Data-driven power system frequency regulation resource security domain construction and safety warning method

Abstract

The present application belongs to the technical field of power generation safety, and proposes a data-driven power system frequency modulation resource safety domain construction and safety early warning method. The present application realizes the analytical characterization of the relationship between safety indicators and frequency modulation resource capacity. A symbolic regression algorithm based on genetic programming is used to autonomously evolve an explicit mathematical expression between the frequency safety indicator and the frequency modulation resource configuration capacity from high-dimensional nonlinear data. This method does not need to preset the function form, has strong complex nonlinear relationship fitting ability, significantly improves the interpretability and fitting accuracy of the safety boundary, and overcomes the limitations of black box model and traditional polynomial regression in expression complexity and accuracy. The present application realizes the visualization of the safety domain and multi-level frequency safety early warning. The present application constructs a visual frequency modulation resource safety domain in a three-dimensional frequency modulation resource capacity space, and intuitively displays the system frequency safety operation boundary.

Description

Technical Field

[0001] This invention relates to the field of power generation safety technology, and in particular to a data-driven method for constructing a frequency regulation resource safety domain and providing early warning of safety in a power system. Background Technology

[0002] In power grids with a high proportion of renewable energy, most existing renewable energy generation equipment and power electronic interfaces lack the ability to actively support system frequency disturbances. This has led to a shortage of frequency regulation resources in power grids in many regions both domestically and internationally. Key safety indicators such as the rate of change of frequency (RoCoF), frequency nadir (FN), and quasi-steady-state frequency deviation (QSSFD) are increasingly approaching operational limits, significantly increasing systemic risks such as low-frequency load shedding and large-scale disconnection of renewable energy from the grid. Against this backdrop, clarifying the boundaries of safe system operation and rationally allocating frequency regulation resources for new power systems have become crucial issues supporting the construction of a reliable frequency security control system.

[0003] Security domain technology, through visualization, characterizes the security boundaries of a system, providing dispatchers with intuitive security margin awareness and proactive defense capabilities. However, current research on frequency modulation (FM) resource security domains largely focuses on the initial inertia stage of the system's frequency response, failing to fully consider the time-scale characteristics of primary FM resources and their dynamic response constraints. A theoretical framework capable of comprehensively characterizing the mapping relationship between FM resource sufficiency and frequency security has not yet been established. Accurate assessment of the frequency security boundary is a crucial foundation for constructing the FM resource security domain. Existing data-driven algorithms, such as generative adversarial networks and extreme learning machines, while suitable for point-by-point security analysis, suffer from poor interpretability due to their black-box nature, making them unsuitable for security domain construction. Methods like multinomial regression have limited accuracy in fitting complex nonlinear relationships.

[0004] In summary, existing research has not yet formed a complete theoretical system and application framework for the frequency regulation resource security domain of power systems oriented towards power grid dispatching decisions. Summary of the Invention

[0005] Therefore, one objective of this invention is to propose a data-driven method for constructing a security domain for frequency regulation resources in power systems and for security early warning, so as to solve the problems mentioned in the background art and overcome the shortcomings of the prior art.

[0006] To achieve the above objectives, this invention provides a data-driven method for constructing and providing early warning of frequency regulation resource security domains in power systems, comprising:

[0007] Based on the day-ahead power generation plan, the frequency regulation resource security domain is defined as the feasible domain of frequency regulation resource configuration capacity combinations that satisfy frequency security index constraints and adjustable capacity constraints.

[0008] The frequency regulation resources include thermal power frequency regulation resources, hydropower frequency regulation resources, and energy storage frequency regulation resources;

[0009] An improved system frequency response model is constructed, a high-precision training dataset is built, and the system frequency security index is calculated and solved based on the improved system frequency response model to obtain the security index matrix.

[0010] The scaled security index matrix is ​​obtained from the security index matrix;

[0011] A genetic programming symbolic regression algorithm is used to learn the explicit functional relationship between the scaled security index and the frequency modulation resource allocation capacity, thereby obtaining an analytical expression for the frequency security index;

[0012] Based on the analytical expression, in the three-dimensional space spanned by the maximum configurable capacity of thermal power frequency regulation resources, hydropower frequency regulation resources and energy storage frequency regulation resources, critical safety isosurfaces corresponding to each single safety index are drawn respectively. Each isosurface divides the frequency regulation resource capacity space into a safe region and an unsafe region that satisfy the constraint of the index. By integrating the intersection region between all frequency safety critical isosurfaces and the upper limit boundary of resource capacity, a frequency regulation resource safety domain is constructed.

[0013] Based on the comparison between the predicted values ​​of the safety indicators at the operating point and the safety threshold, the comprehensive safety margin is calculated, and a graded early warning is triggered according to the preset margin threshold.

[0014] Preferably, the frequency security constraints include:

[0015] Frequency change rate constraint: The maximum frequency change rate shall not exceed a safety threshold. ;

[0016] Maximum transient frequency deviation constraint: The maximum transient frequency deviation shall not exceed the low-frequency load shedding setting value. ;

[0017] Quasi-steady-state frequency deviation constraint: The quasi-steady-state frequency deviation shall not exceed the allowable deviation. ;

[0018] The adjustable capacity constraint includes:

[0019] Thermal power resource capacity constraints: ;

[0020] Hydropower resource capacity constraints: ;

[0021] Energy storage resource capacity constraints: ;

[0022] in, This represents the maximum rate of change of the system frequency. As a safety threshold, This is the initial low-frequency load shedding setting value for the system. The maximum deviation of the system transient frequency. This represents the quasi-steady-state frequency deviation of the system after a single frequency modulation. As a constraint threshold, These are the frequency regulation resource allocation capacities for thermal power, hydropower, and energy storage, respectively. These refer to the installed capacity of thermal power, hydropower, and energy storage units, respectively. The power outputs are planned for thermal power, hydropower, and energy storage units, respectively.

[0023] As a preferred approach, during the intraday phase, when the adjustable capacity of some resources is fixed, a low-dimensional frequency modulation resource security domain is constructed through dimensionality reduction. The frequency security constraints that the operating points within the frequency modulation resource security domain must strictly satisfy are as follows:

[0024] Frequency change rate constraint:

[0025] ;

[0026] Maximum deviation constraint of transient frequency:

[0027] ;

[0028] Quasi-steady-state frequency deviation constraint:

[0029] ;

[0030] in, This represents the maximum rate of change of the system frequency. This represents the change in system frequency deviation over time t after the disturbance. As a safety threshold, This is the initial low-frequency load shedding setting value for the system. The maximum deviation of the system transient frequency. This represents the quasi-steady-state frequency deviation of the system after a single frequency modulation. This is the constraint threshold.

[0031] Preferably, the improved system frequency response model includes:

[0032] Transfer function of frequency response of thermal power unit: ;

[0033] Hydropower unit frequency response transfer function: ;

[0034] Energy storage frequency response transfer function: ;

[0035] in, The steam volume time constant is For high-pressure turbine coefficient, The reheater time constant is... The time constant of the reheat turbine governor. This is the droop coefficient of the reheat turbine governor. For the Laplace operator, The time constant for turbine reset is... For the permanent decline rate, For the temporary decline rate, The time constant of the water hammer effect. The time constant of the turbine governor. This refers to the droop coefficient of the turbine governor. To simulate the inertial time constant, The droop factor for primary frequency modulation. This represents the response delay time constant of frequency control. This represents the change in system frequency.

[0036] Preferably, the scaled security index matrix is ​​obtained by linearly scaling the security index matrix:

[0037] ;

[0038] in, This is a diagonal matrix of scaling factors. Each corresponds to a scaling factor for a specific security indicator. For safety indicators, This is the scaled output matrix.

[0039] Preferably, the genetic programming symbolic regression algorithm includes:

[0040] Initial population generation: Randomly generate symbolic expressions that satisfy preset constraints;

[0041] Fitness evaluation: The fitness value is calculated based on the loss function and the complexity penalty function;

[0042] Genetic manipulation: A tournament selection mechanism is used to select superior individuals as parents, and offspring individuals are generated through crossover and mutation operations;

[0043] Population update: newly generated offspring individuals are merged with parent individuals, and Pareto front solutions are selected from the merged population based on non-dominated sorting and crowding distance calculation.

[0044] Iteration Termination and Output of Optimal Solution: Repeat fitness evaluation, genetic operations and population update until the training result meets the preset fitness convergence threshold or reaches the maximum number of iterations, and select the comprehensive optimal symbolic expression from the Pareto front solution set as the safety index to fit the model.

[0045] Preferably, the fitness function is defined as:

[0046] ;

[0047] in, Let C be the loss function for the safety metric m, and C be the expression complexity. The scaled value of the safety index m is the true value of the sample p. Let m be the explicit function prediction value of the m-th safety index obtained by the genetic programming symbolic regression algorithm. This is the complexity penalty coefficient. For the total sample size, For the p-th column of the input matrix, The total number of nodes in the expression tree. The preset weight is the weight corresponding to the operator or operand of the q-th node.

[0048] Preferably, the overall safety margin is as follows:

[0049] ;

[0050] in, Let m be the predicted value of the safety index at the operating point. , This refers to the threshold for safety indicators.

[0051] Preferably, the tiered early warning includes:

[0052] When the system operates at an ultra-high safety margin, that is This triggers a notification signal;

[0053] When the system operates within a normal safety margin, i.e. No signal is triggered.

[0054] When the system operates with a low safety margin, i.e. Issue a warning signal.

[0055] When the operating point has a low safety margin, i.e. It issues an alarm signal.

[0056] Another aspect of the present invention provides a data-driven power system frequency regulation resource security domain construction and security early warning system, comprising:

[0057] The feasible domain definition module is used to define the frequency regulation resource security domain as the feasible domain of frequency regulation resource configuration capacity combination that satisfies the frequency security index constraint and the adjustable capacity constraint based on the day-ahead power generation plan.

[0058] The frequency regulation resources include thermal power frequency regulation resources, hydropower frequency regulation resources, and energy storage frequency regulation resources;

[0059] The model building and index generation module is used to build an improved system frequency response model, construct a high-precision training dataset, calculate and solve the system frequency security index based on the improved system frequency response model, and obtain the security index matrix.

[0060] The index scaling module is used to obtain a scaled security index matrix based on the security index matrix.

[0061] The expression generation module is used to learn the explicit functional relationship between the scaled security index and the frequency regulation resource allocation capacity using a genetic programming symbolic regression algorithm, and obtain the analytical expression of the frequency security index.

[0062] The security domain construction module is used to draw critical security isosurfaces corresponding to each single security index in a three-dimensional space spanned by the maximum configurable capacity of thermal power frequency regulation resources, hydropower frequency regulation resources and energy storage frequency regulation resources, based on the analytical expression. Each isosurface divides the frequency regulation resource capacity space into a safe region and an unsafe region that satisfy the constraint of the index. By integrating the intersection region between all frequency security critical isosurfaces and the upper limit boundary of resource capacity, the frequency regulation resource security domain is constructed.

[0063] The graded early warning module is used to calculate the comprehensive safety margin based on the comparison between the predicted value of the safety index at the operating point and the safety threshold, and to trigger graded early warnings according to the preset margin threshold.

[0064] Compared with the prior art, the advantages and beneficial effects of the present invention are as follows:

[0065] This invention achieves an analytical representation of the relationship between safety indicators and frequency regulation resource capacity. It employs a symbolic regression algorithm based on genetic programming to autonomously derive an explicit mathematical expression between frequency safety indicators and frequency regulation resource allocation capacity from high-dimensional nonlinear data. This method does not require a pre-defined function form, possesses strong fitting capabilities for complex nonlinear relationships, significantly improves the interpretability and fitting accuracy of the safety boundary, and overcomes the limitations of black-box models and traditional polynomial regression in terms of expression complexity and accuracy.

[0066] This invention achieves visualization of the security domain and multi-level frequency security early warning. It constructs a visualized frequency modulation (FM) resource security domain within a three-dimensional FM resource capacity space, intuitively displaying the system's frequency security operation boundary. Furthermore, a hierarchical early warning mechanism based on comprehensive security margins enables multi-level frequency security status awareness, from "prompt" to "alarm," assisting dispatchers in timely adjusting FM resource allocation strategies and enhancing system defense capabilities. Simultaneously, the explicit expression of the security domain can be embedded into the current / intraday optimized scheduling model, achieving coordinated optimization of economy and security under frequency security constraints.

[0067] The security domain constructed in this invention has good scalability and real-time performance. When introducing new frequency security indicators or frequency modulation resource types, only the corresponding critical security isosurface needs to be superimposed, without the need to reconstruct the entire security domain system. In addition, the genetic programming symbolic regression training and security domain construction process has high computational efficiency and can be completed within minutes, meeting the real-time requirements of minute-level rolling scheduling.

[0068] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0069] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0070] Figure 1 This is a schematic diagram of the method steps in an embodiment of the present invention;

[0071] Figure 2 This is a schematic diagram of the SR-FRRSR construction and scheduling application process according to an embodiment of the present invention;

[0072] Figure 3 This is a diagram of an improved SFR model for the frequency regulation capacity limitation of the unit, as shown in this embodiment of the invention.

[0073] Figure 4 This is a visualization diagram of the SR-FRRSR construction in an embodiment of the present invention;

[0074] Figure 5 This is a schematic diagram of the system structure according to an embodiment of the present invention. Detailed Implementation

[0075] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0076] like Figure 1 As shown in the figure, an embodiment of the present invention provides a data-driven method for constructing a security domain for frequency regulation resources in a power system and for security early warning, comprising:

[0077] Step S1: Based on the day-ahead power generation plan, define the frequency regulation resource security domain as the feasible domain of frequency regulation resource configuration capacity combinations that satisfy frequency security index constraints and adjustable capacity constraints.

[0078] The frequency regulation resources include thermal power frequency regulation resources, hydropower frequency regulation resources, and energy storage frequency regulation resources.

[0079] This invention, based on day-ahead power generation planning, defines the constructed safety domain concept as the feasible region consisting of frequency regulation resource allocation capacity combinations that simultaneously satisfy frequency safety index constraints and adjustable capacity constraints under given system operating conditions (power output plan, load level, and maximum possible power disturbance). Mathematical representation of FRRSR. for:

[0080] ;

[0081] In the formula, constraints (a)-(c) are system frequency security constraints, and constraints (d)-(f) are the frequency regulation resource allocation capacities of thermal power, hydropower, and energy storage. The range of values ​​is constrained. For the unit's assembly capacity, For the current planned output, the subscripts R, H, and S represent thermal power, hydropower, and energy storage, respectively. When the capacity of all three types of frequency regulation resources in the system is adjustable, the FRRSR is represented as a three-dimensional spatial domain. The FRRSR dimension can be reduced when the adjustable capacity of some resources is fixed during the intraday phase. The frequency safety constraints that the operating point within the FRRSR must strictly satisfy are expressed as follows:

[0082] 1) RoCoF: Maximum RoCoF of the system This typically occurs in the initial moments after a disturbance. To prevent malfunctions in distributed generation anti-islanding protection, It must not exceed the safety threshold. , is represented as:

[0083] ;

[0084] In the formula, This represents the change in system frequency deviation over time t after the disturbance.

[0085] 2) FN: To prevent triggering low-frequency load shedding, the lowest frequency after the disturbance should be greater than the system's initial low-frequency load shedding setting value. Therefore, the maximum deviation of the system transient frequency Constraints can be represented as:

[0086] ;

[0087] 3) QSSFD: To ensure stable system operation, the quasi-steady-state frequency deviation of the system after primary frequency modulation. It should be restored to within the safe allowable deviation range, and its constraint threshold is denoted as... The frequency deviation constraint of the system after quasi-steady state is expressed as:

[0088] ;

[0089] Step S2: Construct an improved system frequency response model, build a high-precision training dataset, calculate and solve the system frequency security index based on the improved system frequency response model, and obtain the security index matrix.

[0090] To address the high-dimensional nonlinear characteristics of power system frequency security indices, this invention proposes a method for training explicit expressions of frequency security indices and constructing security domains by integrating GPSR and improved SFR models. The main process is as follows: Figure 2 As shown. To adapt the GPSR algorithm to frequency security assessment requirements under various source-load scenarios, a high-precision training dataset was constructed based on the SFR model, and the following was adopted. Figure 3 The analytical method based on the System Frequency Model (SFR) is shown to calculate the system frequency safety index. For conventional thermal and hydropower units, the SFR model mainly considers the prime mover-governor model, which reflects the active power regulation characteristics. The frequency response transfer model of a thermal power unit can be expressed as:

[0091] ;

[0092] In the formula, The steam volume time constant is For high-pressure turbine coefficient, The reheater time constant is... The time constant of the reheat turbine governor. denoted as the droop coefficient of the reheat turbine governor, and s is the Laplace operator.

[0093] The frequency response transfer function of a hydroelectric generator can be expressed as:

[0094] ;

[0095] In the formula, For thermal power units participating in frequency regulation. The time constant for turbine reset is... For the permanent decline rate, For the temporary decline rate, The time constant of the water hammer effect. The time constant of the turbine governor. This is the droop coefficient of the turbine governor.

[0096] By configuring energy storage to simulate the inertial response of a synchronous machine and primary frequency regulation, the frequency response capability of energy storage power stations and wind-solar-storage power distribution can be expressed as:

[0097] ;

[0098] In the formula, For energy storage to participate in frequency regulation power, To simulate the inertial time constant, The droop factor for primary frequency modulation. This represents the response delay time constant for frequency control.

[0099] The equivalent inertial time constant of the system It can be defined as:

[0100] ;

[0101] In the formula, For the unit's assembly capacity, the subscript is... , , These represent the i-th thermal power unit, the j-th hydropower unit, and the k-th energy storage unit, respectively. This represents the current total system load level. (·) represents the simulation inertial time constant of the power generation unit / energy storage unit. (·) indicates the unit's online frequency regulation status. (·)=1 indicates that the device is online and has frequency modulation capability. (·)=0 indicates offline or not participating in frequency modulation).

[0102] Percentage of online capacity of different types of generating units , , The equivalent frequency regulation parameters of the generating units can be weighted and aggregated according to the installed capacity of the online generating units. For generator fault-related disturbances, the frequency regulation capability of the generating units after a line disconnection is not considered.

[0103] ;

[0104] In the formula, This is the reserve capacity reserved for the unit for other safety controls. , These represent the opening limit values ​​corresponding to the maximum load limit of the primary frequency regulation of the governors for thermal and hydropower units, respectively. In summary, the improved SFR model considering the unit frequency regulation capacity limit can be expressed as: Figure 3 As shown.

[0105] High-precision frequency dynamic simulation was performed based on the improved SFR model, and the safety index was solved to obtain the output matrix vector Y:

[0106] ;

[0107] In the formula, , , Let represent the frequency safety index of the p-th sample.

[0108] Step S3: Obtain the scaled security index matrix based on the security index matrix.

[0109] Since GPSR itself is insensitive to the dimensions of input features and does not require normalization, but because the output safety index matrix Y in this invention has a small range of variation, model training is easily dominated by some input features. To enhance the algorithm's ability to learn the mapping relationship between input and output and improve training accuracy, the output matrix Y is linearly scaled:

[0110] ;

[0111] In the formula, This is a diagonal matrix of scaling factors. These correspond to scaling factors for each security metric, and Y' is the scaled output matrix. The goal of GPSR is to learn the scaled security metric Y' and frequency modulation resource allocation capacity from the dataset. Explicit functional relationship between them:

[0112] ;

[0113] Step S4: Use a genetic programming symbolic regression algorithm to learn the explicit functional relationship between the scaled security index and the frequency regulation resource allocation capacity, and obtain the analytical expression of the frequency security index.

[0114] To obtain an analytical expression representing the explicit functional relationship between the frequency security index and the input variables, the GPSR training process in this invention includes the following core steps:

[0115] 1) Initial population generation. The GPSR method first randomly generates a set of symbolic expressions that satisfy preset constraints, forming multiple initial populations;

[0116] 2) Fitness assessment and genetic manipulation. Genetics is the core of GPSR training. First, the performance of individuals in the population is assessed based on the fitness function. Then, a tournament selection mechanism is used to select dominant individuals as parents. Finally, offspring expressions are generated through operations such as crossover and mutation to achieve population evolution.

[0117] To quantify and evaluate the model's fitting accuracy and complexity to the scaled frequency safety index Y', and to guide the population towards a better solution through genetic evolution while preventing excessive complexity in individual expressions during evolution, a training fitness function is constructed based on the loss function and complexity penalty function as follows:

[0118] ;

[0119] In the formula, the first part is the loss function of the safety index m. The smaller the value, the more accurate the model fit. m∈M={ , , }, The scaled value of the safety index m is the true value of the sample p. Let m be the explicit function prediction value of the m-th safety indicator obtained from GPSR learning. The complexity penalty coefficient is obtained by... Adjusting the penalty for expression complexity encourages the algorithm to prioritize expressions with simple structure and strong interpretability while ensuring accuracy.

[0120] 3) Population Update. The offspring and parent populations are merged, and based on a classic multi-objective optimization algorithm framework, non-dominated sorting and crowding distance calculation are used to select the Pareto front solution set. This solution set represents the optimal population that balances prediction accuracy (minimizing the loss function) and model complexity.

[0121] 4) Iteration Termination and Optimal Solution Output. Repeat steps 2-3 until the training results meet the preset fitness convergence threshold or the maximum number of iterations is reached. Then, select the symbolic expression from the Pareto front solution set that best combines prediction accuracy, structural simplicity, and generalization ability as the model fitting indicator. , .

[0122] Step S5: Based on the analytical expression, in the three-dimensional space spanned by the maximum configurable capacity of thermal power frequency regulation resources, hydropower frequency regulation resources and energy storage frequency regulation resources, the critical safety isosurfaces corresponding to each single safety index are drawn respectively. Each isosurface divides the frequency regulation resource capacity space into a safe region and an unsafe region that satisfy the constraint of the index. By integrating the intersection region between all frequency safety critical isosurfaces and the upper limit boundary of resource capacity, the frequency regulation resource safety domain is constructed.

[0123] For each set frequency security threshold, critical security isosurfaces for each individual security index are plotted within the three-dimensional frequency regulation resource capacity space based on the explicit expressions of the frequency security indices obtained from GPSR training. Each isosurface divides the frequency regulation resource space into safe and unsafe regions that satisfy the constraints of that index. A FRRSR is constructed in the three-dimensional space spanned by the maximum configurable capacity of three key frequency regulation resources: thermal power, hydropower, and energy storage. The intersection of all critical frequency security isosurfaces and the upper limit boundary of the configurable capacity is the solved FRRSR. Its boundary represents the minimum capacity combination required for the synergistic effect of the three types of frequency regulation resources to satisfy specific frequency security constraints, such as... Figure 4 As shown.

[0124] Step S6: Calculate the comprehensive safety margin based on the comparison between the predicted value of the safety index at the operating point and the safety threshold, and trigger a graded early warning according to the preset margin threshold.

[0125] Finally, to quantitatively characterize the running point The frequency safety margin level is used to assess and warn of the system's frequency regulation resource safety margin. Based on the comparison between the predicted value of the safety index at the operating point and its safety threshold, the comprehensive safety margin is defined as the normalized relative safety margin under the most stringent safety constraints at that point:

[0126] ;

[0127] In the formula, Let m be the predicted value of the index at the running point. This is a safety margin threshold, reflecting the overall frequency safety level of the system dominated by the most stringent safety constraints. When )>0, the system is in a safe state; A value of ≤0 indicates that at least one safety indicator at the operating point is in a critical safety state or there is a risk of exceeding the frequency limit.

[0128] To assist dispatchers in assessing the adequacy level of system frequency regulation resources, the comprehensive safety margin can be... As a core early warning indicator, a tiered early warning mechanism is constructed. State division and signal triggering are based on preset safety margin thresholds, as shown in Table 1:

[0129] Table 1. Early warning mechanism for frequency modulation resource sufficiency based on comprehensive security margin.

[0130]

[0131] When the system operates at an ultra-high safety margin, a prompt signal is triggered, which can appropriately reduce the use of frequency modulation resources to optimize operating economy; when the system operates at a normal safety margin, no signal is triggered, indicating that the current frequency modulation resource configuration meets safety requirements and is at a reasonable level; when the system operates at a low safety margin, a warning signal is issued, indicating that the current frequency modulation resource level is at a critical level; when the operating point is at a low safety margin, an alarm signal is issued, indicating that the current frequency modulation resources are severely insufficient and frequency modulation resources need to be configured to restore the system's frequency modulation capability.

[0132] This invention achieves an analytical representation of the relationship between safety indicators and frequency modulation resource capacity through a symbolic regression algorithm based on genetic programming. This method does not require a predefined function form and can autonomously derive an explicit mathematical expression between frequency safety indicators and frequency modulation resource capacity from high-dimensional nonlinear data. This significantly improves the interpretability and fitting accuracy of the safety boundary, overcoming the limitations of traditional black-box models and multinomial regression in terms of complexity and accuracy.

[0133] This invention further constructs a visualized security domain within the three-dimensional frequency modulation resource capacity space, clearly displaying the system's frequency security operation boundary, and establishes a multi-level frequency security early warning mechanism from "prompt" to "alarm" based on comprehensive security margins. This mechanism can assist dispatchers in adjusting resource allocation strategies in a timely manner, enhancing the system's defense capabilities. Simultaneously, the explicit mathematical expression of the security domain can be embedded into the current / intraday optimized scheduling model, achieving synergistic optimization of security and economy.

[0134] The security domain constructed by this invention possesses excellent scalability and real-time performance. When introducing new frequency security indicators or frequency modulation resource types, only the corresponding critical security isosurface needs to be superimposed, without the need to reconstruct the entire security domain system. Furthermore, the training and security domain construction process based on genetic programming symbolic regression is computationally efficient and can be completed within minutes, meeting the real-time requirements of 5-minute rolling scheduling.

[0135] like Figure 5 As shown, another embodiment of the present invention provides a data-driven power system frequency regulation resource security domain construction and security early warning system, including:

[0136] The feasible domain definition module is used to define the frequency regulation resource security domain as the feasible domain of frequency regulation resource configuration capacity combination that satisfies the frequency security index constraint and the adjustable capacity constraint based on the day-ahead power generation plan.

[0137] The frequency regulation resources include thermal power frequency regulation resources, hydropower frequency regulation resources, and energy storage frequency regulation resources;

[0138] The model building and index generation module is used to build an improved system frequency response model, construct a high-precision training dataset, calculate and solve the system frequency security index based on the improved system frequency response model, and obtain the security index matrix.

[0139] The index scaling module is used to obtain a scaled security index matrix based on the security index matrix.

[0140] The expression generation module is used to learn the explicit functional relationship between the scaled security index and the frequency regulation resource allocation capacity using a genetic programming symbolic regression algorithm, and obtain the analytical expression of the frequency security index.

[0141] The security domain construction module is used to draw critical security isosurfaces corresponding to each single security index in a three-dimensional space spanned by the maximum configurable capacity of thermal power frequency regulation resources, hydropower frequency regulation resources and energy storage frequency regulation resources, based on the analytical expression. Each isosurface divides the frequency regulation resource capacity space into a safe region and an unsafe region that satisfy the constraint of the index. By integrating the intersection region between all frequency security critical isosurfaces and the upper limit boundary of resource capacity, the frequency regulation resource security domain is constructed.

[0142] The graded early warning module is used to calculate the comprehensive safety margin based on the comparison between the predicted value of the safety index at the operating point and the safety threshold, and to trigger graded early warnings according to the preset margin threshold.

[0143] Furthermore, the frequency security index constraints include:

[0144] Frequency change rate constraint: The maximum frequency change rate shall not exceed a safety threshold. ;

[0145] Maximum transient frequency deviation constraint: The maximum transient frequency deviation shall not exceed the low-frequency load shedding setting value. ;

[0146] Quasi-steady-state frequency deviation constraint: The quasi-steady-state frequency deviation shall not exceed the allowable deviation. ;

[0147] The adjustable capacity constraint includes:

[0148] Thermal power resource capacity constraints: ;

[0149] Hydropower resource capacity constraints: ;

[0150] Energy storage resource capacity constraints: ;

[0151] in, This represents the maximum rate of change of the system frequency. As a safety threshold, This is the initial low-frequency load shedding setting value for the system. The maximum deviation of the system transient frequency. This represents the quasi-steady-state frequency deviation of the system after a single frequency modulation. To constrain the threshold, These are the frequency regulation resource allocation capacities for thermal power, hydropower, and energy storage, respectively. These refer to the installed capacity of thermal power, hydropower, and energy storage units, respectively. The power outputs are planned for thermal power, hydropower, and energy storage units, respectively.

[0152] Furthermore, during the intraday phase, when the adjustable capacity of some resources is fixed, a low-dimensional frequency modulation resource security domain is constructed through dimensionality reduction. The frequency security constraints that the operating points within the frequency modulation resource security domain strictly satisfy are as follows:

[0153] Frequency change rate constraint:

[0154] ;

[0155] Maximum deviation constraint of transient frequency:

[0156] ;

[0157] Quasi-steady-state frequency deviation constraint:

[0158] ;

[0159] in, This represents the maximum rate of change of the system frequency. This represents the change in system frequency deviation over time t after the disturbance. As a safety threshold, This is the initial low-frequency load shedding setting value for the system. The maximum deviation of the system transient frequency. This represents the quasi-steady-state frequency deviation of the system after a single frequency modulation. This is the constraint threshold.

[0160] Furthermore, the improved system frequency response model includes:

[0161] Transfer function of frequency response of thermal power unit: ;

[0162] Hydropower unit frequency response transfer function: ;

[0163] Energy storage frequency response transfer function: ;

[0164] in, The steam volume time constant is For high-pressure turbine coefficient, The reheater time constant is... The time constant of the reheat turbine governor. This is the droop coefficient of the reheat turbine governor. For the Laplace operator, The time constant for turbine reset is... For the permanent decline rate, For the temporary decline rate, The time constant of the water hammer effect. The time constant of the turbine governor. This refers to the droop coefficient of the turbine governor. To simulate the inertial time constant, The droop factor for primary frequency modulation. This represents the response delay time constant of frequency control. This represents the change in system frequency.

[0165] Furthermore, the scaled security index matrix is ​​obtained by linearly scaling the security index matrix:

[0166] ;

[0167] in, This is a diagonal matrix of scaling factors. Each corresponds to a scaling factor for a specific security indicator. For safety indicators, This is the scaled output matrix.

[0168] Furthermore, the genetic programming symbolic regression algorithm includes:

[0169] Initial population generation: Randomly generate symbolic expressions that satisfy preset constraints;

[0170] Fitness evaluation: The fitness value is calculated based on the loss function and the complexity penalty function;

[0171] Genetic manipulation: A tournament selection mechanism is used to select superior individuals as parents, and offspring individuals are generated through crossover and mutation operations;

[0172] Population update: newly generated offspring individuals are merged with parent individuals, and Pareto front solutions are selected from the merged population based on non-dominated sorting and crowding distance calculation.

[0173] Iteration Termination and Output of Optimal Solution: Repeat fitness evaluation, genetic operations and population update until the training result meets the preset fitness convergence threshold or reaches the maximum number of iterations, and select the comprehensive optimal symbolic expression from the Pareto front solution set as the safety index to fit the model.

[0174] Furthermore, the fitness function is defined as:

[0175] ;

[0176] in, Let C be the loss function for the safety metric m, and C be the expression complexity. The scaled value of the safety index m is the true value of the sample p. Let m be the explicit function prediction value of the m-th safety index obtained by the genetic programming symbolic regression algorithm. This is the complexity penalty coefficient. For the total sample size, For the p-th column of the input matrix, The total number of nodes in the expression tree. The preset weight is the weight corresponding to the operator or operand of the q-th node.

[0177] Furthermore, the overall safety margin is as follows:

[0178] ;

[0179] in, Let m be the predicted value of the safety index at the operating point. , This refers to the threshold for safety indicators.

[0180] Furthermore, the tiered early warning system includes:

[0181] When the system operates at an ultra-high safety margin, that is This triggers a notification signal;

[0182] When the system operates within a normal safety margin, i.e. No signal is triggered.

[0183] When the system operates with a low safety margin, i.e. Issue a warning signal.

[0184] When the operating point has a low safety margin, i.e. It issues an alarm signal.

[0185] This invention employs a genetic programming symbolic regression (GPSR) algorithm to autonomously derive an explicit mathematical expression relating frequency security indicators and frequency modulation resource capacity from operational data. This method does not rely on a pre-defined function form, possesses both high accuracy and strong interpretability, and significantly outperforms traditional black-box machine learning and polynomial fitting methods.

[0186] This invention designs a method for constructing a safety domain based on the intersection of multiple frequency safety critical isosurfaces and physical capacity constraints. This method can realize the visual representation of the safety operation boundary in three-dimensional resource space, allowing schedulers to intuitively grasp the system's safety margin.

[0187] This invention defines a comprehensive security margin quantification index and constructs a multi-level frequency security early warning mechanism based on the comprehensive security margin. This evaluation system provides a quantitative basis for scheduling decisions.

[0188] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0189] It will be readily understood by those skilled in the art that this invention includes any combination of the inventive description and specific embodiments outlined in the foregoing specification, as well as the various parts shown in the accompanying drawings. Due to space limitations and for the sake of brevity, not all of these combinations have been described in detail. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

[0190] Although embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A data-driven method for constructing a security domain for frequency regulation resources in a power system and for security early warning, characterized in that, include: Based on the day-ahead power generation plan, the frequency regulation resource security domain is defined as the feasible domain of frequency regulation resource configuration capacity combinations that satisfy frequency security index constraints and adjustable capacity constraints. The frequency regulation resources include thermal power frequency regulation resources, hydropower frequency regulation resources, and energy storage frequency regulation resources; An improved system frequency response model is constructed, a high-precision training dataset is built, and the system frequency security index is calculated and solved based on the improved system frequency response model to obtain the security index matrix. The scaled security index matrix is ​​obtained from the security index matrix; A genetic programming symbolic regression algorithm is used to learn the explicit functional relationship between the scaled security index and the frequency modulation resource allocation capacity, thereby obtaining an analytical expression for the frequency security index; Based on the analytical expression, in the three-dimensional space spanned by the maximum configurable capacity of thermal power frequency regulation resources, hydropower frequency regulation resources and energy storage frequency regulation resources, critical safety isosurfaces corresponding to each single safety index are drawn respectively. Each isosurface divides the frequency regulation resource capacity space into a safe region and an unsafe region that satisfy the constraint of the index. By integrating the intersection region between all frequency safety critical isosurfaces and the upper limit boundary of resource capacity, a frequency regulation resource safety domain is constructed. Based on the comparison between the predicted values ​​of the safety indicators at the operating point and the safety threshold, the comprehensive safety margin is calculated, and a graded early warning is triggered according to the preset margin threshold. The improved system frequency response model includes: Transfer function of frequency response of thermal power unit: ; Hydropower unit frequency response transfer function: ; Energy storage frequency response transfer function: ; in, The steam volume time constant is For high-pressure turbine coefficient, The reheater time constant is... The time constant of the reheat turbine governor. This is the droop coefficient of the reheat turbine governor. For the Laplace operator, The time constant for turbine reset is... For the permanent decline rate, For the temporary decline rate, The time constant of the water hammer effect. The time constant of the turbine governor. This refers to the droop coefficient of the turbine governor. To simulate the inertial time constant, The droop factor for primary frequency modulation. This represents the response delay time constant of frequency control. This represents the change in system frequency.

2. The data-driven method for constructing and providing early warning of frequency regulation resource security domains in power systems as described in claim 1, characterized in that, The frequency security constraints include: Frequency change rate constraint: The maximum frequency change rate shall not exceed a safety threshold. ; Maximum transient frequency deviation constraint: The maximum transient frequency deviation shall not exceed the low-frequency load shedding setting value. ; Quasi-steady-state frequency deviation constraint: The quasi-steady-state frequency deviation shall not exceed the allowable deviation. ; The adjustable capacity constraint includes: Thermal power resource capacity constraints: ; Hydropower resource capacity constraints: ; Energy storage resource capacity constraints: ; in, This represents the maximum rate of change of the system frequency. As a safety threshold, This is the initial low-frequency load shedding setting value for the system. The maximum deviation of the system transient frequency. This represents the quasi-steady-state frequency deviation of the system after a single frequency modulation. As a constraint threshold, These are the frequency regulation resource allocation capacities for thermal power, hydropower, and energy storage, respectively. These refer to the installed capacity of thermal power, hydropower, and energy storage units, respectively. The power outputs are planned for thermal power, hydropower, and energy storage units, respectively.

3. The data-driven method for constructing and providing early warning of frequency regulation resource security domains in power systems as described in claim 2, characterized in that, During the intraday phase, when the adjustable capacity of some resources is fixed, a low-dimensional frequency modulation resource security domain is constructed through dimensionality reduction. The frequency security constraints that the operating points within the frequency modulation resource security domain must strictly satisfy are as follows: Frequency change rate constraint: ； Maximum deviation constraint of transient frequency: ； Quasi-steady-state frequency deviation constraint: ； in, This represents the maximum rate of change of the system frequency. This represents the change in system frequency deviation over time t after the disturbance. As a safety threshold, This is the initial low-frequency load shedding setting value for the system. The maximum deviation of the system transient frequency. This represents the quasi-steady-state frequency deviation of the system after a single frequency modulation. This is the constraint threshold.

4. The data-driven method for constructing and providing early warning of frequency regulation resource security domains in power systems as described in claim 1, characterized in that, The scaled security index matrix is ​​obtained by linearly scaling the security index matrix: ； in, This is a diagonal matrix of scaling factors. Each corresponds to a scaling factor for a specific security indicator. For safety indicators, This is the scaled output matrix.

5. The data-driven method for constructing and providing early warning of frequency regulation resource security domains in power systems as described in claim 1, characterized in that... The genetic programming symbolic regression algorithm includes: Initial population generation: Randomly generate symbolic expressions that satisfy preset constraints; Fitness evaluation: The fitness value is calculated based on the loss function and the complexity penalty function; Genetic manipulation: A tournament selection mechanism is used to select superior individuals as parents, and offspring individuals are generated through crossover and mutation operations; Population update: merge the offspring and parent populations, and use non-dominated sorting and crowding distance calculation to select the Pareto front solution set based on the classic multi-objective optimization algorithm framework; Iteration Termination and Output of Optimal Solution: Repeat fitness evaluation, genetic operations and population update until the training result meets the preset fitness convergence threshold or reaches the maximum number of iterations, and select the comprehensive optimal symbolic expression from the Pareto front solution set as the safety index to fit the model.

6. The data-driven method for constructing and providing early warning of frequency regulation resource security domains in power systems as described in claim 5, characterized in that, The fitness function is defined as: ； in, Let C be the loss function for the safety metric m, and C be the expression complexity. Let m be the true value of the safety index after scaling the sample p. Let m be the explicit function prediction value of the m-th safety index obtained by the genetic programming symbolic regression algorithm. This is the complexity penalty coefficient. For the total sample size, For the p-th column of the input matrix, The total number of nodes in the expression tree. The preset weight is the weight corresponding to the operator or operand of the q-th node.

7. The data-driven method for constructing and providing early warning of frequency regulation resource security domains in power systems as described in claim 1, characterized in that, The overall safety margin is as follows: ； in, Let m be the predicted value of the safety index at the operating point. , This refers to the threshold for safety indicators.

8. The data-driven method for constructing and providing early warning of frequency regulation resource security domains in power systems as described in claim 1, characterized in that, The tiered early warning system includes: When the system operates at an ultra-high safety margin, that is This triggers a notification signal; When the system operates within a normal safety margin, i.e. No signal is triggered. When the system operates with a low safety margin, i.e. Issue a warning signal. When the operating point has a low safety margin, i.e. It issues an alarm signal.

9. A data-driven power system frequency regulation resource security domain construction and security early warning system, characterized in that, include: The feasible domain definition module is used to define the frequency regulation resource security domain as the feasible domain of frequency regulation resource configuration capacity combination that satisfies the frequency security index constraint and the adjustable capacity constraint based on the day-ahead power generation plan. The frequency regulation resources include thermal power frequency regulation resources, hydropower frequency regulation resources, and energy storage frequency regulation resources; The model building and index generation module is used to build an improved system frequency response model, construct a high-precision training dataset, calculate and solve the system frequency security index based on the improved system frequency response model, and obtain the security index matrix. The index scaling module is used to obtain a scaled security index matrix based on the security index matrix. The expression generation module is used to learn the explicit functional relationship between the scaled security index and the frequency regulation resource allocation capacity using a genetic programming symbolic regression algorithm, and obtain the analytical expression of the frequency security index. The security domain construction module is used to draw critical security isosurfaces corresponding to each single security index in a three-dimensional space spanned by the maximum configurable capacity of thermal power frequency regulation resources, hydropower frequency regulation resources and energy storage frequency regulation resources, based on the analytical expression. Each isosurface divides the frequency regulation resource capacity space into a safe region and an unsafe region that satisfy the constraint of the index. By integrating the intersection region between all frequency security critical isosurfaces and the upper limit boundary of resource capacity, the frequency regulation resource security domain is constructed. The graded early warning module is used to calculate the comprehensive safety margin based on the comparison between the predicted value of the safety index at the operating point and the safety threshold, and to trigger graded early warnings according to the preset margin threshold. The improved system frequency response model includes: Transfer function of frequency response of thermal power unit: ; Hydropower unit frequency response transfer function: ; Energy storage frequency response transfer function: ; in, The steam volume time constant is For high-pressure turbine coefficient, The reheater time constant is... The time constant of the reheat turbine governor. This is the droop coefficient of the reheat turbine governor. For the Laplace operator, The time constant for turbine reset is... For the permanent decline rate, For the temporary decline rate, The time constant of the water hammer effect. The time constant of the turbine governor. This refers to the droop coefficient of the turbine governor. To simulate the inertial time constant, The droop factor for primary frequency modulation. This represents the response delay time constant of frequency control. This represents the change in system frequency.

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