Event-triggered mechanism based robust fault-tolerant control for networked wind energy conversion system

0 Introduction

Wind energy is a renewable and clean source of energy.With the gradual maturing of wind power generation technology, an increasing number of wind turbines are being put into operation [1-4].Control, computation, and communication technologies are widely applied to WECS to improve the stability and reliability of the complex WECS [5-7].Because of the increasing number of WECS network communication nodes in WECS control scheme,information transmission plays a key role, as shown in Fig.1.The solid line represents the data information shared between wind turbine controllers, and the dotted line represents the network communication links.Owing to limited network resources, information communication in a WECS is limited by time delays and package losses.The reliability of the network information transmission is important for the stability of WECS.Owing to the randomness and uncertainty in the WECS, fault-tolerant control (FTC) has attracted considerable attention.If some components of the control system fail, the FTC ensures that the system can still complete the control task safely as the expected performance index; in some cases, the performance index is slightly reduced (but acceptable).The research on FTC has improved the safety and reliability of complex systems.Thus, safe and reliable operation of wind turbines using FTC can be guaranteed.

Several studies have been conducted on the application of FTC to WECSs to meet the high-reliability requirement.Reference [8] introduces the latest developments in improving wind turbine reliability.A multi-observer switching control scheme for robust fuzzy FTC of variable speed WECS considering system parameter uncertainty and sensor failure was proposed in reference [9].A fault-tolerant tracking-control method for double-fed induction generator(DFIG) actuator based on fuzzy observer was proposed in reference [10].Based on an adaptive cooperative observer and a reconfigurable controller, a cooperative fault-tolerant control scheme was proposed to compensate for pitch actuator fault in wind turbine [11].An observer-based FTC method was proposed for controlling pitch system of windturbine blades in reference [12].The simulation results demonstrated that the proposed FTC scheme can maintain the system’s performance under multiple sensor failures.The stability of WECS considering sensor failure was enhanced by designing a state observer for wind turbine in reference [13].A fault-tolerant controller was proposed for variable-speed wind turbine operating in the low wind speed range [14].The designed controller ensures maximum wind energy tracking can be achieved even under sensor failure.A model-based fault diagnosis method was proposed in reference [15], and a fuzzy controller was designed to ensure system robustness under sensor failure.The problem of robust distributed fault estimation for nonlinear multiagent systems with actuator and sensor faults is discussed in reference [16-17].The present study proposes a novel wind turbine FTC, which is a combination of communication system, intelligent algorithm, and control system.

According to the discussion above, the application of event-triggered FTC on WECS has not yet been reported,which was the motivation for the present study.In this study, a horizontal-axis wind turbine having three blades placed in an upwind wind direction was considered.An event-triggered mechanism (ETM) based WECS can be considered as a discrete jump linear system, and its transition jump can be modeled as a finite-state Markov chain.In this study, an ETM based nonlinear networked WECS modeling method with stochastic delay and communication constraints based on a quasi T-S fuzzy model is proposed.A robust integrity design for ETM based WECS is analyzed based on robust control theory.The remainder of this paper is organized as follows.The ETM based WECS is described in Section 2.Section 3 introduces the robust integrity design for the ETM-based networked WECS.In Section 4, a doubly-fed asynchronous wind turbine is considered, and the simulation analysis results demonstrate that the proposed scheme is feasible and effective.Finally, Section 5 summarizes the study.

1 Modeling for ETM based networked WECS

1.1 Event-triggered communication mechanisms

The grid-connected WECS belongs to the class of cyber-physical systems which deeply integrates the physical power grid and information network [18-21].Owing to the continuous development of network informatization,network communication plays an important role in intelligent WECS.An intelligent WECS manages and controls information through a network system, and can also exchange the information between equipment in realtime through the network system.With the continuous development of related technology, the automation level and operational efficiency of the WECS have improved considerably.The gradual intellectualization of power systems can prevent large-scale cascading faults and significantly improve the reliability of the system.Networked wind turbines have more flexibility and control modes than traditional wind turbines.Whereas, network integration also introduces new challenges into the WECSs,such as the delay in data information transmission and data packet dropout [22-24].

A schematic of WECS operation based on an eventtriggered communication mechanism in which wind turbine is controlled by measurement feedback to counteract the effect of disturbances is shown in Fig.2.The mechanism is depicted by the link from system sensor i to remote controller i.The ETM consists of a sampler, event generator, and buffer; the dynamic rule decides when to transmit the current measurement of each sensor to the remote controller, which can make a more efficient use of network communication resources than periodic triggered scheme.More specifically, according to the predefined data information transmission conditions, the event generator is used to generate a series of dynamic trigger events.The buffer is configured to retain the latest data packages, check whether the difference between the current measurement value of the wind turbine and the latest transmitted measurement value exceeds the threshold.The event generator determines when the current measurement should be broadcasted over a resource-constrained network channel or sent to a remote controller.Compared with the traditional periodic trigger method, which selectively transmits data and information, this trigger method is more intelligent.

The node with ETM compares the value to be sent to the network x with the data value of the previous successful transfer xsent, or the defined event-triggered parameter δt.If the following conditions are satisfied, no updates are transmitted to the network.Data transmission trigger rule for WECS see Fig.3.

The number of messages broadcasted by nodes decreases with the increase in event-trigger parameters.The ETM can reduce network traffic; however, it introduces uncertainty in the system state.Therefore, it is necessary to evaluate whether the uncertainty leads to system instability and performance degradation.

1.2 Dynamic Modeling of WECS

A wind turbine converts wind energy into mechanical energy.Letωr(t) be the angular speed of the wind turbine,the wind speed vr (t ), air density ρ, wind energy utilization coefficient Cp, and rotor swept area A determine the output energy of the wind turbine; Cp is a nonlinear function of tip speed ratio λ(t), and pitch angle β(t).The aerodynamic torque Ta (t ) of the wind turbine is

Let Jr be the sum of the wind turbine inertia and rotational inertia of the main drive shaft, and Jg be the sum of the generator rotational inertia and rotational inertia of the secondary drive shaft.The gearbox transmission ratio Ng, torsional stiffness Kdt, and torsional damping Bdt are combined to obtain the torsional angle θ(t).Let transmission system efficiency, generator torque, and rotation rate be ηdt, Tg(t), and ωg(t), respectively.The transmission system model is as follows:

The pitch system with communication delay is described as follows, where βref(t-td) is the reference value of the pitch angle and τd denotes the communication time delay.

In addition to the pitch control system described in equation (5), considering practical engineering applications,the pitch rate and range should be considered in the pitch process.

A generator converts the mechanical energy to electrical energy, which is transmitted to the power grid through a converter to improve the output power quality.The generator torque is adjusted according to the torque reference value Tg,ref (t).The dynamic characteristics of the converter are described by first-order inertia mitigation.The generator and converter models can be described as follows:

where ηg is the generator efficiency and Pg (t ) denotes generator output power.

Consider the state-space model of WECS as follows:

The discrete state feedback control law is given by

where x(t), u(k), and y(t) denote the state vector, control input vector, and system output vector, respectively; A, B, C,and K have compatible dimensions.

1.3 T-S Fuzzy modeling for WECS with parameters uncertainties

The new WECS model based on ETM integrates the control and network parameters.In this study, we model the given nonlinear WECS with random time delays and network transimission constraints by Quasi Takagi-Sugeno(T-S) fuzzy model.Implementing the event-triggered scheme can reduce the network transmission traffic and maintain the desired system performance.

1.3.1 T-S Fuzzy modeling for WECS

The T-S fuzzy model is described by if-then rule of the local linear system input-output relationship, which is proposed by Takagi and Sugeno [25-27].Based on this, we establish WECS model with random time delays by introducing IF-THEN rule, and take the probability of time delays as the fuzzy membership function.Thus,a global fuzzy model for the WECS with random time delay is obtained.Consider a WECS with the following uncertainties:

Plant rule i:i =0,1,2…,M

If z1(k)isMi1,z 2 (k ) is Mi2, …, z p(k) is Mip,

Then

where x(k )=φ(k ), ηt = η0, t∈[-d,0], and i =0,1,2…,m.z1(k ),…,z p(k) is the known premise variable and a function of state variables.Mij , (j =1,2,…,p) denote fuzzy set, and m are model rules.φ(k) represents the system initialization conditions.The overall state space equation can be described as:

where

whereis z j(k ) membership function of the fuzzy set Mij, μi(z) denotes membership corresponding to the ith rule.μi(z) satisfy μi(z)≥0,i N=1,2…, andThus μi(z)≥0,i =1,2…,N and=1.

1.3.2 System uncertainties description

System uncertainties are assumed to be norm bounded and time-varying.They can be described as follows:

Where Di(ηk), Ddi(ηk), EAi (ηk ), EBi (ηk) and Edi(ηk)describe the uncertain matrix function satisfying

≤ I , ∀ηt ∈S, all matrices hav e appropriate dimensions.Assuming that the Markov processes {ηk,t≥0} and system states are available at t for the fuzzy time-delay jump system, the fuzzy controller is obtained as

Controller Rule i:

If z1(k ) is Mi1, z 2 (k ) is Mi2, …, z p(k) is Mip,i =1,2…,M.

Then u(k )= K i (ηk)x(k ), i =1,2…, M, ηt∈S, where K i(ηk)∈ Rn×n is partly state-feedback gain, which depends on ηk.Therefore, the overall state- feedback control input is

The networked WECS with parameters uncertainties is given as follows:

where,

1.4 ETM based Networked WECS

With the increasing capacity of wind turbines and the continuous innovation in wind power technology, increasing number of sensors with high sampling frequencies are installed on the wind turbines.Moreover, many network information transmission nodes require a wider and more stable network transmission environment.To alleviate the phenomenon of network congestion, in contrast to the general static time-trigger mode, the network selectively transmits data to reduce the number of packets transmitted on the network, and prevents the frequent action of the actuator on the premise of ensuring the system performance.The sensor node with ETM compares the current sampling value with the data successfully transmitted at the previous time, and decides whether to transmit the current sampling value through the network.

If z1(k ) is Mi1, z 2 (k ) is Mi2, …, z p(k) is Mip, and(r - 1)Ts ＜ τ ＜ rTs , i =1,2…,m, r =1,2…,n.In view of the ETMs proposed in this study, the system’s real state is x = xb ±δxb.The control rules for the systems in the inner layer are as follows:

Subsequently, the outer control rule is as follows:

Then

where represents Fuzzy “blending”, then

wherethe ETM-based WECS with time-varying delays can be described as

2Robust integrity design for ETM-based networked WECS

The FTC is keeps the system stable and ensures the expected performance in the case of ETM-based WECS failure.Integrity design is a method of designing FTC such that the WECS remains asymptotically stable if sensor or actuator failure occurs.

If the ETM-based WECS (19) is under sensor failure,the concept of switching matrix M is introduced; M lies between feedback gain matrix K and the system state x(kh),

where M = diag{m1,m2 ,…,mn}.

Let

then the event-triggered networked WECS is described as

The objective of the integrity design is to find that keeps the ETM-based WECS asymptotically stable under sensor failure, M∈Ω, where Ω represents a collection of all possible sensor failure-switching matrices.For the sake of convenience, two useful lemmas are introduced as follows:

Theorem 1: Considering system (20), the ETM-based WECS with event-triggered parameter δ, and given ε＞0,for all permitted parameter uncertainties, if there exist positive definite matrices R and S, such that

then the ETM-based WECS has the capacity of faulttolerant control for sensor failure, M∈Ω.Where Γi,r =Hi,r ( I+ δ)-1 MS, r =1,2…,n.i =1,2…,m.

Proof: considering the Lyapunov function for the ETM-based WECS as

Taking the function V(k) difference along the ETMbased WECS (20) for any vector v1, v2 and matrix Y,

and

where X denotes positive define matrix, then

The sufficient condition for the ETM-based WECS (20)to be asymptotically stable is ΔV(k)＜0, then

where Φ i, r = Hi,r(I +δ)-1; therefore, the following inequality can be obtained:

i =1,2…,m, r =1,2…,n,α=1,2…,m.

Multiplying the inequalities equation (29) and equation(30) on the left and right hand side by P-1, define matrix S=P-1, we have

i=1,2…,m, r=1,2…,n,α=1,2…,m.LetΓα, r =Φα,rMS,r=1,2…,n, α=1,2…,m, forS＞0,fortheconvenience of solution, the above inequalities can be transformed into linear matrix inequality by Schur complement lemma.

i =1,2…,m, r =1,2…,n, α=1,2…,m.Then

i =1,2…,m, r =1,2…,n,α=1,2…,m.

This completes the proof of Theorem 1.

If the ETM-based WECS (19) with has an actuator failure, the concept of switching matrix L is introduced; L lies between system matrix B and feedback gain matrix K,where Li = diag{l1,l2 ,…,l n}.

Let

then the ETM-based WECS can be modelled as

The objective of the integrity design is to findthat keeps the ETM-based WECS asymptotically stable in the presence of actuator failure∈Ω′, where Ω′ represents a collection of all possible actuator failure-switching matrices.

Theorem 2: Considering system (37), the ETM-based WECS with event-triggered parameter δ, given ε＞0, for the uncertainties of all admissible parameters, if there are positive definite matrices R and S that satisfy

Then, the ETM-based WECS has the capacity of fault-tolerant control for actuator failure, L∈Ω′, where Γi,r =Hi, r ( I+ δ)-1S, r =1,2…,n, i =1,2…,m.

The proof of Theorem 2 is similar to Theorem1.

3 Numerical simulations

3.1 Simulation conditions

In this section, the variable-speed constant-frequency DFIG units are presented, and ETM-based WECS Block diagram is shown in Fig.4.

The power coefficient function C p(λ(t ),β(t)) is a nonlinear function and is expressed as

Simulation wind speeds are from 9 m/s to 14 m/s.The sampling period was selected as Ts=20 ms [30].In order to further discuss the design scheme proposed in this paper,we consider the following wind turbine control in the case of non-ideal network transimission.Assuming that ETM-WECS data packets are transmitted between nonideal network transimission channels, in view of proposed event triggered transimission scheme, some packets will be discarded in order to save network resources.

The ETM-FTC was designed with the parameters in linear matrix inequalities and using the feasp and mincx solvers of MATLAB Robust Control Toolbox [31].Considering the event-triggered matrix, the corresponding controller gain Ki can be get from the solution of linear matrix inequalities.It can be seen from Theorem 1 and Theorem 2 that the selection of trigger parameter determines the ETM-WECS performance.Meanwhile, a larger δ indicates that fewer packets need to be transmitted.

3.2 Case analysis of ETM-based WECS

The event-triggered parameter is defined at the network node; therefore, it can learn the final value sent to the network.If one node does not have a new event-triggered communication mechanism, all the other network nodes still consider the previous value valid.To validate the effectiveness of the proposed scheme, the following four cases are presented:

Case 1: ETM-based WECS with sensor failure and no fault-tolerant controller: In this case, the event-triggered parameters for the sensor and controller nodes are δs=0.03,δs=0.02, respectively.The WECS with sensor failure,variation of pitch angle, generator torque, electrical power,and rotor speed are shown in Figs.5-8 (dotted lines),respectively.

Case 2: ETM-based WECS with sensor failure and FTC:The event-triggered parameters for the sensor node and controller node are δs=0.03, δc=0.02, respectively.From numerical simulation result, we can conclude that when a sensor failure occurs in the ETM-based WECS, the system maintains stable operation after short fluctuations.The responses of the WECS are shown in Figs.5-8 (solid lines).

Case 3: ETM-based WECS with actuator failure: the event-triggered parameters for the actuator and controller nodes are δa=0.01and δc=0.02 respectively.From numerical simulation result, we can conclude that when an actuator failure occurs in the ETM-based WECS, the system maintains stable operation after short fluctuations.The response of the WECS is shown in Figs.9-12.(solid lines ETM-FTC-2).

Case 4: ETM-based WECS with actuator failure: The event-triggered parameters for the actuator and controller nodes are δa=0.03 and δc=0.05, respectively.The responses of the WECS are shown in Figs.9-12.(dotted lines ETMFTC-1).From numerical simulation result, we can conclude that when the WECS experiences an actuator failure, the system performance decreases with increasing eventtriggered parameters.

Event-triggered parameter selection has an impact on the performance of the system.Appropriate event-triggered parameter selection is a key factor to be considered in the FTC design for ETM based WECS.

Case 1 considers the system’s output response when the event-driven fault-tolerant controller is not adopted.The corresponding output overshoot is considerably large,which is not conducive for the safe and stable operation of the WECS; the adjustment time increases, and the system performance deteriorates.In Case 2, the same trigger parameters are adopted, and the fault-tolerant controller based on the event-triggered mode proposed in this paper is adopted.The solid lines in Figs.5-8 show that when some sensors fail, the information data is selectively transmitted.The performance of the WECS improves, and the overshoot reduces and the adjustment time shortens.Moreover, by selectively transmitting the information, the number of packets transmitted in the network channel is small, which can improve the network utilization efficiency.The comparison between Cases 1 and 2 demonstrates the effectiveness of the ETM-based fault-tolerant controller designed in this study.

Case 3 and Case 4 consider the dynamic response characteristics of the WECS when the actuator fails.However, the trigger parameters of the network nodes are different from those for Case 1 and Case 2.Under the same conditions, the larger the trigger parameters, the lesser the data packet transmission, as shown in Fig.12.It can be seen from the known conditions and simulation results that when a WECS actuator node fails, not all the data of the sampling periods are transmitted through the network, but the data are transmitted selectively.Under different event-triggered parameters, the smaller the trigger parameters, the smaller the system overshoot and shorter the adjustment time, as depicted by the solid line in Figs.9-12.The fault-tolerant controller based on event-triggered parameters ensures WECS stability and acceptable dynamic performance when selecting appropriate trigger parameters.A comparison between Cases 3 and Cases 4 validates the effectiveness of the proposed fault-tolerant controller.

In order to more intuitively explain the data transmission based on event-triggered mode under different trigger thresholds, Table 1 lists the comparison of trigger parameters, trigger times, and data transmission rates.Under limited network communication resources, the proposed ETM-based FTC scheme reduces the number of packet transmissions by properly adjusting the trigger parameters, facilitating the effective utilization of network communication resources and ensuring significant system performance.As shown in Fig.13, with the ETM-FTC scheme, state information is selectively transmitted in the way of event triggering.This design method reduces the information packets in the network transmission channel and actuator frequent action.For the turbine part of the WECS,mechanical equipment action time, and frequent start and stop due to actuators can be reduced using the proposed controller to prevent the wear and tear of mechanical parts for frequent regulating pitch actuators.The numerical example in Section 4 demonstrates the effectiveness of the ETM-FTC scheme.

4 Conclusion

In this paper, a novel ETM-based robust FTC design is proposed for WECS over a communication network subjected to actuator and sensor failures.Considering the limited network tranmission bandwidth, the ETM is introduced in system data transmission, and a T-S fuzzy model with parameter uncertainty is used to model the nonlinear WECS.Using the Lyapunov stability analysis method, the parametric expression for the controller, based on feasible solution of the linear matrix inequalities, is given.The introduction of the eventtriggered communication mechanism can reduce network packets transmission pressure and increase network resource utilization efficiency.Selective data information transmission can also prevent frequent actuator action and improve the WECS reliability.Considering a variable-speed constant-frequency wind turbine unit, the system stability considering parameter uncertainties and sensor/actuator failure is analyzed.The simulation results verify the ETM based robust FTC design scheme is reliable and effective.

Acknowledgements

This work was supported by Ministry of Science and Technology of Peoples Republic of China (No.2019YFE0104800).

Declaration of Competing Interest

We declare that we have no conflict of interest.