A power grid stability analysis system based on swarm intelligence algorithm

Abstract

The present disclosure discloses a power grid stability analysis system based on a swarm intelligence algorithm, which relates to the technical field of power systems. The system includes: a power grid admittance matrix construction unit, a stability index calculation unit, and a stability analysis unit; the power grid admittance matrix construction unit is configured to determine the total number of nodes in the target power grid, calculate the admittance between each pair of nodes, and thus construct the admittance matrix of the target power grid; the stability index calculation unit is configured to calculate the voltage stability index, frequency stability index, and angle stability index of the target power grid based on the admittance matrix; the stability analysis unit is configured to calculate the optimal power grid stability value based on the voltage stability index, frequency stability index, and angle stability index. The present invention significantly improves the accuracy, real-time performance, and reliability of power grid stability analysis, enhances the dynamic response ability and numerical stability of the power grid, and has strong adaptability and robustness.

Description

Technical Field

[0001] The present disclosure relates to, but is not limited to, the technical field of power systems, and in particular, to a power grid stability analysis system based on swarm intelligence algorithms. Background Art

[0002] With the rapid development of modern power systems and the wide application of smart grids, the operation stability and reliability of power grids have become crucial research topics in power system engineering. Power grid stability not only relates to the reliable supply of electric energy, but also has a direct impact on the safe operation and economic benefits of power grids. In a complex power grid environment, voltage stability, frequency stability, and angle stability are the three key indicators for measuring the operation state of power grids. How to monitor and improve the overall stability of power grids in real time through effective analysis methods and optimization algorithms is one of the key research directions in current power system research. In the prior art, traditional power grid stability analysis methods mainly rely on linear analysis and static models, and these methods are effective to a certain extent when dealing with simple and small-scale power grids. However, with the continuous expansion of power grid scale and the increasing complexity of the structure, traditional analysis methods gradually expose many limitations. For example, linear analysis methods are difficult to accurately describe the dynamic characteristics of power grids under non-linear operating conditions, and static models cannot reflect the transient response of power grids under load changes and fault disturbances in real time. These limitations make it difficult for the prior art to meet the high-precision and real-time requirements of power grid stability analysis in practical applications.

[0003] In recent years, power grid stability analysis methods based on intelligent algorithms have gradually become a research hotspot. Among them, swarm intelligence algorithms such as particle swarm optimization algorithm (PSO), ant colony algorithm (ACO), and genetic algorithm (GA) have been widely used due to their strong global search ability and fast convergence speed. For example, researchers have achieved certain results by using the particle swarm optimization algorithm to optimize the power flow distribution of power grids. These studies show that swarm intelligence algorithms have significant superiority in dealing with complex power grid stability analysis problems. However, there are still some problems and challenges in the application of existing swarm intelligence algorithms in power grid stability analysis. First, traditional swarm intelligence algorithms are prone to falling into local optima when dealing with large-scale and multi-dimensional power grid stability analysis problems, resulting in unsatisfactory optimization results. Second, existing algorithms usually ignore the dynamic changes of power grid operation parameters and the non-linear characteristics in actual operation during the calculation process, resulting in a large deviation between the analysis results and the actual operation situation. In addition, existing algorithms still need to be improved in terms of real-time performance and calculation efficiency, and it is difficult to meet the requirements of real-time monitoring and dispatching of modern power grids. Summary of the Invention

[0004] The present disclosure aims to provide a power grid stability analysis system based on swarm intelligence algorithms, which significantly improves the accuracy, real-time performance, and reliability of power grid stability analysis, enhances the dynamic response ability and numerical stability of the power grid, and has strong adaptability and robustness.

[0005] To solve the above problems, the technical solution of the present invention is implemented as follows:

[0006] A power grid stability analysis system based on swarm intelligence algorithms, the system includes: a power grid admittance matrix construction unit, a stability index calculation unit, and a stability analysis unit; the power grid admittance matrix construction unit is used to determine the total number of nodes in the target power grid, calculate the admittance between each pair of nodes, and then create a matrix with the admittances between each pair of nodes as the elements in the matrix to construct the admittance matrix of the target power grid; the stability index calculation unit is used to calculate the voltage stability index, frequency stability index, and angle stability index of the target power grid based on the admittance matrix; the stability analysis unit is used to calculate the real-time power grid stability value based on the voltage stability index, frequency stability index, and angle stability index; using swarm intelligence algorithms to calculate the optimal power grid stability value, specifically including: using the operating parameters of the real-time target power grid as the initial values to initialize the particle swarm; defining the objective function and calculating the fitness value of each particle according to the objective function; according to the fitness value, iteratively update the individual optimal position and global optimal position of each particle using a non-linear strategy, and introduce an adaptive mutation mechanism during the iterative update process, and then iteratively update the velocity and position of the particles; when the number of iterative updates reaches the set number of times, calculate the power grid stability value corresponding to the particles at this time as the optimal power grid stability value.

[0007] Further, let the total number of nodes in the target power grid be n; the types of the nodes at least include: generator nodes, load nodes, and connection nodes; create an n×n square matrix, and the obtained admittance matrix Y bus is represented by the following formula:

[0008]

[0009] where, y ij represents the admittance between node i and node j; both i and j are subscript indices, and their values are all integers from 1 to n; the diagonal elements of the admittance matrix are representing the sum of the admittances of node i and all the nodes connected to it, and k is also a subscript index with a value ranging from 1 to n; y ij =g ij +θb ij ; where, g ij represents the conductance between node i and j, indicating the transmission capacity of active power; b ij: The susceptance between nodes i and j, representing the reactive power transmission capacity; θ is the imaginary symbol.

[0010] Furthermore, the stability index calculation unit calculates the voltage stability index VSI of the target power grid based on the admittance matrix through the following formula:

[0011]

[0012] where det(J red ) represents the determinant of the reduced-order Jacobian matrix; V i is the voltage magnitude of node i; V nom is the rated voltage.

[0013] Furthermore, the stability index calculation unit calculates the frequency stability index FSI of the target power grid based on the admittance matrix through the following formula:

[0014]

[0015] where H j is the inertia constant of the j-th node, which is 0 when the node is a connection node or a load node; S base,j is the rated capacity of the j-th node, which is 0 when the node is a connection node or a load node; P L,j is the active power of the j-th node, which is 0 when the node is a connection node or a generator node; f j is the frequency of the j-th node; f nom is the rated frequency; K D,j is the preset frequency sensitivity coefficient of the j-th node; Δf j is the frequency deviation of the j-th node; λ max (Y bus ) represents the largest eigenvalue of the admittance matrix Y bus ; t is the time variable.

[0016] Furthermore, the stability index calculation unit calculates the angle stability index ASI of the target power grid based on the admittance matrix through the following formula:

[0017]

[0018] where P max,m is the maximum transmission power of the m-th generator node; P e,m is the actual transmission power of the m-th generator node; M is the number of generator nodes; δ m is the power angle of the m-th generator node; δ crit,m is the critical power angle of the m-th generator node; T j,mis the mechanical starting time constant of the m-th generator node; is the rate of change of the power angle of the m-th generator node; δ i , δ j are the power angles of nodes i and j.

[0019] Furthermore, the stability analysis unit calculates the real-time power grid stability value SI through the following formula:

[0020]

[0021] where, α v is the weight of the voltage stability index; α f is the weight of the frequency stability index; α a is the weight of the angle stability index; VSI ref is the reference value of the voltage stability index; FSI ref is the reference value of the frequency stability index; ASI ref is the reference value of the angle stability index; κ(Y bus ) is the condition number of the admittance matrix; κ max is the preset maximum acceptable condition number.

[0022] Furthermore, the stability analysis unit sets the total number of iterative updates as c, and the defined objective function JMAX is expressed by the following formula:

[0023]

[0024] where, X c is the global optimal position obtained in the c-th iteration; VSI(X c ) is the voltage stability index under the global optimal position; FSI(X c ) is the frequency stability index under the global optimal position; ASI(X c ) is the angle stability index under the global optimal position; Y bus (X c ) is the admittance matrix under the global optimal position.

[0025] A power grid stability analysis system based on swarm intelligence algorithm of the present invention has the following beneficial effects: First, the present invention has significant advantages in improving the stability of the power grid. By comprehensively considering voltage stability index (VSI), frequency stability index (FSI) and angle stability index (ASI), the present invention can comprehensively evaluate the overall stability of the power grid. The system utilizes the global search ability of the particle swarm optimization algorithm to achieve high efficiency and accuracy in power grid stability analysis and optimization in a complex and changeable power grid environment. Compared with traditional linear analysis and static models, the method of the present invention can more accurately reflect the dynamic characteristics of the power grid under non-linear operating conditions, thus providing more reliable stability assessment results. The present invention enhances the real-time performance and dynamic response ability of power grid stability analysis. In modern power systems, load fluctuations and external disturbances occur frequently, and traditional static analysis methods are difficult to cope with these real-time changes. The system of the present invention can quickly respond to changes in the operating state of the power grid by receiving the operating parameters of the power grid in real time and using the particle swarm optimization algorithm for dynamic adjustment and optimization. Through non-linear strategies and adaptive mutation mechanisms, the system can maintain a large search range in the initial stage of the search to avoid falling into local optima; in the later stage of the search, it can finely adjust the positions of the particles to improve the search accuracy. This dynamic response ability ensures that the power grid always maintains an efficient and stable operating state under various complex and changeable operating conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 FIG. is a schematic structural diagram of a power grid stability analysis system based on swarm intelligence algorithm provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0027] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present disclosure clearer and more understandable, the present disclosure will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present disclosure and are not used to limit the present disclosure..

[0028] Example 1: Refer to Figure 1, A power grid stability analysis system based on swarm intelligence algorithm, the system includes: a power grid admittance matrix construction unit, a stability index calculation unit and a stability analysis unit; the power grid admittance matrix construction unit is used to determine the total number of nodes in the target power grid, calculate the admittance between each node, and then create a matrix, and use the admittance between each node as the elements in the matrix to construct the admittance matrix of the target power grid; the stability index calculation unit is used to calculate the voltage stability index, frequency stability index and angle stability index of the target power grid based on the admittance matrix; the stability analysis unit is used to calculate the real-time power grid stability value based on the voltage stability index, frequency stability index and angle stability index; use the swarm intelligence algorithm to calculate the optimal power grid stability value, specifically including: using the operation parameters of the real-time target power grid as the initial value to initialize the particle swarm; defining the objective function, and calculating the fitness value of each particle according to the objective function; according to the fitness value, using a non-linear strategy to iteratively update the individual optimal position and global optimal position of each particle, and introducing an adaptive mutation mechanism during the iterative update process, and then iteratively update the speed and position of the particle; when the number of iterative updates reaches the set number of times, calculate the power grid stability value corresponding to the particle at this time as the optimal power grid stability value.

[0029] Specifically, the power grid admittance matrix is a matrix used to describe the admittance relationship between nodes in the power grid and can accurately reflect the electrical characteristics of the power grid. In this system, first, by determining the total number of nodes in the target power grid, all the power grid nodes that need to be analyzed are identified. This step is crucial because the accuracy of the total number of nodes directly affects the integrity and accuracy of the admittance matrix. Next, the system calculates the admittance values between each pair of nodes. The calculation of admittance values needs to consider the reactance and conductance between each pair of nodes in the power grid. Reactance and conductance are basic electrical parameters in the power grid, which determine the power transmission characteristics and loss conditions in the power grid. The calculation of admittance values can be achieved through the admittance formula, which comprehensively considers the effects of reactance and conductance. When constructing the admittance matrix, the system fills the admittance values between each pair of nodes as the elements in the matrix, thus forming a complete admittance matrix. Each element of this matrix represents the electrical connection characteristics between two nodes, that is, the admittance between them. Specifically, the diagonal elements in the admittance matrix represent the total admittance of each node to all other connected nodes, while the off-diagonal elements represent the direct admittance between nodes. In this way, the admittance matrix can comprehensively reflect the electrical connection conditions between nodes in the power grid and provide an accurate data basis for the subsequent calculation of stability indicators. The process of constructing the power grid admittance matrix is not just a simple matrix filling but involves complex electrical parameter calculations and mathematical processing. In practical applications, the number of nodes in the power grid may be very large, which requires the system to have powerful computing capabilities and efficient algorithms to ensure the construction speed and accuracy of the admittance matrix. In addition, to improve the reliability and accuracy of the admittance matrix, the system may also adopt some data preprocessing techniques, such as noise filtering and outlier processing, to exclude possible interference factors. The accurate construction of the admittance matrix is crucial for the stability analysis of the power grid because it directly affects the calculation results of stability indicators. In the stability analysis of the power grid, the admittance matrix is used as input data to calculate key indicators such as voltage stability, frequency stability, and angle stability. Voltage stability reflects the ability of the power grid to maintain a stable voltage under various load conditions; frequency stability reflects the ability of the power grid to maintain a stable frequency in the face of load fluctuations; angle stability reflects the stability of the relative phase angles between nodes in the power grid when subjected to disturbances. Through the accurate construction of the admittance matrix, the system can provide reliable data support for the subsequent calculation of stability indicators. The stability analysis unit will further calculate the real-time power grid stability value based on these stability indicators and use swarm intelligence algorithms for optimization to find the optimal power grid stability value. Swarm intelligence algorithms solve complex optimization problems by simulating group behavior. It can find the optimal solution in a large-scale and multi-dimensional search space, thereby improving the overall stability and security of the power grid.

[0030] Voltage stability indices reflect the ability of the power grid to maintain stable voltage under different load conditions. In the actual operation of the power grid, the change of load will cause the fluctuation of node voltage. Excessive voltage fluctuation may lead to the damage of power equipment or the collapse of the power grid. Therefore, voltage stability is an important index in the power grid stability analysis. The stability index calculation unit calculates the voltage stability index of each node through the admittance matrix, combined with the voltage amplitude and phase angle of the node. These indices can reflect whether the voltage of the power grid nodes is within the safe range under different operating conditions. Frequency stability indices reflect the ability of the power grid to maintain stable frequency in the face of load fluctuations. The frequency of the power grid is one of the important indices to measure the power quality. Excessive frequency fluctuation will affect the normal operation of power equipment and may even lead to system collapse. The stability index calculation unit calculates the frequency stability index of the system through the admittance matrix and the operating data of the power grid. These indices can evaluate whether the power grid can maintain stable frequency under different load changes to ensure the stability of power quality. Angle stability indices reflect the stability of the relative phase angles between nodes in the power grid when it is disturbed. The phase angle difference in the power grid is a key factor affecting power transmission and system stability. Excessive phase angle difference may lead to the loss of synchronization of the power grid, and then trigger large-scale power outages. The stability index calculation unit calculates the angle stability index of the power grid through the admittance matrix, combined with the phase angle information of each node. These indices can evaluate whether the power grid can quickly return to a stable state and maintain synchronous operation between nodes when disturbed. Through the above steps, the stability index calculation unit can generate detailed voltage stability, frequency stability and angle stability indices to provide a comprehensive evaluation of the operating state of the power grid. These stability indices can not only reflect the current operating conditions of the power grid, but also provide an important reference for subsequent optimization and regulation. In practical applications, the operating environment of the power grid is complex and changeable, and the change of load and external disturbances may affect the stability of the power grid. Therefore, accurately calculating and analyzing stability indices is crucial for ensuring the safe operation of the power grid. In addition, the stability index calculation unit also has the ability of real-time calculation and update. During the operation of the power grid, the system can dynamically update the stability indices according to real-time data to timely reflect the operating state of the power grid. This real-time calculation and update ability, combined with the optimization ability of swarm intelligence algorithms, can realize the real-time monitoring and control of the power grid stability to ensure that the power grid can maintain efficient and safe operation under various operating conditions. The application of swarm intelligence algorithms in the present invention further improves the intelligent level of the power grid stability analysis system. Swarm intelligence algorithms can efficiently find the optimal solution in a large-scale search space by simulating group behaviors, such as the particle swarm optimization algorithm, to optimize the stability indices of the power grid. In the process of calculating the optimal power grid stability value, the system first initializes the particle swarm and uses the real-time target power grid operating parameters as the initial values.Then, by defining the objective function, the individual optimal position and the global optimal position of the particles are iteratively updated according to the fitness value, and an adaptive mutation mechanism is introduced to gradually approach the optimal solution. When the number of iterations reaches the set value, the system calculates the power grid stability value of the particles and finally determines the optimal power grid stability value.

[0031] The stability analysis unit first receives various types of index data from the stability index calculation unit, including voltage stability, frequency stability, and angle stability. These data reflect the real-time state of the power grid under different operating conditions. The voltage stability index mainly evaluates the ability of the power grid to maintain voltage stability under various load conditions; the frequency stability index measures the ability of the power grid to maintain frequency stability during load fluctuations; the angle stability index reflects the stability of the relative phase angles between nodes. After obtaining these key indexes, the stability analysis unit begins to evaluate the overall stability of the power grid. During the evaluation process, the stability analysis unit not only simply synthesizes each individual index, but also considers the mutual influence and coupling effect between them. For example, voltage fluctuations may affect frequency stability, and angle changes may affect the relationship between voltage and frequency. Therefore, the stability analysis unit adopts a systematic analysis method to comprehensively evaluate these indexes and form a unified power grid stability value. This comprehensive stability value can more comprehensively reflect the overall health state of the power grid. Based on these comprehensive stability values, the stability analysis unit further uses swarm intelligence algorithms for optimal solution. Swarm intelligence algorithms, such as the particle swarm optimization algorithm (PSO), search for the optimal solution of the problem by simulating the collective behavior in nature, such as the foraging process of a flock of birds. First, the system initializes the particle swarm with the current operating parameters of the power grid as the initial values. These parameters include the voltage, frequency, and phase angle of each node, etc. During the initialization process, each particle represents a possible power grid state, and its fitness value reflects the stability of the power grid in that state. Next, the stability analysis unit defines the objective function, which is used to evaluate the fitness value of each particle. The objective function not only considers the current voltage, frequency, and angle stability indexes, but also comprehensively takes into account the operating cost and reliability requirements of the power grid. By calculating the fitness value, the system can identify the superior and inferior individuals in the current particle swarm. During the iteration process, the particles update their positions and velocities according to the fitness value, gradually approaching the global optimal solution. In each iteration, the system introduces an adaptive mutation mechanism to avoid falling into local optima and improve the globality and convergence speed of the optimization process. When the iteration reaches the set number of times or meets the convergence condition, the system calculates the stability value of the particles at this time as the optimal power grid stability value. This optimal stability value not only reflects the optimal operating state of the current power grid, but also provides an important reference for the dispatching and control of the power grid. Through this optimization solution process, the stability analysis unit can adjust and optimize the operating strategy of the power grid in real time in a complex power grid environment, improving the stability and security of the power grid.

[0032] Embodiment 2: Assume that the total number of nodes in the target power grid is n; the types of the nodes at least include: generator nodes, load nodes, and connection nodes; create an n×n square matrix, and then the obtained admittance matrix Y bus is represented by the following formula:

[0033]

[0034] where y ij represents the admittance between node I and node J; both i and j are subscript indices, and their values are all integers from 1 to n; the diagonal elements of the admittance matrix are which represents the sum of the admittances of node I and all the nodes connected to it, and k is also a subscript index, and its value is an integer from 1 to n; y ij = g ij + θb ij ; where, g ij represents the conductance between node i and j, representing the transmission capacity of active power; b ij : the susceptance between node i and j, representing the transmission capacity of reactive power; θ is the imaginary symbol.

[0035] Specifically, in the power grid, conductance and susceptance respectively represent the transmission characteristics of active power and reactive power during the power transmission process. Specifically, the conductance g ij represents the transmission capacity of active power through the line between node i and node j, which is inversely proportional to the resistance. The smaller the resistance, the larger the conductance, and the more effective the active power transmission. And the susceptance b ij represents the transmission capacity of reactive power, which is usually related to inductance and capacitance, and reflects the process of energy storage and release in the power grid. The diagonal element bus of the admittance matrix Y represents the sum of the admittances of node i and all the nodes connected to it. This sum value reflects the total connection strength of node i and is an important index of the connection importance of this node in the entire power grid. For the non-diagonal element -y ij, it represents the direct admittance between node i and node j. These values are symmetric negative numbers in the matrix, indicating the interaction between the two nodes. Through the calculation and construction of these elements, the admittance matrix comprehensively reflects the electrical connection status of the power grid. In practical applications, the construction of the admittance matrix should consider not only the static structure of the power grid but also its dynamic operating state. The load, power generation, and other operating parameters of the power grid change over time, and these changes affect the calculation of the admittance values. Therefore, the stability analysis unit needs to have the ability to update the admittance matrix in real time to reflect the changes in the operating conditions of the power grid. The dynamic update ability of the admittance matrix is an important basis for realizing real-time stability analysis and optimization. The accurate construction and real-time update of the admittance matrix provide accurate data support for the stability analysis of the power grid. During the stability analysis process, the system uses the admittance matrix to calculate the voltage stability, frequency stability, and angle stability indicators of the power grid. These indicators are important parameters for evaluating the operating state of the power grid and directly affect the safety and reliability of the power grid. The voltage stability indicator evaluates the ability of the power grid to maintain a stable voltage under different load conditions by analyzing the voltage fluctuations of the nodes; the frequency stability indicator evaluates the ability of the power grid to maintain a stable frequency during load fluctuations by analyzing the changes in the system frequency; the angle stability indicator evaluates the synchronous operation ability between the nodes of the power grid when it is disturbed by analyzing the changes in the relative phase angles between the nodes. After obtaining these indicators, the stability analysis unit further optimizes the operating state of the power grid through a swarm intelligence algorithm. The swarm intelligence algorithm searches for the optimal solution in a large-scale and multi-dimensional search space by simulating the group behavior in nature, such as the particle swarm optimization algorithm (PSO). The system first uses the real-time operating parameters of the power grid as the initial values to initialize the particle swarm and defines an objective function to evaluate the fitness value of each particle. The higher the fitness value, the better the power grid stability of the current particle. During the iteration process, the particles update their positions and velocities according to the fitness values and introduce an adaptive mutation mechanism to avoid falling into local optima, thereby gradually approaching the global optimal solution. When the iteration reaches the set number of times or meets the convergence condition, the system calculates the stability value of the particles as the optimal stability value of the power grid. This optimal stability value not only reflects the optimal operating state of the current power grid but also provides a scientific reference basis for the dispatching and control of the power grid.

[0036] Embodiment 3: The stability index calculation unit calculates the voltage stability index VSI of the target power grid based on the admittance matrix through the following formula:

[0037]

[0038] where det(J red ) represents the determinant of the reduced Jacobian matrix; V i is the voltage amplitude of node i; V nom is the rated voltage.

[0039] Specifically, first, det(J red ) in the formula represents the determinant of the reduced-order Jacobian matrix. The Jacobian matrix is an important tool in power system analysis, used to describe the sensitivity of system state variables (such as voltage and current) to changes in input variables (such as power injection and resistance). By reducing the order, the Jacobian matrix can be simplified, retaining the most critical variables, thus making the calculation more efficient. The determinant of the Jacobian matrix reflects the linear independence and stability of the system: the larger the value of the determinant, the more stable the system. This is because a larger determinant value indicates that the system has a stronger ability to resist disturbances. Therefore, in the VSI formula, the determinant of the reduced-order Jacobian matrix plays an important role. Second, in the formula represents the geometric mean of the ratios of all node voltage magnitudes to the rated voltage. In the power grid, the fluctuation of node voltage is an important indicator for evaluating the stability of the power grid. By calculating the geometric mean, the voltage levels of all nodes can be comprehensively considered and standardized to a unified scale. This helps to identify which nodes' voltages deviate from the rated value and whether the overall power grid is operating stably within the rated voltage range. The use of the geometric mean can smooth out extreme values of individual nodes, providing a more stable and reliable voltage evaluation result. The last part of the formula is This part takes into account the absolute value of the admittance between nodes and the influence of the voltage difference. The admittance Y ij represents the electrical connection strength between node i and node j, including conductance and susceptance. Through the admittance value, the power transmission capacity and loss situation between nodes can be reflected. The exponential part in the formula reflects the negative impact of voltage differences on the stability of the power grid by accumulating the products of the admittance values and voltage differences between all node pairs and performing an exponential operation. The negative sign in the exponential operation indicates that when the voltage difference between nodes is larger and the admittance is larger, the impact of this part on VSI is more negative, meaning the stability of the power grid is worse. The introduction of this term enables the formula to more comprehensively consider the voltage distribution in the power grid and its impact on the overall stability.

[0040] Overall, the calculation formula of VSI provides a comprehensive method for evaluating the grid voltage stability through the determinant of the reduced-order Jacobian matrix, the geometric mean of the ratio of the node voltage amplitude to the rated voltage, and the exponential operation of the admittance and voltage difference between nodes. This method not only considers the voltage levels of each node but also comprehensively takes into account the electrical connections and voltage differences between nodes, thus being able to accurately reflect the voltage stability of the grid under various operating conditions. In practical applications, the stability index calculation unit first receives the grid admittance matrix generated by the admittance matrix construction unit. Based on this matrix, the system can obtain the admittance values of each node and calculate the determinant of the reduced-order Jacobian matrix through calculation. This step involves complex linear algebra operations, but with the support of modern computing technologies, it can be efficiently completed. Next, the system obtains the voltage values V i and the rated voltage V nom , and calculates the geometric mean of the ratio of the voltage amplitudes of all nodes to the rated voltage. This calculation realizes the evaluation of the overall voltage level of the grid by traversing all nodes and performing multiplication and square root operations. Finally, the system calculates the product of the admittance between nodes and the voltage difference and performs an exponential operation. This step requires processing each element in the admittance matrix and calculating in combination with the actual voltage difference. Through this part of the calculation, the impact of voltage differences on the grid stability can be identified and integrated into the final VSI value. In this way, the system can dynamically update the voltage stability index according to real-time voltage and admittance data, providing a scientific reference for the dispatching and control of the grid. Based on the above principles, the stability index calculation unit can calculate and update the voltage stability index in real time during the operation of the grid. Combining the optimization ability of swarm intelligence algorithms, the system can search for the optimal solution in a large-scale and multi-dimensional search space, continuously optimize the operating state of the grid, and ensure stability under various load and disturbance conditions. This not only improves the reliability and safety of the grid but also promotes the development and application of smart grids, reflecting the innovation and practicality of the present invention in the field of grid stability analysis. Through this method, the present invention realizes the comprehensive evaluation and optimization of the grid voltage stability, providing a strong guarantee for the safe operation of the grid.

[0041] Embodiment 4: The stability index calculation unit calculates the frequency stability index FSI of the target grid based on the admittance matrix through the following formula:

[0042]

[0043] where H j is the inertia constant of the j-th node, which takes the value of 0 when the node is a connection node or a load node; S base,J is the rated capacity of the j-th node, which takes the value of 0 when the node is a connection node or a load node; P L,jis the active power of the j-th node, which is 0 when the node is a connection node or a generator node; f j is the frequency of the j-th node; f nom is the rated frequency; K D,j is the preset frequency sensitivity coefficient of the j-th node; Δf j is the frequency deviation of the j-th node; λ max (Y bus ) represents the admittance matrix Y bus 's largest eigenvalue; t is the time variable.

[0044] Specifically, the core part of the FSI formula involves the inertia constants and rated capacities of each node in the power grid. The inertia constant H j is an important parameter to measure the energy required by a node when the frequency changes, mainly applicable to generator nodes. For connection nodes or load nodes, since they do not participate in frequency regulation, the inertia constant is 0. By calculating the product of the inertia constant and rated capacity of each generator node and dividing the sum by the total active power load of all nodes in the power grid, the ratio of the overall inertia of the power grid to the load power can be obtained. This part of the formula reflects the anti-disturbance ability of the power grid in the face of load fluctuations. A larger ratio indicates that the power grid has higher frequency stability. Secondly, the exponential part in the formula reflects the influence of the frequency change rate of each node in the power grid on frequency stability. The frequency change rate represents the rate of change of the frequency of the j-th node over time. This parameter is crucial for evaluating the dynamic response characteristics of the power grid when a disturbance occurs. By averaging the absolute values of the frequency change rates of all nodes, the overall frequency fluctuation of the power grid can be measured. The negative sign in the exponential part indicates that the larger the frequency change rate, the more negative the impact on the FSI, meaning the worse the frequency stability of the power grid. The introduction of this term enables the formula to more comprehensively consider the dynamic characteristics in the power grid and evaluate the frequency stability of the power grid under disturbance conditions. In addition, the formula also includes the influence part of the frequency deviation where K D,j is the preset frequency sensitivity coefficient, and Δf j is the frequency deviation of the j-th node. This part of the formula evaluates the deviation degree of the frequency of each node in the actual operation of the power grid by considering the frequency deviation of the node. The frequency deviation is an important indicator in the operation of the power grid, reflecting the difference between the actual frequency of the node and the rated frequency. By introducing the frequency deviation and the frequency sensitivity coefficient, the role of the node in frequency regulation can be evaluated more accurately. The frequency sensitivity coefficient K of the node D,jFor quantifying the contribution of node frequency to the power grid frequency stability, a higher frequency sensitivity coefficient indicates that the node is more sensitive to frequency fluctuations, which helps to improve the power grid frequency stability. Finally, there is also an influence part of the maximum eigenvalue of the admittance matrix in the formula, exp(-λ max (Y bus ))), where λ max (Y bus ) represents the maximum eigenvalue of the admittance matrix Y bus . The admittance matrix Y bus is an important tool reflecting the electrical connection relationship between nodes in the power grid, and its maximum eigenvalue represents the most significant electrical characteristics in the power grid. By calculating the maximum eigenvalue of the admittance matrix, the electrical connection strength and complexity of the power grid can be evaluated. The larger the eigenvalue, the stronger the electrical connection of the power grid and the higher the frequency stability of the system. Therefore, this part in the formula further improves the accuracy and reliability of the frequency stability index by considering the eigenvalue of the admittance matrix.

[0045] Generally speaking, the calculation formula of the frequency stability index (FSI) provides a comprehensive method for evaluating frequency stability through the comprehensive calculation of multiple parts. Each part of the formula has specific physical meanings and mathematical functions, and combined together, it can accurately reflect the frequency stability of the power grid under different load and disturbance conditions. By calculating the ratio of the inertia constant to the rated capacity of each node in the power grid, the anti-disturbance ability of the power grid can be evaluated; by analyzing the frequency change rate of the node, the dynamic response characteristics of the power grid can be evaluated; by considering the frequency deviation and frequency sensitivity coefficient of the node, the contribution of the node to frequency regulation can be accurately evaluated; by calculating the maximum eigenvalue of the admittance matrix, the electrical connection strength and complexity of the power grid can be evaluated. In practical applications, the stability index calculation unit first receives the power grid admittance matrix generated by the admittance matrix construction unit and the operation data of each node. These data include the voltage, frequency, inertia constant, rated capacity, active power load, frequency change rate, and frequency deviation of each node, etc. By substituting these data into the FSI calculation formula, the system can calculate the frequency stability index of the power grid in real time. Combining the optimization ability of the swarm intelligence algorithm, the system can search for the optimal solution in a large-scale and multi-dimensional search space, continuously optimize the operation state of the power grid, and ensure the stability of the power grid under various load and disturbance conditions. The frequency stability analysis method of the present invention enables the power grid to respond and adjust quickly under complex and changeable operating conditions through accurate calculation and optimization, ensuring the safe and reliable operation of the power grid.

[0046] Embodiment 5: The stability index calculation unit calculates the angle stability index ASI of the target power grid based on the admittance matrix through the following formula:

[0047]

[0048] Among them, P max,m is the maximum transmission power of the m-th generator node; P e,m is the actual transmission power of the m-th generator node; M is the number of generator nodes; δ m is the power angle of the m-th generator node; δ crit,m is the critical power angle of the m-th generator node; T j,m is the mechanical starting time constant of the m-th generator node; is the rate of change of the power angle of the m-th generator node; δ i , δ j are the power angles of nodes i and j.

[0049] Specifically, here, P max,m is the maximum transmission power of the m-th generator node, representing the maximum power that the generator can transmit under the most ideal conditions; P e,m is the actual transmission power, reflecting the actual output of the generator in the current state. By calculating the relative difference between these two power values, the load capacity and margin of the generator can be evaluated. The ratio in the formula is larger, indicating that the generator has more ability to cope with sudden load changes, thereby improving the angular stability of the system. A larger ratio means that the generator has a larger power reserve under the current load conditions, which is very important for coping with instantaneous load fluctuations and maintaining system stability. Secondly, the sine function part considers the relationship between the power angle δ m of the generator node and the critical power angle δ crit,m . The power angle δ m reflects the difference between the generator voltage phase and the system reference voltage phase, while the critical power angle δ crit,m is the critical value of power angle stability. By introducing the sine function, the power angle deviation can be standardized and made to fluctuate within the range of [0, 1], so as to more intuitively reflect the impact of the power angle deviation on system stability. This part of the formula further evaluates the stability of the generator node during actual operation by reflecting the severity of the power angle deviation. The exponential part in the formula then considers the influence of the mechanical starting time constant T j,m of the generator node and the rate of change of the power angle . The mechanical starting time constant T j,m reflects the time required for the generator to run from stationary to full speed and is an important parameter of the generator response speed. The rate of change of the power angle represents the rate of change of the power angle with respect to time, reflecting the dynamic response characteristics of the generator during a disturbance. Through the exponential function, the effects of the mechanical starting time constant and the power angle change rate can be combined to evaluate the stability of the generator under dynamic conditions. A smaller power angle change rate and a larger mechanical starting time constant contribute to improving the system stability, as this means the generator can respond smoothly to changes in the system and avoid drastic power angle fluctuations. Finally, the denominator part in the formula takes into account the admittance Y ij between each pair of nodes in the power grid and the power angle difference |δ i - δ j |. The admittance Y ij represents the electrical connection strength between node i and node j, including conductance and susceptance. The power angle difference |δ i - δ j | reflects the phase difference between the two nodes. By introducing this part, the combined effect of the electrical connection between nodes and the power angle difference on the system stability can be evaluated. Smaller admittance values and power angle differences contribute to improving the system stability, as this means the electrical connection between nodes is weaker and the phase difference is smaller, thus reducing the possible power angle fluctuations in the system.

[0050] Overall, the calculation formula of the angle stability index (ASI) provides a comprehensive method for evaluating angle stability through the combined calculation of multiple parts. Each part of the formula has a specific physical meaning and mathematical function, and when combined, it can accurately reflect the angle stability of the power grid under different load and disturbance conditions. By calculating the relative ratio of the difference between the maximum transmission power and the actual transmission power of the generator node, the load capacity and margin of the generator can be evaluated; by introducing the sine function, the power angle deviation can be standardized to evaluate the impact of the power angle deviation on the system stability; by using the exponential function, the mechanical starting time constant and the power angle change rate can be combined to evaluate the stability of the generator under dynamic conditions; by calculating the denominator part, the combined effect of the electrical connection between nodes and the power angle difference on the system stability can be evaluated. In practical applications, the stability index calculation unit first receives the power grid admittance matrix generated by the admittance matrix construction unit and the operation data of each node. This data includes the power angle, maximum transmission power, actual transmission power, mechanical starting time constant, and power angle change rate of each node, etc. By substituting this data into the ASI calculation formula, the system can calculate the angle stability index of the power grid in real time. Combining the optimization ability of the swarm intelligence algorithm, the system can search for the optimal solution in a large-scale and multi-dimensional search space, continuously optimize the operation state of the power grid, and ensure the stability of the power grid under various load and disturbance conditions. The angle stability analysis method of the present invention enables the power grid to respond and adjust quickly under complex and changeable operating conditions through accurate calculation and optimization, ensuring the safe and reliable operation of the power grid.

[0051] Example 6: The stability analysis unit calculates the real-time power grid stability value SI through the following formula:

[0052]

[0053] where α v is the weight of the voltage stability index; α f is the weight of the frequency stability index; α a is the weight of the angle stability index; VSI ref is the reference value of the voltage stability index; FSI ref is the reference value of the frequency stability index; ASI ref is the reference value of the angle stability index; κ(Y bus ) is the condition number of the admittance matrix; κ max is the preset maximum acceptable condition number.

[0054] Specifically, the core part of the formula involves the weighted sum of three key stability indices. The α v , α f and α a in the formula are the weights of the voltage stability index, frequency stability index, and angle stability index respectively. These weight coefficients reflect the relative importance of each stability index in the overall stability assessment. In practical applications, different power grids may have different requirements for voltage, frequency, and angle stability. By adjusting these weights, the needs of different power grids can be flexibly adapted. Through weighted sum calculation, the formula combines the voltage, frequency, and angle stability indices into an overall index, reflecting the comprehensive stability of the power grid under the current operating state. Next, the exponential part in the formula is used to standardize the product of the three stability indices and introduce a non-linear function to amplify or reduce its impact. Here, VSI ref , FSI ref and ASI ref are the reference values of the voltage, frequency, and angle stability indices respectively, usually set as the maximum or target values of these indices under ideal conditions. By comparing the actual indices with the reference values, the formula can reflect the deviation of the current state of the power grid from the ideal state. The introduction of the exponential part makes the contribution to the overall stability increase significantly when each index approaches its reference value, while its impact weakens when the deviation is large. This non-linear amplification effect can more sensitively reflect the changes in the power grid stability indices, thereby improving the accuracy of the evaluation results. In addition, the formula also includes an exponential decay term related to the condition number The condition number κ(Y bus) is an important indicator to measure the ill - conditioning degree of the matrix, reflecting the stability and accuracy of the power grid in numerical calculations. A larger condition number indicates that the matrix is close to singularity and numerical calculations may be unstable, while a smaller one indicates relatively higher stability. The preset maximum acceptable condition number κ max is an empirical value or a value determined through simulation, used to standardize the condition number of the current admittance matrix. By introducing this term, the numerical stability of the admittance matrix can be incorporated into the overall power grid stability assessment, ensuring that the actual operating state of the power grid is considered in numerical calculations. The role of the exponential decay term is that when the condition number of the admittance matrix approaches or exceeds the maximum acceptable value, the negative impact on the overall stability increases significantly, thus reminding the system to take measures to improve the numerical stability of the power grid.

[0055] Generally speaking, the calculation formula of the real - time power grid stability value (SI) provides a comprehensive power grid stability assessment method through the comprehensive calculation of multiple parts. Each part of the formula has specific physical meanings and mathematical functions, and when combined, it can accurately reflect the overall stability of the power grid under different load and disturbance conditions. Through weighted sum calculation, the relative importance of different stability indicators can be flexibly adjusted to meet the needs of different power grids; through the non - linear exponential function, the changes of each stability indicator can be more sensitively reflected, providing more accurate assessment results; by considering the condition number of the admittance matrix, the numerical stability of the power grid can be ensured in numerical calculations, further improving the reliability of the assessment results. In practical applications, the stability analysis unit first receives the calculation results of each stability indicator, including the voltage stability indicator (VSI), the frequency stability indicator (FSI), and the angle stability indicator (ASI). These indicators are calculated by the aforementioned stability indicator calculation unit based on the admittance matrix and power grid operation data. Next, the system, according to the set weight coefficients α v 、α f and α a , performs a weighted sum calculation on these indicators to obtain a preliminary comprehensive stability value. Then, the system compares the comprehensive stability value with the reference value and amplifies or reduces its influence through the non - linear exponential function to obtain a more sensitive stability assessment result. Finally, the system introduces the condition number of the admittance matrix and incorporates the numerical stability into the overall assessment through the exponential decay term to ensure the accuracy and reliability of the assessment result.

[0056] Example 7: For the stability analysis unit, let the total number of iterative updates be c, and the defined objective function JMAX is expressed by the following formula:

[0057]

[0058] where, X c is the globally optimal position obtained in the c - th iteration; VSI(X c) is the voltage stability index at the globally optimal position; FSI(X c ) is the frequency stability index at the globally optimal position; ASI(X c ) is the angle stability index at the globally optimal position; Y bus (X c ) is the admittance matrix at the globally optimal position.

[0059] Specifically, in the power grid stability analysis system based on the swarm intelligence algorithm of the present invention, the process of calculating the optimal power grid stability value involves using the real-time target power grid operation parameters as the initial values, initializing the particle swarm, defining the objective function, and iteratively updating the positions and velocities of the particle swarm through a series of optimization strategies to find the optimal power grid operation state. The core of this process lies in leveraging the powerful search and optimization capabilities of the swarm intelligence algorithm and combining the specific requirements in power grid stability analysis to ensure that the power grid maintains the best stability under various operating conditions. First, the system uses the real-time target power grid operation parameters as the initial values to initialize the particle swarm. The particle swarm optimization algorithm (PSO) is an optimization algorithm based on swarm behavior that solves complex optimization problems by simulating natural phenomena such as bird flocks foraging. In the power grid stability analysis system, the initialization process of the particle swarm involves using the various operation parameters of the power grid (such as voltage, frequency, power angle, etc.) as the initial positions of the particles, and these positions represent the specific parameters of the power grid in the current operating state. Each particle has a position and a velocity in the search space. The position represents the current solution, and the velocity represents the search direction and step size. Next, the system defines the objective function to evaluate the fitness value of each particle. The objective function JMAX combines the voltage stability index (VSI), the frequency stability index (FSI), and the angle stability index (ASI), and comprehensively reflects the overall stability of the power grid through the nonlinear amplification effect and the condition number of the admittance matrix. Specifically, the calculation formula of the objective function is as follows:

[0060]

[0061] By calculating the fitness value of each particle, the system can evaluate the stability of the current power grid parameter combination and continuously optimize this stability during the iteration process. During the iteration process, the system adopts a nonlinear strategy to update the individual optimal position and the global optimal position of each particle. The key of the particle swarm optimization algorithm lies in guiding the movement of the particles through the update of the individual optimal position and the global optimal position. The individual optimal position refers to the best position found by the particle itself during the search process, and the global optimal position is the best position found in the entire particle swarm. The update formula of each particle usually includes three parts: the current velocity, the influence of the individual optimal position, and the influence of the global optimal position. The specific update formula can be expressed as:

[0062]

[0063] Among them, is the velocity of particle i at the k-th iteration, is the position of the particle, ω is the inertia weight, c1 and c2 are learning factors, r1 and r2 are random numbers, is the individual optimal position of the particle, and g k is the global optimal position. The application of the nonlinear strategy is reflected in the dynamic adjustment of the inertia weight ω and the learning factors c1 and c2. The inertia weight usually decreases with the increase of the number of iterations, so as to maintain a large search range in the initial stage of the search, avoid falling into the local optimum, and finely adjust the position of the particle in the later stage of the search to improve the search accuracy. The learning factors c1 and c2 can be dynamically adjusted to balance the roles of individual learning and group learning, thereby improving the search efficiency.

[0064] During the iterative update process, an adaptive mutation mechanism is introduced to further improve the diversity of the search and the global search ability. The adaptive mutation mechanism adjusts the position of the particles by introducing random perturbations, thereby increasing the coverage of the search space and preventing the algorithm from falling into local optima. Specifically, when the fitness value of the particles does not improve significantly after a certain number of iterations, the adaptive mutation mechanism will randomly mutate the velocity or position of the particles to explore new search spaces. The amplitude and direction of the mutation can be dynamically adjusted according to the current state of the search space and the historical information of the particles, thereby improving the effectiveness of the mutation. The adaptive mutation mechanism can be implemented in the following way: First, a mutation probability is set, and when certain conditions are met, the velocity or position of the particles is mutated. The amplitude of the mutation can be determined according to the current iteration number and the change in the fitness value. For example, in the initial stage of the search, the amplitude of the mutation can be larger to increase the diversity of the search; in the later stage of the search, the amplitude of the mutation can be gradually reduced to improve the accuracy of the search. At the same time, the mutation direction can be determined according to the historical position and velocity information of the particles to ensure that the mutated particles still move in the direction of the global optimal position. When the number of iterative updates reaches the set number, the system calculates the power grid stability value corresponding to the particles at this time as the optimal power grid stability value. Through multiple iterations and optimizations, the particle swarm gradually converges to the global optimal position, thereby finding the operating parameter combination that maximizes the power grid stability indicators (VSI, FSI, ASI). The final optimal power grid stability value not only reflects the best stability of the power grid under the current operating state but also provides a scientific reference for the dispatching and control of the power grid. In practical applications, the stability analysis unit first receives the real-time operating parameters of the power grid, initializes the particle swarm, and defines the objective function. Through multiple iterative updates and adaptive mutations, the system gradually optimizes the operating state of the power grid and calculates the fitness value of the particles in each iteration. Finally, the system finds the global optimal position, calculates, and outputs the optimal power grid stability value, providing a strong guarantee for the safe and reliable operation of the power grid.

[0065] The power grid stability analysis system based on the swarm intelligence algorithm of the present invention realizes a comprehensive evaluation and optimization of the overall stability of the power grid through accurate calculation and optimization. By combining voltage, frequency, and angle stability indicators and adopting a non-linear strategy and an adaptive mutation mechanism, the system can quickly respond and adjust under complex and changeable operating conditions to ensure that the power grid remains stable under various loads and disturbances. This not only improves the reliability and safety of the power grid but also promotes the development and application of smart grids, reflecting the innovation and practicality of the present invention in the field of power grid stability analysis. Through this method, the present invention realizes a comprehensive evaluation and optimization of the overall stability of the power grid, provides a scientific reference for the dispatching and control of the power grid, and further ensures the safe operation of the power grid.

[0066] The preferred embodiments of the present disclosure have been described above with reference to the accompanying drawings, and thus do not limit the scope of the rights of the present disclosure. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and essence of the present disclosure shall fall within the scope of the rights of the present disclosure.

Claims

1. A power grid stability analysis system based on swarm intelligence algorithm, characterized in that: The system comprises: a power grid admittance matrix construction unit, a stability index calculation unit and a stability analysis unit; the power grid admittance matrix construction unit is used to determine the total number of nodes in the target power grid, calculate the admittance between each node, and then create a matrix, and use the admittance between each node as an element in the matrix to construct the admittance matrix of the target power grid; the stability index calculation unit is used to calculate the voltage stability index, frequency stability index and angle stability index of the target power grid based on the admittance matrix; the stability analysis unit is used to calculate the real-time power grid stability value based on the voltage stability index, frequency stability index and angle stability index; and the swarm intelligence algorithm is used to calculate the optimal power grid stability value. , specifically including: taking the real-time operating parameters of the target power grid as the initial value to initialize the particle swarm; defining the objective function, and calculating the fitness value of each particle according to the objective function; according to the fitness value, adopting a nonlinear strategy to iteratively update the individual optimal position and the global optimal position of each particle, and in the iterative update process, introducing an adaptive mutation mechanism, and then iteratively updating the speed and position of the particle; when the number of iterative updates reaches the set number, calculating the power grid stability value corresponding to the particle at this time as the optimal power grid stability value; assuming that the total number of nodes in the target power grid is n; the types of the nodes include at least: generator nodes, load nodes and connection nodes; creating a square matrix with n rows and n columns, the resulting admittance matrix Y bus Use the following formula to express it: Among them, y ij represents the admittance between node i and node j; i and j are both subscript indices, and their values ​​are integers from 1 to n; the diagonal elements of the admittance matrix are represents the sum of the admittances of node i and all the nodes connected to it, k is also a subscript index, and its value is an integer from 1 to n; y ij =g ij +θb ij ; Among them, g ij represents the conductance between nodes i and j, indicating the transmission capacity of active power; b ij : The susceptance between nodes i and j, indicating the transmission capacity of reactive power; θ is the imaginary sign; The stability index calculation unit calculates the voltage stability index VSI of the target power grid based on the admittance matrix by the following formula: Among them, det(J red ) represents the determinant of the reduced Jacobian matrix; V i is the voltage amplitude of node i; V nom is the rated voltage; The stability index calculation unit calculates the frequency stability index FSI of the target power grid based on the admittance matrix by the following formula: Among them, H j is the inertia constant of the jth node. When the node is a connection node or a load node, the value is 0; S base,j is the rated capacity of the jth node. When the node is a connection node or a load node, the value is 0; P L,j is the active power of the jth node. When the node is a connection node or a generator node, the value is 0; f j is the frequency of the jth node; f nom is the rated frequency; K D,j is the frequency sensitivity coefficient of the preset j-th node; Δf j is the frequency deviation of the jth node; max (Y bus ) represents the admittance matrix Y bus The maximum eigenvalue of ; t is the time variable; The stability index calculation unit calculates the angle stability index ASI of the target power grid based on the admittance matrix by the following formula: Among them, P max,m is the maximum transmission power of the mth generator node; P e,m is the actual transmission power of the mth generator node; M is the number of generator nodes; δ m is the power angle of the mth generator node; δ crit,m is the critical power angle of the mth generator node; T j,m is the mechanical starting time constant of the mth generator node; is the power angle change rate of the mth generator node; δ i ,δ j is the power angle of nodes i and j.

2. The power grid stability analysis system based on swarm intelligence algorithm according to claim 1, characterized in that: The stability analysis unit calculates the real-time grid stability value SI through the following formula: Among them, α v is the voltage stability index weight; α f is the frequency stability index weight; α a is the angle stability index weight; VSI ref FSI is the reference value of voltage stability index; ref ASI is the reference value of frequency stability index; ref is the reference value of the angle stability index; κ(Y bus ) is the condition number of the admittance matrix; κ max is the preset maximum acceptable number of conditions.

3. The power grid stability analysis system based on swarm intelligence algorithm according to claim 2, characterized in that: Stability analysis unit, assuming the total number of iterative updates is c, the defined objective function JMAX is expressed using the following formula: Among them, X c is the global optimal position obtained in the cth iteration; VSI(X c ) is the voltage stability index at the global optimal position; FSI(X c ) is the frequency stability index at the global optimal position; ASI(X c ) is the angle stability index under the global optimal position; Y bus (X c ) is the admittance matrix at the global optimal position.

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