An event-triggered interval estimation method for permanent magnet direct-drive wind turbine system under stealthy cyber attack

Abstract

This invention discloses an event triggering interval estimation method for a permanent magnet direct-drive wind turbine system under stealth deception attacks. First, based on Markov jump system theory and fuzzy control theory, a discrete-time T-S fuzzy Markov jump model of the permanent magnet direct-drive wind turbine system is established. A fusion event triggering mechanism based on ring events and a dynamic threshold update law composed of system output and error-dependent triggering parameters are designed to balance triggering performance and system performance. Then, under stealth deception attacks, a proportional-integral iterative observer is designed to reconstruct the system state and external disturbances. Finally, based on Zonotope technology, an interval estimation method is designed to obtain a tighter state interval. When applied to a permanent magnet direct-drive wind turbine system, this method achieves good interval estimation results and significantly reduces communication frequency.

Description

Technical Field

[0001] This invention relates to an interval method, specifically to an event-triggered interval estimation method for a permanent magnet direct-drive wind turbine system under stealth deception attacks. Background Technology

[0002] Today, governments and businesses are making further efforts to promote the large-scale application of renewable energy and guide the use of clean energy to produce electricity. Among these energy sources, wind power is widely recognized as a clean and sustainable energy solution due to its higher cost-effectiveness compared to traditional fossil fuels and nuclear energy. This advantage has inspired researchers to study the stability problems of wind turbine systems. The most commonly used generator in wind power generation is the permanent magnet synchronous generator, which has advantages such as direct drive capability, low speed, and low maintenance costs. As is well known, permanent magnet direct-drive wind turbine systems have complex nonlinear dynamic characteristics, and existing estimation methods cannot obtain a tight state interval. A tight state interval is the basis for subsequent efficient control strategies and helps improve the power generation efficiency of wind turbines. In addition, wind speed has a random variation characteristic, and traditional methods can only handle systems under specific wind conditions. Markov processes can effectively model this random characteristic of wind speed. Therefore, it is necessary to apply Markov jump system theory and fuzzy control theory to develop an interval estimation method for permanent magnet direct-drive wind turbine systems.

[0003] Furthermore, with the widespread adoption of communication technologies and their integration with industrial systems, networked control has become an important approach to driving the development of permanent magnet direct-drive wind turbine systems. In networked control frameworks, data exchange is conducted through network channels employing a time-triggered (periodic) mode. However, with the expansion of system scale and the indiscriminate release of redundant data packets, network congestion looms over the entire system. Therefore, there is an urgent need to adopt effective communication schemes in permanent magnet direct-drive wind turbine systems to reduce data transmission frequency and conserve limited network resources. However, existing research mainly focuses on static event-triggered strategies, offering limited reductions in network load. Moreover, the impact of outlier data on event generators is not considered. Therefore, it is necessary to improve existing event-triggered strategies to save bandwidth usage.

[0004] Besides limited network resources, exposed data transmissions are also vulnerable to hacker attacks. In recent years, there has been considerable research on spoofing attacks and denial-of-service attacks. However, further research is needed on undetectable, stealthy spoofing attacks. Summary of the Invention

[0005] The purpose of this invention is to propose an event triggering interval estimation method for permanent magnet direct-drive wind turbine systems under stealth deception attacks, which can effectively improve the state interval estimation performance of permanent magnet direct-drive wind turbine systems under limited bandwidth and stealth deception attacks.

[0006] The specific technical solution of this invention is as follows: A method for estimating the event triggering interval of a permanent magnet direct-drive wind turbine system under stealth deception attacks, comprising the following steps:

[0007] Based on Markov jump system theory and fuzzy control theory, a discrete-time TS fuzzy Markov jump model of a permanent magnet direct-drive wind turbine system is established:

[0008] According to the principles of aerodynamics, the power generated by wind energy is expressed as follows:

[0009]

[0010] Wherein, ρ(Kg / m 3 () represents air density, and π represents pi. Indicates the length of the turbine blades. Represents the power coefficient, ω w (m / s) represents wind speed. ω represents the tip speed ratio. t (rpm) represents the turbine speed, β (rad) represents the pitch angle. Additionally, δ i (t) is

[0011] The corresponding mechanical torque is calculated as follows:

[0012]

[0013] Typically, the dynamic characteristics of a pitch pusher are:

[0014]

[0015] Where τ is the time constant, β a It is a control signal.

[0016] Next, the wind speed is broken down into a low-frequency stable component ω. ws and high-frequency interference part ω wp and mechanical torque Perform a Taylor expansion at the stable point:

[0017]

[0018] in, ω wd =ω w -ω ws Indicates deviation.

[0019] At the operation point of the above formula Performing a Taylor expansion, we obtain the following deviation equation:

[0020]

[0021] in, The horizontal bar and wavy line above the variable represent the operation point and deviation, respectively.

[0022] Next, the nonlinear model of the permanent magnet direct-drive wind turbine system is established as follows:

[0023]

[0024] In the formula, Indicates stator resistance. Represents the stator inductance on the d-axis. Represents the stator inductance on the q-axis. This represents the magnetic flux of a permanent magnet. Represents the extreme number. and Representing the q-axis and d-axis voltages respectively, i q (t) and i d (t) represents the q-axis and d-axis currents, respectively.

[0025] The electrical torque applied by the permanent magnet synchronous motor can be further rewritten as:

[0026]

[0027] Set according to wind speed The operation points are used to model the random variation of wind speed as a Markov process. Then, the model of the permanent magnet direct-drive wind turbine can be further represented as:

[0028]

[0029] in, d(t)=ω wd Let y(t) represent the system state, control input, disturbance, and system output, respectively. Furthermore, the system matrix is ​​shown below:

[0030]

[0031]

[0032] in, Indicates the i-th operation partition That is also true. To simplify the notation, let's assume...

[0033] For the nonlinear terms present in the system, fuzzy control theory is used for processing. Assume... And select the fuzzy membership function as:

[0034]

[0035] Here, θ1 and θ2 are available prerequisite variables.

[0036] Next, applying the fuzzy membership function to the state-space expression of the aforementioned permanent magnet direct-drive wind turbine system yields the following fuzzy model:

[0037] Fuzzy rule i: If It is θ i ,So

[0038]

[0039] in,

[0040]

[0041] Next, setting the sampling interval to T and using the Euler method, the above continuous-time TS fuzzy Markov jump system can be transformed into the following discrete system model:

[0042] Fuzzy rule i: If It is θ j ,So

[0043]

[0044] in,

[0045] Thus far, the discrete-time TS fuzzy Markov jump model of the permanent magnet direct-drive wind turbine system has been successfully established.

[0046] Furthermore, a dynamic event triggering mechanism based on ring events and a dynamic threshold update law composed of system output and error-dependent triggering parameters are designed to balance triggering performance and system performance. The specific steps are as follows:

[0047] To reduce network transmission burden, the estimated signal is first verified using event criteria, and then transmitted to the controller via an ideal network. The dynamic event triggering mechanism is constructed as follows:

[0048] k s+1 =inf{k>k s |σ1(k s f1(k) < f2(k) < σ2(k) s f1(k)}

[0049] Among them, e y (k)=y(k)-y(k s The ) indicates the trigger error of the output. Ψ i This represents the weight matrix to be designed. k s Indicates the last trigger time, k s+1 Indicates the next trigger time. Dynamic threshold σ q (k s (q=1,2) is updated by the following formula:

[0050]

[0051] in, μ q It is the weighting parameter, γ aq and γ bq It is a sensitivity parameter.

[0052] Furthermore, under the threat of stealth deception attacks, a proportional-integral iterative observer is designed to reconstruct the system state and external disturbances. The specific steps are as follows:

[0053] When the trigger output is transmitted to the observer, an adversary can attack it by forging the transmitted data. The adversary's goal is to tamper with the trigger output without being detected. This attack mode is called a stealth deception attack. Once the attack is successful, the transmitted data will be rewritten as follows:

[0054] y a (k)=y(k s )+a f ·(k),

[0055] Among them, a f (k) is a pre-compiled attack signal.

[0056] The mth iteration:

[0057]

[0058] in, Let represent the estimated value of the system state at the m-th iteration. This represents the estimated value of the disturbance at the m-th iteration. Indicates the cumulative error. also, and It is the gain of the observer to be designed.

[0059] set up The following error system can be obtained:

[0060]

[0061] in,

[0062] set up The error system can be further simplified as:

[0063]

[0064]

[0065] This observer can guarantee the stochastic stability of the error system under stealth deception attacks. The proof is as follows:

[0066] D001: Select the following form of composite energy function:

[0067]

[0068] D002: Among them,

[0069] D003: Next, calculate the difference ΔV [m] (ΔV [m] =V [m] (k+1)-V [m] (k) and consider H ∞ Performance can be obtained as follows:

[0070]

[0071] D004: In the formula,

[0072] D005: If Then the stochastic stability of the error system can be guaranteed. To achieve this goal, for The following results can be obtained by administering Shure supplement:

[0073]

[0074] D006: Next, the event triggering conditions will be introduced into the analysis.

[0075]

[0076] D007: In the formula, ∈1 and ∈2 are positive scalars.

[0077] D008: Substituting D005 into D004, we get:

[0078]

[0079] D009: If it can be guaranteed So Therefore, the error system is stochastically stable.

[0080] Furthermore, based on the Zonotope technique, an interval estimation method is designed to obtain more compact state intervals. The specific steps are as follows:

[0081] If we can find the upper and lower bounds of the state estimation error Then we can obtain the range of states:

[0082]

[0083] Next, based on the Zonotope technique, the upper and lower bounds of the state estimation error are obtained through analysis. The specific steps are as follows:

[0084] E001: Regarding state estimation error have:

[0085]

[0086] E002: In the formula, for l = 1, ..., k-1, also,

[0087] E003: On the one hand, analyze the range of the stealth deception attack signal:

[0088]

[0089] E004: In the formula, for l = 1, ..., k-1, also,

[0090] E005: Let a f The reachable set of (k) is Λ a We can obtain:

[0091]

[0092] E006: On the other hand, for (k-1-l∈[k s k s+1 )),set up In addition, The reachable set can be obtained as follows:

[0093]

[0094] E007: According to E006, interval It can be represented as:

[0095]

[0096] E008: Due to set up We can obtain:

[0097]

[0098] E009: Combining E007 and E008, we can obtain

[0099]

[0100] Thus, the state estimation error is obtained. The interval. Based on From the range, we can further obtain the close range of the permanent magnet direct-drive wind turbine system state. Attached Figure Description

[0101] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0102] Figure 2 The method proposed in this invention is used in the embodiments. Interval estimation plot;

[0103] Figure 3 The method proposed in this invention is used in the embodiments. Interval estimation plot;

[0104] Figure 4 The method proposed in this invention is used in the embodiments. Interval estimation plot;

[0105] Figure 5 The method proposed in this invention is used in the embodiments. Interval estimation plot;

[0106] Figure 6 This is a response diagram of the event triggering threshold under the method proposed in this invention, as shown in the embodiment.

[0107] Figure 7 This is a trigger diagram for event triggering using the method proposed in this invention, as shown in the embodiment. Detailed Implementation

[0108] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading the present invention, any modifications of the present invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0109] like Figure 1 As shown, a method for estimating the event triggering interval of a permanent magnet direct-drive wind turbine system under stealth deception attack includes the following steps:

[0110] Step 1: Set initial values ​​for each parameter;

[0111] Step 2: Sample the sensor output y(k);

[0112] Step 3: Update the threshold parameter σ q (k);

[0113] Step 4: Use the threshold parameter σ q (k) verifies the event triggering condition with the output y(k), and updates the triggering output y(k). s );

[0114] Step 5: Use the altered output signal y from the attacked system. a (k) Update the observer and output the result of the m-th iteration. and And save it to the register;

[0115] Step 6: Repeat steps 2, 3, 4, and 5 until the end of one iteration.

[0116] Step 7: Repeat the above steps for n iterations, perform residual analysis on all data stored in the registers using the Zonotope technique, and output the state estimation error. interval

[0117] Step 8: Based on the state estimation error interval The section of the synthetic permanent magnet direct drive wind turbine system

[0118] An embodiment of the present invention is described below:

[0119] Consider the system parameters shown in the table below:

[0120]

[0121] Figure 1 The system structure diagram is shown in the embodiment of the present invention; the state interval estimation diagram of the permanent magnet direct-drive wind turbine system under the designed interval estimation method is shown in the figure below. Figure 2-5 As shown, the designed dynamic threshold response diagram is as follows: Figure 6 As shown in the figure, the trigger interval diagram of the designed dynamic event triggering mechanism is as follows: Figure 7 As shown. From Figure 2-5 As can be seen, the proposed dynamic event-triggered interval estimation method successfully estimates the state of a permanent magnet direct-drive wind turbine system under a stealth deception attack, and the estimation performance improves with the number of iterations. Figure 6-7 It can be seen that the proposed event triggering mechanism, while ensuring the same system performance, further reduces the number of signal transmissions and lowers the network bandwidth usage.

[0122] References

[0123] [1] Yan, S., Gu, Z., Park, J.H., & Xie, X. (2021). Adaptive memory-event-triggered static output control of T-S fuzzy wind turbine systems. IEEE Transactions on Fuzzy Systems, 30(9), 3894 - 3904.

[0124] [2] Peng, C., & Yang, T.C. (2013). Event-triggered communication and H∞ control co-design for networked control systems. Automatica, 49(5), 1326 - 1332.

Claims

1. A method for estimating the event triggering interval of a permanent magnet direct-drive wind turbine system under stealth deception attack, characterized in that, Includes the following steps: Based on Markov jump system theory and fuzzy control theory, a discrete-time TS fuzzy Markov jump model of permanent magnet direct-drive wind turbine system is established. Design a fusion event triggering mechanism based on ring events and a dynamic threshold update law composed of system output and error-dependent triggering parameters to balance triggering performance and system performance; Design a proportional-integral iterative observer to reconstruct the system state and external disturbances under stealth deception attacks; Based on the Zonotope technique, an interval estimation method is designed to obtain a more compact state interval.

2. The event triggering interval estimation method for a permanent magnet direct-drive wind turbine system under stealth deception attack as described in claim 1, characterized in that, Based on Markov jump system theory and fuzzy control theory, a discrete-time TS fuzzy Markov jump model of a permanent magnet direct-drive wind turbine system is established. The specific steps are as follows: According to the principles of aerodynamics, the power generated by wind energy It is expressed as follows: ， in, Indicates air density, Represents pi (π). Indicates the length of the turbine blades. Indicates the power factor. Indicates wind speed. Indicates the tip speed ratio, Indicates turbine speed. Indicates the pitch angle; in addition, for ; corresponding mechanical torque The calculation is as follows: ， The dynamic characteristics of the pitch pusher are: in, It is a time constant. It is a control signal; Next, the wind speed was broken down into low-frequency stable components. and high-frequency interference section and mechanical torque Perform a Taylor expansion at the stable point: in, Indicates deviation; Mechanical torque Electrical torque applied by the permanent magnet synchronous motor They cancel each other out; this interaction affects the motor speed. The effects are as follows: in, Represents the moment of inertia. Indicates the coefficient of friction; At the operation point of the above formula Performing a Taylor expansion, we obtain the following deviation equation: in, , , , The horizontal bar and wavy line above the variable represent the operation point and deviation, respectively. Next, the nonlinear model of the permanent magnet direct-drive wind turbine system is established as follows: ， In the formula, Indicates stator resistance. Represents the stator inductance on the d-axis. Represents the stator inductance on the q-axis. This represents the magnetic flux of a permanent magnet. , Represents the extreme number. and These represent the voltages along the q-axis and d-axis, respectively. and These represent the q-axis and d-axis currents, respectively. The electrical torque applied by the permanent magnet synchronous motor can be further rewritten as: ， Set according to wind speed The operation points are used to model the random variation of wind speed as a Markov process. Then, the model of the permanent magnet direct-drive wind turbine can be further represented as: ， in, , , , These are the system state, control input, disturbance, and system output, respectively; furthermore, the system matrix is ​​shown below: ， In order to simplify the symbols, let , , This indicates an operation on the partition index; Indicates the i-th operation partition , , , That is also true; For the nonlinear terms present in the system, fuzzy control theory is used to handle them; assuming And select the fuzzy membership function as: in, , These are available prerequisite variables; Next, applying this fuzzy membership function to the state-space expression of the permanent magnet direct-drive wind turbine system yields the following fuzzy model: Fuzzy rules if yes ,So ， in, It is a fuzzy rule index; The expression is as follows: ； Next, set the sampling interval to Furthermore, using the Euler method, the continuous-time TS fuzzy Markov jump system can be transformed into the following discrete system model: Fuzzy rules if yes ,So ， in, Indicates the sampling interval. , , ; Thus far, the discrete-time TS fuzzy Markov jump model of the permanent magnet direct-drive wind turbine system has been successfully established.

3. The event triggering interval estimation method for a permanent magnet direct-drive wind turbine system under stealth deception attack as described in claim 2, characterized in that, To balance triggering performance and system performance, a dynamic event triggering mechanism based on ring events and a dynamic threshold update law composed of system output and error-dependent triggering parameters are designed. The specific steps are as follows: To reduce network transmission burden, the estimated signal is first verified using event criteria, and then transmitted to the controller via an ideal network; the dynamic event triggering mechanism is constructed as follows: ， in, This indicates the trigger error of the output. , ; This represents the weight matrix to be designed; Indicates the last trigger time. Indicates the next trigger time; dynamic threshold Updated by the following formula: in, , These are weight parameters. and It is a sensitivity parameter.

4. The event triggering interval estimation method for a permanent magnet direct-drive wind turbine system under stealth deception attack as described in claim 3, characterized in that, To reconstruct the system state and external disturbances under stealth deception attacks, a proportional-integral iterative observer is designed. The specific steps are as follows: When the trigger output is transmitted to the observer, the enemy can attack it by forging the transmitted data; the enemy's goal is to tamper with the trigger output without being detected; this attack mode is called a stealth deception attack; once the attack is successful, the transmitted data will be rewritten as: in, It is a pre-compiled attack signal; Next, the proportional-integral iterative observer is designed as follows: The mth iteration: ， in, Let represent the estimated value of the system state at the m-th iteration. This represents the estimated value of the disturbance at the m-th iteration. Indicates the cumulative error. ;also, , , and It is the gain of the observer to be designed; set up , The following error system can be obtained: ， in, ; set up , , The error system can be further simplified as: 。 5. The method for estimating the event triggering interval of a permanent magnet direct-drive wind turbine system under stealth deception attack as described in claim 4, characterized in that, Based on the Zonotope technique, an interval estimation method is designed to obtain more compact state intervals. The specific steps are as follows: If we can find the upper and lower bounds of the state estimation error Then we can obtain the interval of the state: ， Next, based on the Zonotope technique, the upper and lower bounds of the state estimation error are obtained through analysis. The specific steps are as follows: C001: Regarding state estimation error have: ， C002: In the formula, , ;also, ; C003: On the one hand, analyze the range of stealth deception attack signals: ， C004: In the formula, for , ;also, ; C005: Let The reachable set is We can obtain: ， C006: On the other hand, when At that time, set The abbreviation is , The abbreviation is , The abbreviation is Furthermore, let for The reachable set can be obtained as follows: ， C007: According to C006, interval It can be represented as: ， C008: Due to ,set up We can obtain: ， C009: Combining C007 and C008, we can obtain ， Thus, the state estimation error is obtained. The interval; based on From the range, we can further obtain the close range of the permanent magnet direct-drive wind turbine system state.

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