Relevance vector machine based fault classification in wind energy conversion system

ABSTRACT


INTRODUCTION
The fault detection in the WECS is an important aspect in the working of the wind power generation system, as the faults occurring in the system would increase the maintenance cost. Development of the overall fault detection including the turbine, generator, converter, pitch and the drive train becomes important considering the cost involved in the maintenance of the WECS. The benchmark model wind turbine for fault identification, which includes the sensor, process and actuator fault condition, is developed [1]. A 4.8 MW WECS model is developed in order to observe the faults in the system. SVM based fault detection is carried out in Wind turbines and compared with the ANN for the accuracy, training and tuning times [2]. The linear SVM performed better in comparison with the ANN. The classification using RVM performed better than the SVM while the training time is said to be higher [3]. Wind generator bearing fault are sensed by the sound and vibration in the tower using empirical mode decomposition method [4]. A nine turbine based wind farm challenge to detect the wind turbine faults in the individual turbine are carried out [5]. A state estimation set membership approach based implementation is found in fault detection of benchmark model with noise [6]. A multi-objective optimization framework for large scale wind turbine system is developed using the actuator faults are included in order to classify the faults according the measurement from different sensors from the WECS. Further the paper is sectioned as follows, Section-II would talk about the different sections of the WECS where the fault is detected.Section-III talks about the RVM implementation on the wind fault detection.Section-IV infers the results and discussion followed by the conclusion and the references.

Wind energy conversion system model
The benchmark model developed in [1] is used in the present implementation. It comprises of the wind model, blade and pitch model, drive train model, generator/converter model, controller and parameters. In the wind model the different sequence of wind is stored as a vector v w , which would be used for the input to the wind turbine. The Blade and Pitch model comprises of the aerodynamic and the pitch model of the turbine as defined in (1).
The aerodynamic torque is defined in equation (1) where r is the Air density (kg/m 3 ) , R is the rotor radius, C q rotor torque coefficient, l tip speed ratio, b blade pitch angle.
If the wind turbine has three blades and thus would have three blade pitch angles. Thus the torque equation would be as defined in (2), which is the sum of torques in all the three blades.
The reason that b value varies for each blade introduces little variation in the torque developed by each blade, though the overall behavior of the model is similar to that of the model with similar b value. The hydraulic pitch system is a closed loop model defined by a second order transfer function which is a piston servo system.  Equation (3) defines the second order transfer function of hydraulic pitch system where V is the damping factor, natural frequency defined by w n . The transfer function is defined for all three-pitch system in similar way. The damping factor is the same for all the three-pitch system if there are no disturbances. Hydraulic power drop and the increase in air pressure is are the parameters that vary when there is a fault occurrence in the pitch system. The parameters for power drop is defined as 2 n  and 2  and that of the air pressure is 3 n  and 3  . The closed loop pitch actuator being the linear system with change in sensor gain affecting it would need mean of two sensor values to be fed to the actuator. Thus the pitch reference would be changed according to the changes sensor values which is indicated as follows.
Where ∈ {1,2,3} and , , [ ] is the reference pitch that gets generated after the disturbance. The model of transferring the torque from rotor to the generator is defined as the drive train model. A gear box in the middle to convert the lower speed to the higher speed is represented as a two mass model defined in (5) and (6).
Where the moment of inertia of low speed shaft is, is the torsion stiffness of the drive train, is the torsion damping coefficient of the drive train, is the viscous friction of the high speed shaft. is the gear ratio, is the moment of inertia of the high speed shaft.
is the efficiency of the drive train. Δ ( ) is the torsion angle of the drive train. The fault in the drive train is due to variation in the drive train efficiency which would be denoted by 2 instead of . The electrical model which comprises of the generator and the converter which works in frequency which is much higher than the benchmark model is defined by the first order transfer function as defined in (7).
Where is the generator and converter parameter. The generator power is defined by (8) where is the efficiency of the generator. The control scheme chosen for this implementation simple as the focus is on the fault detection of WECS. In order to simplify the benchmark model the drive train damper is avoided. There are two modes in which this implementation would work, one is the power optimization mode and the reference power mode. The power optimization mode is when the speed of the wind is greater than the nominal speed. The controller starts when there is less power generated from the wind energy due to wind speed less than the nominal speed. It is denoted as where is the nominal generator speed and the mode changes from this mode 2 to the mode 1 if where Δ is the offset that is subtracted from the nominal speed to avoid the change from mode 1 to mode 2 and vice versa frequently. The conditions of fault and the mode variation along with the model parameters are used as it is from [1].

RELEVANCE VECTOR MACHINE BASED IMPLEMENTATION OF FAULT DETECTION
The different fault conditions are trained on the Relevance Vector Machine (RVM) and a multi class RVM structure is developed in order to test the different fault condition of the wind fault that is considered in [1]. The multiple RVM structures are developed as discussed in [11]. The different fault conditions are as given in the Table 1 is introduced for training the RVM and testing it.

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The pitch positions are considered for the implementation of the 1a and 1b faults that would be taken as the vector for the RVM training. The vector that reflects the sensor faults in blade positions is as given in the following Where k=1,2,3 which is the denoting blade number and i=1,2 denotes the mode in which the WECS is working. And  , , , are used for training. The vector for training is given by the following.
The measurement is filtered in order to avoid sudden variation by using g with t=0.02s and r with t=0.06s. In order to increase the ability to measure distinctly the Gaussian variance is increased to 15 while measuring. For faults 4a and 6 the vector is as defined in the following, RVM is used to develop ten separate training models for different fault conditions. For ten different faults ten different regression functions is articulated. The regression function is used to map the input to different regions of the state space. The function that is used for the regression function is given as below, The mapping function is generated for each of this implementation by applying the regression algorithm explained in [12]. The RVM is trained for each fault situation and the trained model is generated after the regression procedure. The parameter is optimized by maximizing the objective function Where * is the maximum a posteriori estimate of hyperparameter . The input x for all the fault condition are defined in the previous section and the RVM training is carried out by the use of the RVM implementation thus introduced in the above .

RESULTS AND DISCUSSIONS
The Matlab based Implementation is carried out and the results are as shown in the following discussion. The third fault scenario as discussed in [1] is applied for the implementation which is the rotor speed sensor fault occurring in the two blades of the turbine. While carrying out the training process the time taken for the training process is calculated for making all the nine faults trained and the models to be developed for each fault.
The model created after the training process comprises of the α,the sparse parameter, and the bias value b along with the kernel structure. The amount of memory space needed for storing it would be a parameter for the hardware feasibility of the proposed method. The memory space required for it be stored is around 160kb of the memory thus allowing it to be feasible in hardware implementation. By giving the different wind speed, which is randomly generation. Due to the variation in the wind the torque generated in the Figure 1.   [11.11, 0.6] to [5.73, 0.45] from 3200 and 3300s. 9. Fault type 5b, parameters in pitch actuator 3 (w n ,z) changed slowly (with a linear function) from [11.11, 0.6] to [3.42, 0.9] over 30s, remained constant during 40s, and then decreased again over 30s from 3400 and 3500s. While carrying out the training process the time taken for training all the fault and the non fault condition for all the nine fault conditions by using RVM is given in Table 2. After training the faults in the RVM implementation. The fault detection is tested with the above faults using the models developed using RVM.
The detection of fault would show the 1 in the detection graph and zero in the detection graph when there is no fault. Figures 1 and 2 displays the wind turbine torque and the wind speed respectively in Turbine. Figures 3 and 4 displays the fault detected in Blade 1 and Blade 2 1200-1300s and 1700-1800s. The hardware feasibility of the proposed algorithm would require the time taken for the training portion and the memory space needed to store the models developed after the training process. The Table 2 displays the time taken for all the nine faults trained and the model generation for all the faults and the space for the models stored in the memory. The table is developed considering the i5 processor, 3.2GHz processor with the 8GB ram.

CONCLUSION
The Relevance Vector Machine based implementation was carried out with the benchmark model developed as mentioned in the literature. The RVM function was trained and ten different models were developed for each kind of fault and the results were found to be satisfactory. The hardware feasibility study takes in to consideration the execution time and the memory usage for the models thus developed while training. The amount of execution time and the memory used clearly supports the hardware feasibility positively.