Multi-region frequency security unit commitment method and device based on bernstein polynomial

Abstract

The application discloses a multi-region frequency safety unit scheduling method and device based on Bernstein polynomials, and the method is based on the optimal distribution of the dynamic primary frequency modulation response of a synchronous generator, a speed governor dead zone and a frequency modulation backup, and a multi-region frequency response model is constructed; the integral-differential algebraic equation of the multi-region frequency response model is approximated through Bernstein polynomials to obtain an algebraic expression of the multi-region frequency dynamics, and a multi-region frequency safety constraint is constructed according to the algebraic expression; the multi-region frequency safety constraint is embedded into a unit combination problem to construct a multi-region frequency safety constraint unit combination model; through a self-adaptive double-layer decomposition algorithm, a mixed integer programming problem of the multi-region frequency safety constraint unit combination model is decomposed into a main problem and a sub-problem; and through solving, a multi-region frequency safety unit scheduling scheme is obtained. The application accurately captures the frequency dynamic difference between regions and improves the frequency safety of a high-proportion new energy power system.

Description

Technical Field

[0001] This invention relates to the field of power system dispatching and frequency security technology, specifically to a multi-region frequency security unit dispatching method and apparatus based on Bernstein polynomials. Background Technology

[0002] With the large-scale integration of renewable energy sources (VRE), primarily wind and solar, into the grid, the power system's inertia level and primary frequency response (PFR) capability have significantly decreased, threatening frequency security. VRE units are often located far from load centers, resulting in regionally differentiated system inertia distribution, which can easily lead to inter-regional frequency oscillations and over-limit issues after a fault. Therefore, it is urgent to comprehensively optimize unit start-up and shutdown as well as PFR reserve within the unit combination (UC) to ensure frequency security across multiple regions.

[0003] Current research addresses the coordination between optimization and frequency stability by introducing frequency safety constraints into Common Coordination Functional (UC). Key methods include: 1) Based on an equivalent single-machine model, aggregating the entire system's synchronous machines into a single machine and deriving the frequency dynamics of the center of inertia (COI), combined with piecewise linearization to generate constraints. However, this method assumes uniform unit response characteristics, ignores regional frequency differences, and suffers from large linearization errors and complex variable scales, failing to obtain the optimal PFR configuration at the unit level; 2) Based on a linear ramp model, assuming the PFR dynamics are linear functions, but ignoring the actual response process and relying on difficult-to-obtain transfer time parameters, leading to conservative results; 3) Using machine learning to approximate frequency dynamics, while reducing computational complexity, the model's effectiveness depends on sample data and lacks scalability. Furthermore, existing techniques still have limitations when analyzing multi-region frequency safety UC, as it is difficult to balance the efficiency and accuracy of solving complex integral-differential equations.

[0004] Therefore, there is an urgent need for a multi-regional frequency security constraint optimization method that balances accuracy and efficiency to support the safe and stable operation of the power system under high-proportion VRE access. Summary of the Invention

[0005] To address this, the present invention provides a multi-regional frequency-safe unit scheduling method and apparatus based on Bernstein polynomials. Bernstein polynomials are used to approximate the complex system of integral-differential algebraic equations governing the frequency response of multiple regions. Simultaneously, an adaptive two-level decomposition algorithm is employed to solve large-scale mixed-integer programming problems, reducing computational complexity. This ensures the tightness and effectiveness of the multi-regional frequency dynamic approximation, accurately capturing the dynamic differences in frequency between regions and improving the frequency security of high-proportion renewable energy power systems.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a multi-regional frequency-safe unit scheduling method based on Bernstein polynomials, comprising:

[0007] Based on the dynamic primary frequency response of synchronous generators, governor dead zone, and optimal allocation of frequency regulation reserves, a multi-region frequency response model is constructed.

[0008] The integral-differential algebraic equation of the multi-region frequency response model is approximated by Bernstein polynomials to obtain the algebraic expression of the multi-region frequency dynamics.

[0009] Based on the algebraic expression of the multi-region frequency dynamics, construct multi-region frequency security constraints;

[0010] The multi-regional frequency security constraints are embedded into the unit combination problem to construct a multi-regional frequency security constraint unit combination model.

[0011] The mixed-integer programming problem of the multi-region frequency security constrained unit combination model is decomposed into a main problem and sub-problems by using an adaptive two-level decomposition algorithm; by solving the main problem and the sub-problems, a multi-region frequency security unit scheduling scheme is obtained.

[0012] As a preferred embodiment of the multi-regional frequency safety unit scheduling method based on Bernstein polynomials, the expression of the multi-regional frequency response model is as follows:

[0013] When the frequency deviation is less than the governor dead zone:

[0014]

[0015] When the frequency deviation is greater than the speed controller dead zone:

[0016]

[0017]

[0018] In the formula, H i Let Δf be the total inertia of region i; i (τ) represents the frequency deviation at time τ in region i; k i L Let be the load damping ratio of region i; Let be the load power of region i; Let be the total primary frequency modulation response power at time τ in region i; Let Ψ be the disturbance power in region i; i X is the set of regions connected to region i; ij η is the reactance of the tie line between region i and region j; η is the integral variable; Δf i DB The action dead zone value for region i; The critical point time of the governor's dead zone; Let i be the set of synchronous generators in region i; Let T be the primary frequency regulation power of generator g at time τ; g K is the response constant of generator g; g U is the droop coefficient of generator g; g It is a 0-1 variable, indicating whether unit g is online; if so, it is 1.

[0019] As a preferred embodiment of the multi-region frequency safety unit scheduling method based on Bernstein polynomials, the algebraic expression for the multi-region frequency dynamics is:

[0020]

[0021] In the formula, l s To divide the time range L of the frequency dynamic response into multiple segments, the length of each segment is given; i and j are both regions; for The column vector formed; B represents the Bernstein spline coefficients corresponding to the time-domain frequencies. m,k (τ) is an m-degree Bernstein polynomial; for The initial value of J; T This is the coefficient matrix of the Bernstein polynomial integral property; This is the column vector of Bernstein spline coefficients corresponding to the total frequency modulation power in the time domain; This is the column vector of Bernstein spline coefficients corresponding to the disturbance power; This is the column vector of Bernstein spline coefficients corresponding to the frequency modulation power of the time-domain unit g; yes The initial value of Δf i DB,B dead zone value Δf i DB The vector formed by the vector; m is the order of the Bernstein polynomial; k = 0, 1, ..., m.

[0022] As a preferred embodiment of the multi-region frequency security unit scheduling method based on Bernstein polynomials, the multi-region frequency security constraints include: initial time frequency change rate constraint, frequency minimum point deviation constraint, quasi-steady-state frequency deviation constraint, and primary frequency regulation reserve constraint.

[0023] The expression for the initial time frequency change rate constraint is:

[0024]

[0025] In the formula, RoCoF max This is the limit of the rate of change of frequency at the initial moment;

[0026] The expression for the frequency minimum point deviation constraint is:

[0027]

[0028] In the formula, V is the enhancement matrix of the inequality equation transformation, which is a constant matrix; Δf max This is the minimum frequency deviation limit;

[0029] The expression for the quasi-steady-state frequency deviation constraint is:

[0030]

[0031] In the formula, Δf ss,max The quasi-steady-state frequency deviation limit;

[0032] The expression for the primary frequency modulation reserve constraint is:

[0033]

[0034] In the formula, R g This is the frequency regulation reserve power for unit g.

[0035] As a preferred embodiment of the multi-regional frequency security-constrained unit scheduling method based on Bernstein polynomials, the objective function expression of the multi-regional frequency security-constrained unit combination model is:

[0036]

[0037] In the formula, Ω G Ω T Ω W Ω B These are collections of thermal power units, dispatch periods, wind power units, and busbars; U gt R is a 0-1 variable, representing whether unit g is online during time period t, where 1 indicates online and 0 indicates offline; gt This refers to the primary frequency regulation reserve power of unit g during time period t; These are the start-up and shutdown costs of unit g and the primary frequency regulation standby cost, respectively. c is the fuel cost of unit g during time period t; W and c B These represent the unit cost of wind curtailment and the cost of load shedding, respectively; ΔP wt Let w be the wind curtailment power of wind turbine w during time period t; Let be the load shedding power of bus b during time period t.

[0038] As a preferred embodiment of the multi-regional frequency security unit scheduling method based on Bernstein polynomials, in the process of decomposing the mixed integer programming problem of the multi-regional frequency security constraint unit combination model into the main problem and the sub-problems through the adaptive two-level decomposition algorithm, the mixed integer programming problem is decomposed into the main problem and the sub-problems iteratively calculated through the Benders decomposition strategy and the adaptive frequency low point time estimation model; by solving the main problem, the unit start-up and shutdown and frequency regulation reserve allocation strategy is obtained; by solving the sub-problems, the multi-regional frequency security constraints are verified.

[0039] This invention also provides a multi-regional frequency safety unit scheduling device based on Bernstein polynomials, which, based on the above multi-regional frequency safety unit scheduling method based on Bernstein polynomials, includes:

[0040] The multi-region frequency response model construction module is used to construct a multi-region frequency response model based on the dynamic primary frequency regulation response of the synchronous generator, the governor dead zone, and the optimal allocation of frequency regulation reserve.

[0041] The module for obtaining the algebraic expression of the multi-region frequency dynamics is used to approximate the integral-differential algebraic equation of the multi-region frequency response model using Bernstein polynomials to obtain the algebraic expression of the multi-region frequency dynamics.

[0042] A multi-region frequency security constraint construction module is used to construct multi-region frequency security constraints based on the algebraic expression of the multi-region frequency dynamics.

[0043] A multi-regional frequency security constraint unit combination model construction module is used to embed the multi-regional frequency security constraints into the unit combination problem and construct a multi-regional frequency security constraint unit combination model.

[0044] The multi-region frequency security constraint unit combination model solution module is used to decompose the mixed integer programming problem of the multi-region frequency security constraint unit combination model into a main problem and sub-problems through an adaptive two-level decomposition algorithm; and to obtain a multi-region frequency security unit scheduling scheme by solving the main problem and the sub-problems.

[0045] As a preferred embodiment of the multi-regional frequency safety unit scheduling device based on Bernstein polynomials, the expression of the multi-regional frequency response model in the multi-regional frequency response model construction module is as follows:

[0046] When the frequency deviation is less than the governor dead zone:

[0047]

[0048] When the frequency deviation is greater than the speed controller dead zone:

[0049]

[0050] In the formula, H i Let Δf be the total inertia of region i; i (τ) represents the frequency deviation at time τ in region i; Let be the load damping ratio of region i; Let be the load power of region i; Let be the total primary frequency modulation response power at time τ in region i; Let Ψ be the disturbance power in region i; i X is the set of regions connected to region i; ij η is the reactance of the tie line between region i and region j; η is the integral variable; Δf i DB The action dead zone value for region i; The critical point time of the governor's dead zone; Let i be the set of synchronous generators in region i; Let T be the primary frequency regulation power of generator g at time τ; g K is the response constant of generator g; g U is the droop coefficient of generator g; g It is a 0-1 variable, indicating whether unit g is online; if so, it is 1.

[0051] As a preferred embodiment of the multi-region frequency safety unit scheduling device based on Bernstein polynomials, the algebraic expression for the multi-region frequency dynamics in the multi-region frequency dynamics acquisition module is:

[0052]

[0053] In the formula, l s To divide the time range L of the frequency dynamic response into multiple segments, the length of each segment is given; i and j are both regions; for The column vector formed; B represents the Bernstein spline coefficients corresponding to the time-domain frequencies. m,k (τ) is an m-degree Bernstein polynomial; for The initial value of J; T This is the coefficient matrix of the Bernstein polynomial integral property; ΔP is the column vector of Bernstein spline coefficients corresponding to the total frequency modulation power in the time domain; i L,B This is the column vector of Bernstein spline coefficients corresponding to the disturbance power; This is the column vector of Bernstein spline coefficients corresponding to the frequency modulation power of the time-domain unit g; yes The initial value of Δfi DB,B dead zone value Δf i DB The column vectors are composed of m, where m is the order of the Bernstein polynomial, and k = 0, 1, ..., m.

[0054] As a preferred embodiment of the multi-region frequency safety unit scheduling device based on Bernstein polynomials, the multi-region frequency safety constraint construction module includes: initial time frequency change rate constraint, frequency minimum point deviation constraint, quasi-steady-state frequency deviation constraint, and primary frequency regulation reserve constraint.

[0055] The expression for the initial time frequency change rate constraint is:

[0056]

[0057] In the formula, RoCoF max This is the limit of the rate of change of frequency at the initial moment;

[0058] The expression for the frequency minimum point deviation constraint is:

[0059]

[0060] In the formula, V is the enhancement matrix of the inequality equation transformation, which is a constant matrix; Δf max This is the minimum frequency deviation limit;

[0061] The expression for the quasi-steady-state frequency deviation constraint is:

[0062]

[0063] In the formula, Δf ss,max The quasi-steady-state frequency deviation limit;

[0064] The expression for the primary frequency modulation reserve constraint is:

[0065]

[0066] In the formula, R g This is the frequency regulation reserve power for unit g.

[0067] As a preferred embodiment of the multi-regional frequency safety unit scheduling device based on Bernstein polynomials, the objective function expression of the multi-regional frequency safety constraint unit combination model in the multi-regional frequency safety constraint unit combination model construction module is:

[0068]

[0069] In the formula, Ω G Ω T ΩW Ω B These are collections of thermal power units, dispatch periods, wind power units, and busbars; U gt R is a 0-1 variable, representing whether unit g is online during time period t, where 1 indicates online and 0 indicates offline; gt This refers to the primary frequency regulation reserve power of unit g during time period t; These are the start-up and shutdown costs of unit g and the primary frequency regulation standby cost, respectively. c is the fuel cost of unit g during time period t; W and c B These represent the unit cost of wind curtailment and the cost of load shedding, respectively; ΔP wt Let w be the wind curtailment power of wind turbine w during time period t; Let be the load shedding power of bus b during time period t.

[0070] As a preferred embodiment of the multi-regional frequency safety unit scheduling device based on Bernstein polynomials, in the multi-regional frequency safety constraint unit combination model solution module, during the process of decomposing the mixed integer programming problem of the multi-regional frequency safety constraint unit combination model into the main problem and the sub-problems through the adaptive two-level decomposition algorithm, the mixed integer programming problem is decomposed into the main problem and the sub-problems iteratively calculated through the Benders decomposition strategy and the adaptive frequency low point time estimation model; by solving the main problem, the unit start-up and shutdown and frequency regulation reserve allocation strategy is obtained; by solving the sub-problems, the multi-regional frequency safety constraints are verified.

[0071] This invention has the following advantages: Based on the dynamic primary frequency response of synchronous generators, the optimal allocation of governor dead zone and frequency regulation reserve, a multi-region frequency response model is constructed. The integral-differential algebraic equations of the multi-region frequency response model are approximated using Bernstein polynomials to obtain an algebraic expression for the multi-region frequency dynamics. Based on this algebraic expression, multi-region frequency safety constraints are constructed. These constraints are embedded into the unit combination problem to construct a multi-region frequency safety constraint unit combination model. An adaptive bi-level decomposition algorithm is used to decompose the mixed-integer programming problem of the multi-region frequency safety constraint unit combination model into a main problem and sub-problems. By solving the main problem and the sub-problems, a multi-region frequency safety unit scheduling scheme is obtained. This invention simultaneously considers the differentiated dynamic frequency response, dead zone, and optimal allocation of frequency regulation reserve of units in the multi-region frequency response model, using Bernstein polynomials to model the integral-differential algebraic equations in the time domain. Based on this, multi-region frequency safety constraints based on Bernstein polynomial approximation are obtained. Furthermore, an adaptive bi-level decomposition algorithm is proposed, which decomposes the original problem into a main problem and sub-problems. Simultaneously, within the sub-problems, the problem size is adaptively reduced by estimating the time of the lowest frequency point, significantly decreasing the dimensionality and time required for optimization. The multi-region frequency response model based on Bernstein polynomial approximation in this invention exhibits tight dynamics and can more accurately simulate multi-region frequency dynamics compared to existing techniques. Compared to traditional single-region models based on the center of inertia, the frequency index values ​​of the proposed method more accurately reflect the actual differences in regional frequency responses. Attached Figure Description

[0072] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0073] The structures, proportions, sizes, etc. illustrated in this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed herein, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0074] Figure 1 This is a schematic diagram of the multi-region frequency safety unit scheduling method based on Bernstein polynomials provided in Embodiment 1 of the present invention;

[0075] Figure 2 This is a schematic diagram of a two-region 12-node system in one possible embodiment of Embodiment 1 of the present invention;

[0076] Figure 3 This is a schematic diagram showing the comparison results between the multi-region frequency dynamics of the present invention and Simulink numerical simulation in one possible embodiment of the present invention provided in Embodiment 1;

[0077] Figure 4 This is a schematic diagram illustrating the deviation between the present invention and the frequency minimum point based on the inertial center model in one possible embodiment provided in Embodiment 1 of the present invention;

[0078] Figure 5 This is a schematic diagram of the initial frequency change rate results of the present invention and the inertial center model in one possible embodiment provided in Embodiment 1 of the present invention;

[0079] Figure 6 This is a schematic diagram of the architecture of the multi-regional frequency safety unit scheduling device based on Bernstein polynomials provided in Embodiment 2 of the present invention. Detailed Implementation

[0080] The following specific embodiments illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0081] Example 1

[0082] See Figure 1 Embodiment 1 of the present invention provides a multi-region frequency-safe unit scheduling method based on Bernstein polynomials, comprising the following steps:

[0083] S1. Based on the dynamic primary frequency response of synchronous generators, the governor dead zone, and the optimal allocation of frequency regulation reserves, a multi-region frequency response model is constructed.

[0084] S2. The integral-differential algebraic equation of the multi-region frequency response model is approximated by Bernstein polynomials to obtain the algebraic expression of the multi-region frequency dynamics.

[0085] S3. Construct multi-region frequency security constraints based on the algebraic expression of the multi-region frequency dynamics;

[0086] S4. Embed the multi-regional frequency security constraints into the unit combination problem to construct a multi-regional frequency security constraint unit combination model;

[0087] S5. Using an adaptive two-level decomposition algorithm, the mixed integer programming problem of the multi-region frequency security constraint unit combination model is decomposed into a main problem and sub-problems; by solving the main problem and the sub-problems, a multi-region frequency security unit scheduling scheme is obtained.

[0088] In this embodiment, in step S1, a multi-region frequency response model is constructed based on the dynamic primary frequency regulation response of the synchronous generator, the governor dead zone, and the optimal allocation of frequency regulation reserves.

[0089] Specifically, the expression for the multi-region frequency response model is as follows:

[0090] When the frequency deviation is less than the governor dead zone:

[0091]

[0092] When the frequency deviation is greater than the speed controller dead zone:

[0093]

[0094] In the formula, H i Let Δf be the total inertia of region i; i (τ) represents the frequency deviation at time τ in region i; Let be the load damping ratio of region i; Let be the load power of region i; Let be the total primary frequency modulation response power at time τ in region i; Let Ψ be the disturbance power in region i; i X is the set of regions connected to region i; ij η is the reactance of the tie line between region i and region j; η is the integral variable; Δf i DB The action dead zone value for region i; The critical point time of the governor's dead zone; Let i be the set of synchronous generators in region i; Let T be the primary frequency regulation power of generator g at time τ; g K is the response constant of generator g; g U is the droop coefficient of generator g; g It is a 0-1 variable, indicating whether unit g is online; if so, it is 1.

[0095] In this embodiment, in step S2, the integral-differential algebraic equation of the multi-region frequency response model is approximated by Bernstein polynomials to obtain the algebraic expression of the multi-region frequency dynamics.

[0096] Specifically, the time range L of the frequency dynamic response is divided into multiple segments, each with a length of l.s . Each l s The range is normalized to [0, 1], and then Bernstein polynomial splines are used to dynamically approximate the frequency of each segment. The frequency Δf of segment s in region i is... i,s The Bernstein polynomial approximation of (τ) is:

[0097]

[0098] In the formula, B m,k (τ) is an m-degree Bernstein polynomial; For the corresponding Δf i,s Bernstein spline coefficients of (τ); and B m (τ) are respectively and B m,k A column vector consisting of (τ).

[0099] Similarly, the Bernstein polynomial approximations of the other continuous-time functions in equations (3)-(7) are as follows:

[0100]

[0101] Then, integrating both sides of equation (3) from 0 to τ, we get:

[0102]

[0103] After time range normalization, in order to keep the physical meaning of the equation unchanged, the differential term in equation (14) needs to be divided by l. s The integral term needs to be multiplied by l. s Equation (14) can be further written as:

[0104]

[0105] For part a in equation (15), apply the properties of Bernstein polynomial integration and equation (8); for part b in equation (15), apply the properties of Bernstein polynomial integration and equation (12); and for part c, since there are two integral symbols, apply the properties of Bernstein polynomial integration to both integrals. Therefore, equation (15) is equivalent to:

[0106]

[0107] In the formula J T This is the coefficient matrix of the Bernstein polynomial integral property; For corresponding Bernstein spline coefficient column vector; ΔP i L,B For corresponding The Bernstein spline coefficient column vector; m is the order of the Bernstein polynomial; k = 0, 1, ..., m; i and j are regions; For segment s The initial value; The initial conditions shown in equation (17) must be met.

[0108] Similarly, equations (5)-(7) are equivalent to:

[0109]

[0110]

[0111] In the formula, For corresponding The Bernstein spline coefficient column vector; It is segmented s The initial value of Δf i DB,B dead zone value Δf i DB The column vector formed by these.

[0112] In this embodiment, in step S3, multi-region frequency security constraints are constructed based on the algebraic expression of the multi-region frequency dynamics.

[0113] Specifically, the multi-region frequency security constraints consider three indicators: the rate of change of frequency at the initial moment, the deviation of the frequency minimum point, and the deviation of the quasi-steady-state frequency. It is assumed that the limits of the three indicators are consistent across all regions.

[0114] Initial frequency change rate constraint:

[0115] Initial time τ = 0 + Located in segment s = 1. Applying the differential properties of Bernstein polynomials, the initial time RoCoF constraint for any region i can be expressed as:

[0116]

[0117] In the formula, RoCoF max This is the limit value for the rate of change of frequency at the initial moment.

[0118] Minimum frequency deviation constraint:

[0119] The frequency deviation at all times should be less than its maximum limit. Applying the solution space transformation property of Bernstein polynomials, the frequency minimum point deviation constraint in any region i can be expressed as:

[0120]

[0121] In the formula, V is the enhancement matrix of the inequality equation transformation, which is a constant matrix; Δfmax This is the minimum frequency deviation limit.

[0122] Quasi-steady-state frequency deviation constraint:

[0123] Due to oscillation decay, the QSS frequency deviation index does not show significant regional differences. The final value theorem can be used to derive the QSS frequency deviation constraint expression:

[0124]

[0125] In the formula, Δf ss,max This is the limit for quasi-steady-state frequency deviation.

[0126] Primary frequency regulation standby constraints:

[0127] The primary frequency regulation power of each generating unit cannot exceed its primary frequency regulation reserve power; therefore, this constraint can also determine the optimal reserve for each unit. Applying the solution space transformation property of Bernstein polynomials, the primary frequency regulation reserve constraint for each unit can be expressed as:

[0128]

[0129] In the formula, R g This is the frequency regulation reserve power for unit g.

[0130] In this embodiment, the complete multi-region frequency security constraints are equations (16)-(25), including the multi-region frequency response model equations (16)-(21) based on Bernstein polynomial approximation; frequency change rate constraint equation (22); frequency minimum point constraint equation (23); quasi-steady-state frequency deviation constraint equation (24); and primary frequency modulation reserve constraint equation (25).

[0131] In this embodiment, in step S4, the multi-regional frequency security constraints are embedded into the unit combination problem to construct a multi-regional frequency security constraint unit combination model.

[0132] Specifically, the expression for the multi-region frequency security-constrained unit combination model is as follows:

[0133]

[0134]

[0135] In the formula, Ω G Ω T Ω W Ω B Ω L These are collections of thermal power units, dispatch periods, wind power units, busbars, and branches; U gt P is a 0-1 variable, representing whether unit g is online during time period t, where 1 indicates online and 0 indicates offline;gt R represents the active power output of unit g during time period t; gt ΔP is the primary frequency regulation reserve power of unit g during time period t; wt Let w be the wind curtailment power of wind turbine w during time period t; Let be the load shedding power of bus b during time period t; p represents the fuel cost of unit g during time period t. gtμ Let g be the active power output of unit g in the μ-th segment of time period t; c gμ These are the start-up and shutdown costs, primary frequency regulation reserve costs, online fixed costs, and the marginal fuel cost of the μth segment, respectively; c W and c B These are the unit cost of wind curtailment and the cost of load shedding, respectively; N μ Number of segments for fuel cost; and These represent the maximum and minimum technical output of unit g, respectively; H i,t fi represents the total inertia of region i during time period t; f0 is the reference frequency, i.e., 50Hz. g For the inertia of unit g; N a The number of regions; and These are the ramp limit and landslide limit for unit g, respectively; and These are the minimum operating time and minimum downtime of unit g, respectively. and P wt These represent the predicted and actual power output of wind turbine w during time period t, respectively. and These represent the predicted load and actual load of bus b during time period t, respectively; ζ lg ζ lw ζ lb These are the power transfer factors of branch l relative to unit g, fan w, and bus b, respectively. The power flow limit for branch l.

[0136] In the above formulas, formula (26) is the objective function of the multi-region frequency security constraint unit combination model, including the unit start / stop cost, fuel cost, primary frequency regulation reserve cost, wind curtailment and load shedding penalty cost. The multi-region frequency security constraints (16)-(25) ignore the exponent t of the UC time period, and formula (27) indicates that the frequency security constraint must be met at any time t. Constraint (28) linearizes the unit's fuel cost piecewise. Formula (29) calculates the total inertia of region i. Formulas (30)-(32) are the upper and lower limits of the unit's output (requiring primary frequency regulation reserve power), ramping constraint and slope constraint, respectively. Formulas (33)-(36) are the minimum start / stop time constraints of the unit. Formulas (37)-(39) are the wind curtailment constraint, load shedding constraint and system power balance constraint, respectively. Formula (40) is the branch DC power flow constraint.

[0137] In this embodiment, in step S5, the mixed integer programming problem of the multi-region frequency security constraint unit combination model is decomposed into a main problem and sub-problems by an adaptive two-level decomposition algorithm; by solving the main problem and the sub-problems, a multi-region frequency security unit scheduling scheme is obtained.

[0138] Specifically, the adaptive two-level decomposition algorithm decomposes a large-scale mixed integer programming problem into a main problem and sub-problems through a Benders decomposition strategy and an adaptive frequency low point time estimation model. The main problem solves the unit start-up and shutdown and frequency regulation reserve allocation, while the sub-problems verify the frequency security constraints of multiple regions.

[0139] Specifically, the multi-region frequency security constraints (16)-(25) contain a large number of 0-1 variables and continuous variables. Therefore, the proposed multi-region frequency security constraint unit combination model is a complex large-scale mixed integer programming problem. It is difficult to solve directly using commercial solvers and a reasonable acceleration algorithm needs to be designed.

[0140] Among them, the frequency change rate index and the frequency minimum point deviation index are affected by the frequency response differences between regions, while the quasi-steady-state frequency deviation index is independent of them. Therefore, the multi-region frequency response model (16)-(21), frequency change rate constraint (22), and frequency minimum point deviation constraint (23) based on the Bernstein polynomial approximation do not need to consider the complete frequency dynamic segment s. For example, when L = 30S, assume l s =2, where s = 1, ..., 15. Assume the time t is the point of lowest frequency. nadir Since the constraints occur when s = 4 (i.e., between 6 and 8S), we only need to consider the constraints (16)-(23) when s = 1, 2, 3, 4, and do not need to consider the complete segment s = 1, 2, ..., 15. This will greatly reduce the size of the model.

[0141] Ignoring regional frequency response differences, frequency dynamics based on the center of inertia are used to estimate the segment s in which the minimum point occurs. nadir When the frequency reaches its lowest point, the primary frequency modulation response power of the entire system equals the disturbance power. A linear ramp is used to simulate the dynamics of the primary frequency modulation response power.

[0142]

[0143] In the formula, ΔP M (τ) represents the total increment of the system's mechanical power at time τ; τ nadir The time it takes for the frequency to reach its lowest point; ΔP L This represents the total power disturbance of the system.

[0144] The swing equation based on the center of inertia is:

[0145]

[0146] In the formula, H sys Let be the total inertia of the system; Δf(τ) be the frequency deviation at time τ.

[0147] Substituting equation (41) into equation (42), we get:

[0148]

[0149] Integrating equation (43) yields the time-domain expression for the approximate parabola Δf(τ):

[0150]

[0151] In equation (44), τ is an unknown variable, and τ nadir Since τ is an unknown constant, to obtain the point of lowest frequency, we must first determine τ. nadir .

[0152] Based on equation (44), the total primary frequency modulation response power of the system in the frequency domain is:

[0153]

[0154] In the formula, G sys (s) is the sum of the dynamic responses of all units:

[0155]

[0156] In the formula, T g K is the response constant of generator g; g Let g be the droop coefficient of the generator.

[0157] Substituting equation (46) into equation (45), we get:

[0158]

[0159] Performing an inverse Laplace transform on equation (47) yields P PF,sys (τ). Also, because P reaches its lowest point when the frequency is at its lowest. PF ,sys (τ) equals ΔP L Therefore:

[0160] P PF,sys (τ nadir )=ΔP L (48)

[0161] Solving equation (48) yields τ. nadir The value of τ is obtained from this. nadir Segment s nadir .

[0162] In this embodiment, Benders decomposition is used to decompose the multi-region frequency security constraint unit combination model (26)-(40) into the UC main problem and the frequency verification subproblem, and the main problem and subproblem are solved iteratively.

[0163] UC main question:

[0164] The main problem is to solve the UC (Unified Value Collection) to obtain the overall system operation mode without considering multi-region frequency security constraints. During iteration, the main problem constraints also need to be supplemented with the cutting planes fed back from the subproblems, and their model is as follows:

[0165]

[0166] After solving the main problem, the unit start-up and shutdown results U are obtained. gt and primary frequency regulation reserve power R gt It determines the feasibility of the subproblem, is a variable passed to the subproblem, and is regarded as a known parameter in the process of solving the subproblem.

[0167] This invention is called This is a frequency subproblem pattern. Among them, They are respectively The column vector formed by the optimal solutions.

[0168] Frequency checkerboard problem:

[0169] The subproblem examines whether the system operation mode obtained from the main problem satisfies the multi-regional frequency security constraints at each time period t. A non-negative slack variable St is introduced to ensure that the subproblem has a solution. The model is as follows:

[0170]

[0171] In the formula, W is the matrix composed of the coefficients on the left side of the inequality in constraints (22) and (23); F max It is a column vector consisting of the constants on the right side of the inequality in constraints (22) and (23).

[0172] If the target value A value greater than 0 indicates that the solution obtained from the main problem will cause the frequency index to exceed the limit in time period t, and the corresponding infeasible cutting plane needs to be returned to the main problem.

[0173]

[0174] In the formula, The optimal value for the subproblem; and Constraints and The optimal solution for the dual variable.

[0175] In one possible embodiment, an example of improved frequency-dynamically constrained unit combination scheduling for a two-region 12-node system is provided as follows:

[0176] like Figure 2 As shown, the system has 12 buses, 13 branches, and 1 tie line. The frequency response time range L is set to 30 seconds, and the length of each segment is l. s Set to 2S, expected disturbance amount Set to 10% of load demand. Load damping ratio. Set to 1% / Hz, frequency specification limit RoCoF max , Δf max With Δf ss,max The speed controller dead zone Δf is set to 0.5Hz / s, 0.5Hz, and 0.3Hz respectively. i DB Set to 0.02Hz. Primary frequency modulation backup cost. Set at $15 / MWh, the cost of wind curtailment / load shedding is c. W and c B The loads are set at $50 / MWh and $100 / MWh respectively. The peak total system load is 540MW, with the load in Region 1 being twice that of Region 2. The installed capacity of wind turbines is 350MW, all located in Region 2.

[0177] The Bernstein polynomial is used to approximate the multi-region frequency response model, resulting in an algebraic expression for the multi-region frequency dynamics. Multi-region frequency security constraints are then constructed, which take into account the frequency change rate, the frequency minimum point, and the quasi-steady-state frequency deviation constraints.

[0178] By embedding multi-regional frequency security constraints into the unit combination problem, a multi-regional frequency security constraint unit combination model is obtained.

[0179] This large-scale mixed-integer programming problem is decomposed into a main unit combination problem and a frequency verification subproblem using an adaptive two-level decomposition algorithm. Solving the model using the Gurobi commercial solver yields a unit scheduling scheme that guarantees frequency security across multiple regions. The economic cost results of the optimal system scheduling scheme are shown in Table 1.

[0180]

[0181] Table 1. Economic Costs of the Optimal Scheduling Scheme for the System

[0182] Taking the results of region 2 as an example, Figure 3 This paper presents a comparison between the multi-region frequency dynamics based on the Bernstein polynomial approximation of this invention and Simulink numerical simulation results. The multi-region frequency-constrained unit combination model of this invention is compared with the traditional frequency-constrained unit combination model based on the center of inertia. Figure 4 The result is the deviation of the lowest frequency points of the two. Figure 5 The initial frequency change rate results for both.

[0183] In summary, this invention constructs a multi-region frequency response model based on the dynamic primary frequency response, governor dead zone, and optimal allocation of frequency regulation reserve of synchronous generators. It approximates the integral-differential algebraic equations of the multi-region frequency response model using Bernstein polynomials to obtain an algebraic expression for the multi-region frequency dynamics. Based on this algebraic expression, multi-region frequency safety constraints are constructed. These constraints are then embedded into the unit combination problem to construct a multi-region frequency safety constraint unit combination model. An adaptive bi-level decomposition algorithm decomposes the mixed-integer programming problem of the multi-region frequency safety constraint unit combination model into a main problem and sub-problems. Solving the main problem and sub-problems yields a multi-region frequency safety unit scheduling scheme. This invention simultaneously considers the differentiated dynamic frequency response, dead zone, and optimal allocation of frequency regulation reserve of units in the multi-region frequency response model, using Bernstein polynomials to model the time-domain integral-differential algebraic equations. Based on this, multi-region frequency safety constraints based on Bernstein polynomial approximation are obtained. Furthermore, an adaptive bi-level decomposition algorithm is proposed, which decomposes the original problem into a main problem and sub-problems. Simultaneously, within the sub-problems, the problem size is adaptively reduced by estimating the time of the lowest frequency point, significantly decreasing the dimensionality and time required for optimization. The multi-region frequency response model based on Bernstein polynomial approximation in this invention exhibits tight dynamics and can more accurately simulate multi-region frequency dynamics compared to existing techniques. Compared to traditional single-region models based on the center of inertia, the frequency index values ​​of the proposed method more accurately reflect the actual differences in regional frequency responses.

[0184] It should be noted that the method of this disclosure embodiment can be executed by a single device, such as a computer or server. The method of this embodiment can also be applied to a distributed scenario, where multiple devices cooperate to complete the task. In such a distributed scenario, one of these devices may execute only one or more steps of the method of this disclosure embodiment, and the multiple devices will interact with each other to complete the method described.

[0185] It should be noted that the above description describes some embodiments of this disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in a different order than that shown in the above embodiments and still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0186] Example 2

[0187] See Figure 6Embodiment 2 of the present invention also provides a multi-regional frequency safety unit scheduling device based on Bernstein polynomials, comprising:

[0188] The multi-region frequency response model construction module 001 is used to construct a multi-region frequency response model based on the dynamic primary frequency regulation response of the synchronous generator, the governor dead zone, and the optimal allocation of frequency regulation reserve.

[0189] The module 002 for obtaining the algebraic expression of the multi-region frequency dynamics is used to approximate the integral-differential algebraic equation of the multi-region frequency response model using Bernstein polynomials to obtain the algebraic expression of the multi-region frequency dynamics.

[0190] The multi-region frequency security constraint construction module 003 is used to construct multi-region frequency security constraints based on the algebraic expression of the multi-region frequency dynamics.

[0191] The multi-regional frequency security constraint unit combination model construction module 004 is used to embed the multi-regional frequency security constraint into the unit combination problem and construct a multi-regional frequency security constraint unit combination model.

[0192] The multi-region frequency security constraint unit combination model solution module 005 is used to decompose the mixed integer programming problem of the multi-region frequency security constraint unit combination model into a main problem and sub-problems through an adaptive two-level decomposition algorithm; and to obtain a multi-region frequency security unit scheduling scheme by solving the main problem and the sub-problems.

[0193] In this embodiment, in the multi-region frequency response model construction module 001, the expression of the multi-region frequency response model is:

[0194] When the frequency deviation is less than the governor dead zone:

[0195]

[0196] When the frequency deviation is greater than the speed controller dead zone:

[0197]

[0198] In the formula, H i Let Δf be the total inertia of region i; i (τ) represents the frequency deviation at time τ in region i; Let be the load damping ratio of region i; Let be the load power of region i; Let be the total primary frequency modulation response power at time τ in region i; Let Ψ be the disturbance power in region i; i X is the set of regions connected to region i; ijη is the reactance of the tie line between region i and region j; η is the integral variable; Δf i DB The action dead zone value for region i; The critical point time of the governor's dead zone; Let i be the set of synchronous generators in region i; Let T be the primary frequency regulation power of generator g at time τ; g K is the response constant of generator g; g U is the droop coefficient of generator g; g It is a 0-1 variable, indicating whether unit g is online; if so, it is 1.

[0199] In this embodiment, in the multi-region frequency dynamic algebraic expression acquisition module 002, the multi-region frequency dynamic algebraic expression is:

[0200]

[0201] In the formula, l s To divide the time range L of the frequency dynamic response into multiple segments, the length of each segment is given; i and j are both regions; for The column vector formed; B represents the Bernstein spline coefficients corresponding to the time-domain frequencies. m,k (τ) is an m-degree Bernstein polynomial; for The initial value of J; T This is the coefficient matrix of the Bernstein polynomial integral property; ΔP is the column vector of Bernstein spline coefficients corresponding to the total frequency modulation power in the time domain; i L,B This is the column vector of Bernstein spline coefficients corresponding to the disturbance power; This is the column vector of Bernstein spline coefficients corresponding to the frequency modulation power of the time-domain unit g; yes The initial value of Δf i DB,B dead zone value Δf i DB The vector formed by the vector; m is the order of the Bernstein polynomial; k = 0, 1, ..., m.

[0202] In this embodiment, the multi-region frequency security constraint construction module 003 includes: initial time frequency change rate constraint, frequency minimum point deviation constraint, quasi-steady-state frequency deviation constraint, and primary frequency modulation backup constraint.

[0203] The expression for the initial time frequency change rate constraint is:

[0204]

[0205] In the formula, RoCoF max This is the limit of the rate of change of frequency at the initial moment;

[0206] The expression for the frequency minimum point deviation constraint is:

[0207]

[0208] In the formula, V is the enhancement matrix of the inequality equation transformation, which is a constant matrix; Δf max This is the minimum frequency deviation limit;

[0209] The expression for the quasi-steady-state frequency deviation constraint is:

[0210]

[0211] In the formula, Δf ss,max The quasi-steady-state frequency deviation limit;

[0212] The expression for the primary frequency modulation reserve constraint is:

[0213]

[0214] In the formula, R g This is the frequency regulation reserve power for unit g.

[0215] In this embodiment, the objective function expression of the multi-regional frequency security constraint unit combination model in the multi-regional frequency security constraint unit combination model construction module 004 is:

[0216]

[0217] In the formula, Ω G Ω T Ω W Ω B These are collections of thermal power units, dispatch periods, wind power units, and busbars; U gt R is a 0-1 variable, representing whether unit g is online during time period t, where 1 indicates online and 0 indicates offline; gt This refers to the primary frequency regulation reserve power of unit g during time period t; These are the start-up and shutdown costs of unit g and the primary frequency regulation standby cost, respectively. c is the fuel cost of unit g during time period t; W and c B These represent the unit cost of wind curtailment and the cost of load shedding, respectively; ΔP wt Let w be the wind curtailment power of wind turbine w during time period t; Let be the load shedding power of bus b during time period t.

[0218] In this embodiment, in the multi-regional frequency security constraint unit combination model solving module 005, during the process of decomposing the mixed integer programming problem of the multi-regional frequency security constraint unit combination model into the main problem and the sub-problems through the adaptive two-level decomposition algorithm, the mixed integer programming problem is decomposed into the main problem and the sub-problems for iterative calculation through the Benders decomposition strategy and the adaptive frequency low point time estimation model; by solving the main problem, the unit start-up and shutdown and frequency regulation reserve allocation strategy is obtained; by solving the sub-problems, the multi-regional frequency security constraints are verified.

[0219] It should be noted that the information interaction and execution process between the modules of the above system are based on the same concept as the method embodiment in Embodiment 1 of this application, and the resulting technical effects are the same as those in the method embodiment of this application. For details, please refer to the description in the method embodiment shown above in this application, and it will not be repeated here.

[0220] Example 3

[0221] Embodiment 3 of the present invention provides a non-transitory computer-readable storage medium storing program code for a multi-region frequency security unit scheduling method based on Bernstein polynomials. The program code includes instructions for executing the multi-region frequency security unit scheduling method based on Bernstein polynomials of Embodiment 1 or any possible implementation thereof.

[0222] Computer-readable storage media can be any available medium that a computer can access, or a data storage device such as a server or data center that integrates one or more available media. The available medium can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media (e.g., solid-state drives, SSDs).

[0223] Example 4

[0224] Embodiment 4 of the present invention provides an electronic device, including: a memory and a processor;

[0225] The processor and the memory communicate with each other via a bus; the memory stores program instructions that can be executed by the processor, and the processor can execute the Bernstein polynomial-based multi-region frequency security unit scheduling method of Embodiment 1 or any possible implementation thereof by calling the program instructions.

[0226] Specifically, a processor can be implemented in hardware or software. When implemented in hardware, the processor can be a logic circuit, an integrated circuit, etc. When implemented in software, the processor can be a general-purpose processor that reads software code stored in memory. This memory can be integrated into the processor or located outside the processor and exist independently.

[0227] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable system. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means.

[0228] It is obvious to those skilled in the art that the modules or steps of the present invention described above can be implemented using general-purpose computing systems. They can be centralized on a single computing system or distributed across a network of multiple computing systems. Optionally, they can be implemented using program code executable by a computing system, thereby storing them in a storage system for execution by the computing system. In some cases, the steps shown or described can be performed in a different order than those presented herein, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the present invention is not limited to any particular combination of hardware and software.

[0229] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A multi-regional frequency-safe unit scheduling method based on Bernstein polynomials, characterized in that, include: Based on the dynamic primary frequency response of synchronous generators, governor dead zone, and optimal allocation of frequency regulation reserves, a multi-region frequency response model is constructed. The integral-differential algebraic equation of the multi-region frequency response model is approximated by Bernstein polynomials to obtain the algebraic expression of the multi-region frequency dynamics. Based on the algebraic expression of the multi-region frequency dynamics, construct multi-region frequency security constraints; The multi-regional frequency security constraints are embedded into the unit combination problem to construct a multi-regional frequency security constraint unit combination model. The multi-regional frequency response model based on the Bernstein polynomial approximation, the frequency change rate constraint, and the frequency minimum point deviation constraint do not need to consider the complete frequency dynamic segmentation; only the frequency dynamic segmentation before the frequency minimum point needs to be considered. The mixed-integer programming problem of the multi-region frequency security constrained unit combination model is decomposed into a main problem and sub-problems by using an adaptive two-level decomposition algorithm; by solving the main problem and the sub-problems, a multi-region frequency security unit scheduling scheme is obtained.

2. The multi-regional frequency safety unit scheduling method based on Bernstein polynomials according to claim 1, characterized in that, The expression for the multi-region frequency response model is: When the frequency deviation is less than the governor dead zone: ； ； When the frequency deviation is greater than the speed controller dead zone: ； ； ； ； ； In the formula, Let i be the total inertia of region i; For time in region i Frequency deviation; For time j in region j Frequency deviation; Let be the load damping ratio of region i; Let be the load power of region i; For time in region i Total primary frequency response power; Let be the disturbance power in region i; The set of regions connected to region i; The reactance of the tie line between region i and region j; For integration variables; The action dead zone value for region i; The critical point time of the governor's dead zone; Let i be the set of synchronous generators in region i; For at any time The primary frequency regulation power of generator g; Let g be the response constant of the generator; Let g be the droop coefficient of the generator; It is a 0-1 variable, indicating whether unit g is online; if so, it is 1.

3. The multi-regional frequency safety unit scheduling method based on Bernstein polynomials according to claim 2, characterized in that, The algebraic expression for the multi-region frequency dynamics is: ； ； ； ； ； ； In the formula, To divide the time range L of the frequency dynamic response into segments s, where each segment has a length of s; i and j are regions; for The column vector formed; These are the Bernstein spline coefficients corresponding to the time-domain frequencies; for The initial value; This is the coefficient matrix of the Bernstein polynomial integral property; This is the column vector of Bernstein spline coefficients corresponding to the total frequency modulation power in the time domain; This is the column vector of Bernstein spline coefficients corresponding to the disturbance power; This is the column vector of Bernstein spline coefficients corresponding to the frequency modulation power of the time-domain unit g; yes The initial value; dead zone value The vector formed by the vector; m is the order of the Bernstein polynomial; k=0,1…,m.

4. The multi-regional frequency safety unit scheduling method based on Bernstein polynomials according to claim 3, characterized in that, The multi-region frequency security constraints include: initial time frequency change rate constraint, frequency minimum point deviation constraint, quasi-steady-state frequency deviation constraint, and primary frequency modulation reserve constraint; The expression for the initial time frequency change rate constraint is: ； In the formula, This is the limit of the rate of change of frequency at the initial moment; The expression for the frequency minimum point deviation constraint is: ； In the formula, It is the enhancement matrix for the transformation of inequality equations, and it is a constant matrix; This is the minimum frequency deviation limit; The expression for the quasi-steady-state frequency deviation constraint is: ； In the formula, The quasi-steady-state frequency deviation limit; N is the number of regions; The expression for the primary frequency modulation reserve constraint is: ； In the formula, This is the frequency regulation reserve power for unit g.

5. The multi-regional frequency safety unit scheduling method based on Bernstein polynomials according to claim 4, characterized in that, The objective function expression for the multi-regional frequency security-constrained unit combination model is: ； In the formula, , , , These are collections of thermal power units, dispatch periods, wind power units, and busbars, respectively. The variable is 0-1, indicating whether unit g is online during time period t, where 1 means online and 0 means offline; This refers to the primary frequency regulation reserve power of unit g during time period t; , These are the start-up and shutdown costs of unit g and the primary frequency regulation standby cost, respectively. Let g be the fuel cost of unit g during time period t; and These are the unit cost of wind curtailment and the cost of load shedding, respectively. Let w be the wind curtailment power of wind turbine w during time period t; Let be the load shedding power of bus b during time period t.

6. The multi-regional frequency safety unit scheduling method based on Bernstein polynomials according to claim 5, characterized in that, In the process of decomposing the mixed integer programming problem of the multi-region frequency security constraint unit combination model into the main problem and the sub-problems through the adaptive two-level decomposition algorithm, the mixed integer programming problem is decomposed into the main problem and the sub-problems through the Benders decomposition strategy and the adaptive frequency low point time estimation model for iterative calculation. By solving the main problem, the unit start-up and shutdown and frequency regulation reserve allocation strategies are obtained; By solving the aforementioned sub-problems, the frequency security constraints of multiple regions are verified.

7. A multi-regional frequency safety unit scheduling device based on Bernstein polynomials, employing the multi-regional frequency safety unit scheduling method based on Bernstein polynomials as described in any one of claims 1-6, characterized in that... include: The multi-region frequency response model construction module is used to construct a multi-region frequency response model based on the dynamic primary frequency regulation response of the synchronous generator, the governor dead zone, and the optimal allocation of frequency regulation reserve. The module for obtaining the algebraic expression of the multi-region frequency dynamics is used to approximate the integral-differential algebraic equation of the multi-region frequency response model using Bernstein polynomials to obtain the algebraic expression of the multi-region frequency dynamics. A multi-region frequency security constraint construction module is used to construct multi-region frequency security constraints based on the algebraic expression of the multi-region frequency dynamics. A multi-regional frequency security constraint unit combination model construction module is used to embed the multi-regional frequency security constraints into the unit combination problem and construct a multi-regional frequency security constraint unit combination model. The multi-region frequency security constraint unit combination model solution module is used to decompose the mixed integer programming problem of the multi-region frequency security constraint unit combination model into a main problem and sub-problems through an adaptive two-level decomposition algorithm; and to obtain a multi-region frequency security unit scheduling scheme by solving the main problem and the sub-problems.

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