Power system node frequency space-time difference mechanism analysis and frequency protection correction method

Abstract

The invention discloses an electric power system node frequency space-time difference mechanism analysis and frequency protection correction method, relates to the technical field of electric power system frequency protection, and is used for solving the problems that an existing single-machine theory cannot reflect frequency space-time characteristics, a multi-machine theory lacks time domain analysis of frequency dynamic response, and mechanism explanation of the system frequency space-time characteristics cannot be realized. The method comprises the following steps: firstly, establishing a two-region equivalent frequency response model, enabling a high-order model to be equivalent to a combination of typical low-order systems, realizing model decoupling by adopting a vibration mode analysis method, and carrying out analytical solution; secondly, analyzing to obtain a maximum value expression of the frequency deviation and the frequency change rate ROCOF of each region; and finally, proposing an action value correction strategy in frequency protection control according to the frequency deviation, the occurrence moment of the ROCOF maximum value and the numerical value difference. According to the method, the fine time domain solution of all three frequency components containing different frequencies or oscillation forms is realized, the analysis precision is improved, and the problem of precise time domain analysis of a two-region high-order model is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of power system frequency protection, and particularly to a method for analyzing the spatio-temporal difference mechanism of node frequencies in a power system and correcting frequency protection. Background Art

[0002] In traditional power systems, the distribution of frequency regulation resources is relatively uniform, the frequency changes of each node are gentle and the differences are small, and the system frequency can be characterized by the inertial center frequency. However, with the increase in the penetration rate of new energy, the spatial distribution of frequency regulation resources such as system inertia and primary frequency regulation reserve becomes more differentiated, and the output of new energy units such as wind and light is volatile, resulting in obvious spatio-temporal distribution characteristics in the dynamic response of the system frequency during large-scale disturbances. In order to more accurately describe the dynamic changes of the system frequency, it is necessary to conduct targeted modeling and calculation of the system to reflect the spatio-temporal distribution characteristics, so as to achieve better control and protection of the system.

[0003] Currently, the commonly used methods for calculating the system frequency response are numerical simulation method and analytical method. Since the influence of the grid structure needs to be considered when calculating the spatio-temporal distribution characteristics of frequencies at different nodes, the larger the scale of the power grid and the more complex the grid structure, the system coupling and the difficulty of analysis will increase linearly. Therefore, the mainstream solutions mostly adopt the numerical simulation method. The numerical simulation method can adapt to the calculation of the frequency response characteristics of various complex network nodes and has high accuracy, but it cannot explain the mechanism of the spatio-temporal distribution characteristics of frequencies, which is not conducive to summarizing the general laws of the spatio-temporal distribution characteristics of the system frequency, and there are certain limitations.

[0004] For the analytical method, there are two types: analytical based on a single-machine model and analytical based on a multi-machine model. Currently, the most studied is the analytical based on a single-machine model. Although the single-machine model and its analysis can quickly calculate the average frequency response characteristics of the system, due to its high aggregation and ignoring the influence of tie lines, it cannot show the spatial distribution characteristics of frequencies. For the analysis based on a multi-machine model, there is a problem that it is difficult to solve the characteristic roots of high-order model parameters.

[0005] In summary, the existing single-machine theory cannot reflect the spatio-temporal characteristics of frequencies, while although some of the multi-machine theories can directly obtain the frequency curves with spatio-temporal distribution characteristics, they lack the time-domain analysis of the frequency dynamic response and cannot achieve the mechanism explanation of the spatio-temporal characteristics of the system frequency. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for analyzing the spatio-temporal difference mechanism of node frequencies in a power system and correcting frequency protection, which is used to solve the problems that the existing single-machine theory cannot reflect the spatio-temporal characteristics of frequencies, and the multi-machine theory lacks the time-domain analysis of the frequency dynamic response and cannot achieve the mechanism explanation of the spatio-temporal characteristics of the system frequency.

[0007] The technical solution adopted by the present invention to solve its technical problems is: a method for analyzing the spatio-temporal difference mechanism of the node frequency in a power system and correcting frequency protection, including the following steps:

[0008] S1. Construct an equivalent frequency response model for two regions

[0009] Based on the typical aggregated single-machine SFR model, by analyzing the power flow characteristics between regions, establish a frequency response model for a two-region interconnected system;

[0010] S2. Reducing the order and decoupling of the equivalent frequency response model for two regions

[0011] By cracking the closed-loop feedback and equivalent substitution, the high-order frequency response model is equivalent to a combination of typical low-order systems, and the modal analysis method is used to achieve model decoupling, and then time-domain analysis and solution are carried out;

[0012] S3. Solve the expressions for the maximum values of the frequency deviation and ROCOF in each region

[0013] Through the mathematical analysis of the regional frequency analytical formula and combining with the typical parameter value range of the power system, the expressions for the maximum values of the frequency deviation and the rate of change of frequency ROCOF in each region are obtained by analysis;

[0014] S4. According to the occurrence time and numerical difference of the frequency deviation and the maximum value of ROCOF, propose an action value correction strategy in frequency protection control.

[0015] Further, in step S1, the matrix equation of the equivalent frequency response model for two regions is In the formula, H is the system inertia time constant matrix, D is the system damping coefficient matrix, K is the system node admittance parameter matrix, ΔP d is the system load power change matrix, ΔP M is the system unbalanced acceleration power matrix, Δδ is the system phase angle change matrix, Δf is the system frequency change matrix, s is the complex variable in the Laplace transform, ω 0 is the rated angular velocity;

[0016] In the formula, H i is the inertia time constant of the equivalent generator in region i, D i is the equivalent damping coefficient in region i, F Hi is the high-pressure cylinder work ratio of the prime mover in region i, T Ri is the reheat time constant of the prime mover in region i, R i is the droop coefficient in region i, ΔP di is the load jump power in region i, Δf i is the frequency change amount in region i.

[0017] Furthermore, in step S1, the active power meters output by each region are P Gi is the active power output by the generator in region i, E qi is the internal node voltage of the equivalent generator in the region, Y 12 is the mutual admittance between the equivalent nodes of the two regions, G ii is the self-conductance of the equivalent node in region i, φ is the mutual admittance angle between the equivalent nodes of the two regions; Δδ = δ 1 -δ 2 δ i is the internal phase angle of the equivalent generator in the region; simplify Equation (3) to ΔP G is the system active output matrix, Δδ is the phase angle change matrix, ΔP G1 is the change in the active power output of region one, ΔP G2 is the change in the active power output of region two, Δδ 1 is the phase angle change in region one, Δδ 2 is the phase angle change in region two; ΔP G =[ΔP G1 ,ΔP G2 T ,Δδ = [Δδ 1 ,Δδ 2 T , where The initial phase angle of the system is δ 10 and δ 20 , Δδ 0 =δ 10 -δ 20 ; In the high-voltage power grid line, the resistance of the line is much smaller than the reactance, and the ground conductance is usually ignored. Therefore, φ = π, and further simplify Equation (4) to where k = E q1 E q2 |B 12 |(7), B 12 is the mutual susceptance between the equivalent nodes of the two regions; for the single machine equivalent to region i, the rotor motion equation is where ΔP Mi is the unbalanced accelerating power of region i, ΔP Gi is the external input power of region i; substitute ΔP Gi in Equation (6) into Equation (8) and obtain Equation (1) in matrix form.

[0018] Furthermore, in step S2, split ΔP M into the sum of a proportional link and a first-order inertia. The proportional link part is combined with the damping matrix D to form an equivalent damping matrix D', that is ​​Adopt the method of closed-loop substitution, and use the center frequency ΔF in the ASF model after aggregating two regions to replace Δf i , After further organizing the two regions, we get In the formula, X are the aggregated three parameters of H, D, and R -1 l i is the conversion factor of region i, S i is the total rated capacity of the generators in region i, S B is the power base value of region i; After order reduction, equation (1) becomes In the formula,

[0019] Furthermore, in step S2, use the modal matrix to transform the phase angle change matrix Δδ in natural coordinates into the modal matrix y in modal coordinates, and decouple the motion equation; specifically: First, assume that the system is viscous damping. According to equation (12), its vibration mode equation is (K - λ 2 H)Φ = 0 (14); In the formula, Φ = [J 1 , J 2 is the eigenvector matrix of equation (12), J 1 and J 2 are eigenvectors, and λ is the eigenvalue; The eigenvalue is obtained from equation (14) as The corresponding eigenvector is (16); Second, establish the connection between Δδ in natural coordinates and the principal coordinates y = [y 1 , y 2 T through Φ, that is, Δδ = Φy (17); In the formula, y 1 and y 2 are two vibration modes; Finally, substitute equation (17) into equation (12) and pre-multiply by the transpose matrix Φ T of Φ to get Φ T HΦys 2 + Φ T DΦys + Φ T KΦy = ω 0 Φ T ΔP F + ω 0 Φ T ΔP d (18), After organizing, its time-domain equation is In the formula, M is a diagonal matrix containing the inertia constants of each region, C is a matrix composed of damping coefficients and inertia constant synthesis coefficients, Z is a diagonal matrix composed of inertia constants and node admittance combination coefficients, and F(t) is a column vector of unbalanced accelerating power and disturbance power Expand equation (19) to get ​At this time, the equation changes from a two-degree-of-freedom vibration equation to two single-degree-of-freedom vibration equations, achieving decoupling.

[0020] Furthermore, in step S2, the steps of time-domain analytical solution are as follows: Solve using the idea of the two-machine aggregated SFR model Using the superposition theorem, in ΔP F and ΔP d When the two excitation forces act alone, solve them separately to obtain and Then add them to get The time-domain analytical expression of the equivalent frequency response model of the two regions is obtained as Furthermore, the steps to solve y 1 are as follows: Aggregate the equivalent frequency response model of the two regions into a low-order simplified SFR model, and the transfer function is: In the formula, ω n1 is the natural oscillation angular frequency of mode y 1 , is the damping coefficient of mode y 1 ; Perform the inverse Laplace transform on equation (23) to obtain ω r1 is the damped oscillation angular frequency of mode y 1 ,

[0021] α is the coefficient of the decaying oscillation term, In the formula, is the initial phase angle of the derivative of mode y1.

[0022] Furthermore, the steps to solve are as follows: First, perform the inverse Laplace transform when ΔP d acts alone, In the formula, Φ ij is the element in the transformation matrix Φ, ω n2 is the natural oscillation angular frequency of mode y 2 , ζ is the damping coefficient of mode y 2 , ω r2 is the damped oscillation angular frequency, and perform the inverse Laplace transform on equation (27) to obtain Then solve when ΔP F acts alone in equation (21), Simplify equation (30) to In the formula, M is the common factor extracted by factorization, A is the coefficient of the s term in the numerator of the factor containing ω n1 after factorization, B is the constant term coefficient in the numerator of the factor containing ω n1 after factorization, C is the coefficient of the factor containing ω after factorizationn2 The coefficient of the s-term in the factored numerator, and D is the coefficient of the constant term in the factored numerator containing ω after factorization. Let n2 The coefficient of the constant term in the factored numerator. Let Taking the inverse Laplace transform of Equation (31), we have

[0023] where ρ 1 is the amplitude of the oscillation of the factor Y 1 (t), and ρ 2 is the amplitude of the oscillation of the factor Y 2 (t). is the initial angle of the combined trigonometric function of the factor Y 1 (t), and is the initial angle of the combined trigonometric function of the factor Y 1 (t). Combining the above equations, we get where γ 1 is the amplitude of the factor with ω 2F as the damped angular frequency in the derivative of the modal component y r1 , and γ 2 is the amplitude of the factor with ω 2F as the damped angular frequency in the derivative of the modal component y r2 .

[0024] Furthermore, in step S3, the maximum value of ROCOF is calculated as follows: The maximum moment of ROCOF in the disturbed opposite region is is the offset angle after differentiation; for the disturbed region i, the maximum value of ROCOF appears at the initial moment of the disturbance; for the opposite region 3 - i, the maximum value of ROCOF appears at the moment shown in Equation (38); the maximum values of the two are (39), ROCOF imax is the maximum ROCOF value of region i, and ROCOF (3-i)max is the maximum ROCOF value of region 3 - i; is the offset angle after differentiation.

[0025] Furthermore, in step S3, the calculation method of the maximum frequency offset is as follows: The extreme point t COI of Δf COI and the extreme point t di of Δf di are where k is a non - negative integer. Let t COI = t di we get (41), k * is the non - negative constant that satisfies t COI = t di condition, and k* After rounding down, there is [k * , and at this time, there is: The maximum frequency offsets of each region are respectively

[0026]

[0027] Δf i (t 1 ) is the frequency change amount of region i at time t 1 , Δf i (t 2 ) is the frequency change amount of region i at time t 2 , Δf i (t 3 ) is the frequency change amount of region i at time t 3 , Δf 3-i (t 1 ) is the frequency change amount of region 3 - i at time t 1 , Δf (3-i) (t 2 ) is the frequency change amount of region 3 - i at time t 2 , Δf (3-i) (t 3 ) is the frequency change amount of region 3 - i at time t 3 .

[0028] Furthermore, in step S4, the correction strategy is: for the maximum frequency offset, substitute the time of equation (42) into equation (22) for comparison, and take its maximum or minimum value according to different perturbations; when the perturbation is positive, that is, ΣΔP di > 0, multiply the maximum frequency deviation by 1.1 - 1.2 times the sensitivity, and then superimpose the initial frequency f N as the frequency upper limit f max of this region; when the perturbation is negative, that is, ΣΔP di < 0, multiply the maximum frequency deviation by 1.1 - 1.2 times the sensitivity, and then superimpose the initial frequency f N as the frequency lower limit f min of this region, that is For frequency protection with the frequency change amount as the threshold, the perturbations are divided into: ① the perturbation occurs in the low - inertia H i_l region, ② the perturbation occurs in the high - inertia H i_h region; for the low - inertia H il region, take the absolute value of the value at time 0 + of ① according to equation (39), and multiply it by 1.1 - 1.2 times the sensitivity as the maximum frequency change rate limit K Hi_l of this region; for the high - inertia Hih Region, according to formula (39), for 0 of ① + moment and t of ② max The values at the moment are compared, and the value with the larger absolute value in formula (39) is taken, and multiplied by a sensitivity of 1.1 - 1.2 times as the maximum frequency change rate limit K of this region Hi_h , that is

[0029] The beneficial effects of the present invention are as follows: According to the generator electromagnetic equation and the rotor motion equation, combined with the network parameter model, the present invention establishes an inter-region frequency response model; by adopting closed-loop equivalent substitution and mode analysis, the order reduction of the power grid frequency control system and the decoupling between frequency components are realized. Further, according to the superposition theorem and the equivalent aggregation idea, the precise time-domain solution of all three frequency components including different frequencies or oscillation forms is realized, the analysis accuracy is improved, and the problem of precise time-domain analysis of the two-region high-order model is solved. According to the solved two-region frequency response analytical formula, the frequency response characteristics of the two regions are analyzed, the spatio-temporal distribution characteristics of the maximum values of frequency deviation and ROCOF and the relevant expressions are obtained, and based on this conclusion, the action value correction strategy of the system frequency protection is proposed. Brief Description of the Drawings

[0030] Figure 1 is the system diagram of two interconnected regions;

[0031] Figure 2 is the Y-type equivalent circuit diagram;

[0032] Figure 3 is the Δ-type equivalent circuit diagram;

[0033] Figure 4 is the single-machine SFR model diagram;

[0034] Figure 5 is the two-region interconnected equivalent frequency response model diagram;

[0035] Figure 6 is for model order reduction processing Figure 1 ;

[0036] Figure 7 is for model order reduction processing Figure 2 ;

[0037] Figure 8 is for ΔP F The solution idea diagram when acting alone;

[0038] Figure 9 is the numerical simulation diagram of typical values;

[0039] Figure 10 is the frequency over-limit detection flow chart. Specific Embodiments

[0040] In the present invention, first, an equivalent frequency response model of two regions is established. By cracking the closed-loop feedback and equivalent substitution, the high-order model is equivalent to a combination of typical low-order systems, and the modal analysis method is used to achieve model decoupling, and then analytical solutions are obtained, solving the problem that high-order systems cannot be analytically solved. Secondly, through the mathematical analysis of the regional frequency analytical formula and combining with the typical parameter value range of the power system, the maximum value expressions of the frequency deviation and the rate of change of frequency (ROCOF) in each region are analytically obtained, and the conclusion and corresponding mechanism explanation of the spatio-temporal difference in the frequency deviation and ROCOF in different regions are obtained and discussed. Furthermore, according to the time and numerical differences in the occurrence moments of the frequency deviation and the maximum value of ROCOF, an action value correction strategy is proposed in frequency protection control. The method of the present invention specifically includes the following contents:

[0041] S1. Construct an equivalent frequency response model of two regions.

[0042] To characterize the spatio-temporal characteristics of the multi-region frequency, based on the typical aggregated single-machine SFR model, by analyzing the power flow characteristics between regions, a frequency response model of the two-region interconnected system is established, providing a basis for subsequent solving the analytical expression of the two-region frequency response and analyzing the spatio-temporal distribution characteristics.

[0043] (1) Regional interconnected equivalent model

[0044] The two interconnected regional systems are as Figure 1 shown in the figure. In the figure, E qi is the internal node voltage of the regional equivalent generator, δ i is the internal phase angle of the regional equivalent generator, U i and θ i are the voltage phase angles of the two-region interconnected ports respectively. Figure 1 The system shown can be equivalent to Figure 2 the Y-type equivalent circuit shown, and through the Y-Δ transformation, it becomes Figure 3 the Δ-type equivalent circuit shown. Let the self-admittance and mutual admittance between regions be In the formula, Y ii is the self-admittance of the equivalent node of region i, Y 12 is the mutual admittance between the equivalent nodes of the two regions, G ii is the self-conductance of the equivalent node of region i, B ii is the self-susceptance of the equivalent node of region i, G 12 is the mutual conductance between the equivalent nodes of the two regions, B 12 is the mutual susceptance between the equivalent nodes of the two regions, φ i is the self-admittance angle of the equivalent node of region i, φ is the mutual admittance angle between the equivalent nodes of the two regions, y i0 is the shunt admittance to the ground on the i side of the node of the Δ-type equivalent circuit, y 12is the admittance between two nodes of the Δ-type equivalent circuit, j is the imaginary unit of the complex coordinate, and the value of i is 1 and 2. The electric power output by the two regions satisfies the power flow equation P Gi +jQ Gi =E qi ∑Y ij E qj i=1,2(2), where P Gi is the active power output by the generator in region i, Q Gi is the active and reactive power output by the generator in region i, Y ij is the self-admittance Y ii or the mutual admittance Y 12 .

[0045] Let Δδ=δ 1 -δ 2 , substitute it into equation (2) and retain the real part, and the expression of the active power output by each region is obtained as The initial phase angles of the system are δ 10 and δ 20 . Linearize at the system operating point, δ 1 =δ 10 , δ 2 =δ 20 , Δδ 0 =δ 10 -δ 20 . Simplify the above formula to where Both ΔP G and Δδ are two-dimensional column vectors, ΔP G =[ΔP G1 ,ΔP G2 T , Δδ=[Δδ 1 ,Δδ 2 T . ΔP G is the active power output matrix of the system, ΔP G1 is the change in the active power output of region one, ΔP G2 is the change in the active power output of region two, Δδ is the system phase angle change matrix, Δδ 1 is the change in the phase angle of region one, Δδ 2 is the change in the phase angle of region two; k 11 , k 12 , k 21 , k 22 are the elements in the constant coefficient transformation matrix of ΔP G and Δδ, k 11 is the parameter value of the first row and first column of the matrix, k 12 is the parameter value of the first row and second column of the matrix, k 21 is the parameter value of the second row and first column of the matrix, k​​22 It is the parameter value of the second row and second column of the matrix.

[0046] In the high-voltage power grid line, since the resistance of the line is much smaller than the reactance and the ground conductance is usually ignored, thus G 12 = 0, φ = π, and Equation (4) is further simplified to In the formula, k = E q1 E q2 |B 12 | (7).

[0047] (2) Interconnected area frequency response model

[0048] All the generating units in a region can be approximately equivalent to a single-machine model that reflects the average frequency response characteristics, that is, the single-machine SFR model. Its frequency control block diagram is as Figure 4 shown. H i is the inertia time constant of the equivalent generator in Region i, D i is the equivalent damping coefficient in Region i, F Hi is the working ratio of the high-pressure cylinder of the prime mover in Region i, T Ri is the reheat time constant of the prime mover in Region i, R i is the droop coefficient in Region i. The aggregation equations for each parameter are: X i = ∑ m∈Vi k im X im (8); In the formula, X i is the partial frequency modulation parameter of the equivalent generator after aggregation in Region i, X im is the partial frequency modulation parameter of the m-th generator in Region i, that is, F Him is the working ratio of the high-pressure cylinder of the prime mover of the m-th generator in Region i, T Rim is the reheat time constant of the prime mover of the m-th generator in Region i, H im is the inertia time constant of the m-th generator in Region i, D im is the damping coefficient of the m-th generator in Region i, R im is the droop coefficient of the m-th generator in Region i, s is the complex variable in the Laplace transform. k im and l im are the conversion factors of different parameters in Region i. S im is the rated capacity of the m-th generator in Region i.

[0049] For the single machine equivalent to Region i, the low-order SFR model shown in Figure 4 is adopted to characterize the frequency response of this region. Its rotor motion equation is where, ΔP Mi is the unbalanced accelerating power of area i, ΔP di is the load jump power of area i, ΔP Gi is the external input power of area i, Δf i is the frequency change of area i, ω 0 is the rated angular velocity.

[0050] Substitute ΔP Gi in Equation (6) into Equation (11) and represent it in matrix form, the matrix equation of the equivalent frequency response model of the two - area is obtained as The corresponding equivalent frequency response control block diagram of the two - area interconnection is as Figure 5 shown. Where, H is the system inertia time constant matrix, D is the system damping coefficient matrix, K is the system node admittance parameter matrix, ΔP d is the system load power change matrix, ΔP M is the system unbalanced accelerating power matrix.

[0051] So far, the equivalent frequency response model of the two - area has been established. Due to the existence of multiple closed - loops, the system is a high - order complex system, and it is difficult to solve the time - domain expression through traditional factorization combined with the inverse Laplace transform. And as Figure 5 shown by the red line, due to the interaction of factors such as power flow between areas, the coupling effect between Δf 1 and Δf 2 makes it difficult to solve for Δf = f(t). To solve the problem of solving the above high - order and highly coupled model, the method of equivalent closed - loop decomposition and mode - shape analysis is used to solve the problems of system order reduction and decoupling, and the time - domain solution of the model parameter expression is obtained through the method of variable separation and equivalent aggregation.

[0052] S2. Reduction and decoupling of the equivalent frequency response model of the two - area

[0053] S2.1. Model order reduction

[0054] S2.1.1. First, split ΔP M into the sum of a proportional link and a first - order inertia. The proportional link part is combined with the damping matrix D to form an equivalent damping matrix D', that is Its transformed form is as Figure 6 shown.

[0055] S2.1.2. Since ΔP fi contains a first - order inertia link and has the property of a low - pass filter. Although the multi - area frequency response Δf i contains higher - order harmonics, for the feedback power value ΔP fiAnd the impact on the regional response is very small, so the closed-loop substitution method is adopted to break Δf i and ΔP i control closed-loop, and use the center frequency ΔF in the ASF model aggregated by two regions to replace Δf i , and its simplified equivalent schematic diagram is as shown in Figure 7 shown, the expression of ΔF is In the formula, each parameter is still aggregated according to formulas (8) and (9), and further sorted out for the two regions to get In the formula, X is the aggregated H, D, R -1 three parameters, l i is the conversion factor of region i, S i is the total rated capacity of the generators in region i, S B is the power base value of region i. After processing, formula (12) becomes In the formula, S2.2. Transformation and decoupling. The above processing reduces the order of formula (17) to 6th order, and it becomes a combination of typical first- and second-order links, and the complexity in form is reduced, but the coupling problem between Δf 1 and Δf 2 is still not solved, and it is still difficult to solve by direct solution. Formally, formula (17) is a vibration equation of two degrees of freedom with damping and excitation force, so the modal analysis method is adopted for processing. Its essence is to use the modal matrix to transform the phase angle change matrix Δδ in the natural coordinates into the modal matrix y in the modal coordinates and realize the decoupling of the motion equation.

[0056] S2.2.1. First, assume that the system is viscous damping, so ignore the damping and force to solve the eigenvalues and eigenvectors. According to formula (17), its vibration mode equation is (K - λ 2 H)Φ = 0 (19). In the formula, Φ = [J 1 , J 2 , which is the eigenvector matrix of formula (17), J 1 and J 2 are eigenvectors, and λ is the eigenvalue. The eigenvalues are obtained from formula (19) as The corresponding eigenvectors are

[0057] S2.2.2. According to the transformation relationship, Δδ in the natural coordinates and the principal coordinates y = [y 1 , y 2 T are related through Φ, that is, Δδ = Φy (22). In the formula, y 1 and y 2 are two vibration modes.

[0058] ​S2.2.3. Substitute the transformation formula (22) into Equation (17) and pre-multiply by the transpose matrix Φ of Φ T to obtain Φ T HΦys 2 + Φ T DΦys + Φ T KΦy = ω 0 Φ T ΔP F + ω 0 Φ T ΔP d (23). After rearrangement, its time-domain equation is where M is a diagonal matrix containing the inertia constants of each region, C is a matrix of the combined coefficients of the damping coefficient and the inertia constant, Z is a diagonal matrix of the combined coefficients of the inertia constant and the nodal admittance, and F(t) is a column vector of the unbalanced accelerating power and the disturbance power. In the formula,

[0059] It can be seen from Equation (25) that C is a non-diagonal matrix, and there is still coupling between y 1 and y 2 , which does not conform to the initial assumption that the system is viscous damping, i.e., C = εM + ηZ. In this case, it is impossible to continue solving for y 1 and y 2 . However, if the system satisfies D 1 ' / 2H 1 = D 2 ' / 2H 2 , then C in Equation (25) is a diagonal matrix, and the assumption holds at this time. Equation (24) can also be decoupled. In an actual large power system, the damping is generally evenly distributed, and this condition naturally holds in most cases. Therefore, the decoupling problem of y 1 and y 2 is solved. Expand (24) under this condition to obtain Equation (26)

[0060] It can be seen that the equation at this time changes from the previous two-degree-of-freedom vibration equation to two single-degree-of-freedom vibration equations, and y 1 and y 2 can be solved separately, and the coupling problem is solved.

[0061] S2.3. Time-domain analytical solution

[0062] The variables y 1 and y 2 in Equation (26) are decoupled, enabling separate solutions for each of them, and further obtaining the analytical expressions of Δδ 1 and Δδ 2 . To solve for Δf 1 and Δf2 For the expression, according to Equations (11) and (22), Therefore, Δf i The expression of and is obtained by solving

[0063] S2.3.1. Solve

[0064] The first equation of Equation (26) is formally the same as the ASF model. Therefore, the idea of the two-machine aggregated SFR model is adopted for solution. In this way, the two-region equivalent frequency response model is aggregated into a low-order simplified SFR model, and the transfer function is: ω n1 is the natural oscillation angular frequency of mode y 1 , and is the damping coefficient of mode y 1 . Taking the inverse Laplace transform of Equation (27), ω r1 is the damped oscillation angular frequency of mode y 1 , and α is the coefficient of the decaying oscillation term. In the formula, is the initial phase angle of the derivative of mode y1.

[0065] S2.3.2 Solve

[0066] The second equation in Equation (26) is relatively complex. Using the superposition theorem, when the two excitation forces ΔP F and ΔP d act alone, they are solved separately to obtain and , and then added together to obtain

[0067] S2.3.2.1. First, when ΔP d acts alone, take the inverse Laplace transform. Let Φ ij be the element in the transformation matrix Φ. In the formula, ω n2 is the natural oscillation angular frequency of mode y 2 , ζ is the damping coefficient of mode y 2 , and ω r2 is the damped oscillation angular frequency. Taking the inverse Laplace transform of Equation (31) gives

[0068] S2.3.2.2. Then, solve Equation (26) when ΔP F acts alone.

[0069] S2.3.2.3. By combining equations (15) and (18), it can be seen that the order of equation (34) is 6. Therefore, there are 6 factor terms, and it is difficult to solve directly. Observing the part of the equation with summation and the fact that the equation contains the expression of the center frequency of the ASF model, whose form is similar to that for solving the SFR model, the idea of aggregating the SFR model is adopted. As Figure 5 shown, this makes equation (34) contain only 2 pairs of conjugate factors, reducing the order of the equation and thus greatly simplifying the calculation. In the formula, Therefore, equation (34) is simplified to

[0070] In the formula, M is the common factor extracted by factorization, A is the coefficient of the s term in the numerator of the factor containing ω n1 after factorization, B is the coefficient of the constant term in the numerator of the factor containing ω n1 after factorization, C is the coefficient of the s term in the numerator of the factor containing ω n2 after factorization, and D is the coefficient of the constant term in the numerator of the factor containing ω n2 after factorization. Equation (36) simplifies the fourth-order expression into the form of the sum of two second-order factors. Now, solve the two second-order factors separately. Let Taking the inverse Laplace transform of equation (36) gives In the formula, ρ 1 is the oscillation amplitude of the factor Y 1 (t), ρ 2 is the oscillation amplitude of the factor Y 2 (t), is the initial angle of the composite trigonometric function of the factor Y 1 (t), is the initial angle of the composite trigonometric function of the factor Y 1 (t). Combining the above equations, we get In the formula, γ 1 is the amplitude of the factor with ω 2F as the damping angular frequency in the derivative of the modal component y r1 , and γ 2 is the amplitude of the factor with ω 2F as the damping angular frequency in the derivative of the modal component y r2 .

[0071] So far, the two components of and have both been solved. In summary, Obtain the time-domain analytical expression of the equivalent frequency response model of the two regions: Equation (43) completes the parameter analytical expressions of Δf in the two regions 1 and Δf 2 in their respective time domains, characterizing the frequency dynamic characteristics of the interconnected system of the two regions from the overall levels of the two regions respectively, which is of great significance for the analysis of the generation mechanism and engineering utilization of the frequency spatio-temporal distribution characteristics of the two regions.

[0072] S3. Solve the expressions for the maximum values of the frequency deviation and ROCOF in each region

[0073] So far, the time-domain analytical formula of the equivalent frequency response model of the two regions has been obtained. Next, it is analyzed at the time-domain level. By means of mathematical derivation and combined with the typical value range, the spatio-temporal distribution differences of the maximum frequency deviation and the maximum ROCOF are obtained, the relevant expressions for the occurrence time and magnitude of the frequency deviation and the maximum ROCOF in different regions are given, and a corrected strategy for frequency-related protection is proposed accordingly.

[0074] S3.1 Time-domain analysis of ROCOF

[0075] It can be seen from Equation (43) that the frequency responses of the two regions have a symmetric form, and their frequency responses are superimposed with a certain oscillation frequency on the basis of the system center frequency. Although the oscillation frequency is relatively complex in form and is the superposition of multiple decaying sine functions, the periods of the oscillation frequencies of the two regions are the same, the oscillation directions are opposite, and the oscillation amplitude is inversely proportional to the equivalent moment of inertia of each region. Now let the three frequency components in Equation (43) be respectively where Δf COI is the system inertia center frequency, and Δf di is the frequency component related to region i and mode y 2d and Δf Fi is the frequency component related to region i and mode y 2F respectively.

[0076] When a disturbance occurs in region i, for this disturbed region i, the signs before Δf COI and Δf di and Δf Fi are the same, while for the opposite region 3 - i, the signs before Δf COI and Δf d(3-i) and Δf F(3-i) are opposite, which makes the frequency responses of the two regions in the early stage quite different. Therefore, taking the occurrence of a disturbance in region two as an example, the ROCOF and the maximum frequency deviation are analyzed.

[0077] From Equation (44), we get where is the offset angle after differentiation. ΔfFi The expression is complex and difficult to directly perform mathematical analysis. Therefore, a method combining numerical simulation is adopted for analysis. The numerical simulation of its typical value is as Figure 8 shown. Combining with the image, it can be seen that within the initial period, the derivative of Δf Fi is much smaller than the derivative of Δf di and its influence on ROCOF is extremely small, so it can be ignored. For the derivative of the inertial center frequency Δf According to the existing research, the maximum value of ROCOF of the inertial center frequency of the system appears at the initial moment of the disturbance. COI of

[0078] For and According to Equation (45), it is known that and is an increasing function of ξ. According to Equation (32), it can be known that ξ = 0.5σλ 2 -1 , where σ = 0.5H -1 (D + F H R -1 ) is less than 2 within the typical parameter value range of the generator. And since ω 0 = 2πf N , f N is the rated frequency of the system. Therefore, within the typical parameter value range ξ >> 1, is close to -π / 2, and we get Equation (47) both reaches the maximum value at the initial moment.

[0079] According to the above analysis, when the disturbance occurs in Region 2, at the initial moment and have the same sign, and both of them take the maximum modulus value at the initial moment. Therefore, the maximum value of ROCOF in Region 2 appears at the initial moment. In the region on the opposite side of the disturbance occurrence, at the initial moment and have opposite signs. According to formula (45), we get the initial moment change rate and the initial moment change rate of is

[0080] It can be seen that the ROCOF at the initial moment in Region 1 is 0. Obviously, the moment when the maximum value of ROCOF in Region 1 appears is not the initial moment. Since and both contain exponential decay terms. According to Equations (29) and (31), it can be known that ω n2 >> ω​n1 For the exponential part, , within the typical value range, this ratio is close to 1, so the exponential decay rates of the two are not very different. For the trigonometric function part, the change period T 1 >>T 2 , so the change speed is much less than In summary, it can be seen that the change of ROCOF in the early stage is mainly affected by . Due to the existence of the decay factor, the maximum value of ROCOF in Region 1 must appear in the first oscillation period of . Approximately taking the first peak moment, that is,

[0081] is the moment of the maximum value of ROCOF in this region. The moment of the maximum value of ROCOF in the region on the opposite side of the disturbance is ROCOF imax is the maximum ROCOF value in Region i, and ROCOF (3-i)max is the maximum ROCOF value in Region 3 - i.

[0082] S3.2, Time - domain Analysis of the Maximum Frequency Deviation

[0083] The traditional method obtains its maximum frequency deviation and the occurrence moment by solving the extreme points of Equation (44). From Equation (45), it can be seen that its differential equation is a transcendental equation, and it is difficult to obtain the parametric solution of the maximum deviation in this way. According to the above analysis, Δf Fi has little influence on the overall derivative, so only Δf COI and Δf di are still considered. The exponential - term decay rates of the two are very close, and the change speed of the trigonometric - function term of Δf COI is much slower than that of Δf di . Therefore, the moment of the maximum deviation of the system appears among the 2 - 3 extreme points near the first extreme point of Δf di when Δf COI . Therefore, according to Equation (45), the extreme points t CPO of Δf COI and the extreme points t di of Δf di are k is a non - negative integer. Let t COI =t di It can be obtained that k * is to satisfy t COI =tdi Non - negative constant of the condition, k * After rounding down, there is [k * , and at this time, there is:

[0084] Assume that the disturbance occurs in area i. When β < 0, that is, in the case of active power under - disturbance, when [k * is odd, t 1 is a minimum point. At this time, the maximum deviation of the disturbed area i is Δf i (t 1 ), and the maximum deviation of area 3 - i may be Δf (3-i) (t 2 ) or Δf (3-i) (t 3 ); when [k * is even, t 1 is a minimum point. At this time, the maximum frequency deviation of the disturbed area i may be Δf i (t 2 ) or Δf i (t 3 ), and the maximum deviation of area 3 - i is Δf 3-i (t 1 ). When β > 0, that is, in the case of active power over - disturbance, the situation is opposite. Therefore, the maximum frequency offsets of each area are respectively Δf i (t 1 ) is the frequency change of area i at time t 1 , Δf i (t 2 ) is the frequency change of area i at time t 2 , Δf i (t 3 ) is the frequency change of area i at time t 3 , Δf 3-i (t 1 ) is the frequency change of area 3 - i at time t 1 , Δf (3-i) (t 2 ) is the frequency change of area 3 - i at time t 2 , Δf (3-i) (t 3 ) is the frequency change of area 3 - i at time t 3 .

[0085] In summary, after a disturbance occurs, the frequency deviation and ROCOF have obvious spatio-temporal distribution characteristics. Regarding the ROCOF, the ROCOF in the disturbance occurrence area reaches its maximum value at the initial moment, while the ROCOF of the spatial nodes at a relatively far distance reaches its maximum after half a cycle of oscillation. The maximum values of ROCOF in each area can be calculated separately by Equation (50). Regarding the maximum frequency deviation, the spatio-temporal distribution gap of the wide-area maximum frequency deviation is relatively small, but the difference in the maximum deviation moment in each area is more significant. The maximum deviation in each area appears at the extreme point where the additional oscillation is near the extreme point of the center frequency, and is calculated by Equations (54) and (55) according to the disturbance type.

[0086] S4. Action value correction strategy for frequency protection

[0087] It can be seen from the above analysis that when a disturbance occurs in the power system, for different regions, the frequency deviation and ROCOF have spatio-temporal distribution characteristics, and there are significant differences in the occurrence time and magnitude of the maximum frequency deviation and the maximum value of ROCOF. This difference will affect the system frequency protection. If the whole network still sets the protection action according to the unified inertial center frequency, it may lead to misoperation or refusal of the protection device.

[0088] The frequency-related protection detection process proposed in the present invention is as Figure 10 shown. The system judges whether the frequency index exceeds the limit by detecting the offset of the tracking frequency on the output side of the converter before and after the fault and the rate of change of frequency. First, collect the system frequency to obtain the system frequency change curve, and obtain the ROCOF curve of the system according to the frequency curve, and compare them with the protection setting values respectively to judge whether the system frequency operates within the set interval, as In the formula, f is the measured value of the system frequency, f min is the lower limit of the frequency protection action, f max is the upper limit of the frequency protection action, R f is the calculated value of the system frequency change rate, and K is the set value of the frequency change protection. When it is detected that the limit is exceeded, that is, f > f max or f < f min or |R| > K, the relevant protection actions.

[0089] Therefore, for the frequency protection with the maximum frequency offset as the threshold, the action value of the frequency protection of the present invention is corrected as follows:

[0090] For the maximum frequency offset, substitute the time in Equation (53) into Equation (43) and compare, and take its maximum or minimum value according to different disturbances, as shown in Equations (54) and (55). When the disturbance is positive, that is, ΣΔP di > 0, take the maximum value of the frequency deviation multiply by 1.1 - 1.2 times the sensitivity, and then superimpose the initial frequency f Nas the upper frequency limit f of this area max When the disturbance is negative, i.e., ΣΔP di < 0, take the maximum value of its frequency deviation multiply by the sensitivity of 1.1 - 1.2 times, and then superimpose the initial frequency f N as the lower frequency limit f of this area min , that is

[0091] For the frequency protection with the frequency change amount as the threshold, when the overall system disturbance remains unchanged and there are differences in the inertia H of the two areas, there are two cases of the disturbance: ① The disturbance occurs in the low-inertia H il area; ② The disturbance occurs in the high-inertia H ih area. According to equations (45) and (50), it can be known that the maximum value of ROCOF in the low-inertia H il area must appear at the 0 + moment of case ①, while the maximum value of ROCOF in the high-inertia H ih area may appear at the initial moment of case ① or at the t max moment of case ②, which is mainly related to the difference in the inertia H of the two areas and the inertia H of this area.

[0092] Therefore, the correction method for the action value of the frequency protection with the frequency change amount as the threshold is as follows:

[0093] For the low-inertia H il area, take the absolute value of the value at the 0 + moment of ① according to equation (50), and multiply by the sensitivity of 1.1 - 1.2 times as the maximum frequency change rate limit K Hi_l of this area; for the high-inertia H ih area, then compare the values at the 0 + moment of ① and the t max moment of ② according to equation (50), take the value with the larger absolute value in the formula, and multiply by the sensitivity of 1.1 - 1.2 times as the maximum frequency change rate limit K Hi_h of this area.

[0094]

[0095] Based on the electromagnetic equations of the generator and the rotor motion equations, combined with the network parameter model, the present invention establishes an inter-regional frequency response model; by adopting closed-loop equivalent substitution and mode shape analysis, the order reduction of the power grid frequency control system and the decoupling between frequency components are realized. Further, according to the superposition theorem and the idea of equivalent aggregation, the precise time-domain solution of all three frequency components including different frequencies or oscillation forms is realized, the analytical accuracy is improved, and the problem of precise time-domain analysis of the two-region high-order model is solved. According to the solved frequency response analytical expressions of the two regions, the frequency response characteristics of the two regions are analyzed, the spatio-temporal distribution characteristics and related expressions of the maximum values of frequency deviation and ROCOF are obtained, and based on this conclusion, an action value correction strategy for system frequency protection is proposed.

Claims

1. Analysis of the spatiotemporal difference mechanism of power system node frequency and frequency protection correction method, characterized in that: The following steps are involved: S1. Constructing a two-region equivalent frequency response model Based on the typical aggregated single-machine SFR model, the frequency response model of the two-region interconnected system is established by analyzing the power flow characteristics between regions. S2, two-region equivalent frequency response model reduction and decoupling By breaking the closed-loop feedback and equivalent substitution, the high-order frequency response model is equivalent to a combination of typical low-order systems, and the vibration mode analysis method is used to achieve model decoupling, and then the time domain analytical solution is performed; S3. Solve the frequency offset and ROCOF maximum expression in each region Through mathematical analysis of regional frequency analytic expressions and combining the range of typical power system parameters, the maximum expressions of frequency offset and frequency change rate ROCOF in each region are obtained. S4. According to the frequency offset and the occurrence time and numerical difference of the ROCOF maximum value, an action value correction strategy is proposed in the frequency protection control.

2. The method for analyzing the spatiotemporal difference mechanism of power system node frequency and correcting frequency protection according to claim 1 is characterized in that: In step S1, the matrix equation of the two-region equivalent frequency response model is: Where H is the system inertia time constant matrix, D is the system damping coefficient matrix, K is the system node admittance parameter matrix, ΔP d is the system load power change matrix, ΔP M is the system unbalanced acceleration power matrix, Δδ is the system phase angle change matrix, Δf is the system frequency change matrix, s is the complex variable in Laplace transform, ω0 is the rated angular velocity; In the formula, H i is the inertia time constant of the equivalent generator in region i, D i is the equivalent damping coefficient of region i, F Hi is the work ratio of the prime mover high-pressure cylinder in area i, T Ri is the prime mover reheating time constant in region i, R i is the adjustment coefficient of area i, ΔP di is the load jump power in area i, Δf i is the frequency change of region i.

3. The method for analyzing the spatiotemporal difference mechanism of power system node frequency and correcting frequency protection according to claim 2 is characterized in that: In step S1, the output active power table of each area is P Gi is the active power output of the generator in region i, E qi is the node voltage in the regional equivalent generator, Y 12 is the mutual admittance between equivalent nodes in two regions, G ii is the self-conductance of the equivalent node in region i, φ is the mutual admittance angle between the equivalent nodes of two regions; Δδ=δ1-δ2, δ i is the regional equivalent generator internal phase angle; Simplify formula (3) to ΔP G is the system active output matrix, ΔP G1 is the output active power change of area 1, ΔP G2 is the output active power change of area 2, Δδ1 is the phase angle change of area 1, and Δδ2 is the phase angle change of area 2; ΔP G =[ΔP G1 ,ΔP G2 ] T , Δδ=[Δδ1,Δδ2] T , where The initial phase angle of the system is δ 10 and δ 20 , Δδ0=δ 10 -δ 20 ; In high-voltage power grid lines, the ground conductivity is usually ignored, so φ = π, and equation (4) is further simplified to Where k = E q1 E q2 |B 12 | (7), B 12 is the mutual susceptance between equivalent nodes in two regions; for a single machine with equal value in region i, the rotor motion equation is Where ΔP Mi is the unbalanced acceleration power in region i, ΔP Gi is the external input power of region i; Substitute ΔP in equation (6) Gi Substituting into equation (8) and expressing it in matrix form, we get equation (1).

4. The method for analyzing the spatiotemporal difference mechanism of power system node frequency and correcting frequency protection according to claim 3 is characterized in that: In step S2, ΔP M It is split into the sum of the proportional link and the first inertia. The proportional link part is combined with the damping matrix D to form the equivalent damping matrix D', that is, The closed-loop substitution method is used to replace Δf with the central frequency ΔF in the ASF model after the two regions are aggregated. i , Further sorting of the two regions In the formula, X is H, D, R after polymerization -1 Three parameters, l i is the reduction factor of region i, S i is the total rated capacity of the generators in region i, S B is the power base value of region i; after being reduced to the lowest order, equation (1) becomes In the formula, 5. The method for analyzing the spatiotemporal difference mechanism of power system node frequency and correcting frequency protection according to claim 4 is characterized in that: In step S2, the phase angle change matrix Δδ in natural coordinates is transformed into the modal matrix y in modal coordinates using the modal matrix, and the decoupling of the motion equation is realized; specifically, firstly, assuming that the system is viscous damping, according to formula (12), its vibration mode equation is (K-λ 2 H)Φ=0(14); where Φ=[J1,J2] is the eigenvector matrix of formula (12), J1 and J2 are eigenvectors, and λ is the eigenvalue; The characteristic value obtained by formula (14) is The corresponding eigenvector is Secondly, the natural coordinate Δδ and the principal coordinate y = [y1, y2] T The connection is established through Φ, that is, Δδ = Φy (17); where y1 and y2 are two vibration modes; finally, substitute equation (17) into equation (12) and multiply it by the transposed matrix Φ of Φ T Get Φ T H 2 +Φ T DΦys+Φ T KΦy=ω0Φ T ΔP F +ω0Φ T ΔP d (18), after rearrangement, the time domain equation is Where M is the diagonal matrix containing the inertia constants of each region, C is the matrix of the combined coefficients of the damping coefficient and the inertia constant, Z is the diagonal matrix of the combined coefficients of the inertia constant and the node admittance, and F(t) is the column vector of the unbalanced acceleration power and the disturbance power. Expanding formula (19), we get At this time, the equation changes from a two-degree-of-freedom vibration equation to two single-degree-of-freedom vibration equations, achieving decoupling.

6. The method for analyzing the spatiotemporal difference mechanism of power system node frequency and correcting frequency protection according to claim 5 is characterized in that: In step S2, the time domain analytical solution is as follows: using the idea of ​​the two-machine aggregate SFR model to solve Using the superposition theorem, in ΔP F and ΔP d When the two excitation forces act separately, we can obtain and Then add up to get The time domain analytical expression of the equivalent frequency response model of the two regions is obtained as follows:

7. The method for analyzing the spatiotemporal difference mechanism of power system node frequency and correcting frequency protection according to claim 6 is characterized in that: Solution The steps are: aggregate the two-region equivalent frequency response models into a low-order simplified SFR model, and the transfer function is: In the formula, ω n1 is the natural oscillation angular frequency of mode y1, is the damping coefficient of mode y1; perform inverse Laplace transform on equation (23) to obtain ω r1 is the damped oscillation angular frequency of mode y1, α is the coefficient of the attenuated oscillation term, In the formula, is the initial phase angle of the derivative of mode y1.

8. The method for analyzing the spatiotemporal difference mechanism of power system node frequency and correcting frequency protection according to claim 7 is characterized in that: Solution The steps are: first ΔP d When acting alone, the inverse Laplace transform is performed. In the formula, Φ ij is the element in the transformation matrix Φ, ω n2 is the natural oscillation angular frequency of mode y2, ζ is the damping coefficient of mode y2, ω r2 is the damped oscillation angular frequency, and the Laplace inverse transform of equation (27) is obtained Then, for ΔP in equation (21) F Solve when acting alone, Simplify formula (30) to In the formula, M is the common factor after factorization, and A is the common factor after factorization containing ω n1 The coefficient of the s term in the factor numerator, B is the factorized term containing ω n1 The coefficient of the constant term in the factored numerator, C is the factorized constant containing ω n2 The coefficient of the s term in the factor numerator, D is the coefficient of the factorized term containing ω n2 Factor the coefficient of the constant term in the numerator, let Performing Laplace inverse transformation on equation (31) yields In the formula, ρ1 is the oscillation amplitude of the factor Y1(t), ρ2 is the oscillation amplitude of the factor Y2(t), The initial angle of the trigonometric function is synthesized by factoring Y1(t), The initial angle of the trigonometric function is synthesized by factoring Y1(t). Combining the above equations, we get In the formula, γ1 is the modal component y 2F The derivative of r1 is the magnitude of the damping angular frequency factor, γ2 is the modal component y 2F The derivative of r2 is the magnitude of the factor that damps the angular frequency.

9. The method for analyzing the spatiotemporal difference mechanism of power system node frequency and correcting frequency protection according to claim 8, characterized in that: In step S3, the maximum value of ROCOF is calculated as follows: the maximum moment of ROCOF in the contralateral region of the disturbance is is the deviation angle after derivation; for the disturbance region i, the maximum ROCOF value appears at the initial moment of the disturbance; for the contralateral region 3-i, the maximum ROCOF value appears at the moment shown in formula (38); the maximum values ​​of the two are respectively ROCOF imax is the maximum ROCOF value of region i, ROCOF (3-i)max is the maximum ROCOF value of region 3-i; is the offset angle after derivation; In step S3, the maximum frequency offset is calculated as: Δf COI The extreme point t COI With Δf di The extreme point t di for k is a non-negative integer, let t COI =t di have to k * To satisfy t COI =t di The condition is a non-negative constant, k * After rounding down, we have [k * ], now we have: The maximum frequency offsets in each region are Δf i (t1) is the frequency change of region i at time t1, Δf i (t2) is the frequency change of region i at time t2, Δf i (t3) is the frequency change of region i at time t3, Δf 3-i (t1) is the frequency change of region 3-i at time t1, Δf (3-i) (t2) is the frequency change of region 3-i at time t2, Δf (3-i) (t3) is the frequency change amount of region 3-i at time t3.

10. The method for analyzing the spatiotemporal difference mechanism of power system node frequency and correcting frequency protection according to claim 9, characterized in that: In step S4, the correction strategy is: for the maximum frequency offset, substitute the time of equation (42) into equation (22) for comparison, and take the maximum or minimum value according to the disturbance; when the disturbance is positive, that is, ΣΔP di >0, take the maximum frequency deviation After multiplying the sensitivity by 1.1-1.2 times, the initial frequency f is superimposed N The upper frequency limit f of this area is then max ; When the disturbance is negative, that is, ΣΔP di <0, take the maximum frequency deviation After multiplying the sensitivity by 1.1-1.2 times, the initial frequency f is superimposed N As the lower frequency limit of this area, f min ,Right now For frequency protection with frequency change as the threshold, the disturbance is divided into: ① The disturbance occurs at low inertia H i_l Region, ② The disturbance occurs in high inertia H i_h Area; for low inertia H il region, according to formula (39), take ①0 + The absolute value of the moment value is multiplied by 1.1-1.2 times the sensitivity as the maximum frequency change rate limit K of the area. Hi_l ; For high inertia H ih Area, according to formula (39) for ①0 + Time and t max The value at the moment is compared, and the value with the larger absolute value in formula (39) is taken, and multiplied by 1.1-1.2 times the sensitivity as the maximum frequency change rate limit K in this area. Hi_h ,Right now

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