A method for power system stability analysis and intelligent event triggering control

Abstract

This invention discloses a method for power system stability analysis and intelligent event triggering control, which relates to the field of power system control. The method includes: modeling the nonlinear factors of turbine valve position using TS fuzzy theory, treating electric vehicle gain as a time-varying function based on state-of-charge changes, and establishing a TS fuzzy LFC system model; using the GWO algorithm to search for an optimal trigger threshold with the optimization goals of minimizing the signal trigger rate and stabilizing the power system as quickly as possible; obtaining event trigger conditions based on the optimal trigger threshold and performing intelligent event triggering control; constructing a new delay segmentation set-related Lyapunov-Krasovskii functional during power system operation using an allowable delay segmentation method; and performing stability analysis on the TS fuzzy LFC system model based on the new delay segmentation set-related Lyapunov-Krasovskii functional to complete the power system stability analysis. This method can achieve optimal utilization of bandwidth resources and stabilize system status.

Description

Technical Field

[0001] The present invention relates to the field of power system control, and in particular to a power system stability analysis and intelligent event triggering control method. Background Art

[0002] Frequency is a key performance indicator in power system operation. Frequency fluctuations are caused by an imbalance between power generation and load demand. The load frequency control (LFC) system is one of the most important components of power system automation. By maintaining a balance between power generation and load demand, it plays a vital role in ensuring that frequency and tie-line power reach rated values. In actual power system operation, it is necessary to ensure that the system frequency remains stable near the rated value and that the balance between power generation and load demand is maintained. This balance is easily disturbed when a large number of electric vehicles (EVs) and wind power are connected to the system. For example, the charging and discharging behavior of EVs causes power fluctuations, and the intermittent and random nature of wind power can also affect the system frequency.

[0003] Modern power systems rely heavily on open communication networks, which introduce transmission delays into the control loops of LFCs. Due to the dynamic nature of network conditions and the environment, time delays often exhibit time-varying characteristics. Numerous studies have focused on identifying the delay margin of LFC systems, as it represents the threshold at which LFC systems may become unstable. Numerous studies have focused on identifying the delay margin of LFC systems, as it represents the threshold at which LFC systems may become unstable. The Lyapunov-Krasovskii functional (LKF) is a commonly used method for studying the stability of power systems with time delays and for identifying the maximum delay.

[0004] Prior art 1 solves the stability and stabilization problems of multi-region LFC power systems containing wind power through Lyapunov stability theory. Prior art 2 introduces a simple LKF, takes into account constant time delays and time-varying time delays, and establishes a time-delay-related stability criterion for multi-region LFC power systems. It should be noted that these basic LKFs do not capture the state information of the system. In order to break through these limitations, prior art 3 proposes an enhanced LKF with triple integrals to obtain a less conservative time-delay-related criterion for the LFC power system. Although considerable progress has been made in studying the time-delay-related stability problem of LFC power systems with time-varying time delays, there is still room for improvement.

[0005] In modern power systems, the application of open communication networks has significantly reduced communication costs and enhanced flexibility, making the design of efficient and reliable communication schemes crucial. In the field of LFC, the time-triggered mechanism was once a widely used communication scheme. However, a large number of redundant data packets wasted network resources. Against this backdrop, many researchers have proposed event-triggered mechanisms (ETMs), under which only data packets that meet specific triggering conditions are allowed to be sent to the network. Currently, improvements to ETMs typically involve setting fixed conditions to filter transmission signals. However, setting the filtering conditions to achieve an optimal balance between information transmission rate and system stability is a challenge. Summary of the Invention

[0006] In view of the above-mentioned deficiencies in the prior art, the present invention provides a power system stability analysis and intelligent event triggering control method that solves the problem that the prior art is difficult to efficiently balance the optimal utilization of bandwidth resources and the stability of the system state.

[0007] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0008] Provided is a power system stability analysis and intelligent event triggering control method, comprising:

[0009] The nonlinear factors of the turbine valve position are modeled using TS fuzzy theory. The electric vehicle gain is treated as a time-varying function based on the state of charge, and a TS fuzzy LFC system model is established. The TS fuzzy LFC system model is used to reflect the actual operating status of the power system.

[0010] Based on the TS fuzzy LFC system model, the optimal triggering threshold is searched using the GWO algorithm with the optimization goals of minimizing the signal triggering rate and stabilizing the power system as quickly as possible.

[0011] Obtain event trigger conditions based on the optimal trigger threshold, determine whether the sampling signal is transmitted based on the event trigger conditions, and complete intelligent event trigger control;

[0012] During the operation of the power system, a new type of delay partition set-related Lyapunov-Krasovskii functional is constructed through the allowed delay partition method;

[0013] The stability analysis of the TS fuzzy LFC system model is carried out based on the Lyapunov-Krasovskii functional related to the new delayed partition set, and the stability analysis of the power system is completed.

[0014] The beneficial effects of the present invention are:

[0015] 1. Based on the nonlinearity of turbine valve position and the SOC of electric vehicles, this method establishes a TS fuzzy LFC system model that is more in line with operating conditions. This TS fuzzy LFC system model can significantly improve the stability of the power system.

[0016] 2. Based on the TS fuzzy LFC system model, this method takes minimizing the signal trigger rate and stabilizing the power system as soon as possible as the optimization goal, and uses the GWO algorithm to search for the optimal trigger threshold, which can optimize bandwidth utilization.

[0017] 3. This method obtains the event trigger condition according to the optimal trigger threshold, determines whether the sampling signal is transmitted based on the event trigger condition, and completes the intelligent event trigger control, which can achieve the optimal utilization of bandwidth resources and the stability of the system status.

[0018] 4. Based on the allowed time delay partitioning method, this method develops a novel time delay partition set-related Lyapunov-Krasovskii functionals (LKFs), which relaxes the requirement that the Lyapunov-Krasovskii functional construction must span the entire time delay and its derivative interval, and realizes accurate analysis of power system stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 Schematic diagram of the process of this method;

[0020] Figure 2 The transfer function block diagram of the LFC system with wind power and electric vehicles;

[0021] Figure 3 Provide a trigger parameter optimization framework for the Intelligent Event Triggering Mechanism (IETM) based on the Grey Wolf Optimization (GWO) algorithm;

[0022] Figure 4 In the embodiment Status response when

[0023] Figure 5 In the embodiment Status response when

[0024] Figure 6 In the embodiment Status response when

[0025] Figure 7 In the embodiment The trigger interval of

[0026] Figure 8 In the embodiment Trigger interval under conditions;

[0027] Figure 9 In the embodiment Trigger interval under conditions;

[0028] Figure 10 In the embodiment Trigger interval under conditions;

[0029] Figure 11 In the embodiment Dynamic trajectory of the load frequency control (LFC) system state;

[0030] Figure 12 In the embodiment Dynamic trajectory of the load frequency control (LFC) system state;

[0031] Figure 13 In the embodiment Dynamic trajectory of the load frequency control (LFC) system state;

[0032] Figure 14 In the embodiment Dynamic trajectory of the load frequency control (LFC) system state when DETAILED DESCRIPTION

[0033] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0034] like Figure 1 As shown, the power system stability analysis and intelligent event triggering control method includes the following steps:

[0035] S1. Model the nonlinear factors of the turbine valve position using TS fuzzy theory, treat the electric vehicle gain as a time-varying function based on the state of charge, and establish a TS fuzzy LFC system model; the TS fuzzy LFC system model is used to reflect the actual operating status of the power system;

[0036] S2. Based on the TS fuzzy LFC system model, the GWO algorithm is used to search for the optimal trigger threshold with the optimization goals of minimizing the signal trigger rate and stabilizing the power system as quickly as possible;

[0037] S3. Obtain the event trigger condition based on the optimal trigger threshold, determine whether the sampling signal is transmitted based on the event trigger condition, and complete the intelligent event trigger control (IETC);

[0038] S4. During the operation of the power system, a new type of delay partitioning set-related Lyapunov-Krasovskii functional is constructed through the allowed delay partitioning method;

[0039] S5. Based on the Lyapunov-Krasovskii functional associated with the new delayed partition set, the stability analysis of the TS fuzzy LFC system model is performed to complete the stability analysis of the power system.

[0040] In this embodiment, the transfer function block diagram of the LFC system with wind power and electric vehicles is as follows: Figure 2 shown. 、 、 、 、 、 and denote the time-varying delay caused by the communication network, frequency deviation, generator mechanical output power, wind turbine generator (WTG) output power, electric vehicle output power, load, and load reference set point, respectively. 、 、 、 、 、 、 They represent the equivalent inertia constant, damping coefficient, turbine time constant, governor constant, governor differential characteristic, electric vehicle time constant, and differential characteristic respectively. and is the participation ratio of the speed regulator and electric vehicle, where .

[0041] Taking into account the nonlinearity of the turbine valve position, yes The nonlinear function of Indicates the actual deviation of the turbine valve position. The upper and lower limits of and .definition , , , Represents a column vector. Note that the LFC system adopts sampling control, and the control command is designed as , ,in Represents the triggering time set of the Intelligent Event Triggering Mechanism (IETM). 、 Represents the communication network k Trigger moment The transmission delay and k +1 trigger moment Therefore, through the TS fuzzy method, the LFC system can be reconstructed as:

[0042] Rule I: If belong ……and belong ……and belong ,but:

[0043]

[0044] in, , Represents the premise variable. , Represents the number of fuzzy rules. represents a fuzzy set, is the number of fuzzy sets. 、 , , The values ​​of have nothing to do with the fuzzy rules, so their values ​​are defined as , , , , specifically expressed as:

[0045]

[0046]

[0047] in, , Therefore, the defuzzified system can be transformed into:

[0048]

[0049] in, , , express exist The weight in .

[0050] In addition, electric vehicle gains Closely related to the SOC charging characteristics of electric vehicles. The relationship with SOC can be described as:

[0051]

[0052] in, 、 、 、 、 They represent the maximum vehicle-to-grid (V2G) regulation of electric vehicles and the upper limit, lower limit, high value and low value of the electric vehicle battery SOC respectively. It can be expressed as:

[0053] .

[0054] because is a time-varying function with a value range of [0,1], so Is a time-varying parameter. Considering the SOC of electric vehicles, there are uncertain parameters The TS fuzzy LFC system can be reconstructed as:

[0055] ;

[0056] With uncertain parameters The TS fuzzy LFC system takes into account various nonlinear conditions in the LFC power system and uses different methods to describe them, which is more in line with the actual situation.

[0057] Since the network bandwidth should be optimized when using the power communication network for information exchange between the remote terminal unit (RTU) and the control center, in this embodiment, the intelligent event triggering mechanism (IETM) will be used to reduce unnecessary information transmission, thereby saving network communication resources. Is the sampling period of RTU. Sampling signal Whether or not to transmit via the IETM generator depends on the following conditions:

[0058]

[0059] in, , . , Represents the output state of the LFC system at the current sampling time, which is equal to , Indicates the system status value at time mh, Refers to the output state triggered and sent by the IETM generator. , is determined by the IETM generator k Trigger moment The system status value. It represents the trigger threshold parameter, which ranges from [0,1] and will be optimized by the Grey Wolf Optimization (GWO) algorithm. , Therefore, the sampling time sequence that meets the event triggering condition is Constructing a trigger moment set , as shown below:

[0060] .

[0061] In addition, this embodiment designs a fuzzy event-triggered PI control rule, through To stabilize the TS fuzzy LFC power system:

[0062] Rule J: If belong ……and belong ……and belong ,but:

[0063] ;

[0064] Through defuzzification, the PI control strategy is constructed as follows:

[0065] .

[0066] Then substitute it into the The TS fuzzy LFC system, the TS fuzzy LFC model integrating event-triggered fuzzy control can be expressed as follows:

[0067] .

[0068] when When , the internal stability of the LFC system equilibrium point is equivalent to the stability of the origin. Therefore, the final expression of the TS fuzzy LFC system model is:

[0069]

[0070] in Indicates that the power system t The first derivative of the state vector at time ; is the number of fuzzy rules; For the A fuzzy membership function that satisfies ; For the A fuzzy membership function; 、 、 are the coefficient matrices related to power system dynamics, communication delay, and output, respectively; Indicates that electric vehicle gains are taken into account The coefficient matrix part of the time-varying characteristics related to the system state vector at time t, Indicates that electric vehicle gains are taken into account The coefficient matrix part of the time-varying characteristics related to the event triggering state; is the gain of TS fuzzy controller; For the power system at the sampling time The state vector of , is determined by the IETM generator k Trigger moment The system status value of For power systems t Output state matrix at time t; Indicates the communication network k Trigger moment The transmission delay, Indicates the communication network k +1 trigger moment transmission delay; , , , , , , , , is a time-varying function based on the change of state of charge, , is the maximum value of electric vehicle gain; is the state of charge of the electric vehicle, 、 、 and They represent the upper limit of the electric vehicle battery SOC, the lower limit of the electric vehicle battery SOC, the high value of the electric vehicle battery SOC and the low value of the electric vehicle battery SOC, respectively. is the trigger threshold, is the electric vehicle time constant, Represents the transpose of a matrix; is the participation rate of electric vehicles; and is a constant between 0 and 1, .

[0071] In this embodiment, the trigger threshold in IETM The value of is related to the signal triggering situation, which in turn affects the bandwidth utilization rate and the stability of the system. In order to achieve the lowest signal trigger rate and make the system stable as soon as possible, obtain the optimal It can be modeled as an optimization problem. GWO algorithm is selected to find the optimal , which is due to its advantages of low computational complexity, high solution accuracy, and ability to converge regardless of the initial conditions.

[0072] This optimization problem can be described as finding an optimal trigger threshold to minimize the total number of triggers of the IETM generator and ensure that the control objectives of the LFC are achieved. Therefore, the following optimization objectives are selected: First, minimize the total number of triggers of the IETM generator. Second, minimize the time integral of the absolute error (ITAE) of the area control error (ACE) signal to make the area exchange power and frequency deviation converge as quickly as possible. The indicator of ACE in LFC is defined as ,in In our method, the two optimization objectives are normalized. Inside, order Indicates the total number of signal triggering times of the IETM generator, Indicates the total number of sampling times of remote terminal units (RTUs) that exchange information with the power system control center. Indicates Pre-calculated within the range Therefore, the expression for the optimization goal of minimizing the signal trigger rate and stabilizing the power system as quickly as possible is:

[0073]

[0074] in represents the optimization objective function; Indicates taking the minimum value; and All are weights; for t The regional control error at the moment, , express t The power deviation of the inter-regional tie line at the moment, is the weight coefficient related to the frequency deviation, express t Frequency deviation caused by the communication network at all times.

[0075] like Figure 3 As shown, in the Grey Wolf Optimization (GWO) algorithm, the trigger threshold is considered as the position of each individual gray wolf. The optimization objective function Represents prey. The process of simulating the collective hunting behavior of gray wolves is essentially to find The trigger threshold is represented by the position of each individual gray wolf as The GWO algorithm uses the formula Calculate the distance between each gray wolf and its prey using the formula Simulate the process of gray wolf individuals moving towards prey. and Respectively represent The positions of prey and wolf individuals at the iteration, and Indicates the The position of the gray wolf at the iteration. Refers to the The distance between the gray wolf and the prey calculated at the iteration. and are the factors used to calculate the encirclement and distance respectively, which can be calculated by the following formula:

[0076]

[0077]

[0078] in is the delay factor, 、 Is a random variable. For the decay factor Processing it so that it first increases from 0 to a maximum value and then decays, rather than decreasing linearly, helps avoid falling into local optimality in complex optimization problems. The decay factor can be set as follows:

[0079]

[0080] in and Represent the maximum number of iterations and the current number of iterations respectively.

[0081] Based on the distance to the prey, the three wolves closest to the prey were designated as Wolf, Wolf and Wolf. The wolf acts as a leader, and other wolves move closer to it to get closer to their prey. Wolf Assist wolves, and provide additional guidance information to other wolves. Wolf and Wolf and The wolves coordinate to ensure the consistency of the pack's actions. In each iteration, each wolf Wolf, Wolf and The wolf updates its own position, continuously reducing the distance to its prey until the stopping condition is met. The wolf's final position is usually considered the optimal solution.

[0082] Among them, the formula:

[0083]

[0084]

[0085]

[0086] Represents the calculation of individual wolves and Wolf, Wolf and The distance between wolves.

[0087] formula:

[0088]

[0089]

[0090]

[0091] Indicates that individual wolves are approaching Wolf, Wolf and Wolves hunt their prey. Finally, individual wolves are classified according to the formula Update your location.

[0092] in 、 and Represents the distance between an individual wolf and the three leading wolves. 、 and They represent the positions of the three leading wolves. 、 and Respectively, they indicate that individual wolves move toward the three leading wolves. Indicates the next iteration The position in.

[0093] Therefore, the specific method of searching for the optimal trigger threshold using the GWO algorithm in this embodiment includes the following sub-steps:

[0094] S2-1. Set the total number of wolves and the maximum number of iterations so that the position of the individual gray wolf in each iteration represents the trigger threshold obtained by the search;

[0095] S2-2, initializing the position of the gray wolf representing the trigger threshold;

[0096] S2-3. Calculate the TS fuzzy controller gain and the position of the gray wolf individual and bring them into the TS fuzzy LFC system model to calculate the optimization objective function ;

[0097] S2-4, according to the optimization objective function Update the position of the alpha wolf and the positions of other individual gray wolves until the maximum number of iterations is reached, and output the optimal trigger threshold and TS fuzzy controller gain.

[0098] In this embodiment, the expression of the event triggering condition is:

[0099]

[0100] in is the weight matrix for measuring signal error and trigger conditions; is the optimal trigger threshold; The IETM generator k A certain output state is triggered and sent, ; is a time-dependent variable, The dynamic characteristics of Decide, , and All coefficients are greater than 0. for The first derivative of .

[0101] In this embodiment, based on the allowed time delay partitioning method, a novel Lyapunov-Krasovsky functional related to the time delay partitioning set is constructed. Conditional and Constraints. Therefore, and Can be divided into two sub-intervals 、 as well as 、 ,in , , Allowable delay set It can be divided into the following four subsets:

[0102]

[0103]

[0104]

[0105]

[0106] It defines and Based on the proposed allowed delay partitioning method, the expression of the Lyapunov-Krasovskii functional associated with the new delay partition set is:

[0107]

[0108] in represents the Lyapunov-Krasovskii functional associated with the new delayed partition set; , is the state vector related to the system state and time delay information, , represents a column vector, and They are defined as and , a and b It represents an arbitrary value. For the unknown matrix and The matrix combination, , , , and denote the minimum and maximum values ​​of the time lag, respectively. for t Time delay in the communication network, , is a random number; , is the system state value at time s; For the unknown matrix and The matrix combination, ; For the unknown matrix and The matrix combination, ; and Delay parameters the lower and upper limits of , for The first derivative of For the unknown matrix and The matrix combination, ; For the unknown matrix and The matrix combination, ; For the unknown matrix and The matrix combination, ; ; for The first derivative of and They are the lower and upper limits of , , , , ; , , , 、 、 and There are four subsets of allowed delays; , For the unknown matrix and The matrix combination, , , ; , For the unknown matrix and The matrix combination, ; For the unknown matrix and The matrix combination, ; , is the unknown matrix and The matrix combination, ; is the unknown matrix and The matrix combination, ; is the unknown matrix and The matrix combination, ; 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 and is any matrix.

[0109] Different from the traditional Lyapunov-Krasovsky functional, we replace the unknown independent matrix in the Lyapunov-Krasovsky functional with the matrix function related to the time delay partition set, thus forming the Lyapunov-Krasovsky functional related to the time delay partition set. Compared with the traditional Lyapunov-Krasovsky functional, the TS fuzzy LFC system model will By incorporating other nonlinear factors, this specialized Lyapunov-Krasovsky functional allows the system to have two flexible time delay sets. Our method is more flexible in developing less conservative stability criteria for TS fuzzy LFC system models, and can obtain less conservative stability criteria with higher practical application value. On the other hand, it is noted that when hour, , which shows that the proposed piecewise function is a continuous functional.

[0110] In this embodiment, the stability analysis of the TS fuzzy LFC system model is performed based on the Lyapunov-Krasovskii functional associated with the new delay partition set. The specific method for completing the stability analysis of the power system includes:

[0111] calculate The first derivative of Add the zero equation of the power system to the calculation of the first derivative of , combined with event trigger conditions , get the subset The corresponding inequality or subset The corresponding inequality , that is, to obtain the conditions for the final stability of the power system (the purpose of doing this here is Lyapunov's method of analyzing system stability, that is, to construct a Lyapunov function V(t), which is a function composed of the system state. The function is positive definite, and then the first-order derivative of time is calculated. The first-order derivative of various realistic conditions (such as the system 0 equation and trigger condition mentioned above) is added to make it less than 0. This shows that the Lyapunov function eventually tends to 0, which means that the system state that constitutes this Lyapunov function eventually tends to 0 and tends to be stable. This is the stability condition of the system. The two inequalities here are the conditions for the final stability of the system); is a matrix of arbitrary dimension; for The first derivative of ; To expand the variables, ;

[0112] is an expression related to the power system state, , , , for The calculation object, , , , , , , , , , , , , , , , represents a diagonal matrix, , , ;

[0113] is an expression related to power system delay, , , , , , , , , is an arbitrary matrix;

[0114] Judging in a given 、 、 、 and Is there a condition that satisfies 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 and , so that the matrix inequality is satisfied on the four allowed delay subsets and , if all of them are satisfied, the power system is judged to be asymptotically stable, otherwise it is judged to be unstable; is a matrix block, , and are all unknown matrices, is the number of fuzzy sets; express ; is a matrix block, , Represents any constant greater than 0. 、 、 、 、 、 、 、 、 、 、 、 、 、 and The conditions to be met are: 、 、 、 、 .

[0115] Therefore, this embodiment provides the following Theorem 1:

[0116] When a given constant 、 、 、 、 If there is any matrix 、 、 、 , meeting the conditions 、 、 、 、 , and matrices of any appropriate dimension , such that:

[0117]

[0118] In the four allowed delay sets 、 、 、 established on.

[0119] Proof: For In the case of , the derivative of the Lyapunov-Krasovsky functional V(t) is calculated as follows:

[0120] .

[0121] above The integral term of is processed by Lemma 1 as follows:

[0122]

[0123] ;

[0124] Theorem 2:

[0125] When a given constant 、 、 、 、 If there is any matrix 、 、 、 , meeting the conditions 、 、 、 、 , and matrices of any appropriate dimension and , such that:

[0126]

[0127]

[0128]

[0129]

[0130]

[0131]

[0132] In the four allowed delay sets 、 、 、 established on.

[0133] prove:

[0134] set up , , , , At the same time, define , , which can be transformed into Optimization problem, where Small enough, the Schur complement can be used to obtain the inequality .right Multiply both sides left and right simultaneously , then we can get the inequality .

[0135] Lemma 2 can be used to eliminate Nonlinear functions in By Schur complement we can get the inequality In short, if the inequality It holds, and it can be deduced that for sufficiently small scalars ,have . The proof is complete.

[0136] Lemma 1:

[0137] For any differentiable function ,matrix as well as , given any scalar , the following inequality holds:

[0138]

[0139] in 、 、 、 、 、 、 .

[0140] Lemma 2:

[0141] For a given real matrix of appropriate dimensions 、 、 ,inequality Established; for any The real matrix , as long as there is a scalar , making .

[0142] In this embodiment, when the power system is determined to be unstable, the parameters and / or trigger thresholds of the TS fuzzy LFC system model are adjusted until the power system is determined to be asymptotically stable. The TS fuzzy controller gain of the TS fuzzy LFC system model can be designed as ,in is a matrix of any appropriate dimension, is the unknown matrix obtained by Theorem 2.

[0143] In one embodiment of the present invention, a typical load frequency control (LFC) power system (J. Yang, Q. Zhong, K. Shi, Y. Yu, and S. Zhong, “Sta-bility and stabilization for t–s fuzzy load frequency control power system with energy storage system,” IEEE Transactions on Fuzzy Systems, vol. 32, pp. 893–905, 2024) is selected, and its parameters are as follows: , , , , , , , , , The delay partition coefficient is randomly set to .

[0144] First, the nonlinear term It can be converted into the following convex combination form:

[0145]

[0146] in, , and then we can get:

[0147] .

[0148] Therefore, the TS fuzzy LFC system model can be described as:

[0149] Rule 1: If for ,but

[0150] .

[0151] Rule 2: If for ,but

[0152] ,

[0153] in , , , , , ;

[0154] Therefore, the defuzzified TS fuzzy LFC system model can be described as:

[0155] .

[0156] In order to verify the superiority of the Lyapunov-Krasovsky functionals (LKFs) associated with the time-delay partition set proposed in this method, the literature was set up , , , .exist and In the case of (J. Yang, Q. Zhong, K. Shi, Y. Yu, and S. Zhong, “Sta-bility andstabilization for t–s fuzzy load frequency control power system with energystorage system,” IEEE Transactions on Fuzzy Systems, vol. 32, pp.893–905, 2024.), the methods in the paper are respectively used for different The delay margin is calculated and the results are listed in Table 1 (where [8] refers to the results of the above-mentioned paper by J. Yang, Q. Zhong, K. Shi, Y. Yu, and S. Zhong). Obviously, compared with the method in the paper, this method greatly reduces the conservatism of the results due to the use of LKFs related to the delay partition set. At the same time, by changing the delay partition coefficient The size of the parameter can further reduce the conservatism of the results.

[0157] The TS fuzzy LFC system model further considers the uncertainty of the electric vehicle (EV) state of charge (SOC). To study the impact of EV SOC uncertainty on the stability of the LFC system, the following three scenarios are set up.

[0158] Case 1: The uncertainty of electric vehicle SOC calculation is not considered, that is .

[0159] Case 2: Consider , , , , and the SOC of the electric vehicle remains , then we can get .

[0160] Case 3: Based on the changing battery power of the electric vehicle, the SOC of the electric vehicle should be in a time-varying state, assuming , , , , , then we can get .

[0161] set up , , , , according to the linear matrix inequality (LMI) based criterion, the fuzzy PI controller gains are calculated for these three cases. Case 1: , ; Case 2: , ; Case 3: , .

[0162] Set the initial state of the LFC system to , the time-varying delay is TS fuzzy LFC system model under three conditions The status response is as follows Figure 4 、 Figure 5 and Figure 6 Obviously, the convergence time of case 2 is longer than that of case 1, which shows that considering the uncertainty of electric vehicles will reduce the stability of the system. In addition, it can be seen from case 3 that considering the time-varying characteristics of SOC will lead to Fluctuations occur, but the robust controller designed by this method will eventually make the state of the LFC system stable.

[0163] Table 1: conditions, and Proportional relationship

[0164]

[0165] During the simulation, the weights of these two optimization objectives are set as Table 2 shows the The total number of trigger times and the trigger rate during the optimization process ( ).

[0166] Table 2: Trigger rate during iteration

[0167]

[0168] Obviously, when When , the total number of trigger times is the least and the trigger rate is the lowest. However, when When it continues to increase, in order to ensure the stability of the system, the number of triggers will increase. It can achieve a balance between stabilizing the system as quickly as possible and minimizing the trigger rate. It is necessary to compare the effectiveness of this method with existing trigger control strategies. For example, the trigger rate of the integral-based event-triggering switched LFC scheme for power system underdeception attack, Expert Systems with Applications, vol. 234, p. 121075, 2023., proposed in the literature (X. Liu, K. Shi, J. Cheng, S. Wen, and Y. Liu, “Adaptive memory-based event-triggering resilient LFC for power system under DoS attack,” Applied Mathematics and Computation, vol. 451, p. 128041, 2023.) and the memory event-triggering control proposed in the literature (X. Liu, K. Shi, C. Ma, Y. Tang, L. Tang, Y. Wei, and Y. Han, “Event-triggering loadfrequency control for multi-area power system based on random dynamic triggering, are both 26.7% and 26.7% respectively. mechanism and two-side closed functional,” ISA transactions, vol. 133, pp. 193–204, 2023) maintains a trigger rate of 24% and 53% respectively. In contrast, the trigger rate of the proposed method can be reduced to 21%, highlighting the superiority of the proposed method in reducing the signal trigger rate. The corresponding signal triggering time and interval are as follows Figure 7 、 Figure 8 、 Figure 9 and Figure 10 shown.

[0169] Similarly, Figure 11 、 Figure 12 、 Figure 13 and Figure 14 Describes the trigger threshold The impact on the dynamic trajectory of the load frequency control (LFC). It can be seen that using the Grey Wolf Optimization (GWO) algorithm to find the optimal threshold can make the system converge faster, which emphasizes the effectiveness of the Grey Wolf Optimization (GWO) algorithm in optimizing the Intelligent Event Triggering Mechanism (IETM). By combining the triggering times (Table 2, Figures 7-10 ) and the changing curves of the system dynamic trajectory, it can be observed that the proposed intelligent event triggered control (IETC) is superior in achieving the optimal convergence performance and the minimum number of triggering times.

[0170] In summary, this paper investigates the stability analysis and intelligent event-triggered control (IETC) design of a TS fuzzy load frequency control (LFC) power system with electric vehicles (EVs) and wind power. By simultaneously considering the nonlinearities of EV gains and valve positions, a TS fuzzy load frequency control power system with nonlinearities (TS fuzzy LFC system model) is constructed. Then, an intelligent event-triggered mechanism (IETM) integrated with the Grey Wolf Optimization (GWO) is proposed. Based on the optimization objective, the Grey Wolf Optimization algorithm is used to obtain the optimal trigger parameters. Furthermore, the designed intelligent event-triggered control (IETC) achieves optimal bandwidth utilization and system stability. Furthermore, the proposed Lyapunov-Krasovsky functionals (LKFs) associated with the delay partitioning set help reduce the conservatism of the results. Finally, several case studies demonstrate the superiority and effectiveness of the proposed method.

Claims

1. A method for power system stability analysis and intelligent event triggering control, characterized in that: include: The nonlinear factors of the turbine valve position are modeled using TS fuzzy theory, and the electric vehicle gain is treated as a time-varying function based on the change of the state of charge to establish a TS fuzzy LFC system model. Among them, the TS fuzzy LFC system model is used to reflect the actual operating status of the power system; Based on the TS fuzzy LFC system model, the optimal triggering threshold is searched using the GWO algorithm with the optimization goals of minimizing the signal triggering rate and stabilizing the power system as quickly as possible. Obtain event trigger conditions based on the optimal trigger threshold, determine whether the sampling signal is transmitted based on the event trigger conditions, and complete intelligent event trigger control; During the operation of the power system, a new type of delay partition set-related Lyapunov-Krasovskii functional is constructed through the allowed delay partition method; The stability analysis of the TS fuzzy LFC system model is performed based on the Lyapunov-Krasovskii functional associated with the new delayed partition set, completing the stability analysis of the power system. The expression of TS fuzzy LFC system model is: in Indicates that the power system t The first derivative of the state vector at time ; is the number of fuzzy rules; For the A fuzzy membership function that satisfies ; For the A fuzzy membership function; 、 、 are the coefficient matrices related to power system dynamics, communication delay, and output, respectively; Indicates that electric vehicle gains are taken into account The coefficient matrix part of the time-varying characteristics related to the system state vector at time t, Indicates that electric vehicle gains are taken into account The coefficient matrix part of the time-varying characteristics related to the event triggering state; is the gain of TS fuzzy controller; For the power system at the sampling time The state vector of , is determined by the IETM generator k Trigger moment The system status value of For power systems t Output state matrix at time t; Indicates the communication network k Trigger moment The transmission delay, Indicates the communication network k +1 trigger moment transmission delay; , , , , , , , , is a time-varying function based on the change of state of charge, , is the maximum value of electric vehicle gain; is the state of charge of the electric vehicle, 、 、 and They represent the upper limit of the electric vehicle battery SOC, the lower limit of the electric vehicle battery SOC, the high value of the electric vehicle battery SOC and the low value of the electric vehicle battery SOC, respectively. is the trigger threshold, is the electric vehicle time constant, Represents the transpose of a matrix; is the participation rate of electric vehicles; and is a constant between 0 and 1, .

2. The power system stability analysis and intelligent event triggering control method according to claim 1, characterized in that: The expression for the optimization goal of minimizing the signal trigger rate and stabilizing the power system as quickly as possible is: in represents the optimization objective function; Indicates taking the minimum value; and All are weights; represents the total number of signal triggering times of the IETM generator; N is the total number of samples of the remote terminal unit that exchanges information with the power system control center; is the calculation period; for t The regional control error at the moment, , express t The power deviation of the inter-regional tie line at the moment, is the weight coefficient related to the frequency deviation, express t Frequency deviation of the power system at the moment; Indicates Pre-calculated within the range The maximum value of .

3. The power system stability analysis and intelligent event triggering control method according to claim 2, characterized in that: The specific methods for searching the optimal trigger threshold using the GWO algorithm include: Set the total number of wolves and the maximum number of iterations so that the position of the individual gray wolf in each iteration represents the trigger threshold obtained by the search; Initialize the gray wolf position representing the trigger threshold; Calculate the TS fuzzy controller gain and the position of the gray wolf individual and bring them into the TS fuzzy LFC system model to calculate the optimization objective function ; According to the optimization objective function Update the position of the alpha wolf and the positions of other individual gray wolves until the maximum number of iterations is reached, and output the optimal trigger threshold and TS fuzzy controller gain.

4. The power system stability analysis and intelligent event triggering control method according to claim 1, characterized in that: The expression of the event trigger condition is: in is the weight matrix for measuring signal error and trigger conditions; is the optimal trigger threshold; The IETM generator k A certain output state is triggered and sent, ; is a time-dependent variable, The dynamic characteristics of Decide, , and All coefficients are greater than 0. for The first derivative of .

5. The power system stability analysis and intelligent event triggering control method according to claim 4 is characterized in that: The expression of the Lyapunov-Krasovskii functional associated with the new delayed partition set is: in represents the Lyapunov-Krasovskii functional associated with the new delayed partition set; , is the state vector related to the system state and time delay information, , represents a column vector, and They are defined as and , a and b It represents an arbitrary value. For the unknown matrix and The matrix combination, , , , and denote the minimum and maximum values ​​of the time lag, respectively. for t Time delay in the communication network, , is a random number; , is the system state value at time s; For the unknown matrix and The matrix combination, ; For the unknown matrix and The matrix combination, ; and Delay parameters the lower and upper limits of , for The first derivative of For the unknown matrix and The matrix combination, ; For the unknown matrix and The matrix combination, ; For the unknown matrix and The matrix combination, ; ; for The first derivative of and They are the lower and upper limits of , , , , ; , , , 、 、 and There are four subsets of allowed delays; , For the unknown matrix and The matrix combination, , , ; , For the unknown matrix and The matrix combination, ; For the unknown matrix and The matrix combination, ; , is the unknown matrix and The matrix combination, ; is the unknown matrix and The matrix combination, ; is the unknown matrix and The matrix combination, ; 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 and is any matrix.

6. The power system stability analysis and intelligent event triggering control method according to claim 5, characterized in that: The stability analysis of the TS fuzzy LFC system model is performed based on the Lyapunov-Krasovskii functional associated with the new delayed partition set. The specific method for completing the stability analysis of the power system includes: calculate The first derivative of Add the zero equation of the power system to the calculation of the first derivative of , combined with event trigger conditions , get the subset The corresponding inequality or subset The corresponding inequality , that is, the conditions for the ultimate stability of the power system are obtained; is a matrix of arbitrary dimension; for The first derivative of ; To expand the variables, ; is an expression related to the power system state, , , , for The calculation object, , , , , , , , , , , , , , , , represents a diagonal matrix, , , ; is an expression related to power system delay, , , , , , , , , is an arbitrary matrix; Judging in a given 、 、 、 and Is there a condition that satisfies 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 and , so that the matrix inequality is satisfied on the four allowed delay subsets and , if all of them are satisfied, the power system is judged to be asymptotically stable, otherwise it is judged to be unstable; is a matrix block, , and are all unknown matrices, is the number of fuzzy sets; express ; is a matrix block, , Represents any constant greater than 0.

7. The power system stability analysis and intelligent event triggering control method according to claim 6, characterized in that: When the power system is determined to be unstable, the parameters and / or trigger threshold of the TS fuzzy LFC system model are adjusted until the power system is determined to be asymptotically stable.

8. The power system stability analysis and intelligent event triggering control method according to claim 6, characterized in that: 、 、 、 、 、 、 、 、 、 、 、 、 、 and The conditions to be met are: 。

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