ELM-based frequency security constraint linearization optimization scheduling method

Abstract

The ELM-based frequency safety constraint linearization optimization scheduling method comprises the following steps: establishing a fire-wind-light multi-energy complementary frequency dynamic response model, and deducing a time domain analytical expression of a frequency safety index by taking a frequency maximum change rate and a frequency maximum deviation as the frequency safety index of a system; considering a frequency lowest point security constraint and a frequency maximum change rate security constraint, and establishing a frequency security constraint-containing optimization scheduling model; a maximum bearable disturbance power linearization mapping method based on ELM is provided, nonlinear frequency security constraints are converted into a series of linear constraint sets, and linearization processing of the frequency security constraints is achieved; and piecewise linearization is carried out on quadratic terms in the established objective function containing the frequency security constraint optimization scheduling model, the overall model is converted into a mixed integer linear model, and a Gurobi solver is used to solve the linearly processed model. The scheduling method can ensure that the system frequency is safe and stable, so that the established optimal scheduling model gives consideration to both economy and frequency safety.

Description

Technical Field

[0001] This invention relates to the field of power system optimization scheduling, and specifically to a frequency security constraint linearization optimization scheduling method based on ELM. Background Technology

[0002] As the penetration rate of new energy generating units in the power system continues to increase, their output exhibits strong random fluctuations, leading to the dual challenges of weak inertia support and insufficient frequency regulation capability for the power grid. When the power grid suffers from high-power disturbances such as unit failures, DC blocking, or continuous commutation failures, it is prone to triggering the cascading action of relay protection devices, resulting in large-scale unit disconnection or load shedding accidents in the regional power grid. Against this backdrop, frequency, as a core parameter reflecting the dynamic stability of the power system, has significant engineering value for the accurate calculation of its transient processes and dynamic characteristic analysis in ensuring the safe operation of the power grid. Currently, frequency stability analysis for low-inertia power systems mainly employs two methods: time-domain simulation analysis and mathematical analysis.

[0003] Time-domain simulation relies on detailed modeling, resulting in low computational efficiency; the frequency minimum point constraint derived by analytical methods is highly nonlinear, making it difficult for commercial solvers to solve directly; while linearizing the generator governor simplifies the calculation process, its error is too large to meet accuracy requirements.

[0004] While existing analytical methods can obtain frequency security indicators after perturbation, they struggle to balance accuracy and computational efficiency. Furthermore, the frequency security constraints obtained through analytical methods are highly nonlinear, making them difficult to solve directly using commercial solvers. In contrast, intelligent algorithms, as a type of prediction method based on sample learning, do not rely on model structure and parameters. After training with a large number of samples, they can quickly and accurately incorporate frequency security constraints into the optimization scheduling model.

[0005] Against this backdrop, in a new power system dominated by a high proportion of new energy sources, using data-driven intelligent evaluation methods to intelligently evaluate frequency safety indicators such as maximum frequency deviation and maximum frequency change rate, and verifying the frequency stability characteristics of the system, is of great significance for ensuring the frequency safety and stable operation of the large power grid in a highly volatile environment. Summary of the Invention

[0006] This invention proposes a frequency security constraint linearization optimization scheduling method based on Extreme Learning Machine (ELM). This method can transform the derived nonlinear frequency security constraints into a series of linear constraint sets and add them to the constraint conditions of the optimization scheduling model, thereby ensuring the frequency security and stability of the system and making the established optimization scheduling model take into account both economy and frequency security.

[0007] The technical solution adopted in this invention is as follows:

[0008] The frequency security-constrained linearization optimization scheduling method based on ELM includes the following steps:

[0009] Step 1: Establish a frequency dynamic response model for multi-energy complementarity of fire, wind, and solar, using the maximum rate of frequency change and the maximum frequency deviation as the frequency safety indicators of the system, and derive the time-domain analytical expression of the frequency safety indicators;

[0010] Step 2: Based on the traditional optimization scheduling model, consider the safety constraints of the lowest frequency point and the maximum rate of change of frequency to establish an optimization scheduling model with frequency safety constraints to ensure the frequency safety and stability of the system;

[0011] Step 3: Propose a linearization mapping method for the maximum tolerable disturbance power based on ELM, which transforms the nonlinear frequency security constraints in Step 2 into a series of linear constraint sets, thereby realizing the linearization of frequency security constraints;

[0012] Step 4: Perform piecewise linearization on the quadratic terms in the objective function of the frequency-constrained optimization scheduling model established in Step 2, transforming the overall model into a mixed-integer linear model, and then use the Gurobi solver to solve the linearized model.

[0013] In step 1, virtual inertia control of wind and solar power units is coupled with frequency regulation of thermal power units to construct a frequency dynamic response model of thermal-wind-solar multi-energy complementarity. The frequency dynamic response process can be expressed as follows:

[0014]

[0015] In the formula, Δf(t) is the frequency deviation at time t, in Hz; D eq H is the equivalent damping coefficient of the model; eq The equivalent inertial time constant of the model; ΔP L The power deficit caused by the disturbance; The system's primary frequency regulation power increment at time t; N represents the total number of units in the system; ΔP G,i (t) represents the increase in the power generation of the i-th generating unit at time t.

[0016] Based on the above model, the frequency dynamic response model in the complex frequency domain is transformed into a time-domain equation. Using the maximum rate of change of frequency and the maximum frequency deviation as the system's frequency safety indicators, the time-domain analytical expression of the frequency safety indicators is derived. The derived expression is as follows:

[0017] (1) Maximum frequency deviation:

[0018]

[0019] In equation (12), △f max D represents the system's maximum frequency deviation. eq T is the equivalent damping coefficient of the model; eq W1 is the time constant of the unit reheater; W1 is the equivalent speed regulation slope coefficient; ω d To attenuate the oscillation angular frequency; ω n t is the natural oscillation frequency; m ε is the time it takes for the system to reach its lowest frequency; λ is the damping ratio; t is the initial phase of the oscillation component; and t is the time variable.

[0020] (2) Maximum rate of change of frequency:

[0021]

[0022] In equation (17), RoCoF max H represents the system's maximum rate of frequency change. eq This is the equivalent inertial time constant of the model.

[0023] In step 2, the established optimized scheduling model, while considering the conventional constraints of the traditional optimized scheduling model, also considers the frequency security constraints, which take the maximum rate of change of frequency and the maximum deviation of frequency as the frequency security indicators of the system. This ensures that the transient frequency indicators of the system are maintained within a safe range, thereby guaranteeing the frequency security and stability of the system.

[0024] The constructed frequency-constrained optimization scheduling model includes thermal power, wind power, and photovoltaic units. Its objective function includes the start-up and shutdown costs of thermal power units, the operating costs of thermal power units, and the curtailment penalty costs of wind farms and photovoltaic power plants. Its expression is as follows:

[0025] F = min{C G +C W +C V +C U} (18);

[0026] In equation (18), F represents the minimum total operating cost of the system; C U C G C W C E These are the start-up and shutdown costs, operating costs, wind curtailment penalty costs, and solar curtailment penalty costs for thermal power units.

[0027] Common constraints include minimum start-up and shutdown time constraints for each unit, power balance constraints for the system, upper and lower limits of output constraints for thermal power, wind power, and photovoltaic units, and ramp / slippage rate constraints for the units.

[0028]

[0029] In the formula, U i,t This represents the start-up and shutdown status of the i-th thermal power unit at time t, where 1 indicates startup and 0 indicates shutdown; T i on T i off These are the minimum continuous start-up and shutdown times for the i-th thermal power unit, respectively; Let P be the continuous start-up time and continuous shutdown time of the i-th unit at time t-1, respectively; G,i.t P represents the output power of the i-th thermal power unit at time t. W,j.t P represents the output power of the j-th wind turbine at time t. V,h.t P represents the output power of the h-th photovoltaic unit at time t. L.t Let be the total load demand at time t; This represents the upper limit of the output of the i-th thermal power unit; This is the lower limit of the output of the i-th thermal power unit; Let be the predicted value of the j-th wind turbine at time t; Let h be the predicted value of the h-th photovoltaic unit at time t; Let be the upper limit of the gradient for the i-th thermal power unit; T represents the lower limit of the ramp rate for the i-th thermal power unit; i on T represents the minimum continuous start-up time of the i-th thermal power unit; i down N represents the minimum downtime of the i-th thermal power unit; W N represents the total number of wind turbine units. V Indicates the total number of photovoltaic units; U i,t-1 P represents the start-up and shutdown status of the i-th thermal power unit at time t-1; G,i,t-1 Let represent the output power of the i-th thermal power unit at time t-1.

[0030] Frequency security constraints:

[0031] f N +f N △f max ≥f min (27);

[0032]

[0033] Equation (4) is the safety constraint at the lowest frequency point; Equation (5) is the safety constraint at the maximum rate of change of frequency; f min The lower limit of the frequency specified by the system; f N The system's rated frequency; Δf max This represents the maximum frequency deviation of the system.

[0034] In step 3, machine learning is used to train and fit the model. To understand the relationship between the unit's operating status and the maximum tolerable disturbance power fitting model based on ELM, this model network constructs a network from the decision variables of the optimization scheduling problem to... The linear mapping relationship is used to achieve the linearization of the minimum point frequency safety constraint; specifically as follows:

[0035] According to equation (12), the maximum frequency deviation is proportional to the system power disturbance. Simultaneously, based on the mapping relationship, the frequency deviation limit Δf... max The maximum disturbance power that the corresponding power system can withstand The expression for this mapping relationship is as follows:

[0036]

[0037] In the formula, Indicates the minimum disturbance power; l and These are the index of the piecewise linear function and the total number of segments, respectively; c g,l h g,l Let Ψ, Φ, H be the slope and intercept constant of the l-th piecewise linear function, respectively; T This represents a vector containing system characteristic parameters; Ψ and Φ are the synthesized characteristic parameters Ψ of each frequency regulation unit. i With the original parameter Φ i The vector formed by H represents the system inertia.

[0038] Step 3, the ELM-based linearization process, includes the following:

[0039] 3.1: Training Data Generation

[0040] a1: Using modeling software such as Simulink, establish a frequency dynamic response model for multi-energy complementarity of fire, wind and solar;

[0041] a2: Perform large-scale simulations, applying various power perturbations to the system under multiple different operating scenarios;

[0042] a3: In each simulation, calculate and record the maximum disturbance power that the system can withstand. The corresponding system operating parameters and this data will be used as training samples for the ELM network.

[0043] 3.2: ELM Network Structure Design:

[0044] b1: Input layer:

[0045] Based on the generated data above, the input features of the ELM network input layer are determined: including the generator reheater time constant T. RThe input characteristics are standardized by taking the power ratio coefficient F of the high-pressure cylinder of the unit, the adjustment coefficient R of the unit, and the system inertia H, as shown in equation (29):

[0046]

[0047] Where: Φ norm For the original parameters; μ Φ and σ Φ These are the mean and standard deviation of the feature, respectively.

[0048] b2: Hidden layer:

[0049] The synthesized feature parameter Ψ i With the original parameter Φ i Combined and used as input elements for training the hidden layers of the ELM network, the standardized features are passed through a randomly initialized weight matrix a. g and bias b g Mapped to the hidden layer:

[0050]

[0051] Where: Φ i Let θ be the original input feature of the i-th frequency regulation unit; θ is the Sigmoid activation function, chosen as θ. x is a linear combination of the inputs a g ·Φ i +b g ;a g and b g For fixed weights (the random initialization property of ELM); i refers to the number of the i-th feature or sample; This represents the sample set.

[0052] b3: Output layer:

[0053] Using a piecewise linear method, we can fit the maximum disturbance power that the system can withstand while maintaining frequency safety.

[0054]

[0055] In the formula: Indicates the minimum disturbance power; l and These are the index of the piecewise linear function and the total number of segments, respectively; c g,l and h g,l These are the slope and intercept constant of the l-th piecewise linear function, respectively; Ψ and Φ are the synthesized characteristic parameters Ψ of each frequency modulation unit. i With the original parameter Φ i The vector is composed of H; H represents system inertia; T represents matrix transpose.

[0056] 3.3: Training the ELM network model:

[0057] c1: Define the training objective as minimizing the sum of errors between the actual maximum tolerable perturbation power and the fitted maximum perturbation power, as shown in equation (32):

[0058]

[0059] Where: N Φ This represents the total amount of training data generated. and These are the actual maximum tolerable disturbance power and the fitted maximum disturbance power for the k-th data sample, respectively. This represents a binary variable representing the selection of segments.

[0060] c2: Set constraints, introduce conservative constraints, and ensure the model's predictions are accurate. The value should not exceed the actual acceptable value; at the same time, binary variables and relevant constraints should be set to correctly select different segments of the piecewise linear function;

[0061]

[0062] In the formula: c is a very large positive constant; l and h l These are the slope and intercept constant of the l-th piecewise linear function, respectively; k represents the index of the data sample; l and These are the index of the piecewise linear function and the total number of segments, respectively; T represents the matrix transpose.

[0063] 3.4: Application of Linearization Constraints

[0064] d1: After the above training and fitting, the nonlinear frequency safety constraint is transformed into a series of linear constraints, and the frequency minimum point safety constraint can be expressed as follows:

[0065]

[0066] In the formula: △P L,t This indicates the power disturbance that may occur during time period t.

[0067] d2: These linearized frequency security constraints are added to the frequency security constraint optimization scheduling model, so as to efficiently solve the power system operation scheme while ensuring frequency security.

[0068] Step 4 includes the following steps:

[0069] Step 4.1: Linearization of the objective function

[0070] The piecewise linearized cost function is shown in equation (35):

[0071]

[0072] In the formula: f i (C G,i ) represents the total operating cost of the unit; U i,t This represents the start / stop status of the i-th thermal power unit at time t; s is the index of the current segment; NL is the number of linearized segments; K L,i,s p is the slope of the s-th segment after linearizing the cost function of the i-th thermal power unit; G,i,t,s For the unit to output power in stages; F L,i,1 To enable the unit to operate at minimum output The coal consumption generated during operation satisfies equation (36):

[0073]

[0074] In the formula: F L,i,1 To enable the unit to operate at minimum output Coal consumption generated during operation; This represents the minimum output of the i-th thermal power unit; Let a represent the maximum output of the i-th thermal power unit; i b i c i Used to define the relationship between power generation and cost: a i b represents fixed costs i and c i These are the coefficients of the linear and quadratic terms, respectively; m is the number of segments, indicating how many segments the generator's power output is divided into; s represents the index of the current segment; l i,s The unit output corresponding to the s-th segment point; l i,s+1 The output of the unit corresponding to the (s+1)th segment is represented by NL; the linearization segment number is represented by F. L,i,s K represents the coal consumption generated by the i-th unit in the s-th section; L,i,s p represents the slope of the s-th segment after linearizing the cost function of the i-th thermal power unit; G,i,t,s Let l represent the segmented output of the i-th thermal power unit; l(:,s) represents the output of all units in segment s; l(:,s-1) represents the output of all units in segment s-1; P G,i,t U represents the output of the i-th thermal power unit at time t; it This indicates the start / stop status of the i-th generating unit at time t; l i,1 This represents the unit output corresponding to the first point after piecewise linearization of the function.

[0075] Step 4.2: Solve the mixed-integer linear model:

[0076] After the above steps are performed to linearize the constraints and objective function, the frequency-safety-constrained optimization scheduling model is transformed into a mixed-integer linear model, which can then be solved directly using the Gurobi solver.

[0077] This invention discloses a frequency security-constrained linearization optimization scheduling method based on ELM, with the following technical advantages:

[0078] 1) To address the nonlinear characteristics of the minimum frequency constraint, this invention proposes a linearized mapping method for the maximum tolerable disturbance power based on ELM. By constructing a linear mapping relationship between the optimization scheduling decision variables and the disturbance power, a safe approximation of complex constraints is achieved. While ensuring approximation accuracy, the solution speed of the model is accelerated, outperforming traditional deep neural network methods, decision tree methods, and direct hyperplane approximation methods.

[0079] 2) This invention establishes an optimized scheduling model for thermal power, wind power, and photovoltaic units that considers frequency security constraints. After considering frequency security constraints, the model proposed in this invention ensures that the lowest frequency point and the maximum rate of frequency change at each time step meet the security limits. Compared to scheduling schemes that do not consider frequency security constraints, the total cost increase is smaller, achieving an effective balance between frequency security and economy.

[0080] 3) The model of this invention is compared with the traditional optimization scheduling model in terms of model solution speed, resource scheduling optimization and economy. The model of this invention can show significant advantages in the above dimensions. Therefore, the model proposed in this invention has practical value in the field of power system frequency security and stability. Attached Figure Description

[0081] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0082] Figure 1 This is a diagram showing the system's dynamic frequency response and adjustment process.

[0083] Figure 2 This is a full-order SFR model diagram for thermal power units.

[0084] Figure 3 This is a diagram of the dynamic response model of fire, wind, and solar frequencies.

[0085] Figure 4 Piecewise linearized function graph of the unit's fuel cost curve.

[0086] Figure 5 Output power graphs for load, wind power, and solar power forecasts.

[0087] Figure 6 This is a graph showing the changes in training time and approximate accuracy based on ELM linearization.

[0088] Figure 7This is a comparison chart of the lowest frequency points under the two schemes.

[0089] Figure 8 This is a comparison chart of the maximum rate of change of frequency under the two schemes. Detailed Implementation

[0090] The optimization scheduling method based on Extreme Learning Machine (ELM) for linearizing frequency security constraints includes the following steps: Step 1: Establish a frequency dynamic response model for multi-energy complementarity of fire-wind-solar energy, and derive the time-domain analytical expressions for the maximum frequency deviation and the maximum rate of change; Step 2: Based on the traditional optimization scheduling model, establish an optimization scheduling model with frequency security constraints to ensure the frequency security and stability of the system; Step 3: Propose a maximum tolerable disturbance power linearization mapping method based on ELM to transform the nonlinear frequency security constraints in the scheduling model into a series of linear constraint sets, thereby achieving the linearization of frequency security constraints; Step 4: Perform piecewise linearization on the quadratic terms in the objective function of the established scheduling model, transforming the overall model into a mixed-integer linear model, and use the Gurobi solver to solve the linearized model.

[0091] According to my country's "Guidelines for the Safety and Stability of Power Systems," power system frequency stability is defined as: the ability of a system to maintain or restore its rated frequency without frequency oscillation or collapse when subjected to various disturbances. According to Chinese regulations, during normal operation of a power system, the frequency is stable at around 50Hz. At this point, if internal losses of generating equipment are not considered, the input power of the prime mover is the same as the output power of the generator. When a sudden power disturbance occurs in the system, due to the influence of mechanical inertia, the prime mover's power regulation exhibits a time lag characteristic. In this case:

[0092]

[0093] Where: m is the total number of generating units; P T,i P represents the total input power of the prime mover of the i-th unit; G,i Let ΔP be the total input power of the prime mover of the i-th unit; K This represents the disturbance power in the system.

[0094] When there is a deviation between the input power of the prime mover and the load demand of the power grid, in order to maintain the power balance of the system, the unit needs to compensate for the power difference by releasing the rotational kinetic energy stored in the rotor. This energy conversion process will directly lead to a decrease in the unit speed and a change in the system frequency, as shown in equation (2):

[0095]

[0096] In the formula: W K,i Let be the kinetic energy of the i-th unit.

[0097] Taking a unit failure (sudden increase in load) as an example, the frequency change response curve of the system after the disturbance is as follows: Figure 1 As shown: Figure 1 In the diagram: t0 is the time when the disturbance occurs; t db The moment when frequency modulation begins to function; t nadir t is the time when the frequency reaches its lowest point; ss f is the time when the frequency reaches a stable value. nadir This represents the lowest frequency point of the system after the disturbance; f ss f0 is the steady-state frequency value of the system after one frequency modulation; f0 is the system frequency value before the disturbance; RoCoF max This represents the maximum rate of change of frequency after the disturbance occurs.

[0098] When the system is disturbed, frequency regulation is divided into three stages: inertial response, primary frequency regulation, and secondary frequency regulation. In the inertial response stage, at the instant the disturbance occurs, the generator relies on rotor inertia to maintain its original speed, providing short-term power support to the system by releasing rotational kinetic energy, effectively suppressing rapid frequency changes. In the primary frequency regulation stage, the generator set automatically responds according to the speed governor, adjusting the prime mover power in real time based on the frequency deviation to maintain the system frequency within the allowable range. In the secondary frequency regulation stage, error-free frequency regulation can be achieved by automatically adjusting the generator's power-frequency characteristic curve using automatic generator control.

[0099] Currently, the evaluation indicators for the dynamic frequency characteristics of power systems mainly include the following three: the maximum rate of frequency change (RoCoF). max Maximum frequency deviation Δf max and steady-state frequency value f ss The maximum frequency deviation reflects the extreme value of the frequency change after the disturbance, Δf max Controlling the frequency within the specified range is an important measure to prevent system low-frequency load shedding; the maximum rate of frequency change reflects how quickly the system frequency changes over time after being disturbed, RoCoF max Frequency is a key indicator for measuring system inertia and dynamic stability, and is crucial for assessing frequency safety during transient processes. This invention uses the maximum rate of change of frequency and the maximum deviation of frequency as frequency safety indicators to formulate reasonable unit start-up and shutdown plans, aiming to achieve optimal economic efficiency while ensuring system frequency safety.

[0100] After a fault occurs, simulating the full-state process of each unit using equivalent calculation methods is currently the mainstream research method for dynamic frequency analysis of power systems. The Average System Frequency (ASF) model retains detailed parameters of the governors and prime movers of each unit, but its solution complexity is high. The System Frequency Response (SFR) model, on the other hand, equates the parameters of all units in the network to a primary frequency regulation response element, simplifying the calculation process. The full-order SFR model of thermal power units is as follows: Figure 2 As shown:

[0101] Figure 2 Chinese: T R For the reheater, is the time constant; F is the proportional coefficient of the high-pressure cylinder; R is the droop coefficient; T is the time constant of the reheater. C T is the time constant of the unit's prime mover; G H is the time constant of the generator governor; D is the equivalent inertia of the system; K is the damping coefficient of the system; and ΔP is the mechanical power gain of the system. G The unit's frequency regulation power generation is increased; Δf is the system frequency deviation; ΔP L The power deficit caused by the disturbance.

[0102] Because the full-order SFR model has high-order nonlinear characteristics, it is difficult to solve, and T C and T G Numerically much smaller than T R Therefore, this invention adopts an ASF model that retains only the reheater stage to simulate the system's frequency dynamic response process. While meeting high accuracy requirements, it preserves the original parameters of each unit and simplifies the solution process. Existing research on optimization scheduling problems with frequency security constraints mainly focuses on the frequency dynamic response characteristics of thermal power units, without systematically considering the impact of high-proportion renewable energy penetration and the integration of new power electronic equipment on the frequency dynamic process. Based on this, this invention constructs a frequency dynamic response model involving multiple types of resources collaboratively, coupling virtual inertia control of wind and solar power units on the basis of thermal power units participating in frequency regulation. The frequency dynamic response model adopted is as follows: Figure 3 As shown.

[0103] Figure 3 Chinese: H G H is the equivalent inertia of the thermal power unit. W For the virtual equivalent inertia of the wind turbine; H V N represents the virtual equivalent inertia of the photovoltaic unit; N is the number of thermal power units; N W N represents the number of wind turbine units. V K represents the number of photovoltaic units. W K is the droop control coefficient for wind turbines. V ΔP is the droop control coefficient for photovoltaic units.W To increase the power output of wind turbines through frequency regulation; △P V To increase the power output of photovoltaic power units by adjusting their frequency.

[0104] Based on the established model, the frequency dynamic response model in the complex frequency domain is transformed into a time-domain equation, and the analytical expression of the frequency safety index is derived (all parameters have been converted to per-unit values ​​during the derivation). When a large disturbance such as a unit failure occurs in the system, the power balance is broken instantaneously. At this time, the disturbance can be modeled as a step response, i.e. Combination Figure 3 We can obtain:

[0105]

[0106]

[0107] In the formula: H eq D is the equivalent inertial time constant of the model; eq is the equivalent damping coefficient of the model.

[0108] Due to the different units' T R Within permissible limits, the impact on frequency is minimal; therefore, this article assumes a T value of approximately 1 for all units. R The same. T in equation (3) R Replace all with T eq Then, equation (3) can be simplified to:

[0109]

[0110] Since equation (6) contains a large number of parameters, in order to reduce the computational scale and solve the problem quickly, the parameters are aggregated, as shown in equations (7) and (8):

[0111]

[0112] Substituting equations (7) and (8) into equation (6), we get:

[0113]

[0114] In the formula, W1 is the equivalent speed regulation slope coefficient; ω d To attenuate the oscillation angular frequency; ω n λ is the natural oscillation frequency; ε is the damping ratio; λ is the initial phase of the oscillation component.

[0115] At this point, the system dynamic frequency formula in the complex frequency domain has been simplified and can be transformed into a frequency expression in the time domain using Laplace transform:

[0116]

[0117] Based on equation (12), the maximum frequency deviation and the maximum frequency change rate in the time domain can be derived.

[0118] (1) Maximum frequency deviation:

[0119] When a disturbance occurs in the system, the active power balance is disrupted, and the system frequency exhibits a dynamic process of first decreasing and then increasing, with its lowest value corresponding to the minimum point of the frequency response curve. At this time, the rate of frequency change is 0, i.e., dΔf / dt = 0. Differentiating equation (12), we can obtain the time it takes for the system to reach its lowest frequency point: t m Substituting into equation (12), the maximum deviation of the system frequency under the per-unit value can be obtained:

[0120]

[0121] In the formula: △f max This represents the maximum deviation of the system frequency.

[0122] (2) Maximum rate of change of frequency:

[0123] The first-order frequency swing equation of the system can be derived from the system's dynamic frequency response transfer function:

[0124]

[0125] At the instant the disturbance occurs, the system relies solely on its inertial response to suppress the frequency drop. At this point, the speed governor has not yet intervened, therefore the system's rate of frequency change reaches its maximum value at the instant the disturbance occurs. If we assume that at this moment the prime mover power and electromagnetic power have not changed, i.e., Δf(0) = 0, ΔP G,i (0) = 0, and the maximum rate of change of frequency can be derived from equation (12):

[0126]

[0127] Step 2 includes the following steps:

[0128] Step 2.1: Symbols and Variables:

[0129] C U Start-up and shutdown costs of thermal power units;

[0130] C G Operating costs;

[0131] C W Costs of wind curtailment penalties;

[0132] C E The cost of penalties for abandoning light;

[0133] T: Total scheduling cycle;

[0134] SG,i : The startup cost of the i-th thermal power unit;

[0135] U i,t : The start-up and shutdown status of the i-th thermal power unit at time t;

[0136] a G,i b G,i c G,i : The coefficient of the quadratic cost function of the i-th thermal power unit;

[0137] P G,i.t : Output power of the i-th thermal power unit at time t;

[0138] P W,j.t : The output power of the j-th wind turbine at time t;

[0139] The predicted value of the j-th wind turbine at time t;

[0140] P V,h.t : Output power of the h-th photovoltaic unit at time t;

[0141] The predicted value of the h-th photovoltaic unit at time t;

[0142] w W : Wind curtailment penalty parameters;

[0143] w V Discard penalty parameters;

[0144] T i on : The minimum continuous start-up of the i-th thermal power unit;

[0145] T i off : Minimum downtime of the i-th thermal power unit;

[0146] The continuous operating time of the i-th unit at time t-1;

[0147] The continuous shutdown time of the i-th unit at time t-1;

[0148] P L.t Total load demand at time t;

[0149] The upper limit of the output of the i-th thermal power unit;

[0150] The lower limit of the output of the i-th thermal power unit;

[0151] The maximum ramp rate of the i-th thermal power unit;

[0152] The lower limit of the ramp rate for the i-th thermal power unit;

[0153] f min The lower limit of the frequency specified by the system;

[0154] Step 2.2: Optimization scheduling model with frequency security constraints:

[0155] The optimized scheduling model constructed in this invention includes thermal power, wind power, and photovoltaic units. Its objective function includes the start-up and shutdown costs of thermal power units, the operating costs of thermal power units, and the curtailment penalty costs of wind farms and photovoltaic power plants. Its expression is as follows:

[0156] F = min{C G +C W +C V +C U} (18);

[0157] The specific calculation methods for each cost are shown in the following formula:

[0158]

[0159] Constraints:

[0160]

[0161] f N +f N △f max ≥f min (27);

[0162]

[0163] In the optimization scheduling model that considers frequency security constraints for thermal power, wind power and photovoltaic units, Equations (18) and (19) are objective functions, aiming to minimize the start-up and shutdown costs of thermal power units, the operating costs of thermal power units, and the curtailment penalty costs of wind farms and photovoltaic power plants; Equations (20) and (21) represent the minimum start-up and shutdown time constraints for each unit; Equation (22) is the power balance constraint of the system; Equations (23), (24) and (25) are the upper and lower limits of the output of thermal power, wind power and photovoltaic units, respectively; Equation (26) is the ramp / slippage rate constraint of the unit; Equations (27) and (28) are the frequency security constraints of the system.

[0164] Step 3 includes the following steps:

[0165] In the aforementioned frequency security constraints, the minimum frequency constraint is highly nonlinear and difficult to solve directly in the optimization scheduling model, requiring appropriate processing. According to equation (15), the maximum frequency deviation is proportional to the system power disturbance. Based on the mapping relationship, the frequency deviation limit Δf... max The maximum disturbance power that the corresponding power system can withstand Meanwhile, the system can withstand the maximum disturbance power. This depends on the operating status of each unit (i.e., the decision variable in the optimal scheduling problem). This invention uses machine learning training and fitting... To understand the relationship between the unit's operating status and the maximum tolerable disturbance power fitting model based on ELM, this network constructs a model from the decision variables of the optimization scheduling problem to... The linear mapping relationship enables the linearization of the minimum point frequency safety constraint.

[0166] The specific steps of the ELM-based linearization process are as follows:

[0167] (1) Training data generation

[0168] Multiple operational scenarios are generated using a traditional optimization scheduling model, recording decision and state variables such as generator start-stop combinations, system inertia, and load distribution. For each scenario, based on the derived frequency response model, a high-order differential equation model built using Simulink is used to simulate the dynamic frequency response under power disturbances, calculating the maximum tolerable power disturbance of the system corresponding to the lowest frequency point. By performing calculations on all scenarios, a large simulation dataset containing parameters for multiple operating conditions can be obtained for subsequent model training.

[0169] Step 1: Construct a dynamic simulation model. Using tools such as Simulink, establish a dynamic simulation model of the power system frequency response that can accurately reflect various operating conditions such as generator parameters, system inertia, load distribution, and unit start-up and shutdown status.

[0170] Step 2: Perform large-scale simulations, applying various power disturbances to the system under different initial system states, load levels, unit combinations, and control variable configurations.

[0171] Step 3: Record data. In each simulation, calculate and record the maximum disturbance power that the system can withstand. And the corresponding system operating parameters (such as generator parameters, system inertia, etc.).

[0172] (2) ELM network architecture design

[0173] Step 1: Input Layer

[0174] Based on the generated data above, the model input features are determined: including the generator reheater time constant T. R The data output labels include: high-pressure cylinder work ratio coefficient F, unit droop coefficient R, and system inertia H. The input features are standardized as shown in equation (29):

[0175]

[0176] Where: μ Φ and σ Φ Here, represents the mean and standard deviation of the feature, respectively, and Φ is the original parameter.

[0177] Step 2: Hidden Layer:

[0178] After the input features are standardized, they are passed to the hidden layer through a linear transformation. The second part of the network synthesizes the feature parameters Ψ. i With the original parameter Φ i These are combined and used as input elements for model training. The standardized features are then passed through a randomly initialized weight matrix a. g and bias b g Mapped to the hidden layer:

[0179]

[0180] Where: Φ i Let θ be the original input feature of the i-th frequency regulation unit; θ is the Sigmoid activation function, chosen as θ.

[0181] a g and b g It uses fixed weights (the random initialization characteristic of ELM).

[0182] Step 3: Output Layer

[0183] In the third part of the ELM network, a piecewise linear method is used to fit the maximum disturbance power that the system can withstand while satisfying frequency security:

[0184]

[0185] In the formula: l and These are the index of the piecewise linear function and the total number of segments, respectively; c g,l and h g,l These are the slope and intercept constant of the l-th piecewise linear function, respectively; Ψ and Φ are the synthesized characteristic parameters Ψ of each frequency modulation unit. i With the original parameter Φ i The vector formed by the vector.

[0186] (3) Model training:

[0187] Based on the ELM network constructed above, the final output is a piecewise linear function containing nonlinear operations, which requires training to obtain the slope and intercept parameters in equation (31). However, most machine learning models are trained using gradient descent and backpropagation algorithms, which can only guarantee the local optimum of the network parameters. This invention will further construct a linear programming model based on mixed integers to accurately obtain the minimum error fitting parameters of the fitted model and obtain the global optimum of the network parameters.

[0188] Step 1: Define the training objective as minimizing the sum of errors between the actual maximum tolerable perturbation power and the fitted maximum perturbation power, as shown in Equation (32):

[0189]

[0190] Where: N Φ This represents the total amount of training data generated in step one. and These are the actual maximum tolerable disturbance power and the fitted maximum disturbance power for the k-th data sample, respectively.

[0191] Step 2: Set constraints, introduce conservative constraints to ensure the model's predictions are accurate. The frequency should not exceed the actual tolerable value to ensure frequency safety; at the same time, binary variables and related constraints should be set to correctly select different segments of the piecewise linear function.

[0192]

[0193] The first constraint is a conservative constraint to ensure that the maximum perturbation power of the model fit does not exceed the actual value, thus avoiding overestimation of the system's frequency perturbation tolerance; the second to fourth constraints use the Big M method to transform the nonlinear piecewise function into a linear constraint set. It is a very large positive number; To select the segmented binary variable.

[0194] (4) Application of linearization constraints:

[0195] Step 1: Forming Linear Constraints. After the above training and fitting, the nonlinear frequency safety constraints can be transformed into a set of linear constraints, and the minimum frequency safety constraint can be expressed as follows:

[0196]

[0197] In the formula: △P L,t This indicates the power disturbance that may occur during time period t;

[0198] Step 2: Integrate into the optimization model. These linearized frequency security constraints are incorporated into the optimization scheduling model, thereby efficiently solving the power system operation scheme while ensuring frequency security.

[0199] Step 4 includes the following steps:

[0200] Step 4.1: Linearization of the objective function:

[0201] Equation (19) contains a quadratic term in the cost function of thermal power units, which can lead to a significant decrease in computational efficiency in large-scale power system optimization. To address this problem, this invention performs piecewise linearization of the quadratic function. When the quadratic function is divided into three pieces, the linearized operating cost function is as follows: Figure 4 As shown, the linearization error decreases with increasing number of segments, but the computation time also increases.

[0202] The piecewise linearized cost function is shown in equation (35):

[0203]

[0204] In the formula: NL is the number of linearized segments; K L,i,s p is the slope of the s-th segment after linearizing the cost function of the i-th thermal power unit; G,i,t,s For the unit to output power in stages; F L,i,1 To enable the unit to operate at minimum output The coal consumption generated during operation satisfies equation (36):

[0205]

[0206] In the formula: l i,1 Let the unit output be the first point corresponding to the piecewise linearized function, and its magnitude be... l i,s The unit output corresponding to the s-th segment point; l i,NL+1 The output of the unit corresponding to the last point of the piecewise linearization of the function is, in magnitude, F l,i,s The unit output is l i,s Coal consumption generated during operation.

[0207] Step 4.2: Solve the mixed-integer linear model:

[0208] After the above steps are performed to linearize the constraints and objective function, the overall optimization scheduling model is transformed into a mixed-integer linear model, which is then solved directly using the Gurobi solver.

[0209] Example:

[0210] To verify the effectiveness of the frequency security constraint linearization method based on ELM proposed in this invention, a modified IEEE 10-machine 39-node test system was used for model verification. The original bus units 38 and 39 were reconnected to 1800MW photovoltaic units and 1800MW wind turbine units, respectively. The example includes eight conventional generators with an installed capacity of 4766MW. The system rated frequency was set to 50Hz, the minimum frequency limit was set to 49.5Hz, the frequency change rate limit was set to 0.35Hz / s, the wind and solar curtailment penalty coefficients were both set to 100 / MW, and the disturbance power was set to 0.1P. L Typical daily system load, wind power, and solar power forecasts are as follows: Figure 5 As shown in Table 1, the system parameters of the thermal power unit are as follows.

[0211] Table 1 System Parameters of Thermal Power Units

[0212]

[0213]

[0214] The ELM-based linearization method uses actual parameters such as generator start-up and shutdown states and system inertia as input features, and uses the maximum tolerable disturbance power of the system corresponding to the lowest frequency point as the output label for model training. To obtain sufficient training data, based on the optimized scheduling model constructed in this invention, optimized scheduling simulations are performed on an improved IEEE 39-node system. Historical data on the total load power of the actual power grid and the power generation power of new energy sources are scaled to fit the IEEE 39-node system and used as input for the optimized scheduling simulation, generating simulation training data for the entire year. After obtaining simulation data for multiple operating conditions such as generator start-up and shutdown states using the above method, time-domain simulations are performed on each generated data sample on the Simulink platform based on the aforementioned system frequency response model, with a time step of 0.02 seconds to obtain the maximum tolerable power disturbance data. Furthermore, to rigorously evaluate the generalization performance of the proposed method, a certain amount of random noise is added to the simulation-generated training dataset to generate another test set of the same size to verify the effectiveness of the model.

[0215] Tests revealed that the training time and fitting accuracy of the ELM-based linearization approximation method exhibited a regular variation, such as... Figure 6 As shown. The size and number of segments of the third layer of the ELM model. It is directly proportional, which shows that when the number of segments As the value increases, the training time gradually increases, and the average accuracy of the final fit also increases accordingly. When, the average fitting error increases with The increase leads to a rapid decrease; when Training time varies The increase is significant. Therefore, the present invention adopts... As the final parameter, the trained piecewise linear function is incorporated into the optimization scheduling model for optimization.

[0216] The simulation environment is as follows: The hardware conditions for performing the simulation in this invention are Intel(R) Core(TM) i5-9400F CPU@2.90GHz and 8GB of RAM.

[0217] 1: Accuracy analysis of frequency minimum point constraint linearization based on ELM:

[0218] To further verify the superiority of the frequency minimum point constraint linearization method proposed in this invention based on ELM, it is compared with existing similar methods, including the method of this invention, the method based on decision trees, the method based on deep neural networks, and the direct hyperplane approximation method. Among them, the method based on decision trees may misjudge an unsafe operation scheme as a safe state, while the method based on deep neural networks can effectively avoid misjudgment by introducing a mixed integer linear constraint with a large number of integer variables to approximate the frequency minimum point constraint. The direct hyperplane approximation method, after giving enough approximate sampling points, solves the model to make it approximate a series of linear hyperplane coefficients with the minimum absolute error. The parameter settings of different methods are as follows: (1) The method proposed in this invention: the number of neurons in the ELM hidden layer is 10, and the total number of segments of the piecewise linear function is 3 (i.e. (2) Optimal decision tree method: the decision tree depth is set to 2; (3) Deep neural network method: the number of hidden layers is 1, and the number of neurons is 256. (4) Direct hyperplane approximation method: the number of sampling points is 100. In order to compare the approximation performance of different methods, the following three indicators are defined, and the comparison results of each indicator of different methods are shown in Table 2.

[0219] (1) Relative accuracy: The relative accuracy between the maximum tolerable disturbance power obtained by the approximation method and the actual maximum tolerable disturbance power is the average of all relative accuracies in the test set.

[0220] (2) Exceeding the limit rate: When the approximate maximum tolerable disturbance power is greater than the actual maximum tolerable disturbance power, the approximate frequency is considered to be exceeding the limit. The ratio of the number of all exceeding the limit points in the statistical test set to the total amount of data is the exceeding the limit rate.

[0221] (3) Solution time increase rate: The average absolute error between the solution time of the approximate linear function obtained by various methods and the solution time of the optimization scheduling model without the approximate linear function is defined as the solution time increase rate of the model.

[0222] Table 2. Indicators for different methods

[0223]

[0224] As shown in Table 2, the method proposed in this invention has the highest relative accuracy, while the method based on deep neural networks has the lowest accuracy. This is because the method of this invention and the method based on optimal decision trees construct an approximate function of the lowest frequency point by solving a linear programming model, which ensures optimal model parameters; while the method based on deep neural networks trains the network through gradient descent and backpropagation algorithms, making it difficult to converge to the global optimum, resulting in poor accuracy. In addition, the optimal decision tree method has the risk of misjudgment, resulting in a non-zero limit violation rate. The limit violation rates of both the method of this invention and the method based on deep neural networks are 0, indicating that the piecewise linear constraints of the proposed method are a safe approximation of the original frequency constraints, which can avoid misjudging unsafe conditions as safe states.

[0225] Regarding solution time, methods based on deep neural networks introduce mixed integer variables, leading to a significant increase in model solution time. The method proposed in this invention exhibits the smallest increase in solution time. Direct hyperplane approximation methods require manually provided approximate sampling points (i.e., hyperplane vertices), and their approximation accuracy depends on the reasonableness and number of vertices. When the number of vertices is 100, its accuracy is close to that of the algorithm proposed in this invention, but a large number of vertices imposes additional computational burden on the subsequent optimization scheduling model, resulting in a significant increase in solution time. The comparison shows that the algorithm of this invention, while maintaining approximation accuracy, does not impose additional computational burden on the subsequent optimization scheduling model solution.

[0226] 2. Model Validity Analysis:

[0227] To analyze the effectiveness of introducing frequency security constraints under a high proportion of renewable energy access, the following two comparative schemes are set up in this section for verification:

[0228] Option 1: Traditional optimization scheduling model that does not consider frequency security constraints.

[0229] Option 2: The model proposed in this invention.

[0230] 1) Cost comparison of different options:

[0231] Table 3 shows a cost comparison between the two schemes. As can be seen from Table 3, Scheme 1, which does not consider frequency security constraints and only aims for economic optimization in its dispatch plan, reduces generation costs by $34,769 and start-up / shutdown costs by $12,300 compared to Scheme 2. Scheme 2, in order to ensure system frequency security under large disturbances, requires keeping more units running, leading to an increase in costs.

[0232] Table 3. Cost Comparison of Different Options

[0233]

[0234] 2) Comparison of frequency security indicators of different schemes:

[0235] The minimum frequency and maximum rate of change of frequency over 24 hours under the two schemes are as follows: Figure 7 and Figure 8 As shown, Scheme 1 does not consider frequency security constraints. When the system experiences large disturbances, the minimum frequency point exceeds the specified lower limit at most times, which can easily lead to serious consequences such as low-frequency load shedding. The maximum rate of frequency change also exceeds the limit between 8:00 and 16:00, which may cause frequency security issues. Scheme 2, on the other hand, considers frequency security constraints. The minimum frequency point and the maximum rate of frequency change meet the requirements at all times, achieving economic optimization while ensuring system frequency security. Therefore, the model proposed in this invention can effectively adapt to the power system dispatching needs under a high proportion of renewable energy access.

Claims

1. A frequency security-constrained linearized optimization scheduling method based on ELM, characterized in that... Includes the following steps: Step 1: Establish a frequency dynamic response model for multi-energy complementarity of fire, wind, and solar, using the maximum rate of frequency change and the maximum frequency deviation as the frequency safety indicators of the system, and derive the time-domain analytical expression of the frequency safety indicators; Step 2: Considering the safety constraints of the lowest frequency point and the maximum rate of change of frequency, establish an optimization scheduling model with frequency safety constraints; Step 3: Propose a linearization mapping method for the maximum tolerable disturbance power based on ELM, which transforms the nonlinear frequency security constraints in Step 2 into a series of linear constraint sets, thereby realizing the linearization of frequency security constraints; Step 4: Perform piecewise linearization on the quadratic terms in the objective function of the frequency-constrained optimization scheduling model established in Step 2, transforming the overall model into a mixed-integer linear model, and then use a solver to solve the linearized model.

2. The frequency security-constrained linearization optimization scheduling method based on ELM according to claim 1, characterized in that: In step 1, virtual inertia control of wind and solar power units is coupled with frequency regulation of thermal power units to construct a frequency dynamic response model of thermal-wind-solar multi-energy complementarity. The frequency dynamic response process is represented as follows: In the formula, Δf(t) is the frequency deviation at time t, in Hz; D eq H is the equivalent damping coefficient of the model; eq The equivalent inertial time constant of the model; ΔP L The power deficit caused by the disturbance; The system's primary frequency regulation power increment at time t; N represents the total number of units in the system; ΔP G,i (t) represents the increase in the power generation of the i-th generating unit at time t.

3. The frequency security-constrained linearization optimization scheduling method based on ELM according to claim 2, characterized in that: The frequency dynamic response model in the complex frequency domain is transformed into a time-domain equation. Using the maximum rate of frequency change and the maximum frequency deviation as the system's frequency safety indicators, the time-domain analytical expression for these indicators is derived as follows: (1) Maximum frequency deviation: In equation (12), △f max D represents the system's maximum frequency deviation. eq T is the equivalent damping coefficient of the model; eq W1 is the time constant of the unit reheater; W1 is the equivalent speed regulation slope coefficient; ω d To attenuate the oscillation angular frequency; ω n t is the natural oscillation frequency; m ε is the time it takes for the system to reach its lowest frequency; λ is the damping ratio; t is the initial phase of the oscillation component; and t is the time variable. (2) Maximum rate of change of frequency: In equation (17), RoCoF max H represents the system's maximum rate of frequency change. eq This is the equivalent inertial time constant of the model.

4. The frequency security-constrained linearization optimization scheduling method based on ELM according to claim 3, characterized in that: In step 2, the constructed frequency-constrained optimization scheduling model has an objective function that includes the start-up and shutdown costs of thermal power units, the operating costs of thermal power units, and the wind and solar curtailment penalty costs of wind farms and photovoltaic power plants. Its expression is as follows: F=min{C G +C W +C V +C U } (18); In equation (18), F represents the minimum total operating cost of the system; C U C G C W C E These are the start-up and shutdown costs, operating costs, wind curtailment penalty costs, and solar curtailment penalty costs for thermal power units.

5. The frequency security-constrained linearization optimization scheduling method based on ELM according to claim 4, characterized in that: Common constraints include minimum start-up and shutdown time constraints for each unit, power balance constraints for the system, upper and lower limits of output constraints for thermal power, wind power, and photovoltaic units, and ramp / slippage rate constraints for the units. In the formula, U i,t This represents the start-up and shutdown status of the i-th thermal power unit at time t, where 1 indicates startup and 0 indicates shutdown; T i on T i off These are the minimum continuous start-up and shutdown times for the i-th thermal power unit, respectively; Let P be the continuous start-up time and continuous shutdown time of the i-th unit at time t-1, respectively; G,i.t P represents the output power of the i-th thermal power unit at time t. W,j.t P represents the output power of the j-th wind turbine at time t. V,h.t P represents the output power of the h-th photovoltaic unit at time t. L.t Let be the total load demand at time t; This represents the upper limit of the output of the i-th thermal power unit; This is the lower limit of the output of the i-th thermal power unit; Let be the predicted value of the j-th wind turbine at time t; Let h be the predicted value of the h-th photovoltaic unit at time t; This represents the maximum ramp speed limit for the i-th thermal power unit. T represents the lower limit of the ramp rate for the i-th thermal power unit; i on This represents the minimum continuous start-up time of the i-th thermal power unit; T i down N represents the minimum downtime of the i-th thermal power unit; W N represents the total number of wind turbine units. V Indicates the total number of photovoltaic units; U i,t-1 P represents the start-up and shutdown status of the i-th thermal power unit at time t-1; G,i,t-1 This represents the output power of the i-th thermal power unit at time t-1; Frequency security constraints: f N +f N △f max ≥f min (27); Equation (4) is the safety constraint at the lowest frequency point; Equation (5) is the safety constraint at the maximum rate of change of frequency; f min f is the lower limit of the frequency specified by the system. N The system's rated frequency; Δf max This represents the system's maximum frequency deviation.

6. The frequency security-constrained linearization optimization scheduling method based on ELM according to claim 5, characterized in that: In step 3, machine learning is used to train and fit the model. To understand the relationship between the unit's operating status and the maximum tolerable disturbance power fitting model based on ELM, this model network constructs a network from the decision variables of the optimization scheduling problem to... The linear mapping relationship is used to achieve the linearization of the minimum point frequency safety constraint; specifically as follows: According to equation (12), the maximum frequency deviation is proportional to the system power disturbance; at the same time, according to the mapping relationship, the frequency deviation limit Δf max The maximum disturbance power that the corresponding power system can withstand The expression for this mapping relationship is as follows: In the formula, Indicates the minimum disturbance power; l and These are the index of the piecewise linear function and the total number of segments, respectively; c g,l h g,l Let Ψ, Φ, H be the slope and intercept constant of the l-th piecewise linear function, respectively; T This represents a vector containing system characteristic parameters; Ψ and Φ are the synthesized characteristic parameters Ψ of each frequency regulation unit. i With the original parameter Φ i The vector formed by H represents the system inertia.

7. The frequency security-constrained linearization optimization scheduling method based on ELM according to claim 6, characterized in that: Step 3, the linearization process based on ELM, includes training data generation: a1: Using modeling software such as Simulink, establish a frequency dynamic response model for multi-energy complementarity of fire, wind and solar; a2: Perform large-scale simulations, applying various power perturbations to the system under multiple different operating scenarios; a3: In each simulation, calculate and record the maximum disturbance power that the system can withstand. The corresponding system operating parameters and this data will be used as training samples for the ELM network.

8. The frequency security-constrained linearization optimization scheduling method based on ELM according to claim 7, characterized in that: Step 3 also includes ELM network architecture design: b1: Input layer: Based on the generated data, the input features of the ELM network input layer are determined: including the generator reheater time constant T. R The power ratio coefficient of the high-pressure cylinder of the unit, the droop coefficient of the unit, and the system inertia H are used to standardize the input characteristics, as shown in equation (29): Where: Φ norm For the original parameters; μ Φ and σ Φ These are the mean and standard deviation of the feature, respectively; b2: Hidden layer: The synthesized feature parameter Ψ i With the original parameter Φ i Combined and used as input elements for training the hidden layers of the ELM network, the standardized features are passed through a randomly initialized weight matrix a. g and bias b g Mapped to the hidden layer: Where: Φ i The original input characteristics of the i-th frequency regulation unit; θ is the Sigmoid activation function, chosen as... x is a linear combination of the inputs a g ·Φ i +b g ;a g and b g For fixed weights; i refers to the number of the i-th feature or sample; Represents the sample set; b3: Output layer: Using a piecewise linear method, we can fit the maximum disturbance power that the system can withstand while maintaining frequency safety. In the formula: Indicates the minimum disturbance power; l and These are the index of the piecewise linear function and the total number of segments, respectively; c g,l and h g,l These are the slope and intercept constant of the l-th piecewise linear function, respectively; Ψ and Φ are the synthesized characteristic parameters Ψ of each frequency modulation unit. i With the original parameter Φ i The vector is composed of H; H represents system inertia; T represents matrix transpose.

9. The frequency security-constrained linearization optimization scheduling method based on ELM according to claim 8, characterized in that: Step 3 also includes: 1): Training the ELM network model: c1: Define the training objective as minimizing the sum of errors between the actual maximum tolerable perturbation power and the fitted maximum perturbation power, as shown in equation (32): Where: N Φ This represents the total amount of training data generated. and These are the actual maximum tolerable disturbance power and the fitted maximum disturbance power for the k-th data sample, respectively. A binary variable representing the selection of segments; c2: Set constraints, introduce conservative constraints, and ensure the model's predictions are accurate. The value should not exceed the actual acceptable value; at the same time, binary variables and relevant constraints should be set to correctly select different segments of the piecewise linear function; In the formula: c is a very large positive constant; l and h l These are the slope and intercept constant of the l-th piecewise linear function, respectively; k represents the index of the data sample; l and These are the index of the piecewise linear function and the total number of pieces, respectively; T represents the matrix transpose. 2): Application of linearization constraints: d1: After the above training and fitting, the nonlinear frequency safety constraint is transformed into a series of linear constraints, and the frequency minimum point safety constraint can be expressed as follows: In the formula: △P L,t This indicates the power disturbance that may occur during time period t; d2: These linearized frequency security constraints are added to the frequency security constraint optimization scheduling model, so as to efficiently solve the power system operation scheme while ensuring frequency security.

10. The frequency security-constrained linearization optimization scheduling method based on ELM according to claim 9, characterized in that: Step 4 includes the following steps: Step 4.1: Linearization of the objective function: The piecewise linearized cost function is shown in equation (35): In the formula: f i (C G,i ) represents the total operating cost of the unit; U i,t This indicates the start / stop status of the i-th thermal power unit at time t; s is the index of the current segment; NL is the number of linearized segments; K L,i,s p is the slope of the s-th segment after linearizing the cost function of the i-th thermal power unit; G,i,t,s For the unit to output power in stages; F L,i,1 To enable the unit to operate at minimum output The coal consumption generated during operation satisfies equation (36): In the formula: F L,i,1 To enable the unit to operate at minimum output Coal consumption generated during operation; This represents the minimum output of the i-th thermal power unit; Let a represent the maximum output of the i-th thermal power unit; i b i c i Used to define the relationship between power generation and cost: a i b represents fixed costs i and c i These are the coefficients of the linear and quadratic terms, respectively; m is the number of segments, indicating how many segments the generator's power output is divided into; s represents the index of the current segment; l i,s The unit output corresponding to the s-th segment point; l i,s+1 The output of the unit corresponding to the (s+1)th segment is represented by NL; the linearization segment number is represented by F. L,i,s K represents the coal consumption generated by the i-th unit in the s-th section; L,i,s p represents the slope of the s-th segment after linearizing the cost function of the i-th thermal power unit; G,i,t,s Let l represent the segmented output of the i-th thermal power unit; l(:,s) represents the output of all units in segment s; l(:,s-1) represents the output of all units in segment s-1; P G,i,t U represents the output of the i-th thermal power unit at time t; it This indicates the start / stop status of the i-th generating unit at time t; l i,1 The unit output corresponding to the first point after piecewise linearization of the function; Step 4.2: Solve the mixed-integer linear model: After the above steps are performed to linearize the constraints and objective function, the frequency-safety-constrained optimization scheduling model is transformed into a mixed-integer linear model, which can then be solved directly using the Gurobi solver.

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