Method and system for analyzing disturbance rejection capability of time-delayed load frequency control system

Abstract

The application discloses a kind of time delay load frequency control system's disturbance suppression capability analysis method and system, it relates to power system load frequency control technical field.The method comprises the following steps: based on the state space model of wind storage combined frequency regulation model construction wind storage combined frequency modulation time delay load frequency control system, and separate time delay related variable and time delay independent variable from state space model;Augmented Lyapunov-Krasovskii functional is constructed, and the disturbance suppression capability and time delay tolerance capability of time delay load frequency control system are evaluated, and the system disturbance suppression capability criterion is obtained;The system disturbance suppression capability criterion is solved, and the disturbance suppression capability analysis result of time delay load frequency control system is obtained.The application significantly reduces the conservativeness of system time delay tolerance capability and disturbance suppression capability, fundamentally improves the adaptability of power grid to renewable energy fluctuation.

Description

Technical Field

[0001] This invention relates to the field of power system frequency control technology, and in particular to a method and system for analyzing the disturbance suppression capability of a time-delay load frequency control system. Background Technology

[0002] Load frequency control systems have always been the core mechanism for maintaining dynamic stability and recovering frequency deviations in power systems. However, with the increasing penetration of renewable energy (wind power) in power systems, the strong fluctuations and randomness of its output, as well as the low inertia and insufficient damping caused by grid connection via inverters, severely affect the system's frequency response capability. When encountering large disturbances, peak loads, or inverter failures, the system is more prone to frequency drops, increased rate of frequency change, and increased steady-state deviations. Traditional frequency regulation methods based on synchronous generators are insufficient to effectively address the dynamic security issues arising from the integration of high proportions of renewable energy.

[0003] Furthermore, time delay is another key factor affecting the stability and performance of load frequency control systems. Time delay mainly originates from signal transmission, sensor sampling, communication links, and controller calculations, and typically exhibits time-varying characteristics. Traditional analysis methods tend to be conservative, and the integration of renewable energy into the grid increases system complexity, making the analysis of disturbance suppression capabilities extremely difficult.

[0004] Traditional frequency regulation methods based on synchronous generators involve two control loops: inertial response and primary and secondary frequency regulation. Inertial response is a passive response, where the synchronous generator's large inertia absorbs frequency changes. Primary frequency regulation adjusts the prime mover valves to change the generated power. It has a fast response but can only stabilize the frequency at the new value and cannot eliminate deviations. Secondary frequency regulation is executed by the automatic generator control unit system, achieving error-free frequency regulation by issuing commands to the generator unit. However, it has a large control loop and a long response time.

[0005] However, due to mechanical inertia and thermal limitations, synchronous generators have a slow adjustment speed that cannot keep up with the fluctuations and disturbances brought by new energy sources. As a result, traditional frequency regulation methods based on synchronous generators are difficult to effectively cope with the dynamic security issues brought about by the high proportion of renewable energy access. Summary of the Invention

[0006] Therefore, it is necessary to provide a method and system for analyzing the disturbance suppression capability of a time-delay load frequency control system to address the aforementioned technical problems.

[0007] This invention provides a method for analyzing the disturbance suppression capability of a time-delay load frequency control system, comprising:

[0008] Construct a joint frequency regulation model that includes wind power generation, electric vehicles, and battery energy storage systems;

[0009] A state-space model of a time-delay load frequency control system for wind-storage joint frequency regulation is constructed based on a joint frequency regulation model. The time-delay-related and time-delay-independent state variables are separated from the state-space model by model reconstruction technology, and time-delay-related and time-delay-independent variables are obtained respectively.

[0010] An augmented Lyapunov-Krasovskii functional is constructed based on time-delay-related and time-delay-independent variables. The disturbance suppression capability and time-delay tolerance capability of the time-delay load frequency control system are evaluated through the augmented Lyapunov-Krasovskii functional, and the system disturbance suppression capability criterion expressed in terms of linear matrix inequalities is obtained.

[0011] The disturbance suppression capability criterion of the system is solved to obtain the disturbance suppression capability analysis results of the time-delay load frequency control system.

[0012] Optionally, a joint frequency regulation model incorporating wind power generation, electric vehicles, and battery energy storage systems is constructed, specifically including:

[0013] By connecting wind power generation to the load side of the power system, connecting battery energy storage system to the primary frequency regulation circuit of the power system, and connecting electric vehicles to the secondary frequency regulation circuit of the power system, a joint frequency regulation model is obtained.

[0014] The battery energy storage system employs a droop control strategy based on state-of-charge feedback.

[0015] Optionally, the droop control strategy based on state-of-charge feedback specifically includes:

[0016] The relationship between the state of charge (SBC) of a battery energy storage system and the power change of the battery energy storage system is determined based on the following formula:

[0017] ;

[0018] in, ( s () represents the state of charge of the battery energy storage system. ( s ) The change in power of battery energy storage. E The nominal capacity of the energy storage system. h Factors in hours and seconds, For the capacity of the battery energy storage system, s It is a complex frequency variable;

[0019] The relationship between the power variation of the battery energy storage system and the frequency deviation of the power system is determined based on the following formula:

[0020] ;

[0021] ;

[0022] in, Let be the time response constant of the battery energy storage system. For droop gain in battery energy storage, ( t () represents the frequency offset. ( t ) for the battery at time t The change in state of charge, Unit conversion factor, This represents the maximum value of the frequency offset. This is the minimum value of the frequency offset. This refers to the charge adjustment range.

[0023] Optionally, the relationship between droop gain and state of charge includes:

[0024] ;

[0025] ;

[0026] in, This refers to the real-time state of charge of the battery energy storage system. The value is at the nominal frequency. This is the upper limit threshold for the state of charge. This is the upper limit threshold for the charged state. This represents the maximum value of the droop coefficient. This represents the minimum value of the droop coefficient. This is the adaptive droop coefficient in discharge mode. This is the adaptive droop coefficient in charging mode;

[0027] When the power system frequency is less than zero, the real-time adaptive droop coefficient of the battery energy storage system Represented as The battery energy storage system discharges;

[0028] When the power system frequency is greater than zero, the real-time adaptive droop coefficient of the battery energy storage system Represented as The battery energy storage system is used for charging.

[0029] Optionally, a state-space model of a time-delay load frequency control system for wind-storage joint frequency regulation is constructed based on a joint frequency regulation model. Then, through model reconstruction techniques, time-delay-dependent and time-delay-independent state variables are separated from the state-space model, yielding time-delay-dependent and time-delay-independent variables, specifically including:

[0030] The state-space model of the time-delay load frequency control system for wind-storage joint frequency regulation is constructed based on the following formula:

[0031] ;

[0032] in, The first derivative of the state variable. For state variables, For the disturbance variable, For the system matrix, For the delay system matrix, Input matrix to the system, This is the controlled output of the time-delay load frequency control system. For the system output matrix, t ( t ) represents a delayed state variable;

[0033] Based on the following formula, delay-dependent and delay-independent state variables are separated from the state-space model using model reconstruction techniques, resulting in delay-dependent and delay-independent variables respectively:

[0034] ;

[0035] in, The first derivative of the time-delay-related variables, A 11 and A 12 For the system matrix related to time delay, F 1 represents the time-delay-dependent perturbation input matrix. For time-delay related state variables, For time-delay-independent state variables, For time-delay related perturbation variables, The first derivative of the time-delay-independent variable, A 21 and A 22 For a system matrix that is independent of time delay, A d For time-delay feedback matrix, F 2 represents the time-delay-independent perturbation input matrix. For time-delay-independent perturbation variables These are the standard basis vectors of the transition matrix.

[0036] Optionally, an augmented Lyapunov-Krasovskii functional can be constructed based on the following equation, considering both delay-dependent and delay-independent variables:

[0037] ;

[0038] in, V ( t () is an augmented Lyapunov-Krasovskii functional. P , Q 1. Q 2. X 1. X 2. Y 1 and Y 2 represents the decision variables of the augmented Lyapunov-Krasovskii functional. s 1. s 2. s 3. s 4. ℓ 1. ℓ 2. ℓ 3 and ℓ 4 represents the state variables of the augmented Lyapunov-Krasovskii functional. h - t + s ) represents the weights that change over time.

[0039] This invention provides a disturbance suppression capability analysis system for a time-delay load frequency control system, comprising:

[0040] The model building module is used to build a joint frequency regulation model that includes wind power generation, electric vehicles and battery energy storage systems.

[0041] The model reconstruction module is used to construct the state space model of the wind-storage joint frequency regulation time-delay load frequency control system based on the joint frequency regulation model, and to separate the time-delay-related state variables and the time-delay-independent state variables from the state space model through model reconstruction technology, so as to obtain the time-delay-related variables and the time-delay-independent variables respectively.

[0042] The evaluation module is used to construct an augmented Lyapunov-Krasovskii functional based on time-delay-related and time-delay-independent variables, and to evaluate the disturbance suppression capability and time-delay tolerance capability of the time-delay load frequency control system through the augmented Lyapunov-Krasovskii functional, thereby obtaining the system disturbance suppression capability criterion expressed in linear matrix inequalities.

[0043] The solver module is used to solve the disturbance suppression capability criteria of the system and obtain the disturbance suppression capability analysis results of the time-delay load frequency control system.

[0044] The disturbance suppression capability analysis method and system for a time-delay load frequency control system provided in this invention have the following advantages compared with the prior art:

[0045] This invention employs a droop control strategy based on state-of-charge feedback, enabling the battery energy storage system to rapidly respond to power deficits based on system frequency deviations and its own state. Furthermore, it separates time-delay-dependent and time-delay-independent variables through model reconstruction technology, accurately characterizing the time-delay effects in the control loop. This design not only directly compensates for the mechanical inertia delay of the synchronous generator through the millisecond-level response speed of the battery energy storage system and electric vehicles, but also ensures the dynamic safety boundary of the power grid with a high proportion of renewable energy under the influence of time delays through stability analysis. This significantly reduces the conservatism of the system's time-delay tolerance and disturbance suppression capabilities, fundamentally improving the grid's adaptability to renewable energy fluctuations. Attached Figure Description

[0046] Figure 1 This is a flowchart illustrating a disturbance suppression capability analysis method for a time-delay load frequency control system provided in one embodiment. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0048] This invention provides a method for analyzing the disturbance suppression capability of a time-delay load frequency control system, the method comprising:

[0049] Construct a joint frequency regulation model that includes wind power generation, electric vehicles and battery energy storage systems.

[0050] A state-space model of a time-delay load frequency control system for wind-storage joint frequency regulation is constructed based on a joint frequency regulation model. The time-delay-related and time-delay-independent state variables are separated from the state-space model by model reconstruction technology, resulting in time-delay-related and time-delay-independent variables, respectively.

[0051] An augmented Lyapunov-Krasovskii functional is constructed based on time-delay-dependent and time-delay-independent variables. The disturbance suppression capability and time-delay tolerance capability of the time-delay load frequency control system are evaluated using the augmented Lyapunov-Krasovskii functional, and the system disturbance suppression capability criterion expressed in terms of linear matrix inequalities is obtained.

[0052] The disturbance suppression capability criterion of the system is solved to obtain the disturbance suppression capability analysis results of the time-delay load frequency control system.

[0053] Preferably, a joint frequency regulation model is constructed, comprising wind power generation, electric vehicles, and battery energy storage systems. Specifically, this involves connecting wind power generation to the load side of the power system, connecting the battery energy storage system to the primary frequency regulation loop of the power system, and connecting the electric vehicles to the secondary frequency regulation loop of the power system, thus obtaining the joint frequency regulation model. The battery energy storage system employs a droop control strategy based on state-of-charge feedback.

[0054] The specific implementation is as follows:

[0055] S1: Construct a joint frequency regulation model including electric vehicles and battery energy storage systems under the premise of wind power grid connection, namely, a time-delay load frequency control system for wind and energy storage joint frequency regulation.

[0056] Among them, electric vehicles and battery energy storage systems (the battery energy storage system adopts a droop control strategy based on state-of-charge feedback) are modules that make up the load frequency control system. The construction process of the wind-storage joint frequency regulation time-delay load frequency control system is as follows: wind power generation is connected to the load end of the power system, the battery energy storage system is connected to the primary frequency regulation circuit of the power system, and electric vehicles are connected to the secondary frequency regulation circuit of the power system.

[0057] S2: Establish a state-space model of the time-delay load frequency control system for wind-storage joint frequency regulation, and separate time-delay-related variables and time-delay-independent variables through model reconstruction.

[0058] The process of constructing a state-space model includes: first, determining the state variables of the system; then, writing the differential equations based on the transfer functions of the state variables; and finally, obtaining the expression for the state-space model of the system based on the differential equations.

[0059] Time-delay-related variables represent variables in a time-delay load frequency control system that are directly related to time delay. By separating these two variables, the analysis of the system's disturbance suppression capability can be performed by focusing primarily on the time-delay-related state variables, rather than analyzing all the system's state variables, thus greatly reducing the complexity of the analysis.

[0060] S3: A time-delay-dependent disturbance suppression capability evaluation method based on the augmented Lyapunov-Krasovskii functional is proposed. The disturbance suppression capability and time delay tolerance capability of the time-delay load frequency control system are evaluated by the augmented Lyapunov-Krasovskii functional, and the system disturbance suppression capability criterion is obtained (the disturbance suppression capability and time delay tolerance capability are obtained by solving the robust performance index and the upper bound of the maximum time delay of the system using the obtained disturbance suppression capability criterion, which are both in numerical form).

[0061] S4: Solve the system disturbance suppression capability criterion to obtain the disturbance suppression capability analysis results of the time-delay load frequency control system.

[0062] Furthermore, the relationship between the state of charge of a battery energy storage system and the change in power of the battery energy storage system can be expressed as:

[0063] ;

[0064] in, ( s () represents the state of charge of the battery energy storage system. ( s ) The change in power of battery energy storage. E The nominal capacity of the energy storage system. h Factors in hours and seconds, For the capacity of the battery energy storage system, s It is a complex frequency variable.

[0065] The power variation of the battery energy storage system and the frequency deviation of the power system ( The relation can be expressed as:

[0066] ;

[0067] ;

[0068] in, Let be the time response constant of the battery energy storage system. For droop gain in battery energy storage, ( t () represents the frequency offset. ( t ) for the battery at time t The change in state of charge, Unit conversion factor, This represents the maximum value of the frequency offset. This is the minimum value of the frequency offset. This refers to the charge adjustment range.

[0069] Furthermore, the state-space model of the time-delay load frequency control system for wind-storage combined frequency regulation is as follows:

[0070] ;

[0071] ;

[0072] ;

[0073] ;

[0074] ;

[0075] ; ;

[0076] By using model reconstruction techniques, delay-dependent and delay-independent state variables are separated from the state-space model, resulting in delay-dependent and delay-independent variables, respectively.

[0077] ; ;

[0078] in, The first derivative of the state variable. For state variables, For the disturbance variable, For the system matrix, For the delay system matrix, Input matrix to the system, This is the controlled output of the time-delay load frequency control system. For the system output matrix, t ( t ) represents a delayed state variable. The first derivative of the time-delay-related variables, A 11 and A 12 For the system matrix related to time delay, F 1 represents the time-delay-dependent perturbation input matrix. For time-delay related state variables, For time-delay-independent state variables, For time-delay related perturbation variables, The first derivative of the time-delay-independent variable, A 21 and A 22 For a system matrix that is independent of time delay, A d For time-delay feedback matrix, F 2 represents the time-delay-independent perturbation input matrix. For time-delay-independent perturbation variables These are the standard basis vectors of the transition matrix.

[0079] Furthermore, the augmented Lyapunov-Krasovskii functional is:

[0080] ;

[0081] in:

[0082] ;

[0083] in, V ( t () is an augmented Lyapunov-Krasovskii functional. P , Q 1. Q 2. X 1. X 2. Y 1 and Y 2 represents the decision variables of the augmented Lyapunov-Krasovskii functional. s 1. s 2. s 3. s 4. ℓ 1. ℓ 2. ℓ 3 and ℓ 4 represents the state variables of the augmented Lyapunov-Krasovskii functional. h - t + s ) represents the weights that change over time.

[0084] Subsequently, through the The derivative of the expression can be transformed into a linear matrix inequality form to obtain the evaluation criteria for disturbance suppression capability.

[0085] Furthermore, the impact of the state of charge (SBC) of a battery energy storage system on system performance was also proposed, with the SBC affecting the droop gain of the battery energy storage system. droop gain Influences the system matrix droop gain The relationship between the state of charge and the state of charge can be expressed as:

[0086] ;

[0087] ;

[0088] in, This refers to the real-time state of charge of the battery energy storage system. The value is at the nominal frequency. This is the upper limit threshold for the state of charge. This is the upper limit threshold for the charged state. This represents the maximum value of the droop coefficient. This represents the minimum value of the droop coefficient. This is the adaptive droop coefficient in discharge mode. This is the adaptive droop coefficient in charging mode.

[0089] When the power system frequency is less than zero, the real-time adaptive droop coefficient of the battery energy storage system Represented as The battery energy storage system discharges. When the power system frequency is greater than zero, the real-time adaptive droop coefficient of the battery energy storage system... Represented as The battery energy storage system is charging.

[0090] This invention establishes a novel power system model for wind-storage joint frequency regulation. By introducing a droop control strategy based on battery state-of-charge feedback, it effectively overcomes the shortcomings of traditional models that either do not consider the energy storage system or, if they do, do not consider the internal state of the energy storage system, thus failing to reflect the actual dynamic characteristics of the energy storage system. By constructing a reconstruction model that considers time-varying delays and combining it with an augmented Lyapunov-Krasovskii functional and integral inequality method, the conservatism of the system's time delay tolerance and disturbance suppression capabilities is significantly reduced. Furthermore, the proposed anti-interference performance evaluation method significantly reduces computational complexity while maintaining accuracy, making it suitable for multi-resource coordinated frequency regulation systems with a high proportion of renewable energy access, and possessing stronger engineering applicability and practical guiding value.

[0091] Based on the same inventive concept, embodiments of the present invention also provide a disturbance suppression capability analysis system for a time-delay load frequency control system, comprising:

[0092] The model building module is used to build a joint frequency regulation model that includes wind power generation, electric vehicles and battery energy storage systems.

[0093] The model reconstruction module is used to construct the state space model of the wind-storage joint frequency regulation time-delay load frequency control system based on the joint frequency regulation model. It also uses model reconstruction technology to separate the time-delay-related state variables and the time-delay-independent state variables from the state space model, thus obtaining the time-delay-related variables and the time-delay-independent variables, respectively.

[0094] The evaluation module is used to construct an augmented Lyapunov-Krasovskii functional based on time-delay-related and time-delay-independent variables, and to evaluate the disturbance suppression capability and time-delay tolerance capability of the time-delay load frequency control system through the augmented Lyapunov-Krasovskii functional, thereby obtaining the system disturbance suppression capability criterion expressed in linear matrix inequalities.

[0095] The solver module is used to solve the disturbance suppression capability criteria of the system and obtain the disturbance suppression capability analysis results of the time-delay load frequency control system.

[0096] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A method for analyzing the disturbance suppression capability of a time-delay load frequency control system, characterized in that, include: Construct a joint frequency regulation model that includes wind power generation, electric vehicles, and battery energy storage systems; A state-space model of a time-delay load frequency control system for wind-storage joint frequency regulation is constructed based on a joint frequency regulation model. The time-delay-related and time-delay-independent state variables are separated from the state-space model by model reconstruction technology, and time-delay-related and time-delay-independent variables are obtained respectively. An augmented Lyapunov-Krasovskii functional is constructed based on time-delay-related and time-delay-independent variables. The disturbance suppression capability and time-delay tolerance capability of the time-delay load frequency control system are evaluated through the augmented Lyapunov-Krasovskii functional, and the system disturbance suppression capability criterion expressed in terms of linear matrix inequalities is obtained. The disturbance suppression capability criterion of the system is solved to obtain the disturbance suppression capability analysis results of the time-delay load frequency control system; The construction of the joint frequency regulation model, which includes wind power generation, electric vehicles, and battery energy storage systems, specifically includes: By connecting wind power generation to the load side of the power system, connecting battery energy storage system to the primary frequency regulation circuit of the power system, and connecting electric vehicles to the secondary frequency regulation circuit of the power system, a joint frequency regulation model is obtained. The battery energy storage system adopts a droop control strategy based on state of charge feedback. The droop control strategy based on state-of-charge feedback specifically includes: The relationship between the state of charge (SBC) of a battery energy storage system and the power change of the battery energy storage system is determined based on the following formula: ； in, ( s () represents the state of charge of the battery energy storage system. ( s () represents the change in power stored in the battery. E The nominal capacity of the energy storage system. h Factors in hours and seconds, For the capacity of the battery energy storage system, s It is a complex frequency variable; The relationship between the power variation of the battery energy storage system and the frequency deviation of the power system is determined based on the following formula: ； ； in, Let be the time response constant of the battery energy storage system. For droop gain in battery energy storage, ( t () represents the frequency offset. ( t ) for the battery at time t The change in state of charge, Unit conversion factor, This represents the maximum value of the frequency offset. This is the minimum value of the frequency offset. For charge regulation range; The relationship between droop gain and the state of charge specifically includes: ； ； in, This refers to the real-time state of charge of the battery energy storage system. The value is at the nominal frequency. This is the upper limit threshold for the state of charge. This is the upper limit threshold for the charged state. This represents the maximum value of the droop coefficient. This represents the minimum value of the droop coefficient. This is the adaptive droop coefficient in discharge mode. This is the adaptive droop coefficient in charging mode; When the power system frequency is less than zero, the real-time adaptive droop coefficient of the battery energy storage system Represented as The battery energy storage system discharges; When the power system frequency is greater than zero, the real-time adaptive droop coefficient of the battery energy storage system Represented as The battery energy storage system is used for charging.

2. The disturbance suppression capability analysis method for a time-delay load frequency control system as described in claim 1, characterized in that, The state-space model of the time-delay load frequency control system for wind-storage joint frequency regulation is constructed based on the joint frequency regulation model. Then, through model reconstruction technology, time-delay-related and time-delay-independent state variables are separated from the state-space model to obtain time-delay-related and time-delay-independent variables, respectively. Specifically, these include: The state-space model of the time-delay load frequency control system for wind-storage joint frequency regulation is constructed based on the following formula: ； in, The first derivative of the state variable. For state variables, For the disturbance variable, For the system matrix, For the delay system matrix, Input matrix to the system, This is the controlled output of the time-delay load frequency control system. For the system output matrix, τ ( t ) represents a delayed state variable; Based on the following formula, delay-dependent and delay-independent state variables are separated from the state-space model using model reconstruction techniques, resulting in delay-dependent and delay-independent variables respectively: ； in, The first derivative of the time-delay-related variables, A 11 and A 12 For the system matrix related to time delay, F 1 represents the time-delay-dependent perturbation input matrix. For time-delay related state variables, For time-delay-independent state variables, For time-delay related perturbation variables, The first derivative of the time-delay-independent variable, A 21 and A 22 For a system matrix that is independent of time delay, A d For time-delay feedback matrix, F 2 represents the time-delay-independent perturbation input matrix. For time-delay-independent perturbation variables, These are the standard basis vectors of the transition matrix.

3. The disturbance suppression capability analysis method for a time-delay load frequency control system as described in claim 1, characterized in that, An augmented Lyapunov-Krasovskii functional is constructed based on the following formula, considering both time-delay-dependent and time-delay-independent variables: ； in, V ( t () is an augmented Lyapunov-Krasovskii functional. P , Q 1. Q 2. X 1. X 2. Y 1 and Y 2 represents the decision variables of the augmented Lyapunov-Krasovskii functional. σ 1. σ 2. σ 3. σ 4. ℓ 1. ℓ 2. ℓ 3 and ℓ 4 represents the state variables of the augmented Lyapunov-Krasovskii functional. h - t + s ) represents the weights that change over time.

4. A disturbance suppression capability analysis system for a time-delay load frequency control system, characterized in that, include: The model building module is used to build a joint frequency regulation model that includes wind power generation, electric vehicles and battery energy storage systems. The model reconstruction module is used to construct the state space model of the wind-storage joint frequency regulation time-delay load frequency control system based on the joint frequency regulation model, and to separate the time-delay-related state variables and the time-delay-independent state variables from the state space model through model reconstruction technology, so as to obtain the time-delay-related variables and the time-delay-independent variables respectively. The evaluation module is used to construct an augmented Lyapunov-Krasovskii functional based on time-delay-related and time-delay-independent variables, and to evaluate the disturbance suppression capability and time-delay tolerance capability of the time-delay load frequency control system through the augmented Lyapunov-Krasovskii functional, thereby obtaining the system disturbance suppression capability criterion expressed in linear matrix inequalities. The solver module is used to solve the disturbance suppression capability criteria of the system and obtain the disturbance suppression capability analysis results of the time-delay load frequency control system. The construction of the joint frequency regulation model, which includes wind power generation, electric vehicles, and battery energy storage systems, specifically includes: By connecting wind power generation to the load side of the power system, connecting battery energy storage system to the primary frequency regulation circuit of the power system, and connecting electric vehicles to the secondary frequency regulation circuit of the power system, a joint frequency regulation model is obtained. The battery energy storage system adopts a droop control strategy based on state of charge feedback. The droop control strategy based on state-of-charge feedback specifically includes: The relationship between the state of charge (SBC) of a battery energy storage system and the power change of the battery energy storage system is determined based on the following formula: ； in, ( s () represents the state of charge of the battery energy storage system. ( s () represents the change in power stored in the battery. E The nominal capacity of the energy storage system. h Factors in hours and seconds, For the capacity of the battery energy storage system, s It is a complex frequency variable; The relationship between the power variation of the battery energy storage system and the frequency deviation of the power system is determined based on the following formula: ； ； in, Let be the time response constant of the battery energy storage system. For droop gain in battery energy storage, ( t () represents the frequency offset. ( t ) for the battery at time t The change in state of charge, Unit conversion factor, This represents the maximum value of the frequency offset. This is the minimum value of the frequency offset. For charge regulation range; The relationship between droop gain and the state of charge specifically includes: ； ； in, This refers to the real-time state of charge of the battery energy storage system. The value is at the nominal frequency. This is the upper limit threshold for the state of charge. This is the upper limit threshold for the charged state. This represents the maximum value of the droop coefficient. This represents the minimum value of the droop coefficient. This is the adaptive droop coefficient in discharge mode. This is the adaptive droop coefficient in charging mode; When the power system frequency is less than zero, the real-time adaptive droop coefficient of the battery energy storage system Represented as The battery energy storage system discharges; When the power system frequency is greater than zero, the real-time adaptive droop coefficient of the battery energy storage system Represented as The battery energy storage system is used for charging.

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