An improved fixed-time-based hierarchical sliding mode control method for power system chaotic phenomena

Abstract

The application discloses a kind of based on improved fixed time power system chaos phenomenon hierarchical sliding mode control method, comprising the following steps: nine-stage power system model is analyzed using chaos analysis tool to model chaos phenomenon;The shortcoming of traditional fixed time sliding mode control is improved to avoid singularity problem, and fixed time nonsingular terminal sliding mode control is combined with adaptive technology, then hierarchical sliding mode is combined with fixed time nonsingular adaptive terminal sliding mode to reduce the number of designed controller, and hyperbolic approach law is added to reduce the chattering phenomenon existing in sliding mode control;Finally, to reduce control parameter search time, on the basis of constructing a new objective function, the improved ant lion algorithm is used to optimize the control parameters, and the research results have reference for controlling actual power system chaos phenomenon.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power system control, and particularly relates to a power system chaotic phenomenon hierarchical sliding mode control method based on improved fixed time. BACKGROUND

[0002] As a highly nonlinear complex dynamic system, modern power system shows rich nonlinear dynamic behaviors. Among them, oscillation is a typical nonlinear dynamic behavior in the transmission process of the power system. In addition to the periodic oscillation in normal operation, the power system sometimes also has sudden, irregular and aperiodic oscillation. With the in-depth research, many scholars have found that the irregular oscillation of the power system is closely related to its chaotic operation behavior. Although such irregular oscillation does not always destroy the overall stability of the system, its potential destructive power to the system safety is huge. Once the system continuously produces irregular oscillation, it will have a great possibility to lead to system splitting, even collapse and cause large-area power failure accidents. In this case, in order to ensure the safe and stable operation of the power system, advanced control theory, technology and method should be continuously researched. SUMMARY

[0003] The purpose of the application is to provide a power system chaotic phenomenon hierarchical sliding mode control method based on improved fixed time. The application designs a new fixed time non-singular adaptive terminal hierarchical sliding mode control method on the basis of the traditional fixed time sliding mode surface. The singularity problem existing in the traditional fixed time sliding mode control is solved by adding a saturation function and using the idea of a segmented function. At the same time, the designed control method estimates the uncertain parameters in the system by using an adaptive method, weakens the chattering phenomenon by using a hyperbolic approach law, combines the hierarchical sliding mode control with the designed sliding mode surface to reduce the number of controllers, and finally finds time to reduce the control parameters. On the basis of constructing a new target function, the improved ant lion algorithm is used to optimize the control parameters.

[0004] The purpose of the application is achieved by the following technical solutions:

[0005] A power system chaotic phenomenon hierarchical sliding mode control method based on improved fixed time, comprising the following steps:

[0006] Step 1: analyzing the chaotic model of the power system and using a chaotic analysis method to analyze the chaotic phenomenon;

[0007] Step 2: improving the traditional fixed time sliding mode control method from different aspects in view of the shortcomings of the method, and establishing an improved fixed time hierarchical sliding mode control method;

[0008] Step 3: In order to shorten the time of searching control parameters, a new objective function is designed and the ant lion algorithm is improved for searching control parameters.

[0009] Further, step 1 is specifically: analyzing the nine-order power system model, and through the state time sequence diagram, system bifurcation diagram, system power spectrum diagram and system phase diagram of each aspect, the existence of chaotic phenomenon is illustrated. Figure Four

[0010] System model:

[0011]

[0012] In the formula, δ v is the power angle of the generator, s v is the engine slip; E d ' and E d " are the transient electromotive force and sub-transient electromotive force of the d-axis of the generator; E q ' and E q " are the transient electromotive force and sub-transient electromotive force of the q-axis of the generator; E fd is the excitation electromotive force of the generator; δ L and V L are the phase angle and amplitude of the load bus voltage; d v is the external periodic disturbance on the generator side; u v , u L1 and u L2 are the control inputs of the system. Among the variables of the controlled system expression, P g , I d , I q , V t , P and Q are functions of the state variables.

[0013] In order to suppress the chaotic oscillation phenomenon, according to the dynamic mathematical characteristics of the power system, three control inputs are designed to control δ v , s v , δ L and V L respectively, that is, the system is divided into three subsystems, and the expressions of the subsystems are as follows:

[0014] Subsystem (I):

[0015]

[0016] Subsystem (II):

[0017]

[0018] Subsystem (III):

[0019] ​

[0020] In the above formula δ Lin and V Lin are the integral of the phase angle and amplitude of the load bus voltage respectively, u L1 , u L2 , u v are the controllers to be designed. From the expression of the system dynamics equation, when the three subsystem states tend to be stable, E d ', E q ', E d ", E q ", E fd will also tend to be stable. Therefore, only three control inputs need to be designed to control the entire system, and the desired value of the system is set as [δ vd , s vd , δ Ld , V Ld ] = [0, 0, 0.78, 1], and the system error is:

[0021]

[0022] Further, step 2 improves the traditional fixed-time sliding mode and combines it with the hierarchical sliding mode: the improved method is:

[0023] Taking the system error e1 as an example, the traditional fixed-time fast sliding surface is:

[0024]

[0025] The traditional fixed-time fast sliding surface can make the system state converge within a fixed time, but there will be a singularity problem, and due to the discontinuous nature of the sign function, the control process will produce a chattering phenomenon. In order to further speed up the convergence of the fixed-time fast sliding surface and solve the chattering phenomenon existing in the traditional sliding surface, the improved fixed-time fast sliding surface is:

[0026]

[0027] In the formula, α1, α2, β1, β2, ψ1, k are all normal numbers greater than zero, the size of the coefficient ψ1, k determines the convergence speed of the entire sliding surface, and the size of α1, α2, β1, β2 is related to the stability of the system, and sat is a saturation function, whose expression is:

[0028]

[0029] where p is a positive constant, the chattering phenomenon existing in the control process can be weakened by replacing the sign function with a saturation function. The sliding mode surface is divided into two parts, when the system state is less than k, i.e. near the equilibrium point, the sliding mode surface (a) converges faster; when the system state is greater than k, i.e. far from the equilibrium point, the sliding mode surface (b) can accelerate the convergence speed of the system. Therefore, when using the improved fixed-time fast sliding mode surface, the system convergence speed can be further accelerated, regardless of whether the system state is far from or near the equilibrium point. Therefore, the improved sliding mode surface weakens the chattering problem existing in the traditional fixed-time fast sliding mode surface, and improves the time of the system to reach the equilibrium point.

[0030] The derivative of formula s1 is:

[0031]

[0032] From the above formula, when e1 is equal to 0, due to a1 being less than 1, a singular point will occur. For the improved fixed-time sliding mode surface, when the sliding mode surface tends to the origin, the following can be obtained:

[0033]

[0034] For the improved sliding mode surface, when ψ1 is greater than 0, e1 is equal to 0, and no singular point will occur, the improved sliding mode surface can solve the singularity problem existing in the traditional fixed-time sliding mode surface. In order to better design the adaptive law for the improved sliding mode surface, the improved fixed-time sliding mode surface is improved, and p = a is set, then the new sliding mode surface is:

[0035]

[0036] After obtaining the sliding mode surface shown in the above formula, the sliding mode reaching law is designed, and the hyperbolic function is selected as the reaching law. The hyperbolic reaching law can achieve fast convergence and weaken chattering of the sliding mode control, and the expression is:

[0037]

[0038] In the above formula, s is the designed sliding mode surface, q is a positive odd number, λ1, λ2, r1, r2 are positive parameters, tanh and asinh are hyperbolic tangent function and inverse hyperbolic sine function, respectively. From the expressions of the two functions, the value range of the hyperbolic tangent function and its derivative is -1 to 1, and the hyperbolic tangent function changes relatively slowly, so it has a linear-like characteristic when the sliding mode surface tends to 0. The inverse hyperbolic sine function has the same characteristics. It is precisely because of this linear-like characteristic that the chattering phenomenon is reduced or even eliminated.

[0039] In the actual power system, the damping coefficient d and the electromagnetic power P mFor better control, the adaptive law is designed for the two uncertain parameters to estimate them:

[0040]

[0041] The derivative of the estimated value of parameter d is shown above; τ1 is the designed adaptive parameter, s v is the engine speed difference, H is the inertia time constant of the generator. According to the different size of the constant parameter change, the control accuracy can be adjusted by adjusting τ.

[0042]

[0043] The derivative of the estimated value of parameter Pm is shown above; τ2 is the designed adaptive parameter, like τ1.

[0044] Hierarchical sliding mode:

[0045] By observing subsystem (two) and subsystem (three), it can be found that the two system equations are closely related. In order to reduce the number of controller designs, the concept of hierarchical sliding mode control is added to the system, and a control input is designed to make subsystem (two) and subsystem (three) converge, that is, u L1 = u L2 = u eq .

[0046] The sliding surface of subsystem s 32 and s 33 is located in the first layer of the sliding mode, and in the second layer, the two sliding surfaces are linearly combined as:

[0047] s4= ms 32 + ns 33

[0048] According to the design process of sliding mode theory, the total control law includes the equivalent control law of the two subsystems and the switching control law of the sliding surface approaching law, so the total control law is designed as:

[0049] u eq = u L2 + u L3 + u sw

[0050] For the approaching law, a constant plus proportional approaching law is selected, and its expression is as follows:

[0051]

[0052] The switching control law u sw is:

[0053]

[0054] Wherein G1 and G2 are control law coefficients, and their expressions are as follows:

[0055]

[0056]

[0057] Further, the existing shortcomings of the ant lion algorithm initialization are improved, and a new target function is designed according to the required control effect to optimize the parameters of the controller, and the specific content is:

[0058] In the traditional ant lion algorithm, a random function is used for initialization, in order to improve the randomness of the initial population and make the population uniformly distributed in the optimization area, the improved initialization method is adopted, that is, the initialization is divided into several regions, and the Logistic mapping model is used to initialize the population in each sub-region, so that the population is more randomly distributed in the parameter range.

[0059] For the optimized target function, the "steady", "accurate" and "fast" of the control requirement are taken as the starting point, the integral time absolute error is selected as the performance standard for the accurate index, and the overshoot, rise time, transition time and peak time are selected as the performance index for the steady and fast performance index, and the proposed target function is as follows:

[0060] OF=(1-e -θ )(M p +ITAE)+e -θ (t s +t r +t p )

[0061] Wherein, M p is the overshoot, ITAE is the integral time absolute error, t s is the transition time of the system, t p is the peak time of the system, t r is the rise time of the system, and θ is a weighting factor, which can be adjusted to meet the designer's requirements for different performance indexes.

[0062] Compared with the prior art, the beneficial effects of the present application are:

[0063] The method of the application is based on fixed-time sliding mode control, considers singularity problem, designs an improved fixed-time non-singular adaptive sliding mode surface, and can make the system state reach stability in fixed time; in order to eliminate the influence of parameter disturbance and other interference, an adaptive law is designed for easy-to-change parameters, meanwhile, the characteristics of saturation function and hyperbolic function are used to weaken the inherent chattering phenomenon of sliding mode control, the simulation results show that the performance of the sliding mode surface is better than that of the traditional fixed-time sliding mode surface, and the hierarchical sliding mode control is combined with the designed improved fixed-time non-singular adaptive sliding mode surface to control the system chaos, and the number of controllers can be reduced, the optimized lion algorithm is used for parameter optimization of the control method, a new control objective function is constructed according to the control performance requirement, so that the control parameters are optimized to better control performance. BRIEF DESCRIPTION OF DRAWINGS

[0064] Figure 1 The control flow chart of the method of the application is shown in the figure;

[0065] Figure 2 The time sequence diagram of each state of the system is shown in the figure;(a) state variable δ v time sequence diagram;(b) state variable s v time sequence diagram;(c) state variable δ L time sequence diagram;(d) state variable V L time sequence diagram;(e) state variable E q time sequence diagram;(f) state variable E d time sequence diagram;(g) state variable E d time sequence diagram;(h) state variable E q time sequence diagram;(i) state variable E fd time sequence;

[0066] Figure 3 The bifurcation diagram of the system is shown in the figure;(a) state variable s v bifurcation diagram;(b) state variable E d bifurcation diagram;

[0067] Figure 4 The power spectrum diagram of the system is shown in the figure;

[0068] Figure 5 The phase diagram of the system is shown in the figure;(a) system phase diagram;(b) strange attractor existing in the system;

[0069] Figure 6 The hierarchical sliding mode structure diagram is shown in the figure;

[0070] Figure 7 The state variable diagram of the system after control is shown in the figure;

[0071] Figure 8 The phase diagram of the system after control is shown in the figure;

[0072] Figure 9 Controlled post-system state diagram; (a) delta v Timing diagram; (b) s v Timing diagram; (c) delta L Timing diagram; (d) V L Timing diagram;

[0073] Figure 10 Controller output value; (a) control u v Output value; (b) control u eq Output value;

[0074] Figure 11 Comparison diagram with or without adaptive parameters. DETAILED DESCRIPTION

[0075] The application will be further described below in combination with the drawings and examples.

[0076] Aiming at the chaotic phenomenon existing in the power system, the application proposes a new fixed-time non-singular adaptive terminal hierarchical sliding mode control. Firstly, the traditional fixed-time terminal sliding mode surface is improved to avoid the singularity problem. Secondly, in order to cope with the challenge of system parameters and other external disturbances to the system control, the fixed-time non-singular terminal sliding mode control is combined with the adaptive technology, a new fixed-time non-singular adaptive terminal sliding mode control is proposed, then the hierarchical sliding mode is combined with the fixed-time non-singular adaptive terminal sliding mode to reduce the number of designed controllers, and the hyperbolic reaching law is added to reduce the chattering phenomenon existing in the sliding mode control. In order to reduce the control parameter searching time, the improved ant lion algorithm is used to optimize the control parameters on the basis of constructing a new target function, and the results show that the proposed control method has good control performance. The control flow block diagram of the method is as shown in Figure 1 The method comprises the following steps:

[0077] Step 1: analyze the chaotic model of the power system, and analyze the chaotic phenomenon by using the chaotic analysis method; system model:

[0078]

[0079] In the formula, delta v is the power angle of the generator, s v is the engine slip; E d ' and E d " are the transient electromotive force and sub-transient electromotive force of the d-axis of the generator; E q ' and E q " are the transient electromotive force and sub-transient electromotive force of the q-axis of the generator; E fd is the excitation electromotive force of the generator; delta L and V L are the phase angle and amplitude of the load bus voltage; dv is the external periodic disturbance on the generator side; u v , u L1 and u L2 are the control inputs of the system. Among the variables in the expression of the controlled system, P g , I d , I q , V t , P and Q are functions of the state variables.

[0080] In order to suppress the chaotic oscillation phenomenon, three control inputs are designed according to the dynamic mathematical characteristics of the power system, to control δ v , s v , δ L and V L respectively, i.e. the system is divided into three subsystems, and the expressions of the subsystems are as follows:

[0081] Subsystem (1):

[0082]

[0083] Subsystem (2):

[0084]

[0085] Subsystem (3):

[0086]

[0087] In the above expressions, δ Lin and V Lin are the integrals of the phase angle and amplitude of the load bus voltage respectively, u L1 , u L2 , u v are the controllers to be designed. According to the expression of the system dynamics equation, when the states of the three subsystems tend to be stable, E d ', E q ', E d '', E q '', E fd will also tend to be stable. Therefore, only three control inputs need to be designed to control the entire system. The desired values of the system are set as [δ vd , s vd , δ Ld , V Ld ] = [0, 0, 0.78, 1], and the system error is:

[0088]

[0089] In order to analyze the chaotic phenomenon, the model machine core of the power system is analyzed by using the chaos analysis tool, Figures 2 to 5All are analysis results, wherein Figure 2 is the system time sequence diagram, it can be seen that the system is in a disordered state, Figure 3 is the system variable s v and E d ′ bifurcation diagram obtained with the increase of electromagnetic power, with the increase of electromagnetic power, s Figure 3 It can be seen that the system is initially in a normal state, when the electromagnetic power increases to 1.24, s v and E d ′ start to appear continuous period-doubling bifurcation, and with the increase of bifurcation parameter, the system appears 4-period, 8-period. When the electromagnetic power reaches 1.360, the system appears a disordered chaotic state, thus leading to the appearance of chaos, and then when the electromagnetic power is 1.394, the system returns to a period-doubling state from the chaotic state. To further show the chaotic state of the system when the electromagnetic power P m is 1.361, it can be seen through the power spectrum and phase diagram of the system, i.e. Figure 4 and Figure 5

[0090] Step 2: In view of the shortcomings of the traditional fixed-time sliding mode control method, the method is improved from different aspects, and an improved fixed-time hierarchical sliding mode control method is established;

[0091] Taking the system error e1 as an example, the traditional fixed-time fast sliding mode surface is:

[0092]

[0093] The traditional fixed-time fast sliding mode surface can make the system state converge in a fixed time, but there will be a singularity problem, and because the sign function has a discontinuous characteristic, it will cause a chattering phenomenon in the control process. In order to further speed up the convergence speed of the fixed-time fast sliding mode surface and solve the chattering phenomenon existing in the traditional sliding mode surface, the improved fixed-time fast sliding mode surface is:

[0094]

[0095] In the formula, α1, α2, β1, β2, ψ1, k are all normal numbers greater than zero, the size of the coefficient ψ1, k determines the convergence speed of the whole sliding mode surface, the size of α1, α2, β1, β2 is related to the stability of the system, and sat is a saturation function, whose expression is:

[0096]

[0097] ​where p is a positive constant, the chattering phenomenon existing in the control process can be weakened by replacing the sign function with a saturation function. The sliding mode surface is divided into two parts, when the system state is less than k, i.e. near the equilibrium point, the sliding mode surface (a) converges faster; when the system state is greater than k, i.e. far from the equilibrium point, the sliding mode surface (b) can accelerate the convergence speed of the system. Therefore, when using the improved fixed-time fast sliding mode surface, the convergence speed of the system can be further accelerated, whether the system state is far from or near the equilibrium point. Therefore, the improved sliding mode surface weakens the chattering problem existing in the traditional fixed-time fast sliding mode surface, and improves the time of the system to reach the equilibrium point.

[0098] The derivative of formula s1 is:

[0099]

[0100] From the above formula, when e1 is equal to 0, due to a1 being less than 1, a singular point will occur. For the improved fixed-time sliding mode surface, when the sliding mode surface tends to the origin, the following can be obtained:

[0101]

[0102] For the improved sliding mode surface, when ψ1 is greater than 0, e1 is equal to 0, and no singular point will occur, the improved sliding mode surface can solve the singularity problem existing in the traditional fixed-time sliding mode surface. In order to better design the adaptive law for the improved sliding mode surface, the improved fixed-time sliding mode surface is improved, and p=a is set, then the new sliding mode surface is:

[0103]

[0104] After obtaining the sliding mode surface shown in the above formula, the sliding mode reaching law is designed, and the hyperbolic function is selected as the reaching law. The hyperbolic reaching law can achieve fast convergence and weaken chattering of the sliding mode control, and the expression is:

[0105]

[0106] In the above formula, s is the designed sliding mode surface, q is a positive odd number, λ1, λ2, r1, r2 are positive parameters, tanh and asinh are hyperbolic tangent function and inverse hyperbolic sine function, respectively. From the expressions of the two functions, the value range of the hyperbolic tangent function and its derivative is-1 to 1, and the hyperbolic tangent function changes relatively slowly, so it has a linear-like characteristic when the sliding mode surface tends to 0. The inverse hyperbolic sine function has the same characteristics. It is precisely because of this linear-like characteristic that the chattering phenomenon is reduced or even eliminated.

[0107] In the actual power system, the damping coefficient d and the electromagnetic power P mFor better control, the adaptive law is designed for the two uncertain parameters to estimate them:

[0108]

[0109] The derivative of the estimated value of parameter d is shown above; τ1 is the designed adaptive parameter, s v is the engine speed difference, and H is the inertia time constant of the generator. According to the different changes of the constant parameters, the control accuracy can be adjusted by adjusting τ.

[0110]

[0111] The derivative of the estimated value of parameter Pm is shown above; τ2 is the designed adaptive parameter, like τ1.

[0112] Hierarchical sliding mode:

[0113] By observing subsystem (two) and subsystem (three), it can be found that the system equations of the two systems are closely related. In order to reduce the number of controller designs, the concept of hierarchical sliding mode control is added to the system, and a control input is designed to make subsystem (two) and subsystem (three) converge, that is, u L1 = u L2 = u eq , the hierarchical structure of the sliding surface of the system is shown in Figure 6

[0114] The sliding surfaces of subsystems s 32 and s 33 are located in the first layer of the sliding mode, and in the second layer, the two sliding surfaces are linearly combined as:

[0115] s4= ms 32 + ns 33

[0116] According to the design process of the sliding mode theory, the total control law includes the equivalent control law of the two subsystems and the switching control law of the sliding surface approaching law, so the total control law is designed as:

[0117] u eq = u L2 + u L3 + u sw

[0118] For the approaching law, a constant plus proportional approaching law is selected, and its expression is shown as follows:

[0119]

[0120] The switching control law u sw is:

[0121] ​

[0122] In the formula, G1 and G2 are the control law coefficients, and their expressions are as follows:

[0123]

[0124]

[0125] Step 3: To shorten the time for finding control parameters, a new objective function was designed, and the Antlion algorithm was improved for optimizing control parameters.

[0126] Furthermore, addressing the shortcomings of the antlion algorithm's initialization, improvements are made, and a new objective function is designed to optimize the controller parameters based on the desired control effect. The specific details are as follows:

[0127] Traditional antlion algorithms use random functions for initialization. To improve the randomness of the initial population and ensure its uniform distribution within the optimization region, this invention employs an improved initialization method. This involves dividing the initialization process into several regions and using a Logistic mapping model to initialize the population within each sub-region. This results in a more random distribution of the population within the parameter range.

[0128] For the objective function of optimization, this invention takes the control requirements of "stability," "accuracy," and "speed" as the starting point. For the accuracy index, the absolute error of integral time is selected as the performance standard. For the stability and speed performance indices, overshoot, rise time, transition time, and peak time are selected as performance indices. The proposed objective function is as follows:

[0129] OF = (1-e) -θ (M) p +ITAE)+e -θ (t s +t r +t p )

[0130] In the formula, M p The overshoot is t, ITAE is the absolute error of the integration time, and t is the time of integration. s t is the system's transition time. p t represents the peak time of the system. r Let θ be the rise time of the system, and let θ be the weighting factor. The weighting factor can be adjusted to meet the designer's requirements for different performance indicators.

[0131] The above steps were performed using MATLAB 2018b platform for programming simulation. Partial system state diagrams obtained from the simulation are shown below. Figure 7 As shown, from Figure 7It can be seen that after the controller is added, all state variables except the controlled state can be transformed from the chaotic oscillation state of the system to the desired value within 1 second, and the system can be successfully restored to the stable state. The chaotic state of the system is suppressed, which shows the effectiveness of the controller design. Figure 8 The phase diagram of the controlled system is shown below. In the diagram, * represents the initial state of the system, and · represents the steady state of the system. Figure 8 and Figure 5 Compared to the phase diagram shown, the strange chaotic attractors have disappeared, and the strange attractors in the phase diagram have evolved into equilibrium fixed points. To illustrate the superiority of the designed sliding surface over the traditional fixed-time sliding surface, the designed sliding surface is compared with the traditional fixed-time sliding surface, and the results are as follows. Figure 9 As shown, from Figure 9 It can be seen that the improved sliding surface tracks the signal faster than the traditional sliding surface in terms of convergence time, and also performs better in terms of system overshoot. Regarding chattering reduction, since layered sliding mode control uses the same control input for both subsystems, dividing the system into two layers with a discontinuous function in the second layer, this can introduce unexpected chattering into the system control. For example... Figure 9 As shown in (c) and 9(d), the traditional fixed-time sliding surface cannot eliminate this chattering phenomenon, while the improved sliding surface can effectively eliminate it. The improved sliding surface is better at dealing with chattering. To further demonstrate the superiority of the improved fixed-time sliding control, the outputs of the traditional fixed-time sliding control and the improved fixed-time sliding control are compared. Figure 10 As shown. From Figure 10 It is clear that traditional fixed-time sliding mode suffers from chattering, while the improved fixed-time sliding mode of this invention exhibits almost no chattering, indicating that the designed controller has practical significance. To demonstrate the effectiveness of the adaptive parameters, periodic disturbances were introduced on the generator side of the system. Taking the generator's power angle as an example, the results are as follows... Figure 11 As shown. From Figure 11 It can be seen that the controller with adaptive parameters can better cope with the impact of external interference on the system, which shows that the controller designed in this invention has good robustness.

[0132] The above description merely illustrates preferred embodiments of the present invention, and while the description is specific and detailed, it should not be construed as limiting the present invention. It should be noted that those skilled in the art can make various modifications, improvements, and substitutions without departing from the concept of the present invention, and these all fall within the scope of protection of the present invention.

Claims

1. A hierarchical sliding mode control method for chaotic phenomena in power systems based on improved fixed-time conditions, characterized in that, Includes the following steps: Step 1: Analyze the chaotic model of the power system and use chaotic analysis methods to analyze the chaotic phenomena; Step 2: Improve the traditional fixed-time sliding mode control method and establish an improved fixed-time layered sliding mode control method; Step 3: To shorten the time for finding control parameters, a new objective function was designed, and the antlion algorithm was improved for optimizing control parameters. The mathematical model for the improved fixed-time layered sliding mode control method established in step 2 is as follows: Improvement methods: Taking the systematic error e1 as an example, the improved fixed-time fast sliding surface is as follows: ； In the formula, α1, α2, β1, β2, ψ1, φ1, φ2, and k are all positive positive constants. The magnitudes of the coefficients ψ1, φ1, φ2, and k determine the convergence rate of the entire sliding surface. The magnitudes of α1, α2, β1, and β2 are related to the system stability. sat is the saturation function, and its expression is: ； In the formula, p is a constant greater than zero. By replacing the sign function with a saturation function, the chattering phenomenon in the control process is reduced. The sliding surface is divided into two parts. When the system state is less than k, that is, when it is near the equilibrium point, the convergence speed of the sliding surface (a) is faster. When the system state is greater than k, that is, when it is far from the equilibrium point, the sliding surface (b) can accelerate the convergence speed of the system. For the improved fixed-time sliding surface, when the sliding surface approaches the origin, we can obtain: ； For the improved sliding surface, it is known that when ψ1 is greater than 0 and e1 is equal to 0, no singularity will occur. In order to design a better adaptive law for the improved sliding surface, the improved fixed-time sliding surface is further improved. Let p=a, then the new sliding surface is: ； After obtaining the sliding surface shown in the above equation, a sliding mode reaching law is designed. A hyperbolic function is chosen as the reaching law. The hyperbolic reaching law can achieve rapid convergence of sliding mode control and reduce chattering. The expression is: ； In the above formula, s is the designed sliding surface, q is a positive odd number, λ1, λ2, r1, r2 are positive parameters, tanh and asinh are the hyperbolic tangent function and the inverse hyperbolic sine function, respectively. From the two function expressions, it can be seen that the hyperbolic tangent function and its derivative are both in the range of -1 to 1, and the hyperbolic tangent function has a quasi-linear characteristic when the sliding surface approaches 0. The inverse hyperbolic sine function has the same properties, and it is precisely because of this quasi-linear characteristic that chattering is reduced or even eliminated. In practical power systems, the damping coefficient d and the generator electromagnetic power P are constant parameters in the system equations. m An adaptive law is designed to estimate these two uncertain parameters: ； The above equation is the derivative of the estimated value of parameter d; τ1 is the adaptive parameter of the design, s v H is the engine slip, and H is the generator inertia time constant. The control accuracy is adjusted by using τ according to the different changes in the constant parameters. ； The above formula is for parameter P m The derivative of the estimated value; τ2 and τ1 are both adaptive parameters of the design.

2. The hierarchical sliding mode control method for chaotic phenomena in power systems based on improved fixed-time conditions as described in claim 1, characterized in that, Step 1 specifically involves analyzing a ninth-order power system model and demonstrating the existence of chaotic phenomena through analysis of four aspects: time sequence diagrams of each state, system bifurcation diagrams, system power spectrum diagrams, and system phase diagrams.

3. The hierarchical sliding mode control method for chaotic phenomena in power systems based on an improved fixed-time method according to claim 1, characterized in that, In step 3, the antlion algorithm is improved, and a new objective function is designed to optimize the controller parameters. Specifically: In the Antlion algorithm, an improved initialization method is adopted, which divides the initialization into several regions and uses the Logistic mapping model to initialize the population in each sub-region, so that the population is more randomly distributed within the parameter range. For the objective function of optimization, based on the control requirements of "stability," "accuracy," and "speed," the absolute error of integral time is selected as the performance standard for accuracy, and overshoot, rise time, transition time, and peak time are selected as performance indicators for stability and speed. The proposed objective function is as follows: ； In the formula, M p The overshoot is t, ITAE is the absolute error of the integration time, and t is the time of integration. s t is the system's transition time. p t represents the peak time of the system. r Let θ be the rise time of the system, and let θ be the weighting factor. The weighting factor is adjusted to meet the designer's requirements for different performance indicators.

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