A NEW IMPROVED CONTROL FOR POWER QUALITY ENHANCEMENT IN DOUBLE FED INDUCTION GENERATOR USING ITERATIVE LEARNING CONTROL

This work presents a new Fault Tolerant Control approach for a doubly fed induction generator using Iterative Learning Control when the fault occurs. The goal of this research is to apply the proposed ILC controller in conjunction with vector control for doubly fed induction generator to enhance its reliability and availability under broken rotor bars. However, the performances of classical VC control are often characterized by their inability to deal with the effects of faults. To overcome these drawbacks, a combination of VC control and iterative learning control is described. The input control signal of the VC controller is gradually regulated by the ILC harmonic compensator in order to eliminate the faults effect. The improvement of this approach related to active and reactive power ripples overshoot and response time have been explained. Which active and reactive power response time have been reduced more than 84% and 87.5 % respectively. The active and reactive power overshoots have been reduced about 45% and 35% respectively. The obtained results emphasize the efficiency and the ability of the proposed FTC to enhance the power quality in faulty condition.


INTRODUCTION
In the last few decade, The Doubly-fed Induction Generator has gained more interest in large wind turbine because of their reliability, robustness, reduced inverter costs, power control capability and full variable speed operation [1]. Despite these advantages, this kind of generator can be affected by several faults that deteriorate their performances, which are current sensor faults, short circuit and rotor failures including broken rotor bars [2]- [3], the broken rotor bars is one of the most common faults in DFIG, it can be created by mechanical cracks or overloads. To overcome this drawback we use the fault tolerant control [4].
The fault tolerant control is the best choice for eliminating previous fault because it allows a system to keep operating even the occurrence of faults, therefore the application of FTC on DFIG provides significant economic benefits to the wind turbine [5]. Much researchers classifies fault tolerant control into two parts [6], the first called active fault tolerant control (AFTC) and the second called passive fault tolerant control (PFTC). The AFTC aims to ensure the stability and performance, by modifying online the parameters or the structure of the controller. This solution requires to be reconfigured based on the block information given for fault detection and isolation on (FDI) [7]- [8], in other hand the passive approach uses a robust controller that can maintain good performance when faults occur; unlike the active approach, this method does not require fault detection and isolation blocks. The PFTC can avoid the time required in the AFTC for online diagnostics and design monitoring, which is very necessary in practical situations [9]- [10].
In recent years, the power quality is still a big challenge. Hence, many research publications have studied the improvement of the power quality using VC controller. This approach are frequently utilized DIAGNOSTYKA, Vol. 24, No. 3 (2023) Djaidja O, Mekki H, Zeghlache S, Djerioui A: A new improved control for power quality … 2 in wind turbines because they have the ability to adjust the DFIG model [11]- [12]. In [13], authors present an improvement of the power derived from wind energy, using direct and indirect vector control, taking into account the variation of wind speed that causes a challenge in energy production. In addition, the work in [14] proposes a new direct vector control (DVC) for a doubly fed induction generator (DFIG) based on space vector modulation (SVM) using in a wind turbine system (WTS). However, the VC control method has poor performance and low robustness when faults occur. Thus, in our paper an effective Fault Tolerant Control (FTC) approach for power quality enhancement in a doubly-fed induction generator is designed. The proposed technique is based on combining an iterative learning controller (ILC) with VC control under the rotor faults. This approach is favourable for industrial power implementations due to its effectiveness and robustness in critical process situations. The ILC technique has broad interest by researchers in systems subjected to periodic faults, because this strategy can modify the input signal repeatedly when the monitoring task is performed in order to get high disturbance rejection [15]- [16]. In [15] two iterative learning control techniques applied in the time and frequency domains, respectively, have been presented to minimize periodic speed ripples caused by torque pulsations. The authors in [16] develop an effective control approach for improving power quality in a four-leg inverter-based standalone system. The suggested scheme combines a sliding mode controller (SMC) with an iterative learning controller (ILC) for harmonic compensation.
In this work, a new combined VC-ILC approach for doubly-fed induction generator has been presented and investigated. The DFIG model and more details of the suggested control technique have been explicated. Active and reactive power ripples, overshoot and time response improvement, and accuracy have all been demonstrated and compared.
The remainder of this article is structured as follows: first the mathematical model of the doublyfed induction generator (DFIG) and the Vector control for active and reactive power controllers is presented in Section 2. Section 3 discusses, the defective model of DFIG. Section 4 develops the proposed FTC (VC-ILC). The simulation results are reported in Section 5. Section 6 gives some concluding remarks.

MATHEMATICAL MODELS
The mathematical model of a Doubly Fed Induction Generator (DFIG) comprises equations for the stator and rotor windings, the magnetic flux, and the electromagnetic torque. The mathematical model is critical for understanding the behavior of DFIGs and for enhancing their performance in wind power systems.

DFIG Model
The DFIG's voltage and flux equations in the park reference are illustrated in E q. as follows [17] = + − (1) The equation below gives the electromagnetic torque Where : LS , Lr and M are stator, rotor and mutual inductances , Idr and Iqr are rotor current components, Ids and Iqs are stator current components, Rs and Rr are the stator and rotor resistance, Vds and Vqs are stator voltage components, Vdr and Vqr are rotor voltage components, indexes d, q stand for the direct and quadrature components. and are the synchronous and rotor speed, is the electromagnetic torque, , , and are the stator and the rotor fluxes, σ is the coefficient of dispersion is the viscous friction coefficient, is the inertia, and is the number of pole pairs.
The equations below represent the classical modelling of the doubly fed induction generator [18] The equations of the Active and reactive stator powers are:

Vector Control
Vector control is among the best choice utilised for electrical devices. It is predicated on the idea that the system is identical to a separate excitation DC machine [13]. In this situation, we suggested a DFIG control rule based on the orientation of the stator flux, which is employed to operate a generator. The latter emphasizes the relation between the stator and rotor components. These connections can help in acting on rotor signals to regulate the interchange of active and reactive power between the machine's stator and the grid. It can be described in the following state equations whose: = and = 0, with neglecting the winding stator resistance Rs [14]. + . = .
The equations below represent the stator powers and rotor currents: The control voltages obtained are expressed by the equations as follows: figure 1. It presents the block diagram of vector control applied to doubly fed induction generator.

DFIG FAULTY MODEL
This part represents the model of DFIG in the event of rotor faults. According to [5], the occurrence of these faults generates asymmetry in the DFIG and makes harmonics in the stator windings, so a sinusoidal component of pulsation = 2 is added to the quadratic and direct components of stator current. The following ecosystem represents the sinusoidal components that caused by the occurrence of faults [19]- [20] ̇= ( ).
∈ ℜ 4 +2 (20) Where ϖ: The pulsations vector, nf : The broken bars faults numbers Where ± , = 1, . . . , are the pulsations of the harmonics caused by the rotor faults. Faults created by broken bars produce harmonics component at the frequency as explained in: Where : The slip ( = − ), f: The supply frequency, k: Positive integer ( = 1, . . . , ) The harmonics' amplitudes and phases are unknown; they depend on the initial state (0) of the ecosystem. Then, the additive sinusoidal terms can be as a suitable combination of the ecosystem state, i.e: The derivative of (23) is given by Where: , , , and describe the fault terms, presented by:

ILC Approach For DFIG
Iterative learning control is a method for enhancing the monitoring efficiency of machines, which function in a repetitive manner over a set length of time. It is beneficial for problems where a system needs to handle various kinds of inputs in the face of modeling uncertainty, design uncertainty, or system nonlinearities in response to periodic input disturbances. The iterative learning controller calculates the error that is saved in the memory for use in the following cycle of operation. [15]- [21]- [22]. The proposed ILC approach is shown in Figure  2, with the learning law as follows: Where ( ) is the control signal that generated from ILC , is the forgetting factor , ( ) is the error signal of the active power with * ( ) − ( ), = 1,2,3. .. is the iteration number , and are the previous and current cycle feedback gains, respectively. (See [15]- [16] for more information about determining the learning gains and ). Figure. 3 describes the overall block diagram of the combination between VC and the proposed control strategy (VC-ILC). When the system is subjected to critical disturbances that can deteriorate the overall system performances. Therefore, the suggested approach can change the input control trajectories when the control operation is repeated, with the objective of converging to zero tracking error, in the meantime, the proposed ILC controller exploits undesirable output voltage disturbances, whose frequencies are encompassed within the bandwidth of the vector controller.

SIMULATION RESULT AND INTERPRETATION
In order to validate the feasibility and robustness of the suggested approach in faulty operation as illustrated in the preceding section, we show some tests of the MATLAB/Simulink for a doubly fed induction generator, that is under the load torque equal 10 Nm applied at t = 2s whose nominal electrical and mechanical parameters are given in Table 1. The Vector control and the suggested VC-ILC are used to assess the performance of the DFIG when the faults occur. Figure 4. reveals the efficiency of the proposed VC-ILC compared to the traditional power trajectories converge to their desired VC when the DFIG is subjected to rotor faults. We can observe that the Active and the reactive references with satisfactory dynamics, when the proposed VC-ILC is applied unlike the traditional VC that appears high ripples.
Depending on Figure.4-5-6, and Table.2, that shows the active and reactive power signals, Direct and quadratic signals with the traditional VC and the proposed VC-ILC in faulty conditions, we notice that: • The Active power response time is minimized more than 84 % (1.65 s for classical VC instead 0.25 s for suggested VC-ILC) .It is apparent that the new FTC (VC-ILC) controller improves the time response of the active power, (see figure  4a). • The Active power overshoot is minimized more than 45 % (33 W for classical VC instead 18W for suggested VC-ILC) (see the zoom A of active power presented in figure 4b).
(a) Reactive power  figure  5b). • The reactive power ripples is decreased for traditional VC from 30 VAR to 0.1 VAR when the suggested approach (VC-ILC) utilizing as described in the figure 5c). The suggested FTC has an improved dynamic, which minimizes the active and reactive power ripples and overshoots considerably. As a result of these characteristics, the new algorithm is appropriate for applications requiring specialized performance.

Robustness test
In order to evaluate the robustness of the suggested control approach, the values of inductances M, Lr and Ls are multiplied by 0.5, the value of the Rs and Rr are multiplied by 2. Figures.7 and 8 show the effects of parameters variation on the active and reactive power responses for the VC and VC-ILC controllers.
(a) Active power  Figure 7, we notice that these modifications have an evident influence on the active and reactive power curves, and the effect appears to be more noticeable for the VC control compared to the VC-ILC method. For example, the time response of the active power is improved from 1.4 s for traditional VC to 0.9 s using the suggested VC-ILC (see Figure 7 a). Thus, it can be concluded that the proposed VC-ILC is more robust than the conventional VC. Table. 3. Comparative results between VC and VC-ILC with parameter variation Table 3 summarizes the major improvement of the suggested VC-ILC compared to the classical VC with parameter variation (Rs×2, Rr×2, Lr×0.5, Lm×0.5, Ls×0.5) we can get some notice: • The Active power response time (s) is decreased for classical VC from 1.4s to 0.9s using suggested VC-ILC) so enhancement for 35 % as shown in figure 7a, 7c; • The response time (s) of the Reactive power is reduced more than 83% (1.35s for conventional VC instead 0.22s using proposed VC-ILC) (see figure 7b, 7d).

CONCLUSION
A fault-tolerant control approach based on the combination between Vector Control (VC) and Iterative Learning Controller (ILC) for doubly fed induction generator to compensate the faults effect was described. The suggested technique is designed for making the DFIG tolerant to unanticipated faults. This technique seems to be an effective choice for improve power quality. The main contributions of this study are the decrease of ripple and overshoot, as well as the enhancement of response time, moreover, the ability of the proposed FTC (VC-ILC) to compensate the faults. Simulation results and table 2-3 present the major enhancement of the suggested FTC (VC-ILC) compared to the classical VC thus the proposed FTC (VC-ILC) is more efficient and has a higher likelihood of being utilized in electric drives compared to traditional VC controllers. In conclusion, the high effectiveness and robustness of the suggested approach can be useful for industrial implementation where the power quality is a significant worry and the operating conditions are critical.