An adaptive sliding mode control method for chaos suppression in controlled power systems

Abstract

The application provides an adaptive sliding mode control method for chaos suppression of a power system, and belongs to the technical field of nonlinear stability control of the power system. The method is based on synchronous transmission technology, and comprises the following steps: a target system is set according to a demand for selecting an output signal for an established n-dimensional nonlinear model of the power system, n >= 2; a first sliding mode surface is constructed according to a state error between the power system and the target system, and then a general sliding mode surface set suitable for a system of any dimension is constructed through recursive combination; a sliding mode controller is designed based on the general sliding mode surface, and an adaptive identification mechanism for uncertain parameters of the system is integrated, so that the state of the power system accurately tracks the signal of the target system, and thus the chaos oscillation is effectively suppressed. The method realizes universal control of power system models of different dimensions, significantly improves the engineering applicability and deployment flexibility of the method, and ensures rapid stabilization and stable operation of the system under various chaotic conditions.

Description

Technical Field

[0001] This invention relates to the field of sliding mode control technology, and in particular to an adaptive sliding mode control method for chaos suppression in controlled power systems. Background Technology

[0002] As the core energy supply network of modern industrial society, the dynamic stability of controlled power systems directly affects national economic security and social order. During the operation of controlled power systems, random signal oscillation is a typical nonlinear dynamic phenomenon. This oscillating behavior stems from the combined influence of complex electromechanical coupling within the system and external random disturbances. Physically, random oscillations in controlled power systems manifest as continuous fluctuations in key parameters such as voltage and frequency. This instability significantly reduces power transmission efficiency, accelerates equipment insulation aging, and in severe cases, may induce cascading faults, leading to regional power outages. Therefore, studying the generation mechanism and suppression methods of random oscillations in controlled power systems is of significant engineering practical importance for ensuring a safe and reliable supply of electrical energy.

[0003] In the field of controlled power system stability control research, sliding mode control has attracted widespread attention due to its unique variable structure characteristics. This method designs specific sliding modes to allow the system state trajectory to converge to a preset sliding surface within a finite time, thereby effectively suppressing random oscillations. In existing technologies, typical sliding mode controller designs usually construct the sliding surface using fixed-dimensional Lyapunov functions and derive the control law based on an accurate system model. While these methods exhibit good transient response and disturbance suppression capabilities in single-dimensional system control, their core limitation lies in the strict correspondence between the controller structure and the system dimension. When facing multi-dimensional analysis requirements of controlled power systems, such as switching between two-dimensional simplified models and seven-dimensional detailed models, traditional sliding mode control methods require independent design of controller parameters for each dimension. This not only increases the complexity of the control system implementation but also leads to performance degradation when the model dimension dynamically changes. Furthermore, existing technologies often employ conservative boundary estimation methods to handle system parameter uncertainties. This over-parameterization design strategy can cause control signal chattering, which in turn exacerbates the mechanical wear of power equipment. Summary of the Invention

[0004] In view of this, the present invention provides an adaptive sliding mode control method for chaos suppression in controlled power systems. First, by designing a dimensionally adaptive sliding mode surface recursively constructed based on synchronization error, a general sliding mode controller framework independent of the specific dimension of the system model is built, fundamentally solving the problem of existing sliding mode control methods heavily relying on specific model dimensions and having poor versatility. Second, by integrating an adaptive online parameter update law based on Lyapunov stability theory within this framework, the controller can identify and compensate for equivalent uncertainties in its own structure in real time, thereby effectively solving the problem of decreased control accuracy caused by comprehensive dynamic uncertainty or time-varying nature of the system, significantly improving the overall robustness and engineering practicality of the control system.

[0005] Therefore, the present invention provides the following technical solution:

[0006] An adaptive sliding mode control method for chaos suppression in power systems, applicable to power systems A nonlinear dynamic model, in which For integers greater than or equal to 2, the method includes: Determine the target system and the target signal output by the target system; Determine the synchronization error between the state vector of the controlled power system and the target signal; Based on the aforementioned synchronization error, a dimension-adaptive sliding surface is recursively constructed. Based on the sliding surface, a sliding mode controller is designed. The output of the sliding mode controller compensates for the comprehensive dynamics of the controlled power system and drives the state of the controlled power system to track the target signal in order to suppress chaotic oscillations.

[0007] Furthermore, the dimension-adaptive sliding surface includes: The first sliding surface is:

[0008] in, This is the first sliding surface; The synchronization error between the state vector of the controlled power system and the target signal; This is the first state variable of the controlled power system. This is the first output signal of the target system.

[0009] No. The sliding surface is:

[0010] in, Index for sliding surface; It is a time-differential operator; For the first Sliding surface; and For respectively the first -1 level linear and nonlinear gain coefficients; For the first -1 level fractional power exponent.

[0011] Furthermore, the sliding mode controller includes an online adjustable adaptive compensation parameter and an adaptive update law for the adaptive compensation parameter. The adaptive compensation parameter is adjusted in real time through the adaptive update law, so that the output of the sliding mode controller compensates for the comprehensive dynamics of the controlled power system.

[0012] Furthermore, the control law of the sliding mode controller includes:

[0013] in, Controlled power system A known nonlinear function in a 3D dynamical form. It is the state vector of the controlled power system; It is the target system's first 2D dynamic nonlinear function It is the target state vector; The online estimated value of the adaptive compensation parameter is determined by the adaptive update law; For the final sliding surface The sign function; Represented as a summation index, traversing from 1 to... Integers of 1; For the corresponding to the first The feedback gain coefficient of the term; For the corresponding to the first The fractional power of the term.

[0014] Furthermore, the estimated values ​​of the adaptive compensation parameters are:

[0015] in, Let be the adaptive gain constant, and .

[0016] Furthermore, the output signal of the target system By system Generate, among which, Different transmission signals are selected based on actual needs.

[0017] Furthermore, the transmitted signal includes a sinusoidal signal; the sinusoidal signal is represented as: ,in, For amplitude, ω is the angular frequency.

[0018] Advantages and positive effects of the present invention: 1. It achieves controller versatility, significantly reducing the threshold and cost of engineering applications: This method constructs a dimension-adaptive sliding mode surface based on recursive generation of synchronization errors, forming a general control architecture decoupled from the specific dimension of the controlled power system model. This architecture completely changes the inherent "one-dimensional, one-design" paradigm of traditional sliding mode control, allowing the same control algorithm to be directly applied to various analysis scenarios with different modeling accuracies, such as two-dimensional simplified models, four-dimensional electromechanical transient models, and even seven-dimensional detailed models, without structural adjustments. This breakthrough not only achieves the standardization and modularization of the controller but also significantly improves the portability and deployment efficiency of the control strategy in different controlled power system simulation and application scenarios. This greatly reduces the costs of repetitive development, system adaptation, and long-term maintenance caused by model dimension switching, fundamentally enhancing the practical value and feasibility of advanced control methods in complex power engineering environments.

[0019] 2. Enhanced system adaptability and robustness, ensuring accurate and reliable control in complex environments: This method integrates an adaptive online parameter update mechanism based on Lyapunov stability theory into a general control framework. This mechanism can identify in real-time the equivalent uncertain parameters within the controller used to compensate for the overall dynamics of the system, and dynamically adjust the control output accordingly. This makes the controller not only insensitive to changes in model dimensions, but also proactively adapt to uncertainties such as internal parameter perturbations and external unknown disturbances. Therefore, even in complex real-world power operation environments with strong nonlinearity and time-varying parameters, this method can still ensure high accuracy, fast response, and strong stability in the chaos suppression process, significantly improving the practical value and operational reliability of the control strategy. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a model diagram of an interconnected controlled power system in the embodiment; Figure 2 For the example Phase diagram; Figure 3 For the example A time series diagram showing the evolution over time; Figure 4 For the steady-state error in the example Evolution over time; Figure 5 Control parameters in the embodiment Identification process; Figure 6 State variables in the embodiment Timing diagram; Figure 7 State variables in the embodiment Timing diagram; Figure 8 The curve showing the evolution of the sliding surface over time in the embodiment is shown. Figure 9 For the steady-state error in the example Evolution over time; Figure 10 Control parameters in the embodiment Recognition image; Figure 11 This is a flowchart of an adaptive sliding mode control method for chaos suppression in controlled power systems. Detailed Implementation

[0022] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0023] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0024] like Figure 11As shown, this invention provides an adaptive sliding mode control method for chaos suppression in controlled power systems. Its core lies in constructing a universal control framework independent of the specific dimensions of the system model. Specifically, it includes the following steps: First, a target system with arbitrarily specifyable output signals is defined and used to form a synchronous control architecture with an n-dimensional (n≥2) nonlinear model of the controlled power system. Second, a set of dimension-adaptive sliding surfaces is recursively constructed based on the state errors between the two systems. The first sliding surface is directly constructed from the basis error, and subsequent sliding surfaces are generated recursively through a linear combination of the preceding sliding surfaces and their derivatives. Finally, a sliding mode controller with adaptive parameter adjustment capability is designed based on this set of sliding surfaces. Through a mechanism that identifies and compensates for the equivalent uncertainties of the system in real time, the controlled power system's state accurately tracks the target signal, thereby effectively suppressing chaotic oscillations.

[0025] Example An adaptive sliding mode control method for chaos suppression in controlled power systems is applied to a two-dimensional model of a controlled power system, comprising the following steps: 1. For example Figure 1 As shown, the controlled power system includes components such as generators, transformers, transmission lines, and loads. A mathematical model of chaotic oscillations in the controlled power system is established, and the system description and characteristic analysis are based on a two-dimensional simplified model. Based on its physical characteristics, working principle, and mathematical models of each component, and combined with the topology of the controlled power system, system models of different dimensions can be established for stability analysis.

[0026] In this embodiment, Figure 1 In this model, G1 and G2 are the equivalent generators of System 1 and System 2, T1 and T2 are transformers, QF1 and QF2 are circuit breakers of System 1 and System 2, and SL is the load. The mathematical model of chaotic oscillation in the controlled power system is expressed as follows: (1) In the formula, The phase angle difference between equivalent generators G1 and G2; Let H be the relative angular velocity of the two systems; H be the equivalent moment of inertia; and D be the equivalent damping coefficient. Electromagnetic power; Mechanical power; This refers to the load disturbance power. The disturbance frequency of the load power.

[0027] In actual operation, a two-dimensional controlled power system, as a nonlinear system, is often accompanied by complex nonlinear oscillations. Therefore, some parameters are fixed:

[0028]

[0029]

[0030]

[0031] The mathematical model of chaotic oscillations in a controlled power system is simplified and expressed as follows: (2) During the operation of a controlled power system, external periodic disturbances such as load periodic fluctuations and grid switching periodic actions are common. When these disturbances are applied to a controlled power system with nonlinear characteristics, they interact in complex ways with the system's inherent characteristics, causing changes in the system's operating state, irregular and non-periodic phase trajectories, and ultimately leading to chaotic oscillations. Therefore, the essence of chaotic oscillations in interconnected controlled power systems is the result of the interaction between the system's inherent nonlinear dynamic characteristics and external periodic disturbances. These periodic disturbances can usually be expressed in expression (2). This indicates that when such disturbances are applied to a strongly nonlinear controlled power system, their spectral components will couple with the system's inherent oscillation modes. Under specific parameter conditions, this coupling will trigger Hopf bifurcation, causing the system's phase trajectory to exhibit typical chaotic characteristics such as aperiodicity and sensitivity to initial conditions, thereby affecting the stable operation of the controlled power system.

[0032] To quantify the critical conditions for the generation of chaos, we assume that in equation (2)... When the values ​​remain constant, meaning the generator input mechanical power, electromagnetic power, and damping remain constant, and only the amplitude of the disturbance load changes, the controlled power system described by equation (2) will change accordingly. Different values ​​result in different states. Therefore, taking... , This study investigates the state of a controlled power system when it encounters different load disturbances. Numerical simulations reveal that when… > When the disturbance power amplitude exceeds the mechanical input power, the system enters a power imbalance state, leading to oscillating instability in the power angle difference δ and relative angular velocity ω. At this time, the system will exhibit chaotic oscillations, such as Figure 2 and Figure 3 As shown. Figure 2 yes Phase diagram, Figure 3 yes A time series diagram showing the evolution over time.

[0033] This paper designs a dimension-independent general sliding mode controller. Through dynamic sliding surface reconstruction and synchronous transmission techniques, it overcomes the dependence of traditional controllers on model dimensions, achieving rapid stabilization of chaotic oscillations in controlled power systems of arbitrary dimensions. Its core objective is to estimate and compensate for unknown load disturbances in real time. This allows the power angle deviation to converge to the stable region in a short time, thus avoiding large-scale power outages.

[0034] 2. Describe the control objective based on synchronous transmission technology, define the state error between the controlled power system and any specified target system; design a dimension-independent recursive sliding surface and a universal sliding mode controller, and construct an adaptive recognition rate for uncertain system parameters; The aforementioned controlled power system model is a two-dimensional model, which typically only considers the basic relationship between the mechanical motion and electromagnetic power of the generator rotor, neglecting some internal electromagnetic transient processes of the generator. It is relatively simple and can reflect some basic dynamic characteristics of the controlled power system, such as the basic characteristics of power angle stability. If it is necessary to further study the dynamic transient characteristics of complex controlled power systems, it is necessary to conduct research through a high-dimensional controlled power system mathematical model. Therefore, the general sliding mode controller designed in this method is not only applicable to two-dimensional controlled power systems, but also applicable to high-dimensional systems.

[0035] To make the explanation more general, assume that the state variables in the controlled power system model are... express, , The mathematical model of a controlled power system is generally expressed as follows: (3) in, For the design to be applied to the first Dimensional control input; For time Differential operators; To describe the first A known nonlinear function in a 3D dynamic state; It is the index of the state variable, traversing from 1 to... All dimensions; It is the total dimension of the system, which is an integer greater than or equal to 2.

[0036] Assume the target signal is output by the following system: (4) In the formula, Different transmission signals can be selected according to actual needs, such as the stable controlled power system model signal of the same dimension as the controlled power system; It describes the target system's first... 2D dynamic nonlinear function; The error between the state variables of the controlled power system and the target signal is defined as: (5) The following relationship is then obtained: (6) generally The sliding mode controller of the dimensional system needs to be designed. This design only requires designing the first sliding surface and a general sliding surface, where the general sliding surface is a combination of the previous sliding surfaces. Through this combination, a... One sliding surface. The specific design of the sliding surface is as follows: (7) (8) in, , , It is a constant. This is the adjustment coefficient.

[0037] From equations (7) and (8), we can obtain: (9) From equation (9), we can see that the first... The time variation rate of each sliding surface is: (10) Before design The sliding mode controller is: ( (11) From equations (6) and (11), we can obtain: (12) Therefore, the first The time change rate of each sliding surface is expressed as: (13) Where n is the total dimension of the system; m represents the summation index, traversing from 1 to n. An integer of 1, used to refer to the first n One sliding surface; This indicates that for the m-th sliding surface Find (n) m)-order time derivative; This is the feedback gain coefficient corresponding to the m-th term; For the corresponding to the first The fractional power of the term.

[0038] 3. Based on Lyapunov stability theory, the stability of the designed controller and parameter adaptive law is rigorously proven to ensure the global asymptotic stability of the system; Theorem: When the controller and parameter recognition rate When it has the following expression, The chaotic state of a controlled power system can be effectively controlled.

[0039] (14) (15) in, For uncertain parameters, and ; This is the adaptive gain constant.

[0040] Proof: Construct the Lyapunov function: (16) (17) Substituting equation (14) into equation (17), we obtain the following expression: (18) Consider equation (15) in the theorem, equation (18) can be simplified to: (19) According to Lyapunov's second method stability criterion If the system is negative definite or semi-negative definite, it is asymptotically stable, and the theorem is proved.

[0041] 4. Through digital simulation experiments, taking a typical two-dimensional controlled power system as an example, the effectiveness and parameter identification capability of the general control strategy in system models of different dimensions are verified.

[0042] Asynchronous operation of generator power angle frequency exacerbates the nonlinear coupling effect between units, significantly increasing the risk of chaotic oscillations. This paper proposes a novel universal sliding mode controller that constructs the dynamic trajectory of the target system through synchronous transmission technology, controlling each unit of the controlled power system to achieve power angle frequency synchronization with the target system, thereby reducing the nonlinear complexity caused by multi-machine interaction. Theoretical analysis shows that when the synchronous transmission system is selected as a reference model of arbitrary dimensions, the controller can ensure the synchronous convergence of electromechanical state variables of the controlled power system in different dimensions through dynamic sliding surface reconstruction and parameter adaptation mechanisms. This synchronization process effectively reduces the dynamic coupling strength of power angle differences between units, enabling the system to form a cooperative response capability under load disturbances and suppressing chaotic oscillations caused by power angle instability. To verify the effectiveness of the controller in cross-dimensional scenarios, this section uses a two-dimensional controlled power system model as an example for verification.

[0043] The system model and parameter settings are as described above. That is, when the controlled power system is in a chaotic oscillation state, the sliding mode controller control rate will be... To facilitate discussion, let equation (2) be added to equation (2). , Then, equation (2) can be written as: (20) Based on the sliding mode controller principle designed in the previous section, the target signal can be arbitrary, therefore It can be any system, here will A sinusoidal signal was used for simulation verification.

[0044] The specific expression is: (twenty one) Based on the controller design principles in the previous section, design the sliding surface and control law of the sliding mode controller. for: (twenty two) (twenty three) Based on the above design, a numerical simulation of the controlled power system was performed, and the simulation results are as follows: Figure 4-8 As shown. By Figure 4 It can be seen that when the controlled power system is in a state of chaotic oscillation, When a sliding mode controller is added to a controlled power system in a state of chaotic oscillation, the state variables of the controlled power system... and The system can track the target system for a short time, achieving a steady-state error of zero. This indicates that the control algorithm and parameter settings are reasonable and effective, capable of adjusting the control input in a timely manner according to the dynamic changes of the system, thus bringing the chaotic controlled power system under control within a short period. Figure 5 It is an unknown parameter The recognition curve is composed of Figure 5 It can be known It is evident that the designed sliding mode controller can accurately identify unknown control parameters in a short time. . Figure 6 and Figure 7 This is the system state variable evolution curve over time. For the first 5 seconds, the system is in a chaotic oscillating state; after 5 seconds, a sliding mode controller is introduced. From... Figure 6 , Figure 7 It can be seen that the system has dynamic characteristics from chaos to stability. After 18.2s, the system is completely synchronized with the target system, and the controlled power system is in a stable operating state. Figure 8 The graph shows the evolution of the sliding surface over time. The designed sliding surface approaches zero at 18.2 s, further demonstrating the controller's ability to synchronize quickly. Although the simulation is based on a two-dimensional model, the control law and sliding surface are designed using universal control laws and sliding surfaces, which can adaptively match the state space of models of any dimension, ensuring the applicability to high-dimensional controlled power systems.

[0045] To achieve synchronous stability in a controlled power system, we further explore the impact of selecting the transmission target on control performance. Theory shows that when the transmission target signal is output from a controlled power system of the same dimension as the controlled power system, synchronization accuracy and response speed can be significantly improved. Assume the target signal is output from the following two-dimensional controlled power system: (twenty four) Based on the design of the general sliding surface and controller in this work, the sliding surface and controller are as follows: (25) (26) Based on the above design, a numerical simulation of the controlled power system was performed, and the simulation results are as follows: Figure 9-10 As shown. By Figure 9 It can be seen that when the controlled power system is in a chaotic oscillation state, adding a sliding mode controller to the system enables it to track the target system within 0.3 seconds, achieving a steady-state error of 0. At this point, the power angle and relative speed of all motors in the controlled power system are synchronized with the target system, indicating that the controller not only has strong tracking capability but also a very fast response speed. Figure 4 In comparison, the target system uses the same controlled power system model as the controlled power system, resulting in a higher response speed. Figure 10 It is an unknown parameter The identification curve, when the target system is selected as a two-dimensional controlled power system model. ,Depend on Figure 10It is evident that the parameter recognition rate can accurately identify unknown parameters in a short time. Therefore, the control strategy designed in this work can effectively drive the controlled power system model to a state consistent with the target model, achieving synchronous transmission and stabilizing the operating state of the controlled power system.

[0046] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An adaptive sliding mode control method for chaos suppression in power systems, characterized in that, Applicable to power systems A nonlinear dynamic model, in which For integers greater than or equal to 2, the method includes: Determine the target system and the target signal output by the target system; Determine the synchronization error between the state vector of the controlled power system and the target signal; Based on the aforementioned synchronization error, a dimension-adaptive sliding surface is recursively constructed. Based on the sliding surface, a sliding mode controller is designed. The output of the sliding mode controller compensates for the comprehensive dynamics of the controlled power system and drives the state of the controlled power system to track the target signal in order to suppress chaotic oscillations.

2. The method according to claim 1, characterized in that, The dimension-adaptive sliding surface includes: The first sliding surface is: in, This is the first sliding surface; The synchronization error between the state vector of the controlled power system and the target signal; This is the first state variable of the controlled power system. This is the first output signal of the target system. No. The sliding surface is: in, Index for sliding surface; It is a time-differential operator; For the first Sliding surface; and For respectively the first -1 level linear and nonlinear gain coefficients; For the first -1 level fractional power exponent.

3. The method according to claim 1, characterized in that, The sliding mode controller includes an online adjustable adaptive compensation parameter and an adaptive update law for the adaptive compensation parameter. The adaptive compensation parameter is adjusted in real time through the adaptive update law, so that the output of the sliding mode controller compensates for the comprehensive dynamics of the controlled power system.

4. The method according to claim 1, characterized in that, The control law of the sliding mode controller includes: in, Controlled power system A known nonlinear function in a 3D dynamical form. It is the state vector of the controlled power system; It is the target system's first 2D dynamic nonlinear function It is the target state vector; The online estimated value of the adaptive compensation parameter is determined by the adaptive update law; For the final sliding surface The sign function; Represented as a summation index, traversing from 1 to... Integers of 1; For the corresponding to the first The feedback gain coefficient of the term; For the corresponding to the first The fractional power of the term.

5. The method according to claim 4, characterized in that, The estimated values ​​of the adaptive compensation parameters are: in, Let be the adaptive gain constant, and .

6. The method according to claim 1, characterized in that, The output signal of the target system By system Generate, among which, Different transmission signals are selected based on actual needs.

7. The method according to claim 6, characterized in that, The transmitted signal includes a sinusoidal signal; the sinusoidal signal is represented as: ,in, For amplitude, ω is the angular frequency.

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