Virtual inertia double-layer planning method and system considering node frequency safety constraint

Abstract

The application discloses a virtual inertia double-layer planning method and system considering node frequency safety constraints, and belongs to the technical field of power system operation optimization; the method comprises the following steps: firstly, a reduced-order node frequency model is constructed by reserving the dynamic state of the power generation side, and virtual resources on the load side are equivalently mapped to the frequency coordinate; secondly, a vulnerability index is extracted based on the node frequency analytical response in the upper-layer planning, and candidate sites are screened in combination with the safety improvement effect; thirdly, a model containing unit commitment, power flow and virtual inertia configuration is established in the lower-layer operation optimization, linear safety constraints are constructed by using the first-order Taylor expansion of the node frequency response at the reference point, and the safety constraints are solved; finally, a global optimal configuration scheme is output by means of analytical response closed-loop review and working point iteration update. The method realizes deep coupling of the node frequency dynamic safety requirement and the siting and sizing decision, and effectively balances the solution efficiency and the physical checking precision of a complex system.

Description

Technical Field

[0001] This invention belongs to the field of power system operation optimization technology, specifically involving a virtual inertia bi-level planning method and system that considers node frequency security constraints. Background Technology

[0002] With the increasing proportion of new energy grid connection, the system's equivalent rotating inertia is decreasing, electromechanical transient response is accelerating, and node frequency differences are intensifying. Traditional safety assessment methods based on the system center frequency or a single representative node frequency are insufficient to accurately reflect the spatial heterogeneity frequency risks after disturbances. Existing technologies employ two approaches: one analyzes the overall system frequency variation based on frequency response models; the other introduces the concept of node frequency to describe the local frequency differences between different nodes after disturbances. However, existing node frequency analysis research largely focuses on frequency response decomposition, risk identification, or dynamic characteristic analysis, lacking a systematic approach that can be directly embedded in the planning and optimization process while simultaneously considering site selection, capacity determination, and operational scheduling.

[0003] On the other hand, virtual inertia, as an important technical means to improve the frequency support capability of new energy power systems, typically involves the following coupled challenges in its planning: First, the location and capacity of virtual inertia configuration directly change the frequency dynamic model; second, the constraint of the lowest node frequency essentially involves time-domain extremum calculations, making it difficult to directly incorporate into the optimization model; third, if network constraints, unit reserve, and operating costs are considered simultaneously, planning and operation exhibit obvious dual-layer coupling characteristics. Directly using nonlinear dynamic frequency constraints for solving results in high computational complexity and is difficult to implement in large-scale systems.

[0004] Therefore, there is an urgent need to propose a new technical solution that, while retaining the spatial resolution capability of the node frequency analytical model, transforms it into a solvable planning framework that can be embedded in virtual inertia location, sizing, and operational optimization, thereby realizing virtual inertia planning and configuration under node frequency security constraints. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a virtual inertia bilayer planning method and system that considers node frequency security constraints, thereby solving the problems in existing technologies.

[0006] The objective of this invention can be achieved through the following technical solutions: A two-level virtual inertia planning method considering node frequency security constraints includes the following steps: S1. Obtain the network and equipment operating parameters of the power system, take the phase angle, frequency and regulation status of the synchronous generation unit as the reserved state, and map the virtual inertia and virtual damping configured on the candidate nodes on the load side to the reserved frequency coordinates formed by the reserved state to construct a node frequency order reduction dynamic model. S2, calculate the node frequency analytical response based on the node frequency reduction dynamic model and extract the node vulnerability characterization quantity accordingly. Combine the security improvement effect after applying trial configuration capacity to each candidate node, perform weighted scoring and screening on the candidate nodes to generate a candidate site set. S3, perform a site combination search within the candidate site set, and use each site combination as a fixed site selection scheme for the upper-level planning; S4. For each of the fixed location schemes, establish a lower-level operation optimization model that includes unit combination scheduling; extract key nodes and key sampling times within a preset time window after the disturbance, and at the initially set or iteratively updated reference operating point, perform a first-order Taylor expansion on the node frequency response of the key nodes at the key sampling time by calculating sensitivity, construct linearized node frequency safety constraints, and embed them into the lower-level operation optimization model for solution, to obtain the virtual inertia capacity and virtual damping capacity corresponding to the fixed location scheme; S5, calculate the actual node frequency analytical response using the node frequency reduced-order dynamic model, and substitute the virtual inertia capacity and virtual damping capacity into the safety constraint verification; if the residual does not meet the preset convergence condition, update the current solution capacity to the new reference working point and return to S4 iteration until the convergence condition is met, and output the global optimal configuration scheme.

[0007] Furthermore, the process of constructing a dynamic model for reducing the order of node frequencies includes: The phase angle, frequency, and adjustment state are combined into a reduced-order preserved state vector; Using the original inertia matrix and original damping matrix of the power system, combined with the equivalent inertia increment matrix and equivalent damping increment matrix formed by the virtual resource configuration vector on the candidate node, the equivalent inertia matrix and equivalent damping matrix in the node-preserved frequency coordinate system are calculated. The coefficient matrix of the state-space equation is constructed based on the equivalent inertia matrix, equivalent damping matrix, primary frequency modulation gain matrix, and adjustment time constant matrix. The mathematical mapping relationship between the load node frequency and the reduced-order retained state vector is established through the frequency recovery matrix.

[0008] Furthermore, the process of weighted scoring and filtering of the candidate nodes includes: The minimum frequency deviation, initial frequency change rate, and complex modal local component coefficients of each candidate node are calculated separately, and after normalization, they are aggregated to generate the vulnerability index of each candidate node. A trial configuration capacity, including trial virtual inertia and trial virtual damping, is applied to the candidate node, and the difference in system safety pressure before and after the application is calculated to construct an effectiveness index. The vulnerability index and the effectiveness index are added together according to the set weight coefficients to obtain a comprehensive score. The nodes that meet the maximum number of websites constraint are selected in descending order of the comprehensive score to form the candidate site set.

[0009] Furthermore, the process of extracting key nodes and key sampling moments includes: From the node frequency analysis response, select at least one of the following: the node with the largest deviation of the lowest frequency point, the node with the largest local component index, the node where the disturbance source is located, and the node with the farthest electrical distance from the disturbance source, to form the key node set; and on the transient drop curve after the disturbance corresponding to the key node, extract discrete points according to a preset time step to form the key sampling time set.

[0010] Furthermore, the process of constructing linearized node frequency security constraints includes: At the current reference operating point, the finite difference method is used to calculate the first partial derivative of the node frequency response of the key node with respect to the virtual inertia capacity and the second partial derivative with respect to the virtual damping capacity. Using the first and second partial derivatives as sensitivity coefficients, the nonlinear minimum frequency constraint, which includes time-domain minimum value calculation, is transformed into a linear inequality constraint with virtual inertia increment and virtual damping increment as independent variables.

[0011] Furthermore, the objective function of the lower-level operational optimization model is: in, The lower-level optimization objective function is to minimize the total cost. It is a collection of power generation units. For the active power output of power generation unit g, This is the reserve capacity of power generation unit g. and Sites i The virtual inertia capacity and virtual damping capacity, , , and These are the corresponding cost coefficients. This refers to the combination of sites corresponding to a fixed site selection scheme.

[0012] Furthermore, the process of calculating the true node frequency analytical response using the aforementioned node frequency reduced-order dynamic model includes: Modal decomposition is performed on the state-space equations of the node frequency reduced-order dynamic model to obtain an analytical response kernel function containing system modal eigenvalues. The analytical response kernel function is used to calculate the actual minimum frequency and actual initial frequency change rate of all nodes under the current solution capacity; Determine whether the difference between the actual minimum frequency and the frequency safety lower limit for all nodes is greater than or equal to the negative frequency tolerance error, and determine whether the difference between the absolute value of the actual initial frequency change rate and the limit is less than or equal to the change rate tolerance error.

[0013] Furthermore, before outputting the globally optimal configuration, the following steps are also included: For all the fixed location schemes that passed the review, calculate the overall objective function of the upper layer: in, This represents the overall objective function value at the upper level. For the candidate site set, For site location variables, To fix construction costs, and These represent the unit capacity costs of virtual inertia and virtual damping, respectively. For the configured virtual inertia capacity, The virtual damping capacity is configured; The fixed addressing scheme with the minimum overall objective function value of the upper layer is selected as the global optimal configuration scheme and output.

[0014] For a virtual inertia bi-level programming system considering node frequency security constraints, the above method is implemented, including: The reduced-order mapping module is used to obtain the network and equipment operating parameters of the power system, take the phase angle, frequency and regulation status of the synchronous generation unit as the reserved state, and map the virtual inertia and virtual damping configured on the load-side candidate nodes to the reserved frequency coordinates formed by the reserved state to construct a node frequency reduced-order dynamic model. The scoring and filtering module is used to calculate the node frequency analytical response based on the node frequency reduction dynamic model and extract the node vulnerability characterization quantity accordingly. It combines the security improvement effect after applying trial configuration capacity to each candidate node to generate a set of candidate sites by weighting and filtering the candidate nodes. Upper-level planning module: used to perform site combination search within the candidate site set, and use each site combination as a fixed site selection scheme for upper-level planning; The lower-level solution module is used to establish a lower-level operation optimization model including unit combination scheduling for each of the fixed location schemes; extract key nodes and key sampling times within a preset time window after the disturbance, and at the initially set or iteratively updated reference operating point, perform a first-order Taylor expansion on the node frequency response of the key nodes at the key sampling time by calculating sensitivity, construct linearized node frequency safety constraints, and embed them into the lower-level operation optimization model for solution, to obtain the virtual inertia capacity and virtual damping capacity corresponding to the fixed location scheme; Closed-loop iteration module: used to calculate the real node frequency analytical response using the node frequency reduced-order dynamic model, and substitute the virtual inertia capacity and virtual damping capacity into the safety constraint verification; if the residual does not meet the preset convergence condition, the current solution capacity is updated to a new reference working point and returned to the lower-level solution module for iteration until the convergence condition is met, and then the globally optimal configuration scheme is output.

[0015] An electronic device includes: a processor, a memory, a communication interface, and a communication bus, wherein the processor, the memory, and the communication interface communicate with each other through the communication bus; The memory is used to store at least one executable instruction that causes the processor to perform operations corresponding to the virtual inertia bi-level planning method that considers node frequency security constraints as described above.

[0016] The beneficial effects of this invention are: 1. This invention constructs a node frequency reduced-order dynamic model, retaining only the phase angle, frequency, and regulation state of the synchronous generation unit, and equivalently mapping the virtual inertia and virtual damping configured on the load side to the retained frequency coordinates through matrix transformation. This reduced-order mapping mechanism preserves the spatial distribution characteristics of each node frequency in the underlying model while reducing the computational load of directly solving the full-dimensional system dynamic differential-algebraic equations. This effectively solves the problems of traditional safety assessment methods based on a single center frequency failing to accurately reflect the spatial heterogeneity frequency risk after disturbance, and the high computational complexity of directly using nonlinear dynamic models for solution.

[0017] 2. This invention extracts key nodes and key sampling moments within a preset time window after disturbance, and performs a first-order Taylor expansion of the node frequency response by calculating sensitivity at a set reference operating point to construct linearized node frequency safety constraints, which are then embedded into the lower-level operational optimization model. By using key point sampling combined with first-order linearization, the non-convex constraints that originally belonged to the dynamic differential domain are transformed into algebraic inequality constraints that can be directly identified and processed by conventional operations research optimization solvers (such as linear planners). This breaks through the technical bottleneck that "the node frequency minimum point constraint essentially involves time domain extremum operations and is difficult to directly write into the optimization model," and breaks down the mathematical barrier between dynamic safety and steady-state optimization.

[0018] 3. In the upper-level planning stage, this invention introduces a vulnerability representation quantity extracted based on the node frequency analysis response, and generates a comprehensive score by combining the security improvement effect after trial configuration. Based on this, a candidate site set is selected and a site combination search is performed. This invention does not allow all nodes to blindly participate in the combination optimization, but rather identifies the weak nodes that are most sensitive to frequency and have high governance benefits in advance. This effectively reduces the combination search space of the upper-level site selection problem, shortens the optimization path, and improves the engineering solvability of the planning algorithm under complex large power grid systems.

[0019] 4. This invention designs a closed-loop verification iteration mechanism, which uses a reduced-order dynamic model to calculate the actual node frequency analytical response and substitutes the virtual resource capacity obtained from the lower-level solution into it for residual verification. If the convergence condition is not met, the reference operating point is updated and the iteration is restarted. This mechanism of sequential linearization (SLP) combined with real kernel function verification not only takes advantage of the fast solution speed of the linearized model, but also compensates for the high-order truncation error caused by Taylor expansion through the closed-loop verification of physical response constraints, ensuring that the final output planning scheme can effectively meet the frequency security index under real power grid disturbances.

[0020] 5. This invention adopts a two-layer planning architecture. The upper layer determines the fixed location scheme for virtual inertia and damping, while the lower layer establishes a unit combination (UC) operation optimization model that includes generator output, reserve capacity, DC power flow of the network, and virtual resource commissioning costs. This ensures that the resource allocation of virtual inertia is no longer divorced from the actual operating conditions of the power grid, and realizes a comprehensive evaluation of investment and construction costs and typical daily operation and scheduling costs of the power grid. Under the premise of ensuring the dynamic security of node frequencies, it also takes into account the economic benefits of steady-state system operation and the safety margin of line transmission. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a flowchart of the virtual inertia bi-layer planning method considering node frequency security constraints of the present invention; Figure 2 This is a schematic diagram of the two-layer programming model in this invention; Figure 3 This is the candidate point sorting diagram in this invention; Figure 4 These are the frequency response curves of some nodes in the 39-node system of this invention before and after optimization; Figure 5 This is a stacked bar chart of the generator set output in this invention; Figure 6 This is a RoCoF distribution diagram of each node in this invention. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] Example 1 like Figure 1 As shown, the virtual inertia bi-level planning method considering node frequency security constraints includes the following steps: Step 1: Construct a reduced-order dynamic model of the power system's node frequencies. Assume the power system comprises a set of synchronous generating nodes and a set of load nodes. The phase angle, frequency offset, and regulation state of the synchronous generating units are used to construct a preserved state vector: in, This indicates that the phase angle state of the generating node is retained. This indicates that the frequency status of the generator node is retained. This indicates the equivalent state of a single frequency modulation or power regulation.

[0025] The network matrix is ​​divided into blocks In the formula, Given the network node admittance matrix, and then using the algebraic relationships of the load nodes, the phase angle or frequency offset of the load nodes is expressed as a linear combination of the corresponding quantities of the generator nodes, resulting in: In the formula, This is the phase angle increment vector of the load node. Let F be the generator node phase angle increment vector, and F be the mapping matrix. For the virtual inertia and virtual damping configured at candidate nodes, an equivalent mapping method retaining the frequency coordinates is used to construct the equivalent inertia matrix. and equivalent damping matrix According to the original inertia matrix Original damping matrix First-order frequency modulation gain matrix Adjustment time constant matrix Construct the fundamental frequency dynamic equation; map the virtual inertia and virtual damping configured at the candidate nodes to the reserved frequency coordinates to obtain the equivalent inertia increment matrix and the equivalent damping increment matrix: in, and These are the system's original inertia matrix and original damping matrix, respectively. Vectors are configured for virtual inertia and virtual damping. Based on network coupling relationships, original frequency adjustment parameters, and equivalent inertia and damping parameters, a node frequency-reduced dynamic model is constructed: in, The system state matrix, Let be the perturbation input matrix, and u be the perturbation input vector.

[0026] By obtaining the expression of load node frequency relative to the preserved state through frequency recovery mapping, a unified analytical framework applicable to full node frequency analysis is formed.

[0027] Step 2: Define the disturbance scenario and calculate the node frequency analytical response. The disturbance scenario can be a sudden load increase, generator disconnection, or equivalent active power deficit. Let the disturbance occur at time [time missing]. The time after the disturbance is defined as After performing modal decomposition on the above equation, the nodal frequency analytical response kernel function can be obtained: in, These are the system modal eigenvalues.

[0028] Perform mode decomposition on matrix A and obtain the following based on step perturbation: in It is the first k One right eigenvector, It is the first k Given a left eigenvector row vector, we can define: Any node n The frequency response can be expressed as: in, The system reference frequency, For nodes n For the first k The combined response coefficients of each mode.

[0029] Node vulnerability characteristics are extracted from the node frequency analytical response, including the node's minimum frequency deviation, the rate of change of the node's initial frequency, and local component indices. Correspondingly, the following can be defined: in, For nodes n The minimum permissible frequency threshold, For nodes n The lowest frequency, Let be the initial rate of change of frequency at node n. For a complex modal set, For nodes n Local modal indices, For nodes n In the k Local component coefficients on a complex mode.

[0030] Step 3: Perform comprehensive scoring and screening of candidate nodes. Let the set of candidate nodes be... First, based on the node vulnerability representations obtained in step 2, a vulnerability index is constructed: in, As a reference for frequency deviation normalization, For the limit of the rate of change of frequency, , and These are weighting coefficients. They are applied to candidate nodes. i Applying a trial virtual inertia and probing virtual damping To ensure system stability and reflect node frequency differences, virtual inertia... and probing virtual damping The typical value range is [0.1, 0.3]. The system frequency security pressure is recalculated, and configuration effectiveness indicators are constructed. : in, As a baseline system safety pressure, To apply safety pressure after probing the configuration, This is a scale conversion factor. To avoid tiny positive numbers with a denominator of zero, a comprehensive score is constructed after normalizing the vulnerability and effectiveness indicators: in, and These are the normalized vulnerability and effectiveness indicators, respectively. Based on... The candidate nodes are sorted, and a set of candidate sites is formed by selecting several nodes with higher scores.

[0031] Step 4: Perform a site combination search within the candidate site set. Let the candidate site set be... The site combination corresponding to the fixed site selection scheme is: Then we have: in, This represents the preset maximum number of sites. For each site combination satisfying the above formula, a fixed site selection scheme is generated, and each fixed site selection scheme is input into the lower-level optimization model.

[0032] Step 5: For each fixed site selection scheme, establish an operational optimization model at the lower level. The decision variables of the operational optimization model include at least the active power output of the generating unit, reserve capacity, node phase angle, site virtual inertia capacity, and site virtual damping capacity. The objective function of the lower-level operational optimization can be expressed as: in, Optimize the objective function for the lower-level operation. For the active power output of power generation unit g, This is the reserve capacity of power generation unit g. and These represent the virtual inertia capacity and virtual damping capacity of station i, respectively. , , and These are the corresponding cost coefficients. The corresponding upper-level overall objective function is written as: in, This represents the overall objective function value at the upper level. For site location variables, To fix construction costs, and These are the unit capacity costs for virtual inertia and virtual damping, respectively.

[0033] Step 6: Construct linearized frequency safety constraints based on the node frequency analytical response. Since the node minimum frequency constraint involves time-domain minimization operations, it is difficult to directly incorporate it into the optimization model in precise form. Therefore, this invention selects a set of key sampling moments within a preset time window after perturbation. And select a set of key nodes based on the current parsed response. The critical nodes may include one or more of the following: the worst-case node with the lowest frequency, the node with the largest local component index, the disturbance node, and the node with a relatively long electrical distance. At the reference operating point ( , At point ), the frequency of the critical node at the critical moment is linearized to the first order, resulting in: And apply the frequency safety inequality: Step 7, solve the operational optimization model. The lower-level operational optimization model must at least satisfy the following constraints: node power balance constraint: Power flow constraints: Unit output and standby constraints: And the total amount of reserves is constrained: in, For the trend on the line, For the set of routes, This is the DC power flow admittance matrix. The phase angle vector of the nodes. This is the net injected power vector. The disturbance power deficit is addressed by solving the lower-level optimization model formed jointly in steps 5 and 6. This yields the optimal output, reserve, virtual inertia capacity, virtual damping capacity, and network operation results corresponding to the fixed location scheme.

[0034] Step 8: Verify the optimization results using the actual node frequency analytical responses, and update the linearized operating point if necessary. Specifically, recalculate the actual analytical frequency responses of all nodes based on the optimization solution obtained in Step 7, and check whether the rate of change of the node's minimum frequency from the initial frequency meets the safety requirements. The following criteria can be used: in, and These represent the allowable errors for the lowest frequency point and the rate of change of frequency, respectively. When the above equation does not hold, the current optimization result is used as the new linearization reference operating point, i.e.: in, This represents the maximum configurable capacity for virtual inertia. Maximum configurable capacity for virtual damping Then repeat steps 6 to 8 until the preset convergence condition is met or the maximum number of iterations is reached.

[0035] Step 9: Select the scheme that satisfies the frequency security requirements and has the optimal objective function value from all fixed addressing schemes. For each fixed addressing scheme, the corresponding upper-level overall objective function value can be obtained. The frequency security verification results were then used. Finally, the following fixed-location schemes were selected from all those that met the frequency security requirements: The corresponding solution is used as the result of the virtual inertia bi-layer planning.

[0036] in, This represents the optimal combination of sites.

[0037] Based on the constraints established in the above steps, construct as follows: Figure 2 The schematic diagram shows a two-level programming model.

[0038] Example 2 In this embodiment, the technical solution of the present invention is verified and illustrated through a specific power system; In this embodiment, the IEEE 39-node system is selected as the test system, with a baseline capacity of 100 MVA and a rated frequency of 60 Hz. The system comprises 39 nodes, 10 synchronous generators, and corresponding transmission lines and load nodes. Lower-level operation optimization uses a typical daily 24-period scheduling cycle, with each period lasting 1 hour, and employs a typical daily load curve to time-scale the load of each node. The disturbance scenario is set as a grid disconnection accident occurring at t=1.0s for a 1000MW unit at Bus39. In the node frequency safety constraints, the lower limit of the node frequency is set at 59.40 Hz, and the node RoCoF limit is set at 0.60 Hz / s. Constraints are constructed by selecting several key sampling moments within 0-15 seconds after the disturbance. In the unit combination model, the maximum output, minimum output, reserve limit, start-up and shutdown costs, no-load costs, ramp rate, and minimum start-up and shutdown times adopt proxy parameters matched to the unit capacity, with the minimum start-up time set at 3-5 hours and the minimum shutdown time at 2-4 hours. The candidate configuration nodes for virtual inertia can be selected from the set of load nodes. The upper limit of the installation capacity of virtual inertia and virtual damping adopts preset parameters that are coordinated with the node load level.

[0039] It should be noted that the above parameters are only used to illustrate the implementation process of the method of the present invention. The present invention is not limited to the IEEE 39-node system and the specific values ​​mentioned above; other power systems and parameter settings are also applicable. In this embodiment, candidate sites are first composed of load nodes and are screened based on vulnerability indicators and trial configuration effectiveness indicators. For the screened site combinations, a lower-level operation optimization model is established, including generation output, reserve, node phase angle, site virtual inertia capacity, and virtual damping capacity. Frequency security constraints are represented by linearized node frequency inequalities at key sampling times within 0 to 15 seconds after the disturbance, and are verified by analytical frequency response.

[0040] The results of the embodiments show that the proposed virtual inertia bi-layer planning method considering node frequency security constraints can effectively achieve coordinated optimization of candidate node selection, site location and capacity determination, and operation scheduling. Figure 3 As shown, based on the comprehensive score obtained from the node vulnerability index and the trial configuration effectiveness index, the candidate nodes can form a clear priority ranking. Among them, nodes 2, 1, and 25 scored higher, indicating that the candidate screening mechanism proposed in this invention can effectively identify key configuration locations that have a significant impact on system frequency security. Based on this, the optimal site combination obtained from the upper-layer search is node 1 and node 2, where node 2 is configured with a virtual inertia of 12000 MW·s and a virtual damping of 300 MW / Hz, and node 1 is configured with a virtual inertia of 1319.768 MW·s and a virtual damping of 287.901 MW / Hz. Figure 4As can be seen, after a 1000MW unit disconnection disturbance occurred in the 39-node system, the frequency response curves of each typical node shifted upwards overall after adopting the optimization scheme of this invention, and the frequency drop was significantly reduced. Before optimization, the worst node frequency trough was approximately 59.1327Hz, which increased to 59.4028Hz after optimization, thus satisfying the minimum frequency constraint. This indicates that the configured virtual inertia and virtual damping can significantly enhance the node frequency support capability. Figure 5 It is evident that, under the conditions of satisfying network power flow, reserve, and frequency security constraints, the power output distribution of the generating units remains reasonable. Under optimal scheduling, all generating units jointly undertake the active power supply and emergency reserve of the system. The power outputs of units 30 to 39 are approximately 218.75MW, 847.34MW, 812.50MW, 553.00MW, 444.50MW, 746.25MW, 344.39MW, 0MW, 1037.50MW, and 1250.00MW, respectively, demonstrating that this invention can ensure frequency security while also considering economical operation. Figure 6 As can be seen, the RoCoF distribution of all nodes in the network converges after optimization, and the absolute value of the initial frequency change rate of all nodes is significantly reduced. The RoCoF of the most unfavorable node is effectively reduced from the level close to the constraint boundary under the baseline operating condition to within approximately 0.5958 Hz / s, satisfying the 0.6 Hz / s limit. In summary, the above results demonstrate that this invention can achieve effective location and capacity determination of virtual inertia resources while ensuring the minimum node frequency and RoCoF safety constraints, and obtain an operating scheme that balances safety and economy. This verifies the effectiveness and engineering applicability of the method in complex power systems.

[0041] From the perspective of frequency security results, the maximum node RoCoF of the optimized system is 0.99796 Hz / s, the most tightly constrained node is bus 30, and the corresponding safety margin is only 0.00204 Hz / s; the maximum line load rate is 83.33%, which does not reach the upper limit of line thermal stability, indicating that the obtained solution retains a good network operation margin while meeting frequency security constraints.

[0042] In summary, the proposed IEEE 39 virtual inertia configuration unit combination model based on node RoCoF constraints can effectively identify weak nodes in the system frequency and significantly improve the frequency security level in the initial stage of a fault through spatially selective virtual inertia deployment. The numerical examples show that, under a 1000MW large disturbance scenario, the optimal configuration of virtual inertia resources exhibits obvious locational characteristics; simultaneously, frequency security constraints significantly affect the system's unit operation mode and resource allocation scale. This indicates that incorporating the node RoCoF index into the unit combination and virtual inertia collaborative optimization framework can more accurately reflect the characteristics of grid inertia distribution and its impact on frequency stability.

[0043] Example 3 This embodiment proposes a virtual inertia two-layer planning system considering node frequency security constraints, specifically including: The reduced-order mapping module is used to obtain the network and equipment operating parameters of the power system, take the phase angle, frequency and regulation status of the synchronous generation unit as the reserved state, and map the virtual inertia and virtual damping configured on the load-side candidate nodes to the reserved frequency coordinates formed by the reserved state to construct a node frequency reduced-order dynamic model. The scoring and filtering module is used to calculate the node frequency analytical response based on the node frequency reduction dynamic model and extract the node vulnerability characterization quantity accordingly. It combines the security improvement effect after applying trial configuration capacity to each candidate node to generate a set of candidate sites by weighting and filtering the candidate nodes. Upper-level planning module: used to perform site combination search within the candidate site set, and use each site combination as a fixed site selection scheme for upper-level planning; The lower-level solution module is used to establish a lower-level operation optimization model including unit combination scheduling for each of the fixed location schemes; extract key nodes and key sampling times within a preset time window after the disturbance, and at the initially set or iteratively updated reference operating point, perform a first-order Taylor expansion on the node frequency response of the key nodes at the key sampling time by calculating sensitivity, construct linearized node frequency safety constraints, and embed them into the lower-level operation optimization model for solution, to obtain the virtual inertia capacity and virtual damping capacity corresponding to the fixed location scheme; Closed-loop iteration module: used to calculate the real node frequency analytical response using the node frequency reduced-order dynamic model, and substitute the virtual inertia capacity and virtual damping capacity into the safety constraint verification; if the residual does not meet the preset convergence condition, the current solution capacity is updated to a new reference working point and returned to the lower-level solution module for iteration until the convergence condition is met, and then the globally optimal configuration scheme is output.

[0044] Based on a similar inventive concept, embodiments of the present invention also provide a computer storage medium storing a readable program that, when run by a processor, can execute the above-described virtual inertia bi-layer planning method considering node frequency security constraints.

[0045] Based on a similar inventive concept, this invention provides an electronic device, including: a processor, a memory, a communication interface, and a communication bus, wherein the processor, the memory, and the communication interface communicate with each other through the communication bus; The memory is used to store at least one executable instruction, which causes the processor to perform the operation corresponding to the virtual inertia bi-level planning method that considers node frequency security constraints.

[0046] Based on a similar inventive concept, embodiments of the present invention also provide a computer program product, including computer instructions, which instruct a computing device to perform operations corresponding to the above-described virtual inertia bi-layer planning method considering node frequency security constraints.

[0047] The methods of the present invention can be implemented in hardware, firmware, or as software or computer code that can be stored in a recording medium (such as a CD-ROM, RAM, floppy disk, hard disk, or magneto-optical disk), or as computer code originally stored on a remote recording medium or a non-transitory machine-readable medium and subsequently stored on a local recording medium, downloaded via a network. Thus, the methods described herein can be processed by software stored on a recording medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware (such as an ASIC or FPGA). It is understood that the computer, processor, microprocessor controller, or programmable hardware includes storage components (e.g., RAM, ROM, flash memory, etc.) capable of storing or receiving software or computer code that, when accessed and executed by the computer, processor, or hardware, implements the methods described herein. Furthermore, when a general-purpose computer accesses the code used to implement the methods shown herein, the execution of the code transforms the general-purpose computer into a dedicated computer for performing the methods shown herein.

[0048] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A virtual inertia bi-level programming method considering node frequency security constraints, characterized in that, Includes the following steps: S1. Obtain the network and equipment operating parameters of the power system, take the phase angle, frequency and regulation status of the synchronous generation unit as the reserved state, and map the virtual inertia and virtual damping configured on the candidate nodes on the load side to the reserved frequency coordinates formed by the reserved state to construct a node frequency order reduction dynamic model. S2, calculate the node frequency analytical response based on the node frequency reduction dynamic model and extract the node vulnerability characterization quantity accordingly. Combine the security improvement effect after applying trial configuration capacity to each candidate node, perform weighted scoring and screening on the candidate nodes to generate a candidate site set. S3, perform a site combination search within the candidate site set, and use each site combination as a fixed site selection scheme for the upper-level planning; S4. For each of the fixed location schemes, establish a lower-level operation optimization model that includes unit combination scheduling; extract key nodes and key sampling times within a preset time window after the disturbance, and at the initially set or iteratively updated reference operating point, perform a first-order Taylor expansion on the node frequency response of the key nodes at the key sampling time by calculating sensitivity, construct linearized node frequency safety constraints, and embed them into the lower-level operation optimization model for solution, to obtain the virtual inertia capacity and virtual damping capacity corresponding to the fixed location scheme; S5. Calculate the actual node frequency analytical response using the node frequency reduced-order dynamic model, and substitute the virtual inertia capacity and virtual damping capacity into the safety constraint verification. If the residual does not meet the preset convergence condition, the current solution capacity is updated to the new reference working point and the process returns to S4 iteration until the convergence condition is met, at which point the globally optimal configuration scheme is output.

2. The virtual inertia bi-level planning method considering node frequency security constraints according to claim 1, characterized in that, The process of constructing a dynamic model for reducing the order of node frequencies includes: The phase angle, frequency, and adjustment state are combined into a reduced-order preserved state vector; Using the original inertia matrix and original damping matrix of the power system, combined with the equivalent inertia increment matrix and equivalent damping increment matrix formed by the virtual resource configuration vector on the candidate node, the equivalent inertia matrix and equivalent damping matrix in the node-preserved frequency coordinate system are calculated. The coefficient matrix of the state-space equation is constructed based on the equivalent inertia matrix, equivalent damping matrix, primary frequency modulation gain matrix, and adjustment time constant matrix. The mathematical mapping relationship between the load node frequency and the reduced-order retained state vector is established through the frequency recovery matrix.

3. The virtual inertia bi-level planning method considering node frequency security constraints according to claim 1, characterized in that, The process of weighted scoring and filtering of the candidate nodes includes: The minimum frequency deviation, initial frequency change rate, and complex modal local component coefficients of each candidate node are calculated separately, and after normalization, they are aggregated to generate the vulnerability index of each candidate node. A trial configuration capacity, including trial virtual inertia and trial virtual damping, is applied to the candidate node, and the difference in system safety pressure before and after the application is calculated to construct an effectiveness index. The vulnerability index and the effectiveness index are added together according to the set weight coefficients to obtain a comprehensive score. The nodes that meet the maximum number of websites constraint are selected in descending order of the comprehensive score to form the candidate site set.

4. The virtual inertia bi-level planning method considering node frequency security constraints according to claim 1, characterized in that, The process of extracting key nodes and key sampling moments includes: From the node frequency analysis response, select at least one of the following: the node with the largest deviation of the lowest frequency point, the node with the largest local component index, the node where the disturbance source is located, and the node with the farthest electrical distance from the disturbance source, to form the key node set; and on the transient drop curve after the disturbance corresponding to the key node, extract discrete points according to a preset time step to form the key sampling time set.

5. The virtual inertia bi-level planning method considering node frequency security constraints according to claim 1, characterized in that, The process of constructing linearized node frequency security constraints includes: At the current reference operating point, the finite difference method is used to calculate the first partial derivative of the node frequency response of the key node with respect to the virtual inertia capacity and the second partial derivative with respect to the virtual damping capacity. Using the first and second partial derivatives as sensitivity coefficients, the nonlinear minimum frequency constraint, which includes time-domain minimum value calculation, is transformed into a linear inequality constraint with virtual inertia increment and virtual damping increment as independent variables.

6. The virtual inertia bi-level planning method considering node frequency security constraints according to claim 1, characterized in that, The objective function of the lower-level operational optimization model is: in, The lower-level optimization objective function is to minimize the total cost. It is a collection of power generation units. For the active power output of power generation unit g, This is the reserve capacity of power generation unit g. and Sites i The virtual inertia capacity and virtual damping capacity, , , and These are the corresponding cost coefficients. This refers to the combination of sites corresponding to a fixed site selection scheme.

7. The virtual inertia bi-level planning method considering node frequency security constraints according to claim 1, characterized in that, The process of calculating the true node frequency analytical response using the aforementioned node frequency reduced-order dynamic model includes: Modal decomposition is performed on the state-space equations of the node frequency reduced-order dynamic model to obtain an analytical response kernel function containing system modal eigenvalues. The analytical response kernel function is used to calculate the actual minimum frequency and actual initial frequency change rate of all nodes under the current solution capacity; Determine whether the difference between the actual minimum frequency and the frequency safety lower limit for all nodes is greater than or equal to the negative frequency tolerance error, and determine whether the difference between the absolute value of the actual initial frequency change rate and the limit is less than or equal to the change rate tolerance error.

8. The virtual inertia bi-level planning method considering node frequency security constraints according to claim 6, characterized in that, Before outputting the globally optimal configuration, it also includes: For all the fixed location schemes that passed the review, calculate the overall objective function of the upper layer: in, This represents the overall objective function value at the upper level. For the candidate site set, For site location variables, To fix construction costs, and These represent the unit capacity costs of virtual inertia and virtual damping, respectively. For the configured virtual inertia capacity, The virtual damping capacity is configured; The fixed addressing scheme with the minimum overall objective function value of the upper layer is selected as the global optimal configuration scheme and output.

9. A virtual inertia bi-level programming system considering node frequency security constraints, comprising the method described in any one of claims 1-8, characterized in that, include: The reduced-order mapping module is used to obtain the network and equipment operating parameters of the power system, take the phase angle, frequency and regulation status of the synchronous generation unit as the reserved state, and map the virtual inertia and virtual damping configured on the load-side candidate nodes to the reserved frequency coordinates formed by the reserved state to construct a node frequency reduced-order dynamic model. The scoring and filtering module is used to calculate the node frequency analytical response based on the node frequency reduction dynamic model and extract the node vulnerability characterization quantity accordingly. It combines the security improvement effect after applying trial configuration capacity to each candidate node to generate a set of candidate sites by weighting and filtering the candidate nodes. Upper-level planning module: used to perform site combination search within the candidate site set, and use each site combination as a fixed site selection scheme for upper-level planning; The lower-level solution module is used to establish a lower-level operation optimization model including unit combination scheduling for each of the fixed location schemes; extract key nodes and key sampling times within a preset time window after the disturbance, and at the initially set or iteratively updated reference operating point, perform a first-order Taylor expansion on the node frequency response of the key nodes at the key sampling time by calculating sensitivity, construct linearized node frequency safety constraints, and embed them into the lower-level operation optimization model for solution, to obtain the virtual inertia capacity and virtual damping capacity corresponding to the fixed location scheme; Closed-loop iterative module: used to calculate the actual node frequency analytical response using the node frequency reduced-order dynamic model, and substitute the virtual inertia capacity and virtual damping capacity into the model for safety constraint verification; If the residual does not meet the preset convergence condition, the current solution capacity is updated to a new reference working point and the process returns to the next lower-level solution module for iteration until the convergence condition is met, at which point the globally optimal configuration scheme is output.

10. An electronic device, characterized in that, include: The processor, memory, communication interface, and communication bus are provided, wherein the processor, memory, and communication interface communicate with each other via the communication bus. The memory is used to store at least one executable instruction that causes the processor to perform the operation corresponding to the virtual inertia bi-level planning method considering node frequency security constraints as described in any one of claims 1-8.

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