A fast frequency response reserve resource space optimal coordination planning method considering extreme risk

Abstract

The application discloses a fast frequency response reserve resource space optimal coordination planning method considering extreme risk, and belongs to the technical field of power systems.The planning method comprises the following steps: S1, a low-order node frequency response analytical model is constructed to realize fast analytical calculation of frequency response of any node; S2, frequency space distribution characteristics are represented and processed; S3, cost and benefit analysis is considered in light of risk preference; S4, a reserve planning model is constructed, which comprises decision variables, an objective function and constraints; and S5, the reserve planning model is solved and a planning scheme is checked.The application can consider frequency space distribution and disturbance uncertainty, formulate optimal reserve resource planning schemes under different risk preferences, realize optimal coordination of reserve resources in the space scale and inertia and primary frequency modulation reserve in the time scale, and avoid the risk of exceeding the system local frequency index limit caused by the scheme formulated according to conventional methods, so that a more stable decision basis is provided for improving the extreme event response capability of the system.

Description

Technical Field

[0001] This invention belongs to the field of power system technology and relates to a fast frequency response space-optimal collaborative planning method for reserve resources that takes into account extreme risks. Background Technology

[0002] With the large-scale grid connection of new energy sources, the proportion of inverter-based resources (IBRs) such as wind power, photovoltaics, and energy storage is constantly increasing, and traditional power sources are being largely replaced. The system's synchronous inertia level is continuously decreasing, weakening the system's frequency response capability and sharply increasing the risk of frequency instability under extreme events. Fast frequency response (FFR) resources can rapidly inject active power within seconds to curb the rate of frequency drop, effectively compensating for the deficiencies in inertia and primary frequency regulation reserves. Therefore, they have been widely studied and applied in planning and operation that considers frequency security.

[0003] However, traditional power system planning methods often assume that all nodes in the power grid operate at the same frequency and optimize based on a unified Center of Inertia (COI) frequency, neglecting the Frequency Spatial Distribution Characteristic (FSDC). Using the COI frequency for planning while ignoring spatial frequency differences not only limits the full utilization of various resources but may also lead to the risk that while the planned scheme meets COI frequency security requirements, local frequency indicators may still exceed limits. Furthermore, most existing planning methods focus only on the interception benefits at the lowest frequency point, failing to consider the risk value of exceeding the Rate of Change of Frequency (RoCoF) limit due to insufficient inertia, potentially leading to insufficient inertia reserves and creating safety hazards. Under extreme events, the system's FSDC becomes more pronounced. Most existing planning methods are based on global accidents, resulting in the overshadowing of extreme events; or they only perform robust planning for extreme scenarios, failing to consider extreme risks while optimally balancing reliability and economy.

[0004] Therefore, it is necessary to study a fast frequency response backup resource spatial optimal collaborative planning method that takes into account extreme risks and frequency spatial distribution characteristics. Summary of the Invention

[0005] The continuous decline in inertia levels in high-proportion renewable energy power systems poses a serious threat to the safe and stable operation of the power grid. However, existing frequency response reserve resource planning largely ignores the spatial distribution characteristics of frequencies, failing to achieve optimal collaborative planning of multiple reserve resources in space; and it does not consider the risk value of RoCoF exceeding limits, potentially leading to inertia reserves not meeting the optimal system requirements. To address these issues, this invention proposes a rapid frequency response reserve resource spatial optimal collaborative planning method that considers extreme risks. This invention utilizes forced decoupling and modal analysis to establish an analytical model of the system node frequency response containing multiple types of regulation resources, enabling rapid analytical calculation of the frequency response of any node in the system under massive planning scenarios; it characterizes the spatial distribution characteristics of the system frequency based on the constructed node frequency index matrix, thereby identifying and planning weak nodes in the system space; furthermore, it establishes a reserve planning model that considers risk preference and spatial distribution, formulates optimal collaborative planning schemes for multiple types of reserve resources at the node level, and verifies the feasibility of the schemes. The proposed method can take into account the spatial distribution of frequency and the uncertainty of disturbances, formulate the optimal planning scheme for reserve resources under different risk preferences, realize the coordinated planning of reserve resources on the spatial scale and the optimal coordination of inertia and primary frequency regulation reserve on the time scale. The planning scheme formulated by this invention can avoid the risk of exceeding the limit of local frequency indicators of the system that may exist when formulating a scheme based on conventional methods, and provide a more reliable decision-making basis for improving the system's ability to respond to extreme events.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A spatially optimal coordinated planning (SOCP) method for rapid frequency response backup resources that takes into account extreme risks, the planning method comprising the following steps: S1: Construct a low-order node frequency response analytical model.

[0007] First, the two basic components of the frequency response model, transmission lines and frequency regulation nodes, are modeled to construct a low-order node frequency response model of the system. Then, the low-order node frequency response model is simplified and analytically derived to construct a Nodal Frequency Response Analytical Model (NFRAM), enabling rapid analytical calculation of the frequency response of any node and providing a fast tool for calculating frequency indicators for subsequent reserve planning. Specifically: S1-1: Modeling basic components.

[0008] S1-1-1: The power exchange and frequency oscillations between nodes in a transmission line are crucial for preserving FSDC in frequency response modeling. For a NFor a power system with nodes, the node admittance matrix can be obtained based on the power system network structure. ,Include g One frequency modulation node and l There are several non-frequency regulating nodes. After an active power disturbance occurs in the power system, the relationship between the phase angle of each node and the active power injected into the grid is described by the power flow equations: (1) In the formula, It is a vector consisting of the power injection quantities of the frequency modulation node. A vector consisting of the power injection amounts at non-frequency-modulated nodes; This is a block submatrix in the nodal admittance matrix that represents the admittance relationship between frequency-modulated nodes. This is a block submatrix in the nodal admittance matrix that represents the admittance relationship between frequency-modulated nodes and non-frequency-modulated nodes. This is a block submatrix in the nodal admittance matrix that represents the admittance relationship between non-frequency-modulated nodes and frequency-modulated nodes. This is a block submatrix in the nodal admittance matrix that represents the admittance relationship between non-frequency-tuned nodes; The rotor angle vector of the frequency modulation node. is the rotor angle vector of the non-frequency-tuned node.

[0009] because The rotor inertia prevents abrupt changes, which can be addressed by eliminating the inertia in formula (1). get : (2) (3) In the formula, Assign an initial matrix to the perturbation; This is the inter-machine oscillation matrix; This represents the power vector of inter-machine oscillations. Assign an initial power vector to the COI.

[0010] S1-1-2: Frequency regulation node modeling involves modeling the frequency response of the frequency regulation resources connected to the frequency regulation node and establishing an equivalent frequency response model for the frequency regulation node. The frequency regulation resources connected to the frequency regulation node mainly consider three types of resources: synchronous generators (SGs) dominated by thermal power units, integrated circuit generators (IBRs) represented by wind power, photovoltaic power, and energy storage, and load-side resources represented by emergency interruptible loads (EILs). Specifically: (1) SGs has an actual rotating rotor, and its inertial response can be described by the rotor motion equation: (4) In the formula, Let be the inertial time constant matrix of SGs; Here is the damping coefficient matrix; Let SGs be the mechanical power increment vector; These are the frequency deviation vectors of SGs; Let be the electromagnetic power vector of SGs; This is the Laplace operator.

[0011] SGs participate in primary frequency regulation through a speed governor. The transfer function of its most representative low-order speed governor model is: (5) In the formula, It is a unit diagonal matrix; This is the power coefficient matrix for the high-pressure cylinder; This is the reheat time constant matrix; This is the adjustment coefficient matrix.

[0012] (2) IBRs need to provide virtual inertial response and primary frequency modulation response capabilities through control strategies. Networked IBRs can actively establish frequencies, and their inertial response characteristics are similar to those of SGs, allowing them to be directly aggregated into the inertial links of the frequency modulation nodes. The primary frequency modulation capability of networked IBRs is achieved through virtual droop control: (6) In the formula, , These are the mechanical power increment vector and frequency vector of the mesh-type IBR, respectively; , These are the response delay matrix and virtual droop coefficient matrix of the network-type IBR, respectively.

[0013] (3) EIL does not have synchronous inertial response capability, but it can provide a fast frequency response by actively cutting off a certain amount of load through event triggering. Its active response can be represented as a step power signal.

[0014] S1-1-3: Based on the modeling of the three types of frequency modulation resources in S1-1-2, the inertial response of a frequency modulation node connecting multiple regulation resources can be described by the equivalent rotor motion equation: (7) In the formula, , These are the rated angular velocity vector and the rated frequency vector, respectively. This is a vector representing the change in mechanical power. This is the equivalent inertia time constant matrix.

[0015] Equivalent inertia time constant matrix of frequency modulation node The results are obtained by aggregating the synchronous inertia of SGs and the virtual inertia of network-type IBRs: (8) In the formula, , These are the resource capacity proportion vectors of SGs and the resource capacity proportion vectors of the network-type IBR, respectively. This is the virtual inertia coefficient matrix of a network-type IBR.

[0016] The vector of mechanical power change at the frequency modulation node for: (9) In the formula, This is the load shedding vector of EIL.

[0017] S1-2: Model simplification and analytical derivation.

[0018] Based on equations (2)-(9), the frequency response model of the low-order nodes of the system is established, and the frequency response of the frequency-modulated nodes in the complex frequency domain is expressed as the vibration equation: (10) (11) In the formula, , , These are the mass matrix, damping matrix, and stiffness matrix of the vibration equation, respectively. , These are the unbalanced mechanical power vectors generated by the approximate preceding and following inertial links, respectively.

[0019] According to equation (2), Depend on Caused COI frequency and Caused oscillation frequency composition: (12) In the formula, This is the frequency response vector of the COI; This is the frequency response vector of the inter-machine oscillation.

[0020] For the One frequency modulation node The frequency oscillations generated by the remaining frequency modulation nodes consist of: (13) In the formula, and Both refer to index variables representing frequency modulation nodes. , .

[0021] Considering and The low-pass filtering characteristics of the first-order inertial link between them will Approximate replacement ,but It can be approximated as : (14) At this point, equation (14) becomes an analytically solvable second-order linear nonhomogeneous differential equation: (15) In the formula, is the external excitation vector for the vibration equation.

[0022] Thus, equation (15) is... N The forced vibration equations of the degrees of freedom are solved using modal analysis. Through forced decoupling, modal analysis, and superposition, the time-domain analytical expression of the frequency response of the frequency-modulated node is derived. According to the frequency divider formula, the frequency response of the non-frequency modulated node... This can be deduced as: (16) Based on (15) and (16), a low-order NFRAM was constructed, which can analytically calculate the frequency response of all nodes, including the frequency response of the frequency-modulated nodes. Frequency response of non-frequency modulated nodes .

[0023] S2: Characterization and processing of frequency spatial distribution characteristics.

[0024] To embed the frequency spatial distribution characteristics into the reserve resource planning model, they need to be characterized and processed. First, two node frequency index matrices are constructed to comprehensively characterize the FSDC; then, system planning partitioning is performed based on the node frequency index matrices, and weak nodes in terms of disturbance resistance are identified; finally, the spatial probability matrix of the disturbance set is used to characterize the disturbance uncertainty.

[0025] S2-1: Construct the node frequency index matrix.

[0026] To incorporate FSDC into the planning, a node frequency index matrix is ​​proposed to comprehensively characterize it. When the disturbance occurs at the... When there are only a few nodes, the frequency response of all nodes in the power system is quickly calculated based on the low-order NFRAM constructed in S1; only the initial RoCoF of the nodes is retained. ) and maximum frequency difference ( These two key frequency indicators, which reflect the nodal inertia and primary frequency modulation response characteristics, constitute the basis for... row vectors and about row vectors By traversing all the perturbed nodes, we can construct information about... Node frequency index matrix Regarding Node frequency index matrix .

[0027] S2-2: System partitioning oriented towards planning.

[0028] Considering that FSDC is generally more significant at the regional level, this invention proposes a column clustering partitioning method based on the node frequency index matrix. and The Column elements ( and ) reflects the first The frequency response characteristics of each node to all possible disturbances in the system. and After standardization, new column vectors are formed. By clustering all column vectors, nodes with similar frequency response characteristics can be assigned to the same planning area.

[0029] In actual reserve planning of power systems, the accuracy of the allocation is determined by the decision-maker, and can be based on the significance of the FSDC (Freedom of Power Controllers). The planning can be refined to the regional level or even down to the node level. The more regionalized the power system, the more detailed the planning scheme, and the higher the complexity of the planning model and the computational cost. The salience of FSDC is determined through... uniformity index To measure, The larger the value, the less significant the FSDC. The uniformity index is obtained by formula (17): (17) in, This refers to the index variable of the column. ; for The Column vector.

[0030] S2-3: Identify nodes with weak resistance to disturbances.

[0031] and The row element ( and The norm of a node frequency index matrix reflects the degree of threat posed by a disturbance location to the system frequency. A larger norm value indicates a greater threat to system frequency security from the disturbance. Based on this, this invention proposes a method for identifying vulnerable nodes based on the row norm of the node frequency index matrix. For the Each node, for and Weighted by norm and maximum value: (18) In the formula, Indicates the first The vulnerability coefficient of each node; CD These are weighting coefficients, depending on the decision-maker's... and Excessive attention and preferences; express The 2-norm; express The 2-norm.

[0032] It can reflect the first The spatial vulnerability of each node. The perturbation node corresponds to... The larger the value, the weaker the spatial immunity of the disturbing node. Based on this, nodes with weak immunity can be identified.

[0033] S2-4: Characterization of disturbance uncertainty.

[0034] In the spatial coordination planning of backup resources, the impact of disturbance locations and their uncertainties on the planning model must be considered. This invention uses Monte Carlo stochastic production simulation, combined with historical power grid disturbance data, equipment aging and failure probabilities, and network topology, to obtain the disturbance set and its spatial probability distribution required for system backup planning. The disturbance set... P all Sort the disturbances by power deficit from smallest to largest, and consider the probability of different disturbances occurring in each region to obtain the spatial probability matrix representation of the disturbance set, as shown in formula (19): (19) In the formula, The index variable refers to the region of disturbance. ; This refers to the index variable used to sort power deficits. ; The number of perturbations in the perturbation set; The power deficit is sorted by size. The disturbance occurred and happened exactly on the 1st The joint probability of each region. Let be the spatial probability matrix of the perturbation set, and let its i-th The conditional probability distribution of the column is ,in Sort by power deficit size The disturbance occurred in the first Conditional probability of each region: (20) S3: Cost-benefit analysis considering risk preference.

[0035] First, an analysis of the value-added risk (VAT) of frequency exceeding limits was conducted, and a system was established. An over-limit penalty mechanism is implemented; then, the risk preference reliability cost of the alternative solution is calculated using the conditional risk preference method; and finally, the risk preference reliability benefit of the alternative solution is calculated using the discrete probability distribution of the over-limit loss.

[0036] S3-1: Value at Risk Analysis of Frequency Exceeding Limits.

[0037] The over-limit loss can be calculated based on the low-frequency load shedding mechanism, however, regarding Penalty mechanisms for exceeding limits are still relatively rare. The losses caused by excessively high frequencies mainly include damage to the internal structure of synchronous generator units, losses due to distributed power generation disconnection from the grid, and additional low-frequency load shedding costs caused by deterioration of frequency indicators. Based on Analysis of losses due to exceeding limits and related factors Constraint criteria, establishment The penalty mechanism for exceeding the limit is shown in equation (21): (twenty one) In the formula, Reference Constraint level, For the first Level constraint, For the first Level Constraints Penalties for exceeding limits. Different levels of penalties. The constraints depend on the relay protection settings of the distributed generation and the unit. Tolerance value.

[0038] S3-2: Calculate the reliability cost of risk preference.

[0039] From frequent, high-volume common disturbances to low-probability extreme events, the risk and losses from power system frequency exceedances increase non-linearly. Different incident levels result in different losses; these costs are known as reliability costs, including... Over-limit losses and low-frequency load shedding losses. For a frequency over-limit incident, what are the backup planning options?r The reliability cost is: (twenty two) In the formula, For the load of the power system, a , b For different Low-frequency load reduction ratio coefficient and unit penalty value under over-limit level; For reliability costs; for Losses due to exceeding limits.

[0040] Reliability cost L ( r ) is a random variable, and it exists in relation to the alternative planning scheme. r The relevant probability distribution, let the probability density distribution function be... To take into account the risk preferences of decision-makers, risk factors are defined. c This reflects the scope of risk the decision-maker is concerned with, i.e., the severity and rarity of losses the decision-maker is concerned with within the overall incident. This invention uses a reliability cost greater than or equal to a certain threshold. Quantify risk factors using probability: (twenty three) In the formula, Indicates risk factors; Let be a random variable relating to the disturbance loss; Indicates alternative planning schemes; This represents the probability distribution between reliability costs and backup plans; This is a mapping function between a threshold and a risk factor; the threshold C L Determined by the decision-maker.

[0041] By changing c This allows for continuous shifts in how decision-makers focus on different risk profiles. c As the number of cases approaches zero, policymakers tend to focus more on extreme events. c When the value approaches 1, there is a greater tendency to focus on overall events. c Down r Relevant conditions, reliability costs for: (twenty four) in, This represents the expected loss corresponding to a disturbance event whose disturbance loss exceeds a threshold. S3-3: Calculate the reliability gains of risk preference.

[0042] The perturbation set of the sampling year P all By inputting the low-order node frequency response analytical model established in S1, the frequency indices for all regions can be obtained. Using the worst-case frequency indices for all regions, based on the low-frequency load shedding strategy and the model established in S3-1... The over-limit penalty mechanism can quickly calculate the loss distribution across the entire risk range. : (25) In the formula, Sort by power deficit size The disturbance occurred in the first When the system operates in a certain region, it causes losses due to exceeding the system frequency limit.

[0043] Using the spatial probability matrix established in S2-4, for By calculating the expected probability of each column, the loss distribution of the system under all disturbance events can be obtained. , in The calculation method is as follows: (26) By sorting the frequency over-limit losses corresponding to all disturbance events, we can obtain The discrete form of the probability distribution. Based on its true discrete probability distribution, different accident ranges can be taken without the need for a continuous expression of the probability distribution function, thereby obtaining different risk factors. c The reliability cost of the backup plan.

[0044] Adding backup equipment can effectively intercept the risk of frequency limits being exceeded, thus improving system reliability. The reduction in reliability costs before and after adding backup equipment is the reliability gain. Therefore, considering the risk appetite, the reliability gain of backup equipment is crucial. Represented as: (27) S4: Construct a backup planning model.

[0045] The alternative planning model consists of decision variables, an objective function, and constraints. First, the decision variables of the alternative planning model are determined, and the objective function is constructed. Then, the constraints that the alternative planning scheme must satisfy are considered, and the constraint function of the alternative planning model is established.

[0046] S4-1: Objective function for constructing the alternative planning model Different backup resources have varying response characteristics and costs, and the benefits of planning them in different locations also differ. Therefore, it is necessary to weigh the backup capacity, location, and backup costs of various resources, and to consider FSDC collaborative planning of diverse and flexible backup resources. Thus, the decision variables in the backup planning model constructed in this invention are the backup capacity of various backup resources in each region. Class resources and There are 10 regions, with a total of 1000 areas. One decision variable: (28) In the formula, Indicates the first The first region Planned capacity of backup resources; For index variables that refer to resource types, ; The number of resource types The reliability benefit of the backup can be obtained from equation (27), and the cost of the backup planning scheme. This mainly includes investment costs. I ( r ) and call cost D ( r The isochronous value method is used to calculate the sampling year. I ( r ); D ( r This is related to the number of effective disturbances in the sampling year. m and the Unit capacity allocation cost of backup resources Related, that is, through J The cumulative cost of resource allocation is obtained D ( r ).

[0047] (29) (30) (31) In the formula, k The discount rate is... α For the lifespan of backup resources, Representing the Total investment cost of similar resources For the first The capacity for calling class-alternative resources, For the first The unit capacity cost of calling up backup resources.

[0048] By combining equations (27) and (29) to obtain the reserve reliability benefits and reserve costs, a reserve planning model considering spatial distribution and risk preference can be established. The net risk preference benefit is then used to calculate the reserve cost. Maximize the objective function: (32) in, As a backup plan In risk factors The reliability gains are calculated using equation (27) in S3-3; As a backup plan In risk factors The planning cost is calculated using equation (29).

[0049] S4-2: Constraints for Constructing the Alternative Planning Model The backup planning model constructed in this invention considers the following constraints: active power balance constraints, generator output constraints, line power flow constraints, and frequency security constraints (including...). Constraints and Constraints include capacity constraints for reserve resources and minimum planning unit constraints. Among them, active power balance constraints, unit output constraints, and line power flow constraints are consistent with traditional planning models. Frequency security constraints are considered in the objective function by the reliability benefits calculated through S3. The capacity constraints and minimum planning unit constraints for various reserve resources are shown in equations (33) and (34): (33) (34) In the formula, For the first Upper limit of capacity planning for backup resources; For the first Minimum planning unit capacity for reserve resources; For integer variables, .

[0050] Thus, by establishing the objective function and constraints, a backup planning model has been constructed, which can be used to optimize the decision variables and find the optimal backup planning scheme.

[0051] S5: Solving the backup planning model and verifying the planning scheme.

[0052] First, an improved particle swarm optimization algorithm is designed to optimize and solve the alternative planning model, and the optimization solution is accelerated by using regional planning weights. Then, the feasibility of the optimized alternative planning scheme is verified and a confidence index is given.

[0053] S5-1: Improved optimization algorithm.

[0054] This invention proposes a prior knowledge-guided multi-start particle swarm optimization (PKG-PSO) algorithm, which uses regional planning weights to guide the search direction of alternative planning schemes in regional capacity allocation, thereby accelerating the optimization solution.

[0055] The system is divided into S2-2. After identifying the regions, the node with the largest vulnerability coefficient within each region is selected to represent the region's vulnerability level, thus obtaining the region's vulnerability coefficient. The greater the vulnerability coefficient of a region, the weaker its spatial vulnerability; more reserve capacity needs to be allocated to this region in the planning to enhance its ability to absorb disturbances, thereby better suppressing the global frequency drop. Considering the uncertainty of the disturbance location, regions with weak spatial vulnerability may have a lower probability of disturbance occurrence. Therefore, the regional planning weights need to comprehensively consider both the vulnerability of the region and the probability of disturbance occurrence. The expected vulnerability of each region can be calculated by combining equations (18) and (19). : (35) In the formula, For the first The power deficits in each region are ranked as follows: The vulnerability coefficient during disturbance; For the first Expected value of the vulnerability of each region to interference.

[0056] For all regions Normalization is performed to obtain the regional planning weights of reserve resources in each region. , , in for: (36) A higher regional planning weight indicates a greater tendency for reserve resources to allocate more capacity to that region. This regional planning weight is introduced as prior knowledge into the traditional PSO algorithm to guide the optimization search direction. Specifically, the improvement is as follows: (1) A multi-granularity weight-guided initialization strategy is adopted. Based on prior knowledge, multiple initialization modes are designed, ranging from fully following the regional weight to slight weight guidance, to generate multiple initial populations in order to balance the convergence speed and global search capability.

[0057] (2) A weight guidance term is added to the PSO velocity update formula to guide particles to move in the direction of weight allocation. The guidance strength decreases linearly with the number of iterations, which accelerates the convergence of the algorithm in the early stage and enhances global exploration in the later stage. When the position of a particle violates the constraints, a repair strategy based on regional planning weights is adopted.

[0058] (3) A multi-starting-point strategy is adopted, starting the search from multiple different initial points to avoid getting trapped in local optima. In each iteration, the historical optimal solution is retained, and some particles are reinitialized to enhance the global exploration capability.

[0059] It should be noted that the regional planning weight guidance is not a mandatory constraint, but rather a suggestion for the search direction. PKG-PSO avoids getting trapped in local optima through multiple starting points and iterative optimizations, and must strictly meet the optimization constraints.

[0060] S5-2: Verify the planning scheme.

[0061] To avoid contingency plans failing to meet actual needs due to the subjective experience of decision-makers, it is necessary to conduct feasibility verification of the plans and provide confidence indicators. Verification costs are a significant part of the contingency planning process. A ( r This includes backup costs and reliability costs associated with exceeding frequency limits, which also exist in the same way as... The relevant probability distribution, analogous to equation (24), risk factors The verification cost Represented as: (37) in, This represents the probability distribution between the verification cost and the alternative planning scheme; The threshold for the verification cost corresponding to the risk factor; This represents the expected verification cost corresponding to a disturbance event where the verification cost exceeds the verification cost threshold. Confidence indicators for backup plans Defined as: (38) in, Indicates risk factors Backup Plan The cost of verification; Indicates risk factors The inspection cost corresponding to not planning for backup; Based on this confidence index, the risk factor is judged. c Backup Plan Is it because the cost is too high that it will not be adopted? s When the value is less than 0, the planning proposal should be rejected; when... s When the confidence index is greater than or equal to 0, the planning scheme can be adopted, and the higher the confidence index, the more worthy the scheme is of adoption.

[0062] The beneficial effects of this invention are as follows: (1) By establishing a low-order node frequency response analytical model, constructing a node frequency index matrix, and representing the disturbance with a spatial probability matrix, this invention considers the frequency spatial distribution characteristics and the uncertainty of the disturbance in the backup planning, and can realize the optimal planning of multiple types of backup resources at the node or regional level. Compared with traditional planning methods, it can effectively reduce the risk of local frequency index exceeding the limit.

[0063] (2) This invention establishes The penalty mechanism for exceeding the limit has been considered. The risk value of exceeding limits and the benefits of inertia reserve planning can achieve optimal coordination of rapid frequency response reserve resources on the inertia and primary frequency regulation time scale, avoid the risks that may be caused by insufficient inertia reserve, and make the planning scheme more comprehensive.

[0064] (3) By introducing risk factors to conduct conditional risk preference analysis, this invention can formulate flexible planning schemes according to different risk preferences of decision-makers, which can effectively prevent extreme events from being overwhelmed by a large number of frequent ordinary events and ensure the system's ability to respond to extreme events. Attached Figure Description

[0065] Figure 1 Flowchart of the optimal collaborative planning method for backup resource space in a fast-frequency response that takes extreme risks into account; Figure 2 Low-order node frequency response model structure diagram; Figure 3 The graph shows the relative error of the calculation of the low-order node frequency response analytical model. Figure 3 (a) in the middle is The relative error of the calculation; Figure 3 (b) in the middle is The relative error of the calculation; Figure 4 For standby capacity and net income c Trend chart of changes; Figure 5 A comparison chart of optimal planning results under different spatial probability matrices; Figure 5 (a) in the figure is a comparison of the optimal planning results of reserve capacity under different spatial probability matrices; Figure 5 (b) in the figure is a comparison of the optimal planning results for net returns under different spatial probability matrices; Figure 6 A comparison chart showing the planning effects of SOCP and traditional FFR reserve planning (TFRP); Figure 6 (a) in the middle is c =0.01 The cumulative distribution function (CDF); Figure 6 (b) in the middle is c =0.01 CDF; Figure 6 (c) in the middle is c =0.8 CDF; Figure 6 (d) in the middle is c =0.08 CDF; Figure 7 A comparison chart showing the planning performance of SOCP and COI frequency-based planning (COIP); Figure 7 (a) in the middle is c =0.01 CDF; Figure 7 (b) in the middle is c =0.01 CDF; Figure 7 (c) in the middle is c =0.3 CDF; Figure 7 (d) in the middle is c =0.3 CDF; Figure 8 This is a feasibility verification diagram for the planning scheme. Detailed Implementation

[0066] The present invention will be further described below with reference to specific embodiments.

[0067] To make the technical solution and advantages of this invention clearer, the IEEE 39-node system is introduced as a test system to perform spatial collaborative planning for four types of reserve resources: hydropower units (HPU), grid-type inter-stationary transformers (IBRs), synchronous compensators (SC), and energy inter-stationary transformers (EIL). A comparative analysis is conducted with COI frequency-based planning (COIP) and traditional FFR reserve planning (TFRP). The computational accuracy and efficiency of the constructed node frequency response analytical model are verified, and the risk preferences of decision-makers, disturbance uncertainties, and other factors are analyzed. The impact of the penalty mechanism for exceeding limits on the planning scheme; and a feasibility verification analysis of the planning scheme.

[0068] Network-type IBR Set to 5 seconds. The response delay is 10. The inertia is 0.1s; SC provides the system with inertia in the form of MW·s, and its inertial constant is set to 5s; The relevant parameter settings for the over-limit penalty mechanism are shown in Table 1. The value is set to 10; the standby life is set to 30 years; the discount rate is 10%; the price parameters and capacity constraints of various standby resources are shown in Table 2, wherein the EIL (Emergency Interval) shall not exceed half of the total standby capacity, and the minimum planning unit for all standby resources is 2MW. This invention uses MATLAB / 2023b for relevant calculations. The technical solution of this invention will be clearly and completely described below with reference to specific embodiments and accompanying drawings.

[0069] Table 1: Parameter table of over-limit penalty mechanism

[0070] Table 2: Price parameters and capacity constraints of various types of backup resources

[0071] A fast-frequency response space-optimal collaborative planning method for backup resources that takes into account extreme risks includes the following steps: A fast-frequency response space-optimal collaborative planning method for backup resources that takes into account extreme risks, the planning method comprising the following steps: S1: Construct a low-order node frequency response analytical model.

[0072] First, the two basic components of the frequency response model, transmission lines and frequency regulation nodes, are modeled to construct a low-order node frequency response model of the system. Then, the low-order node frequency response model is simplified and analytically derived to construct a Nodal Frequency Response Analytical Model (NFRAM), enabling rapid analytical calculation of the frequency response of any node and providing a fast tool for calculating frequency indicators for subsequent reserve planning. Specifically: S1-1: Modeling basic components.

[0073] S1-1-1: The power exchange and frequency oscillations between nodes in a transmission line are crucial for preserving FSDC in frequency response modeling. For a N For a power system with nodes, the node admittance matrix can be obtained based on the power system network structure. ,Include g One frequency modulation node and l There are several non-frequency regulating nodes. After an active power disturbance occurs in the power system, the relationship between the phase angle of each node and the active power injected into the grid is described by the power flow equations: (1) In the formula, It is a vector consisting of the power injection quantities of the frequency modulation node. A vector consisting of the power injection amounts at non-frequency-modulated nodes; This is a block submatrix in the nodal admittance matrix that represents the admittance relationship between frequency-modulated nodes. This is a block submatrix in the nodal admittance matrix that represents the admittance relationship between frequency-modulated nodes and non-frequency-modulated nodes. This is a block submatrix in the nodal admittance matrix that represents the admittance relationship between non-frequency-modulated nodes and frequency-modulated nodes. This is a block submatrix in the nodal admittance matrix that represents the admittance relationship between non-frequency-tuned nodes; The rotor angle vector of the frequency modulation node. is the rotor angle vector of the non-frequency-tuned node.

[0074] because The rotor inertia prevents abrupt changes, which can be addressed by eliminating the inertia in formula (1). get : (2) (3) In the formula, Assign an initial matrix to the perturbation; This is the inter-machine oscillation matrix; This represents the power vector of inter-machine oscillations. Assign an initial power vector to the COI.

[0075] S1-1-2: Frequency regulation node modeling involves modeling the frequency response of the frequency regulation resources connected to the frequency regulation node and establishing an equivalent frequency response model for the frequency regulation node. The frequency regulation resources connected to the frequency regulation node mainly consider three types of resources: synchronous generators (SGs) dominated by thermal power units, integrated circuit generators (IBRs) represented by wind power, photovoltaic power, and energy storage, and load-side resources represented by emergency interruptible loads (EILs). Specifically: (1) SGs has an actual rotating rotor, and its inertial response can be described by the rotor motion equation: (4) In the formula, Let be the inertial time constant matrix of SGs; Here is the damping coefficient matrix; Let SGs be the mechanical power increment vector; These are the frequency deviation vectors of SGs; Let be the electromagnetic power vector of SGs; This is the Laplace operator.

[0076] SGs participate in primary frequency regulation through a speed governor. The transfer function of its most representative low-order speed governor model is: (5) In the formula, It is a unit diagonal matrix; This is the power coefficient matrix for the high-pressure cylinder; This is the reheat time constant matrix; This is the adjustment coefficient matrix.

[0077] (2) IBRs need to provide virtual inertial response and primary frequency modulation response capabilities through control strategies. Networked IBRs can actively establish frequencies, and their inertial response characteristics are similar to those of SGs, allowing them to be directly aggregated into the inertial links of the frequency modulation nodes. The primary frequency modulation capability of networked IBRs is achieved through virtual droop control: (6) In the formula, , These are the mechanical power increment vector and frequency vector of the mesh-type IBR, respectively; , These are the response delay matrix and virtual droop coefficient matrix of the network-type IBR, respectively.

[0078] (3) EIL does not have synchronous inertial response capability, but it can provide a fast frequency response by actively cutting off a certain amount of load through event triggering. Its active response can be represented as a step power signal.

[0079] S1-1-3: Based on the modeling of the three types of frequency modulation resources in S1-1-2, the inertial response of a frequency modulation node connecting multiple regulation resources can be described by the equivalent rotor motion equation: (7) In the formula, , These are the rated angular velocity vector and the rated frequency vector, respectively. This is a vector representing the change in mechanical power. This is the equivalent inertia time constant matrix.

[0080] Equivalent inertia time constant matrix of frequency modulation node The results are obtained by aggregating the synchronous inertia of SGs and the virtual inertia of network-type IBRs: (8) In the formula, , These are the resource capacity proportion vectors of SGs and the resource capacity proportion vectors of the network-type IBR, respectively. This is the virtual inertia coefficient matrix of a network-type IBR.

[0081] The vector of mechanical power change at the frequency modulation node for: (9) In the formula, This is the load shedding vector of EIL.

[0082] S1-2: Model simplification and analytical derivation.

[0083] Based on equations (2)-(9), the frequency response model of the low-order nodes of the system is established, and the frequency response of the frequency-modulated nodes in the complex frequency domain is expressed as the vibration equation: (10) (11) In the formula, , , These are the mass matrix, damping matrix, and stiffness matrix of the vibration equation, respectively. , These are the unbalanced mechanical power vectors generated by the approximate preceding and following inertial links, respectively.

[0084] According to equation (2), Depend on Caused COI frequency and Caused oscillation frequency composition: (12) In the formula, This is the frequency response vector of the COI; This is the frequency response vector of the inter-machine oscillation.

[0085] For the One frequency modulation node The frequency oscillations generated by the remaining frequency modulation nodes consist of: (13) In the formula, and Both refer to index variables representing frequency modulation nodes. , .

[0086] Considering and The low-pass filtering characteristics of the first-order inertial link between them will Approximate replacement ,but It can be approximated as : (14) At this point, equation (14) becomes an analytically solvable second-order linear nonhomogeneous differential equation: (15) In the formula, is the external excitation vector for the vibration equation.

[0087] Thus, equation (15) is... N The forced vibration equations of the degrees of freedom are solved using modal analysis. Through forced decoupling, modal analysis, and superposition, the time-domain analytical expression of the frequency response of the frequency-modulated node is derived. According to the frequency divider formula, the frequency response of the non-frequency modulated node... This can be deduced as: (16) Based on (15) and (16), a low-order NFRAM was constructed, which can analytically calculate the frequency response of all nodes, including the frequency response of the frequency-modulated nodes. Frequency response of non-frequency modulated nodes .

[0088] To verify the computational accuracy and efficiency of the low-order NFRAM constructed by S1, a perturbation of 600MW was applied at load node 4 and node 27, respectively, and the values ​​of all nodes were calculated. and Using the simulation results as a baseline, the relative error (RE) of the analytical model for the nodal frequency response is as follows: Figure 5 As shown.

[0089] Depend on Figure 5 As can be seen, the RE and mean absolute percentage error (MAPE) of the low-order NFRAM are both around 2%, indicating high computational accuracy. In terms of computational speed, compared to PSASP's computation time of 2.375s, the node frequency response analytical model's computation time is only 8.434ms. This significant improvement in computational speed while maintaining high accuracy provides a fast and accurate computational tool for massive planning scenarios.

[0090] S2: Characterization and processing of frequency spatial distribution characteristics.

[0091] To embed the frequency spatial distribution characteristics into the reserve resource planning model, they need to be characterized and processed. First, two node frequency index matrices are constructed to comprehensively characterize the FSDC; then, system planning partitioning is performed based on the node frequency index matrices, and weak nodes in terms of disturbance resistance are identified; finally, the spatial probability matrix of the disturbance set is used to characterize the disturbance uncertainty.

[0092] S2-1: Construct the node frequency index matrix.

[0093] To incorporate FSDC into the planning, a node frequency index matrix is ​​proposed to comprehensively characterize it. When the disturbance occurs at the... When there are only a few nodes, the frequency response of all nodes in the power system is quickly calculated based on the low-order NFRAM constructed in S1; only the initial RoCoF of the nodes is retained. ) and maximum frequency difference ( These two key frequency indicators, which reflect the nodal inertia and primary frequency modulation response characteristics, constitute the basis for... row vectors and about row vectors By traversing all the perturbed nodes, we can construct information about... Node frequency index matrix Regarding Node frequency index matrix .

[0094] S2-2: System partitioning oriented towards planning.

[0095] Considering that FSDC is generally more significant at the regional level, this invention proposes a column clustering partitioning method based on the node frequency index matrix. and The Column elements ( and ) reflects the first The frequency response characteristics of each node to all possible disturbances in the system. and After standardization, new column vectors are formed. By clustering all column vectors, nodes with similar frequency response characteristics can be assigned to the same planning area.

[0096] In actual reserve planning of power systems, the accuracy of the allocation is determined by the decision-maker, and can be based on the significance of the FSDC (Freedom of Power Controllers). The planning can be refined to the regional level or even down to the node level. The more regionalized the power system, the more detailed the planning scheme, and the higher the complexity of the planning model and the computational cost. The salience of FSDC is determined through... uniformity index To measure, The larger the value, the less significant the FSDC. The uniformity index is obtained by formula (17): (17) in, This refers to the index variable of the column. ; for The Column vector.

[0097] The system is divided into four regions to be planned using column vector clustering: {G9}, {G2, G3}, {G4, G5, G6, G7}, and {G1, G8, G10}. Conditional probability distribution of all column vectors Set all to =[0.06140.2650 0.35260.3210] T This is used for subsequent backup resource space planning.

[0098] S2-3: Identify nodes with weak resistance to disturbances.

[0099] and The row element ( and The norm of a node frequency index matrix reflects the degree of threat posed by a disturbance location to the system frequency. A larger norm value indicates a greater threat to system frequency security from the disturbance. Based on this, this invention proposes a method for identifying vulnerable nodes based on the row norm of the node frequency index matrix. For the Each node, for and Weighted by norm and maximum value: (18) In the formula, Indicates the first The vulnerability coefficient of each node; CD These are weighting coefficients, depending on the decision-maker's... and Excessive attention and preferences; express The 2-norm; express The 2-norm.

[0100] It can reflect the first The spatial vulnerability of each node. The perturbation node corresponds to... The larger the value, the weaker the spatial immunity of the disturbing node. Based on this, nodes with weak immunity can be identified.

[0101] S2-4: Characterization of disturbance uncertainty.

[0102] In the spatial coordination planning of backup resources, the impact of disturbance locations and their uncertainties on the planning model must be considered. This invention uses Monte Carlo stochastic production simulation, combined with historical power grid disturbance data, equipment aging and failure probabilities, and network topology, to obtain the disturbance set and its spatial probability distribution required for system backup planning. The disturbance set... P all Sort the disturbances by power deficit from smallest to largest, and consider the probability of different disturbances occurring in each region to obtain the spatial probability matrix representation of the disturbance set, as shown in formula (19): (19) In the formula, The index variable refers to the region of disturbance. ; This refers to the index variable used to sort power deficits. ; The number of perturbations in the perturbation set; The power deficit is sorted by size. The disturbance occurred and happened exactly on the 1st The joint probability of each region. Let be the spatial probability matrix of the perturbation set, and let its i-th The conditional probability distribution of the column is ,in Sort by power deficit size The disturbance occurred in the first Conditional probability of each region: (20) S3: Cost-benefit analysis considering risk preference.

[0103] First, an analysis of the value-added risk (VAT) of frequency exceeding limits was conducted, and a system was established. An over-limit penalty mechanism is implemented; then, the risk preference reliability cost of the alternative solution is calculated using the conditional risk preference method; and finally, the risk preference reliability benefit of the alternative solution is calculated using the discrete probability distribution of the over-limit loss.

[0104] S3-1: Value at Risk Analysis of Frequency Exceeding Limits.

[0105] The over-limit loss can be calculated based on the low-frequency load shedding mechanism, however, regarding Penalty mechanisms for exceeding limits are still relatively rare. The losses caused by excessively high frequencies mainly include damage to the internal structure of synchronous generator units, losses due to distributed power generation disconnection from the grid, and additional low-frequency load shedding costs caused by deterioration of frequency indicators. Based on Analysis of losses due to exceeding limits and related factors Constraint criteria, establishment The penalty mechanism for exceeding the limit is shown in equation (21): (twenty one) In the formula, Reference Constraint level, For the first Level constraint, For the first Level Constraints Penalties for exceeding limits. Different levels of penalties. The constraints depend on the relay protection settings of the distributed generation and the unit. Tolerance value.

[0106] S3-2: Calculate the reliability cost of risk preference.

[0107] From frequent, high-volume common disturbances to low-probability extreme events, the risk and losses from power system frequency exceedances increase non-linearly. Different incident levels result in different losses; these costs are known as reliability costs, including... Over-limit losses and low-frequency load shedding losses. For a frequency over-limit incident, what are the backup planning options? r The reliability cost is: (twenty two) In the formula, For the load of the power system, a , b For different Low-frequency load reduction ratio coefficient and unit penalty value under over-limit level; For reliability costs; for Losses due to exceeding limits.

[0108] Reliability cost L ( r ) is a random variable, and it exists in relation to the alternative planning scheme. r The relevant probability distribution, let the probability density distribution function be... To take into account the risk preferences of decision-makers, risk factors are defined. c This reflects the scope of risk the decision-maker is concerned with, i.e., the severity and rarity of losses the decision-maker is concerned with within the overall incident. This invention uses a reliability cost greater than or equal to a certain threshold. Quantify risk factors using probability: (twenty three) In the formula, Indicates risk factors; Let be a random variable relating to the disturbance loss; Indicates alternative planning schemes; This represents the probability distribution between reliability costs and backup plans; This is a mapping function between a threshold and a risk factor; the threshold C L Determined by the decision-maker.

[0109] By changing c This allows for continuous shifts in how decision-makers focus on different risk profiles. c As the number of cases approaches zero, policymakers tend to focus more on extreme events. c When the value approaches 1, there is a greater tendency to focus on overall events. c Down r Relevant conditions, reliability costs for: (twenty four) in, This represents the expected loss corresponding to a disturbance event whose disturbance loss exceeds a threshold. S3-3: Calculate the reliability gains of risk preference.

[0110] The perturbation set of the sampling year P all By inputting the low-order node frequency response analytical model established in S1, the frequency indices for all regions can be obtained. Using the worst-case frequency indices for all regions, based on the low-frequency load shedding strategy and the model established in S3-1... The over-limit penalty mechanism can quickly calculate the loss distribution across the entire risk range. : (25) In the formula, Sort by power deficit size The disturbance occurred in the first When the system operates in a certain region, it causes losses due to exceeding the system frequency limit.

[0111] Using the spatial probability matrix established in S2-4, for By calculating the expected probability of each column, the loss distribution of the system under all disturbance events can be obtained. , in The calculation method is as follows: (26) By sorting the frequency over-limit losses corresponding to all disturbance events, we can obtain The discrete form of the probability distribution. Based on its true discrete probability distribution, different accident ranges can be taken without the need for a continuous expression of the probability distribution function, thereby obtaining different risk factors. c The reliability cost of the backup plan.

[0112] Adding backup equipment can effectively intercept the risk of frequency limits being exceeded, thus improving system reliability. The reduction in reliability costs before and after adding backup equipment is the reliability gain. Therefore, considering the risk appetite, the reliability gain of backup equipment is crucial. Represented as: (27) S4: Construct a backup planning model.

[0113] The alternative planning model consists of decision variables, an objective function, and constraints. First, the decision variables of the alternative planning model are determined, and the objective function is constructed. Then, the constraints that the alternative planning scheme must satisfy are considered, and the constraint function of the alternative planning model is established.

[0114] S4-1: Objective function for constructing the alternative planning model Different backup resources have varying response characteristics and costs, and the benefits of planning them in different locations also differ. Therefore, it is necessary to weigh the backup capacity, location, and backup costs of various resources, and to consider FSDC collaborative planning of diverse and flexible backup resources. Thus, the decision variables in the backup planning model constructed in this invention are the backup capacity of various backup resources in each region. Class resources and There are 10 regions, with a total of 1000 areas. One decision variable: (28) In the formula, Indicates the first The first region Planned capacity of backup resources; For index variables that refer to resource types, ; The number of resource types The reliability benefit of the backup can be obtained from equation (27), and the cost of the backup planning scheme. This mainly includes investment costs. I ( r ) and call cost D ( r The isochronous value method is used to calculate the sampling year. I ( r ); D ( r This is related to the number of effective disturbances in the sampling year. m and the Unit capacity allocation cost of backup resources Related, that is, through J The cumulative cost of resource allocation is obtained D ( r ).

[0115] (29) (30) (31) In the formula, k The discount rate is... α For the lifespan of backup resources, Representing the Total investment cost of similar resources For the first The capacity for calling class-alternative resources, For the first The unit capacity cost of calling up backup resources.

[0116] By combining equations (27) and (29) to obtain the reserve reliability benefits and reserve costs, a reserve planning model considering spatial distribution and risk preference can be established. The net risk preference benefit is then used to calculate the reserve cost. Maximize the objective function: (32) in, As a backup plan In risk factors The reliability gains are calculated using equation (27) in S3-3; As a backup plan In risk factors The planning cost is calculated using equation (29).

[0117] S4-2: Constraints for Constructing the Alternative Planning Model The backup planning model constructed in this invention considers the following constraints: active power balance constraints, generator output constraints, line power flow constraints, and frequency security constraints (including...). Constraints and Constraints include capacity constraints for reserve resources and minimum planning unit constraints. Among them, active power balance constraints, unit output constraints, and line power flow constraints are consistent with traditional planning models. Frequency security constraints are considered in the objective function by the reliability benefits calculated through S3. The capacity constraints and minimum planning unit constraints for various reserve resources are shown in equations (33) and (34): (33) (34) In the formula, For the first Upper limit of capacity planning for backup resources; For the first Minimum planning unit capacity for reserve resources; For integer variables, .

[0118] Thus, by establishing the objective function and constraints, a backup planning model has been constructed, which can be used to optimize the decision variables and find the optimal backup planning scheme.

[0119] S5: Solving the backup planning model and verifying the planning scheme.

[0120] First, an improved particle swarm optimization algorithm is designed to optimize and solve the alternative planning model, and the optimization solution is accelerated by using regional planning weights. Then, the feasibility of the optimized alternative planning scheme is verified and a confidence index is given.

[0121] S5-1: Improved optimization algorithm.

[0122] This invention proposes a prior knowledge-guided multi-start particle swarm optimization (PKG-PSO) algorithm, which uses regional planning weights to guide the search direction of alternative planning schemes in regional capacity allocation, thereby accelerating the optimization solution.

[0123] The system is divided into S2-2. After identifying the regions, the node with the largest vulnerability coefficient within each region is selected to represent the region's vulnerability level, thus obtaining the region's vulnerability coefficient. The greater the vulnerability coefficient of a region, the weaker its spatial vulnerability; more reserve capacity needs to be allocated to this region in the planning to enhance its ability to absorb disturbances, thereby better suppressing the global frequency drop. Considering the uncertainty of the disturbance location, regions with weak spatial vulnerability may have a lower probability of disturbance occurrence. Therefore, the regional planning weights need to comprehensively consider both the vulnerability of the region and the probability of disturbance occurrence. The expected vulnerability of each region can be calculated by combining equations (18) and (19). : (35) In the formula, For the first The power deficits in each region are ranked as follows: The vulnerability coefficient during disturbance; For the first Expected value of the vulnerability of each region to interference.

[0124] For all regions Normalization is performed to obtain the regional planning weights of reserve resources in each region. , , in for: (36) A higher regional planning weight indicates a greater tendency for reserve resources to allocate more capacity to that region. This regional planning weight is introduced as prior knowledge into the traditional PSO algorithm to guide the optimization search direction. Specifically, the improvement is as follows: (1) A multi-granularity weight-guided initialization strategy is adopted. Based on prior knowledge, multiple initialization modes are designed, ranging from fully following the regional weight to slight weight guidance, to generate multiple initial populations in order to balance the convergence speed and global search capability.

[0125] (2) A weight guidance term is added to the PSO velocity update formula to guide particles to move in the direction of weight allocation. The guidance strength decreases linearly with the number of iterations, which accelerates the convergence of the algorithm in the early stage and enhances global exploration in the later stage. When the position of a particle violates the constraints, a repair strategy based on regional planning weights is adopted.

[0126] (3) A multi-starting-point strategy is adopted, starting the search from multiple different initial points to avoid getting trapped in local optima. In each iteration, the historical optimal solution is retained, and some particles are reinitialized to enhance the global exploration capability.

[0127] It should be noted that the regional planning weight guidance is not a mandatory constraint, but rather a suggestion for the search direction. PKG-PSO avoids getting trapped in local optima through multiple starting points and iterative optimizations, and must strictly meet the optimization constraints.

[0128] S5-2: Verify the planning scheme.

[0129] To avoid contingency plans failing to meet actual needs due to the subjective experience of decision-makers, it is necessary to conduct feasibility verification of the plans and provide confidence indicators. Verification costs are a significant part of the contingency planning process. A ( r This includes backup costs and reliability costs associated with exceeding frequency limits, which also exist in the same way as... The relevant probability distribution, analogous to equation (24), risk factors The verification cost Represented as: (37) in, This represents the probability distribution between the verification cost and the alternative planning scheme; The threshold for the verification cost corresponding to the risk factor; This represents the expected verification cost corresponding to a disturbance event where the verification cost exceeds the verification cost threshold. Confidence indicators for backup plans Defined as: (38) in, Indicates risk factors Backup Plan The cost of verification; Indicates risk factors The inspection cost corresponding to not planning for backup; Based on this confidence index, the risk factor is judged. c Backup Plan Is it because the cost is too high that it will not be adopted? s When the value is less than 0, the planning proposal should be rejected; when... s When the confidence index is greater than or equal to 0, the planning scheme can be adopted, and the higher the confidence index, the more worthy the scheme is of adoption.

[0130] To verify the effectiveness and feasibility of the proposed SOCP method, spatial collaborative planning was performed on four types of reserve resources: hydropower (HPU), GFM-IBR, synchronous condenser (SC), and EIL. Table 3 presents the optimal planning scheme and net benefit under different risk factors. Total reserve capacity and net benefit vary with... c The trend chart of change is as follows Figure 4 As shown.

[0131] Table 3 Optimal Planning Scheme and Net Returns under Different Risk Factors

[0132] From Table 3 and Figure 4 It can be seen that, with c As risk appetite decreases and decision-makers shift their focus from global emergencies to extreme events, the demand for reserves continuously increases, and the net benefits generated by reserves also rise. The proposed planning method can continuously characterize the impact of decision-makers' risk appetite on reserve planning schemes, obtain optimal reserve space planning schemes under different risk ranges, and avoid being overwhelmed by extreme events.

[0133] Further analysis of Table 3 reveals that HPU was not prioritized for planning due to its relatively high price; EIL, due to its flexibility and price advantage, mostly had its capacity at the upper limit of constraints; SC can be converted from decommissioned thermal power plants, and has a price advantage over HPU and GFM, therefore, with the growth of standby demand, SC is also prioritized for planning; GFM is only planned in extreme risk ranges (…). c< Planning is achieved at 10%). Therefore, to improve the system's ability to respond to extreme events, new energy power plants need to be equipped with GFM equipment to provide inertia and primary frequency regulation capabilities. Furthermore, the spatial planning schemes for backup resources differ under different risk ranges; Region 1 has sufficient inertia and a low probability of disturbance, so backup resources are mostly allocated among the other three regions. The proposed planning method, by balancing the backup capacity, location, and cost of various resources, can achieve optimal spatial collaborative planning of backup resources.

[0134] To analyze the impact of the uncertainty of the disturbance location on the planning scheme, an additional different disturbance spatial probability matrix was set up. The disturbance was assumed to occur only in region 1, i.e. Set all to r s1= [1 0 0 0] T . Figure 5 The total reserve capacity and net revenue are given under two perturbation probability matrices. c A bar chart showing the changes. Table 4 shows... c Alternative planning schemes under two perturbation probability matrices when the value is 0.01.

[0135] Table 4 r s and r s1 The optimal planning scheme

[0136] To verify the superiority of the proposed planning method in jointly planning inertia and primary frequency regulation reserve, it is compared with the traditional method that only considers... A comparative analysis of the interception effectiveness of the FFFR single planning (TFRP) method is conducted. Table 5 presents the alternative planning results of TFRP and SOCP under different risk factors.

[0137] Table 5. Results of TFRP and SOCP contingency planning

[0138] As shown in Table 5, the reserve requirements and returns of TFRP are lower than those of SOCP under different risk ranges. This is because traditional TFRP ignores... The risk value exceeding the limit means that the inertia reserve cannot meet the optimal requirements of the system, and the optimal coordination of the reserve in terms of inertia and primary frequency regulation time scale cannot be achieved.

[0139] The effectiveness of the planning scheme in reducing the risk of frequency index exceeding limits is evaluated by comparing the CDF of the frequency index corresponding to the disturbance sets before and after the planning. Figure 6 Extreme risks are given ( c (Take 0.01) and general risk ( c A comparison chart of the planning effects of SOCP and TFRP at a setting of 0.8. From... Figure 6 As can be seen, SOCP can effectively reduce the probability of system frequency indicators exceeding limits, and its effect is better than TFRP; with Rof m The increased risk value beyond the limit further highlights this advantage.

[0140] To verify the superiority of the proposed SOCP in considering FSDC for spatial optimal collaborative planning, it is compared with the traditional COIP based on COI frequency. Table 6 shows the backup planning results of COIP and SOCP under different risk factors.

[0141] Table 6. Contingency Planning Results for COIP and SOCP

[0142] As shown in Table 6, SOCP's reserve capacity level and reserve benefits are higher than COIP under different risk ranges. This is because COIP ignores the risk of local frequency overruns, resulting in overly conservative reserve requirements that do not meet actual needs. Furthermore, COIP only applies under more extreme risk ranges (…). γ≤ Only 30% of events are considered for backup; this means that under global risk, using COIP would completely homogenize extreme events with ordinary events, making reasonable backup planning impossible and potentially creating security vulnerabilities. The proposed SOCP can consider the risk value of node frequency exceeding limits, and the planning results are more in line with actual needs.

[0143] To verify the superiority of SOCP in reducing the risk of frequency index exceeding limits, Figure 7 Given the extreme risk ( c Comparison of planning performance between SOCP and COIP (using values ​​of 0.01 and 0.3). It can be seen that SOCP, by considering the risk value of node frequency exceeding limits and performing spatially optimal planning for multiple types of backup resources, is more effective than COIP in reducing the probability of frequency exceeding limits.

[0144] Decision-makers' risk preferences are subjective and may not reflect actual objective conditions. Therefore, a feasibility analysis of the planning scheme is necessary. (See Table 3 for details.) c Taking the optimized result of 1124MW with a capacity of 0.3 as an example, a verification analysis is conducted. Figure 8 Confidence indices for planning schemes under different risk factors and verification costs before and after reserve investment are given. c When the value is 0.83, the verification cost before and after the backup deployment is equal, corresponding to a confidence index of 0. At this point, the feasibility of the scheme is at the critical point. That is, at... c When the value is less than 0.816, deploying 1124MW of reserve is feasible; while when... c When the value is greater than 0.816, none of the proposed plans should be accepted due to the excessively high cost of adding equipment. It can be seen that... c The feasibility of the scheme was verified when the value was 0.3.

[0145] Therefore, the fast frequency response backup resource spatial optimal collaborative planning method proposed in this invention, which takes into account extreme risks, can consider the frequency spatial distribution and disturbance uncertainty, formulate optimal planning schemes for backup resources under different risk preferences, realize the collaborative planning of backup resources on the spatial scale and the optimal coordination of inertia and primary frequency regulation backup on the time scale. Using the planning scheme formulated in this invention, the risk of exceeding the limit of local frequency indicators of the system that may exist when formulating schemes based on conventional methods can be avoided, providing a more reliable decision-making basis for improving the system's ability to respond to extreme events.

[0146] The above-described embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A fast-frequency response spatial optimal collaborative planning method for reserve resources that takes into account extreme risks, characterized in that, The planning method includes the following steps: S1: Construct a low-order node frequency response analytical model; A low-order node frequency response model is constructed, which is then simplified and analytically derived. A low-order node frequency response analytical model NFRAM is constructed to achieve fast analytical calculation of the frequency response of any node. S2: Characterization and processing of frequency spatial distribution characteristics; To embed the frequency spatial distribution characteristics into the reserve resource planning model, they are characterized and processed. First, two node frequency index matrices are constructed to comprehensively represent the FSDC. Second, based on the node frequency index matrices, system planning partitioning is performed and weak nodes in terms of disturbance resistance are identified. Finally, the spatial probability matrix of the disturbance set is used to characterize the disturbance uncertainty. Specifically: S2-1: Construct the node frequency index matrix; S2-2: System partitioning oriented towards planning; S2-3: Identify nodes with weak anti-interference capabilities; S2-4: Characterization of disturbance uncertainty; S3: Cost-benefit analysis considering risk appetite; First, an analysis of the risk value of frequency exceeding limits is conducted, and a system is established. The system implements an over-limit penalty mechanism; then, it calculates the risk-preference reliability cost of the alternative solution using the conditional risk-preference method; finally, it calculates the risk-preference reliability benefit of the alternative solution using the discrete probability distribution of the over-limit loss. S4: Construct a backup planning model; The standby planning model consists of decision variables, objective function, and constraints. First, the decision variables of the standby planning model are determined, and the objective function of the standby planning model is constructed. Then, the constraints that the standby planning scheme needs to satisfy are considered, and the constraint function of the standby planning model is established. S5: Solving the backup planning model and verifying the planning scheme; An improved particle swarm optimization algorithm is designed to optimize and solve the alternative planning model. The optimization solution is accelerated by using regional planning weights. The feasibility of the optimized alternative planning scheme is verified and a confidence index is given.

2. The method for optimal collaborative planning of backup resource space considering extreme risks in a fast frequency response according to claim 1, characterized in that, Specifically, S1 refers to: S1-1: Basic component modeling; S1-1-1: For a N For a power system with nodes, the node admittance matrix is ​​obtained based on the power system network structure. ,Include g One frequency modulation node and l There are several non-frequency regulating nodes; after an active power disturbance occurs in the power system, the relationship between the phase angle of each node and the active power injected into the grid is described by the power flow equations: (1) In the formula, It is a vector consisting of the power injection quantities of the frequency modulation node. A vector consisting of the power injection amounts at non-frequency-modulated nodes; This is a block submatrix in the nodal admittance matrix that represents the admittance relationship between frequency-modulated nodes. This is a block submatrix in the nodal admittance matrix that represents the admittance relationship between frequency-modulated nodes and non-frequency-modulated nodes. This is a block submatrix in the nodal admittance matrix that represents the admittance relationship between non-frequency-modulated nodes and frequency-modulated nodes. This is a block submatrix in the nodal admittance matrix that represents the admittance relationship between non-frequency-tuned nodes; The rotor angle vector of the frequency modulation node. The rotor angle vector of the non-frequency-tuned node; By eliminating the formula (1) get : (2) (3) In the formula, Assign an initial matrix to the perturbation; This is the inter-machine oscillation matrix; This represents the power vector of inter-machine oscillations. Assign an initial power vector to the COI; S1-1-2: Model the frequency response of the frequency regulation resources connected to the frequency regulation node and establish the equivalent frequency response model of the frequency regulation node; the frequency regulation resources connected to the frequency regulation node mainly consider three types of resources: synchronous generator sets (SGs) dominated by thermal power units, IBRs represented by wind power, photovoltaic and energy storage, and load-side resources represented by emergency interruptible loads (EIL). S1-1-3: Based on the modeling of the three types of frequency modulation resources in S1-1-2, the inertial response of a frequency modulation node connecting multiple modulation resources is described by the equivalent rotor motion equation: (7) In the formula, , These are the rated angular velocity vector and the rated frequency vector, respectively. This is a vector representing the change in mechanical power. This is the equivalent inertia time constant matrix; Equivalent inertia time constant matrix of frequency modulation node The results are obtained by aggregating the synchronous inertia of SGs and the virtual inertia of network-type IBRs: (8) In the formula, , These are the resource capacity proportion vectors of SGs and the resource capacity proportion vectors of the network-type IBR, respectively. The virtual inertia coefficient matrix of the network-type IBR; The vector of mechanical power change at the frequency modulation node for: (9) In the formula, This is the load shedding vector for EIL; S1-2: Model simplification and analytical derivation; Based on equations (2)-(9), the frequency response model of the low-order nodes of the system is established, and the frequency response of the frequency-modulated nodes in the complex frequency domain is expressed as the vibration equation: (10) (11) In the formula, , , These are the mass matrix, damping matrix, and stiffness matrix of the vibration equation, respectively. , These are the unbalanced mechanical power vectors generated by the approximate preceding and following inertial links, respectively. According to equation (2), Depend on Caused COI frequency and Caused oscillation frequency composition: (12) In the formula, This is the frequency response vector of the COI; This is the frequency response vector of the inter-machine oscillation; For the One frequency modulation node The frequency oscillations generated by the remaining frequency modulation nodes consist of: (13) In the formula, and Both refer to index variables representing frequency modulation nodes. , ; Considering and The low-pass filtering characteristics of the first-order inertial link between them will Approximate replacement ,but It can be approximated as : (14) At this point, equation (14) becomes an analytically solvable second-order linear nonhomogeneous differential equation: (15) In the formula, The external excitation vector is the one defined in the vibration equation. Thus, equation (15) is... N The forced vibration equations of the degrees of freedom are solved using modal analysis. Through forced decoupling, modal analysis, and superposition, the time-domain analytical expression of the frequency response of the frequency-modulated node is derived. According to the frequency divider formula, the frequency response of the non-frequency modulated node... The derivation is as follows: (16) Based on (15) and (16), a low-order NFRAM is constructed, and the frequency response of all nodes, including the frequency response of the frequency-modulated nodes, is calculated analytically. Frequency response of non-frequency modulated nodes .

3. The method for optimal collaborative planning of backup resource space considering extreme risks in a fast frequency response according to claim 2, characterized in that, In S1-1-2, the three resources are specifically: (1) SGs has an actual rotating rotor, and its inertial response is described by the rotor motion equation: (4) In the formula, Let be the inertial time constant matrix of SGs; Here is the damping coefficient matrix; Let SGs be the mechanical power increment vector; These are the frequency deviation vectors of SGs; Let be the electromagnetic power vector of SGs; For the Laplace operator; SGs participate in primary frequency regulation through a speed governor. The transfer function of its most representative low-order speed governor model is: (5) In the formula, It is a unit diagonal matrix; This is the power coefficient matrix for the high-pressure cylinder; This is the reheat time constant matrix; This is the adjustment coefficient matrix; (2) IBRs provide virtual inertial response and primary frequency modulation response capabilities through control strategies; networked IBRs can be directly aggregated into the inertial links of frequency modulation nodes; the primary frequency modulation capability of networked IBRs is achieved through virtual droop control: (6) In the formula, , These are the mechanical power increment vector and frequency vector of the mesh-type IBR, respectively; , These are the response delay matrix and virtual droop coefficient matrix of the network-type IBR, respectively; (3) EIL provides a fast frequency response by actively cutting off a certain amount of load through event triggering, and its active power response is represented as a step power signal.

4. The method for optimal collaborative planning of backup resource space considering extreme risks in a fast frequency response according to claim 3, characterized in that, Specifically, S2 is: S2-1 specifically refers to: A node frequency index matrix is ​​proposed to comprehensively characterize it; when the disturbance occurs at the , When there are only a few nodes, the frequency response of all nodes in the power system is quickly calculated based on the low-order NFRAM constructed in S1; only the initial RoCoF and maximum frequency difference of the nodes are retained as key frequency indicators to form a sequence about the frequency response of the nodes. row vectors and about row vectors ; Traverse all perturbation nodes and construct information about them. Node frequency index matrix Regarding Node frequency index matrix ; S2-2 specifically refers to: A column-based clustering partitioning method based on the node frequency index matrix is ​​proposed. and The Column elements and Reflecting the The frequency response characteristics of each node to all possible disturbances in the system; and After standardization, new column vectors are formed. By clustering all column vectors, nodes with similar frequency response characteristics can be divided into the same planning area. In actual power system reserve planning, the accuracy of allocation is determined by decision-makers; the significance of FSDC is determined by... uniformity index measure, The larger the value, the less significant the FSDC; the uniformity index is obtained by formula (17): (17) in, This refers to the index variable of the column. ; for The Column vector; S2-3 specifically refers to: and The The norm of a row element reflects the degree of threat posed by the disturbance location to the system frequency; a method for identifying vulnerable nodes based on the row norm of the node frequency index matrix is ​​proposed; for the Each node, for and Weighted by norm and maximum value: (18) In the formula, Indicates the first The vulnerability coefficient of each node; c, d These are weighting coefficients, depending on the decision-maker's... and Excessive attention and preferences; express The 2-norm; express The 2-norm; Able to reflect the first The spatial vulnerability of each node; the perturbation node corresponding to... The larger the value, the weaker the spatial immunity of the disturbing node; based on this, nodes with weak immunity to disturbance are identified. S2-4 specifically refers to: Through Monte Carlo stochastic production simulation, combined with historical power grid disturbance data, equipment aging and failure probabilities, and network topology, the disturbance set required for system reserve planning and its spatial probability distribution are obtained; the disturbance set is then... P all Sort the disturbances by power deficit from smallest to largest, and consider the probability of different disturbances occurring in each region to obtain the spatial probability matrix representation of the disturbance set, as shown in formula (19): (19) In the formula, The index variable refers to the region of disturbance. ; This refers to the index variable used to sort power deficits. ; The number of perturbations in the perturbation set; The power deficit is sorted by size. The disturbance occurred and happened exactly on the 1st The joint probability of each region; Let be the spatial probability matrix of the perturbation set, and let its i-th The conditional probability distribution of the column is ,in Sort by power deficit size The disturbance occurred in the first Conditional probability of each region: (20)。 5. The method for optimal collaborative planning of backup resource space considering extreme risks in a fast frequency response according to claim 4, characterized in that, Specifically, S3 is: S3-1: Risk Value Analysis of Frequency Exceeding Limits; based on Analysis of losses due to exceeding limits and related factors Constraint criteria, establishment The penalty mechanism for exceeding the limit is shown in equation (21): (21) In the formula, Reference Constraint level, For the first Level constraint, For the first Level Constraints Penalties for exceeding limits; different levels The constraints depend on the relay protection settings of the distributed generation and the unit. Tolerance value; S3-2: Calculate the reliability cost of risk preference; Different accident levels result in different losses, which are defined as reliability costs, including Over-limit losses and low-frequency load shedding losses; for a frequency over-limit accident, backup planning scheme. r The reliability cost is: (22) In the formula, For the load of the power system, a , b For different Low-frequency load reduction ratio coefficient and unit penalty value under over-limit level; For reliability costs; for Losses due to exceeding limits; Reliability cost L ( r ) is a random variable, and it exists in relation to the alternative planning scheme. r The relevant probability distribution, let the probability density distribution function be... By defining risk factors γ This reflects the scope of risks it focuses on; it uses reliability costs greater than or equal to a certain threshold. Quantify risk factors using probability: (23) In the formula, Indicates risk factors; Let be a random variable relating to the disturbance loss; Indicates alternative planning schemes; This represents the probability distribution between reliability costs and backup plans; This is a mapping function between a threshold and a risk factor; the threshold C L Determined by the decision-maker; By changing γ That is, it can continuously change the decision-maker's focus on different risk ranges; when γ As the number of cases approaches zero, policymakers tend to focus more on extreme events. γ When the value approaches 1, there is a greater tendency to focus on overall events; exist γ Down r Relevant conditions, reliability costs for: (24) in, This represents the expected loss corresponding to a disturbance event whose disturbance loss exceeds a threshold. S3-3: Calculate the reliability returns of risk preference; The perturbation set of the sampling year P all Input the low-order node frequency response analytical model in S1 to obtain the frequency indices for all regions; using the worst-case frequency indices for all regions, based on the low-frequency load reduction strategy and the model established in S3-1... The over-limit penalty mechanism can quickly calculate the loss distribution across the entire risk range. : (25) In the formula, Sort by power deficit size The disturbance occurred in the first When the system frequency exceeds the limit in a certain area, it will cause a loss due to the system frequency exceeding the limit. Using the spatial probability matrix established in S2-4, for By calculating the expected probability of each column, we can obtain the loss distribution of the system under all disturbance events. , in The calculation method is as follows: (26) The frequency over-limit loss corresponding to all disturbance events is sorted to obtain the following: The discrete form; based on its true discrete probability distribution, different accident ranges can be taken and different risk factors can be obtained without the need for a continuous expression of the probability distribution function. γ The reliability cost of the backup plan; Ultimately, the backup reliability benefit is considered in terms of risk appetite. Represented as: (27)。 6. The method for optimal collaborative planning of backup resource space considering extreme risks in a fast frequency response according to claim 5, characterized in that, Specifically, S4 is: S4-1: Objective function for constructing the alternative planning model The decision variables in the constructed reserve planning model are the reserve capacity of various reserve resources in each region. Class resources and There are 10 regions, with a total of 1000 areas. One decision variable: (28) In the formula, Indicates the first The first region Planned capacity of backup resources; For index variables that refer to resource types, ; The number of resource types The reliability benefit of the backup is obtained from equation (27), and the cost of the backup planning scheme is... Mainly includes investment costs I ( r ) and call cost D ( r The sampling year is calculated using the isochronous value method. I ( r ); D ( r This is related to the number of effective disturbances in the sampling year. m and the Unit capacity allocation cost of backup resources Related, through J The cumulative cost of resource allocation is obtained D ( r ); (29) (30) (31) In the formula, k The discount rate is... α For the lifespan of backup resources, Representing the Total investment cost of similar resources For the first The capacity for calling class-alternative resources, For the first The unit capacity cost of accessing standby resources; Combining equations (27) and (29), the reserve reliability benefits and reserve costs are obtained, and a reserve planning model considering spatial distribution and risk preference is established; the net risk preference benefit is used as the basis for calculation. Maximize the objective function: (32) in, As a backup plan In risk factors The reliability gains are calculated using equation (27) in S3-3; As a backup plan In risk factors The planning cost is calculated using equation (29); S4-2: Constraints for Constructing the Alternative Planning Model The constraints considered in the reserve planning model include active power balance constraints, generator output constraints, line power flow constraints, frequency security constraints, reserve resource capacity constraints, and minimum planning unit constraints. Among these, frequency security constraints include... Constraints and Constraints: Active power balance constraints, generator output constraints, and line power flow constraints are consistent with traditional planning models; Frequency security constraints are considered in the objective function based on the reliability benefits calculated by S3; Capacity constraints and minimum planning unit constraints for various reserve resources are shown in equations (33) and (34): (33) (34) In the formula, For the first Upper limit of capacity planning for backup resources; For the first Minimum planning unit capacity for reserve resources; For integer variables, ; By constructing an alternative planning model using the objective function and constraints, the decision variables are optimized to find the optimal alternative planning scheme.

7. The method for optimal collaborative planning of backup resource space considering extreme risks in a fast frequency response according to claim 6, characterized in that, Specifically, S5 is: S5-1: Improved optimization algorithm; A multi-starting-point particle swarm optimization algorithm PKG-PSO based on prior knowledge is proposed. By guiding the search direction of alternative planning schemes in regional capacity allocation through regional planning weights, the optimization solution is accelerated. The system is divided into S2-2. After identifying a region, the node with the highest immunity vulnerability coefficient within that region is selected to represent the region's immunity vulnerability, thus obtaining the region's immunity vulnerability coefficient. The regional planning weights need to comprehensively consider the regional vulnerability and the probability of disturbance occurrence; the expected vulnerability of each region can be obtained by combining equations (18) and (19). : (35) In the formula, For the first The power deficits in each region are ranked as follows: The vulnerability coefficient during disturbance; For the first Expected value of the vulnerability to interference in each region; For all regions Normalization is performed to obtain the regional planning weights of reserve resources in each region. , , in for: (36) Introducing regional planning weights as prior knowledge into the traditional PSO algorithm to guide the search direction for optimization; S5-2: Verify the planning scheme; During the contingency planning process, verify the costs. A ( r This includes backup costs and reliability costs associated with exceeding frequency limits, which also exist in the same way as... The relevant probability distribution, analogous to equation (24), risk factors The verification cost Represented as: (37) in, This represents the probability distribution between the verification cost and the alternative planning scheme; The threshold for the verification cost corresponding to the risk factor; This represents the expected verification cost corresponding to a disturbance event where the verification cost exceeds the verification cost threshold. Confidence indicators for backup plans Defined as: (38) in, Indicates risk factors Backup Plan The cost of verification; Indicates risk factors The inspection cost corresponding to not planning for backup; Based on this confidence index, the risk factor is judged. γ Backup Plan Is it because the cost is too high that it will not be adopted? σ When the value is less than 0, the planning proposal is rejected; when... σ When the confidence index is greater than or equal to 0, the planning scheme is adopted, and the higher the confidence index, the more worthy it is of adoption.

8. The method for optimal collaborative planning of backup resource space considering extreme risks in a fast frequency response according to claim 7, characterized in that, In S5-1, the specific improvement to introducing regional planning weights as prior knowledge into the traditional PSO algorithm is as follows: (1) A multi-granularity weight-guided initialization strategy is adopted. Based on prior knowledge, multiple initialization modes are designed, ranging from fully following the regional weight to slight weight guidance, to generate multiple initial populations. (2) Add a weight guiding term to the PSO velocity update formula to guide the particles to move in the direction of weight allocation; when the position of the particles violates the constraints, adopt a repair strategy based on regional planning weights. (3) Adopt a multi-starting point strategy and start the search from multiple different initial points; In each iteration, the historical best solution is retained, and some particles are reinitialized.

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