An event-triggered fault-tolerant control method for power systems based on intermediate observers

Abstract

This invention discloses an event-triggered fault-tolerant control method for power systems based on an intermediate observer. This method first uses linearization techniques to establish a dynamic model of a power system that considers electric vehicle integration. Next, an intermediate observer method is designed using augmented states to estimate faults. A dynamic input trigger mechanism consisting of system input and error-dependent trigger parameters is designed to reduce communication transmission frequency. Finally, a fault-tolerant controller is designed to ensure uniformly bounded stability for the power system that considers electric vehicle integration. When applied to a power system that considers electric vehicle integration, this method improves the speed and accuracy of fault estimation, ensuring normal system operation under fault conditions.

Description

Technical Field

[0001] The present invention relates to an event-triggered fault-tolerant control method for a power system considering grid connection of electric vehicles, and in particular to a dynamic event-triggered fault-tolerant control method for a power system based on an intermediate observer. Background Art

[0002] Due to the complexity of power system operation, measurement faults masked by noise and interference are often difficult to detect, potentially leading to degraded system performance. Fault detection and fault-tolerant control, as essential components of fault diagnosis, are crucial for improving system safety and reliability. There are two main approaches to implementing fault-tolerant control: designing robust controllers to make the system robust to faults, and estimating and proactively compensating for faults. Based on this concept, researchers have conducted extensive research on the design of fault-tolerant controllers and achieved a series of successful results.

[0003] Furthermore, newly built power systems today typically utilize network control methods, which are simple to install and highly scalable. However, due to limited network bandwidth, data packets inevitably experience latency, packet loss, and timing errors during transmission. Event-triggered control is crucial for reducing the frequency of communication transmissions without sacrificing optimal stability and performance. In an event-triggered control environment, communication transmission only occurs when pre-set conditions are violated.

[0004] However, the aforementioned research primarily focuses on estimating specific fault types, resulting in poor estimation results for more general faults. Furthermore, the aforementioned research primarily focuses on event-triggered fault-tolerant control for power systems that incorporate electric vehicles, without considering network bandwidth. Therefore, it is necessary to employ intermediate observers to estimate faults and dynamic event-triggered strategies to conserve bandwidth. Summary of the Invention

[0005] The purpose of the present invention is to propose a power system dynamic event-triggered fault-tolerant control method based on an intermediate observer, which can effectively improve the performance of fault estimation and fault-tolerant control of the power system under bandwidth-limited conditions.

[0006] The specific technical solution of the present invention is as follows: A method for dynamic event-triggered fault-tolerant control of a power system based on an intermediate observer, comprising the following steps:

[0007] Using linearization technology, the dynamic model of the power system considering the integration of electric vehicles is established as follows:

[0008]

[0009]

[0010] Where x T (t) = [f(t)X g (t)P g (t)P e (t)Δ(t)] represents the system state, u(t) represents the system input, and f a (t) represents system failure, d(t) represents external disturbance, and f s (t) represents sensor failure, y(t) represents system output, z(t) represents regulation output, f(t) represents frequency deviation, X g (t) represents the governor position, P g (t) represents the turbine output power, P e (t) represents the incremental change of the electric vehicle, Δ(t) = ∫ACE(t)dt, ACE(t) represents the regional control deviation, D represents the load damping coefficient, M represents the inertia constant, R g Indicates the speed regulator deceleration characteristics, T g Indicates the speed regulator, T t represents the turbine time constant, ρ e Indicates the deceleration characteristics of electric vehicles, represents the electric vehicle control gain, T e represents the electric vehicle time constant, b represents the frequency bias constant, α g represents the thermal turbine participation factor, α e represents the electric vehicle participation coefficient;

[0011] An intermediate observer method is designed to reconstruct the system state and estimate the fault. The specific steps are as follows:

[0012] The intermediate variable η(t) is designed as follows:

[0013]

[0014] The intermediate observer is designed as follows:

[0015]

[0016] Where, and denote the estimated values ​​of system state, sensor fault and intermediate variables respectively, represents the cumulative estimation error, represents the estimated value of the system fault, L and S are the observer gains to be designed;

[0017] Furthermore, a dynamic input trigger mechanism consisting of system input and error-dependent trigger parameters is designed. The specific steps are as follows:

[0018] t k+1=inf{t}t>t k ,||e u (t)|| ∞ ≥σ(t)},

[0019] Where, e u (t)=u(t)-u(t k ) represents the measurement error, t k Indicates the last triggering time, t k+1 represents the next triggering time, σ(t) represents the triggering parameter and is updated by the following formula:

[0020]

[0021] Where, and σ They represent the upper and lower bounds of the trigger parameter, μ represents the weight parameter, and α1 and α2 represent the sensitivity parameters;

[0022] Furthermore, a fault-tolerant control scheme for power system event triggering considering electric vehicle grid connection involved in the present invention is established, and the specific steps are as follows:

[0023]

[0024] Where K is the feedback gain matrix, m is the number of columns in B, and ε is a positive constant. This algorithm can ensure that the system is uniformly bounded and stable. The proof process is as follows:

[0025] C001: Select the following composite energy function:

[0026]

[0027] C002: represents the state observation error of the system, represents the estimation error of the intermediate variable, P1, P2, P3 and P4 represent the Lyapunov variable matrix, and Y is the given coordination matrix;

[0028] C003: Calculate the derivative of V(t) and consider H ∞ Performance, including:

[0029]

[0030] C004: In the formula, γ represents H ∞ Performance level indicators;

[0031] C005: Further consideration According to C003, the following formula can be obtained:

[0032]

[0033] C006: Where ∈ is any positive constant

[0034] C007: Further, considering the special properties of the hyperbolic tangent function, we can get the following formula:

[0035]

[0036] C008: Further, select ζ(t)=[ξ 丅 (t), d 丅 (t)] 丅 , from C003, C005 and C006, we can get that when Ξ<0:

[0037]

[0038] C009: Where Ξ is a matrix with 8 rows and 8 columns, and each element in Ξ is:

[0039]

[0040]

[0041]

[0042]

[0043] Elements in unmentioned positions are all-zero matrices of appropriate dimensions;

[0044] C010: According to C009, the power system considering the grid connection of electric vehicles is uniformly bounded and stable under the event-triggered fault-tolerant controller designed by the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0046] Figure 2 Response diagram of the system state x(t) when the method proposed in the present invention is used in the embodiment without control;

[0047] Figure 3 Response diagram of the system state x(t) under controlled conditions using the method proposed in the embodiment;

[0048] Figure 4 The fault estimation method of the present invention is used in the embodiment Response graph of ;

[0049] Figure 5Response diagram of event trigger threshold variable σ(t) using the method proposed in the embodiment of the present invention; DETAILED DESCRIPTION

[0050] The present invention is further illustrated below with reference to specific examples. It should be understood that these examples are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention made by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0051] like Figure 1 As shown, a power system event-triggered fault-tolerant control method based on an intermediate observer includes the following steps:

[0052] Step 1: Set the initial values ​​of various parameters;

[0053] Step 2: Update the threshold parameter σ(t);

[0054] Step 3: Use the threshold parameter σ(t) and the system input u(t) to verify the event trigger condition and update the trigger output u(t k );

[0055] Step 4: Use trigger output u(t k ), update the measurement output y(t);

[0056] Step 5: Use the system output y(t) to estimate the system state and fault estimation

[0057] Step 6: Estimation based on state and fault estimation Generate control input u(t) in real time;

[0058] Step 7. Repeat steps 3, 4, 5, and 6 until the running time ends.

[0059] An embodiment of the present invention is described below:

[0060] Consider the problem of event-triggered fault-tolerant control method for power systems based on intermediate observers. The corresponding dynamic model is:

[0061]

[0062]

[0063] The system parameters are: D = 0.0083, M = 0.1667, R g =2.4, T g =0.08, T t =0.3,ρ e =1 / Rg , T e =0.3, b=0.425, α g =0.8,α e =0.2;

[0064] Figure 1 is a flow chart of the method of an embodiment of the present invention; when the proposed method is applied, the state response diagram under no control is as follows Figure 2 As shown, the state response diagram under control is as follows Figure 3 As shown in the figure, the fault estimation diagram is as follows Figure 4 As shown, the change of event trigger threshold variable is as follows Figure 5 As shown in Figure 2, it can be seen that the proposed fault estimation method based on the intermediate observer effectively estimates the fault, and the proposed event-triggered fault-tolerant controller effectively compensates for the impact of the fault on the system.

[0065] References

[0066] [1] JWZhu, GHYang, H.Wang, F.Wang. Fault estimation for a class of nonlinear systems based on intermediate estimator. IEEE Transactions on Automatic Control, vol.61, pp.2518-2524, 2015.

[0067] [2] S.Yan, Z.Gu, JHPark, X.Xie.Adaptive memory-event-triggered staticoutput control of TS fuzzy wind turbine systems. IEEE Transactions on FuzzySystems, vol.30, pp.3894-3904, 2021.

Claims

1. An event-triggered fault-tolerant control method for a power system based on an intermediate observer, characterized in that: The following steps are involved: First, a linearization technique is used to establish a dynamic model of the power system considering the integration of electric vehicles into the grid: Where x T (t) = [f(t)X g (t)P g (t)P e (t)△(t)] represents the system state, u(t) represents the system input, f a (t) represents system failure, d(t) represents external disturbance, and f s (t) represents sensor failure, y(t) represents system output, z(t) represents regulation output, f(t) represents frequency deviation, X g (t) represents the governor position, P g (t) represents the turbine output power, P e (t) represents the incremental change of the electric vehicle, △(t)=∫ACE(t)dt, ACE(t) represents the regional control deviation, D represents the load damping coefficient, M represents the inertia constant, R g Indicates the speed regulator deceleration characteristics, T g Indicates the speed regulator, T t represents the turbine time constant, ρ e Indicates the deceleration characteristics of electric vehicles, represents the electric vehicle control gain, T e represents the electric vehicle time constant, b represents the frequency bias constant, α g represents the thermal turbine participation factor, α e represents the electric vehicle participation coefficient; Then, based on the above dynamic model, using the augmented state An intermediate observer is designed to reconstruct the system state, system faults, and sensor faults. The intermediate variable η(t) is designed as follows: Where L and S are the observer gains to be designed; The intermediate observer is designed as follows: Where, and They represent the system state x(t), sensor fault f s (t) and the estimated values ​​of the intermediate variable η(t), represents the cumulative estimation error, represents an estimate of system failure; Then, the system state and system faults reconstructed by the observer are used to design a fault-tolerant controller. The specific steps are as follows: Where K is the feedback gain matrix, E4 = [I 0], m is the number of columns in B, and ε is a positive constant; Finally, a dynamic input trigger mechanism consisting of system input and error-dependent trigger parameters is designed to reduce the communication transmission frequency. The specific steps are as follows: Based on the above control signal u(t), the following dynamic input trigger mechanism is designed: t k+1 =inf{t|t>t k ,||e u (t)|| ∞ ≥σ(t)}, Where, e u (t)=u(t)-u(t k ) represents the input trigger error, t k Indicates the last triggering time, t k+1 represents the next triggering moment, σ(t) represents the dynamic threshold and is updated by the following formula: Where, and σ They represent the upper and lower bounds of the threshold, μ represents the weight parameter, and α1 and α2 represent the sensitivity parameters; This method can ensure that the system is uniformly bounded and stable. The specific proof steps are as follows: B001: Select the following composite energy function: Where, represents the state observation error of the system, represents the estimated error of the intermediate variable, P1, P2, P3 and P4 represent the Lyapunov variable matrix, and Y is the preset coordination matrix; B002: Calculate the derivative of V(t) and consider H ∞ Performance, including: Where γ represents H ∞ Performance level indicators; B003: Further consideration The following formula can be obtained: Where, ∈ is any positive constant; B004: Further, considering the special properties of the hyperbolic tangent function, we can get the following formula: B005: Further, select and From B002, B003 and B004, we can get that when Ξ<0, Where Ξ is a matrix with 8 rows and 8 columns, and each element in Ξ is: Elements in unmentioned positions are all-zero matrices of appropriate dimensions; B006: According to B005, the power system considering the grid connection of electric vehicles is uniformly bounded and stable under the event-triggered fault-tolerant controller designed by the present invention.

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