimensions) are shown in Figure 7 As shown, the eigenvalue distributions of the original system and the reduced-order system (24 dimensions) are as follows Figure 8 shown.

[0139] It can be seen from the eigenvalue distribution diagram that with the increase of the dimension of the reduced-order system, the eigenvalue distribution of the reduced-order system and the original system will become closer and closer. When the dimension of the reduced-order system is 16, the dominant eigenvalues ​​of the reduced-order system and the original system are very close; when the dimension of the reduced-order system is 24, the eigenvalue distribution of the reduced-order system and the original system is basically the same. It can be seen from the figure that while simplifying the model and reducing the amount of calculation, it can fit the original system well. On the basis of the 16-dimensional reduced-order model, the 24-dimensional reduced-order model further reduces the model error and reflects the damping and oscillation characteristics of the original system more carefully. That is, due to the reduction of the complexity and computational burden of the simulation, the Krylov subspace method helps to reduce the required computing resources, such as memory and processing power. Under complex operating conditions, such as variable load or multi-source interaction, the Krylov subspace method makes the simulation more flexible and reliable by providing a more efficient model.

[0140] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A regional distribution network model reduction method based on Krylov subspace, characterized in that: include: Collect the operation data of the regional distribution network and perform pre-processing; Describe the dynamic behavior and electrical characteristics of the power system through differential equations and algebraic equations, and establish a dynamic model for dynamic simulation of the power system; Linearize the differential algebraic equations of the power system, generate a linearized small signal model, and extract the system's state variables, algebraic variables, and input-output relationships; The Krylov subspace method is applied to select the dimension of the reduced-order system, the Arnoldi algorithm is used to construct the projection space, and the matrix of the reduced-order system is calculated.

2. The regional distribution network model reduction method based on Krylov subspace as claimed in claim 1, characterized in that: The operation data of the distribution network in the acquisition area includes power angle, rotation speed, mechanical torque, input voltage of the excitation system, machine terminal voltage, bus voltage, active power and reactive power of the load.

3. The regional distribution network model reduction method based on Krylov subspace as claimed in claim 2, characterized in that: The establishment of a dynamic model for dynamic simulation of the power system includes establishing a differential equation of the dynamic simulation model of the power system, the formula is: Among them, δ i is the power angle of the synchronous generator, ω s and ω i Respectively represent the rated speed and speed of the synchronous generator, M i represents the inertia constant of the synchronous generator, T Mi Denotes the mechanical torque of the synchronous generator, D i represents the damping of the synchronous generator, e qi ' represents the quadrature axis transient potential of the synchronous generator, e di ' represents the direct axis transient potential of the synchronous generator, I qi and I di They represent the quadrature-axis current and direct-axis current of the synchronous generator, respectively, and K Ei represents the amplification constant of the excitation system, S E Indicates the saturation coefficient of the excitation system, T Ei Represents the time constant of the excitation system, V Ri Indicates the input voltage of the excitation system, E fdi represents the excitation voltage, R Fi Represents the control signal, T Fi represents the time constant of the control system, K Ai Represents the amplification constant of the excitation system, V i Represents the terminal voltage of the synchronous generator, V refi Indicates the reference voltage of the excitation system, K Fi represents the constant of the excitation system, X di represents the direct-axis reactance of the synchronous generator, X di ' represents the direct-axis transient reactance of the synchronous generator, X qi represents the quadrature-axis reactance of the synchronous generator, X qi ' represents the quadrature-axis transient reactance of the synchronous generator, T qi ' represents the quadrature axis transient time constant of the synchronous generator, T di ' represents the direct-axis transient time constant of the synchronous generator, and m represents the number of synchronous generators.

4. The method for reducing the order of a regional distribution network model based on Krylov subspace according to claim 3, characterized in that: The establishing of a dynamic model for dynamic simulation of the power system also includes establishing an algebraic equation of the dynamic simulation model of the power system, the formula is: Among them, v i represents the voltage amplitude of bus i, Y ik and α ik Respectively represent the amplitude and phase angle of the node admittance matrix, P Li and Q Li Respectively represent the active power and reactive power of the load, R si represents the internal impedance of the synchronous generator, θ i represents the bus voltage phase angle, and n represents the number of system nodes.

5. The regional distribution network model reduction method based on Krylov subspace as claimed in claim 4, characterized in that: The generation of the linearized small signal model includes calculating the input-output model of the differential algebraic equation of the power system. The general form of the power system dynamic model is expressed as: Where x represents the system state variables, including the power angle δ of the synchronous generator i , speed ω i , the quadrature axis transient potential e of the synchronous generator qi ', the direct axis transient potential of the synchronous generator e di ', Excitation voltage e fdi , input voltage V of the excitation system Ri , control signal R Fi ; y represents the system algebraic variables, including the direct-axis current I of the synchronous generator di and the quadrature axis current I qi , bus voltage amplitude V i and phase angle θ i ; u represents the system input, including the excitation reference voltage of the excitation system and the mechanical torque T of the synchronous generator Mi ; Linearize equation (3) to get equation (4): Eliminating the algebraic variable y, we obtain: Among them, A sys The conditions are: A sys =A-BD -1 C (6) Linearize the differential equation (1): The state matrix A is obtained, which is expressed as: Among them, blockdiag represents block diagonal operation; make Where T represents the transposed symbol; the matrix B is shown in formula (9): The matrix E is shown in formula (10): Linearizing (2) can also get matrix C and matrix D. From formula (5), we can get matrix A sys .

6. The method for reducing the order of a regional distribution network model based on Krylov subspace according to claim 5, characterized in that: The calculation of the matrix of the reduced-order system includes representing the input-output model of the differential algebraic equation of the power system as shown in formula (11): Among them, A=A sys , B = E, the output matrix C depends on the variable to be observed. When the observed variable is the power angle δ of the synchronous generator i , speed ω i and excitation voltage e fd When , C is as shown in formula (12): After the dynamic simulation model of the power system is established, the model is reduced based on the Krylov subspace method.

7. The method for reducing the order of a regional distribution network model based on Krylov subspace according to claim 6, characterized in that: The model reduction based on the Krylov subspace method includes selecting the dimension k of the reduced-order system, applying the Arnoldi algorithm to equation (10) to construct the projection space V t , and we get the matrix of the reduced-order system: The k-dimensional reduced-order system is expressed as: The k-dimensional reduced-order system is used as the final reduced-order system.

8. A regional distribution network model reduction system based on Krylov subspace using the method according to any one of claims 1 to 7, characterized in that: Data collection and preprocessing module: collects the operating data of the regional distribution network and performs preprocessing; Dynamic model building module: describes the dynamic behavior and electrical characteristics of the power system through differential equations and algebraic equations, and builds a dynamic model for dynamic simulation of the power system; Small signal model generation module: linearizes the differential algebraic equations of the power system, generates a linearized small signal model, and extracts the system's state variables, algebraic variables, and input-output relationships; Model Reduction Module: Apply the Krylov subspace method, select the dimension of the reduced-order system, use the Arnoldi algorithm to construct the projection space, and calculate the matrix of the reduced-order system.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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