Power system dispatch optimization method based on linear embedding with maximum frequency deviation constraint

Abstract

The application discloses a power system scheduling optimization method based on maximum frequency deviation constraint linear embedding, and the method comprises the following steps: obtaining an approximate linear constraint function based on a nonlinear maximum frequency deviation constraint, combining variable replacement and a second-order Taylor expansion formula; constructing a first algorithm based on a security-oriented weight and a physical prior regularization mechanism; obtaining a rotating second-order cone constraint by iteratively solving the approximate linear constraint function based on the first algorithm; and performing scheduling optimization based on the rotating second-order cone constraint and an optimal scheduling model of the power system.

Description

Technical Field

[0001] This invention relates to the field of power systems, and in particular to a power system dispatch optimization method based on linear embedding of maximum frequency deviation constraints. Background Technology

[0002] In recent years, the power system has exhibited "dual high" characteristics—a high proportion of renewable energy grid connection and a high proportion of power electronic equipment application. However, these "dual high" characteristics have also brought new security risks, among which frequency security is particularly prominent: renewable energy output is random and fluctuating, and power electronic equipment lacks the inertial support of traditional synchronous generators, which can easily lead to increased frequency fluctuations and decreased frequency regulation capabilities, thereby threatening the safe and stable operation of the power system. To ensure frequency security, embedding easily solvable and effective frequency security constraints into the power system optimization operation problem is currently a major research focus.

[0003] In existing optimization methods considering transient frequency security constraints, the maximum frequency deviation constraint exhibits high nonlinearity and nonconvexity. To solve this problem, current techniques generally consider piecewise linearization, introducing a large number of binary variables and increasing computational burden; or they consider intelligent algorithms, relying on tools such as neural networks to implicitly fit complex nonlinear relationships. However, due to their black-box nature and the lack of physical mechanisms in the process, they heavily rely on massive and complete historical operating data, resulting in extremely poor generalization ability, difficulty in guaranteeing global optimum, and long computation time, failing to meet the dual requirements of computational efficiency and accuracy for real-time dispatching of large power grids; or they use time-domain simulation to solve high-order differential-algebraic equations, which can realistically and losslessly reproduce the nonlinear dynamic process of the system with extremely high computational accuracy, but the computation is extremely slow, and it is impossible to extract mathematical expressions with analytical form, making it impossible to embed them into the solution model for use with CPLEX or Gurobi mathematical programming solvers. In other words, in existing techniques, the maximum frequency deviation constraint, due to its nonlinearity and nonconvexity, is difficult to embed into the optimal dispatching model of the power system, resulting in an inability to simultaneously meet the dual requirements of efficiency and accuracy.

[0004] Therefore, a new technical solution is urgently needed to address the technical problem of how to perform power system dispatch optimization based on linear embedding of maximum frequency deviation constraints. Summary of the Invention

[0005] This invention provides a power system dispatch optimization method based on linear embedding of maximum frequency deviation constraints, which solves the technical problem of how to perform power system dispatch optimization based on linear embedding of maximum frequency deviation constraints.

[0006] To achieve the above objectives, this invention provides a power system dispatch optimization method based on linear embedding of maximum frequency deviation constraints, comprising: An approximate linear constraint function is obtained by combining nonlinear maximum frequency deviation constraints with variable substitution and second-order Taylor expansion formula; The first algorithm is constructed based on security-oriented weights and physical prior regularization mechanisms; Based on the first algorithm, the approximate linear constraint function is solved iteratively to obtain the rotational second-order cone constraint; Scheduling optimization is performed based on an optimal scheduling model for a combined power system with rotating second-order cone constraints.

[0007] Preferably, the nonlinear maximum frequency deviation constraint includes: The power regulation of the primary frequency is modeled as a piecewise linear function to construct a frequency dynamic model of the power system: ; ; in, It's a frequency deviation; It is a frequency regulation power; It is the system's inertial time constant; It is load damping, by We obtain, among which D Let be the load damping constant. It is the total system load; Power disturbance; It is the time it takes for the frequency deviation to reach the dead zone. It is the PFR capacity. This is the PFR delivery time. It is the PFR (Proportional Rate of Progress) climbing speed; The nonlinear maximum frequency deviation constraint is obtained based on the frequency dynamic model: ; ; in, It is a predefined limit for the lowest frequency price; It is a frequency dead zone; This is an intermediate quantity.

[0008] Preferably, the approximate linear constraint function obtained based on the nonlinear maximum frequency deviation constraint combined with variable substitution and second-order Taylor expansion includes: Define variables , and ,in, and Correlation analysis through critical points It is a constant; , and Represented as: ; variables , and Replacing it with the nonlinear maximum frequency deviation constraint, we obtain the first expression: ; Define auxiliary variables Within the actual operating domain of the system, the logarithmic terms of the first expression exist Perform a second-order Taylor series expansion at this point: ; ; ; It can be known and Having a linear relationship, we can approximate the relationship using a linear function to obtain an approximate linear constraint function: ; in, and These are the slope and intercept of the approximate linear constraint function, respectively.

[0009] Preferably, the first algorithm, constructed based on safety-oriented weights and physical prior regularization mechanisms, includes: A two-way safety-oriented weighting coefficient is constructed based on the approximation of the lowest frequency point of the sample points to the system safety limit; a comprehensive objective function is constructed based on the two-way safety-oriented weighting coefficient and the slope and intercept of the approximately linear constraint function. The overall objective function includes the data fitting residual term and the first term; the first term includes the product of the physical prior regularization term and the regularization hyperparameter; the regularization hyperparameter is obtained by combining the data fitting residual term and the physical prior regularization term with the L-curve method; The first algorithm includes: in this iteration, constructing equivalent one-dimensional projected weights for sample points based on the slope estimate of the approximate linear constraint function from the previous iteration; obtaining iterative residuals based on the slope and intercept estimates of the approximate linear constraint function from the previous iteration; constructing an equivalent weight matrix based on the equivalent one-dimensional projected weights and iterative residuals; obtaining a regularized generalized normal equation based on the equivalent weight matrix and the comprehensive objective function; solving the regularized generalized normal equation to obtain estimates of the slope and intercept of the approximate linear constraint function in this iteration; determining whether the iteration converges based on the relationship between the estimates obtained in this iteration and the previous iteration, combined with a preset criterion; if it does not converge, proceeding to the next iteration; if it converges, outputting the slope and intercept estimates.

[0010] Preferably, the bidirectional safety-oriented weighting coefficients constructed based on the approximation of the lowest frequency point of the sample points to the system safety limit include: Regarding the first A running sample point, defining its horizontal direction. Shaft basic safety guidance weight coefficient for: ; in, For sample points The precise lowest frequency point calculated under the frequency dynamic model; These are the frequency safety limits specified for the operation of power systems. To prevent extremely small positive numbers with a denominator of zero; Based on the basic safety orientation weight coefficient Constructing vertical security-oriented weights : ; in, The base variance ratio is used to set the baseline error penalty strength to ensure fitting accuracy under normal inertia conditions. This is a heteroscedasticity penalty term. The penalty intensity coefficient, This is the attenuation coefficient.

[0011] Preferably, the comprehensive objective function constructed based on the bidirectional safety-oriented weighting coefficients and the slope and intercept of the approximately linear constraint function includes: The overall objective function is expressed as: ; ; ; in, The residual term is used to fit the data; This is a regularization hyperparameter used to balance the weight ratios of the two terms; For physical prior regularization terms; and The residuals are bidirectional. This represents the total number of sample points; These are higher-order truncation sensitivity weights, used to quantify the impact of higher-order Taylor truncation errors under different operating conditions. P Curvature sensitivity index; In order to be in The value obtained by taking a preset step size within the set interval. One sample; Based on The result obtained by calculating the first expression; Two-way residuals and Satisfies the equation of the straight line: .

[0012] Preferably, the regularization hyperparameter is obtained by combining the data fitting residual term and the physical prior regularization term with the L-curve method, including: Define the data loss function in logarithmic coordinates as follows: The physical penalty function is ;along with The change in value is due to The resulting parametric trajectory presents a standard L-shaped curve on a two-dimensional plane; calculate the curvature of the standard L-shaped curve. The regularization hyperparameter is obtained by finding the inflection point where the curvature is maximum. : ; in, These are the first and second derivatives of the data loss function, respectively. These are the first and second derivatives of the physical penalty function, respectively.

[0013] Preferably, the equivalent one-dimensional projected weights of the sample points are constructed based on the slope estimate of the approximate linear constraint function in the previous iteration; the iterative residuals are obtained based on the slope and intercept estimates of the approximate linear constraint function in the previous iteration; and the equivalent weight matrix is ​​constructed based on the equivalent one-dimensional projected weights and the iterative residuals, including: Define the linear coefficient vector obtained by solving the regularized generalized normal equation in the previous iteration as: This includes the slope and intercept estimates obtained at the end of the previous iteration. and , is represented as: ; according to Will shaft and The error of the axis is projected along the analytic geometric normal direction to construct an equivalent one-dimensional projective weight. , is represented as: ; Introduce a dynamic asymmetric adjustment factor driven by the current iteration residual. , No. In the first iteration, the... Iteration residual of each sample point for: ; ; in, The coefficient is an asymmetric penalty. Based on dynamic asymmetric adjustment factor and equivalent one-dimensional projection weights Obtain the elements of the equivalent weight matrix : ; Based on the elements of the equivalent weight matrix Obtain the equivalent weight matrix : .

[0014] Preferably, the regularized generalized normal equation is obtained based on the equivalent weight matrix and the comprehensive objective function; solving the regularized generalized normal equation yields estimates of the slope and intercept of the approximate linear constraint function for this round, including: Define the input feature matrix With the target vector Y The input feature matrix Each row corresponds to the input feature of one sample point, represented as: ; ; in, T This indicates the transpose; and The first sample points and ; By deriving the extremum condition of the comprehensive objective function and combining it with the input feature matrix, Target vector Y and equivalent weight matrix We obtain the regularized generalized normal equation. , is represented as: ; Solving the regularized generalized normal equation yields estimates of the slope and intercept of the approximate linear constraint function for this round.

[0015] Preferably, the rotational second-order cone constraint is obtained by iteratively solving the approximate linear constraint function based on the first algorithm, including: The approximate linear constraint function is solved iteratively based on the first algorithm, and the slope and intercept estimates are output after convergence. Based on variables and expression, It is positively correlated with system disturbances. Since it is positively correlated with the system rotation, the approximately linear constraint function is transformed into an inequality that serves as a constraint, resulting in the first inequality: ; The slope and intercept estimates, and the defined variables and Substituting the expression into the first inequality, we obtain the rotating second-order cone form constraint for the maximum frequency deviation constraint: ; Define frequency safety stress index : ; The rotational second-order cone form constraint of the maximum frequency deviation constraint simplifies to: .

[0016] The present invention has the following beneficial effects: This invention presents a power system dispatch optimization method based on linear embedding of maximum frequency deviation constraints. By transforming nonlinear constraints into linearly approximate forms and using a proposed algorithm to solve for the slope and intercept required to express the linear relationship, the linear approximation is substituted into the original constraints to derive the form of a rotating second-order cone constraint. This constraint is then embedded into the subsequent model, enabling the construction of a commercial solver to efficiently handle rotating second-order cone constraints. This achieves power system dispatch optimization based on linear embedding of maximum frequency deviation constraints. This method can quickly solve frequency constraint optimization problems without increasing model complexity, improving the frequency stability of low-inertia power systems under large disturbances, and is applicable to generation dispatch scenarios.

[0017] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0018] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a schematic diagram of the method flow of a preferred embodiment of the present invention.

[0019] Figure 2 This is a schematic diagram of the RMSE results of a preferred embodiment of the present invention; wherein, (a) are the RMSE values ​​of the four algorithms in two scenarios; (b) are the RMSE values ​​under different noise levels in scenario one; and (c) are the RMSE values ​​under different noise levels in scenario two.

[0020] Figure 3 This is a schematic diagram of the fitting of two parameters by four algorithms of the preferred embodiment of the present invention under four noise levels and two scenarios; wherein, (a) is the slope difference of different noise levels in scenario one; (b) is the intercept of different noise levels in scenario one; (c) is the slope difference of different noise levels in scenario two; and (d) is the intercept of different noise levels in scenario two.

[0021] Figure 4 This is a schematic diagram of the system's lowest frequency considering the FN constraint constructed by the method of the present invention, the FN constraint constructed by OLS, and the case without considering the FN constraint, according to a preferred embodiment of the present invention; wherein, (a) is the case of the system's lowest frequency considering the FN constraint constructed by the method of the present invention and the FN constraint constructed by OLS; and (b) is the case of the system's lowest frequency without considering the FN constraint. Detailed Implementation

[0022] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings, but the present invention can be implemented in many different ways as defined and covered by the claims.

[0023] See Figure 1 In a preferred embodiment of the present invention, a power system dispatch optimization method based on linear embedding of maximum frequency deviation constraints is provided, comprising: S1. An approximate linear constraint function is obtained based on the nonlinear maximum frequency deviation constraint combined with variable substitution and the second-order Taylor expansion formula. The nonlinear maximum frequency deviation constraint includes: The power regulation of primary frequency is modeled as a piecewise linear function to construct a frequency dynamic model of the power system: ; ; in, It's a frequency deviation; It is a frequency regulation power; It is the system's inertial time constant; It is load damping, by We obtain, among which D Let be the load damping constant. It is the total system load; Power disturbance; It is the time it takes for the frequency deviation to reach the dead zone. It is the PFR capacity. This is the PFR delivery time. It is the PFR (Proportional Rate of Progress) climbing speed; The nonlinear maximum frequency deviation constraint is obtained based on the frequency dynamic model: ; ; in, It is a predefined limit for the lowest frequency price; It is a frequency dead zone; This is an intermediate quantity.

[0024] In a preferred embodiment of the present invention, the approximate linear constraint function obtained based on the nonlinear maximum frequency deviation constraint combined with variable substitution and the second-order Taylor expansion formula includes: Define variables , and ,in, and Correlation analysis through critical points It is a constant; , and Represented as: ; variables , and Replacing it with the nonlinear maximum frequency deviation constraint, we obtain the first expression: ; Define auxiliary variables Within the actual operating domain of the system, the logarithmic terms of the first expression exist Perform a second-order Taylor series expansion at this point: ; ; ; It can be known and Having a linear relationship, we can approximate the relationship using a linear function to obtain an approximate linear constraint function: ; in, and These are the slope and intercept of the approximate linear constraint function, respectively.

[0025] S2. The first algorithm is constructed based on safety-oriented weights and physical prior regularization mechanisms. S2 specifically includes: A two-way safety-oriented weighting coefficient is constructed based on the approximation of the lowest frequency point of the sample points to the system safety limit; a comprehensive objective function is constructed based on the two-way safety-oriented weighting coefficient and the slope and intercept of the approximately linear constraint function. The overall objective function includes the data fitting residual term and the first term; the first term includes the product of the physical prior regularization term and the regularization hyperparameter; the regularization hyperparameter is obtained by combining the data fitting residual term and the physical prior regularization term with the L-curve method; The first algorithm includes: in this iteration, constructing equivalent one-dimensional projected weights for sample points based on the slope estimate of the approximate linear constraint function from the previous iteration; obtaining iterative residuals based on the slope and intercept estimates of the approximate linear constraint function from the previous iteration; constructing an equivalent weight matrix based on the equivalent one-dimensional projected weights and iterative residuals; obtaining a regularized generalized normal equation based on the equivalent weight matrix and the comprehensive objective function; solving the regularized generalized normal equation to obtain estimates of the slope and intercept of the approximate linear constraint function in this iteration; determining whether the iteration converges based on the relationship between the estimates obtained in this iteration and the previous iteration, combined with a preset criterion; if it does not converge, proceeding to the next iteration; if it converges, outputting the slope and intercept estimates.

[0026] In a preferred embodiment of the present invention, constructing a bidirectional safety-guided weighting coefficient based on the approximation of the lowest frequency point of the sample points to the system safety limit includes: Regarding the first A running sample point, defining its horizontal direction. Shaft basic safety guidance weight coefficient for: ; in, For sample points The precise lowest frequency point calculated under the frequency dynamic model; These are the frequency safety limits specified for the operation of power systems. To prevent extremely small positive numbers with a denominator of zero; Based on the basic safety orientation weight coefficient Constructing vertical security-oriented weights : ; in, The base variance ratio is used to set the baseline error penalty strength to ensure fitting accuracy under normal inertia conditions. This is a heteroscedasticity penalty term. The penalty intensity coefficient, This is the attenuation coefficient.

[0027] In a preferred embodiment of the present invention, constructing the comprehensive objective function based on the bidirectional safety-oriented weighting coefficients and the slope and intercept of the approximately linear constraint function includes: The overall objective function is expressed as: ; ; ; in, The residual term is used to fit the data; This is a regularization hyperparameter used to balance the weight ratios of the two terms; For physical prior regularization terms; and The residuals are bidirectional. This represents the total number of sample points; The higher-order truncation sensitivity weight is used to quantify the influence of higher-order Taylor truncation error under different operating conditions. According to the Taylor expansion characteristics of the swing equation, the lower the system inertia, the more severe the influence of the higher-order residual terms, and the greater the truncation error. P The curvature sensitivity index is set to 3. In order to be in The value obtained by taking a preset step size within the set interval. One sample; Based on The result obtained by calculating the first expression; Two-way residuals and Satisfies the equation of the straight line: .

[0028] In a preferred embodiment of the present invention, the data fitting residual term The core objective is to minimize the weighted orthogonal distance of bidirectional evaluation noise, breaking through the limitation of traditional least squares which only considers longitudinal errors, while also taking into account the influence of lateral and longitudinal measurement errors; physical prior regularization term The design aims to suppress higher-order Taylor truncation errors in the low-inertia region.

[0029] In a preferred embodiment of the present invention, the regularization hyperparameter is obtained by combining the data fitting residual term and the physical prior regularization term with the L-curve method, including: Regularization hyperparameters To control the data fitting residuals in the objective function With higher-order truncation bias in physics The key parameters between them are determined using the L-curve method. To find the optimal value and ensure the objectivity and scientific nature of the algorithm.

[0030] Define the data loss function in logarithmic coordinates as follows: The physical penalty function is ;along with The change in value is due to The resulting parametric trajectory presents a standard L-shaped curve on a two-dimensional plane; calculate the curvature of the standard L-shaped curve. The regularization hyperparameter is obtained by finding the inflection point where the curvature is maximum. : ; in, These are the first and second derivatives of the data loss function, respectively. These are the first and second derivatives of the physical penalty function, respectively.

[0031] In a preferred embodiment of the present invention, the equivalent one-dimensional projected weights of the sample points are constructed based on the slope estimate of the approximate linear constraint function in the previous iteration; the iterative residuals are obtained based on the estimated slopes and intercepts of the approximate linear constraint function in the previous iteration; and the equivalent weight matrix is ​​constructed based on the equivalent one-dimensional projected weights and the iterative residuals, including: Define the linear coefficient vector obtained by solving the regularized generalized normal equation in the previous iteration as: This includes the slope and intercept estimates obtained at the end of the previous iteration. and , is represented as: ; according to Will shaft and The error of the axis is projected along the analytic geometric normal direction to construct an equivalent one-dimensional projective weight. , is represented as: ; Introduce a dynamic asymmetric adjustment factor driven by the current iteration residual. , No. In the first iteration, the... Iteration residual of each sample point for: ; ; in, The coefficient is an asymmetric penalty. Based on dynamic asymmetric adjustment factor and equivalent one-dimensional projection weights Obtain the elements of the equivalent weight matrix : ; Based on the elements of the equivalent weight matrix Obtain the equivalent weight matrix : .

[0032] In a preferred embodiment of the present invention, the regularized generalized normal equation is obtained based on the equivalent weight matrix and the comprehensive objective function; solving the regularized generalized normal equation yields estimates of the slope and intercept of the approximate linear constraint function for this round, including: Define the input feature matrix With the target vector Y The input feature matrix Each row corresponds to the input feature of one sample point, represented as: ; ; in, T This indicates the transpose; and The first sample points and ; By deriving the extremum condition of the comprehensive objective function and combining it with the input feature matrix, Target vector Y and equivalent weight matrix We obtain the regularized generalized normal equation. , is represented as: ; Solving the regularized generalized normal equation yields estimates of the slope and intercept of the approximate linear constraint function for this round.

[0033] In a preferred embodiment of the present invention, the convergence of the iteration is determined based on the relationship between the estimated values ​​obtained in the current iteration and the previous iteration, combined with a preset criterion. If the iteration does not converge, the next iteration begins; if the iteration converges, the slope and intercept estimates are output, including: The preset criteria include: ; in, The value is a preset minimum positive number. If the preset criterion is met, then output the value. Otherwise, proceed to the next iteration.

[0034] S3. Based on the first algorithm, iteratively solve the approximate linear constraint function to obtain the rotated second-order cone constraint. S3 specifically includes: The approximate linear constraint function is solved iteratively based on the first algorithm, and the slope and intercept estimates are output after convergence. Based on variables and expression, It is positively correlated with system disturbances. Since it is positively correlated with the system rotation, the approximately linear constraint function is transformed into an inequality that serves as a constraint, resulting in the first inequality: ; The slope and intercept estimates, and the defined variables and Substituting the expression into the first inequality, we obtain the rotating second-order cone form constraint for the maximum frequency deviation constraint: ; Define frequency safety stress index : ; The rotational second-order cone form constraint of the maximum frequency deviation constraint simplifies to: .

[0035] S4. Optimize scheduling based on the optimal scheduling model of the combined power system with rotating second-order cone constraints.

[0036] The solution is obtained by integrating the rotational second-order cone constraint into the optimal scheduling model of the power system, i.e., solving simultaneously; the optimal scheduling model of the power system includes: The objective function aims to minimize total cost, including unit operating cost and PFR cost. Unit operating cost includes the start-up and shutdown costs of synchronous generators, generation costs, renewable energy curtailment costs, and energy storage operating costs. PFR cost is the sum of the products of the cost coefficients of the three frequency regulation resources and the frequency regulation reserve capacity. Constraints include synchronous generator constraints, renewable energy constraints, energy storage operation constraints, system constraints, and frequency security constraints. Constraints include, but are not limited to: Synchronous generator start-up and shutdown logic constraints, synchronous generator maximum output and reserve constraints, synchronous generator frequency regulation reserve constraints, synchronous generator minimum output constraints, synchronous generator upward ramp constraints, synchronous generator downward ramp constraints, synchronous generator minimum continuous start-up time constraints and synchronous generator minimum continuous shutdown time constraints, energy storage charging and discharging state mutual exclusion constraints, energy storage charging power constraints, energy storage discharging power and frequency regulation reserve constraints, energy storage discharging power non-negativity constraints, energy storage frequency regulation reserve energy constraints, energy storage operation auxiliary linearization constraints, energy storage state of charge continuity constraints, energy storage upper and lower limit constraints, energy storage start-end energy balance constraints, renewable energy available power upper limit constraints, renewable energy frequency regulation reserve capacity limit constraints and system active power balance constraints, maximum frequency change rate constraints, system total equivalent inertia assessment constraints, system total primary frequency regulation reserve aggregation constraints, quasi-steady-state frequency deviation limit constraints and system total frequency regulation ramp rate calculation constraints.

[0037] This invention presents a power system dispatch optimization method based on linear embedding of maximum frequency deviation constraints. By transforming nonlinear constraints into linearly approximate forms and using a proposed algorithm to solve for the slope and intercept required to express the linear relationship, the linear approximation is substituted into the original constraints to derive the form of a rotating second-order cone constraint. This constraint is then embedded into the subsequent model, enabling the construction of a commercial solver to efficiently handle rotating second-order cone constraints. This achieves power system dispatch optimization based on linear embedding of maximum frequency deviation constraints. This method can quickly solve frequency constraint optimization problems without increasing model complexity, improving the frequency stability of low-inertia power systems under large disturbances, and is applicable to generation dispatch scenarios.

[0038] Verification section: To verify the effectiveness and computational performance of the method of this invention, simulation experiments were conducted on a modified IEEE-39 node test system. This test system includes 10 traditional synchronous generator sets with a total installed capacity of 5091MW; 5 renewable energy power plants with a total installed capacity of 1310MW; and 5 energy storage systems with a total installed capacity of 750MW. Simulation experiments were conducted based on two scenarios: Scenario 1: Normal inertia level power system, at this time... Scenario 2: Low-inertia power systems, i.e. .

[0039] To fully examine the system's dynamic frequency response characteristics under low inertia and the adequacy of primary frequency regulation reserves, a risk of sudden large active power disturbances is pre-defined within each scheduling step. The active power disturbance amount for each scheduling period is... The threshold value is set to 400MW, and this is used as the critical verification boundary for the lowest trigger frequency (FN). Set to 49.2Hz.

[0040] To further verify this invention, the method is named ITLS-SW-PI and compared with existing algorithms such as OLS (Ordinary Least Squares), WLS (Weighted Least Squares), and TLS (Total Least Squares) to compare the root mean square error (RMSE) values ​​calculated by the four algorithms. Figure 2 As shown, compared with other algorithms, the RMSE result calculated by the method of the present invention is the smallest under various noise levels, which shows that the method of the present invention can achieve a fast and accurate solution for the maximum frequency deviation. Figure 3 The slope difference is given by the two-parameter fitting results of four algorithms under four noise levels and two scenarios. The intercept is β. Figure 4 To consider the FN constraints constructed by the method of this invention, the FN constraints constructed by OLS, and the case of the lowest system frequency without considering the FN constraints, Table 1 shows the corresponding costs and solution times.

[0041] Table 1. Comparison of optimization results in the modified IEEE-39 node system. ; The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A power system dispatch optimization method based on linear embedding of maximum frequency deviation constraints, characterized in that, include: An approximate linear constraint function is obtained by combining nonlinear maximum frequency deviation constraints with variable substitution and second-order Taylor expansion formula; The first algorithm is constructed based on security-oriented weights and physical prior regularization mechanisms; Based on the first algorithm, the approximate linear constraint function is iteratively solved to obtain the second-order rotating cone constraint; Scheduling optimization is performed based on the optimized scheduling model of the rotating second-order cone-constrained combined power system.

2. The power system dispatch optimization method based on linear embedding of maximum frequency deviation constraints according to claim 1, characterized in that, Nonlinear maximum frequency deviation constraints include: The power regulation of primary frequency is modeled as a piecewise linear function to construct a frequency dynamic model of the power system: ； ； in, It's a frequency deviation; It is a frequency regulation power; It is the system's inertial time constant; It is load damping, by We obtain the value where D is the load damping constant. It is the total system load; Power disturbance; It is the time it takes for the frequency deviation to reach the dead zone. It is the PFR capacity. This is the PFR delivery time. It is the PFR (Proportional Rate of Progress) climbing speed; The nonlinear maximum frequency deviation constraint is obtained based on the aforementioned frequency dynamic model: ； ； in, It is a predefined limit for the lowest frequency price; It is a frequency dead zone; This is an intermediate quantity.

3. The power system dispatch optimization method based on linear embedding of maximum frequency deviation constraints according to claim 2, characterized in that, Based on the nonlinear maximum frequency deviation constraint, combined with variable substitution and second-order Taylor expansion, the approximate linear constraint function is obtained, including: Define variables , and ,in, and Correlation analysis through critical points It is a constant; , and Represented as: ； variables , and Substituting this into the nonlinear maximum frequency deviation constraint, we obtain the first expression: ； Define auxiliary variables Within the actual operating domain of the system, the logarithmic terms of the first expression exist Perform a second-order Taylor series expansion at this point: ； ； ； It can be known and Having a linear relationship, the relationship is approximated by a linear function, resulting in the approximate linear constraint function: ； in, and These are the slope and intercept of the approximate linear constraint function, respectively.

4. The power system dispatch optimization method based on linear embedding of maximum frequency deviation constraints according to claim 3, characterized in that, The first algorithm, based on safety-oriented weights and physical prior regularization, includes: A two-way safety-oriented weighting coefficient is constructed based on the degree of approximation between the lowest frequency point of the sample points and the system safety limit; a comprehensive objective function is constructed based on the two-way safety-oriented weighting coefficient and the slope and intercept of the approximate linear constraint function; The comprehensive objective function includes a data fitting residual term and a first term; the first term includes the product of a physical prior regularization term and a regularization hyperparameter; the regularization hyperparameter is obtained by combining the data fitting residual term and the physical prior regularization term with the L-curve method. The first algorithm includes: in the current iteration, constructing equivalent one-dimensional projected weights for sample points based on the slope estimate of the approximate linear constraint function in the previous iteration; obtaining iterative residuals based on the estimated slope and intercept of the approximate linear constraint function in the previous iteration; constructing an equivalent weight matrix based on the equivalent one-dimensional projected weights and the iterative residuals; obtaining a regularized generalized normal equation based on the equivalent weight matrix and the comprehensive objective function; solving the regularized generalized normal equation to obtain the estimated slope and intercept of the approximate linear constraint function in the current iteration; determining whether the iteration converges based on the relationship between the estimated values ​​obtained in the current iteration and the previous iteration, combined with a preset criterion; if it does not converge, proceeding to the next iteration; if it converges, outputting the estimated slope and intercept values.

5. The power system dispatch optimization method based on linear embedding of maximum frequency deviation constraints according to claim 4, characterized in that, The bidirectional safety-oriented weighting coefficients are constructed based on the degree of approximation between the lowest frequency point of the sample points and the system safety limit, including: Regarding the first A running sample point, defining its horizontal direction. Shaft basic safety guidance weight coefficient for: ； in, For sample points The precise lowest frequency point calculated under the frequency dynamic model; These are the frequency safety limits specified for the operation of power systems. To prevent extremely small positive numbers with a denominator of zero; Based on the aforementioned basic safety guidance weight coefficient Constructing vertical security-oriented weights : ； in, The base variance ratio is used to set the baseline error penalty strength to ensure fitting accuracy under normal inertia conditions. This is a heteroscedasticity penalty term. The penalty intensity coefficient, This is the attenuation coefficient.

6. The power system dispatch optimization method based on linear embedding of maximum frequency deviation constraints according to claim 5, characterized in that, The comprehensive objective function is constructed based on the bidirectional safety-oriented weighting coefficients and the slope and intercept of the approximate linear constraint function, including: The overall objective function is expressed as: ； ； ； in, The residual term is used to fit the data; This is a regularization hyperparameter used to balance the weight ratios of the two terms; For physical prior regularization terms; and For two-way residuals; n is the total number of sample points; These are higher-order truncation sensitivity weights, used to quantify the impact of higher-order Taylor truncation errors under different operating conditions. Curvature sensitivity index; In order to be in The value obtained by taking a preset step size within the set interval. One sample; Based on The result obtained by calculating the first expression; Two-way residuals and Satisfies the equation of the straight line: 。 7. The power system dispatch optimization method based on linear embedding of maximum frequency deviation constraints according to claim 6, characterized in that, The regularization hyperparameter is obtained by combining the data fitting residual term and the physical prior regularization term using the L-curve method, including: Define the data loss function in logarithmic coordinates as follows: The physical penalty function is ;along with The change in value is due to The resulting parametric trajectory presents a standard L-shaped curve on a two-dimensional plane; the curvature of the standard L-shaped curve is calculated. The regularization hyperparameter is obtained by finding the inflection point where the curvature is maximum. : ； in, These are the first and second derivatives of the data loss function, respectively. These are the first and second derivatives of the physical penalty function, respectively.

8. The power system dispatch optimization method based on linear embedding of maximum frequency deviation constraints according to claim 7, characterized in that, The equivalent one-dimensional projected weights of the sample points are constructed based on the slope estimate of the approximate linear constraint function in the previous iteration; the iterative residuals are obtained based on the slope and intercept estimates of the approximate linear constraint function in the previous iteration; the equivalent weight matrix is ​​constructed based on the equivalent one-dimensional projected weights and the iterative residuals, including: Define the linear coefficient vector obtained by solving the regularized generalized normal equation in the previous iteration as: This includes the slope and intercept estimates obtained at the end of the previous iteration. and , is represented as: ； according to Will shaft and The error of the axis is projected along the analytic geometric normal direction to construct an equivalent one-dimensional projective weight. , is represented as: ； Introduce a dynamic asymmetric adjustment factor driven by the current iteration residual. , No. In the first iteration, the... Iteration residual of each sample point for: ； ； in, The coefficient is an asymmetric penalty. According to the dynamic asymmetric adjustment factor and equivalent one-dimensional projection weights Obtain the elements of the equivalent weight matrix : ； Based on the elements of the equivalent weight matrix The equivalent weight matrix is ​​obtained. : 。 9. The power system dispatch optimization method based on linear embedding of maximum frequency deviation constraints according to claim 8, characterized in that, The regularized generalized normal equation is obtained based on the equivalent weight matrix and the comprehensive objective function; solving the regularized generalized normal equation yields estimates of the slope and intercept of the approximate linear constraint function for this round, including: Define the input feature matrix With the target vector The input feature matrix Each row corresponds to the input feature of one sample point, represented as: ； ； in, This indicates the transpose; and The first sample points and ; By deriving the extremum condition of the comprehensive objective function and combining it with the input feature matrix, The target vector and the equivalent weight matrix The regularized generalized normal equation is obtained. , is represented as: ； Solving the regularized generalized normal equation yields estimates of the slope and intercept of the approximate linear constraint function for this round.

10. The power system dispatch optimization method based on linear embedding of maximum frequency deviation constraints according to claim 9, characterized in that, Based on the iterative solution of the approximate linear constraint function using the first algorithm, the rotational second-order cone constraint is obtained, including: Based on the first algorithm, the approximate linear constraint function is solved iteratively, and the slope and intercept estimates are output after convergence. Based on variables and expression, It is positively correlated with system disturbances. If the system rotation is positively correlated, then the approximately linear constraint function is transformed into an inequality that serves as a constraint, resulting in the first inequality: ； The slope and intercept estimates, and the defined variables and Substituting the expression into the first inequality, we obtain the rotating second-order cone form constraint of the maximum frequency deviation constraint: ； Define frequency safety stress index : ； The maximum frequency deviation constraint, in its second-order cone form, simplifies to: 。

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