A transformer area operation security domain promotion method and device, a terminal and a storage medium

Abstract

This application provides a method, device, terminal, and storage medium for enhancing the operational safety domain of a power distribution area, relating to the field of power electronic grid stability assessment technology. The method includes: constructing an impedance model of a grid-connected inverter in a target power distribution area; equivalently transforming the polygonal network of the target power distribution area into a ray network, and calculating the source-grid impedance ratio based on the equivalent ray network and the impedance model of the grid-connected inverter; inputting the source-grid impedance ratio into a constructed global proxy model and outputting the phase margin; calculating the sensitivity index of each feed-in node in the target power distribution area based on the phase margin, and quantitatively identifying the target critical nodes affecting system stability based on the sensitivity index of each feed-in node; and coordinating the control parameters of the grid-connected inverter corresponding to the target critical nodes with the optimization objective of maximizing the generalized volume of the multidimensional safe operating domain, thereby enhancing the operational safety domain of the target power distribution area. This application can improve the efficiency of system-level safety assessment.

Description

Technical Field

[0001] This application relates to the field of power electronic grid stability assessment technology, and in particular to a method, device, terminal and storage medium for improving the operational safety domain of a transformer substation. Background Technology

[0002] In system-level safety assessment, characterizing the safe operating domain provides an effective perspective for quantifying the stable operating range of a system. Early research focused on the power angle stability domain of traditional synchronous machine systems. With the increasing penetration of new energy sources, the research focus shifted to the capacity configuration and interactive stability of grid-connected inverters. However, based on the static short-circuit ratio scalar index as a hard boundary constraint, it is impossible to continuously characterize the intuitive oscillation safety domain morphology and analytical expression in the multi-dimensional power space. In addition, the short-circuit ratio index is widely used to assess grid strength, but it is limited to deriving a global system strength measurement tool under non-rated operating conditions, and has failed to form a multi-dimensional operating safety domain construction mechanism for continuous power output of multiple power plants. On this basis, further explorations have been made of access capacity analysis constrained by the short-circuit ratio and stability domain characterization methods considering multiple operating parameters. However, the optimization methods are based on specific site selection planning of macroscopic strength, which cannot achieve rapid prediction of phase margin fluctuations and real-time tuning of inverter parameters under massive operating conditions.

[0003] Furthermore, most studies focus on single inverters or simplified grid scenarios. For actual distribution areas containing multiple lines, nodes, and inverter clusters, systematic solutions for aggregation methods of overall impedance characteristics and stability assessment processes are still lacking. Secondly, in actual operation, the output levels of each inverter within a distribution area and their power distribution ratios are constantly changing. These changes in operating points significantly alter the system's output impedance characteristics, thus affecting its stable operation. While traditional impedance analysis methods or frequency domain sweep methods yield accurate results, they are computationally time-consuming and struggle to rapidly traverse massive operating conditions and provide intuitive stability assessments. Moreover, the ability to rapidly construct and accurately characterize safety domains needs improvement. Traditional methods for determining safety domain boundaries based on traversal scanning or simulation are computationally expensive and inefficient, failing to meet the needs of numerous safety assessment scenarios in practical engineering. Summary of the Invention

[0004] This application provides a method, apparatus, terminal, and storage medium for enhancing the security domain of a distribution center, in order to solve the problem of low efficiency in system-level security assessment in the prior art.

[0005] Firstly, this application provides a method for enhancing the security domain of a transformer substation, including: Construct impedance models for grid-connected inverters in the target distribution area; The polygonal network of the target transformer area is equivalently transformed into a ray network, and the source-to-grid impedance ratio is calculated based on the equivalent ray network and the impedance model of the grid-type inverter. The source-network impedance ratio is input into the constructed global proxy model, and the phase margin of the system at the cross-frequency is output. The global proxy model is constructed based on the non-intrusive spectral projection polynomial chaotic expansion method. Based on the phase margin, the sensitivity index of each feed node in the target area is calculated, and based on the sensitivity index of each feed node, the target key nodes affecting system stability are quantitatively identified. With the goal of maximizing the generalized volume of the multidimensional safe operation domain, the control parameters of the grid-connected inverters corresponding to the key nodes of the target are coordinated and tuned to improve the operating safety domain of the target transformer area.

[0006] Secondly, this application provides a transformer area operation safety domain enhancement device, comprising: The model building module is used to build impedance models of grid-connected inverters in the target distribution area. The impedance ratio calculation module is used to transform the polygonal network of the target transformer area into an equivalent ray network, and calculate the source-grid impedance ratio based on the equivalent ray network and the impedance model of the grid-type inverter. The margin determination module is used to input the source-network impedance ratio into the constructed global proxy model and output the phase margin of the system at the cross-frequency. The global proxy model is constructed based on the non-intrusive spectral projection polynomial chaotic expansion method. The node determination module is used to calculate the sensitivity index of each feed node in the target area based on the phase margin, and to quantitatively identify the target key nodes that affect the stability of the system based on the sensitivity index of each feed node. The collaborative tuning module is used to collaboratively tune the control parameters of the grid-connected inverter corresponding to the target key node with the optimization objective of maximizing the generalized volume of the multidimensional safe operating domain, so as to improve the operating safety domain of the target area.

[0007] Thirdly, this application provides a terminal including 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 method as described in the first aspect or any possible implementation of the first aspect above.

[0008] Fourthly, this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method as described in the first aspect or any possible implementation of the first aspect.

[0009] This application provides a method, device, terminal, and storage medium for enhancing the operational safety domain of a transformer substation. By constructing a grid-connected inverter impedance model and calculating the source-grid impedance ratio using an equivalent network, this application can accurately locate weak points in the substation's stability, fundamentally avoiding the problem of "blindly modifying" traditional governance methods and significantly improving the operational stability of the substation. In addition, a global proxy model built based on the non-intrusive spectral projection polynomial chaotic expansion method can quickly output phase margin and calculate node sensitivity, accurately identifying core nodes affecting system stability without complex simulations, thus reducing the cost of analysis and computing power. Simultaneously, by coordinating the tuning of inverter control parameters with the goal of maximizing the generalized volume of the multidimensional safe operation domain, the operational safety boundary of the substation can be significantly broadened without adding large-scale hardware investment, adapting to scenarios with high proportions of distributed photovoltaic and charging pile access, reducing the probability of oscillation faults such as voltage over-limit and inverter grid disconnection, and improving the operational stability and voltage qualification level of the substation. Attached Figure Description

[0010] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 This is a schematic diagram illustrating the implementation process of the transformer area operation security domain enhancement method provided in the embodiments of this application; Figure 2 This is a schematic diagram of the structure of a new energy cluster multi-infeed station area system provided in an embodiment of this application; Figure 3 This is a schematic diagram of the inverter main circuit and control structure provided in the embodiments of this application; Figure 4 This is a schematic diagram of a phase-locked loop structure considering small-signal disturbances in phase angle, provided in an embodiment of this application. Figure 5 This is a schematic diagram of the ray-shaped network structure provided in the embodiments of this application; Figure 6 This is a schematic diagram of the polygonal network structure provided in the embodiments of this application; Figure 7 This is a simplified schematic diagram of the transformer substation network and inverter impedance provided in the embodiments of this application; Figure 8 This is a simplified schematic diagram of the transformer substation network and inverter impedance provided in the embodiments of this application; Figure 9 This is a simplified model diagram of the impedance recursive aggregation of the transformer network provided in the embodiments of this application; Figure 10This is a schematic diagram of the IEEE 9-node system architecture provided in an embodiment of this application; Figure 11 This is a schematic diagram of a two-dimensional secure operating domain based on an IEEE 9-node system provided in an embodiment of this application; Figure 12 This is a schematic diagram provided in this application embodiment of the observation of the impact of changes in the power of nodes 4 and 9 on the overall phase margin of the IEEE 13-node system, under the premise that the fixed powers of nodes 10 and 13 are 20kW and 40kW respectively. Figure 13 This is a schematic diagram provided in this application embodiment of the observation of the impact of changes in the power of nodes 4 and 10 on the overall phase margin of the IEEE 13-node system, under the premise that the fixed power of nodes 9 and 13 is 40kW and 40kW respectively. Figure 14 This is a schematic diagram provided in this application embodiment, showing the impact of changes in the power of nodes 4 and 13 on the overall phase margin of the IEEE 13-node system, under the premise that the fixed powers of nodes 9 and 10 are 40kW and 60kW respectively. Figure 15 This is a schematic diagram provided in this application embodiment of the observation of the impact of changes in the power of nodes 9 and 10 on the overall phase margin of the IEEE 13-node system, under the premise that the fixed powers of nodes 4 and 13 are 40kW and 20kW respectively. Figure 16 This is a schematic diagram provided in this application embodiment of the observation of the impact of changes in the power of nodes 9 and 13 on the overall phase margin of the IEEE 13-node system, under the premise that the fixed powers of nodes 4 and 10 are 40kW and 60kW respectively. Figure 17 This is a schematic diagram provided in this application embodiment of the observation of the impact of changes in the power of nodes 10 and 13 on the overall phase margin of the IEEE 13-node system, under the premise that the fixed powers of nodes 4 and 9 are 60kW and 60kW respectively. Figure 18 This is a schematic diagram of the IEEE 13-node system architecture provided in an embodiment of this application; Figure 19 This is a comparison diagram of the security domain surface before and after security domain elevation provided in the embodiments of this application; Figure 20 This is a schematic diagram of the structure of the transformer area operation safety zone lifting device provided in the embodiments of this application; Figure 21 This is a schematic diagram of the terminal provided in the embodiments of this application. Detailed Implementation

[0012] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0013] To make the objectives, technical solutions, and advantages of this application clearer, the following description will be provided in conjunction with the accompanying drawings and specific embodiments.

[0014] Figure 1 The implementation flowchart of the transformer area operation security domain enhancement method provided in the embodiments of this application is described in detail below: In step 101, the impedance model of the grid-connected inverter in the target distribution area is constructed.

[0015] In this embodiment, for all grid-connected inverters within the target distribution area that serve as new energy grid-connection interfaces, a refined impedance model of the grid-connected inverters is established using the harmonic linearization modeling approach, considering small-signal disturbances in the phase-locked loop phase angle and the dynamic characteristics of the control loop. The structure of the target distribution area can be referenced from... Figure 2 As shown, it consists of a complex network of multiple new energy clusters connected to the grid via grid-connected inverters.

[0016] In one possible implementation, constructing the impedance model of the grid-connected inverter in the target distribution area can include: Obtain the grid connection point sampling voltage collected by the phase-locked loop of the grid-connected inverter in the target area; The sampling voltage at the grid connection point is decomposed by an initial coordinate transformation based on the fundamental frequency phase-locked angle to obtain the steady-state reference voltage component without phase disturbance. The steady-state reference voltage component with superimposed perturbation phase angle is decomposed by a quadratic coordinate transformation based on the perturbation phase angle, and the perturbation voltage component containing phase perturbation coupling characteristics is obtained. By combining the main circuit equations and the full-link control transfer function corresponding to the steady-state reference voltage component and the disturbance voltage component, the impedance model of the grid-connected inverter is derived.

[0017] Optionally, in constructing the impedance model, this application fully considers the nonlinear coupling effects of small-signal disturbances in the phase-locked loop (PLL) phase angle with the control structure and sampling delay. Unlike traditional simplified models that ignore phase angle fluctuations, this application adopts a harmonic linearization modeling approach, decomposing the coordinate transformation process of the PLL's grid-connected sampling voltage into an initial transformation based on the fundamental frequency phase angle and a secondary transformation based on the disturbance phase angle, accurately capturing the negative impedance characteristics introduced by the PLL in a weak grid environment. By simultaneously solving the core equations of the main circuit and the control path including voltage feedforward coefficients, current sampling, and filter angular frequency delay, an analytical impedance expression that truly reflects the external characteristics of the inverter is derived, providing accurate physical support for subsequent system-level stability analysis.

[0018] For example, based on Figure 3 The grid-connected inverter main circuit shown can be analyzed separately for phase A. By performing a Laplace transform, the expressions for the midpoint voltage of phase A arm, the grid connection point voltage, and the grid connection current are as follows: in, The voltage at the midpoint of phase A bridge arm. The voltage at the grid connection point. This is the grid-connected current.

[0019] A positive-sequence small-signal current disturbance is injected at the grid connection point, namely: in, The fundamental frequency, This represents the peak value of the positive sequence current disturbance. This is the frequency of the positive-sequence current disturbance. This is the phase of the positive sequence current disturbance.

[0020] Based on the harmonic linearization modeling concept, the response voltage at the disturbance frequency can be obtained given the disturbance current. The time-domain variables in equation (1) can be transformed to the frequency domain using Euler's formula, including the fundamental frequency component and the disturbance sequence component, i.e.: in, This is the positive-sequence disturbance current. This is the positive sequence response voltage.

[0021] by For example, the specific expression is: ,in, Given the positive-sequence disturbance current angular frequency, the impedance of phase A can be defined as: When solving the impedance model considering the control loop, one can start from the small-signal disturbance at the input, traverse the small-signal path of the control structure until the modulated small signal at the output is obtained, further perform the Park transformation on the modulated small signal to express the DC input voltage, and substitute it into the core equation of the main circuit to obtain the impedance model.

[0022] For grid-connected converter systems employing phase-locked loops (PLLs), the phase-locking process for the grid voltage needs to consider the impact of phase angle disturbances. The phase angle of the PLL output can be expressed as... ,in, This represents the small-signal disturbance component of the phase angle. In this case, frequency domain modeling of the phase-locked loop is required to analyze the impact of the small-signal disturbance of the phase angle on the control loop.

[0023] like Figure 4 As shown, the phase-locked loop samples the voltage at the grid connection point. , , And by performing a coordinate transformation, it can be reduced to a two-step coordinate transformation. First, the fundamental frequency phase angle is used as the basis for the transformation. Performing the Park transform yields the result based on the fundamental frequency phase-locked angle. and Then, using phase angle Transform to obtain and The phase-locked angle is output after passing through a proportional-integral (PI) controller and then an integral stage. The expression for the Park transform matrix of the fundamental frequency phase angle is given below. The expression for the Park transform matrix of the perturbation phase angle They are respectively: By performing a coordinate transformation on the three-phase voltage, we can obtain The shaft voltage is: And by Figure 4 It can be known that: in, This is the proportional gain of the phase-locked loop. The integral coefficients of the phase-locked loop are... This is the transfer function for the phase-locked loop.

[0024] Assumption For positive sequence voltage and The relationship between them, namely: By combining formulas (6) and (7), we can obtain the answer. for: The output current is subjected to a Park transform that takes into account phase angle disturbances, and the phase angle disturbances are ignored. as well as The component can be used to calculate the d-axis current when considering the phase angle disturbance caused by the phase-locked loop. q-axis current and d-axis voltage q-axis voltage : according to Figure 3 The control structure in the calculation can be obtained Axis control signals, namely: For d-axis control signal q-axis control signal The three-phase modulation voltage under positive-sequence perturbation is obtained by inverse Park transform. , , ,Right now: Transformed into: Ignoring the frequency coupling effect of the second harmonic mirror generated during the inverse Park transform, the following applies to the positive-sequence perturbation, taking the A-phase modulated signal as an example: Then Substituting into the core equation of the main circuit shown in formula (1), where Substituting back into the impedance analytical expression, we can obtain the impedance model, which is: in, This is the analytical expression for the impedance model. For the Laplace operator, DC input voltage, For the filter inductor on the grid-connected inverter side, For grid-side filter inductance, For the filter capacitor on the grid-connected inverter side, This is the parasitic resistance of the capacitor. For controller gain, The peak value of the fundamental current. The fundamental current angular frequency, The phase of the fundamental current. For voltage feedforward coefficients, Let be the transfer function of the PI controller. Let be the equivalent transfer function of the current sampling delay stage. Let be the equivalent transfer function of the voltage sampling delay stage. The current decoupling coefficient is... The fundamental peak value of the response voltage at the disturbance frequency. This is the small-signal linearized transfer function for the phase-locked loop.

[0025] This application embodiment can accurately decouple the disturbance voltage component with phase disturbance coupling characteristics by performing two coordinate transformations of the base frequency phase-locked angle and the disturbance phase angle, avoiding the problem of phase disturbance and steady-state component superposition in traditional modeling, and greatly improving the modeling accuracy. In addition, after accurately separating the phase disturbance coupling component, the resonance point of the inverter output impedance and the grid impedance in a specific frequency band can be identified in advance, avoiding the instability problems such as subsynchronous oscillation and current distortion that are common under weak grid conditions from the source of modeling, and improving the overall operational robustness of the transformer area.

[0026] In step 102, the polygonal network of the target transformer area is equivalently transformed into a ray network, and the source-to-grid impedance ratio is calculated based on the equivalent ray network and the impedance model of the grid-type inverter.

[0027] In this embodiment, the target distribution network is mostly a polygonal closed-loop topology with interconnected nodes and intersecting branches, which cannot be directly aggregated in series and parallel. Therefore, for the complex topological connections in the target distribution area, an equivalent mathematical relationship is established based on the network current flowing into each node, simplifying the complex polygonal network into an equivalent single-source ray structure, and then performing impedance recursive aggregation in sequence, thereby accurately extracting the system-level equivalent impedance model, and using it to calculate the source-network impedance ratio.

[0028] In one possible implementation, the polygonal network of the target station area is equivalently transformed into a radial network, which may include: Establish an equivalent transformation matrix based on the node current balance relationship; By using the network current flowing into each feed node in the target area as input to the equivalent transformation matrix, the polygonal network of the target area is equivalently transformed into a radial network.

[0029] Optionally, by comparing the current balance relationships flowing into each node in a ray network and a polygonal network, a mathematical model (i.e., an equivalent transformation matrix) for the equivalent transformation of branch impedance is established. Based on the network currents flowing into each node, a relationship is established, and the equivalent transformation matrix simplifies the irregular polygonal closed-loop network into an equivalent ray structure. In the polygonal network, the branch impedance connecting any node is remapped through this model to the impedances of each feed node and the reference node. The equivalent impedance between them is used to simplify the topology.

[0030] Specifically, local electrical networks with complex transmission networks cannot directly aggregate their impedances. Instead, the polygonal network is first converted into an equivalent radial network, and then the impedances of each node are aggregated sequentially.

[0031] Ray-shaped networks, such as Figure 5 As shown, at nodes 1, 2, 3, 4, ..., n and node Each of the polygonal networks is connected to a resistor, such as... Figure 6 As shown, a resistor is connected between any nodes in the sequence 1, 2, ..., n. The following discussion will focus on this. Figure 5 and Figure 6 Equivalent transformation.

[0032] When the ray network is equivalent to a polygonal network, a comparison of the currents in the two networks yields the following: in, For the current flowing into node 1 of the ray-shaped network, For the current flowing into node 1 of the ray-shaped network, For nodes and nodes The resistance between them For nodes and nodes The resistance between them .

[0033] The resistance formula for a polygonal network connection can be obtained by simplification: If we consider the polygonal network as equivalent to a ray network, then the equation is: The equivalent resistance of the ray network can be obtained by simplification as follows: This application embodiment establishes an equivalent transformation matrix through node current balance, which can accurately transform complex polygonal transformer network into a clearly structured ray network, significantly reducing the topological complexity of transformer impedance modeling and stability analysis, and reducing the computational overhead of subsequent calculations.

[0034] In one possible implementation, the source-grid impedance ratio is calculated based on the impedance models of the equivalent ray network and the root-grid inverter, which may include: The impedance model of each feed-in node in the target area and the grid inverter is connected in series with the line impedance in the corresponding ray network to obtain the aggregated impedance components of each feed-in node. Following the rule of progressively pushing from the end of the renewable energy cluster in the distribution area to the preset grid reference node, the impedance components of all feed-in nodes are aggregated to obtain the system-level aggregated impedance, and the system-level aggregated impedance is used as the source-side impedance. The ratio of the grid-side impedance to the source-side impedance is used as the source-grid impedance ratio.

[0035] Optionally, after completing the equivalent transformation of the network structure, the network impedance is further aggregated sequentially. Following the branching paths of nodes within the distribution area, starting from the last renewable energy cluster, the impedance of each inverter is connected in series with its connected line impedance, and parallel aggregation calculations are performed on each parallel feed-in branch. First, the local ring network is simplified, and the aggregated impedance components are calculated sequentially, ultimately yielding the system-level aggregated impedance containing the characteristics of all inverter clusters. This aggregated impedance is then combined with the grid equivalent impedance simplified to a pure inductance model to calculate the source-grid impedance ratio, reflecting the global characteristics of the system. This embodiment uses this as the basis for judging whether the grid-connected system can operate stably. By simplifying and then aggregating the complex transmission network, the overall impedance-frequency characteristics of a multi-node, multi-feed-in system under complex topological constraints can be accurately described, providing a crucial model foundation for the subsequent accurate characterization of the oscillation safety domain based on phase margin.

[0036] Specifically, after completing the equivalent transformation from a polygonal complex network to a ray network, they are then aggregated sequentially. The specific system impedance is obtained by simplifying and calculating the inverter impedance and network impedance, taking the IEEE 9-node dual-feed structure as an example: First, the system-level aggregated impedance is obtained by aggregating the impedance models of the target distribution network and the grid-connected inverters. The target distribution area network and inverter impedance diagram are shown below. Figure 7 As shown. First, the ring network is simplified, and then the simplified network is aggregated step by step. The result is as follows. Figure 8 As shown.

[0037] in, Represents line impedance. Represents the inverter impedance, then , , The value of is shown in the following formula, that is: By calculating the series and parallel impedances, the system-level aggregate impedance can be obtained. ,Right now: in, , All are polymer impedances, reference Figure 8 , The polymerization impedance is shown on the left side. This represents the polymerization impedance on the right side.

[0038] Then, the grid-side equivalent impedance model mainly consists of the leakage inductance of transmission lines and transformers. Its resistive component is usually much smaller than its inductive reactance component. Therefore, in the analysis, the grid side is simplified to a pure inductive model, that is: in, The system angular frequency, This is the equivalent inductance on the grid side.

[0039] Then refer to Figure 9 As shown, the source-to-network impedance ratio is: In this embodiment, the inverter impedance of each feed node is series-aggregated with the corresponding line impedance, which perfectly matches the topological characteristics of the radial network. This avoids the result deviation caused by ignoring the line impedance in traditional impedance calculations, and significantly improves the accuracy of the source-network impedance ratio calculation.

[0040] In step 103, the source-network impedance ratio is input into the constructed global proxy model, and the phase margin of the system at the cross-frequency is output. The global proxy model is constructed based on the non-intrusive spectral projection polynomial chaotic expansion method.

[0041] In this embodiment, the concept of an oscillation-safe operating domain is introduced. A non-intrusive spectral projection polynomial chaos expansion (NISP-PCE) method is used to construct a global proxy model of the phase margin with respect to the feed power of each node. That is, in Hilbert space, the power random variable with finite second moments is projected onto a basis composed of Legendre orthogonal basis functions. The spectral projection calculation of the expansion coefficients is completed by Gauss-Legendre integration. Thus, the time-consuming frequency domain traversal and frequency sweeping process is replaced by explicit analytical polynomials, realizing a fast and accurate characterization of the boundary of the oscillation-safe operating domain in multidimensional parameter space in milliseconds, and then outputting the phase margin of the system at the crossing frequency.

[0042] The global proxy model is constructed as follows: First, it is assumed that the power of each feed node follows a uniform distribution within a given range. Then, the power variables of the original physical interval are mapped to the standard interval through equal probability transformation. The input variables are standard random variables. Following the Wiener-Askey scheme, Legendre polynomials are chosen as orthogonal basis functions for input variables following a uniform distribution, and the tensor product of univariate polynomials in each dimension is used to construct multivariate basis functions for the multidimensional system. For coefficient solving, the spectral projection principle of NISP technology is used, leveraging the orthogonality of the basis functions to transform the complex frequency domain physical model solution process into Gauss-Legendre discrete summation operations, thus avoiding the need for differentiation or intrusive modifications to the physical model. By calling the refined impedance model on the tensor network's quadrature nodes to obtain the system response, PCE expansion coefficients can be quickly extracted with a very small number of samples, constructing a global analytical mapping proxy model for the phase margin. This improvement significantly outperforms traditional point-by-point traversal scanning or simulation methods, not only drastically reducing the time for a single stability assessment from seconds to milliseconds, effectively solving the pain points of computational time consumption and low efficiency under massive operating conditions, but also directly outputting high-order boundary analytical expressions with the feed power of each node as independent variables. Furthermore, based on the global proxy model coefficients, the embodiments of this application can also analyze and calculate the sensitivity index of each feed node, thereby quantitatively identifying the core critical nodes that affect the stability of the system, which greatly improves the description accuracy, visualization effect, and ease of application in actual engineering scheduling of the safe operation domain boundary in the multi-dimensional parameter space.

[0043] Specifically, polynomial chaotic expansion constructs a random space using polynomial basis functions and leverages the orthogonality of orthogonal polynomials to establish a proxy model for the mapping process from random variable input to response. The aim is to replace the original relationship between phase margin and power. This method represents the system's phase margin as a linear combination of a set of orthogonal basis functions: in, For phase margin, For the input standard random variable, To map to standard intervals The power input of each cluster within the system.

[0044] for Dimensional system, if the maximum number of times is The full expansion, the number of basis functions It grows exponentially with increasing dimensionality: The input standard random variables are mapped to a standard interval by an equal probability transformation of the power variables of each node. Standard random variables within : in, For feed node power, This is the lower limit of the feed power. This represents the upper limit of the feed power.

[0045] In the design, the input variable is the feed power of each node, which follows a uniform distribution. Therefore, according to the Wiener-Askey scheme, Legendre polynomials are chosen as the orthogonal basis functions, i.e.: in, For Legendre polynomials.

[0046] Based on the selected sequence of basis functions, for multidimensional variables, their multivariate basis functions are constructed through the univariate polynomial tensor product of each dimension: By utilizing the orthogonality of basis functions, in Hilbert space, Take the inner product of both sides with the basis function of the specific term you want to obtain, that is: According to the definition of orthogonality, when At that time, inner product Therefore, only the right side of formula (34) remains. The terms, namely: Therefore, the formula for calculating the expansion coefficient is: in, This is the squared norm of the basis functions, which is 1 for an orthonormal basis.

[0047] However, in practical applications, it is difficult to calculate analytical integrals, so numerical integration must be used for approximation. Therefore, the above continuous integral is transformed into a discrete summation using Gaussian integration, and Legendre polynomials are chosen as orthogonal basis functions, hence the choice of Gauss-Legendre integration. The multidimensional integral is transformed into a weighted summation of discrete points: in, , These are the Gaussian integral nodes and their corresponding weights. The set of all nodes. The order of the nodes.

[0048] The multivariate basis functions obtained at this point and expansion coefficient Substituting back into equation (38), we obtain the global proxy model of the phase margin with respect to the power of each node, namely: After outputting the phase margin, a phase margin greater than zero is used as the stability criterion. The expression for the stability criterion is: in, The intersection of the source and network impedance amplitude-frequency characteristics corresponds to the crossover frequency of the impedance ratio amplitude. This represents the phase margin.

[0049] Since the system impedance model differs under different operating conditions, frequency domain calculations need to be performed again. Furthermore, calculating the phase margin at the cross-frequency is quite complex, involving logarithmic and complex number operations. In contrast, the advantage of using a global proxy model in this application is that the global proxy model is a polynomial of the phase margin with respect to the power of each node. When analyzing different operating conditions, it is only necessary to substitute the operating condition into the proxy model, without performing the aforementioned complex calculations.

[0050] In step 104, based on the phase margin, the sensitivity index of each feed node in the target area is calculated, and based on the sensitivity index of each feed node, the target key nodes affecting the stability of the system are quantitatively identified.

[0051] In this embodiment, the analytical characteristics of the global proxy model are fully utilized, and the first-order sensitivity index of the power of each feed node is directly calculated analytically through the model expansion coefficients. According to the principle of variance decomposition, this index is characterized as the ratio of the sum of squares of the coefficients corresponding to the basis function index of only a single variable to the total variance of the system. This allows for the quantification of the contribution of independent power changes of each node to the system phase margin fluctuation, and accurate identification of the core critical nodes that play a dominant role in the stability of the transformer area oscillation.

[0052] The sensitivity index of each feed node in the target area is calculated using the first formula: in, For the first Sensitivity index of each feed node For only containing the first A set of basis function indices for each feed node. To satisfy the orthogonality of the first multivariate basis functions of order 1 For the first order expansion coefficients, The number of basis functions. This represents the sequence number. The larger this sensitivity index, the greater the impact of power changes at the feed node on system stability.

[0053] In step 105, with the optimization objective of maximizing the generalized volume of the multidimensional safe operation domain, the control parameters of the grid-connected inverters corresponding to the target key nodes are coordinated and tuned to improve the operating safety domain of the target transformer area.

[0054] In this embodiment, with the goal of maximizing the generalized volume of the multidimensional safe operating domain, the particle swarm optimization algorithm guides the coordinated tuning of the control parameters of the grid-type inverter, thereby improving the target area's potential for absorbing new energy and the system's safe and stable operation level.

[0055] In this embodiment, the generalized volume of the safe operating domain is represented by large-scale Monte Carlo random sampling across the full power space and rapid prediction of phase margin using a global surrogate model. The volume is approximated by the proportion of sampling points with a phase margin greater than or equal to a preset stability threshold. For identified high-sensitivity critical nodes, this embodiment prioritizes the use of particle swarm optimization (PSO) to collaboratively tune the control loop parameters of the grid-connected inverter, optimizing its output impedance characteristics and improving system stability margin. This fundamentally broadens the boundary for the absorption of renewable energy power in the distribution area, achieving a technological leap from traditional passive stability assessment to active safety enhancement, and providing effective mathematical support and engineering decision-making basis for the safety analysis and operation optimization of complex distribution areas.

[0056] The objective function, which aims to maximize the generalized volume of the multidimensional safe operating domain, is as follows: in, The generalized volume of the safe operating domain of the system under control parameters. This represents the number of Monte Carlo random sampling points across the full power domain. For the first Subsampled multi-cluster power injection vector The phase margin threshold for stable system operation. For indicator functions, For phase margin, To determine the upper limit of the physical feasible domain for the control parameters of the grid-connected inverter, This is the lower limit of the physical feasible domain for the control parameters of the grid-connected inverter.

[0057] To verify the feasibility of the embodiments of this application, Figure 10 The IEEE 9-node system shown is Figure 11The two-dimensional oscillation safe operating domain is demonstrated. Nodes 2 and 3 are selected as renewable energy feed-in nodes, with their power feed-in range set to 40kW to 120kW. This embodiment uses a phase margin of zero under the impedance ratio criterion as the critical condition for stable system operation. A global proxy model is used to perform millisecond-level rapid scanning across the full power operating space to characterize the safety boundary. Figure 11 In the Cartesian coordinate system, the black solid line represents the boundary of stable operation. The blue area above and to the left of the line contains all the operating points that meet the stability requirements, while the red area outside the boundary represents the instability risk zone where the system cannot operate stably.

[0058] For more general multi-feed scenarios, such as Figure 12-17 As shown, this embodiment demonstrates a IEEE 13-node four-feed system (e.g., Figure 18 The results of the multidimensional safe operating domain characterization are presented. Since the system contains four feed nodes (node ​​4, node 9, node 10 and node 13), its safe operating domain is in a four-dimensional parameter space. By fixing the feed power of two of the nodes and selecting the other two nodes as independent variables, six sets of representative two-dimensional operating cross-sectional diagrams were created for the high-dimensional safe domain.

[0059] The six cross-sectional diagrams clearly demonstrate that the system's stability region exhibits a significant nonlinear shift trend with changes in the power distribution among different nodes. Under the impedance interaction of a complex multi-feed network, system stability depends not only on the total power but also profoundly on the power allocation ratio of each cluster. Example results show that this embodiment takes only 2.1 seconds to compute on the IEEE 13-node system, a 2460.7% improvement in computational efficiency compared to the 71.8 seconds of the traditional traversal method. Simultaneously, the global proxy model exhibits extremely high fitting accuracy. It reaches 0.999286, with a root mean square error of only 0.100239 degrees.

[0060] After quantitatively identifying the target critical nodes that play a dominant role in system stability, and using the maximization of the generalized volume of the safety region as the objective function, the phase-locked loop proportional coefficients of the control parameters of the target critical nodes are optimized using the particle swarm optimization algorithm. and current loop proportionality coefficient Perform global collaborative optimization. For example... Figure 19 As shown, the optimized safety domain coverage is significantly expanded, and the phase margin across the entire domain is significantly improved, with the phase margin across the entire power domain being elevated above the safety threshold. This not only broadens the safe absorption boundary for high-proportion renewable energy in complex distribution areas but also enhances the renewable energy carrying capacity and operational stability of the distribution areas.

[0061] This application provides a method for enhancing the operational safety domain of a transformer substation. By constructing an impedance model of the grid-connected inverter and calculating the source-grid impedance ratio using an equivalent network, this method can accurately locate weak points in the substation's stability, fundamentally avoiding the problem of "blindly modifying" traditional governance methods and significantly improving the operational stability of the substation. In addition, a global proxy model built based on the non-intrusive spectral projection polynomial chaotic expansion method can quickly output phase margin and calculate node sensitivity, accurately identifying core nodes affecting system stability without complex simulations, thus reducing the cost of analysis and computing power. Simultaneously, by coordinating the tuning of inverter control parameters with the goal of maximizing the generalized volume of the multidimensional safe operation domain, the safe operation boundary of the substation can be significantly broadened without adding large-scale hardware investment, adapting to scenarios with high proportions of distributed photovoltaic and charging pile access, reducing the probability of oscillation faults such as voltage over-limit and inverter grid disconnection, and improving the operational stability and voltage qualification level of the substation.

[0062] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0063] The following are device embodiments of this application. For details not described in detail, please refer to the corresponding method embodiments described above.

[0064] Figure 20 A schematic diagram of the structure of the transformer area operation safety zone lifting device provided in an embodiment of this application is shown. For ease of explanation, only the parts related to the embodiment of this application are shown, and are described in detail below: like Figure 20 As shown, the transformer area operation safety zone enhancement device 20 includes: Model building module 201 is used to build the impedance model of the grid-connected inverter in the target distribution area; Impedance ratio calculation module 202 is used to transform the polygonal network of the target transformer area into an equivalent ray network, and calculate the source-grid impedance ratio based on the equivalent ray network and the impedance model of the grid-type inverter. The margin determination module 203 is used to input the source-network impedance ratio into the constructed global proxy model and output the phase margin of the system at the cross frequency. The global proxy model is constructed based on the non-intrusive spectral projection polynomial chaotic expansion method. The node determination module 204 is used to calculate the sensitivity index of each feed node in the target area based on the phase margin, and to quantitatively identify the target key nodes that affect the stability of the system based on the sensitivity index of each feed node. The collaborative tuning module 205 is used to collaboratively tune the control parameters of the grid-connected inverter corresponding to the target key node with the optimization objective of maximizing the generalized volume of the multidimensional safe operating domain, so as to improve the operating safety domain of the target area.

[0065] This application provides a device for enhancing the safety domain of a transformer substation. By constructing an impedance model of the grid-connected inverter and calculating the source-grid impedance ratio using an equivalent network, this device can accurately locate weak points in the substation's stability, fundamentally avoiding the problem of "blindly modifying" traditional governance methods and significantly improving the operational stability of the substation. In addition, a global proxy model built using the non-intrusive spectral projection polynomial chaotic expansion method can quickly output phase margin and calculate node sensitivity, accurately identifying core nodes affecting system stability without complex simulations, thus reducing the cost of analysis and computing power. Simultaneously, by coordinating the tuning of inverter control parameters with the goal of maximizing the generalized volume of the multidimensional safe operation domain, the safe operation boundary of the substation can be significantly broadened without adding large-scale hardware investment, adapting to scenarios with high proportions of distributed photovoltaic and charging pile access, reducing the probability of oscillation faults such as voltage over-limit and inverter grid disconnection, and improving the operational stability and voltage qualification level of the substation.

[0066] In one possible implementation, the model building module can be used for: Obtain the grid connection point sampling voltage collected by the phase-locked loop of the grid-connected inverter in the target area; The sampling voltage at the grid connection point is decomposed by an initial coordinate transformation based on the fundamental frequency phase-locked angle to obtain the steady-state reference voltage component without phase disturbance. The steady-state reference voltage component with superimposed perturbation phase angle is decomposed by a quadratic coordinate transformation based on the perturbation phase angle, and the perturbation voltage component containing phase perturbation coupling characteristics is obtained. By combining the main circuit equations and the full-link control transfer function corresponding to the steady-state reference voltage component and the disturbance voltage component, the impedance model of the grid-connected inverter is derived.

[0067] In one possible implementation, the impedance model's analytical expression is: in, This is the analytical expression for the impedance model. For the Laplace operator, DC input voltage For the filter inductor on the grid-connected inverter side, For grid-side filter inductors, For the filter capacitor on the grid-connected inverter side, This is the parasitic resistance of the capacitor. For controller gain, This is the peak value of the fundamental current. The fundamental current angular frequency, The phase of the fundamental current. For voltage feedforward coefficients, This is the transfer function of the PI controller. Let be the equivalent transfer function of the current sampling delay stage. Let be the equivalent transfer function of the voltage sampling delay stage. The current decoupling coefficient is... The fundamental peak value of the response voltage at the disturbance frequency. This is the small-signal linearized transfer function for the phase-locked loop.

[0068] In one possible implementation, the impedance ratio calculation module can be used for: Establish an equivalent transformation matrix based on the node current balance relationship; By using the network current flowing into each feed node in the target area as input to the equivalent transformation matrix, the polygonal network of the target area is equivalently transformed into a radial network.

[0069] In one possible implementation, the impedance ratio calculation module can also be used for: The impedance model of each feed-in node in the target area and the grid inverter is connected in series with the line impedance in the corresponding ray network to obtain the aggregated impedance components of each feed-in node. Following the rule of progressively pushing from the end of the renewable energy cluster in the distribution area to the preset grid reference node, the impedance components of all feed-in nodes are aggregated to obtain the system-level aggregated impedance, and the system-level aggregated impedance is used as the source-side impedance. The ratio of the grid-side impedance to the source-side impedance is used as the source-grid impedance ratio.

[0070] In one possible implementation, the node determination module can be used to: The sensitivity index of each feed node in the target area is calculated using the first formula, which is: in, For the first Sensitivity index of each feed node For only containing the first A set of basis function indices for each feed node. To satisfy the orthogonality of the first multivariate basis functions of order 1 For the first order expansion coefficients, The number of basis functions. is the sequence number.

[0071] In one possible implementation, the objective function for maximizing the generalized volume of the multidimensional safe operating domain is: in, The generalized volume of the safe operating domain of the system under control parameters. This represents the number of Monte Carlo random sampling points across the full power domain. For the first Subsampled multi-cluster power injection vector The phase margin threshold for stable system operation. For indicator functions, For phase margin, To determine the upper limit of the physical feasible domain for the control parameters of the grid-connected inverter, This is the lower limit of the physical feasible domain for the control parameters of the grid-connected inverter.

[0072] Figure 21 This is a schematic diagram of the terminal provided in an embodiment of this application. For example... Figure 21 As shown, the terminal 21 in this embodiment includes: a processor 210, a memory 211, and a computer program 212 stored in the memory 211 and executable on the processor 210. When the processor 210 executes the computer program 212, it implements the steps in the above embodiments of the various station area operation security domain enhancement methods, for example... Figure 1 Steps 101 to 105 are shown. Alternatively, when the processor 210 executes the computer program 212, it implements the functions of each module / unit in the above-described device embodiments, for example... Figure 20 The functions of each module are shown.

[0073] For example, the computer program 212 can be divided into one or more modules / units, which are stored in the memory 211 and executed by the processor 210 to complete this application. The one or more modules / units can be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the computer program 212 in the terminal 21. For example, the computer program 212 can be divided into... Figure 20 The modules shown.

[0074] The terminal 21 may be a computing device such as a desktop computer, laptop, handheld computer, or cloud server. The terminal 21 may include, but is not limited to, a processor 210 and a memory 211. Those skilled in the art will understand that... Figure 21 This is merely an example of terminal 21 and does not constitute a limitation on terminal 21. It may include more or fewer components than shown, or combine certain components, or different components. For example, the terminal may also include input / output devices, network access devices, buses, etc.

[0075] The processor 210 may be a central processing unit (CPU), or other general-purpose processors, 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.

[0076] The memory 211 can be an internal storage unit of the terminal 21, such as a hard disk or memory of the terminal 21. The memory 211 can also be an external storage device of the terminal 21, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc., equipped on the terminal 21. Furthermore, the memory 211 can include both internal storage units and external storage devices of the terminal 21. The memory 211 is used to store the computer program and other programs and data required by the terminal. The memory 211 can also be used to temporarily store data that has been output or will be output.

[0077] 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.

[0078] 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.

[0079] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein 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 implementation should not be considered beyond the scope of this application.

[0080] In the embodiments provided in this application, 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 displayed or discussed mutual coupling or direct coupling or communication connection may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0081] 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.

[0082] Furthermore, the functional units in the various embodiments of this application 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.

[0083] 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 above-described embodiments 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 above-described embodiments of the security domain elevation method for each operating area. 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.

[0084] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for enhancing the operational security domain of a transformer substation, characterized in that, include: Construct impedance models for grid-connected inverters in the target distribution area; The polygonal network of the target transformer area is equivalently transformed into a ray network, and the source-to-grid impedance ratio is calculated based on the equivalent ray network and the impedance model of the grid-type inverter. The source-network impedance ratio is input into the constructed global proxy model, and the phase margin of the system at the cross-frequency is output. The global proxy model is constructed based on the non-intrusive spectral projection polynomial chaotic expansion method. Based on the phase margin, the sensitivity index of each feed node in the target area is calculated, and based on the sensitivity index of each feed node, the target key nodes affecting system stability are quantitatively identified. With the goal of maximizing the generalized volume of the multidimensional safe operation domain, the control parameters of the grid-connected inverters corresponding to the key nodes of the target are coordinated and tuned to improve the operating safety domain of the target transformer area.

2. The method for enhancing the operational security domain of a transformer substation according to claim 1, characterized in that, The impedance model of the grid-connected inverter in the target distribution area includes: Obtain the grid connection point sampling voltage collected by the phase-locked loop of the grid-connected inverter in the target transformer area; The sampling voltage at the grid connection point is decomposed by an initial coordinate transformation based on the fundamental frequency phase-locked angle to obtain a steady-state reference voltage component without phase disturbance. The steady-state reference voltage component with superimposed perturbation phase angle is decomposed by a quadratic coordinate transformation based on the perturbation phase angle to separate the perturbation voltage component containing phase perturbation coupling characteristics. By combining the main circuit equations and the full-link control transfer function corresponding to the steady-state reference voltage component and the disturbance voltage component, the impedance model of the grid-connected inverter is derived.

3. The method for enhancing the operational safety domain of a transformer substation according to claim 2, characterized in that, The impedance analytical expression of the impedance model is: in, This is the analytical expression for the impedance model. For the Laplace operator, DC input voltage, For the filter inductor on the grid-connected inverter side, For grid-side filter inductors, For the filter capacitor on the grid-connected inverter side, This is the parasitic resistance of the capacitor. For controller gain, This is the peak value of the fundamental current. The fundamental current angular frequency, The phase of the fundamental current. For voltage feedforward coefficients, This is the transfer function of the PI controller. Let be the equivalent transfer function of the current sampling delay stage. Let be the equivalent transfer function of the voltage sampling delay stage. The current decoupling coefficient is... The fundamental peak value of the response voltage at the disturbance frequency. This is the small-signal linearized transfer function for the phase-locked loop.

4. The method for enhancing the operational security domain of a transformer substation according to claim 1, characterized in that, The process of transforming the polygonal network of the target station area into an equivalent radial network includes: Establish an equivalent transformation matrix based on the node current balance relationship; By using the network current flowing into each feed node in the target area as input to the equivalent transformation matrix, the polygonal network of the target area is equivalently transformed into the radial network.

5. The method for enhancing the operational security domain of a transformer substation according to claim 1, characterized in that, The source-grid impedance ratio is calculated based on the impedance model of the equivalent ray network and the grid-type inverter, including: The impedance model of each feed node and the grid inverter in the target area is connected in series with the line impedance in the corresponding ray network to obtain the aggregated impedance components of each feed node. Following the rule of progressively pushing from the end of the new energy cluster in the distribution area to the preset grid reference node, the impedance components of all feed-in nodes are aggregated to obtain the system-level aggregated impedance, and the system-level aggregated impedance is used as the source-side impedance. The ratio of the grid-side impedance to the source-side impedance is used as the source-grid impedance ratio.

6. The method for enhancing the operational security domain of a transformer substation according to claim 1, characterized in that, The step of calculating the sensitivity index of each feed node in the target area based on the phase margin includes: The sensitivity index of each feed node in the target area is calculated using the first formula, which is: in, For the first Sensitivity index of each feed node For only containing the first A set of basis function indices for each feed node. To satisfy the orthogonality of the first multivariate basis functions of order 1 For the first order expansion coefficients, The number of basis functions. is the sequence number.

7. The method for enhancing the operational security domain of a transformer substation according to claim 1, characterized in that, The objective function that optimizes by maximizing the generalized volume of the multidimensional safe operating domain is: in, The generalized volume of the safe operating domain of the system under control parameters. This represents the number of Monte Carlo random sampling points across the full power domain. For the first Subsampled multi-cluster power injection vector The phase margin threshold for stable system operation. For indicator functions, For the phase margin, To determine the upper limit of the physical feasible domain for the control parameters of the grid-connected inverter, This is the lower limit of the physical feasible domain for the control parameters of the grid-connected inverter.

8. A device for raising the safety zone of a transformer substation, characterized in that, include: The model building module is used to build impedance models of grid-connected inverters in the target distribution area. The impedance ratio calculation module is used to transform the polygonal network of the target transformer area into an equivalent ray network, and calculate the source-grid impedance ratio based on the equivalent ray network and the impedance model of the grid-type inverter. The margin determination module is used to input the source-network impedance ratio into the constructed global proxy model and output the phase margin of the system at the cross-frequency. The global proxy model is constructed based on the non-intrusive spectral projection polynomial chaotic expansion method. The node determination module is used to calculate the sensitivity index of each feed node in the target area based on the phase margin, and to quantitatively identify the target key nodes that affect the stability of the system based on the sensitivity index of each feed node. The collaborative tuning module is used to collaboratively tune the control parameters of the grid-connected inverter corresponding to the target key node with the optimization objective of maximizing the generalized volume of the multidimensional safe operating domain, so as to improve the operating safety domain of the target area.

9. A terminal, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the area operation security domain enhancement method as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the area operation security domain elevation method as described in any one of claims 1 to 7.

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