An alternating current power system power flow calculation method based on virtual dynamic system integration

Abstract

This invention discloses a power flow calculation method for AC power systems based on virtual dynamic system integration, belonging to the field of power system power flow calculation technology. The method first acquires network and operational data of the AC power system, classifying nodes according to the type of known quantities: known active power, known reactive power, given voltage amplitude, and voltage phase angle. It then constructs a virtual dynamic system driven by power mismatch, transforming the power flow equation solution into a dynamic system equilibrium point solution problem. An explicit integration method is used to iteratively update the node voltage phase angle and amplitude, using the maximum power imbalance as the convergence criterion. An equilibrium point extrapolation acceleration strategy based on local exponential decay characteristics is introduced to improve the solution efficiency in the later stages of integration. This invention avoids dependence on the Jacobian matrix and linear equation system solutions, exhibits excellent convergence robustness under complex conditions such as heavy loads and weak supports, and has good parallelism in the calculation process, making it suitable for fast power flow calculations of large-scale AC power systems.

Description

Technical Field

[0001] This invention belongs to the field of power system power flow calculation technology, specifically relating to an AC power system power flow calculation method based on virtual dynamic system integral. Background Technology

[0002] Power flow calculation is a fundamental computational step in power system planning, design, operation scheduling, and security analysis. Its purpose is to determine steady-state operating parameters such as voltage amplitude, phase angle, and branch power distribution at each node, given network topology, equipment parameters, generation output, and load levels. With the large-scale integration of new energy sources, power electronic equipment, and AC / DC hybrid systems, modern power systems exhibit a dual characteristic of "high proportion of new energy and high proportion of power electronic equipment," resulting in more flexible and varied system operation modes and making it easier for operating points to approach stability boundaries. This trend places unprecedentedly higher demands on the convergence, computational efficiency, and adaptability to complex operating conditions of power flow calculation methods.

[0003] Commonly used power flow calculation methods in engineering include Newton's method, fast decoupling method, and various improved Newton's methods. Among them, Newton's method, by linearizing the power flow equations, constructing the Jacobian matrix, and solving the linear correction equations, has high computational accuracy and fast local convergence speed, and is currently the most widely used method. Fast decoupling method utilizes the approximate decoupling relationship between active power and phase angle, and reactive power and voltage amplitude in AC power systems to simplify the correction equations, thereby reducing the computational load per iteration. Damped Newton's method, optimal multiplier method, Levenberg-Marquardt method, homotopy method, and other methods improve the convergence performance of power flow calculations by adjusting the step size, adjusting the search direction, or introducing auxiliary parameters.

[0004] However, most existing power flow calculation methods still suffer from the following insurmountable technical defects: Poor convergence robustness under complex operating conditions: All Newton-type methods rely to varying degrees on Jacobian matrix construction, matrix decomposition, or solving linear equations. When the system is under complex conditions such as heavy load, weak support, unreasonable parameter configuration, or approaching the stability limit, the Jacobian matrix is ​​prone to ill-conditioned or even singular behavior, leading to oscillations, convergence difficulties, or even divergence in the iterative process. Especially in weak power grids with a high proportion of renewable energy integration, the system's equivalent impedance increases, the condition number of the Jacobian matrix rises sharply, and the convergence failure rate of traditional methods increases significantly.

[0005] Large-scale systems have low computational efficiency: the computational complexity of solving linear equation systems is O(n^2). 3 As the scale of power systems continues to expand (the number of nodes increases from thousands to tens of thousands or even hundreds of thousands), the computational overhead grows exponentially, making it difficult to meet the time requirements for real-time scheduling and online security analysis.

[0006] Parallel implementation is challenging: The core computational steps of traditional methods—matrix factorization and solving linear equations—have strong data dependencies, making efficient parallelization difficult. Even with parallel solvers, the speedup is limited by the serial nature of the algorithm itself, failing to fully utilize the performance advantages of modern heterogeneous computing platforms such as multi-core CPUs and GPUs.

[0007] The improved methods have obvious limitations: while existing improved Newton's method can improve convergence to some extent, it still relies on solving linear equations and cannot fundamentally solve the matrix ill-conditioned problem. Furthermore, some improved methods introduce complex auxiliary parameters and computational procedures, which actually increases the difficulty of implementation and computational overhead.

[0008] Against this backdrop, there is an urgent need for a new power flow calculation method that can avoid solving linear equations, has stable convergence under complex conditions, and has good potential for parallel expansion. Summary of the Invention

[0009] The technical problem to be solved by this invention is to address the shortcomings of the prior art by providing a method for calculating AC power flow based on virtual dynamic system integrals. This method achieves stable solutions for AC power flow by avoiding the solution of linear equations. It addresses the technical problems of existing power flow calculation methods that rely on Jacobian matrix construction and linear equation solving under complex or ill-conditioned conditions, which easily lead to convergence difficulties, iterative divergence, large computational overhead, and limited parallel implementation.

[0010] The present invention adopts the following technical solution: A method for calculating AC power flow based on virtual dynamic system integration includes the following steps: S1. Obtain parameter data and operating data of the AC power system. The parameter data and operating data include at least the node admittance matrix, active power and reactive power data of each node, voltage phase angle and voltage amplitude of the slack node; classify the system nodes according to the known and unknown quantities of the nodes, and determine the nodes with known active power, nodes with known reactive power, nodes with given voltage amplitude and nodes with given voltage phase angle. S2. Construct state variables using the phase angle and magnitude of the voltage at the node to be determined. Calculate the active and reactive power of each node according to the power flow equations to form active power imbalance and reactive power imbalance, and construct the power flow imbalance vector. S3. Based on the coupling relationship between active power and voltage phase angle and the coupling relationship between reactive power and voltage amplitude, construct a virtual dynamic system, wherein the active power loss corresponds to the voltage phase angle dynamic equation and the reactive power loss corresponds to the voltage amplitude dynamic equation, so that the state variables are updated according to the active power loss and reactive power loss during integral iteration. S4. Set the initial state and integral parameters of the virtual dynamic system, and use the explicit integration method to perform integral updates to obtain the updated node voltage phase angle and node voltage amplitude. S5. After each integral update, recalculate the active power imbalance and reactive power imbalance, and use the maximum value of the active power imbalance and reactive power imbalance as the current imbalance. S6. When the current imbalance is less than the preset power flow convergence threshold, output the node voltage phase angle and node voltage amplitude as the power flow calculation result; when the current imbalance is greater than or equal to the preset power flow convergence threshold, continue to execute S4 to S5.

[0011] Preferably, in step S1, classifying system nodes according to known and unknown quantities includes: determining nodes with known active power as nodes with known active power, determining nodes with known reactive power as nodes with known reactive power, determining nodes with given voltage amplitude as nodes with given voltage amplitude, and determining nodes with given voltage phase angle as nodes with given voltage phase angle.

[0012] Preferably, in step S2, the state quantity consists of the phase angle of the voltage to be determined corresponding to the node with known active power and the amplitude of the voltage to be determined corresponding to the node with known reactive power.

[0013] Preferably, in step S2, the active power loss is the difference between the node's given active power and the node's calculated active power, and the reactive power loss is the difference between the node's given reactive power and the node's calculated reactive power.

[0014] Preferably, in step S4, the integration parameters include at least the integration step size and the maximum number of integrations; the step of using an explicit integration method for integration update includes using an improved Euler method: first, the predicted state is calculated based on the current state variables, and then the rate of change under the current state and the predicted state is used for correction and update.

[0015] Preferably, in step S4, setting the initial state of the virtual dynamic system includes: The initial value of the phase angle of the node voltage to be determined is set to the phase angle of the balanced node voltage, and the initial value of the amplitude of the node voltage to be determined is set to a preset per-unit value; the preset per-unit value is 1.0.

[0016] Preferably, in step S5, the current imbalance is the maximum value among the absolute values ​​of each active power imbalance and each reactive power imbalance.

[0017] Preferably, after step S6 is completed, when the current imbalance is less than the preset acceleration trigger threshold, the balance value is estimated based on the local exponential decay characteristics of the state quantity during the integration process, and the estimated state quantity is substituted into the power flow equation for imbalance verification; if the imbalance decreases after verification, the estimated state quantity is accepted, otherwise the estimated state quantity is rejected, the state quantity is returned to the state quantity before extrapolation, and step S4 is continued.

[0018] Preferably, the equilibrium value estimation based on the local exponential decay characteristics of the state variables during the integration process includes: sampling the state variables at multiple consecutive integration steps, calculating the decay parameters based on the sampling results, and estimating the equilibrium value accordingly; the imbalance verification includes substituting the estimated state variables into the power flow equations and calculating the verification imbalance degree.

[0019] Secondly, embodiments of the present invention provide an AC power flow calculation system based on virtual dynamic system integrals, comprising: The data acquisition module is configured to acquire parameter data and operating data of the AC power system, and classify the system nodes according to the known and unknown quantities of the nodes. The imbalance measurement construction module is configured to construct state variables with the phase angle and magnitude of the voltage at the node to be determined, and calculate the active power and reactive power of each node according to the power flow equation, forming active power imbalance measurement and reactive power imbalance measurement, and constituting the power flow imbalance vector. The virtual dynamic system construction module is configured to construct a virtual dynamic system based on the coupling relationship between active power and voltage phase angle and the coupling relationship between reactive power and voltage amplitude. The active power loss corresponds to the voltage phase angle dynamic equation, and the reactive power loss corresponds to the voltage amplitude dynamic equation. The integral update module is configured to set the initial state and integral parameters of the virtual dynamic system, and to perform integral updates using an explicit integration method to obtain the updated node voltage phase angle and node voltage amplitude. The convergence determination module is configured to recalculate the active power imbalance and reactive power imbalance after each integral update, take the maximum value of the active power imbalance and reactive power imbalance as the current imbalance, and output the power flow calculation result when the current imbalance is less than the preset power flow convergence threshold.

[0020] Thirdly, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the above-described AC power flow calculation method based on virtual dynamic system integral.

[0021] Fourthly, embodiments of the present invention provide a computer-readable storage medium including a computer program, which, when executed by a processor, implements the steps of the above-described AC power flow calculation method based on virtual dynamic system integrals.

[0022] Fifthly, a chip includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described AC power flow calculation method based on virtual dynamic system integral.

[0023] In a sixth aspect, embodiments of the present invention provide an electronic device including a computer program, which, when executed by the electronic device, implements the steps of the above-described AC power flow calculation method based on virtual dynamic system integral.

[0024] Compared with the prior art, the present invention has at least the following beneficial effects: A power flow calculation method for AC power systems based on virtual dynamic system integration transforms the traditional problem of solving nonlinear algebraic equations for AC power flow into a problem of finding the equilibrium point of a virtual dynamic system. By acquiring system data and classifying nodes, a state variable update mechanism driven by power mismatch is constructed. An explicit integration method is used for iterative solution, with the maximum power imbalance as the convergence criterion for outputting the power flow result. Employing an explicit integration strategy, only the power mismatch needs to be calculated and the state variables updated, resulting in low computational complexity and avoiding convergence collapse issues caused by matrix ill-conditioning. Furthermore, the direct use of power mismatch to drive state variable correction is logically intuitive. Since no complex matrix operations are required, it possesses excellent parallel computing potential in large-scale systems, making it highly suitable for modern multi-core processors or GPU architectures. This significantly improves the computational efficiency of large-scale power grid analysis, addressing the shortcomings of existing technologies in terms of poor robustness and low computational efficiency under complex operating conditions.

[0025] Furthermore, the specific criteria for node classification are clearly defined. Nodes are divided into four categories based on the type of known quantities: known active power, known reactive power, given voltage amplitude, and given voltage phase angle. This is fully compatible with the node definitions used in traditional power flow calculations, requiring no modification to the original system data format and reducing the difficulty of engineering implementation of the algorithm. At the same time, the clear classification criteria avoid confusion in the processing logic for different node types, improving the standardization and maintainability of the code implementation.

[0026] Furthermore, the state variables are explicitly defined as consisting of the unknown voltage phase angles of nodes with known active power and the unknown voltage amplitudes of nodes with known reactive power. This state variable construction method perfectly matches the channel-driven mechanism of the virtual dynamic system, ensuring that each state variable is driven only by its corresponding power mismatch and avoiding cross-interference. Simultaneously, the dimension of the state vector is linearly related to the system size; as the number of nodes increases, the computational complexity grows gradually, making it suitable for power flow calculations in ultra-large-scale power systems.

[0027] Furthermore, the active power mismatch is defined as the difference between the given active power and the calculated active power at the node, and the reactive power mismatch is defined as the difference between the given reactive power and the calculated reactive power at the node. This ensures the compatibility and comparability of the calculation results of the method in this invention with those of existing engineering software. Simultaneously, as the sole driving source of the virtual dynamic system, the accurate calculation of the mismatch directly determines the correctness of the direction of state updates, providing a core guarantee for the stable convergence of the algorithm.

[0028] Furthermore, the integration parameters are clearly defined, including the integration step size and the maximum number of integration iterations. The explicit integration method employs a modified Euler method, updating the state variables through a two-step prediction-correction mechanism. This prediction-correction mechanism effectively suppresses numerical oscillations during the integration process and expands the range of stable integration step sizes. Simultaneously, specifying the maximum number of integration iterations avoids infinite iterations under extreme conditions, ensuring robustness and controllable computation time.

[0029] Furthermore, the initial state is specified to adopt a flat start method, with the initial value of the phase angle to be determined set to the phase angle of the equilibrium node, and the initial value of the voltage amplitude to be determined set to 1.0 per unit value. This conforms to the voltage range of normal operation of the power system and ensures that the initial point falls within the attraction domain of the virtual dynamic system equilibrium point, avoiding convergence failure caused by improper initial values. At the same time, the unified initial state setting facilitates performance comparison between different methods and engineering applications.

[0030] Furthermore, the current imbalance is defined as the maximum value among the absolute values ​​of all active and reactive power mismatches. The calculation is simple and efficient, requiring only one pass through the system without incurring additional computational overhead. Simultaneously, this convergence criterion is completely consistent with the traditional Newton-Raphson method, ensuring that the calculation accuracy of the method in this invention meets the requirements of power system engineering applications.

[0031] Furthermore, an equilibrium point extrapolation acceleration strategy is introduced. When the imbalance is less than the acceleration trigger threshold, the equilibrium value is estimated based on the local exponential decay characteristic. A mismatch check is used to determine whether to accept the extrapolated result. Explicit integration methods typically experience slower convergence speeds as they approach the equilibrium point due to step size limitations imposed by numerical stability. This invention directly predicts the equilibrium point position by identifying the local exponential decay characteristic of the state variables, thus achieving a leapfrog approximation. More importantly, a check and backoff mechanism is introduced: the result is accepted only when the extrapolated mismatch decreases; otherwise, it is backed up. This utilizes mathematical principles to accelerate convergence while preserving the stability baseline of numerical integration. Experiments show that this strategy can reduce the number of integration steps from thousands to hundreds, significantly improving the computational efficiency of the algorithm in the fine-grained convergence phase and overcoming the inherent defect of slow convergence tails in explicit integration methods.

[0032] Furthermore, by sampling on continuous integration steps, the dynamic decay trend of the system can be captured in real time, rather than relying on fixed theoretical values. This allows the method to adapt to the dynamic characteristics of different systems and operating conditions. Substituting the estimated values ​​into the power flow equations for verification is a necessary means to ensure the physical correctness of the calculation results. Because extrapolation is an approximation based on the assumption of local linearity / exponentiality, it must be verified through the original equations. This ensures that the acceleration process does not introduce excessive truncation errors, guarantees the high accuracy of the final results, and achieves a perfect balance between speed and accuracy.

[0033] It is understood that the beneficial effects of the second to sixth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0034] In summary, the method of this invention addresses the power flow calculation problem in AC power systems by constructing a virtual dynamic system driven by power mismatch and employing explicit integration to solve for its equilibrium point, thereby obtaining the system power flow solution. This method avoids the dependence on Jacobian matrix construction and linear equation solving found in traditional power flow calculations, offering advantages such as simple implementation, clear physical meaning, good parallelization potential, and strong adaptability to complex operating conditions. Furthermore, the method improves the efficiency of the later stages of integration through an equilibrium point extrapolation acceleration strategy, making it particularly suitable for large-scale AC power systems, heavy-load conditions, and power flow calculation scenarios where traditional Newton-type methods are prone to matrix ill-conditioning and convergence difficulties.

[0035] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the overall process of the AC power system power flow calculation method based on virtual dynamic system integral as described in this invention; Figure 2This is a schematic diagram illustrating the construction principle of the virtual dynamic system based on the phase angle of the active power mismatch driving voltage and the amplitude of the reactive power mismatch driving voltage as described in this invention. Figure 3 This is a schematic diagram showing the exponential decay characteristic of the state variables in the neighborhood of the equilibrium point of the virtual dynamic system described in this invention. Figure 4 This is a schematic diagram of the execution flow of the equilibrium point extrapolation acceleration strategy described in this invention; Figure 5 This is a topology diagram of the IEEE 39-node AC power system used in this embodiment of the invention; Figure 6 This is a graph showing the integral convergence curves of the node voltage phase angle and node voltage amplitude of the IEEE 39-bus system under normal operating conditions in an embodiment of the present invention. Figure 7 This is a convergence curve of node voltage phase angle and node voltage amplitude in the IEEE 39-node system after introducing the equilibrium point extrapolation acceleration strategy in an embodiment of the present invention. Figure 8 This is a convergence characteristic evolution curve of the virtual dynamic system integral method during the formation of pathological operating conditions in this embodiment of the invention; Figure 9 This is a curve showing the convergence characteristics of the traditional Newton's method during the formation of the pathological working condition in an embodiment of the present invention. Figure 10 This is a curve illustrating the convergence characteristics of the rapid decoupling method during the formation of pathological operating conditions in this embodiment of the invention. Figure 11 A schematic diagram of a computer device provided in an embodiment of the present invention; Figure 12 This is a block diagram of a chip provided according to an embodiment of the present invention.

[0037] Among them, 60. Computer equipment; 61. Processor; 62. Memory; 63. Computer program; 600. Electronic device; 610. Processing unit; 620. Storage unit; 6201. Random access memory unit; 6202. Cache memory unit; 6203. Read-only memory unit; 6204. Program / utility; 6205. Program module; 630. Bus; 640. Display unit; 650. Input / output interface; 660. Network adapter; 700. External device. Detailed Implementation

[0038] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0040] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0041] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0042] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0043] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0044] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0045] This invention provides a power flow calculation method for AC power systems based on virtual dynamic system integration. Based on the strong correlation between active power and node voltage phase angle, and reactive power and node voltage amplitude in AC power systems, a virtual dynamic system is constructed for power flow calculation. This transforms the problem of solving the nonlinear algebraic equations of traditional power flow equations into the problem of finding the equilibrium point of the virtual dynamic system. During the solution process, an explicit integration method is employed, using the power mismatch at each node to drive the updating of node voltage phase angle and voltage amplitude, thereby avoiding Jacobian matrix inversion, matrix decomposition, and solving linear equations. Furthermore, to address the issue of slower convergence speed near the equilibrium point in the later stages of integration, an equilibrium point extrapolation acceleration strategy based on local exponential decay characteristics is introduced, improving the overall solution efficiency while ensuring the stability of power flow calculation.

[0046] Please see Figure 1 This invention discloses a power flow calculation method for AC power systems based on virtual dynamic system integration. First, it obtains the basic data required for AC power flow calculation. This basic data includes: network topology, node numbers, branch connection relationships, line parameters, transformer parameters, node admittance matrix, generator active power output, generator reactive power output, load active power, load reactive power, voltage amplitude of slack nodes, voltage phase angle of slack nodes, and voltage amplitude of nodes with given voltage amplitudes. The specific steps are as follows: S1. Obtain network and operational data of the AC power system to determine the basic information required for power flow calculation.

[0047] S101. Obtain data such as network topology, line parameters, transformer parameters, node admittance matrix, generator active and reactive power output, load active and reactive power, node voltage setpoint, and slack node phase angle of AC power system. Assume the AC power system has a total of N There are n nodes, and the node admittance matrix is ​​denoted as... Y , its first i Line number j Column elements are denoted as: (1) S102. Based on the different known and unknown quantities at each node, classify the system nodes to determine the nodes with known active power, nodes with known reactive power, nodes with given voltage amplitude, and nodes with given voltage phase angle. Traditional power flow calculations typically include PQ nodes, PV nodes, and slack nodes. To facilitate the construction of the virtual dynamic system in this invention, the nodes are redescribed according to known quantities. P node, Q node, V Nodes and θ Nodes. Among them, P A node represents a node with known active power. Q A node represents a node whose reactive power is known. V A node represents a node whose voltage amplitude is known. θ A node represents a node whose voltage phase angle is known.

[0048] Under the above classification method, traditional PQ nodes also belong to P Nodes and Q Nodes, traditional PV nodes also belong to P Nodes and V Nodes, traditional balanced nodes are both V nodes and θ Nodes. This classification method does not change the mathematical meaning of the original power flow equations; it is only for the purpose of constructing a virtual dynamic system for "active power mismatch driving voltage phase angle and reactive power mismatch driving voltage amplitude".

[0049] S103. Using the node voltage phase angle and node voltage magnitude that need to be solved as state variables, a set of state variables to be solved is formed for power flow calculation.

[0050] for P Nodes, their voltage phase angles θ As a quantity to be determined; for Q Nodes, their voltage amplitude U Assume there are n P nodes and m [other nodes] in the system. Q For each node, all the phase angles and magnitudes of the voltages to be determined are combined into a state vector: (2) in, n express P The number of phase angles to be determined for each node, m represents Q The number of voltage amplitudes to be determined corresponding to each node. x This represents the state vector in the virtual dynamic system. After the above processing, the AC power flow calculation problem is transformed into solving for the state vector. x The problem is that the state vector contains the node voltage phase angles and node voltage magnitudes required for steady-state operation of the AC power system.

[0051] S2. Establish the power flow equations of the AC power system and calculate the power mismatch at the nodes.

[0052] S201. Based on the admittance matrix of the AC power system nodes and the current node voltage magnitude and phase angle, calculate the active power and reactive power injected into the power network by each node. Based on the current state vector x Obtain the voltage amplitude at each node U and voltage phase angle θ And construct the node complex voltage, for any node i Its voltage is expressed as: (3) S202. For nodes with known active power, calculate the active power mismatch between their given active power and the network active power under the current state. Establish an active power balance function for node P, for any P node i Its active power mismatch is expressed as: (4) in, This represents a vector consisting of all the quantities to be determined. Represents a node i and j Interphase difference; The first node admittance matrix represents the... i Line number j Column elements; and These represent the active power of the generator and the active power of the load at the node, respectively.

[0053] S203. For nodes with known reactive power, calculate the reactive power mismatch between their given reactive power and the network reactive power under the current state. For any Q node i Its reactive power mismatch is expressed as: (5) in, and These represent the generator reactive power and load reactive power of the node, respectively.

[0054] S204. Combine all active power mismatch and reactive power mismatch to form a power flow equation mismatch vector, which is used to characterize the deviation between the current state variables and the power flow equilibrium solution.

[0055] All P Active power mismatch at nodes and allQ The combination of reactive power mismatches at nodes yields the power flow mismatch vector: (6) in, This represents the vector of all active and reactive power balance functions.

[0056] S3. Construct a virtual dynamic system for power flow calculation.

[0057] S301. Based on the strong correlation between active power and voltage phase angle in AC power systems, for nodes with known active power, construct a dynamic equation for voltage phase angle driven by active power mismatch, so that the active power mismatch at the node gradually decreases through phase angle changes. Please see Figure 2 For any P node i Construct the following virtual dynamic equation: (7) in, For nodes i The self-susceptance is negative. The physical meaning of equation (7) is that when the net injected active power of the virtual dynamic system is greater than / less than the outflow active power, the phase of the node increases / decreases. The increase / decrease of the phase of the node will cause the outflow active power to increase / decrease, thereby reducing the active power imbalance and constructing a negative feedback of active power to phase.

[0058] S302. Based on the strong correlation between reactive power and voltage amplitude in AC power systems, for nodes with known reactive power, construct a dynamic equation for voltage amplitude driven by reactive power mismatch, so that the reactive power mismatch at the node gradually decreases through changes in voltage amplitude. For any Q node i Construct the following virtual dynamic equation: (8) The physical meaning of equation (8) is that when the net reactive power injected into the virtual dynamic system is greater than or less than the reactive power flowing out, the voltage of the node increases or decreases. The increase or decrease of the voltage of the node will cause the reactive power to increase or decrease, thereby reducing the reactive power imbalance and constructing a negative feedback of reactive power to voltage.

[0059] S303. Combine the dynamic equations of voltage phase angle and voltage magnitude corresponding to all nodes to form a virtual dynamic system for power flow calculation. All P The phase angle dynamic equations corresponding to the nodes and all Q By simultaneously solving the dynamic equations for the voltage magnitudes at the nodes, a virtual dynamic system of the following form is obtained: (9) in, It is a constant diagonal matrix, where the diagonal elements represent the negative values ​​of the reciprocals of the self-susceptance of the corresponding nodes, and are constants.

[0060] S304. The zeros of the power flow equations are equivalent to the equilibrium points of the virtual dynamic system, thus transforming the AC power flow calculation problem into a problem of solving the equilibrium points of the virtual dynamic system.

[0061] When a certain state vector x 0 satisfies: (10) Sometimes, (11) For a stable system, when The initial value is at the equilibrium point. When the system remains within its attractive field, it will eventually reach an equilibrium point over time. .

[0062] Step S3 is the key step that distinguishes this invention from the traditional Newton-Raphson method for power flow calculation. The traditional Newton-Raphson method requires constructing a Jacobian matrix and solving linear correction equations, while this invention constructs a virtual dynamic system, transforming the power flow solution into a state evolution process driven by power mismatch, thus avoiding the repeated solution of linear equations.

[0063] S4. Set the initial state and integral parameters of the virtual dynamic system.

[0064] S401. For the node whose voltage phase angle is to be determined, the initial phase angle is set using a flat start method. Preferably, the initial phase angle is consistent with the phase angle of the node with the given phase angle. For the voltage phase angle to be determined P The node, whose initial phase angle is preferably set to θ The phase angle of the node, which is usually taken as the phase angle of the slack node; for the voltage amplitude to be determined... Q The initial voltage amplitude of the node is preferably set to 1.0 per unit. This forms the initial state vector.

[0065] S402. For nodes whose voltage amplitude is to be determined, the initial voltage amplitude is set using a flat start method. Preferably, the initial voltage amplitude is set to 1 per unit value. S403. Set the explicit integration step size, power flow convergence threshold, maximum number of iterations, and the trigger threshold, sampling interval, and consistency judgment threshold required for subsequent extrapolation acceleration.

[0066] S5. Solve the virtual dynamic system using the explicit integration method.

[0067] S501. Calculate the complex voltage of the node based on the current node voltage magnitude and phase angle, and calculate the active power and reactive power of each node in the current state based on the node admittance matrix. S502. Calculate the active power mismatch and reactive power mismatch of each node under the current state according to step S2. S503. Based on the virtual dynamic system constructed in step S3, calculate the direction of change of the current state quantity; S504. The virtual dynamic system state is advanced by using an explicit integration method to update the voltage phase angle of nodes with known active power and the voltage amplitude of nodes with known reactive power. S505. The explicit integration method adopts the improved Euler method, calculates the predicted state with the current state quantity, and then performs correction and update by combining the virtual dynamic system change quantity under the current state and the predicted state. During the iteration process, the computational workload mainly lies in solving the problem. . The solution is actually the mismatch amount. Multiply by a coefficient. Therefore, the main computational burden of the above iterative process is the mismatch. The calculation is performed without solving any system of linear equations.

[0068] (12) S506. In the above integral update process, it is only necessary to calculate the node power mismatch and update the state variables, without needing to solve the linear equations corresponding to the Jacobian matrix.

[0069] S6. Determine whether the power flow calculation has converged.

[0070] S601. After each explicit integral update, recalculate the power mismatch of each node; S602. Select the maximum value among all active power mismatch and reactive power mismatch as the unbalance quantity for the current power flow calculation. S603. If the current maximum imbalance is less than the preset power flow convergence threshold, it is considered that the virtual dynamic system has reached the vicinity of the power flow equilibrium point, and the voltage amplitude and voltage phase angle of each node are output as the power flow solution of the AC power system. S604. If the current maximum imbalance does not meet the convergence threshold, continue to execute step S5 until the convergence requirement is met or the preset maximum number of integration steps is reached.

[0071] S7. Accelerate the process by extrapolating the equilibrium point of the state variables in the later stages of integration.

[0072] Because the changes in state variables in a virtual dynamic system may gradually slow down after approaching the equilibrium point, a larger number of steps are required in the later stages of integration to achieve high accuracy. To improve computational efficiency, this invention further introduces an equilibrium point extrapolation acceleration strategy. The theoretical basis of this strategy is as follows: Figure 3 As shown, the specific execution process is as follows: Figure 4 As shown.

[0073] S701. When the current maximum imbalance is less than the preset extrapolation trigger threshold, it is considered that the virtual dynamic system state is gradually entering the equilibrium point neighborhood, and the equilibrium point extrapolation acceleration strategy is started. For the first i There are several variables, and when the time interval is obtained, H of , and Then, if the simulation has entered the neighborhood of the equilibrium point, then: (13) S702, After entering the extrapolation acceleration phase, every [time] H The state quantity is sampled once every preset number of integration steps to obtain multiple state quantity sampling points at equal intervals; S703. Calculate the attenuation coefficient of the state variable in the neighborhood of the equilibrium point based on the change relationship between adjacent state variable sampling points. S704. Compare whether the attenuation coefficients calculated from different sampling intervals meet the consistency requirements. If the consistency requirements are met, it is considered that the state variable has local exponential decay characteristics in the current stage and meets the conditions for extrapolation of the equilibrium point. (14) S705. For state variables that satisfy the extrapolation conditions, estimate the corresponding equilibrium point value based on their local exponential decay characteristics to obtain the extrapolated voltage phase angle or voltage amplitude. (15) All state components that satisfy the extrapolation conditions are replaced with their corresponding equilibrium point estimates to obtain the extrapolated state vector. For state components that do not satisfy the extrapolation conditions, the original integral values ​​are kept unchanged.

[0074] S706. Substitute the extrapolated state variables into the AC power flow equations and recalculate the maximum power mismatch. S707. If the maximum power mismatch after extrapolation is less than the maximum power mismatch before extrapolation, then accept the extrapolation result; if the maximum power mismatch after extrapolation does not decrease, then discard the extrapolation result and revert to the integration state before extrapolation, and continue to proceed according to the explicit integration process. S708. Repeat the extrapolation judgment, extrapolation estimation, mismatch check and accept rollback process until the power flow calculation meets the convergence requirements.

[0075] Waiting after each extrapolation H t After one integration step, extrapolation is performed again.

[0076] By employing the aforementioned extrapolation acceleration strategy, this invention can predict power flow solutions by utilizing the local exponential decay law of state variables in the neighborhood of the equilibrium point without disrupting the original explicit integration convergence direction. This reduces the small step-by-step advancement process in the later stages of integration and improves the overall power flow solution efficiency.

[0077] In another embodiment of the present invention, an AC power system flow calculation system based on virtual dynamic system integral is provided. This system can be used to implement the above-mentioned AC power system flow calculation method based on virtual dynamic system integral. Specifically, the AC power system flow calculation system based on virtual dynamic system integral includes a data acquisition module, a loss measurement construction module, a virtual dynamic system construction module, an integral update module, and a convergence determination module.

[0078] The data acquisition module is configured to acquire parameter data and operating data of the AC power system, and classify the system nodes according to the known and unknown quantities of the nodes. The imbalance measurement construction module is configured to construct state variables with the phase angle and magnitude of the voltage at the node to be determined, and calculate the active power and reactive power of each node according to the power flow equation, forming active power imbalance measurement and reactive power imbalance measurement, and constituting the power flow imbalance vector. The virtual dynamic system construction module is configured to construct a virtual dynamic system based on the coupling relationship between active power and voltage phase angle and the coupling relationship between reactive power and voltage amplitude. The active power loss corresponds to the voltage phase angle dynamic equation, and the reactive power loss corresponds to the voltage amplitude dynamic equation. The integral update module is configured to set the initial state and integral parameters of the virtual dynamic system, and to perform integral updates using an explicit integration method to obtain the updated node voltage phase angle and node voltage amplitude. The convergence determination module is configured to recalculate the active power imbalance and reactive power imbalance after each integral update, take the maximum value of the active power imbalance and reactive power imbalance as the current imbalance, and output the power flow calculation result when the current imbalance is less than the preset power flow convergence threshold.

[0079] This invention provides a terminal device comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or corresponding function. The processor described in this embodiment can be used for the operation of an AC power system power flow calculation method based on virtual dynamic system integration, including: Acquire parameter and operational data of the AC power system, including at least the node admittance matrix, active and reactive power data for each node, and voltage phase angle and voltage amplitude of the slack node. Classify system nodes according to known and unknown quantities, identifying nodes with known active power, known reactive power, given voltage amplitude, and given voltage phase angle. Construct state variables using the voltage phase angle and voltage amplitude of the unknown nodes. Calculate the active and reactive power of each node according to the power flow equations, forming active power imbalance and reactive power imbalance measures, and constructing a power flow imbalance vector. Based on the coupling relationship between active power and voltage phase angle, and the coupling relationship between reactive power and voltage amplitude, construct a virtual dynamic system, in which active power imbalance... The dynamic equations for active and reactive power imbalances are used to update the state variables according to the active and reactive power imbalances during integral iteration. An initial state and integral parameters of the virtual dynamic system are set, and an explicit integral method is used for integral updates to obtain the updated node voltage phase angle and node voltage amplitude. After each integral update, the active and reactive power imbalances are recalculated, and the maximum value of the active and reactive power imbalances is used as the current imbalance degree. When the current imbalance degree is less than a preset power flow convergence threshold, the node voltage phase angle and node voltage amplitude are output as the power flow calculation result. When the current imbalance degree is greater than or equal to the preset power flow convergence threshold, the explicit integral method is used for integral updates.

[0080] Please see Figure 11 The terminal device is a computer device. In this embodiment, the computer device 60 includes a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When executed by the processor 61, the computer program 63 implements the AC power flow calculation method based on virtual dynamic system integrals in this embodiment. To avoid repetition, details are omitted here. Alternatively, when executed by the processor 61, the computer program 63 implements the functions of each model / unit in the AC power flow calculation system based on virtual dynamic system integrals in this embodiment. To avoid repetition, details are omitted here.

[0081] Computer device 60 can be a desktop computer, laptop, handheld computer, cloud server, or other computing device. Computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will understand that... Figure 11 This is merely an example of computer device 60 and does not constitute a limitation on computer device 60. It may include more or fewer components than shown, or combine certain components, or different components. For example, computer device may also include input / output devices, network access devices, buses, etc.

[0082] The processor 61 may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0083] The memory 62 can be an internal storage unit of the computer device 60, such as a hard disk or memory of the computer device 60. The memory 62 can also be an external storage device of the computer device 60, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on the computer device 60.

[0084] Furthermore, the memory 62 may include both internal storage units of the computer device 60 and external storage devices. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 can also be used to temporarily store data that has been output or will be output.

[0085] Please see Figure 12 The terminal device is an electronic device 600, which is manifested in the form of a general-purpose computing device. The components of the electronic device may include, but are not limited to: at least one processing unit 610, at least one storage unit 620, a bus 630 connecting different platform components (including storage unit 620 and processing unit 610), a display unit 640, etc.

[0086] The storage unit stores program code, which can be executed by the processing unit 610 to perform the steps described in the method section of this specification according to various exemplary embodiments of the present invention. For example, the processing unit 610 can perform actions such as... Figure 1 The steps are shown in the figure.

[0087] Storage unit 620 may include readable media in the form of volatile storage units, such as random access memory (RAM) 6201 and / or cache memory 6202, and may further include read-only memory (ROM) 6203.

[0088] Storage unit 620 may also include a program / utility 6204 having a set (at least one) program module 6205, such program module 6205 including but not limited to: operating system, one or more application programs, other program modules and program data, each or some combination of these examples may include an implementation of a network environment.

[0089] Bus 630 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the multiple bus structures.

[0090] Electronic device 600 can also communicate with one or more external devices 700 (e.g., keyboard, pointing device, Bluetooth device, etc.), and with one or more devices that enable a user to interact with electronic device 600, and / or with any device that enables electronic device 600 to communicate with one or more other computing devices (e.g., router, modem). This communication can be performed via input / output interface 650. Furthermore, electronic device 600 can also communicate with one or more networks (e.g., local area network, wide area network, and / or public network, such as the Internet) via network adapter 660. Network adapter 660 can communicate with other modules of electronic device 600 via bus 630. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with electronic device 600, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage platforms.

[0091] Example 4 This invention also provides a storage medium, specifically a computer-readable storage medium, which is a memory device in a terminal device for storing programs and data. It is understood that the computer-readable storage medium here can include both built-in storage media in the terminal device and extended storage media supported by the terminal device; it can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor, which can be one or more computer programs (including program code). More specific examples of the computer-readable storage medium include: an electrical connection with one or more wires, a portable disk, a hard disk, random access memory, read-only memory, erasable programmable read-only memory, optical fiber, portable compact disk read-only memory, optical storage device, magnetic storage device, or any suitable combination thereof.

[0092] Computer-readable storage media also include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable storage medium can also be any readable medium other than a readable storage medium that can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium can be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, radio frequency, etc., or any suitable combination thereof.

[0093] Program code for performing the operations of this invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0094] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the AC power system power flow calculation method based on virtual dynamic system integrals in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor to perform the following steps: Acquire parameter and operational data of the AC power system, including at least the node admittance matrix, active and reactive power data for each node, and voltage phase angle and voltage amplitude of the slack node. Classify system nodes according to known and unknown quantities, identifying nodes with known active power, known reactive power, given voltage amplitude, and given voltage phase angle. Construct state variables using the voltage phase angle and voltage amplitude of the unknown nodes. Calculate the active and reactive power of each node according to the power flow equations, forming active power imbalance and reactive power imbalance measures, and constructing a power flow imbalance vector. Based on the coupling relationship between active power and voltage phase angle, and the coupling relationship between reactive power and voltage amplitude, construct a virtual dynamic system, in which active power imbalance... The dynamic equations for active and reactive power imbalances are used to update the state variables according to the active and reactive power imbalances during integral iteration. An initial state and integral parameters of the virtual dynamic system are set, and an explicit integral method is used for integral updates to obtain the updated node voltage phase angle and node voltage amplitude. After each integral update, the active and reactive power imbalances are recalculated, and the maximum value of the active and reactive power imbalances is used as the current imbalance degree. When the current imbalance degree is less than a preset power flow convergence threshold, the node voltage phase angle and node voltage amplitude are output as the power flow calculation result. When the current imbalance degree is greater than or equal to the preset power flow convergence threshold, the explicit integral method is used for integral updates.

[0095] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0096] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0097] To verify the effectiveness of the method described in this invention, the following description uses the IEEE 39-bus AC power system as an example. The system topology is as follows: Figure 5 As shown, the system includes components such as generator nodes, load nodes, transmission lines, and transformers, comprising a total of 39 AC nodes, covering three categories: generator nodes, load nodes, and ordinary tie nodes. Ten synchronous generators, labeled G1 to G10, provide active and reactive power output support for the system. An interconnected network of transmission lines and transformers enables power transfer between nodes, corresponding to the line and transformer parameters calculated in the handover document. Nodes are interconnected by region, forming a typical regional power grid structure, including weak receiving-end nodes. This allows for the simulation of ill-conditions such as heavy loads and weak support, making it suitable for verifying the convergence performance of AC power flow calculation methods under normal operating conditions, extrapolated accelerated operating conditions, and heavy load ill-conditions.

[0098] In this embodiment, the line parameters, transformer parameters, node type, generator output, and load power data of the IEEE 39-node system are first read to construct the system node admittance matrix. Then, the power flow mismatch vector and virtual dynamic system are established according to steps 1 to 3. The initial state is set using a flat-start method, that is, the initial value of the phase angle to be determined is set to the phase angle of the slack node, and the initial value of the voltage amplitude to be determined is set to 1.0 per unit.

[0099] The preferred calculation parameters are: integration step size. h =1, power flow convergence threshold PFtol =1×10 -6 Extrapolated trigger threshold ε ext =5×10 -2 Extrapolated sampling interval H =20, extrapolation waiting interval H t =100, and the attenuation coefficient consistency threshold is 0.15.

[0100] Under normal operating conditions, power flow calculations are performed using the virtual dynamic system integration method described in this invention. Figure 6 It is evident that the phase angles of the representative node voltages adjust rapidly during the initial integration phase and then gradually stabilize; the magnitudes of the representative node voltages also converge from their initial values ​​to their steady-state values. This result demonstrates that the method of this invention can drive the evolution of state variables through power mismatch, enabling the node voltage phase angles and magnitudes to converge stably to the AC power flow solution.

[0101] Furthermore, under the same IEEE 39-node system and the same parameter settings, an equilibrium point extrapolation acceleration strategy is introduced. Figure 7 As can be seen, after introducing extrapolation acceleration, the state variables still maintain stable convergence, and a rapid approach to the equilibrium point occurs near the extrapolation trigger position. Compared with the 3034 integration steps required without extrapolation acceleration, only 937 steps are needed to achieve the same convergence accuracy after introducing extrapolation acceleration. This result shows that the equilibrium point extrapolation acceleration strategy described in this invention can effectively reduce the small step-by-step process in the later stages of integration and improve the overall power flow solution efficiency.

[0102] To further verify the robustness of this invention under complex operating conditions, this embodiment selects a typical weak receiving node in the IEEE 39-node system and gradually increases its active power load, causing the system operating point to gradually approach a heavy load and pathological operating condition from a normal operating condition. To facilitate comparison of the convergence performance of different power flow calculation methods during the pathological condition formation process, the virtual dynamic system integration method described in this invention, the traditional Newton method, and the fast decoupling method are used for power flow solutions, and their convergence characteristics are as follows: Figure 8 , Figure 9 and Figure 10 As shown.

[0103] Please see Figure 8 As the load increases, the number of integration steps required by the virtual dynamic system integration method of the present invention gradually increases, indicating that the convergence speed decreases when the system approaches a heavy load state. However, under each group of heavy load conditions, the integration trajectory can still remain stable and eventually converge, indicating that the method of the present invention has good convergence robustness in the process of pathological power flow formation.

[0104] Please see Figure 9 Under the same load increase path, the traditional Newton method can complete the power flow solution under the condition of low load increase. However, when the system is further close to the heavy load and ill state, its iterative process diverges, the power mismatch cannot continue to decrease, and finally fails to obtain a feasible power flow solution.

[0105] Please see Figure 10 The fast decoupling method is more sensitive to ill-conditioning. Under some heavy-load conditions, although the power mismatch decreases in the early stage of iteration, it then stagnates or even rebounds, and can never reach the convergence threshold.

[0106] Figure 8 , Figure 9 and Figure 10 Using the same load aggravation factor and the same operating condition number, the convergence differences of the three power flow calculation methods can be intuitively reflected as the system gradually approaches the ill-conditioned operating region. The comparison results show that the virtual dynamic system integration method described in this invention can maintain stable convergence under all operating conditions, while the traditional Newton method and fast decoupling method are more prone to convergence difficulties or calculation failures when the degree of ill-conditioned load increases. This indicates that the method of this invention has better adaptability to complex operating conditions and robustness in solving heavy-load power flow problems.

[0107] Furthermore, to verify the applicability and computational efficiency of the method of the present invention in AC power systems of different scales, this embodiment selects the IEEE 118-node system, IEEE 145-node system, ACTIVS g200-node system, IEEE 300-node system, ACTIVS g500-node system, and ACTIVS g2000-node system for power flow calculation comparison. In each test system, the same flat-start conditions and the same convergence accuracy requirements are used. Under the premise of obtaining a consistent power flow solution, the computation time of the traditional Newton method, the virtual dynamic system integration method without equilibrium point extrapolation acceleration, and the virtual dynamic system integration method with equilibrium point extrapolation acceleration are statistically analyzed. The results are shown in Table 1.

[0108] Table 1 Comparison of computation time for systems of different sizes

[0109] Table 1 shows that the computation time of each method generally increases with the increase of system scale. Comparing the three methods, the unaccelerated virtual dynamic method shows a more significant increase in computation time in larger systems, indicating that the slow convergence in the later stages of integration has a certain impact on overall computational efficiency. After introducing the extrapolation acceleration strategy, the computation time of the virtual dynamic method is significantly reduced in all test systems, and is superior to Newton's method and the unaccelerated virtual dynamic method. This shows that the proposed acceleration strategy can effectively shorten the computation process in the later stages of integration and improve the power flow solution efficiency under different system scales. Overall, the extrapolated accelerated virtual dynamic method maintains stable convergence while exhibiting good computational efficiency and scale adaptability.

[0110] From an algorithmic perspective, traditional Newton's method and its improvements still rely on solving linear equations. Their computational performance, especially their parallel acceleration, largely depends on the quality of the solver implementation. In contrast, the virtual dynamic method's computation in each step mainly consists of mismatch calculation and state updates, eliminating the need to construct and solve linear equations during integration. This structure provides a better foundation for parallel implementation, making it particularly suitable for further optimization on multi-core or heterogeneous computing platforms. Therefore, it has the potential to further improve computational efficiency and even far surpass Newton-like methods under parallel implementation conditions.

[0111] In summary, this invention provides a power flow calculation method for AC power systems based on virtual dynamic system integration. This method can solve AC power flow problems without solving linear equations and maintains good convergence performance under both normal and heavily loaded ill-conditioned conditions. Furthermore, by employing an equilibrium point extrapolation acceleration strategy, this invention improves the solution efficiency in the later stages of integration. It is suitable for large-scale AC power systems, complex operating modes, and power flow calculation scenarios where traditional Newton-type methods are prone to matrix ill-conditioning and convergence difficulties.

[0112] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0113] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0114] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0115] In the embodiments provided by this invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0116] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0117] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0118] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random-access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0119] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus, and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0120] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0121] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0122] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for calculating power flow in an AC power system based on virtual dynamic system integration, characterized in that, Includes the following steps: S1. Obtain parameter data and operating data of the AC power system. The parameter data and operating data include at least the node admittance matrix, active power and reactive power data of each node, voltage phase angle and voltage amplitude of the slack node; classify the system nodes according to the known and unknown quantities of the nodes, and determine the nodes with known active power, nodes with known reactive power, nodes with given voltage amplitude and nodes with given voltage phase angle. S2. Construct state variables using the phase angle and magnitude of the voltage at the node to be determined. Calculate the active and reactive power of each node according to the power flow equations to form active power imbalance and reactive power imbalance, and construct the power flow imbalance vector. S3. Based on the coupling relationship between active power and voltage phase angle and the coupling relationship between reactive power and voltage amplitude, construct a virtual dynamic system, wherein the active power loss corresponds to the voltage phase angle dynamic equation and the reactive power loss corresponds to the voltage amplitude dynamic equation, so that the state variables are updated according to the active power loss and reactive power loss during integral iteration. S4. Set the initial state and integral parameters of the virtual dynamic system, and use the explicit integration method to perform integral updates to obtain the updated node voltage phase angle and node voltage amplitude. S5. After each integral update, recalculate the active power imbalance and reactive power imbalance, and use the maximum value of the active power imbalance and reactive power imbalance as the current imbalance. S6. When the current imbalance is less than the preset power flow convergence threshold, output the node voltage phase angle and node voltage amplitude as the power flow calculation result; when the current imbalance is greater than or equal to the preset power flow convergence threshold, continue to execute S4 to S5.

2. The virtual dynamic system integration based ac power system power flow calculation method of claim 1, wherein, In step S1, classifying system nodes according to known and unknown quantities includes: determining nodes with known active power as nodes with known active power, nodes with known reactive power as nodes with known reactive power, nodes with given voltage amplitude as nodes with given voltage amplitude, and nodes with given voltage phase angle as nodes with given voltage phase angle.

3. The virtual dynamic system integration based ac power system power flow calculation method of claim 1, wherein, In step S2, the state variables consist of the phase angle of the voltage to be determined corresponding to the node with known active power and the amplitude of the voltage to be determined corresponding to the node with known reactive power.

4. The virtual dynamic system integration based ac power system power flow calculation method of claim 1, wherein, In step S2, the active power loss is the difference between the node's given active power and the node's calculated active power, and the reactive power loss is the difference between the node's given reactive power and the node's calculated reactive power.

5. The AC power system power flow calculation method based on virtual dynamic system integral as described in claim 1, characterized in that, In step S4, the integration parameters include at least the integration step size and the maximum number of integration attempts; The method of using explicit integration for integral updates includes using an improved Euler method: first, the predicted state is calculated based on the current state variables, and then the rate of change under the current and predicted states is used for correction and update.

6. The virtual dynamic system integration based ac power system power flow calculation method of claim 1, wherein, In step S4, the initial state setting of the virtual dynamic system includes: The initial value of the phase angle of the node voltage to be determined is set to the phase angle of the balanced node voltage, and the initial value of the amplitude of the node voltage to be determined is set to a preset per-unit value; the preset per-unit value is 1.

0.

7. The virtual dynamic system integration based ac power system power flow calculation method of claim 1, wherein, In step S5, the current imbalance is the maximum value among the absolute values ​​of each active power imbalance and each reactive power imbalance.

8. The virtual dynamic system integration based ac power system power flow calculation method of claim 1, wherein, After step S6 is completed, when the current imbalance is less than the preset acceleration trigger threshold, the balance value is estimated based on the local exponential decay characteristics of the state quantity during the integration process, and the estimated state quantity is substituted into the power flow equation for imbalance verification. If the imbalance decreases after verification, the estimated state quantity is accepted; otherwise, the estimated state quantity is rejected, the state quantity is returned to the state quantity before extrapolation, and step S4 is continued.

9. The virtual dynamic system integration based ac power system power flow calculation method of claim 8, wherein, The equilibrium value estimation based on the local exponential decay characteristics of the state variables during the integration process includes: sampling the state variables at multiple consecutive integration steps, calculating the decay parameters based on the sampling results, and estimating the equilibrium value accordingly; the imbalance verification includes substituting the estimated state variables into the power flow equations and calculating the verification imbalance degree.

10. An alternating current power system power flow calculation system based on virtual dynamic system integration, characterized by, include: The data acquisition module is configured to acquire parameter data and operating data of the AC power system, and classify the system nodes according to the known and unknown quantities of the nodes. The imbalance measurement construction module is configured to construct state variables with the phase angle and magnitude of the voltage at the node to be determined, and calculate the active power and reactive power of each node according to the power flow equation, forming active power imbalance measurement and reactive power imbalance measurement, and constituting the power flow imbalance vector. The virtual dynamic system construction module is configured to construct a virtual dynamic system based on the coupling relationship between active power and voltage phase angle and the coupling relationship between reactive power and voltage amplitude. The active power loss corresponds to the voltage phase angle dynamic equation, and the reactive power loss corresponds to the voltage amplitude dynamic equation. The integral update module is configured to set the initial state and integral parameters of the virtual dynamic system, and to perform integral updates using an explicit integration method to obtain the updated node voltage phase angle and node voltage amplitude. The convergence determination module is configured to recalculate the active power imbalance and reactive power imbalance after each integral update, take the maximum value of the active power imbalance and reactive power imbalance as the current imbalance, and output the power flow calculation result when the current imbalance is less than the preset power flow convergence threshold.

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