Time-delay load frequency control stability analysis method considering electric vehicle access

Abstract

The invention discloses a time-delay load frequency control stability analysis method considering electric vehicle access, and relates to the technical field of load frequency control stability analysis, and the method comprises the steps: building a nominal load frequency control model of a load frequency control system through the power generation characteristics of an electric vehicle and a distributed power supply through model reconstruction, establishing a determined load frequency control model of the load frequency control system according to the electric vehicle charge state fluctuation; introducing an auxiliary polynomial, constructing two types of improved relaxation matrix functions, combining multiple integrals, and respectively obtaining an asymptotic stability criterion of a nominal load frequency control system and a robust stability criterion of an uncertain load frequency control system by using a Lyapunov stability analysis method and a Bessel-Legendre inequality; time-delay load frequency control stability analysis is completed; the reliability and the accuracy of load frequency control analysis of the power system and the applicability of the analysis method are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of load frequency control stability analysis, and in particular to a method for analyzing the stability of load frequency control with a time lag considering electric vehicle access. Background Art

[0002] With the access of electric vehicles and various distributed energy sources, severe requirements and challenges are put forward for the load frequency control of the power system. However, in a networked transmission environment, the rate of change of the current state of the power system is inevitably affected by the past state, that is, the movement law of the system not only depends on the movement state at the current moment, but also is related to the movement state at a certain moment or several moments in the past. This time lag is often an important factor that causes system performance degradation or even system instability. Therefore, the analysis and control of the power system needs to fully consider the impact of time lag under the access of electric vehicles and distributed power sources to improve the performance of the power system and ensure the stable operation of the power system.

[0003] Chinese patent, publication number: CN117407646A, publication date: January 16, 2024, discloses a method for analyzing the stability of load frequency control of a multi-regional time-delay power system, including: constructing a frequency control mathematical model of a multi-regional time-delay power system; performing time-delay separation processing on the frequency control mathematical model to construct an augmented LK functional; processing the derivative of the augmented LK functional based on the second-order BL inequality and the improved inverse convex combination lemma, and constructing a stability analysis model based on the processing result; and performing stability analysis on the load frequency control of a multi-regional time-delay power system based on the stability analysis model. The present invention has the technical effect of reducing the computational complexity of solving the system delay margin based on model reconstruction, thereby improving the computational efficiency; introducing a double integral term when constructing the augmented LK functional to reduce the conservatism of the system delay margin; using the second-order BL inequality combined with the improved inverse convex combination to estimate the integral term of the LK functional derivative, further reducing the conservatism of the system delay margin. However, the invention does not take into account the access of electric vehicles and wind power generation, nor the uncertainty of load frequency control of the power system due to the battery charge state, and is not suitable for the stability analysis scenario of load frequency control of the power system under the access of electric vehicles. Summary of the invention

[0004] The purpose of the present invention is to address the problem that the existing load frequency control stability analysis method lacks comprehensive consideration of the access of electric vehicles and distributed power sources, resulting in inaccurate and unreliable results of power system stability analysis; a time-delay load frequency control stability analysis method considering the access of electric vehicles is proposed, a nominal load frequency control model of the load frequency control system is established by model reconstruction through the power generation characteristics of electric vehicles and distributed power sources, and a determinate load frequency control model of the load frequency control system is established according to the charge state fluctuation of the electric vehicle; auxiliary polynomials are introduced to construct two types of improved relaxation matrix functions, and combined with multiple integrals, the Lyapunov stability analysis method and the Bessel-Legendre inequality are used to respectively perform asymptotic stability analysis of the nominal load frequency control system and robust stability analysis of the uncertain load frequency control system; the reliability and accuracy of the load frequency control analysis of the power system and the applicability of the analysis method are significantly improved.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is: a method for analyzing the stability of time-delay load frequency control considering the access of electric vehicles, comprising the following steps: S1. Construct an uncertain load frequency control model under the access of electric vehicles and distributed power sources; S2. Reconstructing the uncertain load frequency control model according to the time-delay change state of the load frequency control system to obtain a nominal load frequency control model; S3, establishing auxiliary polynomials according to the time lag state of the electric vehicle and the distributed power source in the load frequency control system, and constructing improved first relaxation matrix functions and second relaxation matrix functions; S4, constructing a first augmented Lyapunov functional model of the nominal load frequency control model by combining the first relaxation matrix function with multiple integrals, and constructing a second augmented Lyapunov functional model of the uncertain load frequency control model by combining the second relaxation matrix function with multiple integrals; S5. Improve the first augmented Lyapunov functional model according to the mutually inverse convex combination lemma, and obtain the asymptotic stability criterion of the load frequency control system by combining the Bessel-Legendre inequality, and complete the asymptotic stability analysis of the load frequency control system under the access of electric vehicles and distributed power sources; S6. Calculate the second augmented Lyapunov functional model to obtain the robust stability criterion of the load frequency control system under the access of electric vehicles and distributed power sources, and complete the robust stability analysis of the load frequency control system.

[0006] In this scheme, by establishing an uncertain load frequency control model and a nominal load frequency control model, the operating characteristics of electric vehicles and distributed power sources are fully considered, and parameter support is provided for the subsequent use of an improved relaxation matrix function, so as to fully reflect the time-delay change information; combining the relaxation matrix function, augmented matrix and multiple integrals, through the Bessel-Legendre inequality, the Lyapunov stability analysis method is used to obtain the asymptotic stability criterion of the nominal load frequency control system and the robust stability criterion of the uncertain load frequency control system, respectively, which fully considers the characteristics of the load frequency control system and the disturbance factors caused by the change of the charge state, and realizes a comprehensive and reliable stability analysis of the power system; further, the system performance is optimized according to the analysis results, which can effectively utilize the characteristic information of the charging process and improve the efficiency of system analysis.

[0007] Preferably, the S1 comprises the following sub-steps: S11, establishing a load frequency state vector based on the operating state parameters of the load frequency control system in the single area connected to the electric vehicle and the distributed power source, and the time lag of the dynamic change of the electric vehicle and the distributed power source in the network transmission; S12, calculating the electric vehicle gain according to the charge state fluctuation of the electric vehicle, and establishing a load frequency control matrix based on the operation characteristics of the electric vehicle and the distributed power source connected to the power system; Wherein, the operating characteristics at least include: turbine droop characteristics, inertia coefficient, load damping coefficient, turbine time constant, governor constant, electric vehicle participation rate, turbine participation rate, electric vehicle droop characteristics; S13. Construct a load frequency control system model based on the load frequency state vector and the load frequency control matrix; S14. Take the stability of the load frequency control system as the goal, improve the load frequency control system model according to the time-varying data of the load frequency control matrix, and obtain the uncertain load frequency control model.

[0008] Preferably, the load frequency state vector is expressed as follows: x(t)=[ΔfΔP m ΔP v ΔP ev ∫ACE] T ; Where Δf represents the frequency deviation, ΔP m Represents the generator mechanical output, ΔP v Indicates valve position, ΔP ev represents the power output deviation, and ∫ACE represents the system frequency difference integral signal.

[0009] Preferably, the electric vehicle gain K ev The calculation formula is as follows: K ev =K max -K max g(t); Among them, SOC max Indicates the maximum state of charge of electric vehicles, SOC min Indicates the minimum state of charge of electric vehicles, SOC high Indicates the high state of charge of electric vehicles, SOC low Indicates the low charge state of electric vehicles, K max represents the maximum V2G droop characteristic, g(t) represents the time-varying limit function, Δf represents the frequency deviation, K ev,a It represents the gain value of electric vehicle under different frequency deviation ranges.

[0010] Preferably, the uncertain load frequency control model is expressed as follows: Where w(t) represents the output power change vector of electric vehicles and distributed power sources within time t, w = [ΔP d ΔP WTG ], x(t) represents the load frequency state vector, ΔP d Represents the output power change vector of the electric vehicle, ΔP WTG represents the output power change of the wind turbine in the distributed power source, η(t) represents the time delay under network transmission, 0≤η(t)≤η, A represents the first system matrix, B represents the system variable matrix, F represents the inertia coefficient matrix, ΔA represents the electric vehicle battery matrix, and ΔB represents the system frequency difference proportional-integral matrix.

[0011] Preferably, the nominal load frequency control model is as follows: Where x1(t) represents the time-delay-dependent state vector, x1=[Δf∫ACE] T , x2(t) represents the time-delay-independent state vector, x2=[ΔP m ΔP v ΔP ev ] T , Δf represents the frequency deviation, ΔP m Represents the generator mechanical output, ΔP v Indicates valve position, ΔP ev represents the power output deviation, ∫ACE represents the system frequency difference integral signal, A 11 , A 12 , A 21 , A 22denote the first system matrix of time-delay separation, represents the system variable matrix after time-delay separation, represents a first model function of the nominal load frequency control model, A second model function representing the nominal load frequency control model.

[0012] Preferably, S3 includes the following sub-steps: Based on the time-delay state of the load frequency control system, a positive definite symmetric matrix function is constructed using adjustable parameters. Based on the time-delay boundary relationship, the time-delay interval is divided and the auxiliary polynomial is established; The positive definite symmetric matrix function is calculated based on the double auxiliary polynomial to obtain an improved relaxation matrix function.

[0013] Preferably, constructing the positive definite symmetric matrix function specifically includes: based on a continuously differentiable function, introducing the variable parameter, and if there is a symmetric matrix of a dimension that conforms to the continuously differentiable function, constructing the positive definite symmetric matrix function based on an augmented function; Establishing the auxiliary polynomial specifically includes: dividing the time lag interval based on the time lag boundary relationship, and establishing the auxiliary polynomial using the adjustable parameters; Calculating the improved relaxation matrix function specifically includes: based on the divided time lag interval, using the auxiliary polynomial in combination with the positive definite symmetric matrix function to construct a relationship equation, simplifying the relationship equation and inserting it into the positive definite symmetric matrix function after variable substitution to obtain a transformed positive definite symmetric matrix function, and using it as the improved relaxation matrix function.

[0014] Preferably, S5 comprises the following sub-steps: Derivative the first augmented Lyapunov functional model to obtain a first derivative result; Differentiating the first relaxation matrix function to obtain a first differential result, and differentiating the second relaxation matrix function to obtain a second differential result; According to the first derivative result and the first differential result, the differential form of the first relaxation matrix function is converted in combination with the change state of the symmetric matrix under the time lag change to obtain a third differential result; The first derivative result, the second differential result and the integral term of the third differential result are defined by using the mutually inverse convex combination lemma, and the first augmented Lyapunov functional model is improved according to the defined results; The Bessel-Legendre inequality is used to perform the Schur complement lemma on the improved first augmented Lyapunov functional model to obtain the asymptotic stability criterion of the load frequency control system and complete the asymptotic stability analysis of the load frequency control system under the access of electric vehicles and distributed power sources.

[0015] Preferably, the S6 comprises the following sub-steps: Differentiating the second augmented Lyapunov functional model to obtain a fourth differential result; The fourth differential result and the augmented matrix of the uncertain load frequency control model are summed. If the summation result satisfies the relational operation conditions between the symmetric matrix and the arbitrary system matrix, the load frequency control system under the access of electric vehicles and distributed power sources is robustly stable.

[0016] Beneficial effects of the present invention: 1. By establishing the uncertain load frequency control model and the nominal load frequency control model, the operating characteristics of electric vehicles and distributed power sources are fully considered, and the relationship between the system state, time lag state, and integral state is effectively included, which helps to fully reflect the time lag change information; 2. Combining the relaxation matrix function, augmented matrix and multiple integrals, through the Bessel-Legendre inequality and the Lyapunov stability analysis method, the asymptotic stability criterion of the nominal load frequency control system and the robust stability criterion of the uncertain load frequency control system are obtained respectively, so as to realize comprehensive and reliable stability analysis of the power system; the system performance is optimized according to the analysis results, and the characteristic information of the charging process can be effectively utilized to improve the efficiency of system analysis, which overcomes the problem that the existing technology lacks comprehensive consideration of the access of electric vehicles and distributed power sources, resulting in inaccurate and unreliable results of power system stability analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Other features, objects and advantages of the present invention will become more apparent by reading the detailed description of non-limiting embodiments made with reference to the following drawings. The drawings are only for the purpose of illustrating preferred embodiments and are not to be considered as limiting the present invention. Also, the same reference symbols are used throughout the drawings to represent the same parts.

[0018] Figure 1 This is a flow chart of a method for analyzing the stability of time-delay load frequency control considering electric vehicle access in this embodiment.

[0019] Figure 2 This is a block diagram of power system frequency control under the access of electric vehicles and wind power generation in this embodiment. DETAILED DESCRIPTION

[0020] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific implementation method described herein is only an optimal embodiment of the present invention, which is only used to explain the present invention and does not limit the scope of protection of the present invention. All other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0021] Example 1: Figure 1 and Figure 2 As shown, a method for analyzing the stability of time-delay load frequency control considering electric vehicle access includes steps S1-S6, wherein: S1. Construct an uncertain load frequency control model under the access of electric vehicles and distributed power sources.

[0022] Specifically, S1 includes the following sub-steps: S11, establishing a load frequency state vector based on the operating state parameters of the load frequency control system in the single area connected to the electric vehicle and the distributed power source, and the time lag of the dynamic change of the electric vehicle and the distributed power source in the network transmission; S12, calculating the electric vehicle gain according to the charge state fluctuation of the electric vehicle, and establishing a load frequency control matrix based on the operation characteristics of the electric vehicle and the distributed power source connected to the power system; The operating characteristics include at least: turbine droop characteristics, inertia coefficient, load damping coefficient, turbine time constant, governor constant, electric vehicle participation rate, turbine participation rate, and electric vehicle droop characteristics; S13, constructing a load frequency control system model according to the load frequency state vector and the load frequency control matrix; S14. Taking the stability of the load frequency control system as the goal, the load frequency control system model is improved according to the time-varying data of the load frequency control matrix to obtain an uncertain load frequency control model.

[0023] Specifically, the load frequency state vector is expressed as follows: x(t)=[Δf ΔP m ΔP v ΔP ev ∫ACE] T (1) Where Δf represents the frequency deviation, ΔP m Represents the generator mechanical output, ΔP v Indicates valve position, ΔP ev represents the power output deviation, and ∫ACE represents the system frequency difference integral signal.

[0024] Specifically, the electric vehicle gain K evThe calculation formula is as follows: K ev =K max -K max g(t)(2) Among them, SOC max Indicates the maximum state of charge of electric vehicles, SOC min Indicates the minimum state of charge of electric vehicles, SOC high Indicates the high state of charge of electric vehicles, SOC low Indicates the low charge state of electric vehicles, K max represents the maximum V2G droop characteristic, g(t) represents the time-varying limit function, Δf represents the frequency deviation, K ev,a It represents the gain value of electric vehicle under different frequency deviation ranges.

[0025] In this embodiment, the electric vehicle itself can be regarded as a distributed energy storage device. When constructing the load frequency control system model, the charge state fluctuation of the electric vehicle is considered, and the energy storage capacity of the electric vehicle can be more effectively utilized. When the grid frequency fluctuates, the frequency fluctuation can be smoothed by charging and discharging operations, thereby improving the overall stability of the power system. In addition, by comprehensively considering the changes in the energy structure of the power system under the access of electric vehicles and other distributed power sources, the adaptability of the load frequency control system model can be improved.

[0026] Specifically, the uncertain load frequency control model is expressed as follows: Where w(t) represents the output power change vector of electric vehicles and distributed power sources within time t, w = [ΔP d ΔP WTG ], x(t) represents the load frequency state vector, ΔP d Represents the output power change vector of the electric vehicle, ΔP WTG represents the output power change of the wind turbine in the distributed power source, η(t) represents the time delay under network transmission, 0≤η(t)≤η, A represents the first system matrix, B represents the system variable matrix, F represents the inertia coefficient matrix, ΔA represents the electric vehicle battery matrix, and ΔB represents the system frequency difference proportional-integral matrix; Among them, the parameters are: M represents the inertia coefficient, D represents the load damping coefficient, T T represents the turbine time constant, T G represents the governor constant, R represents the turbine droop characteristic, β represents the conversion coefficient between system power and frequency, T evrepresents the electric vehicle time constant, K ev represents the electric vehicle gain, α0 is the turbine participation rate, α1 is the electric vehicle participation rate, α0+α1=1; ρ represents the electric vehicle droop characteristic, K P Represents the proportional coefficient of the proportional-integral load frequency control strategy, K I Indicates the integral coefficient of the load frequency control strategy; ΔA(t)=H1g(t)E1, ΔB(t)=H2g(t)E2; E1=

[10000] ,E2=[βK P 000K I ] Wherein, H1 represents the first state vector of the electric vehicle battery, H2 represents the second state vector of the electric vehicle battery, E1 is a constant vector, and E2 is a proportional-integral coefficient vector; The proportional-integral load frequency control strategy u(t) is expressed as follows: u(t)=K P ACE(t)-K I ∫ACE(t)dt(6) ACE=βΔf, which represents the system frequency deviation control signal.

[0027] S2. Reconstruct the uncertain load frequency control model according to the time-delay change state of the load frequency control system to obtain the nominal load frequency control model.

[0028] The nominal load frequency control model is shown as follows: Where x1(t) represents the time-delay-dependent state vector, x1=[Δf∫ACE] T , x2(t) represents the time-delay-independent state vector, x2=[ΔP m ΔP v ΔP ev ] T , Δf represents the frequency deviation, ΔP m Represents the generator mechanical output, ΔP v Indicates valve position, ΔP ev represents the power output deviation, ∫ACE represents the system frequency difference integral signal, A 11 , A 12 , A 21 , A 22 denote the first system matrix of time-delay separation, represents the system variable matrix after time-delay separation, Represents the first model function of the nominal load frequency control model, Represents the second model function of the nominal load frequency control model.

[0029] In this embodiment, the uncertain load frequency control model is a model established by considering the fluctuation of the electric charge state of the electric vehicle, so as to effectively perform the robust stability analysis of the uncertain closed loop of the load frequency control system under the access of the electric vehicle and the distributed power source. The nominal load frequency control model is established by defining the corresponding state vector according to the time-delay related state and the time-delay independent state of the load frequency control system through the model reconstruction technology without considering the change in the output power of the electric vehicle and the distributed power source, which helps to fully reflect the time-delay change information through the improved relaxation matrix function and realize the asymptotic stability analysis of the load frequency control system.

[0030] S3. According to the time-delay state of the electric vehicle and the distributed power source in the load frequency control system, an auxiliary polynomial is established to construct an improved first relaxation matrix function and a second relaxation matrix function.

[0031] Specifically, S3 includes the following sub-steps: Based on the time-delay state of the load frequency control system, a positive definite symmetric matrix function is constructed using adjustable parameters. Based on the time-delay boundary relationship, the time-delay interval is divided and the auxiliary polynomial is established; The positive definite symmetric matrix function is calculated based on double auxiliary polynomials to obtain an improved relaxation matrix function.

[0032] Specifically, constructing a positive definite symmetric matrix function specifically includes: based on a continuously differentiable function, introducing a variable parameter, if there is a symmetric matrix of a dimension that meets the continuously differentiable function, constructing a positive definite symmetric matrix function based on an augmented function; The establishment of the auxiliary polynomial specifically includes: dividing the time delay interval based on the time delay boundary relationship, and establishing the auxiliary polynomial using adjustable parameters; Calculating the improved relaxation matrix function specifically includes: based on the divided time-delay interval, using auxiliary polynomials combined with positive definite symmetric matrix functions to construct a relational equation, simplifying the relational equation and inserting it into the positive definite symmetric matrix function after variable substitution to obtain a transformed positive definite symmetric matrix function, and using it as the improved relaxation matrix function.

[0033] Specifically, the positive definite symmetric matrix function expression is as follows: Among them, V S1 (t,x) represents the first positive definite symmetric matrix function, V S2 (t,x) represents the second positive definite symmetric matrix function, T represents the transformation matrix, K1 represents the first adjustable parameter, K2 represents the second adjustable parameter, R and U represent symmetric matrices, R = [R ij ] 3×3 >0, U=[U ij ] 3×3 >0, x represents a differentiable function, x:[t-η,t]→R n , s represents the relaxation factor, σ1(t) is the column vector integral of the symmetric matrix in the first positive definite symmetric matrix function, σ2(t) is the column vector integral of the symmetric matrix in the second positive definite symmetric matrix function, col represents the column vector, and They represent the symmetric positive definite matrices related to time t, sym{} represents the variable matrix, Y1(C) and Y2(C) represent the proportional coefficient vectors of adjustable parameters, and I is a constant.

[0034] Specifically, the time lag interval [t-η, t] is divided into [t-η(t), t]∪[t-η, t-η(t)], and based on the time lag interval [t-η(t), t], a first auxiliary polynomial λ is established. 11 (s) and λ 12 (s), the calculation formula is as follows: Based on the time lag interval [t-η, t-η(t)], establish the second auxiliary polynomial λ 12 (s) and λ 22 (s), the calculation formula is as follows: Through the first positive definite symmetric matrix function and the first auxiliary polynomial, the following relationship holds: In the formula, R 11 , R12 , R 13 , R 22 , R 23 are the elements in the symmetric matrix R respectively; Summarizing the above relationships, we can obtain the improved first relaxation matrix function: in, Similarly, through the second positive definite symmetric matrix function and the second auxiliary polynomial, the improved second relaxation matrix function can be obtained: in, Since R>0 and U>0, we can get V S1 (t)>0,V S2 (t)>0.

[0035] S4. A first augmented Lyapunov functional model of a nominal load frequency control model is constructed by combining a first relaxation matrix function with multiple integrals, and a second augmented Lyapunov functional model of an uncertain load frequency control model is constructed by combining a second relaxation matrix function with multiple integrals.

[0036] The calculation formula of the first augmented Lyapunov functional model is as follows: In the formula, The calculation formula of the second augmented Lyapunov functional model is as follows: In the formula, ψ T (t) is the column of the matrix of the delay-dependent state vector and the delay-independent state vector, ψ T (t) = {x1(t), x2(t)}, where P, W, and Z are any positive definite symmetric matrices.

[0037] S5. According to the mutually inverse convex combination lemma, the first augmented Lyapunov functional model is improved, and the asymptotic stability criterion of the load frequency control system is obtained by combining the Bessel-Legendre inequality. The asymptotic stability analysis of the load frequency control system under the access of electric vehicles and distributed power sources is completed.

[0038] Specifically, S5 includes the following sub-steps: Derivative the first augmented Lyapunov functional model to obtain the first derivative result; Differentiating the first relaxation matrix function to obtain a first differential result, and differentiating the second relaxation matrix function to obtain a second differential result; According to the first derivative result and the first differential result, the differential form of the first relaxation matrix function is converted in combination with the change state of the symmetric matrix under the time lag change to obtain the third differential result; The first derivative result, the second differential result and the integral term of the third differential result are defined by using the mutually inverse convex combination lemma, and the first augmented Lyapunov functional model is improved according to the defined results. The Bessel-Legendre inequality is used to perform the Schur complement lemma on the improved first augmented Lyapunov functional model to obtain the asymptotic stability conditions of the load frequency control system and complete the asymptotic stability analysis of the load frequency control system under the access of electric vehicles and distributed generation.

[0039] S6. Calculate the second augmented Lyapunov functional model to obtain the robust stability criterion of the load frequency control system under the access of electric vehicles and distributed power sources, and complete the robust stability analysis of the load frequency control system.

[0040] Specifically, S6 includes the following sub-steps: Differentiate the second augmented Lyapunov functional model and obtain the fourth differential result; The fourth differential result is summed with the augmented matrix of the uncertain load frequency control model. If the summation result satisfies the relational operation conditions between the symmetric matrix and the arbitrary system matrix, the load frequency control system under the access of electric vehicles and distributed power sources is robustly stable.

[0041] As an implementation method, to simplify the expression, the following parameter expression is defined: l1=col{e1,e9}, ι2=col{e 01 , e 02}, ε=col{e, e5, e7}, ε1=col{e 01 ,0,0} For given scalars η, μ, κ1 and κ2, if there exists a symmetric matrix R = [R ij ] 3×3 >0, U=[U ij ] 3×3 >0, P>0, W>0, Z>0 and any matrix M m and T m (m=1,2), satisfying the following relationship: Then, the nominal load frequency control system connected to electric vehicles and wind power generation reaches asymptotic stability.

[0042] The process of asymptotic stability analysis for load frequency control systems is as follows: Taking the derivative of V(t) we get: in, V s1 (t) Differentiate it and we get It cannot be expressed in a linear form as ζ(t), through The time-delay correlation matrix of , the third differential result is obtained: in, According to the inverse convex combination lemma, if there exists any matrix M of suitable dimension m and N m , then the integral definition results are as follows: in: According to the definition results, the first augmented Lyapunov functional model is improved to obtain: Based on the Bessel-Legendre inequality, by Schur complement lemma, if Then the asymptotic stability of the load frequency control system under the access of electric vehicles and distributed generation is as follows:

[0043] The robust stability analysis process for load frequency control system uncertainty is as follows: For any matrix X1, X2, there is the following relationship: When differentiating the second augmented Lyapunov functional model, plus the right side of equation (39), if the relational operation conditions between the symmetric matrix and the arbitrary system matrix are satisfied, the robust stability of the uncertain load frequency control system under the access of electric vehicles and distributed generation, the relational operation conditions between the symmetric matrix and the arbitrary system matrix are as follows: Among them, η, μ, κ1, κ2 and φ are given scalars, φ>0, X m is an arbitrary matrix.

[0044] Beneficial effects of the embodiment: The characteristics of the load frequency control system and the disturbance factors caused by the change of the charge state are fully considered, and a robust stability analysis method is established. By introducing auxiliary polynomials with variable parameters, two types of improved relaxation matrix functions are proposed, which effectively include the relationship between the system state, the time-delay state, and the integral state. Thanks to the time-delay product setting of the relaxation matrix function, the time-delay change information can be fully reflected. Combining the relaxation matrix function, the augmented matrix and the multiple integrals, through the Bessel-Legendre inequality, the Lyapunov stability analysis method is adopted to obtain the asymptotic stability criterion of the nominal load frequency control system and the robust stability criterion of the uncertain load frequency control system, respectively, to achieve system performance optimization and improve the scope of use of the method. In addition, the characteristic information of the charging process can be effectively utilized to improve the efficiency of system analysis.

[0045] The above specific implementations are preferred implementations of the present invention, and are not intended to limit the specific implementation scope of the present invention. The scope of the present invention includes but is not limited to the present specific implementations. All equivalent changes made in accordance with the shape, structure, and method of the present invention are within the protection scope of the present invention.

Claims

1. A stability analysis method for time-delay load frequency control considering electric vehicle access, characterized by: The steps include: S1. Construct an uncertain load frequency control model under the access of electric vehicles and distributed power sources; S2. Reconstructing the uncertain load frequency control model according to the time-delay change state of the load frequency control system to obtain a nominal load frequency control model; S3, establishing auxiliary polynomials according to the time lag state of the electric vehicle and the distributed power source in the load frequency control system, and constructing improved first relaxation matrix functions and second relaxation matrix functions; S4, constructing a first augmented Lyapunov functional model of the nominal load frequency control model by combining the first relaxation matrix function with multiple integrals, and constructing a second augmented Lyapunov functional model of the uncertain load frequency control model by combining the second relaxation matrix function with multiple integrals; S5. Improve the first augmented Lyapunov functional model according to the mutually inverse convex combination lemma, obtain the asymptotic stability criterion of the load frequency control system by combining the Bessel-Legendre inequality, and complete the asymptotic stability analysis of the load frequency control system under the access of electric vehicles and distributed power sources; S6. Calculate the second augmented Lyapunov functional model to obtain the robust stability criterion of the load frequency control system under the access of electric vehicles and distributed power sources, and complete the robust stability analysis of the load frequency control system.

2. The method for analyzing the stability of time-delay load frequency control considering electric vehicle access according to claim 1 is characterized in that: The S1 comprises the following sub-steps: S11, establishing a load frequency state vector based on the operating state parameters of the load frequency control system in the single area connected to the electric vehicle and the distributed power source, and the time lag of the dynamic change of the electric vehicle and the distributed power source in the network transmission; S12, calculating the electric vehicle gain according to the charge state fluctuation of the electric vehicle, and establishing a load frequency control matrix based on the operation characteristics of the electric vehicle and the distributed power source connected to the power system; Wherein, the operating characteristics at least include: turbine droop characteristics, inertia coefficient, load damping coefficient, turbine time constant, governor constant, electric vehicle participation rate, turbine participation rate, electric vehicle droop characteristics; S13, constructing a load frequency control system model according to the load frequency state vector and the load frequency control matrix; S14. Taking the stability of the load frequency control system as the goal, the load frequency control system model is improved according to the time-varying data of the load frequency control matrix to obtain the uncertain load frequency control model.

3. The method for analyzing the stability of time-delay load frequency control considering electric vehicle access according to claim 2 is characterized in that: The load frequency state vector is expressed as follows: x(t)=[ΔfΔP m ΔP v ΔP ev ∫ACE] T ; Where Δf represents the frequency deviation, ΔP m Represents the generator mechanical output, ΔP v Indicates valve position, ΔP ev represents the power output deviation, and ∫ACE represents the system frequency difference integral signal.

4. The method for analyzing the stability of time-delay load frequency control considering electric vehicle access according to claim 2 is characterized in that: Electric vehicle gain K ev The calculation formula is as follows: K ev =K max -K max g(t); Among them, SOC max Indicates the maximum state of charge of electric vehicles, SOC min Indicates the minimum state of charge of electric vehicles, SOC high Indicates the high state of charge of electric vehicles, SOC low Indicates the low charge state of electric vehicles, K max represents the maximum V2G droop characteristic, g(t) represents the time-varying limit function, Δf represents the frequency deviation, K ev,a It represents the gain value of electric vehicle under different frequency deviation ranges.

5. The method for analyzing the stability of time-delay load frequency control considering electric vehicle access according to claim 2 is characterized in that: The uncertain load frequency control model is expressed as follows: Where w(t) represents the output power change vector of electric vehicles and distributed power sources within time t, w = [ΔP d ΔP WTG ], x(t) represents the load frequency state vector, ΔP d Represents the output power change vector of the electric vehicle, ΔP WTG represents the output power change of the wind turbine in the distributed power source, η(t) represents the time delay under network transmission, 0≤η(t)≤η, A represents the first system matrix, B represents the system variable matrix, F represents the inertia coefficient matrix, ΔA represents the electric vehicle battery matrix, and ΔB represents the system frequency difference proportional-integral matrix.

6. The method for analyzing the stability of time-delay load frequency control considering electric vehicle access according to claim 1 is characterized in that: The nominal load frequency control model is shown as follows: Where x1(t) represents the time-delay-dependent state vector, x1=[Δf∫ACE] T , x2(t) represents the time-delay-independent state vector, x2=[ΔP m ΔP v ΔP ev ] T , Δf represents the frequency deviation, ΔP m Represents the generator mechanical output, ΔP v Indicates valve position, ΔP ev represents the power output deviation, ∫ACE represents the system frequency difference integral signal, A 11 , A 12 , A 21 , A 22 denote the first system matrix of time-delay separation, represents the system variable matrix after time-delay separation, represents a first model function of the nominal load frequency control model, A second model function representing the nominal load frequency control model.

7. The method for analyzing the stability of time-delay load frequency control considering electric vehicle access according to claim 1 is characterized in that: The S3 comprises the following sub-steps: Based on the time-delay state of the load frequency control system, a positive definite symmetric matrix function is constructed using adjustable parameters. Based on the time-delay boundary relationship, the time-delay interval is divided and the auxiliary polynomial is established; The positive definite symmetric matrix function is calculated based on the double auxiliary polynomial to obtain an improved relaxation matrix function.

8. The method for analyzing the stability of time-delay load frequency control considering electric vehicle access according to claim 7 is characterized in that: Constructing a positive definite symmetric matrix function specifically includes: based on a continuously differentiable function, introducing the variable parameter, if there is a symmetric matrix of a dimension that conforms to the continuously differentiable function, constructing the positive definite symmetric matrix function based on an augmented function; Establishing the auxiliary polynomial specifically includes: dividing the time lag interval based on the time lag boundary relationship, and establishing the auxiliary polynomial using the adjustable parameters; Calculating the improved relaxation matrix function specifically includes: based on the divided time lag interval, using the auxiliary polynomial in combination with the positive definite symmetric matrix function to construct a relationship equation, simplifying the relationship equation and inserting it into the positive definite symmetric matrix function after variable substitution to obtain a transformed positive definite symmetric matrix function, and using it as the improved relaxation matrix function.

9. The method for analyzing the stability of time-delay load frequency control considering electric vehicle access according to claim 1 is characterized in that: The S5 comprises the following sub-steps: Derivative the first augmented Lyapunov functional model to obtain a first derivative result; Differentiating the first relaxation matrix function to obtain a first differential result, and differentiating the second relaxation matrix function to obtain a second differential result; According to the first derivative result and the first differential result, the differential form of the first relaxation matrix function is converted in combination with the change state of the symmetric matrix under the time lag change to obtain a third differential result; The integral terms of the first derivative result, the second differential result and the third differential result are defined using the mutually inverse convex combination lemma, and the first augmented Lyapunov functional model is improved based on the definition results; the Schur complement lemma is applied to the improved first augmented Lyapunov functional model using the Bessel-Legendre inequality to obtain the asymptotic stability criterion of the load frequency control system, and to complete the asymptotic stability analysis of the load frequency control system under the access of electric vehicles and distributed power sources.

10. The method for analyzing the stability of time-delay load frequency control considering electric vehicle access according to claim 1, characterized in that: The S6 comprises the following sub-steps: Differentiating the second augmented Lyapunov functional model to obtain a fourth differential result; The fourth differential result and the augmented matrix of the uncertain load frequency control model are summed. If the summation result satisfies the relational operation conditions between the symmetric matrix and the arbitrary system matrix, the load frequency control system under the access of electric vehicles and distributed power sources is robustly stable.

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