Multi-area frequency security constrained day-ahead scheduling method considering random disturbances and faults

Abstract

The application discloses a kind of multi-area frequency safety constraint day-ahead scheduling methods considering random disturbance and fault, it is related to power system dispatching and operation control technical field, this method includes: the high-dimensional joint distribution of multi-area random disturbance is constructed, and the set of multi-area joint disturbance scene is generated in combination with accidental fault parameters;Establish a multi-area joint frequency response target model, calculate regional frequency safety index;Train progressive latent bottleneck physical information neural network, linearize regional frequency minimum point as frequency safety proxy constraint;Based on disturbance scene set, regional frequency rate of change and frequency safety proxy constraint, construct random frequency safety constraint;With day-ahead total cost minimization as target, combine random frequency safety constraint and system operation constraint, construct and solve day-ahead scheduling optimization model to obtain day-ahead scheduling scheme.The application improves the coordination ability of frequency safety and operation economy of multi-area power grid under the superposition of random disturbance and accidental fault scene.

Description

Technical Field

[0001] This application relates to the field of power system dispatching and operation control technology, and in particular to a multi-regional frequency security constraint day-ahead dispatching method that takes into account random disturbances and faults. Background Technology

[0002] With a high proportion of renewable energy being integrated into the power system, system inertia is decreasing, power fluctuations and uncertainties are increasing, posing greater challenges to grid frequency security. Renewable energy prediction errors exhibit spatiotemporal correlation, with deviations potentially occurring simultaneously in multiple regions, resulting in a "spatial amplification" of disturbances. Simultaneously, the system still needs to withstand the impact of occasional faults such as unit tripping and line failures. In the complex scenario of random disturbances superimposed with occasional faults, indicators such as the Frequency Nadir (Nadir) and the Rate of Change of Frequency (RoCoF) are more prone to exceeding limits, and the risks exhibit tail-like and extreme characteristics. Traditional scheduling methods based on deterministic or independent stochastic assumptions are insufficient to effectively cover these risks.

[0003] Relevant frequency-constrained scheduling often employs a Center of Inertia (COI) or a single-region equivalent model, which fails to reflect regional inertia differences, uneven distribution of primary frequency regulation resources, and cross-regional coupling effects caused by interconnection lines, easily masking local regional risks. Simultaneously, uncertainty modeling is often based on independent or low-dimensional correlation assumptions, making it difficult to characterize the spatial joint structure of multi-region prediction errors, leading to deviations between scenario generation and risk assessment. Furthermore, dynamic indicators such as the frequency minimum point are strongly coupled with the response process; directly embedding them into day-ahead optimization significantly increases the solution difficulty, while using rigid constraints across the entire scenario is overly conservative, driving up backup costs.

[0004] Therefore, how to cope with the combined impact of random disturbances and occasional faults in multi-regional power grids with a high proportion of renewable energy access, and how to achieve effective coordination between frequency security constraints and economic dispatch while avoiding the masking of local frequency over-limit risks and avoiding overly conservative reserve configurations, is an urgent problem to be solved in this field. Summary of the Invention

[0005] The purpose of this application is to provide a multi-regional frequency security-constrained day-ahead scheduling method that takes into account random disturbances and faults, so as to improve the coordination capability of frequency security and operation economy of multi-regional power grids under the scenario of random disturbances superimposed on occasional faults.

[0006] To achieve the above objectives, this application provides the following solution: In a first aspect, this application provides a multi-region frequency security constraint day-ahead scheduling method that takes into account random disturbances and faults, the multi-region frequency security constraint day-ahead scheduling method that takes into account random disturbances and faults includes: Acquire historical dispatch data of multi-regional power grids during various dispatch periods; the historical dispatch data includes at least: new energy prediction error samples and occasional fault parameters; Based on the new energy prediction error samples, the marginal cumulative distribution function of random disturbance deviation in each region is constructed, and based on the marginal cumulative distribution function, a high-dimensional joint distribution of random disturbance in multiple regions is constructed, thereby obtaining the sampled value of random disturbance deviation in each region during each scheduling period. The sampled values ​​of the random disturbance deviation are superimposed with the occasional fault parameters to obtain the equivalent active power disturbance of each region in each scheduling period, and then a multi-region joint disturbance scenario set containing the equivalent active power disturbance of all regions is obtained. Based on the equivalent active disturbance of the multi-region joint disturbance scenario, an initial model of the multi-region joint frequency response is established; the initial model of the multi-region joint frequency response is a function of the regional frequency deviation and the mutual power deviation between regions. Based on the regional frequency deviation, a frequency support resource response model is established, and the frequency support resource response model is substituted into the initial model to obtain a multi-regional joint frequency response target model. Solve the target model to obtain the frequency response trajectory of each region, and calculate the regional frequency security index based on the frequency response trajectory of each region; the regional frequency security index includes: regional frequency change rate and regional frequency minimum point; Based on the scheduling decision feature vector, the regional minimum frequency point, the primary frequency modulation support power and regional mutual assistance power deviation at the moment when the frequency reaches the regional minimum frequency point, and the loss function introduced by using the frequency dynamic equation as the physical residual regularization term, the progressive potential bottleneck physical information neural network is trained to obtain the trained progressive potential bottleneck physical information neural network model. The lowest regional frequency point in the encoder output of the trained progressive potential bottleneck physical information neural network model is linearized into a mixed integer linear constraint to obtain the frequency security proxy constraint. Based on a multi-regional joint disturbance scenario set, regional frequency change rate and frequency security proxy constraints, a stochastic frequency security constraint in the form of conditional risk value is constructed. With minimizing the total day-ahead cost as the optimization objective and the random frequency security constraints and system operation constraints as the constraints, a random frequency security constraint day-ahead scheduling optimization model is constructed. Solve the day-ahead scheduling optimization model with random frequency security constraints to obtain the day-ahead scheduling scheme.

[0007] In one embodiment, based on the new energy prediction error samples, a marginal cumulative distribution function of the random disturbance deviation for each region is constructed, and based on the marginal cumulative distribution function, a high-dimensional joint distribution of random disturbances in multiple regions is constructed, thereby obtaining the sampled values ​​of the random disturbance deviation for each region in each scheduling period, specifically including: Using the kernel density estimation method, the marginal probability density function of random disturbance deviation in each region is constructed based on the new energy prediction error sample; Integrating the marginal probability density function yields the marginal cumulative distribution function of the random disturbance deviation in each region; Random disturbance biases are mapped to the quantile space through the marginal cumulative distribution function to obtain quantile variables; Using the quantile variables as input, a high-dimensional joint distribution of multi-regional random perturbations is constructed using the Vine Copula framework; Samples are taken from the high-dimensional joint distribution, and the sampled values ​​of random disturbance deviations of each region during each scheduling period are obtained by inverse transformation of the cumulative distribution function at the edge of each region.

[0008] In one embodiment, the frequency support resource response model includes: an inertia response model and a primary frequency modulation model; Based on regional frequency deviation, a frequency support resource response model is established. This model is then substituted into the initial model to obtain a multi-regional joint frequency response target model, specifically including: The inter-regional mutual aid power deviation in the initial model is made explicit to obtain an explicit expression for the mutual aid power deviation with respect to the regional frequency deviation. Substituting the inertial response model, the primary frequency modulation model, and the explicit expression of the mutual power deviation with respect to the regional frequency deviation into the initial model, a multi-region joint frequency response target model is obtained.

[0009] In one embodiment, the inter-regional mutual aid power deviation in the initial model is made explicit to obtain an explicit expression for the mutual aid power deviation with respect to the regional frequency deviation, specifically including: Based on the equivalent reactance between regions, voltage amplitude, and phase angle at the operating point, the sinusoidal term in the inter-regional mutual power deviation in the initial model is linearized by a first-order Taylor expansion near the operating point to obtain the expression for the linearized mutual power deviation. Substituting the integral relationship between phase angle increment and frequency deviation into the linearized expression for mutual power deviation, we obtain an explicit expression for mutual power deviation with respect to the frequency deviation in each region.

[0010] In one embodiment, based on the scheduling decision feature vector, the regional minimum frequency point, the primary frequency modulation support power at the moment the frequency reaches the regional minimum frequency point, and the regional mutual assistance power deviation, the frequency dynamic equation is introduced as a physical residual regularization term into the total loss function. This is used to perform multi-round iterative training on the progressive potential bottleneck physical information neural network. Specifically, the training process in any given iteration round includes: The scheduling decision feature vector is input into the encoder in the current iteration round, and the predicted value of the lowest regional frequency point is output. The predicted value of the lowest regional frequency is input into the decoder in the current iteration round, and the primary frequency modulation support power and regional mutual assistance power deviation at the moment when the frequency in the current iteration round reaches the lowest regional frequency are output. Calculate the total loss function under the current iteration round and determine whether the current iteration round has reached the iteration stopping condition; the iteration stopping condition is that the total loss function under the current iteration round converges or the current iteration round reaches the preset maximum round; the total loss function includes encoder loss, decoder loss and physical regularization loss introduced by using the frequency dynamic equation as a physical residual regularization term; If so, then stop training and use the encoder and decoder of the current iteration as the trained progressive potential bottleneck physical information neural network model; If not, then continue training in the next iteration.

[0011] In one embodiment, the process of iteratively training the progressive potential bottleneck physical information neural network in multiple rounds further includes: Based on the convergence degree and gradient scale of each loss term in the encoder loss, decoder loss, and physical regularization loss under the current iteration, the relative proportion of the physical regularization loss term in the total loss function value is dynamically adjusted.

[0012] In one implementation, based on a multi-regional joint disturbance scenario set, regional frequency change rates, and frequency security proxy constraints, a stochastic frequency security constraint in the form of conditional value of risk is constructed, specifically including: For each disturbance scenario in a multi-regional joint disturbance scenario, a regional frequency security loss function is constructed for each disturbance scenario. The regional frequency security loss function includes: the regional frequency change rate loss function and the regional frequency minimum point loss function. At a preset confidence level, the conditional value at risk of the regional frequency change rate is determined based on the regional frequency change rate loss, the value at risk of the regional frequency change rate, and the slack variable corresponding to each disturbance scenario in the multi-regional joint disturbance scenario set. At a preset confidence level, the conditional value at risk of the regional frequency minimum point is determined based on the regional frequency minimum point loss, the risk value variable of the regional frequency minimum point, and the slack variable corresponding to each disturbance scenario in the multi-region joint disturbance scenario set. Establish the constraint relationship between the regional frequency change rate loss and the corresponding slack variable under each disturbance scenario, as well as the constraint relationship between the regional frequency minimum point loss and the corresponding slack variable; Set the maximum permissible risk level, and ensure that the conditional risk value of the regional frequency change rate and the conditional risk value of the regional frequency minimum point are less than or equal to the corresponding maximum permissible risk level, thereby determining the stochastic frequency safety constraints in the form of conditional risk values.

[0013] In one embodiment, the system operation constraints include: regional power balance constraints, inter-regional interconnection line power constraints, synchronous generator operation constraints, energy storage system operation constraints, and new energy output and reserve constraints; wherein, the synchronous generator operation constraints include: output upper and lower limit constraints, ramping constraints, and start-stop logic and minimum start-stop time constraints; the energy storage system operation constraints include: charging and discharging power constraints and energy capacity constraints.

[0014] In one implementation, the total cost per day The expression is: ; in, Index for scheduling periods; For the set of scheduling periods; For regional indexes; For a set of regions; For power generation resource indexing; For the region Internal power generation resource collection; For the first Power generation resources during different time periods The cost of generating electricity from conventional generating units; For the first Power generation resources during different time periods The costs associated with starting and stopping; For the first Power generation resources during different time periods Backup costs.

[0015] In one embodiment, solving the random frequency security-constrained day-ahead scheduling optimization model yields a day-ahead scheduling scheme, specifically including: A mixed-integer linear programming solver is used to solve the day-ahead scheduling optimization model with random frequency security constraints, and the values ​​of each scheduling decision variable for each scheduling period are obtained. The scheduling decision variables include: the start-stop status of synchronous generators in each region, the output of synchronous generators, the primary frequency regulation reserve capacity, the charging and discharging power of the energy storage system, the energy state of the energy storage system, the wind power output arrangement, the photovoltaic power output arrangement, and the power of the inter-regional interconnection line.

[0016] The values ​​of each scheduling decision variable for each scheduling period are used as the output of the day-ahead scheduling scheme.

[0017] According to the specific embodiments provided in this application, this application has the following technical effects: This application discloses a multi-regional frequency security constraint day-ahead scheduling method that considers random disturbances and faults. First, by constructing a high-dimensional joint distribution of multi-regional random disturbances and generating relevant disturbance scenarios, the method superimposes occasional fault parameters with random deviations, accurately characterizing the spatial correlation of new energy prediction errors and the "joint amplification" effect of disturbances, thus effectively addressing the risk underestimation problem under compound shocks. Second, it establishes an initial model of multi-regional joint frequency response that includes inter-regional mutual power deviations, and calculates the frequency change rate and frequency minimum point at the regional scale. This explicitly captures the inertia differences and cross-regional coupling effects of each region, avoiding the local frequency exceedance risk that may be masked by the traditional system inertia center model. Then, it utilizes a gradual... The potential bottleneck physical information neural network transforms nonlinear frequency dynamics into embedded optimization mixed-integer linear constraints (i.e., frequency security proxy constraints), solving the problem that dynamic indicators are difficult to directly participate in day-ahead optimization. Combined with stochastic frequency security constraints in the form of conditional risk value, it only quantifies and controls tail risks, rather than forcing absolute security in all scenarios, thereby avoiding excessive reserve configuration caused by rigid constraints across all scenarios. Finally, with the goal of minimizing the total day-ahead cost, the scheduling scheme is solved under the premise of satisfying the above risk constraints and system operation constraints, achieving coordination between frequency security and economy, and improving the ability of multi-regional power grids to coordinate frequency security and operational economy under scenarios of random disturbances and occasional faults. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a schematic flowchart of a multi-region frequency security constraint day-ahead scheduling method that takes into account random disturbances and faults, provided as an embodiment of this application. Detailed Implementation

[0020] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0021] With a high proportion of renewable energy being integrated into the power system, system inertia is decreasing, power fluctuations and uncertainties are increasing, and the impact of sporadic faults such as unit tripping and line failures is compounded, significantly increasing the frequency security risks of power grids in multiple regions. At the same time, renewable energy forecasting errors have spatial correlations, and disturbances may be amplified simultaneously in multiple regions. Traditional scheduling and verification methods based on deterministic or independent stochastic assumptions are unable to accurately characterize the cross-regional coupling effects and tail risk characteristics, making it urgent to develop a new day-ahead scheduling method that can balance frequency security and economy.

[0022] Therefore, this application proposes a multi-region frequency security constraint day-ahead scheduling method that takes into account random disturbances and faults, thereby ensuring frequency security while also taking into account scheduling economy.

[0023] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0024] In one exemplary embodiment, such as Figure 1 As shown, a multi-region frequency security-constrained day-ahead scheduling method considering random disturbances and faults is provided, including the following steps: Wherein: Step S1: Obtain historical dispatch data of the multi-regional power grid during each dispatch period; the historical dispatch data includes at least: new energy prediction error samples and occasional fault parameters.

[0025] Specifically, the new energy prediction error sample refers to: during the scheduling period within, area The sample sequence formed by the difference between the predicted and actual power output of new energy sources such as wind power and photovoltaic power is used to characterize the random disturbance bias term. .

[0026] Intermittent fault parameters refer to the equivalent capacity or amplitude of occasional accident disturbances such as unit tripping and sudden load drops occurring in various regions, expressed as parameters. The corresponding disturbance pattern is represented by the transient time variable after the disturbance occurs. unit step function on This indicates a step injection used to characterize accidental disturbances.

[0027] Historical dispatch data also includes load / output plan data, namely the planned load values ​​for each region in each dispatch period given in the daily dispatch and the planned output power of various power sources. This data is used to calculate the prediction error (comparison between planned value and actual value) and serve as a benchmark for constructing disturbance deviation samples, while also providing a planning benchmark for dispatch in subsequent scenarios.

[0028] Step S2: Based on the new energy prediction error samples, construct the marginal cumulative distribution function of random disturbance deviation in each region, and based on the marginal cumulative distribution function, construct the high-dimensional joint distribution of random disturbance in multiple regions, thereby obtaining the sampled value of random disturbance deviation in each region during each scheduling period.

[0029] As an optional implementation method, step S2 specifically includes: Step S21: Using the kernel density estimation method, based on the new energy prediction error samples, construct the marginal probability density function of random disturbance deviation in each region.

[0030] Step S22: Integrate the edge probability density function to obtain the edge cumulative distribution function of random disturbance deviation in each region.

[0031] Step S23: Map the random disturbance bias to the quantile space through the marginal cumulative distribution function to obtain the quantile variable.

[0032] Step S24: Using the quantile variable as input, construct a high-dimensional joint distribution of multi-regional random perturbations using the Vine Copula framework.

[0033] Step S25: Sample from the high-dimensional joint distribution and obtain the sampled value of the random disturbance deviation of each region in each scheduling period by inverse transformation of the cumulative distribution function at the edge of each region.

[0034] Specifically, obtaining data on multi-regional power grids during dispatch periods. Historical scheduling data within the region is used to construct the region. During the period Equivalent active disturbance : (1) in, For the region Equivalent capacity / amplitude for occasional faults; Transient time variables after the disturbance occurs The unit step function on; This refers to the random disturbance bias caused by the error in new energy prediction.

[0035] The marginal probability density function (PDF) for the random perturbation bias in each region is established using kernel density estimation (KDE): (2) in, For the region The marginal probability density function of random perturbation bias; The number of samples; For bandwidth parameters; For kernel functions; For the first A random perturbation bias sample.

[0036] Further integration yields the marginal cumulative distribution function (CDF): (3) (4) in, This represents the total number of regions included in the system.

[0037] To facilitate subsequent Copula modeling, random perturbation biases are mapped to their marginal CDF values. The quantile space is defined, and quantile variables are defined as follows: (5) in, For the region The quantile variable is used to unify the random disturbance biases of different regions to the same scale in order to characterize the inter-regional dependencies.

[0038] To characterize the spatial correlation of random disturbances in multiple regions, quantile variables were used. As input, a high-dimensional joint distribution is constructed using the VineCopula framework. For any region... Given a set of conditions The conditional correlation PDF is represented by a Gaussian pair-copula representation of its conditional probability density function: (6) in, Indicates the set of condition variables Lower region With the region The conditional pair-copula density function; , In the set of conditions Lower region and The corresponding conditional quantile variables; Representing an edge The set of condition variables; Edge index in the VineCopula structure The corresponding correlation coefficient parameter, ; The standard normal CDF; It is the inverse function of the standard normal CDF; The correlation coefficient is The two-dimensional standard normal joint distribution function.

[0039] Next, the joint copula density of the multi-region quantile vectors can be decomposed according to Vine into the product of the conditional pair-copula densities of each layer and each edge: (7) in, The high-dimensional copula density is used to characterize the joint spatial correlation between random perturbation biases in different regions; the Vine structure consists of Z-1 layer trees. For the first The set of edges of a layered tree.

[0040] Then, using Sklar's theorem, we obtain the joint probability density of the multi-regional random bias (i.e., the high-dimensional joint distribution of the multi-regional random perturbation): (8).

[0041] New scene generation based on a high-dimensional joint distribution of regional random perturbations: Suppose we need to generate S independent and identically distributed scenes, each scene s corresponding to a set of joint sampled values. First, we sample from VineCopula to obtain quantile vectors. Then, by inverse transformation of the marginal distribution function of each region, the scheduling time of each region can be obtained. random disturbance bias .

[0042] Step S3: The sampled value of the random disturbance deviation is superimposed with the occasional fault parameter to obtain the equivalent active power disturbance of each region in each scheduling period, and then a multi-region joint disturbance scenario set containing the equivalent active power disturbance of all regions is obtained.

[0043] Specifically, the scheduling periods for each region will be... random disturbance bias Substituting into equation (1), the equivalent active power disturbance of each region in each scenario and each scheduling period is obtained, thereby constructing a multi-region joint disturbance scenario set. Among them, one scenario Corresponding to the same scheduling period Below, all areas within the system ( The corresponding equivalent active disturbance set .

[0044] Step S4: Based on the equivalent active disturbance in the multi-region joint disturbance scenario set, establish an initial model of the multi-region joint frequency response; the initial model of the multi-region joint frequency response is a function of regional frequency deviation and inter-regional mutual power deviation.

[0045] Specifically, the initial model for the joint frequency response of the multiple regions is as follows: (9) in, The continuous time following the occurrence of the disturbance; For the region Frequency deviation; The rated frequency; and These are the equivalent inertia constant of the region and the load damping coefficient, respectively. The set of resources within the region participating in primary frequency regulation. For resources The primary frequency modulation power; This refers to the power deviation in the inter-regional mutual assistance.

[0046] This step yields the frequency deviation of the included region. and inter-regional mutual assistance power deviation Initial model of multi-region joint frequency response.

[0047] Step S5: Based on the regional frequency deviation, establish a frequency support resource response model, and substitute the frequency support resource response model into the initial model to obtain a multi-regional joint frequency response target model.

[0048] As an optional implementation, the frequency support resource response model includes: an inertia response model and a primary frequency modulation model; then step S5 specifically includes: Step S51: The inter-regional mutual power deviation in the initial model is made explicit to obtain an explicit expression for the mutual power deviation with respect to the regional frequency deviation.

[0049] Step S52: Substitute the inertial response model, the primary frequency modulation model, and the explicit expression of the mutual power deviation with respect to the regional frequency deviation into the initial model to obtain the multi-region joint frequency response target model.

[0050] As an optional implementation, step S51 specifically includes: Step S511: Based on the equivalent reactance between regions, voltage amplitude, and phase angle at the operating point, perform a first-order Taylor expansion linearization on the sine term in the inter-regional mutual power deviation in the initial model near the operating point to obtain the linearized expression for the mutual power deviation.

[0051] Step S512: Substitute the integral relationship between phase angle increment and frequency deviation into the linearized expression for mutual power deviation to obtain an explicit expression for mutual power deviation with respect to the frequency deviation of each region.

[0052] Specifically, due to differences in disturbance characteristics and frequency support capabilities across different regions, a phase difference will occur after a frequency disturbance, leading to cross-regional oscillations and power exchange. The regional mutual power deviation after the disturbance will alter the regional power balance under steady state and act as an external disturbance to other regions. Therefore, this step explicitly represents the inter-regional mutual power deviation in the initial model as a function of the frequency deviation of each region.

[0053] Consideration Area Its adjacent regions The changing trends. Let's assume... For the region its adjacent areas Interval equivalent reactance; This represents the equivalent voltage amplitude for the region. Phase angle at the running point; This represents the phase angle trajectory after the disturbance. Region The explicit expression for the mutual power deviation is shown in equation (10) below: (10).

[0054] Consider at the running point Small deviations in the vicinity allow for linearization of the sine term using a first-order Taylor expansion, thus linearizing the sine term. At steady-state operating point The first-order Taylor expansion at the point is approximated as shown in equation (11): (11).

[0055] Increase the phase angle We can obtain the following formula (12): (12).

[0056] To correlate the phase angle increment with the frequency difference, considering the derivative of the phase angle increment, we obtain the following equation (13): (13).

[0057] For the regional electrical angle, For the region's angular velocity, Given the synchronous angular velocity, we obtain the following equation (14): (14).

[0058] On the fast timescale of the frequency response, assuming the operating point on the slow timescale is quasi-static, the phase angle corresponding to the slow timescale is... satisfy Substituting equation (14) into equation (12) and integrating, we obtain the mutual power deviation with respect to the frequency deviation of each region. The explicit expression for is shown in equation (15): (15) It should be noted that, Corresponding to the time scale (seconds) of the frequency response process, while This corresponds to the time scale (hours) of the scheduling process.

[0059] Based on the inter-regional mutual power deviation, the system frequency response process can be divided into an inertial response process and a primary frequency modulation response process. When the system frequency deviation falls within the dead zone... At that time, only the inertial control mode is activated; when the frequency deviation exceeds the dead zone range... At the same time, the droop control mode also participates in the frequency response.

[0060] (A) During the inertial response process, inertial control reproduces the rotor dynamic behavior of synchronous generators, wind turbines (WTs), and energy storage systems (ESSs), providing rapid frequency support. The corresponding inertial response model is expressed as follows: (16) (17) (18) in, , , For at any time Inertial response power of synchronous generators, wind turbines, and energy storage systems; , , The inertial response coefficients of synchronous generators, wind turbines, and energy storage systems; The system's rated frequency is uniformly set to 50Hz.

[0061] An equivalent center of inertia (COI) is used for each region to converge local inertia effects; different regions use their own COIs to characterize the spatially heterogeneous inertia properties. The COI expression is: (19) in, For the region The equivalent inertia constant; Indicates in The generator's start-up and shutdown status is synchronized at all times, and the generator is in operation when the unit is in operation. When in shutdown state ; , , They represent in The capacity of generators, wind turbines, and energy storage systems is synchronized at all times.

[0062] (B) In the primary frequency regulation phase, droop control is used to describe the primary frequency regulation behavior of synchronous generators, wind turbines, and energy storage systems. The corresponding frequency response process (i.e., the primary frequency regulation model) is expressed as: (20) (twenty one) (twenty two) in, , , These represent the primary frequency response power of the synchronous generator, wind turbine, and energy storage system, respectively. , , These are the time constants of the primary frequency response of the synchronous generator, wind turbine, and energy storage system, respectively. , These are the droop control response coefficients for synchronous generators, wind turbines, and energy storage systems, respectively.

[0063] By regional mutual power deviation The inertia response model, along with the primary frequency modulation model, are substituted into the initial model of the multi-region joint frequency response to obtain a complete regional frequency dynamic response model that includes cross-regional coupling, inertia support, and primary frequency modulation support. The frequency response trajectories of each region are then solved to obtain the results. .

[0064] Step S6: Solve the target model to obtain the frequency response trajectory of each region, and calculate the regional frequency security index based on the frequency response trajectory of each region; the regional frequency security index includes: regional frequency change rate and regional frequency minimum point.

[0065] Specifically, regional frequency security indicators are constructed based on the dynamic process of frequency response. The regional frequency change rate after the occurrence of the equivalent active disturbance as defined in equation (1) Defined as the derivative of the regional frequency with respect to time: (twenty three).

[0066] The lowest frequency point in the region (Nadir) is denoted as , refers to the lowest frequency reached by the system after the disturbance occurs, representing the maximum deviation relative to the steady-state frequency, and its corresponding condition is: (twenty four).

[0067] Using the above model, under a given joint perturbation scenario, the values ​​of each region can be obtained. and and calculate the corresponding and This serves as the input for subsequent frequency security constraint embedding optimization.

[0068] Step S7: Based on the scheduling decision feature vector, the lowest regional frequency point, the primary frequency modulation support power and regional mutual assistance power deviation at the moment the frequency reaches the lowest regional frequency point, and the loss function introduced by using the frequency dynamic equation as the physical residual regularization term, the progressive potential bottleneck physical information neural network is trained to obtain the trained progressive potential bottleneck physical information neural network model.

[0069] As an optional implementation, in step S7, based on the scheduling decision feature vector, the lowest regional frequency point, the primary frequency modulation support power at the moment the frequency reaches the lowest regional frequency point, and the regional mutual assistance power deviation, the frequency dynamic equation is introduced as a physical residual regularization term into the total loss function to perform multiple rounds of iterative training on the progressive potential bottleneck physical information neural network. Specifically, the training process in any iteration round includes: Step S71: Input the scheduling decision feature vector into the encoder in the current iteration round and output the predicted value of the lowest regional frequency point; Step S72: Input the predicted value of the lowest regional frequency point into the decoder in the current iteration round, and output the primary frequency modulation support power and regional mutual assistance power deviation when the frequency in the current iteration round reaches the lowest regional frequency point. Step S73: Calculate the total loss function under the current iteration round and determine whether the current iteration round has reached the iteration stopping condition; the iteration stopping condition is that the total loss function under the current iteration round converges or the current iteration round reaches the preset maximum round; the total loss function includes encoder loss, decoder loss and physical regularization loss introduced by using the frequency dynamic equation as a physical residual regularization term; If so, stop training and use the encoder and decoder in the current iteration as the trained progressive potential bottleneck physical information neural network model. Step S75: If not, continue training in the next iteration.

[0070] As an optional implementation, the process of iteratively training the progressive potential bottleneck physical information neural network through multiple rounds also includes: Based on the convergence degree and gradient scale of each loss term in the encoder loss, decoder loss, and physical regularization loss under the current iteration, the relative proportion of the physical regularization loss term in the total loss function value is dynamically adjusted.

[0071] Specifically, due to the lowest regional frequency point The nonlinear differential dynamics determine the mutual power deviation of the interconnects (see equation (24)). The frequency difference is integrally coupled (see Equation (15)), making it difficult to directly embed frequency security constraints into the day-ahead scheduling optimization model. To address this, we propose the ProgressiveLatent-Bottleneck Physics-Informed Neural Network (PLB-PINN) to represent key frequency security indicators using an "optimization-compatible" surrogate model.

[0072] First, examine the regional frequency security indicators output in step S6, especially the lowest regional frequency point. and regional mutual assistance power deviation Perform proxy modeling.

[0073] First, construct the encoder network. :set up The scheduling decision feature vector consists of the primary frequency regulation reserve capacity of synchronous generators, wind turbines, and energy storage systems within the region. An encoder is constructed, whose output is the point of lowest regional frequency. Encoder network residuals The encoder structure expression is: (25) (26) (27) (28) in, The output of the encoder network; For the encoder's network function; This is the set of weight parameters for the encoder network, including the weight matrix of the encoder's first hidden layer. The weight matrix of the second hidden layer of the encoder The weight matrix of the encoder output layer ; The set of bias parameters for the encoder, including the bias vector of the encoder's first hidden layer. The bias vector of the second hidden layer of the encoder The bias vector of the encoder output layer ; This is the output vector of the encoder's first hidden layer; This is the output vector of the encoder's second hidden layer; To modify the activation function of the linear unit.

[0074] Next, a decoder is constructed: the decoder uses the minimum frequency predicted by the encoder as the network input, and outputs the primary frequency modulation support power of the system at the Nadir time. Regional mutual assistance power deviation and decoder network residuals This network is used to characterize the impact of the scheduling decision-making frequency response process. The mapping relationship of the decoder network is represented as follows: (29) (30) (31) (32) in, This is the output of the decoder network; For the decoder network; This is the set of weight parameters for the decoder network, including the weight matrix of the first hidden layer of the decoder. The weight matrix of the second hidden layer of the decoder Weight matrix of decoder output layer .

[0075] Then, a physical information constraint term is introduced to ensure that the network output satisfies the regional frequency dynamic equation. Substituting the correlation quantity of the physical characteristic frequency trajectory of the lowest frequency point obtained from the encoding prediction into equation (9), a physical residual regularization term is constructed: (33) in, For physical residual regularization terms; For the sample used to calculate the physical residual; This represents the network weights and bias parameters of PLB-PINN.

[0076] Furthermore, the overall loss function of PLB-PINN is constructed, which is a weighted sum of the encoder network loss, decoder network loss, and physical regularization loss term: (34) in, , , These are the weighting coefficients corresponding to each loss component.

[0077] Next, to avoid the imbalance between network loss and physical regularization loss caused by fixing weights during training, an adaptive weight update mechanism is introduced to dynamically adjust their relative proportions in the overall loss function. This mechanism autonomously updates the weight ratios of each loss term based on the convergence degree and gradient scale changes during training, thereby suppressing training instability and convergence bias caused by a single loss term dominating optimization.

[0078] Because different loss components differ in their units and numerical scales, without proper weight guidance, a particular loss term may be over-amplified or over-suppressed during network training. Therefore, target weights for the loss components need to be set to provide a reference benchmark for adaptive weight updates. Let the initial loss weights for each loss component be... , , The target weight of the physical information network It can be represented as: (35) in, This is a scaling factor used to suppress the influence of physical constraints in the early stages of training. This is a numerically stable term used to avoid division by zero.

[0079] To further enhance training robustness, a temperature-increase scheduling strategy is adopted to gradually activate the physical information regularization term. Specifically, a monotonic activation factor is introduced. : (36) in, Indicates the current training round; This indicates the number of training rounds during the warm-up phase.

[0080] Subsequently, the weights of the regularization term based on the physical mechanism. It can be represented as: (37).

[0081] Step S8: Linearize the lowest regional frequency point of the encoder output in the trained progressive potential bottleneck physical information neural network model into a mixed integer linear constraint to obtain the frequency security proxy constraint.

[0082] Specifically, the output of the trained PLB-PINN network is further processed and used to optimize embeddings. Since PLB-PINN is a non-linear model, to make it embeddable into Mixed Integer Linear Programming (MILP), the network activation function is uniformly represented as ReLU, and the Big-M method is used for exact linearization. The ReLU function is defined as: (38) Introducing binary variables With a sufficiently large constant ReLU can be equivalently transformed into the following mixed-integer linear constraints: (39) when hour, ,thereby ;when hour, but .

[0083] In actual embedding, only the frequency safety index output by the encoder is incorporated into the scheduling optimization model. The decoder is used to assist in reconstructing the physical response process and does not directly participate in solving the scheduling decision variables. This transforms the frequency dynamic safety constraints into an "optimizable embeddable" proxy constraint form.

[0084] Step S9: Based on the multi-regional joint disturbance scenario set, regional frequency change rate, and frequency security proxy constraints, construct a stochastic frequency security constraint in the form of conditional risk value.

[0085] As an optional implementation, step S9 specifically includes: Step S91: For each disturbance scenario in the multi-region joint disturbance scenario set, construct the regional frequency security loss function for each disturbance scenario; the regional frequency security loss function includes: regional frequency change rate loss function and regional frequency minimum point loss function.

[0086] Step S92: Under a preset confidence level, determine the conditional value of risk of the regional frequency change rate based on the regional frequency change rate loss, the value-at-risk variable of the regional frequency change rate, and the slack variable corresponding to each disturbance scenario in the multi-region joint disturbance scenario set.

[0087] Step S93: Under a preset confidence level, determine the conditional value of risk of the regional frequency minimum point based on the regional frequency minimum point loss, the risk value variable of the regional frequency minimum point, and the slack variable corresponding to each disturbance scenario in the multi-region joint disturbance scenario set.

[0088] Step S94: Establish the constraint relationship between the regional frequency change rate loss and the corresponding slack variable under each disturbance scenario, as well as the constraint relationship between the regional frequency minimum point loss and the corresponding slack variable. Step S95: Set the maximum permissible risk level for over-limit, and ensure that the conditional risk value of the regional frequency change rate and the conditional risk value of the lowest point of regional frequency in each region are less than or equal to the corresponding maximum permissible risk level, thereby determining the random frequency safety constraint in the form of conditional risk value.

[0089] Specifically, for each disturbance scenario Define a regional frequency security loss function to characterize the degree to which frequency indicators exceed the security threshold. Let... For the scene Lower region The rate of change of frequency, Its safety threshold; For the scene The lowest frequency point in the lower region, Given its safety threshold, the regional frequency security loss function is: (40) in, The loss function is the rate of change of regional frequency. This is the loss function for the lowest frequency point in the region.

[0090] At confidence level Below, we introduce the VaR variable (i.e., the regional frequency change rate of value at risk). Value at Risk (VaR) variables at the lowest regional frequency and the slack variable of the rate of change of regional frequency Slack variables at the lowest regional frequency CVaR expression was obtained using the Rockafellar–Uryasev form. Let... If the number of scenes is: (41) in, For the preset confidence level The conditional value of risk for the regional frequency change rate; For the preset confidence level Below, the conditional risk value at the lowest point of regional frequency.

[0091] And satisfy the relationship between scene loss and slack variables: (42) In equations (40) and (41) The terms can be linearized using the Big-M method, thus allowing the frequency risk constraint to be incorporated into the MILP model. Furthermore, the maximum permissible level of excess risk is given. and Thus, we obtain the stochastic frequency security constraint in the form of conditional value of risk: (43) This step transforms the generated disturbance scenarios and frequency security indices into CVaR risk constraints that can be solved in the optimization model, resulting in a stochastic frequency security constraint expression. This constraint serves as the input for subsequent system operation constraints.

[0092] Step S10: With minimizing the total day-ahead cost as the optimization objective and the random frequency security constraints and system operation constraints as the constraints, construct a random frequency security constraint day-ahead scheduling optimization model.

[0093] As an optional implementation method, the system operation constraints include: regional power balance constraints, inter-regional interconnection line power constraints, synchronous generator operation constraints, energy storage system operation constraints, and new energy output and reserve constraints; among which, the synchronous generator operation constraints include: output upper and lower limit constraints, ramping constraints, and start-stop logic and minimum start-stop time constraints; the energy storage system operation constraints include: charging and discharging power constraints and energy capacity constraints.

[0094] As an optional implementation method, the total cost is as follows: The expression is: (44) in, Index for scheduling periods; For the set of scheduling periods; For regional indexes; For a set of regions; This is an index for power generation resources, which include synchronous generators, new energy units (wind turbines and photovoltaic units), energy storage systems, etc., all of which are indexed using... express; For the region Internal power generation resource collection; For the first Power generation resources during different time periods The cost of generating electricity from conventional generating units; For the first Power generation resources during different time periods The costs associated with starting and stopping; For the first Power generation resources during different time periods Backup costs.

[0095] Specifically, based on the generated multi-regional related disturbance scenarios and incorporating embeddable frequency security indicators, a day-ahead scheduling optimization model considering random frequency security is constructed. This model aims to minimize the total day-ahead cost while simultaneously satisfying system operation and unit constraints, and controls frequency over-limit risk through CVaR tail risk constraints.

[0096] Establish the day-ahead scheduling objective function: Let For the set of scheduling periods, For a set of regions, For the region Given the set of internal resources, the total cost per day is as shown in equation (44), which gives the objective function for scheduling per day (i.e., minimizing the total cost per day as the optimization objective).

[0097] Further processing of random frequency security constraints, incorporating system operation constraints, forms a complete day-ahead scheduling constraint system.

[0098] Among them, for each time period With the region This satisfies the regional power balance constraint. Let... For the first The synchronous generator during the time period Those who have made meritorious contributions; For the first A new energy unit during the period The predicted output of new energy sources; , energy storage system During the period The discharge power and charging power; For the first Each load node during the time period The active power demand; For the region During the period If the net power transmitted is less than or equal to the net power transmitted, then the system power balance constraint is: (45) And satisfy the power conservation of cross-regional interconnection lines: (46) Using a DC power flow model with regional equivalent nodes, the interconnect power limit is: (47) in, This is the lower limit of the interconnect power; For the time period From the region To the area The actual power of the interconnects; This is the upper limit of the interconnect power. Formulas (46) and (47) form the power constraints for cross-region interconnects.

[0099] Next, synchronous generator operating constraints are added (i.e., equations 48-51). The output and reserve of the synchronous generator satisfy the output constraints: (48) in, For the first The synchronous generator during the time period Start-stop status, and The first The upper and lower limits of the output of the synchronous generator; For the first The synchronous generator during the time period The primary frequency regulation reserve capacity.

[0100] The climbing constraint is: (49) in, For the first The synchronous generator during the time period -1 is the amount of active power; For the first The synchronous generator during the time period -1 primary frequency regulation reserve capacity; , The first The synchronous generator during the time period The upper and lower limits of the uphill climb.

[0101] The start / stop logic and minimum start / stop time constraints are as follows: (50) (51) in, For the first The synchronous generator during the time period -1 indicates start / stop status; , The first The synchronous generator during the time period Start-up indicator variables and stop indicator variables; For the first Minimum start-up time and minimum shutdown time of the synchronous generator.

[0102] The energy storage charging and discharging power and energy constraints (i.e., energy storage operation constraints) are as follows: (52) (53) (54) (55) in, For energy storage systems During the period The discharge power; For energy storage systems During the period The charging power; , They represent energy storage systems. During the period Discharge efficiency and charging efficiency; For energy storage systems Reserved frequency spare capacity; For energy storage systems Maximum power output; For energy storage systems During the period Remaining energy at the end; For energy storage systems In the previous period Remaining energy at the end; For energy storage systems Remaining energy at the end of the last period of the scheduling cycle; For energy storage systems Initial energy at the start of the scheduling cycle; and They represent energy storage systems. At any moment The lower limit and upper limit of energy capacity.

[0103] The constraints on new energy output and reserves are as follows: (56) in, For the first individual wind turbine units during the period The actual contribution of the individual; For the first individual wind turbine units during the period Reserved primary frequency regulation backup capacity; For the first The maximum available output of each wind turbine unit; For the first A photovoltaic unit during the time period The actual contribution of the individual; For the first The maximum available output of a single photovoltaic unit.

[0104] Through this step, the obtained random frequency security constraints, system regional power balance constraints, inter-regional interconnection power constraints, synchronous unit operation constraints, energy storage system operation constraints, and new energy output and reserve constraints are all incorporated into the random frequency security constraint day-ahead scheduling optimization model to obtain a complete random frequency security constraint day-ahead scheduling optimization model.

[0105] Step S11: Solve the random frequency security constraint day-ahead scheduling optimization model to obtain the day-ahead scheduling scheme.

[0106] As an optional implementation, step S11 specifically includes: A mixed-integer linear programming solver is used to solve the day-ahead scheduling optimization model with random frequency security constraints, and the values ​​of each scheduling decision variable for each scheduling period are obtained. The scheduling decision variables include: the start-stop status of synchronous generators in each region, the output of synchronous generators, the primary frequency regulation reserve capacity, the charging and discharging power of the energy storage system, the energy state of the energy storage system, the wind power output arrangement, the photovoltaic power output arrangement, and the power of the inter-regional interconnection line.

[0107] Specifically, the frequency safety index expression obtained by linearizing the encoder (including ReLU) is combined with the CVaR linearization and incorporated into the above system operation constraints to form a mixed integer linear programming model. The model is then solved by the MILP solver to obtain the values ​​of each scheduling decision variable for each scheduling period, thereby achieving economic scheduling under the random frequency safety constraint of "controllable tail risk".

[0108] Beneficial effects: (1) Based on the equivalent disturbance modeling principle of “accident step disturbance and new energy prediction error deviation superposition”, the edge probability density function of random disturbance deviation in each region is constructed by kernel density estimation and the edge cumulative distribution function is obtained by integration; further, the Vine-Copula framework is introduced to construct the high-dimensional joint distribution of random disturbance in multiple regions, and the joint disturbance scene set in multiple regions is obtained through the relevant scene generation mechanism, which accurately portrays the cross-regional correlation and disturbance heterogeneity, overcomes the risk underestimation problem caused by the traditional independent assumption, and provides more realistic random input for frequency security assessment and scheduling.

[0109] (2) Based on the multi-region coupling frequency response mechanism, the regional inertia difference, primary frequency modulation response and interconnection power coupling term are incorporated into the initial model of multi-region joint frequency response, and safety indicators such as regional frequency change rate and regional frequency minimum point are calculated at the regional scale. Compared with the existing method that only uses the system inertia center index, it can explicitly identify the frequency over-limit risk in local areas, avoid "the system meets the requirements but local violations are covered up", and improve the pertinence and effectiveness of frequency safety constraints.

[0110] (3) Based on the principle of physical information constraints and potential bottleneck modeling, a progressive potential bottleneck physical information neural network is constructed and trained to transform dynamic indicators such as the lowest regional frequency point, which are difficult to be directly embedded in optimization, into frequency security proxy constraints that can be called. Through physical residual regularization, adaptive weight update and warming scheduling strategies, the physical consistency and generalization ability of the model are enhanced, while taking into account proxy accuracy and stability, and reducing the modeling and solution complexity caused by directly embedding dynamic frequency constraints into day-ahead scheduling optimization.

[0111] (4) Based on the tail risk measurement principle, conditional risk value is introduced to quantify and constrain the risk of exceeding the limit of regional frequency change rate and regional frequency minimum point, and combined with network linearization processing to form a solvable mixed integer linear programming model; while ensuring that frequency security risk is controllable, the excessively conservative reserve configuration is reduced, and a controllable trade-off between security and economy is achieved, thus obtaining a day-ahead dispatch scheme suitable for multi-regional power grids with a high proportion of new energy.

[0112] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0113] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A multi-region frequency security-constrained day-ahead scheduling method considering random disturbances and faults, characterized in that, The multi-region frequency security-constrained day-ahead scheduling method that takes into account random disturbances and faults includes: Acquire historical dispatch data of multi-regional power grids during various dispatch periods; the historical dispatch data includes at least: new energy prediction error samples and occasional fault parameters; Based on the new energy prediction error samples, the marginal cumulative distribution function of random disturbance deviation in each region is constructed, and based on the marginal cumulative distribution function, a high-dimensional joint distribution of random disturbance in multiple regions is constructed, thereby obtaining the sampled value of random disturbance deviation in each region during each scheduling period. The sampled values ​​of the random disturbance deviation are superimposed with the occasional fault parameters to obtain the equivalent active power disturbance of each region in each scheduling period, and then a multi-region joint disturbance scenario set containing the equivalent active power disturbance of all regions is obtained. Based on the equivalent active disturbance of the multi-region joint disturbance scenario, an initial model of the multi-region joint frequency response is established; the initial model of the multi-region joint frequency response is a function of the regional frequency deviation and the mutual power deviation between regions. Based on the regional frequency deviation, a frequency support resource response model is established, and the frequency support resource response model is substituted into the initial model to obtain a multi-regional joint frequency response target model. Solve the target model to obtain the frequency response trajectory of each region, and calculate the regional frequency security index based on the frequency response trajectory of each region; the regional frequency security index includes: regional frequency change rate and regional frequency minimum point; Based on the scheduling decision feature vector, the regional minimum frequency point, the primary frequency modulation support power and regional mutual assistance power deviation at the moment when the frequency reaches the regional minimum frequency point, and the loss function introduced by using the frequency dynamic equation as the physical residual regularization term, the progressive potential bottleneck physical information neural network is trained to obtain the trained progressive potential bottleneck physical information neural network model. The lowest regional frequency point in the encoder output of the trained progressive potential bottleneck physical information neural network model is linearized into a mixed integer linear constraint to obtain the frequency security proxy constraint. Based on a multi-regional joint disturbance scenario set, regional frequency change rate and frequency security proxy constraints, a stochastic frequency security constraint in the form of conditional risk value is constructed. With minimizing the total day-ahead cost as the optimization objective and the random frequency security constraints and system operation constraints as the constraints, a random frequency security constraint day-ahead scheduling optimization model is constructed. Solve the day-ahead scheduling optimization model with random frequency security constraints to obtain the day-ahead scheduling scheme.

2. The multi-region frequency security-constrained day-ahead scheduling method considering random disturbances and faults according to claim 1, characterized in that, Based on the new energy prediction error samples, a marginal cumulative distribution function of random disturbance deviations for each region is constructed. Then, based on the marginal cumulative distribution function, a high-dimensional joint distribution of random disturbances across multiple regions is constructed, thereby obtaining the sampled values ​​of random disturbance deviations for each region during each scheduling period. Specifically, this includes: Using the kernel density estimation method, the marginal probability density function of random disturbance deviation in each region is constructed based on the new energy prediction error sample; Integrating the marginal probability density function yields the marginal cumulative distribution function of the random disturbance deviation in each region; Random disturbance biases are mapped to the quantile space through the marginal cumulative distribution function to obtain quantile variables; Using the quantile variables as input, a high-dimensional joint distribution of multi-regional random perturbations is constructed using the Vine Copula framework; Samples are taken from the high-dimensional joint distribution, and the sampled values ​​of random disturbance deviations of each region during each scheduling period are obtained by inverse transformation of the cumulative distribution function at the edge of each region.

3. The multi-region frequency security-constrained day-ahead scheduling method considering random disturbances and faults according to claim 1, characterized in that, Frequency support resource response models include: inertia response model and primary frequency modulation model; Based on regional frequency deviation, a frequency support resource response model is established. This model is then substituted into the initial model to obtain a multi-regional joint frequency response target model, specifically including: The inter-regional mutual aid power deviation in the initial model is made explicit to obtain an explicit expression for the mutual aid power deviation with respect to the regional frequency deviation. Substituting the inertial response model, the primary frequency modulation model, and the explicit expression of the mutual power deviation with respect to the regional frequency deviation into the initial model, a multi-region joint frequency response target model is obtained.

4. The multi-region frequency security-constrained day-ahead scheduling method considering random disturbances and faults according to claim 3, characterized in that, The inter-regional mutual aid power deviation in the initial model is made explicit to obtain an explicit expression for the mutual aid power deviation with respect to the regional frequency deviation, specifically including: Based on the equivalent reactance between regions, voltage amplitude, and phase angle at the operating point, the sinusoidal term in the inter-regional mutual power deviation in the initial model is linearized by a first-order Taylor expansion near the operating point to obtain the expression for the linearized mutual power deviation. Substituting the integral relationship between phase angle increment and frequency deviation into the linearized expression for mutual power deviation, we obtain an explicit expression for mutual power deviation with respect to the frequency deviation in each region.

5. The multi-region frequency security-constrained day-ahead scheduling method considering random disturbances and faults according to claim 1, characterized in that, Based on the scheduling decision feature vector, the regional minimum frequency point, the primary frequency modulation support power at the moment the frequency reaches the regional minimum frequency point, and the regional mutual assistance power deviation, the frequency dynamic equation is introduced as a physical residual regularization term into the total loss function. This allows for multi-round iterative training of the progressive potential bottleneck physical information neural network. The training process in any given iteration specifically includes: The scheduling decision feature vector is input into the encoder in the current iteration round, and the predicted value of the lowest regional frequency point is output. The predicted value of the lowest regional frequency is input into the decoder in the current iteration round, and the primary frequency modulation support power and regional mutual assistance power deviation at the moment when the frequency in the current iteration round reaches the lowest regional frequency are output. Calculate the total loss function under the current iteration round and determine whether the current iteration round has reached the iteration stopping condition; the iteration stopping condition is that the total loss function under the current iteration round converges or the current iteration round reaches the preset maximum round; the total loss function includes encoder loss, decoder loss and physical regularization loss introduced by using the frequency dynamic equation as a physical residual regularization term; If so, then stop training and use the encoder and decoder of the current iteration as the trained progressive potential bottleneck physical information neural network model; If not, then continue training in the next iteration.

6. The multi-region frequency security-constrained day-ahead scheduling method considering random disturbances and faults according to claim 5, characterized in that, The process of iteratively training a neural network for progressively latent bottleneck physical information also includes: Based on the convergence degree and gradient scale of each loss term in the encoder loss, decoder loss, and physical regularization loss under the current iteration, the relative proportion of the physical regularization loss term in the total loss function value is dynamically adjusted.

7. The multi-region frequency security-constrained day-ahead scheduling method considering random disturbances and faults according to claim 1, characterized in that, Based on a multi-regional joint disturbance scenario set, regional frequency change rates, and frequency security proxy constraints, a stochastic frequency security constraint in the form of conditional value of risk is constructed, specifically including: For each disturbance scenario in a multi-regional joint disturbance scenario, a regional frequency security loss function is constructed for each disturbance scenario. The regional frequency security loss function includes: the regional frequency change rate loss function and the regional frequency minimum point loss function. At a preset confidence level, the conditional value at risk of the regional frequency change rate is determined based on the regional frequency change rate loss, the value at risk of the regional frequency change rate, and the slack variable corresponding to each disturbance scenario in the multi-regional joint disturbance scenario set. At a preset confidence level, the conditional value at risk of the regional frequency minimum point is determined based on the regional frequency minimum point loss, the risk value variable of the regional frequency minimum point, and the slack variable corresponding to each disturbance scenario in the multi-region joint disturbance scenario set. Establish the constraint relationship between the regional frequency change rate loss and the corresponding slack variable under each disturbance scenario, as well as the constraint relationship between the regional frequency minimum point loss and the corresponding slack variable; Set the maximum permissible risk level, and ensure that the conditional risk value of the regional frequency change rate and the conditional risk value of the regional frequency minimum point are less than or equal to the corresponding maximum permissible risk level, thereby determining the stochastic frequency safety constraints in the form of conditional risk values.

8. The multi-region frequency security-constrained day-ahead scheduling method considering random disturbances and faults according to claim 1, characterized in that, System operation constraints include: regional power balance constraints, inter-regional interconnection line power constraints, synchronous generator operation constraints, energy storage system operation constraints, and new energy output and reserve constraints; among them, synchronous generator operation constraints include: output upper and lower limit constraints, ramping constraints, and start-stop logic and minimum start-stop time constraints; energy storage system operation constraints include: charging and discharging power constraints and energy capacity constraints.

9. The multi-region frequency security-constrained day-ahead scheduling method considering random disturbances and faults according to claim 1, characterized in that, Total cost as of today The expression is: ； in, Index for scheduling periods; For the set of scheduling periods; For regional indexes; For a set of regions; For power generation resource indexing; For the region Internal power generation resource collection; For the first Power generation resources during different time periods The cost of generating electricity from conventional generating units; For the first Power generation resources during different time periods The costs associated with starting and stopping; For the first Power generation resources during different time periods Backup costs.

10. The multi-region frequency security-constrained day-ahead scheduling method considering random disturbances and faults according to claim 1, characterized in that, Solving the random frequency security-constrained day-ahead scheduling optimization model yields the day-ahead scheduling scheme, which specifically includes: A mixed-integer linear programming solver is used to solve the day-ahead scheduling optimization model with random frequency security constraints, and the values ​​of each scheduling decision variable for each scheduling period are obtained. The scheduling decision variables include: the start-stop status of synchronous generators in each region, the output of synchronous generators, the primary frequency regulation reserve capacity, the charging and discharging power of the energy storage system, the energy state of the energy storage system, the wind power output arrangement, the photovoltaic power output arrangement, and the power of the inter-regional interconnection line. The values ​​of each scheduling decision variable for each scheduling period are used as the output of the day-ahead scheduling scheme.

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