Method for analyzing time-delay power system stability of single-area pi-type load frequency control

Abstract

The application discloses a kind of single-area PI type load frequency control time-delay power system stability analysis method, comprising the following steps: 1) establish single-area PI type load frequency control power system mathematical model;2) considering the influence of time delay on power system, on the basis of power system mathematical model, establish time-delay power system mathematical model;3) construct Lyapunov functional;4) the derivation of Lyapunov functional;5) the integral term of the Lyapunov functional after derivation is estimated using the first lemma, and the stability of the time-delay power system mathematical model is analyzed using a two-parameter quadratic polynomial function and the Schur complement theorem, to obtain a less conservative stability criterion.The application has the advantages of less conservative, lower analysis process complexity, etc.

Description

TECHNICAL FIELD

[0001] The present application mainly relates to the technical field of power system, and particularly relates to a time delay power system stability analysis method for single-region PI type load frequency control. BACKGROUND

[0002] Load frequency control (LFC) has been applied in power system for many years due to its excellent ability to keep the frequency and power exchange of adjacent regions at a predetermined value, and also lays the foundation for the development of smart grid. At present, with the continuous development of smart grid, people's research on load frequency is also more and more.

[0003] The model of load frequency control scheme with communication channel is generally considered as a typical delay system. Time delay phenomenon has become one of the most important unreliable factors, which will weaken the dynamic performance of the system, and even lead to the instability of the LFC scheme. This means that the control area does not meet the control standard, produces deviation, and has a negative impact on the stable operation of the power system. Therefore, it is of great significance to find the maximum allowable delay for the power system using LFC scheme to maintain stable operation.

[0004] At present, there are two ways to determine the maximum delay. One is to calculate the critical characteristic value and characteristic root of the system according to the characteristic equation of the system, so as to directly calculate the accurate maximum allowable time delay. However, the difficulty of calculation of this method is related to the size of the system, and when the size of the system is very large, the efficiency of this method is very low. The second is an indirect method based on Lyapunov stability theory to calculate the maximum time delay. Since the indirect method based on Lyapunov stability theory can handle constant and time-varying time delay at the same time, it has become a mainstream method, although this method is somewhat conservative. SUMMARY

[0005] The technical problem to be solved by the present application is that, in view of the technical problems existing in the prior art, the present application provides a time delay power system stability analysis method for single-region PI type load frequency control with less conservatism.

[0006] To solve the above technical problems, the technical scheme provided by the present application is:

[0007] A time delay power system stability analysis method for single-region PI type load frequency control, comprising the steps of:

[0008] 1) establishing a mathematical model of power system for single-region PI type load frequency control;

[0009] 2) considering the influence of time delay on power system, establishing a mathematical model of time delay power system on the basis of the mathematical model of power system;

[0010] 3) constructing Lyapunov function;

[0011] 4) deriving Lyapunov function;

[0012] 5) estimating the integral term of the derived Lyapunov function by using the first lemma, and using the double-parameter quadratic polynomial function and the Schur complement theorem to analyze the stability of the mathematical model of the time-delay power system, so as to obtain a stability criterion with less conservativeness.

[0013] Preferably, the specific process of establishing the mathematical model of the single-region PI type load frequency control power system in step 1) is as follows:

[0014] The mathematical model of the power system is:

[0015]

[0016]

[0017] wherein x(t) is the state vector of the system, u(t) is the control input, and w(t) is the external disturbance, is the system matrix, wherein:

[0018]

[0019] wherein D is the generator damping coefficient, M is the generator damping coefficient, T ch is the time constant of the turbine, T g is the time constant of the generator, R is the speed droop coefficient of the governor, Δf is the frequency deviation, Δp m is the change of the mechanical power of the generator, Δp v is the change of the valve opening, and β is the frequency deviation factor;

[0020] Considering the regional control error ACE and the PI type negative frequency controller, there is

[0021] u(t) = -K p ACE-K I ∫ACE.

[0022] wherein K p and K I are the proportional gain and the integral gain of the PI controller respectively, and ACE = βDf.

[0023] Let K = [K P , K I ], and y(t) = [y(t), ∫y(t)] T , and there is u(t) = -Ky(t).

[0024] ​Preferably, the specific process of step 2) is:

[0025] Considering the influence of time delay, there is u(t) = -Ky(t-h(t)), where h(t) represents the time delay function, and satisfies 0 < h(t) < h, where h is the maximum time delay.

[0026] Definition Only considering the stability of the power system, without considering the external disturbance of the system, thus W(t) = 0, so there is

[0027] Where

[0028] Preferably, the specific process of step 3) is:

[0029] Construct Lyapunov functional:

[0030] V (t) = V1(t) + V2(t) + V3(t)

[0031]

[0032]

[0033]

[0034] Where:

[0035]

[0036]

[0037] Preferably, the specific process of step 4) is:

[0038] Derive the Lyapunov functional:

[0039]

[0040]

[0041]

[0042] Preferably, in step 5), the integral term of the derived Lyapunov functional is estimated by using the preset first lemma, and the following is obtained:

[0043]

[0044]

[0045] Summarizing the above, we get That is is about h2 The correlation function of (t).

[0046] Preferably, the quadratic polynomial function f(s) = a2s 2 +a1s+a0 in step 5) is a quadratic polynomial function f(s) = a2s i is an arbitrary matrix.

[0047] The application further discloses a time-delay power system stability analysis system of single-region PI type load frequency control, which comprises:

[0048] A first program module is used for establishing a power system mathematical model of single-region PI type load frequency control.

[0049] A second program module is used for considering the influence of time delay on the power system and establishing a time-delay power system mathematical model on the basis of the power system mathematical model.

[0050] A third program module is used for constructing a Lyapunov functional.

[0051] A fourth program module is used for deriving the Lyapunov functional.

[0052] A fifth program module is used for estimating the integral term of the derived Lyapunov functional by using a preset first lemma, and performing stability analysis on the time-delay power system mathematical model by using a double-parameter quadratic polynomial function and a Schur complement theorem, so that a stability criterion with less conservativeness is obtained.

[0053] The application further discloses a computer readable storage medium, which has a computer program stored thereon, and the computer program performs the steps of the method when being run by a processor.

[0054] The application further discloses a computer device, which comprises a memory and a processor, and the memory has a computer program stored thereon, and the computer program performs the steps of the method when being run by the processor.

[0055] Compared with the prior art, the application has the following advantages:

[0056] The time-delay power system stability analysis method of single-region PI type load frequency control has the advantages that the power system stability is analyzed by using the Lyapunov functional and the negative condition of the double-parameter quadratic polynomial function and the related lemma, and the maximum time delay that can maintain the stability of the power system is solved; and the simulation results show that the method has less conservativeness and lower complexity in the stability analysis of the power system with time delay of load frequency control. BRIEF DESCRIPTION OF DRAWINGS

[0057] Figure 1 It is a structure block diagram of the single-region PI type load frequency control.

[0058] Figure 2 A state response diagram of a time-delay power system for the single-area PI type load frequency control of the application.

[0059] Figure 3 A flowchart of the method of the application in an embodiment. DETAILED DESCRIPTION

[0060] The application is further described below in conjunction with the accompanying drawings and specific embodiments.

[0061] As shown in the drawings, the method for analyzing the stability of a time-delay power system for the single-area PI type load frequency control of the application comprises the steps of: Figure 3

[0062] 1) establishing a mathematical model of a power system with single-area PI type load frequency control;

[0063] 2) considering the influence of time delay on the power system, establishing a mathematical model of a time-delay power system on the basis of the mathematical model of the power system;

[0064] 3) constructing a suitable Lyapunov-Krasovskii functional;

[0065] 4) taking the derivative of the Lyapunov-Krasovskii functional;

[0066] 5) estimating the integral term of the derivative of the Lyapunov-Krasovskii functional by using a preset first lemma, and using a two-parameter quadratic polynomial function and the Schur complement theorem to analyze the stability of the mathematical model of the time-delay power system, to obtain a stability criterion with less conservatism.

[0067] The method for analyzing the stability of a time-delay power system for the single-area PI type load frequency control of the application analyzes the stability of the power system by using the Lyapunov-Krasovskii functional and the negative definite condition of the two-parameter quadratic polynomial function and the related lemmas, and solves the maximum time delay that can maintain the stability of the power system; the method has less conservatism and lower complexity in the stability analysis of the power system with load frequency control and time delay (as shown in the subsequent simulation results).

[0068] To facilitate understanding of the application, two lemmas and a theorem are given as follows:

[0069] Lemma 1: Given two scalars a and b, a positive definite matrix R, a differentiable function x, matrices Φ i and H i (i = 1, 2, 3) and a vector ξ, the following inequality holds:

[0070] ​

[0071] where ξ is an arbitrary vector

[0072] matrix

[0073]

[0074]

[0075] Φ1ξ = x(b) - x(a)

[0076]

[0077]

[0078]

[0079] Lemma 2: The quadratic polynomial function f(s) = a2s 2 +a1s+a0, where a i is an arbitrary matrix, if given scalar C1∈[0,1], C2∈[1,2], if f(s) < 0 can be established in s∈[0,h], then:

[0080] f(0) < 0

[0081] f(h) < 0

[0082]

[0083]

[0084]

[0085]

[0086] In order to make the symbol expression simple, convenient to use, give the following symbol definition:

[0087]

[0088] e i =[O n×(i-1)n ,I n ,O n×(q-i)n ] i=1,2,…,9

[0089] e s =Ae1+A d e2

[0090] where O n×(i-1)n is n×(i-1)n dimension 0 matrix, O n×(q-i)n is n×(q-i)n dimension 0 matrix, In I and O are identity and zero matrices, respectively; A, A d is the system matrix.

[0091] Theorem: For scalar h, μ, c1∈[0, 1], c2∈[1, 2], there exist positive definite matrices P1, P2, S1, S2, R, and arbitrary matrices N1, N2, if the single-area power system is stable, then the following linear matrix inequalities hold:

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098] where:

[0099]

[0100]

[0101] π1 = col{e s ,e9,e1-e3}

[0102] π2 = col{e1,e3,(h-h(t))e4+h(t)e6}

[0103] π3 = col{e1,e3,e1,e s ,0}

[0104] π4 = col{e1,e3,e2,e8,h(t)e6}

[0105] π5 = col{h(t)e1,h(t)e3,h(t)e6,e1-e2,h(t) 2 (e6-e7)}

[0106] π6 = col{e s ,e9,e0,e0,1}

[0107] π7 = col{e1,e3,e3,e9,(h-h(t))e4+h(t)e6}

[0108] π8=col{he1,he3,e3,e9,(hh(t))e4+h(t)e6,e1-e3,}

[0109]

[0110] A -1 and A T R represents the inverse and transpose of matrix A; n Represents n-dimensional Euclidean space; R n×m Let P represent an n×m real matrix; P > 0 indicates that matrix P is symmetric and positive definite; diag{…} represents a block diagonal matrix; I and O represent the identity matrix and the zero matrix, respectively; * represents the symmetric term in a symmetric matrix, Sym{X} = X + X. T ,col represents a column vector.

[0111] In one specific embodiment, the specific process of step 1) is as follows:

[0112] Establish a power system model with single-region PI-type load frequency control:

[0113]

[0114]

[0115] in Let u(t) be the system's state vector, u(t) be the control input, and w(t) be the external disturbance. Let be the system matrix, where:

[0116]

[0117] Where D is the generator damping coefficient, M is the generator damping coefficient, and T is the generator damping coefficient. ch T is the time constant of the turbine. g R is the time constant of the generator, R is the speed drop coefficient of the governor, Δf is the frequency deviation, and Δp is the frequency deviation. m Δp is the change in the mechanical power of the generator. v β represents the change in valve opening, and β is the frequency deviation factor.

[0118] Considering the area control error ACE and the PI-type negative frequency controller, then:

[0119] u(t) = -K p ACE-K I ∫ACE.

[0120] Where K p and K I These are the proportional gain and integral gain of the PI controller, respectively, and ACE = βDf;

[0121] Let K = [K P ,K I ], y(t) = [y(t), ∫y(t)] T , then u(t) = -Ky(t).

[0122] In a specific embodiment, the specific process of step 2) is as follows: because the time delay is inevitable when the control signal is transmitted, the influence of the time delay is considered, and u(t) = -Ky(t) h(t) is obtained, where h(t) represents the time delay function, and 0 < h(t) < h. where μ is the maximum rate of change of the time delay;

[0123] Definition Only the stability of the power system is considered, and the external disturbance of the system is not considered, so W(t) = 0, and

[0124] where,

[0125] In a specific embodiment, the specific process of step 3) is as follows:

[0126] The Lyapunov function is constructed as follows:

[0127] V(t) = V1(t) + V2(t) + V3(t)

[0128]

[0129]

[0130]

[0131] where,

[0132]

[0133]

[0134] In a specific embodiment, the specific process of step 4) is as follows:

[0135] The derivative of the established function is as follows:

[0136]

[0137]

[0138]

[0139] In a specific embodiment, the specific process of step 5) is as follows: the integral term after the derivative of the function is estimated by using Lemma 1, and the following is obtained:

[0140]

[0141]

[0142] In summary:

[0143] Obviously, it can be seen that, is the correlation function of h 2 (t), therefore, by using lemma 2 and the Schur complement theorem, it can be obtained that the matrix inequalities (1) - (6) are established, and thus Therefore, it is proved that the single-area power system is asymptotically stable, and the proof is completed.

[0144] Simulation verification: consider a single-area power simulation system as follows, wherein, the related parameters are respectively: T ch = 0.3, T g = 0.1, R = 0.05, D = 1.0, β = 21, M = 10, c1 = 0.5, c2 = 1.5, and the given proportional gain Kp range is between [0, 1], the integral gain KI range is between [0.05, 1], for μ = 0 and μ = 0.9 two cases, according to the calculated time delay upper bound h as shown in Table 1, it can be known from Table 1 that the obtained time delay upper bound is higher than the results obtained in other prior arts, and thus the stability criterion obtained by the method has obvious advantages.

[0145] In addition, when Kp = 0.1, KI = 0.15, μ = 0, h = 9.31, the initial position x (0) = [0.8069; 1; 1.2462; 1.6158], the state response of the single-area power system is as shown in Figure 2 (the dotted line x4 represents the method of the application, x1-x3 represents the methods [1]-[3] in Table 1, and the shapes are basically the same), and it can be known from Figure 2 that the state of the system is gradually convergent to 0, and thus the effectiveness of the method is proved.

[0146] Table 1: Time delay upper bound h of single-area power system

[0147]

[0148] Reference in Table 1:

[0149] [1] New stability criteria of delayed load frequency control system via infinite-series-based inequality

[0150] [2]Delay-dependent stability for load frequency control with constant and time-varyins decays

[0151] [3]stability criteria for non linearly perturbed load fregnency system with time-deloy。

[0152] The embodiment of the present application further provides a single-area PI type load frequency control time-delay power system stability analysis system, comprising:

[0153] A first program module is used for establishing a single-area PI type load frequency control power system mathematical model;

[0154] A second program module is used for considering the influence of time delay on the power system, and establishing a time-delay power system mathematical model based on the power system mathematical model;

[0155] A third program module is used for constructing a Lyapunov functional;

[0156] A fourth program module is used for deriving the Lyapunov functional;

[0157] A fifth program module is used for estimating the integral term of the derived Lyapunov functional by using a preset first lemma, and performing stability analysis on the time-delay power system mathematical model by using a double-parameter quadratic polynomial function and a Schur complement theorem, so that a stability criterion with less conservativeness is obtained.

[0158] The analysis system of the present application corresponds to the above-mentioned analysis method, and also has the advantages of the above-mentioned analysis method.

[0159] The embodiment of the present application further provides a computer readable storage medium, which stores a computer program, and the computer program performs the steps of the method according to any one of the above embodiments when executed by a processor. The embodiment of the present application further provides a computer device, which comprises a memory and a processor, and the memory stores a computer program, and the computer program performs the steps of the method according to the above embodiments when executed by the processor. The embodiment of the present application implements all or part of the processes of the above method, and can also be completed by a computer program instructing related hardware. The computer program can be stored in a computer readable storage medium, and the computer program can implement the steps of the above method embodiments when executed by a processor. The computer program comprises computer program code, which can be in a form of source code, object code, executable file or some intermediate form. The computer readable medium comprises any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier wave signal, telecommunication signal and software distribution medium, etc. The memory is used to store the computer program and / or modules, and the processor realizes various functions by running or executing the computer program and / or modules stored in the memory, and calling the data stored in the memory. The memory can comprise a high-speed random access memory, and can further comprise a nonvolatile memory, for example, a hard disk, a memory, a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, at least one magnetic disk storage device, a flash memory device or other volatile solid-state memory device, etc.

[0160] The above is only the preferred embodiment of the present application, and the protection scope of the present application is not limited to the above embodiment. Any technical solution falling within the concept of the present application belongs to the protection scope of the present application. It should be noted that, for ordinary skilled in the art, some improvements and refinements without departing from the principle of the present application should be considered as the protection scope of the present application.

Claims

1. A stability analysis method for a time-delay power system with single-region PI-type load frequency control, characterized in that, Including the following steps: 1) Establish a mathematical model for a power system with single-region PI-type load frequency control; 2) Considering the impact of time delay on the power system, establish a time-delay power system mathematical model based on the power system mathematical model; 3) Construct the Lyapunov functional; 4) Differentiate the Lyapunov functional; 5) The integral term of the Lyapunov functional after differentiation is estimated by using the first lemma, and then the stability analysis of the mathematical model of the time-delay power system is carried out by using the two-parameter quadratic polynomial function and the Schul complement theorem to obtain a stability criterion with low conservatism. In step 5), the integral term of the differentiated Lyapunov functional is estimated using the pre-defined first lemma, resulting in: In summary That is, to obtain It is about Related functions; where R is a time-varying time-delay function; R is a positive definite matrix.

2. The stability analysis method for time-delay power systems with single-region PI-type load frequency control according to claim 1, characterized in that, The specific process of establishing the power system mathematical model for single-region PI-type load frequency control in step 1) is as follows: The mathematical model of the power system is as follows: in Let u(t) be the system's state vector, u(t) be the control input, and w(t) be the external disturbance. , , Let be the system matrix, where: ， ， ， Where D is the generator damping coefficient, and M is the generator damping coefficient. The time constant of the turbine. R is the time constant of the generator, and R is the speed drop coefficient of the governor. Frequency deviation This represents the change in the mechanical power of the generator. This represents the change in valve opening. This is the frequency deviation factor; Considering the area control error ACE and the PI-type negative frequency controller, then we have in and These are the proportional gain and integral gain of the PI controller, respectively. ; make , Then there is .

3. The stability analysis method for time-delay power systems with single-region PI-type load frequency control according to claim 2, characterized in that, The specific process of step 2) is as follows: Considering the effect of time delay, we have ,in Represents a time-varying time-delay function and satisfies , ;in The maximum rate of change with time delay; definition Considering only the stability of the power system and neglecting external disturbances, we have W(t) = 0, and thus we have ; in , , .

4. The stability analysis method for time-delay power systems with single-region PI-type load frequency control according to claim 3, characterized in that, The specific process of step 3) is as follows: Constructing Lyapunov functionals: in: 。 5. The stability analysis method for time-delay power systems with single-region PI-type load frequency control according to claim 4, characterized in that, The specific process of step 4) is as follows: Differentiate the Lyapunov functional: 。 6. The stability analysis method for time-delay power systems with single-region PI-type load frequency control according to claim 1, characterized in that, The quadratic polynomial function in step 5) ,in Let be any matrix.

7. A stability analysis system for a time-delay power system with single-region PI-type load frequency control, used to perform the steps of the method as described in any one of claims 1 to 6, characterized in that, include: The first program module is used to establish a mathematical model of a power system with single-region PI-type load frequency control. The second program module is used to consider the impact of time delay on the power system and to establish a time-delay power system mathematical model based on the power system mathematical model. The third program module is used to construct the Lyapunov functional; The fourth program module is used to differentiate the Lyapunov functional; The fifth program module is used to estimate the integral term of the Lyapunov functional after differentiation using the preset first lemma, and then use the two-parameter quadratic polynomial function and Schul complement theorem to perform stability analysis on the mathematical model of the time-delay power system, and obtain a stability criterion with relatively low conservatism.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, The computer program, when run by a processor, performs the steps of the method as described in any one of claims 1 to 6.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, The computer program, when run by a processor, performs the steps of the method as described in any one of claims 1 to 6.

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